2.1.1. Accretion and jet ejection

The process of disk accretion and jet ejection is ubiquitous across astrophysics (e.g. de Gouveia Dal Pino Reference de Gouveia Dal Pino2005), and where compact objects are involved those jets are typically relativistic (e.g. Bromberg et al. Reference Bromberg, Nakar, Piran and Sari2011b ) with similar characteristics that depend primarily on the accretor mass, accretion rate, and ejection velocity. In the context of radio transients, we focus on relativistic jets from AGN and X-ray binaries (XRBs), which we discuss below.

AGN dominate the radio sky at flux densities above a few millijanskys (at centimetre wavelengths), and most show little variability (Hovatta et al. Reference Hovatta, Tornikoski, Lainela, Lehto, Valtaoja, Torniainen, Aller and Aller2007; Hodge et al. Reference Hodge, Becker, White and Richards2013; Stewart et al. Reference Stewart2016; Mooley et al. Reference Mooley2016; Bell et al. Reference Bell2019; Murphy et al. Reference Murphy2021), although fluctuations of a few to few tens of percent are not uncommon (e.g. Falcke et al. Reference Falcke, Lehár, Barvainis, Nagar, Wilson, Peterson and Pogge2001; Mundell et al. Reference Mundell, Ferruit, Nagar and Wilson2009) and variations are both more significant and faster at higher radio frequencies (e.g. Ackermann et al. Reference Ackermann2011; Hovatta et al. Reference Hovatta, Tornikoski, Lainela, Lehto, Valtaoja, Torniainen, Aller and Aller2007), especially for sub-classes of AGN such as blazars (Max-Moerbeck Reference Max-Moerbeck2014; Richards et al. Reference Richards2011a ).

Aside from extrinsic causes (see Section 2.5.1) most of these changes are thought to be due to modest changes in the jets (e.g. Nyland et al. Reference Nyland2020), such as the propagation of shocks along the jets (Marscher & Gear Reference Marscher and Gear1985; Hughes, Aller, & Aller Reference Hughes, Aller and Aller1989, disk instabilities (Czerny et al. Reference Czerny, Siemiginowska and Janiuk2009; Janiuk & Czerny Reference Janiuk and Czerny2011), or changes in accretion power (Koay et al. Reference Koay, Vestergaard, Bignall, Reynolds and Peterson2016; Wołowska et al. 2017). These effects can be magnified by the jet orientation, with jets directed close to the line of sight having larger variability on shorter timescales due to relativistic effects (Lister Reference Lister2001): changes in orientation can therefore dominate any intrinsic changes in their effects on variability.

However, a subset of these sources show higher variability (e.g. Barvainis et al. Reference Barvainis, Lehár, Birkinshaw, Falcke and Blundell2005). This may be due to large-scale changes in the jet orientation from accretion instabilities or interaction within a binary super massive black hole (Palenzuela, Lehner, & Liebling Reference Palenzuela, Lehner and Liebling2010; An et al. Reference An, Baan, Wang, Wang and Hong2013), or large-scale changes in the jet power from changes in the accretion flow (Mooley et al. Reference Mooley2016; Nyland et al. Reference Nyland2020). These sources apparently transition from radio-quiet (often undetectable) to radio-loud (although the distinction may not be so simple, e.g. Kellermann et al. Reference Kellermann, Condon, Kimball and Perley2016), with the radio luminosity apparently increasing by more than an order of magnitude over several decades, potentially as a result of newly-launched jets.

Such changes in the jet behaviour can be replicated on much smaller scales (both physical and mass) through accreting X-ray binaries hosting neutron stars or black holes (Fender, Belloni, & Gallo Reference Fender, Belloni and Gallo2004a ; Fender et al. Reference Fender, Stirling, Spencer, Brown, Pooley, Muxlow and Miller-Jones2006; Fender Reference Fender2016). Here, small-scale changes in the jet power during the hard state correspond to normal AGN variability, while significant launching of superluminal jet components in the transition between hard and soft states correspond to the radio-quiet to radio-loud transitions of AGN.

2.1.2. Explosions and shocks

In contrast to the scenarios above, where accretion leads to jets that can vary as the accretion rate or direction varies, the radio emission from transient events such as classical novae (Chomiuk, Metzger, & Shen Reference Chomiuk, Metzger and Shen2021a ; Chomiuk et al. Reference Chomiuk2021b ), supernovae (Weiler et al. Reference Weiler, Panagia, Montes and Sramek2002), long and short gamma-ray bursts (Piran Reference Piran2004; Berger Reference Berger2014), magnetars (Frail, Kulkarni, & Bloom Reference Frail, Kulkarni and Bloom1999a ), neutron star mergers (Hallinan et al. Reference Hallinan2017), tidal disruption events (Levan et al. Reference Levan2011; Bloom et al. Reference Bloom2011) and similar phenomena lead more naturally to variable radio emission. These sorts of explosions/ejections have been among the most anticipated targets for large-area radio surveys (e.g. Metzger, Williams, & Berger Reference Metzger, Williams and Berger2015b ). Note that even though some of these sources, like gamma-ray bursts, may be powered by very short-lived relativistic jets, we discuss them separately from Section 2.1.1 as the jets themselves are not seen at radio wavelengths, but only their impact on the surrounding medium.

The basic scenario here is where an explosion leads to a rapid ejection of material. This outflow can be Newtonian or relativistic, and it can be collimated or spherical. Eventually the ejecta will impact the surrounding medium (typically circumstellar or interstellar material) leading to shock waves that amplify any magnetic fields present and accelerate electrons to relativistic energies, leading to synchrotron emission (Chevalier Reference Chevalier1982). This so-called ‘afterglow’ model is present in many variants in many different physical scenarios, where the mass, velocity, and angular profile of the ejecta and the radial profile of the surrounding medium can all change (Sari, Piran, & Narayan Reference Sari, Piran and Narayan1998; Chevalier & Li Reference Chevalier and Li2000; Chandra & Frail Reference Chandra and Frail2012; Mooley et al. Reference Mooley2018a ,Reference Mooleyc; Troja et al. Reference Troja2018; Lazzati et al. Reference Lazzati, Perna, Morsony, Lopez-Camara, Cantiello, Ciolfi, Giacomazzo and Workman2018).

Normally, for very energetic events like gamma-ray bursts the ejecta are observed to be ultrarelativsistic and jetted (Rhoads Reference Rhoads1997; Mészáros & Rees Reference Mészáros and Rees1997), such that the initial afterglow emission is beamed into a solid angle of $\sim 1/\Gamma^2$ (where $\Gamma$ is the bulk Lorentz factor) centred on the jet axis, which is also where the $\gamma$ -rays themselves are visible. At later times the Lorentz factor will decrease so the solid angle will increase, leading to increasing visibility of the late-time afterglow emission. Eventually, when $1/\Gamma$ approaches the intrinsic jet size the entire jet will be visible. This tends to happen at the same time as the jet material will begin to expand sideways (Sari, Piran, & Halpern Reference Sari, Piran and Halpern1999). Together these lead to an achromatic ‘jet break’ in the lightcurve (Sari et al. Reference Sari, Piran and Halpern1999; Rhoads Reference Rhoads1999). Measurement of jet breaks can then be used to infer the jet size and hence intrinsic energetics of collimated explosions (Frail et al. Reference Frail2001).

This also gives rise to the concept of an ‘orphan afterglow’, where only the late-time radio emission is visible from our line of sight (Rhoads Reference Rhoads2003; Ghirlanda et al. Reference Ghirlanda2014). Such an event would have a steeper and shorter rise than an on-axis GRB, but merge onto the same power-law in the decline (see Figure 2).

Figure 2. Model GRB lightcurves, computed using Ryan et al. (Reference Ryan, van Eerten, Piro and Troja2020) and inspired by Piran (Reference Piran2004). These models use the simplest possible model for a relativistic jet. The top dash-dotted curves are for infinite frequency (ignoring any effects of self-absorption), while the lower solid curves are for a frequency of 1 GHz. All curves are normalised at 10 d. For both frequencies, we show jet opening angles of $\theta_\mathrm{jet}=5\deg$ (blue), $15\deg$ (orange), and $30\deg$ (green) with an on-axis observer ( $\theta_\mathrm{obs}=0$ ). The infinite frequency models show jet breaks when the jet has decelerated to a bulk Lorentz factor of $1/\theta_\mathrm{jet}$ , after which they have a similar power-law behaviour with $F_\nu \propto \nu^{-p}$ (black dotted line), where p is the power-law index of the electron distribution. We also show a jet seen by an off-axis observer, potentially an ‘orphan afterglow’, since the observer would miss any high-energy emission (red dashed curve). This has similar late-time behaviour but is much fainter at early times.

The general behaviour for all of these afterglows is a series of power-law increases and declines (Sari et al. Reference Sari, Piran and Narayan1998), where the increase reflects the expanding shock front as well as the changing level of self-absorption. This increase happens first at higher frequencies because the self-absorption is less significant there. Eventually the entire afterglow becomes optically thin, at which point it transitions into a decline phase as the ejecta expand and slow down. During this phase a standard non-thermal steep spectrum is present (Weiler et al. Reference Weiler, Panagia, Montes and Sramek2002). This is illustrated in Figure 2, which shows lightcurves with and without the effect of self-absorption. If absorption is not an issue, the peak on-axis flux density is expected to occur when the shock has swept up a mass comparable to its own material and starts to decelerate, and it will scale with the energy of the explosion (Nakar & Piran Reference Nakar and Piran2011; Metzger et al. Reference Metzger, Williams and Berger2015b ). The time until the peak will scale with the energy of the explosion to the $\frac{1}{3}$ power (neglecting cosmological effects).

We can also see in Figure 2 the lightcurve from a potential orphan afterglow. One clear difficulty with all of these lightcurves is that they have the same late-time behaviour, so without a lucky early detection or robust limits on prompt high-energy emission (complicated when the explosion time is also weakly constrained), many different phenomena can be fit with the same data.

2.5.1. Diffractive and refractive scintillation

When the radio waves from a source propagate through an inhomogeneous ionised medium, the waves can bend and diffract to form spatial variations in the wavefront. If the observer is moving relative to the wavefront, this can result in temporal variability known as scintillation (Rickett Reference Rickett1990; Narayan Reference Narayan1992). Such scintillation has been observed coming from the heliosphere and interplanetary medium (IPS; Hewish et al. Reference Hewish, Scott and Wills1964) as well as the interstellar medium (interstellar scintillation or ISS; Scheuer Reference Scheuer1968; Rickett Reference Rickett1969). Interstellar scintillation is only detectable for the most compact radio sources, such as compact cores of AGN (Lovell et al. Reference Lovell, Jauncey, Bignall, Kedziora-Chudczer, Macquart, Rickett and Tzioumis2003), distance relativistic explosions (Goodman Reference Goodman1997; Frail et al. Reference Frail, Kulkarni, Nicastro, Feroci and Taylor1997), or pulsars and fast radio bursts. Moreover, scintillation can have a range of properties depending on the source size and observing frequency.

Relevant for scintillation is the Fresnel scale, $r_\mathrm{F} \equiv \sqrt{\frac{\lambda d}{2\pi}}$ , for a source at distance d observed at wavelength $\lambda$ . Also relevant is the diffraction scale $r_\mathrm{d}$ over which the phase variance is 1 rad. The ratio of these then defines the scintillation strength, $ r_\mathrm{F}/r_\mathrm{d}$ . At higher frequencies and for closer sources the scintillation is typically in the ‘weak’ regime ( $r_\mathrm{F}/r_\mathrm{ d} \ll 1$ ), with small ( $\ll 1$ ) rms phase perturbations on the Fresnel scale (Rickett Reference Rickett1990; Cordes & Lazio Reference Cordes and Lazio1991; Narayan Reference Narayan1992; Hancock et al. Reference Hancock, Charlton, Macquart and Hurley-Walker2019), leading to fractional variability $\ll 1$ .

More interesting is the ‘strong’ regime ( $r_\mathrm{F}/r_\mathrm{d} \gg 1$ ), where the phase fluctuations over the Fresnel scale are large. In this regime we can observe both diffractive (Scheuer Reference Scheuer1968) and refractive (Sieber Reference Sieber1982; Rickett, Coles, & Bourgois Reference Rickett, Coles and Bourgois1984) effects.

Diffractive scintillation results from multipath propagation (Goodman et al. Reference Goodman, Romani, Blandford and Narayan1987) from many independent patches which can add constructively or destructively, leading to large intensity fluctuations in a frequency-dependent manner. The patches each scatter radiation into an angle $\theta_\mathrm{r}=r_\mathrm{r}/d$ , with the refractive scale $r_\mathrm{ r}\equiv r_\mathrm{F}^2/r_\mathrm{d}$ . This phenomenon requires very small sources, with angular sizes $\theta_\mathrm{d}\equiv r_\mathrm{d}/d \ll \theta_\mathrm{ r}$ , and so is usually limited to pulsars, although compact relativistic explosions like GRBs can also scintillate diffractively in their early phases (Goodman Reference Goodman1997). For diffractive scintillation, the timescale and bandwidth both increase with observing frequency, and the modulation can saturate at $\sim 100$ % although it can also appear to be lower when averaging over multiple ‘scintles’ (time-frequency maxima).

Refractive scintillation, on the other hand, is due to large scale focusing and defocusing over scales $r_\mathrm{r}$ , and where the sources need to be compact compared to $\theta_\mathrm{r}$ . Refractive scintillation corresponds to lower modulation over longer timescales and wider bandwidths.

2.5.2. Extreme scattering events

Beyond the stochastic variations caused by the turbulent interstellar medium discussed above, systematic monitoring of compact extragalactic radio sources discovered discrete high-amplitude changes in source brightness with a characteristic shape, called ‘extreme scattering events’ (ESEs; Fiedler et al. Reference Fiedler, Dennison, Johnston and Hewish1987). Subsequently also seen in Galactic pulsars (Cognard et al. Reference Cognard, Bourgois, Lestrade, Biraud, Aubry, Darchy and Drouhin1993), ESEs are believed to be due to coherent lensing structures within the interstellar medium (ISM) (Fiedler et al. Reference Fiedler, Dennison, Johnston, Waltman and Simon1994). However, significant questions remain regarding the natures of those structures that seem much denser and with higher pressure than the average ISM (Clegg et al. Reference Clegg, Fey and Lazio1998). Whether the structures are one dimensional (filaments), two dimensional (sheets), or three dimensional is still debated (Romani, Blandford, & Cordes Reference Romani, Blandford and Cordes1987; Pen & King Reference Pen and King2012; Henriksen & Widrow Reference Henriksen and Widrow1995; Walker & Wardle Reference Walker and Wardle1998), as the models need to reproduce the temporal and frequency structure of ESEs (Walker Reference Walker, Haverkorn and Goss2007; Vedantham Reference Vedantham and Murphy2018).

There is considerable work ongoing to improve real-time detection of ESEs (Bannister et al. Reference Bannister, Stevens, Tuntsov, Walker, Johnston, Reynolds and Bignall2016), which would lead to better observations of their environments. At the same time there are studies of the models of the structures that cause ESEs (Jow, Pen, & Baker Reference Jow, Pen and Baker2024; Dong, Petropoulou, & Giannios Reference Dong, Petropoulou and Giannios2018; Rogers & Er Reference Rogers and Er2019), as well as attempts to identify the underlying causes of the ISM inhomogeneities (Walker et al. Reference Walker, Tuntsov, Bignall, Reynolds, Bannister, Johnston, Stevens and Ravi2017).

2.5.3. Gravitational lensing

Separate from variability induced by scintillation, extragalactic radio sources may exhibit variability induced by gravitational lensing along the line of sight. This has been predicted to appear in several ways. Radio sources that already showed multiple lensed images could have substructure lensed by small compact objects (typical masses $\sim M_\odot$ ) within the lensing galaxy (Gopal-Krishna & Subramanian 1991; Koopmans & de Bruyn Reference Koopmans and de Bruyn2000; Biggs Reference Biggs2023), showing correlated but not identical variations between the separate images on timescales of days. However, this can be hard to distinguish from scintillation (Koopmans et al. Reference Koopmans2003; Biggs Reference Biggs2021) – indeed there have been many reports of microlensing in the radio that have been difficult to verify (Koopmans & de Bruyn Reference Koopmans and de Bruyn2000; Vernardos et al. Reference Vernardos2024). While gravitational lensing should be achromatic, and hence show different behaviour from scintillation, the varying size of the radio emission region – assumed to be a knot of synchrotron-emitting material within a Doppler-boosted relativistic jet – with frequency can cause apparent frequency dependence.

A related phenomenon could be seen with larger lensing masses. In this case (Vedantham et al. Reference Vedantham2017; Peirson et al. Reference Peirson2022) the lens masses would be $10^{3-6}\,{\rm M}_\odot$ , causing achromatic variability on timescales of months–years in the lightcurve of a single source (the lensed images are not separable). This would be similar to lensing observed from high-energy blazars in $\gamma$ -rays (e.g. Barnacka, Glicenstein, & Moudden Reference Barnacka, Glicenstein and Moudden2011), although the details of the lensed sources are likely different (Spingola et al. Reference Spingola2016).

3.1.1. Radio detection of gamma-ray bursts

The detection of gamma-ray bursts was first reported by Klebesadel et al. (Reference Klebesadel, Strong and Olson1973), and their origin remained the subject of debate for over two decades. Observations from the Burst And Transient Source Experiment provided a key breakthrough, showing that the sky distribution of GRBs was isotropic (Meegan et al. Reference Meegan, Fishman, Wilson, Paciesas, Pendleton, Horack, Brock and Kouveliotou1992; Briggs et al. Reference Briggs1996); and hence ruling out progenitors such as Galactic neutron stars. The focus then shifted to identifying a counterpart at other wavelengths so that a distance scale could be established. The detection of a counterpart, now called an ‘afterglow,’ to GRB 970228 in X-ray (Costa et al. Reference Costa1997) and optical (van Paradijs et al. Reference van Paradijs1997) wavebands, in a host galaxy at $z = 0.695$ , established that GRBs were cosmological. A review of early gamma-ray burst afterglow observations, and our derived understanding, is given by van Paradijs et al. (Reference van Paradijs, Kouveliotou and Wijers2000).

The first GRB for which a radio afterglow was detected was GRB 970508 (Frail et al. Reference Frail, Kulkarni, Nicastro, Feroci and Taylor1997). High variability was observed in the first month after the explosion, which was attributed to diffractive scintillation. Since diffractive scintillation occurs only when the source is smaller than a characteristic size, the transition from the diffractive to refractive regime could be used to measure the angular size of the fireball, determining that it was a relativistically expanding explosion. The subsequent monitoring of this event in radio (Frail, Waxman, & Kulkarni Reference Frail, Waxman and Kulkarni2000b ) demonstrated the utility of radio observations in measuring the calorimetric properties of GRBs.

The next decade and a half of radio follow-up campaigns is summarised by Chandra & Frail (Reference Chandra and Frail2012). They collate observations of 304 afterglows at frequencies between 0.6 and 660 GHz. Of the 306 GRBs with radio follow-up observations, 95 were detected in radio (31%). Of these, 65 had radio lightcurves (three or more detections in the same band). A key issue is that if a source was not detected early in a follow-up program, it was generally not observed subsequently. This is one factor motivating untargeted searches for GRB afterglows.

In the rest of this section we discuss our current understanding of long and short GRBs, and the connection between short GRBs and neutron star mergers.

3.1.2. Long gamma-ray bursts

Once GRB studies became more fruitful with the launch of dedicated satellites, it was quickly determined (Kouveliotou et al. Reference Kouveliotou, Meegan, Fishman, Bhat, Briggs, Koshut, Paciesas and Pendleton1993) that there appeared to be two separate populations of GRBs delineated mostly by burst duration but also somewhat by spectral characteristics, short-hard GRBs (SGRBs) with durations $\lt2\,$ s and long GRBs (LGRBs) with longer durations, although there are other subtleties as well (e.g. low-luminosity long GRBs, GRBs with extended emission; Campana et al. Reference Campana2006; Norris & Bonnell Reference Norris and Bonnell2006). Long GRBs are generally understood in the ‘collapsar’ model (Woosley Reference Woosley1993; Paczyński 1998; MacFadyen & Woosley Reference MacFadyen and Woosley1999; Piran Reference Piran2004). In this model the GRB originates from the collapse of a massive star (confirmed through observations of associated supernovae; Galama et al. Reference Galama1998), leading to a jetted, relativistic outflow and then an afterglow when the jet hits the surrounding interstellar medium and/or the remains of the progenitor’s winds (Section 2.1.2).

Early radio observations made important contributions to the studies of relativistic expansion (Frail et al. Reference Frail, Kulkarni, Nicastro, Feroci and Taylor1997; Taylor et al. Reference Taylor, Frail, Berger and Kulkarni2004), the nature of the progenitors (Li & Chevalier Reference Li and Chevalier2001; Frail et al. Reference Frail2000a ), the effects of viewing geometry on observables (Mészáros, Rees, & Wijers Reference Mészáros, Rees and Wijers1998), the structure of the jet (van der Horst et al. Reference van der Horst, Rol, Wijers, Strom, Kaper and Kouveliotou2005; Panaitescu, Mészáros, & Rees Reference Panaitescu, Mészáros and Rees1998), the passage of the reverse shock (Kulkarni et al. Reference Kulkarni1999), and the basic energetics of GRBs (Frail et al. Reference Frail2001, Reference Frail, Kulkarni, Berger and Wieringa2003, Reference Frail, Soderberg, Kulkarni, Berger, Yost, Fox and Harrison2005).

More recent observations and larger samples have refined and complicated this picture, providing constraints on the environment and related selection effects at multiple wavelengths (Schroeder et al. Reference Schroeder2022; Osborne, Bagheri, & Shahmoradi Reference Osborne, Bagheri and Shahmoradi2021); information on the shock structure (Horesh et al. Reference Horesh, Cenko, Perley, Kulkarni, Hallinan and Bellm2015; Laskar et al. Reference Laskar2016; McMahon, Kumar, & Piran Reference McMahon, Kumar and Piran2006) and the nature of the central engine (Li, Zhang, & Rice Reference Li, Zhang and Rice2015); and revealing a diversity in progenitors (Lloyd-Ronning & Fryer Reference Lloyd-Ronning and Fryer2017). See van Paradijs et al. (Reference van Paradijs, Kouveliotou and Wijers2000) and Piran (Reference Piran2004) for early reviews of GRBs, and Chandra (Reference Chandra2016), Resmi (Reference Resmi2017) and Anderson et al. (Reference Anderson2018) for more recent discussions focusing on radio observations.

Current sensitive, wide-band, surveys have enabled searches for larger samples of afterglows at later times, building on earlier results like Seaton & Partridge (Reference Seaton and Partridge2001) to move beyond the biases present in other studies. For instance, Peters et al. (Reference Peters2019) did a dedicated search for late-time radio emission from three supernovae associated with GRBs, while Leung et al. (Reference Leung2021) used ASKAP data to do a similar search. This approach helps explore late-time afterglow behaviour, which is affected by the progenitor’s wind output many years before the explosion.

However, those searches still targeted GRBs known from high-energy triggers. One of the longstanding goals of radio surveys (e.g. Murphy et al. Reference Murphy2013; Metzger et al. Reference Metzger, Williams and Berger2015b ; Mooley et al. Reference Mooley2016; Lacy et al. Reference Lacy2020) is understanding the true rate of cosmic explosions through the detection of orphan afterglows, which are not viewed along the jet axis. While early results were encouraging (e.g. Levinson et al. Reference Levinson, Ofek, Waxman and Gal-Yam2002), they were hard to validate as the candidates were discovered many years after the putative events, making followup impossible. More recent surveys have come some way to rectifying this, with much better candidates that are amenable to followup (Law et al. Reference Law, Gaensler, Metzger, Ofek and Sironi2018b ; Mooley et al. Reference Mooley2022) or robust limits (Leung et al. Reference Leung, Murphy, Lenc, Edwards, Ghirlanda, Kaplan, O’Brien and Wang2023), although the numbers are still small and it can be hard to definitively determine the cause of a synchrotron transient due to their similarity across many source types (e.g. tidal disruption events and supernovae).

3.1.3. Short gamma-ray bursts

Neutron star mergers have long been believed to be the origin of short gamma-ray bursts (Eichler et al. Reference Eichler, Livio, Piran and Schramm1989; Kochanek & Piran Reference Kochanek and Piran1993; although it can be more complicated, as in Troja et al. Reference Troja2022b ; Rastinejad et al. Reference Rastinejad2022). Like with long GRBs there is a collimated, relativistic jet that impacts the surrounding medium, and so many of the phenomena related to long GRBs could also take place in short GRBs (Granot & van der Horst Reference Granot and van der Horst2014; Berger Reference Berger2014).

This means that we expect similar relativistic afterglows for short GRBs (Section 2.1.2). However, in contrast to long GRBs, the radio emission is considerably fainter (Panaitescu, Kumar, & Narayan Reference Panaitescu, Kumar and Narayan2001) and hence the first detections were not made until years later (Berger et al. Reference Berger2005; Soderberg et al. Reference Soderberg2006c). This is due to both the difference in the energetics of the GRBs themselves, as well as considerably lower circumburst medium densities (Berger Reference Berger2014; Fong et al. Reference Fong, Berger, Margutti and Zauderer2015; O’Connor, Beniamini, & Kouveliotou Reference O’Connor, Beniamini and Kouveliotou2020; with the flux density scaling as the density to the 0.5 power). This environmental difference likely relates to the different underlying model (merger of compact objects instead of an exploding massive star) as well as the resulting change in delay time between formation and burst, which can be much longer in the cases of short GRBs (Gyr vs. Myr; Zevin et al. Reference Zevin, Nugent, Adhikari, Fong, Holz and Kelley2022). For a full review, see Granot & van der Horst (Reference Granot and van der Horst2014) and Berger (Reference Berger2014).

After years of meagre (but important) returns at radio wavelengths (e.g. Fong et al. Reference Fong, Berger, Margutti and Zauderer2015), the advent of more sensitive radio instruments and surveys has improved the prospects for radio detections of short GRBs (Schroeder et al. Reference Schroeder2025). Combined with X-ray observations, radio afterglow measurements constrain the energetics, geometry, and environment of short GRBs (e.g. Jin et al. Reference Jin2018; Dichiara et al. Reference Dichiara, Troja, O’Connor, Marshall, Beniamini, Cannizzo, Lien and Sakamoto2020; Rouco Escorial et al. Reference Rouco Escorial2023). Radio observations are especially important for measuring jet collimation (Fong et al. Reference Fong2014; Troja et al. Reference Troja2016), and deviations from a simple shock model that could indicate prolonged energy injection and/or passage of the reverse shock (e.g. Lloyd-Ronning Reference Lloyd-Ronning2018; Lamb et al. Reference Lamb2019; Troja et al. Reference Troja2019; Schroeder et al. Reference Schroeder2024; Anderson et al. Reference Anderson2024).

In the future, observations with more sensitive instruments (Lloyd-Ronning & Murphy Reference Lloyd-Ronning and Murphy2017) and untargeted surveys should detect a larger number of sources in a wider range of environments, exploring whether the conclusions drawn so far are biased and how they may relate to the related populations of Galactic neutron star binaries and extragalactic neutron star mergers (e.g. Chattopadhyay et al. Reference Chattopadhyay, Stevenson, Hurley, Rossi and Flynn2020; Gaspari et al. Reference Gaspari, Levan, Chrimes and Nelemans2024).

3.1.4. Neutron star mergers

While short GRBs have been studied with the understanding that they are most likely the result of neutron star mergers, this was largely untested empirically until the first (and so far still only) multi-messenger detection of a neutron star merger, GW170817/GRB170817A (Abbott et al. Reference Abbott2017a ,Reference Abbott b ). In this case a mildly relativistic off-axis afterglow was detected at radio wavelengths (Hallinan et al. Reference Hallinan2017) after first being detected at X-ray wavelengths (Troja et al. Reference Troja2017; Margutti et al. Reference Margutti2017). The proximity of this event allowed detailed study (e.g. Mooley et al. Reference Mooley2018a ; Alexander et al. Reference Alexander2017b ; Dobie et al. Reference Dobie2018; Troja et al. Reference Troja2018; Corsi et al. 2018; Mooley et al. Reference Mooley2018c) giving constraints on the structure, opening-angle, and viewing geometry (e.g. Lazzati et al. Reference Lazzati, Perna, Morsony, Lopez-Camara, Cantiello, Ciolfi, Giacomazzo and Workman2018). Further observations, including very long baseline interferometry (VLBI) astrometry, allowed more robust constraints on the geometry (Mooley et al. Reference Mooley2018b ; Ghirlanda et al. Reference Ghirlanda2019) that in turn allowed direct constraints on the Hubble parameter (Hotokezaka et al. Reference Hotokezaka, Nakar, Gottlieb, Nissanke, Masuda, Hallinan, Mooley and Deller2019).

While a burst of gamma-rays was seen from GW170817/GRB170817A (Goldstein et al. Reference Goldstein2017), it was considerably lower luminosity than from most GRBs. The distinction is that the observer needs to be on-axis to see a GRB, while the more general neutron star merger phenomena could be observed off-axis, as was the case with GW170817/GRB170817A. Most subsequent searches for neutron star mergers at radio wavelengths still rely on multi-messenger triggers. Given the uncertain nature of many of those triggers and the wide sky areas they point to (e.g. Petrov et al. Reference Petrov2022), even triggered searches still retain some aspects of wide-field radio surveys, with many sources to consider and tight control over false positives required. With these triggered searches, non-detections can still be used to constrain the geometry, energetics, and environments of neutron star mergers (Gulati et al. Reference Gulati2025). But even without such a trigger, the collimated afterglow from a SGRB/neutron star merger could still be detectable by wide-field radio surveys (Metzger et al. Reference Metzger, Williams and Berger2015b ; Hotokezaka et al. Reference Hotokezaka, Nissanke, Hallinan, Lazio, Nakar and Piran2016; Lin & Totani Reference Lin and Totani2020), although as with many similar events it may be a challenge to distinguish them from other related synchrotron transients. Nonetheless, they are promising targets to understand the diversity in jet launching and how neutron star mergers are tied to their environments. If detected, followup observations including astrometry and searches for scintillation can then be used to determine the jet geometry and energetics (Dobie et al. Reference Dobie, Kaplan, Hotokezaka, Murphy, Deller, Hallinan and Nissanke2020), especially with next-generation radio facilities (Dobie et al. Reference Dobie, Murphy, Kaplan, Hotokezaka, Bonilla Ataides, Mahony and Sadler2021; Corsi et al. Reference Corsi, Eddins, Lazio, Murphy and Osten2024).

Beyond the collimated, relativstic ejecta there are also predictions for an additional component, with mildly-relativistic dynamical ejecta interacting with the surrounding medium and causing a second afterglow-like component (Nakar & Piran Reference Nakar and Piran2011; Piran, Nakar, & Rosswog Reference Piran, Nakar and Rosswog2013; Hotokezaka & Piran Reference Hotokezaka and Piran2015; Hotokezaka et al. Reference Hotokezaka, Kiuchi, Shibata, Nakar and Piran2018). Unlike the jet launching discussed above, detecting this dynamical ejecta could allow studies of the neutron star equation of state and merger dynamics. So far there has not been a definitive radio detection of this emission from GW170817/GRB170817A (Hajela et al. Reference Hajela2019b ; Balasubramanian et al. Reference Balasubramanian2022), and while there have been claims of a second emission component at X-ray wavelengths (Hajela et al. Reference Hajela2022), this is currently a subject of debate (Troja et al. Reference Troja2022a ; Ryan et al. Reference Ryan, van Eerten, Troja, Piro, O’Connor and Ricci2024; Katira et al. Reference Katira, Mooley and Hotokezaka2025). Nonetheless, for future events these transients should be detectable by wide-field radio surveys (Metzger et al. Reference Metzger, Williams and Berger2015b ; Hotokezaka et al. Reference Hotokezaka, Nissanke, Hallinan, Lazio, Nakar and Piran2016; Corsi et al. Reference Corsi, Eddins, Lazio, Murphy and Osten2024; Bartos et al. Reference Bartos, Lee, Corsi, Márka and Márka2019).

Finally, there are models of neutron star mergers where the gravitational wave signal is expected to be accompanied by a coherent burst of low-frequency radio waves, potentially even before the gravitational wave signal (e.g. Usov & Katz Reference Usov and Katz2000; Totani Reference Totani2013; Zhang Reference Zhang2020b ; Yamasaki, Totani, & Kiuchi Reference Yamasaki, Totani and Kiuchi2018; Wang et al. Reference Wang, Peng, Wu and Dai2018; Cooper et al. Reference Cooper, Gupta, Wadiasingh, Wijers, Boersma, Andreoni, Rowlinson and Gourdji2023, and for candidate detections see Moroianu et al. Reference Moroianu, Wen, James, Ai, Kovalam, Panther and Zhang2023; Rowlinson et al. Reference Rowlinson2024). Identification of prompt emission would aid in prompt localisation of the gravitational wave event (thus aiding further electromagnetic followup), potentially provide a dispersion measure-based distance (e.g. Palmer Reference Palmer1993), and help understand the physical conditions at the site of the merger. These signals would not generally be detectable by most of the imaging surveys discussed here, but could be identified by beam-forming surveys, especially wide-area/all-sky surveys (Section 7.5).

3.2.1. Luminous fast blue optical transients

Sitting at the intersection of core-collapse SNe and GRBs, there are expected to be a variety of relativistic explosions that would lack high-energy emission (e.g. Mészáros & Waxman Reference Mészáros and Waxman2001). Such sources have begun to be discovered in increasing numbers by large optical surveys. The first of these from an emerging new class is AT2018cow (Prentice et al. Reference Prentice2018; Perley et al. Reference Perley2019; Ho et al. Reference Ho2019; Margutti et al. Reference Margutti2019; Nayana & Chandra Reference Nayana and Chandra2021), which was notable for having bright, fast, blue optical emission along with very bright and long-lasting (sub)millimetre emission transitioning, along with quickly declining centimetre emission whose properties are not easily reconciled with the millimetre emission (Margutti et al. Reference Margutti2019; Ho et al. Reference Ho2019, Reference Ho2022) in the usual way for synchrotron explosions. These sources are called ‘(luminous) fast blue optical transients’ or (L)FBOTs, with LFBOTs those with the highest peak luminosities ( $10^{44}\,\mathrm{erg\,s}^{-1}$ ) that are achieved in the shortest times (few days), although FBOTs can span a range of lower luminosities and slower timescales (e.g. Drout et al. Reference Drout2014).

While the model for these sources is not clear (e.g. Kuin et al. Reference Kuin2019; Lyutikov & Toonen Reference Lyutikov and Toonen2019; Lyutikov Reference Lyutikov2022; Mohan, An, & Yang Reference Mohan, An and Yang2020; Pellegrino et al. Reference Pellegrino2022; Chen & Shen Reference Chen and Shen2022; Pasham et al. Reference Pasham2021; Vurm & Metzger Reference Vurm and Metzger2021), with models including tidal disruptions of white dwarfs, ongoing central engines, accretion, and circumstellar interactions in unusual environments, many observations suggest that they are related to relativistic explosions from massive stars although this is far from certain (Metzger Reference Metzger2022; Migliori et al. Reference Migliori2024). Increasing numbers of LFBOTs are being identified through optical surveys (e.g. Ho et al. Reference Ho2023b ), which are now able to optimise their selection procedures (Bright et al. Reference Bright2022; Ho et al. Reference Ho2020; Coppejans et al. Reference Coppejans2020; Perley et al. Reference Perley2021; Ofek et al. Reference Ofek2021; Ho et al. Reference Ho2023a ; Yao et al. Reference Yao2022; Chrimes et al. Reference Chrimes2024a ), and radio followup is playing a crucial role in understanding their properties and hence progenitor models. What is still lacking, though, are discoveries beginning with radio or millimetre wavelengths, although this may change with the next generation of millimetre surveys (Eftekhari et al. Reference Eftekhari2022). Like the supernova cases above, such discoveries can help understand the biases in the optical selection functions and what the true underlying rates are.

3.5.1. O & B type main sequence stars

The dominant source of radio emission from hot ( $ \sim 10\,000$ K to $\gt50\,000$ K), massive ( $\gt10\,{{\rm M}_\odot}$ ), OB stars is their stellar winds (Güdel Reference Güdel2002). As the stars shed their strongly ionised winds, they produce thermal (free-free) radio emission (Section 2.2); and indeed radio observations are a well-established way of measuring stellar mass loss rates in OB stars (Leitherer, Chapman, & Koribalski Reference Leitherer, Chapman and Koribalski1995; Scuderi et al. Reference Scuderi, Panagia, Stanghellini, Trigilio and Umana1998). The associated radio emission is predicted to have a positive spectral index ( $\alpha \sim+0.6$ ) and not be variable (Wright & Barlow Reference Wright and Barlow1975). However, these theoretical models assume a steady, spherically symmetric wind. In cases where the wind is inhomogeneous, filaments and clumps in the wind can cause variations in the radio flux density. This has been observed in, for example, P Cygni, a luminous blue variable star, and the first OB star detected in radio (Wendker, Baars, & Altenhoff Reference Wendker, Baars and Altenhoff1973). VLBI observations by Skinner et al. (Reference Skinner, Exter, Barlow, Davis and Bode1997) and Exter et al. (Reference Exter, Watson, Barlow and Davis2002) demonstrated that the stellar wind of P Cyg is highly inhomogeneous and as a result its integrated flux density changes on timescales of days.

Both blue and red supergiants (the highly evolved counterparts of massive OB stars) exhibit thermal radio emission from their stellar atmospheres, and where present, their stellar winds, via the same mechanisms as main sequence OB stars (Scuderi et al. Reference Scuderi, Panagia, Stanghellini, Trigilio and Umana1998). See, for example, radio studies of $\alpha$ Ori (Betelguese) (Lim et al. Reference Lim, Carilli, White, Beasley and Marson1998; O’Gorman et al. Reference O’Gorman2020).

Up to 25–40% of radio-detected OB stars have been found to have signatures of non-thermal radio emission (Bieging, Abbott, & Churchwell Reference Bieging, Abbott and Churchwell1989), and in some cases this dominates the thermal component (Abbott, Bieging, & Churchwell Reference Abbott, Bieging and Churchwell1984). This emission, due to synchrotron radiation (Section 2.1), has a characteristic flat or negative spectral index, and can be variable on short timescales (e.g. Bieging et al. Reference Bieging, Abbott and Churchwell1989; Persi et al. Reference Persi, Tapia, Rodriguez, Ferrari-Toniolo and Roth1990). Synchrotron emission implies the presence of strong magnetic fields and shocks. Initially there were a range of hypotheses for the source of non-thermal emission, considering both single stars and binary systems. However, it is now established that most (if not all) OB stars that show non-thermal emission are binary systems (see Table 2 in De Becker Reference De Becker2007). The emission is caused by shocks in the colliding-wind region of binary OB systems, where the winds from both stars in the binary interact (see also Section 3.5.6). This has been demonstrated in a number of systems through the observed periodicity of the radio variability (see the series of papers studying stars in the Cyg OB association for examples Blomme et al. Reference Blomme, van Loo, De Becker, Rauw, Runacres, Setia Gunawan and Chapman2005; van Loo et al. Reference van Loo, Blomme, Dougherty and Runacres2008; Blomme et al. Reference Blomme, De Becker, Volpi and Rauw2010). A review of non-thermal radio emission in massive stars is given by De Becker (Reference De Becker2007).

Table 2. Properties of long period transients and related Galactic sources. The sources are broadly grouped according to how they are reported in the literature. We have only included published objects here, but we know of a number of new discoveries currently in preparation.

Periods given are the primary radio periods, but these may be a mix of rotation and orbital periods or even beat frequencies, depending on the source; where both orbital and rotation periods are known they are given separately. Many sources show multiple modes with differing pulse widths and polarisation properties, and are highly variable. Properties given as “?” could not be determined from the available information. An up-to-date version of this table is available at https://vast-survey.org/LPTs. Also see Dong et al. (Reference Dong2025b ) and https://lpt.mwa-image-plane.cloud.edu.au/published/tables/1 for related samples.

Citations: 1 — Hyman et al. (Reference Hyman, Lazio, Kassim, Ray, Markwardt and Yusef-Zadeh2005); 2 — Hyman et al. (Reference Hyman, Roy, Pal, Lazio, Ray, Kassim and Bhatnagar2007); 3 — Roy et al. (Reference Roy, Hyman, Pal, Lazio, Ray and Kassim2010); 4 — Kaplan et al. (Reference Kaplan, Hyman, Roy, Bandyopadhyay, Chakrabarty, Kassim, Lazio and Ray2008); 5 — Hyman et al. (Reference Hyman, Lazio, Kassim and Bartleson2002); 6 — Hyman et al. (Reference Hyman, Wijnands, Lazio, Pal, Starling, Kassim and Ray2009); 7 — Wang et al. (Reference Wang2021b ); 8 — Dong et al. (Reference Dong2025b ); 9 — Hurley-Walker et al. (Reference Hurley-Walker2022b ); 10 — Rea et al. (Reference Rea2022); 11 — Hurley-Walker et al. (Reference Hurley-Walker2023); 12 — Wang et al. (Reference Wang2025c); 13 — Caleb et al. (Reference Caleb2024); 14 — Dobie et al. (Reference Dobie2024); 15 — McSweeney et al. (Reference McSweeney2025a ); 16 — Lee et al. (Reference Lee2025); 17 — Castro Segura et al. (Reference Castro Segura2025); 18 — Marsh et al. (Reference Marsh2016); 19 — Stanway et al. (Reference Stanway, Marsh, Chote, Gänsicke, Steeghs and Wheatley2018); 20 — Pelisoli et al. (Reference Pelisoli2023); 21 — Bloot et al. (Reference Bloot2025); 22 — Dong et al. (Reference Dong2025a ); 23 — Anumarlapudi et al. (Reference Anumarlapudi2025); 24 — de Ruiter et al. (Reference de Ruiter2025); 25 — Hurley-Walker et al. (Reference Hurley-Walker2024); 26 — Rodriguez (Reference Rodriguez2025); 27 — Wang et al. (Reference Wang2025d); 28 — Caleb et al. (Reference Caleb2022).

3.5.2. Wolf-Rayet stars

Wolf-Rayet (W-R) stars are the helium-burning remnants of massive OB stars. They are highly evolved, having lost their hydrogen-rich outer layers through the processes of Roche lobe overflow to a companion (in close binaries), mass loss by a strong stellar wind (in single stars), or a combination of both (Crowther Reference Crowther2007). W-R stars have extremely hot, dense stellar winds, and so exhibit strong thermal radio emission, via the same mechanisms as OB stars, and are some of the most luminous stellar radio sources (Abbott et al. Reference Abbott, Beiging, Churchwell and Torres1986). As with OB stars, this radio emission can also be used to measure stellar mass loss rates, which, for W-R stars, are very high (Nugis & Lamers Reference Nugis and Lamers2000).

A subset of W-R stars exhibit non-thermal synchrotron radiation, and as with OB stars, most (if not all) of these are in binary systems (see Table 1 in De Becker Reference De Becker2007). The archetypal example is WR 140, a W-R $+$ O star binary, with a 7.9 year orbit. Extensive monitoring with the VLA by White & Becker (Reference White and Becker1995) showed variability in the non-thermal emission, clearly correlated with the orbital phase. Further work by Dougherty et al. (Reference Dougherty, Beasley, Claussen, Zauderer and Bolingbroke2005) showed that the spectral index is also correlated with the orbital phase, suggesting that the relative importance of emission, absorption and plasma processes changes with stellar separation (and hence electron and ion density) throughout the orbit. For more information we refer the reader to the review of non-thermal radio emission in massive stars (including W-R stars) by De Becker (Reference De Becker2007).

3.5.3. A & early F type main sequence stars

A and early F-type stars ( $\sim 6\,500$ K to $\lt10\,000$ K) have neither the strong ionised stellar winds of OB type stars, nor the dynamo-generated magnetic fields of later type stars (Güdel Reference Güdel2002, and see below). Hence they are generally expected to have weak thermal emission from their atmospheres, and mostly not be detectable at radio wavelengths (Brown et al. Reference Brown, Veale, Judge, Bookbinder and Hubeny1990). A small number of nearby objects have been detected in radio, for example Sirius A (A0/1; White et al. Reference White, Aufdenberg, Boley, Hauschildt, Hughes, Matthews and Wilner2018, Reference White2019) and Procyon (F5; Drake, Simon, & Brown Reference Drake, Simon and Brown1993). For Procyon, the observed quiescent emission is thermal (free-free) chromospheric emission from the entire stellar disk. The variable emission is potentially due to either (a) active regions on the corona, analogous to our Sun; or (b) flares or bursts due to localised magnetic fields, again analogous to our Sun. See also the discussion of thermal radio emission detected from the late F9 star $\eta$ Cas A by Villadsen et al. (Reference Villadsen, Hallinan, Bourke, Güdel and Rupen2014).

A subset of A-type (and B-type) stars that do show strong radio emission are the magnetic chemically peculiar (Ap and Bp type) stars. We discuss these separately in Section 3.5.4.

3.5.4. Magnetic chemically peculiar stars

Magnetic chemically peculiar stars (MCPs, also referred to as Ap and Bp type stars), are a subset of main sequence stars that have strong (kilogauss), organised magnetic fields, and unusual chemical abundances on their surfaces (Preston Reference Preston1974; Landstreet Reference Landstreet1992).

There were many searches for radio emission from these stars, carried out over several decades (e.g. Trasco, Wood, & Roberts Reference Trasco, Wood and Roberts1970; Turner Reference Turner1985), until Drake et al. (Reference Drake, Abbott, Bastian, Bieging, Churchwell, Dulk and Linsky1987) successfully detected five systems with the VLA: $\sigma$ Ori E, HR 1890, and $\delta$ Ori C, IQ Aur, and Babcock’s star (HD 215441). Subsequent work by Linsky et al. (Reference Linsky, Drake and Bastian1992) showed the radio emission was consistent with gyrosynchrotron radiation from particles in the magnetosphere, accelerated due to interactions with the stellar wind.

The geometry of magnetic fields in MCP stars is generally dipolar, with the magnetic axis inclined with respect to the rotational axis. Hence the observed magnetic field of the star is modulated by its rotational period (Landstreet Reference Landstreet1992). Consistent with this, Leone & Umana (Reference Leone and Umana1993) showed that the observed radio emission of two MCPs (HD 37017 and $\sigma$ Ori E) was periodic, and varied with the rotational period of the star.

However, the gyrosynchrotron mechanism can not explain the observed radio emission of all MCPs. Observations of CU Vir by Trigilio et al. (Reference Trigilio, Leto, Leone, Umana and Buemi2000) detected bright, highly directional, and highly circularly polarised emission, that required a coherent mechanism to explain it. They showed this was consistent with electron cyclotron maser emission, a result supported by long-term monitoring observations of CU Vir (e.g. Trigilio et al. Reference Trigilio, Leto, Umana, Buemi and Leone2008; Ravi et al. Reference Ravi2010; Lo et al. Reference Lo2012)

The current generation of radio telescopes (and in particular widefield radio surveys) has enabled the detection of an increased number of magnetic chemically peculiar stars, including at lower radio frequencies. See Hajduk et al. (Reference Hajduk, Leto, Vedantham, Trigilio, Haverkorn, Shimwell, Callingham and White2022), Das et al. (Reference Das2022) and Das et al. (Reference Das2025) for recent results from LOFAR, GMRT (the Giant Metrewave Radio Telescope), and ASKAP respectively.

3.5.5. Late F, G & K type main sequence stars

Late F-type to early K-type main sequence stars are often referred to as ‘solar-type’ stars, as they are broadly similar to our Sun in terms of temperature, mass, and other physical processes. The Sun is extremely well-studied in radio: see Dulk (Reference Dulk1985) and Bastian, Benz, & Gary (1998) for earlier reviews of solar radio emission, and Benz & Güdel (Reference Benz and Güdel2010) for a more recent review of solar flares across the electromagnetic spectrum. Kowalski (Reference Kowalski2024) provides an equivalent review of stellar flares.

Like our Sun, F, G and K-type stars are observed to have quiescent thermal radio emission (Villadsen et al. Reference Villadsen, Hallinan, Bourke, Güdel and Rupen2014). If the Sun’s thermal radio emission was scaled to the distance of stars in our local neighbourhood, it would only reach $\mu$ Jy levels, which until recently was below the detection threshold of most radio telescopes. Hence the stars detected to date tend to be more luminous than the Sun.

F to K-type stars (and many other main sequence stars) have a magnetic corona like our Sun, and hence have magnetic fields generated by a dynamo at the interface between the radiative core and the convective envelope. They therefore show stellar flares, with both thermal and non-thermal components (e.g. Gudel Reference Gudel1992; Lim & White Reference Lim and White1995; Budding et al. Reference Budding, Carter, Mengel, Slee and Donati2002).

Solar-type stars have also been observed to flare with much higher energies than our own Sun (so-called ‘superflares’; Maehara et al. Reference Maehara2012). Superflares are caused by magnetic reconnection, and often linked to starspot activity. Superflares have not been definitively detected at radio wavelengths to date.

Finally, some F, G & K stars exhibit coherent bursts from a range of mechanisms (e.g. Matthews Reference Matthews2025), although in general the stellar equivalents of solar radio bursts have been primarily studied on K & M dwarfs due to their extremely strong magnetic fields, since these result in stronger and more frequent flare activity (see Section 3.5.7).

3.5.6. RS CVn and Algol binaries

RS Canum Venaticorum (RS CVn) and Algol stars are two subtypes of chromospherically active binary star systems.

RS CVn binaries consist of a subgiant or giant star of spectral type F–K with a companion main sequence star of spectral type G–M. They have typical orbital periods of 1–30 days, and typical separations of $\sim R_\odot$ (Hall Reference Hall and Fitch1976). They have active chromospheres, high rotational velocities and strong magnetic fields.

Algol binaries consist of two semi-detached stars, in which one is a hot (B or A-type) main sequence star, and the second is a more evolved (G or K-type) giant or subgiant. They have typical orbital periods of 1–20 days and typical separations of $\sim 10$ – $40\,{\rm R}_\odot$ (Giuricin, Mardirossian, & Mezzetti Reference Giuricin, Mardirossian and Mezzetti1983).

At gigahertz frequencies, these stellar systems exhibit quiescent emission, due to mildly relativistic electrons radiating gyrosynchrotron emission in magnetic fields (Güdel Reference Güdel2002). Both RS CVn and Algol-type binaries also show variability in this gyrosynchrotron emission, on timescales of minutes to hours. This activity can be present for a significant fraction ( $\sim30\%$ ) of the time (Lefevre, Klein, & Lestrade Reference Lefevre, Klein and Lestrade1994). In addition, they show significant radio flaring activity (Drake et al. Reference Drake, Simon and Linsky1989; Lefevre et al. Reference Lefevre, Klein and Lestrade1994; Umana et al. Reference Umana, Trigilio and Catalano1998).

At low radio frequencies, coherent emission mechanisms dominate in RS CVn binaries. Toet et al. (Reference Toet, Vedantham, Callingham, Veken, Shimwell, Zarka, Röttgering and Drabent2021) propose that this electron cyclotron maser emission could be generated by enhanced chromospheric flaring due to tidal forces or the interaction between the two binary stars, analogous to the Jupiter-Io interaction.

Two well-studied active binary systems are the RS CVn binary HR 1099 (e.g. Owen, Jones, & Gibson Reference Owen, Jones and Gibson1976; Feldman et al. Reference Feldman, Taylor, Gregory, Seaquist, Balonek and Cohen1978; Osten et al. Reference Osten2004; Slee, Wilson, & Ramsay Reference Slee, Wilson and Ramsay2008) and the canonical Algol binary, $\beta$ Persei (Mutel et al. Reference Mutel, Lestrade, Preston and Phillips1985, Reference Mutel, Molnar, Waltman and Ghigo1998).

3.5.7. M dwarf and ultracool dwarf stars

M-dwarfs are very low mass (typically $0.1$ – $0.6$ M $_\odot$ ), cool ( $T \lt 3\,800$ K) stars. They are long lived, and extremely abundant, accounting for roughly 75% of the stars in our local neighbourhood (Winters et al. Reference Winters2019). M-dwarfs show bright radio bursts across all wavebands, associated with their extremely strong (up to kilogauss; Shulyak et al. Reference Shulyak, Reiners, Engeln, Malo, Yadav, Morin and Kochukhov2017) magnetic fields.

The observed radio emission comes from a range of different emission mechanisms. Intense and highly polarised electron cyclotron maser emission often dominates (e.g. Hallinan et al. Reference Hallinan, Antonova, Doyle, Bourke, Lane and Golden2008; Lynch et al. Reference Lynch, Lenc, Kaplan, Murphy and Anderson2017; Villadsen & Hallinan Reference Villadsen and Hallinan2019). This likely originates both from magnetic active regions, and from auroral emission (e.g. Hallinan et al. Reference Hallinan2015), analogous to solar system planets (Zarka Reference Zarka1998). M-dwarfs also show quiescent and flaring emission due to gyrosynchrotron radiation (e.g. Berger et al. Reference Berger2001a ; Lynch et al. Reference Lynch, Murphy, Ravi, Hobbs, Lo and Ward2016).

Ultracool dwarfs (later than M7-type) are the coolest ( $T \lt 2\,900$ K) stellar and substellar objects. Only ten L & T-type dwarfs have been detected in radio to date (see Table 2 in Rose et al. Reference Rose2023, and in addition the recently published detection by Guirado et al. Reference Guirado, Climent, Bergasa, Pérez-Torres, Marcaide and Peña-Moñino2025), but these observations have provided evidence for kilogauss magnetic fields even in the coolest of substellar objects (Kao et al. Reference Kao, Hallinan, Pineda, Stevenson and Burgasser2018). Given that ultracool dwarfs are fully convective (without a radiative core), this requires an alternative dynamo mechanism (e.g. Browning Reference Browning2008).

Like M-dwarfs, ultracool dwarfs can show quiescent, flaring and auroral radio emission (e.g. Route & Wolszczan Reference Route and Wolszczan2012; Kao et al. Reference Kao, Hallinan, Pineda, Escala, Burgasser, Bourke and Stevenson2016). Because radio observations allow us to probe the magnetic field strength, they are critical for understanding energy generation in ultracool stars and substellar objects.

Radio observations complement X-ray and optical observations by providing direct measurements of the magnetic field strengths and plasma densities associated with stellar activity (Benz & Güdel Reference Benz and Güdel2010). Because coherent emission mechanisms often dominate, many M-dwarf and ultracool dwarf stars do not fit the empirically established (over 10 orders of magnitude) Gudel-Benz relation between quiescent gyrosynchrotron radio and soft X-ray luminosity.

Untargeted searches with current telescopes are enabling detection of larger samples of M dwarf and ultracool dwarf stars than were previously available (e.g. Callingham et al. Reference Callingham2021). They also enable searches that are unbiased by the properties of the stars in other wavebands (previous samples were often selected on the basis of their known chromospheric activity (e.g. Lynch et al. Reference Lynch, Lenc, Kaplan, Murphy and Anderson2017; Crosley & Osten Reference Crosley and Osten2018).

3.5.8. Star-planet interactions and exoplanetary systems

Radio emission is expected from exoplanetary systems, in analogy to what we observe from the magnetised planets in our own solar system (Zarka Reference Zarka2007). This predicted emission originates from several different mechanisms: (i) auroral emission from the interaction between the host stellar wind and the exoplanetary magnetosphere, as seen in magnetised planets in our solar system (Zarka Reference Zarka1998; Farrell, Desch, & Zarka Reference Farrell, Desch and Zarka1999); (ii) electron cyclotron maser emission from the magnetic interaction between a so-called ‘hot Jupiter’ and its host star (referred to as star-planet interactions, or SPI; Zarka Reference Zarka2007); (iii) emission from the interaction between an exoplanet and its exomoon/s, analogous to the Jupiter-Io system (Noyola, Satyal, & Musielak Reference Noyola, Satyal and Musielak2014).

There has been substantial theoretical and empirical work in predicting the flux densities expected (e.g. Lazio et al. Reference Lazio, Farrell, Dietrick, Greenlees, Hogan, Jones and Hennig2004; Grieß meier, Zarka, & Spreeuw 2007; Hess & Zarka Reference Hess and Zarka2011; Lynch et al. Reference Lynch, Murphy, Lenc and Kaplan2018). For (i) the radio emission has a cutoff frequency determined by the strength of the exoplanetary magnetic field, and hence is only likely to be detectable at low radio frequencies ( $\lt 300$ MHz). For (ii), the emission frequency can be higher (up to gigahertz), as it is determined by the magnetic field strength of the host star rather than the planet.

Over the past two decades there have been many searches for radio emission from exoplanetary systems, from targeted observations of individual exoplanets considered likely to be detectable (e.g. Bastian, Dulk, & Leblanc Reference Bastian, Dulk and Leblanc2000; Lazio & Farrell Reference Lazio and Farrell2007; Vidotto et al. Reference Vidotto, Fares, Jardine, Donati, Opher, Moutou, Catala and Gombosi2012) to large-scale searches for emission from known exoplanetary systems in both targeted (e.g. Ortiz Ceballos et al. Reference Ortiz Ceballos, Cendes, Berger and Williams2024) and untargeted radio surveys (e.g. Murphy et al. Reference Murphy2015). In recent years, there have been a number of tentative detections (e.g. Vedantham et al. Reference Vedantham2020; Turner et al. Reference Turner2021), although none have yet been definitively confirmed as originating from star-planet interactions.

The improved sensitivity of current and future telescopes, and the capability of widefield surveys to target many systems at once means detecting exoplanetary systems at radio wavelengths is increasingly likely (see Zarka et al. Reference Zarka, Lazio and Hallinan2015, for a discussion of SKAO capabilities). However, a significant observational challenge is that the emission is beamed, and dependent on the orbital period of the planet. Although beaming can make the emission brighter, the high directionality reduces the probability of detection. In addition, once radio emission has been detected from an exoplanetary system, it is challenging to distinguish between an exoplanet-related cause, and emission from the host star (see, for example, the discussion in Pineda & Villadsen Reference Pineda and Villadsen2023). See Callingham et al. (Reference Callingham2024) for a recent review of radio emission from star planet interactions and space weather in exoplanetary systems.

3.8.1. Nascent pulsar/magnetar wind nebulae

When a supernova leaves behind a compact object, the luminosity of this object (both particle and electromagnetic) can power a new pulsar wind nebula (PWN; Gaensler & Slane Reference Gaensler and Slane2006; Olmi & Bucciantini Reference Olmi and Bucciantini2023) or magnetar wind nebula, depending on the nature of the compact object. This represents a transition from the supernova stage to a supernova remnant, a phase that may span a decade or so and is poorly probed observationally (e.g. Milisavljevic et al. Reference Milisavljevic, Patnaude, Chevalier, Raymond, Fesen, Margutti, Conner and Banovetz2018; Milisavljevic & Fesen Reference Milisavljevic, Fesen, Alsabti and Murdin2017) but can help constrain the population of newly formed compact objects and tie them to the properties of their parent supernovae (e.g. Metzger et al. Reference Metzger, Margalit, Kasen and Quataert2015a ; Fransson et al. Reference Fransson2024). This is especially relevant for sub-classes of supernovae (including Type Ic-BL and superluminous supernovae) that may be powered by ongoing emission from a central engine, often thought to be a magnetar (Thompson, Chang, & Quataert Reference Thompson, Chang and Quataert2004; Kasen & Bildsten Reference Kasen and Bildsten2010; Dessart Reference Dessart2024).

So far, direct radio searches for transitional sources have been mixed. Broad and targeted radio surveys of supernovae (e.g. Law et al. Reference Law2019; Eftekhari et al. Reference Eftekhari2019) have only yielded a few detections of new wind nebula candidates. Results from untargeted radio surveys have also only discovered a small number of sources (Dong & Hallinan Reference Dong and Hallinan2023; Marcote et al. Reference Marcote, Nimmo, Salafia, Paragi, Hessels, Petroff and Karuppusamy2019), and the interpretation of these discoveries is often unclear (Mooley et al. Reference Mooley2022) since the nature of the synchrotron emission is degenerate between many classes. Nonetheless, continued deep radio observations of large samples of supernovae from diverse classes, whether done as targeted searches or just parts of broad surveys, will help to further resolve this question and establish links between different supernova types and potential central engines.

3.8.2. Fast radio burst persistent radio sources

While we are not in general discussing FRBs in this review, we will briefly discuss the related phenomenon of ‘persistent radio sources’ (PRSs). First identified following the first FRB localisation (Chatterjee et al. Reference Chatterjee2017), PRSs are long-lived compact ( $\sim$ mas; Marcote et al. Reference Marcote2017; Bhandari et al. Reference Bhandari2023) non-thermal radio sources that are co-located with (so far) repeating FRBs (Chatterjee et al. Reference Chatterjee2017; Marcote et al. Reference Marcote2017; Niu et al. Reference Niu2022; Bruni et al. Reference Bruni2024b ; Bruni et al. Reference Bruni2024a ). They are spatially offset from the nuclei of their host galaxies and have properties inconsistent with star-formation such as very high degrees of magnetisation (Michilli et al. Reference Michilli2018; Niu et al. Reference Niu2022) that appears to be tied to their luminosities (Yang, Li, & Zhang Reference Yang, Li and Zhang2020). This suggests a common origin with FRBs and perhaps an interpretation as a magnetar-powered nebula (Margalit & Metzger Reference Margalit and Metzger2018), although other models are possible (e.g. Zhang Reference Zhang2020a ; Sridhar & Metzger Reference Sridhar and Metzger2022, Ibik et al. Reference Ibik2024 and references therein). If confirmed, this interpretation would allow persistent radio sources to be used as FRB calorimeters and place constraints on the origin and evolution of FRBs and their progenitors.

Note that, while called ‘persistent’, PRSs do in fact have significant changes in both their Faraday rotation measure (Michilli et al. Reference Michilli2018; Niu et al. Reference Niu2022) and in their flux densities (Rhodes et al. Reference Rhodes, Caleb, Stappers, Andersson, Bezuidenhout, Driessen and Heywood2023; Zhang et al. Reference Zhang2023), likely from intrinsic causes. This then open an avenue for discovery of new PRSs: searching for compact, non-thermal, potentially variable radio sources either associated with known FRBs (Ibik et al. Reference Ibik2024; Eftekhari et al. Reference Eftekhari, Berger, Williams and Blanchard2018) or not (Ofek Reference Ofek2017; Dong & Hallinan Reference Dong and Hallinan2023). Such searches can help constrain the rate and lifetimes of repeating FRBs and PRSs, although care must be taken to not be confused by galactic nuclei, chance alignments, or thermal radio emission (e.g. Ravi et al. Reference Ravi2022a ; Dong et al. Reference Dong2024).

4.2.1. A figure of merit for transient surveys

In this context, Cordes et al. (Reference Cordes, Lazio and McLaughlin2004) proposed a figure of merit for transient detection surveys:

(4) \begin{equation}\mathrm{FOM}_\mathrm{CLM} \equiv A \Omega_\mathrm{epoch} \left(\frac{T}{\Delta T}\right)\end{equation}

that should be maximised for a given survey (subject to various constraints regarding actual telescope designs etc.). In this figure of merit, A is the collecting area of the telescope, $\Omega_\mathrm{epoch}$ is the solid angle coverage in a single epoch (not an instantaneous field-of-view like the usage in a classical étendue), T is the total duration of the observation, and $\Delta T$ is the time resolution. For continuum imaging surveys, the trade-off has typically been between sensitivity and area, spending a finite total time either on a smaller number of deeper pointings or a larger number of shallow ones (e.g. the LOFAR Two-metre Sky Survey (LoTSS) covering $20\,000\,\mathrm{deg}^2$ with a rms of $2\,000$ $\mu$ Jy beam $^{-1}$ vs. LoTSS Deep covering $30\,\mathrm{ deg}^2$ at 10 $\mu$ Jy beam $^{-1}$ rms; Shimwell et al. Reference Shimwell2017; Best et al. Reference Best2023).

For the figure of merit in Equation (4), increasing the collecting area, A, increases the instantaneous sensitivity of the observations, which means a fainter source population can be probed. Increasing the solid angle coverage, $\Omega_\mathrm{epoch}$ , means the sky can be covered more efficiently, increasing the survey speed. Increasing the total duration of the observation, T, increases the sensitivity to phenomena on the timescale of the observations, and increasing the time resolution, $\Delta T$ , broadens the range of timescales that can be explored by the survey.

However, there are limitations to the metric in Equation (4), especially when comparing surveys with very different telescopes at very different frequencies over very different timescales.

Firstly, A is not an ideal way to fully parameterise the sensitivity of a telescope. Better would be $A/T_\mathrm{sys}$ (where $T_\mathrm{sys}$ is the system temperature, including both the receiver temperature and the sky temperature, and A could also include the antenna efficiency $\eta_A$ to define the effective area $A_\mathrm{ eff}\equiv\eta_A A$ ). Alternately, especially when considering surveys done at a range of timescales, more appropriate might be the delivered RMS noise $\sigma$ , which can include contributions from the system-equivalent flux density (related to $A/T_\mathrm{sys}$ ; e.g. Crane & Napier Reference Crane, Napier, Perley, Schwab and Bridle1989; Wrobel & Walker Reference Wrobel and Walker1999; Lorimer & Kramer Reference Lorimer and Kramer2012) but also things like confusion noise, and which will depend on the angular resolution and the timescale probed ( $\sigma(\Delta T) \propto \Delta T^{-1/2}$ typically, if not dominated by confusion). This can be further modified to account for varying sensitivity as a function of observing frequency. Since most of the sources considered here have non-thermal spectra (the overall population will have a median spectral index of $\alpha\approx -0.7$ or lower) we will use $\sigma (\nu/\nu_0)^{-\alpha}$ comparing to some reference frequency $\nu_0$ (this is also done elsewhere, as in Best et al. Reference Best2023). And unlike A or $A/T_\mathrm{eff}$ , which we seek to maximise, smaller values of $\sigma$ are better.

Figure 7. This plot shows how the effective survey volume, using the figure of merit in Equation (5) has evolved over time. Estimates are included for upcoming, but as yet unpublished, surveys. Some individual surveys of interest are labelled. The surveys are coloured by observing frequency, the shape corresponds to the telescope, and the size corresponds to the survey timescale (if multiple results are reported for a single survey on different timescales, it is plotted multiple times). Information has been updated from the survey compendium by Kunal Mooley and Deepika Yadav http://www.tauceti.caltech.edu/kunal/radio-transient-surveys/index.html. Labelled surveys include: GT86 (Gregory & Taylor Reference Gregory and Taylor1986); MR90 (McGilchrist & Riley Reference McGilchrist and Riley1990; Riley Reference Riley1993); MR00 (Minns & Riley Reference Minns and Riley2000); L+02 (Levinson et al. Reference Levinson, Ofek, Waxman and Gal-Yam2002); dV+04 (de Vries et al. Reference de Vries, Becker, White and Helfand2004); T+11 (Thyagarajan et al. Reference Thyagarajan, Helfand, White and Becker2011); M+13 (Mooley et al. Reference Mooley, Frail, Ofek, Miller, Kulkarni and Horesh2013); R+16 (Rowlinson et al. Reference Rowlinson2016); P+16 (Polisensky et al. Reference Polisensky2016); S+21 (Sarbadhicary et al. Reference Sarbadhicary2021); M+21 (Murphy et al. Reference Murphy2021); D+22 (Dobie et al. Reference Dobie2022); and C+24 (Chastain et al. Reference Chastain2025). Additional surveys from Table 4 are RACS-low, VAST-G (for VAST-Galactic), VLASS, LoTSS, and GPM, as well as a projection for using the VASTER fast-imaging pipeline (Wang et al. Reference Wang2023) on the EMU survey (Hopkins et al. Reference Hopkins2025).

Secondly, the survey area is hard to compare between telescopes that have very different angular resolutions. For example, some low-frequency dipole arrays (e.g. the Long Wavelength Array) have essentially instantaneous fields-of-view of $2\pi$ sr, but might have limited resolutions of a few arcmin or worse changed (which can lead to a higher confusion limit), while others (e.g. LOFAR) have intrinsic fields-of-view of $2\pi\,$ sr but are limited by beam-formed to focus on smaller areas. This compares with traditional dish-based interferometers at higher frequencies (e.g. the VLA and the Australia Telescope Compact Array; ATCA) that have fields-of-view of arcmin $^2$ but resolutions of arcsec. Therefore instead of just $\Omega_\mathrm{epoch}$ we use $\Omega_\mathrm{epoch}/\theta^2$ , with $\theta$ the angular resolution. This effectively normalises to the rough number of independent pixels (ignoring oversampling) or potential sources in a pointing. For a traditional interferometer this reduces to roughly $B^2/D^2$ , where B is the maximum baseline and D the element diameter, but systems like phased-array feeds (Hotan et al. Reference Hotan2021) can increase this significantly.

Finally, rather than use $T/\Delta T$ separately we just use the number of epochs, $N_\mathrm{epochs}$ , which has the same value. Putting these together we choose:

(5) \begin{equation} \mathrm{FOM} \equiv N_\mathrm{epochs}(\Delta T) \left(\frac{\Omega_\mathrm{epoch}}{\theta^2}\right) \left(\frac{\nu}{\nu_0}\right)^\alpha \frac{1}{\sigma(\Delta T)}\end{equation}

as the figure-of-merit that a survey should maximise, where we retain the explicit dependence of $N_\mathrm{epochs}$ and $\sigma$ on the time-scale probed since the same data can be processed in multiple ways, although this assumes that there are sufficient sources on the relevant timescales to make this reprocessing worthwhile. This functions like an effective survey volume, multiplying the number of epochs times the number of sources divided by the noise. It could in principle be further modified to account for the total physical volume probed and various source number density scalings (such as $N(\geq S_\nu)\propto S_\nu^{-3/2}$ for standard candles in a Euclidean universe), which would adjust the relative importance of going wider versus deeper, but we do not do that here. Such explorations can be done, but are best tied to individual source types and do not generalise to the entire field as well.

Our figure of merit here expands on the commonly used survey speed metric (the number of square degrees per hour needed to achieve a given sensitivity; e.g. Johnston et al. Reference Johnston2007) which is more relevant for design of a telescope than a particular survey (indeed we revisit it in Section 7 when discussing future facilities). Firstly, we divide the survey speed by the synthesized beam solid angle $\theta^2$ to allow comparison of widely different telescopes. Secondly, we do an explicit frequency correction assuming a spectral index $\alpha$ to allow comparison of widely different frequencies. But most importantly we explicitly consider the number of individual epochs and the timescale over which that sensitivity is achieved, to make sure that we probe variability on the timescales of interest.

4.2.2. Comparing transient surveys

In the ideal case, a survey that optimised all of the parameters in Equation (5) would be suitable for detecting and monitoring radio time domain phenomena across all timescales (which, as Figure 1 shows, span many orders of magnitude). In practice, in any given survey to date, some aspects of this ideal were significantly compromised, limiting the effectiveness of the survey for particular phenomena. In addition, in many of the surveys conducted to date, it has not been possible to control the time sampling or integration times, because they relied on archival data (e.g. Levinson et al. Reference Levinson, Ofek, Waxman and Gal-Yam2002; Bower et al. Reference Bower, Saul, Bloom, Bolatto, Filippenko, Foley and Perley2007; Bannister et al. Reference Bannister, Murphy, Gaensler, Hunstead and Chatterjee2011).

Over the past two decades there have been a large number of radio transient surveys, which we discuss in Section 4.3. Figure 7 shows how the effective survey ‘volume’ has evolved over time, using the figure of merit in Equation (5). It is important to note that while this way of representing the surveys does distinguish between different sampling times $\Delta T$ , it does not look at how sources vary over such timescales, as discussed below.

To compare the effectiveness of different surveys, a range of metrics have been used, most of which involve collapsing down the time dimension to form a ‘two-epoch equivalent’ source density parameter, introduced by Bower et al. (Reference Bower, Saul, Bloom, Bolatto, Filippenko, Foley and Perley2007). For the two-epoch source density to provide a meaningful comparison, it requires the assumption that we do not know the characteristic timescale of variability of the underlying population/s, and hence a survey of 10 epochs spanning hours is equivalent to a survey of 10 epochs spanning months. Clearly this is not a valid assumption for any given, known source type: a survey with a total duration spanning hours would not be optimal for detecting gamma-ray bursts and supernovae, which evolve over months. However, the two-epoch source density has proved to be a useful tool in comparing surveys as the field has grown, from the four surveys listed by Bower et al. (Reference Bower, Saul, Bloom, Bolatto, Filippenko, Foley and Perley2007) to the more than 50 that have been conducted to date, some of which are shown in Figure 7 In Section 4.3 we discuss the evolution of radio transient surveys over the past two decades.

4.2.3. Other survey properties

Looking beyond the pure detection capabilities, survey design also affects the capacity for multi-wavelength follow-up, which is often critical for classification and identification of radio transients. A survey with two epochs separated by years (such as the NVSS versus FIRST comparison conducted by Levinson et al. Reference Levinson, Ofek, Waxman and Gal-Yam2002) can identify objects that have changed on those timescales, which is useful for estimating transient rates. However, confirming the nature of the individual objects (in that case, trying to distinguish between orphan afterglows, radio supernova and scintillating AGN) is made challenging by (a) the length of time after the transient event that the detection is made; (b) the lack of precision in identifying when the event occurred; and (c) the poor sampling of the event. So in addition to optimising the survey figure of merit, an ideal radio transients survey would also have:

• • A radio reference survey at a similar, or better, sensitivity;

• • Sampling of a wide range of timescales;

• • Rapid data processing to enable rapid identification;

• • Effective RFI and artefact rejection;

• • Archival multi-wavelength survey data;

• • Contemporaneous multi-wavelength observations;

• • Capability to trigger follow-up with other telescopes.

Triggered follow-up is often important in identifying transients, particularly those identified at higher frequency wavebands (optical, X-ray) or with multi-messenger detectors. The most notable example of a comprehensive multi-wavelength follow-up campaign in recent years is that of the binary neutron star merger GW170817, detected in gravitational waves (Abbott et al. Reference Abbott2017a ), with a counterpart identified in electromagnetic radiation (Abbott et al. Reference Abbott2017b ) and followed up in all wavebands from gamma-rays to radio, providing an incredibly detailed picture of the event (Kasliwal et al. Reference Kasliwal2017).

For many phenomena discovered in radio, follow-up is complicated by the fact that radio emission arrives later than X-ray, optical and other higher frequency emission due to the nature of the underlying physical processes. Taking GW170817 as an example, gamma-rays were detected 1.7s after the gravitational wave event (Goldstein et al. Reference Goldstein2017), optical/IR at 10.9 h post-event (Coulter et al. Reference Coulter2017), X-ray after 9 days (Troja et al. Reference Troja2017), and finally radio at 15 days after the event (Hallinan et al. Reference Hallinan2017). Had the radio been detected first, say as an orphan afterglow, triggers at other wavelengths would most likely have been too late to detect the event itself, or the subsequent time evolution of the emission.

For more short-lived phenomena, such as flares or bursts from radio stars, triggering from radio is also problematic, as it is rare that the burst is detected in real time, due to the data processing times. Fender et al. (Reference Fender, Anderson, Osten, Staley, Rumsey, Grainge and Saunders2015b ) demonstrated that rapid triggering (in this case the Arcminute Microkelvin Imager Large Array (AMI-LA), operating at 15 GHz, responding to a Swift burst) can been successful in detecting stellar flares, but these examples are relatively uncommon. An ideal survey for detecting these phenomena would have simultaneous, or contemporaneous, multi-wavelength monitoring.

There have been a number of successful coordinated monitoring programs. For example, Osten et al. (Reference Osten2004) reports on a 4-year monitoring campaign of RS CVn system V711 Tau, spanning radio, ultraviolet, extreme ultraviolet, and X-ray; and MacGregor et al. (Reference MacGregor2021) reported an extreme flaring event on Proxima Centauri, detected during a joint monitoring campaign with radio, millimetre and optical telescopes. Of course several challenges of this approach are the resources required, and the difficulty of coordinating time availability on competitive-access telescopes. The ideal for future large scale projects would be dedicated facilities for conducting shadowing observations in other wavebands. A demonstrator of this approach is the MeerLICHT telescope (Bloemen et al. Reference Bloemen, Hall, Gilmozzi and Marshall2016) that was built to shadow MeerKAT observations, hence providing optical lightcurves once a radio transient is identified (e.g. Andersson et al. Reference Andersson2022).

4.3.1. Targeted monitoring of stars and radio galaxies

Early radio observations were not expected to be sensitive enough to detect radio stars (and here we mean actual stars), on the assumption that the stars were similar in brightness to our own Sun (Lovell Reference Lovell1964). However, the discovery that flare stars (for which UV Ceti is the prototype) had flares several orders of magnitude greater than the Sun in optical (Luyten Reference Luyten1949) saw renewed attempts to detect stellar radio emission. These attempts faced two main challenges: firstly the sensitivity of the telescopes, and secondly the difficulty of distinguishing flares from radio frequency interference (see, for example, the discussion of stellar flare rates by Lynch et al. Reference Lynch, Lenc, Kaplan, Murphy and Anderson2017).

To unambiguously determine that observed flares were associated with a given star, combined optical and radio monitoring programs were carried out, resulting in simultaneous optical and radio flares detected on several stars including UV Ceti and V371 Ori (Slee, Solomon, & Patston Reference Slee, Solomon and Patston1963; Lovell et al. Reference Lovell, Whipple and Solomon1963). Calculations from these observations implied a non-thermal emission mechanism, but the nature of this emission mechanism was not determined until much later. See Hjellming & Wade (Reference Hjellming and Wade1971) for a contemporaneous review of early radio star discoveries, and Dulk (Reference Dulk1985) for a review of stellar emission mechanisms.

The first quasar to be discovered and confirmed as extragalactic (quasar 3C 273; Schmidt Reference Schmidt1963) was also one of the first extragalactic radio sources to have its variability characterised through monitoring (Dent Reference Dent1965). Over the next decade a number of teams conducted long-term repeated observations of radio galaxies and quasars from low to high radio frequencies (e.g. Pauliny-Toth & Kellermann Reference Pauliny-Toth and Kellermann1966; Hunstead Reference Hunstead1972; Schilizzi et al. Reference Schilizzi, Cohen, Romney, Shaffer, Kellermann, Swenson, Yen and Rinehart1975)

The 1960s also saw the discovery of, and further searches for, interplanetary scintillation (e.g. Hewish et al. Reference Hewish, Scott and Wills1964; Cohen et al. Reference Cohen, Gundermann, Hardebeck, Harris, Salpeter and Sharp1966), which ultimately led to the discovery of pulsars (Hewish et al. Reference Hewish, Bell, Pilkington, Scott and Collins1968). It was recognised from the start that IPS was a tool for measuring the angular size of extragalactic objects (e.g. Cohen et al. Reference Cohen, Gundermann, Hardebeck and Sharp1967).

In the 1980s, monitoring of extragalactic radio sources continued, including on shorter timescales (e.g. Heeschen et al. Reference Heeschen, Krichbaum, Schalinski and Witzel1987) and lower frequencies (e.g. Slee & Siegman Reference Slee and Siegman1988). By the end of the decade it was a well established that a majority of the observed variability could be explained by interstellar scintillation (e.g. Blandford, Narayan, & Romani Reference Blandford, Narayan and Romani1986; Rickett Reference Rickett1990). In other words, it was a propagation effect extrinsic to the source itself (Section 2.5.1).

Later work identified annual cycles in the observed variability due to interstellar scintillation (e.g. Jauncey & Macquart Reference Jauncey and Macquart2001) caused by the relative velocity of the scintillation pattern as the Earth orbits the Sun. Eventually large surveys of compact extragalactic sources were conducted, most notably the Microarcsecond Scintillation-Induced Variability (MASIV; Lovell et al. Reference Lovell, Jauncey, Bignall, Kedziora-Chudczer, Macquart, Rickett and Tzioumis2003; Lovell et al. Reference Lovell2008) survey. However, all of this work still involved targeted observations of individual objects.

4.3.2. The first imaging surveys for radio variability

The advent of synthesis imaging meant it was possible to conduct untargeted surveys for variability, observing a (relatively) large sample of sources, with better flux stability and source localisation than what had previously been available.

The first radio transient detected in a synthesis image was the X-ray binary Cygnus X-3, which was found in a Westerbork search for radio counterparts to X-ray sources (Braes & Miley Reference Braes and Miley1972) and which led to numerous followup studies (e.g. Hjellming, Hermann, & Webster Reference Hjellming, Hermann and Webster1972; Hjellming & Balick Reference Hjellming and Balick1972; Gregory et al. Reference Gregory, Kronberg, Seaquist, Hughes, Woodsworth, Viner and Retallack1972; Seaquist et al. Reference Seaquist, Gregory, Perley, Becker, Carlson, Kundu, Bignell and Dickel1974; Molnar, Reid, & Grindlay Reference Molnar, Reid and Grindlay1984). About a decade later, in the 1980s, the first larger scale searches for radio transients and variability commenced.

At low frequencies, McGilchrist & Riley (Reference McGilchrist and Riley1990), followed by Riley (Reference Riley1993) and Minns & Riley (Reference Minns and Riley2000) conducted a $\sim$ 600 deg $^2$ survey over 10 yr, at 151 MHz, with the Cambridge Low Frequency Synthesis Telescope. Riley & Green (Reference Riley and Green1995, Reference Riley and Green1998) conducted a 100 deg $^2$ survey at 408 MHz with the Dominion Radio Astrophysical Observatory Synthesis Telescope. In both cases, the sampling was roughly yearly, and these projects found that only a very small percentage of radio sources ( $\lt$ 1–2%) were highly variable at low frequencies, although that percentage was much higher for steep spectrum sources.

The conclusions of these surveys were that most radio sources were not highly variable, and that most observed variability was consistent with scintillation. However, it is important to note that the sensitivity and limited time sampling meant that most timescales were not well explored.

Table 3. Specifications of past large scale single-epoch radio continuum surveys, in order of observing frequency.

$^\mathrm{a}$ The resolution depends on the declination as $\csc |\delta|$ .

$^\mathrm{b}$ There was an earlier epoch of MGPS (Green et al. Reference Green, Cram, Large and Ye1999). However, only images were released, not a source catalogue.

$^\mathrm{c}$ At 154 MHz.

$^\mathrm{d}$ At 154 MHz, roughly.

$^\mathrm{e}$ For the combined 170–231 MHz image.

4.3.3. Widefield few-epoch searches

The possibility of detecting orphan afterglows from gamma-ray bursts motivated the next phase of radio transient searches, including both dedicated surveys and uses of archival data. Rather than focusing on characterising variability, as the previous imaging surveys had done, this wave of surveys had the stated aim of finding explosive ‘transient’ objects. Here (and in Section 4.3.4), astronomers made use of existing single-epoch large-scale surveys. The properties of some of the key large-scale continuum surveys are summarised in Table 3. By comparing sources between individual surveys, multi-epoch transient searches could be done.

The first of these was Levinson et al. (Reference Levinson, Ofek, Waxman and Gal-Yam2002), who used two of the primary radio continuum reference surveys, Faint Images of the Radio Sky at Twenty centimeters (FIRST; Becker, White, & Helfand Reference Becker, White and Helfand1995; White et al. Reference White, Becker, Helfand and Gregg1997) and the NRAO VLA Sky Survey (NVSS; Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998), to search for isolated compact sources (with a flux density limit of 6 mJy beam $^{-1}$ at 1.4 GHz) that were present in one catalogue but not detected in the other. They found nine candidate afterglows, and identified that the most likely confusing source types were radio-loud AGN and radio supernovae. Subsequent radio and optical follow-up of these candidates by Gal-Yam et al. (Reference Gal-Yam2006) found that five were not true variables, one was an AGN and one a known pulsar. One of the objects was likely to be a radio supernova, and the other remained unidentified, but the authors concluded it was unlikely to be a GRB afterglow. The analysis presented in this pair of papers provided a foundation for radio transient searches for the next decade.

Several 2–3 epoch VLA surveys followed, each exploring different timescales and sensitivities. Carilli et al. (Reference Carilli, Ivison and Frail2003) explored timescales of 19 days and 17 months, at submillijansky sensitivities in the Lockman Hole region. de Vries et al. (Reference de Vries, Becker, White and Helfand2004) used a repeat observation of the FIRST Southern Galactic Cap zero-declination strip region to explore timescales of 7 yr at millijansky sensitivities. Neither survey found any transients (objects that had appeared or disappeared between the epochs) and the authors set limits on the expected transient rate, as well as calculating the percentage of highly variable objects.

In the following decade, Croft et al. (Reference Croft2010) used the Allen Telescope Array Twenty-Centimetre Survey (ATATS) to do a two-epoch comparison with NVSS. They took the combined catalogue of 12 epochs of ATATS and compared to the NVSS, observed 15 yr earlier. At the same time, Bower et al. (Reference Bower2010) conducted a similar analysis with the ATA Pi GHz Sky Survey (PiGSS) with a smaller sky area but better sensitivity. Neither survey found any radio transients, and both put limits on the number of transients and variables expected in an all-sky survey.

Most surveys in future years were much better sampled than these. However, there were a few more widefield few-epoch surveys, such as Heywood et al. (Reference Heywood2016) and Murphy et al. (Reference Murphy2017). Both of these found one candidate transient or highly variable object, but did not have enough information to identify the likely source class.

These few-epoch transient surveys provided a good starting point for initial characterisation of the dynamic radio sky. However, it was evident that to do useful science, it would be necessary to have more observation epochs, better sensitivity, and timely analysis to enable follow-up.

4.3.4. Exploring archival data and surveys

To get more information about the dynamic radio sky before future surveys became available, researchers delved deeper into archival datasets in order to exploit repeated observations that had been done for other purposes, for example calibration. The first example of this was by Bower et al. (Reference Bower, Saul, Bloom, Bolatto, Filippenko, Foley and Perley2007) who searched 5 and 8.4 GHz observations from the VLA data archives. The dataset consisted of 944 epochs of the same calibrator field, taken over 22 yr. They found 10 transients, which had no optical counterparts (Ofek et al. Reference Ofek, Breslauer, Gal-Yam, Frail, Kasliwal, Kulkarni and Waxman2010), and were not able to be identified. Later re-analysis by Frail et al. (Reference Frail, Kulkarni, Ofek, Bower and Nakar2012) showed that most of these were likely to be imaging and calibration artefacts, but at the time the results motivated the exploration of a number of other archival searches.

Bower & Saul (Reference Bower and Saul2011) built on this work to conduct a search using 1.4 GHz observations of the same calibrator field (3C 286). Using more stringent criteria, they found no transient candidates, and calculated limits on the expected all-sky rate. Bell et al. (Reference Bell2011) further expanded on the work, using an automatic pipeline developed for the LOFAR transients project (Fender et al. Reference Fender, Wijers and Stappers2008). They analysed 5 037 observations of seven calibrator fields, primarily at 5 and 8.4 GHz. They also found no transient sources on timescales of 4–45 days, and reported new limits on the all-sky rate.

Bannister et al. (Reference Bannister, Murphy, Gaensler, Hunstead and Chatterjee2011) conducted an analysis of the Molonglo Observatory Synthesis Telescope (MOST; Bock et al. Reference Bock, Large and Sadler1999) archive, consisting of 22 yr of observations at 843 MHz. Although most of the fields were only observed once as part of the Sydney University Molonglo Sky Survey (SUMSS; Mauch et al. Reference Mauch, Murphy, Buttery, Curran, Hunstead, Piestrzynski, Robertson and Sadler2003) and Molonglo Galactic Plane Surveys (Green et al. Reference Green, Cram, Large and Ye1999; Murphy et al. Reference Murphy, Mauch, Green, Hunstead, Piestrzynska, Kels and Sztajer2007), about 30% of the fields were observed multiple times for calibration, data quality, or monitoring of specific objects. This search found 15 transients, some of which were identified with known objects (e.g. Nova Muscae 1991) and some of which remained unknown.

Thyagarajan et al. (Reference Thyagarajan, Helfand, White and Becker2011) conducted a similar analysis of repeated observations from the FIRST survey. Each field was observed 2–7 times, and a large number of variable sources (but no transients) were identified. These projects demonstrated the challenges of working with an extremely inhomogeneous dataset in terms of time sampling, and the challenge of doing meaningful follow-up and analysis of transients that occurred many years before discovery. To make substantial progress, continuum surveys designed specifically for time domain science were required.

4.3.5. Multi-epoch radio transient surveys (2010s)

The 2010s saw the emergence of designed-for-purpose multi-epoch radio transient surveys. Some of the first of these were conducted with the Allen Telescope Array (ATA; DeBoer Reference DeBoer2006), an instrument designed for SETI searches. Croft et al. (Reference Croft, Bower, Keating, Law, Whysong, Williams and Wright2011) published results from a 12-epoch, 690 deg $^2$ survey (ATATS) at 1.4 GHz. Bower & Saul (Reference Bower and Saul2011) and Croft et al. (Reference Croft, Bower and Whysong2013) presented results from the PiGSS survey at 3 GHz. Neither of these surveys detected any transients (which they defined as varying by a factor of $\gt10$ ). However, they set more stringent limits on transient rates. Unfortunately, due to funding changes, radio imaging surveys did not continue after these initial results, and the full potential of the array as a transient machine was not realised.

There were also a set of relatively small area (0.02–60 deg $^2$ ) multi-epoch surveys conducted with the VLA (e.g. Ofek et al. Reference Ofek, Frail, Breslauer, Kulkarni, Chandra, Gal-Yam, Kasliwal and Gehrels2011; Hodge et al. Reference Hodge, Becker, White and Richards2013; Mooley et al. Reference Mooley, Frail, Ofek, Miller, Kulkarni and Horesh2013; Alexander, Soderberg, & Chomiuk Reference Alexander, Soderberg and Chomiuk2015) and the ATCA (e.g. Bell et al. Reference Bell, Huynh, Hancock, Murphy, Gaensler, Burlon, Trott and Bannister2015; Hancock et al. Reference Hancock, Drury, Bell, Murphy and Gaensler2016). Only one of these, Ofek et al. (Reference Ofek, Frail, Breslauer, Kulkarni, Chandra, Gal-Yam, Kasliwal and Gehrels2011), detected a transient object, which, although not unambiguously identified, they state is consistent with being from a neutron star merger. These more sensitive surveys, with multiple epochs, were able to be used to start characterising the variability of the radio source population beyond a single numerical metric, for example looking at how variability changed with flux density, timescale and Galactic latitude. Radcliffe et al. (Reference Radcliffe, Beswick, Thomson, Garrett, Barthel and Muxlow2019) was notable for exploring the variability of radio sources at $\mu$ Jy sensitivities (and finding the rates comparable to those at mJy sensitivities).

The re-evaluation of the Bower et al. (Reference Bower, Saul, Bloom, Bolatto, Filippenko, Foley and Perley2007) transient results and the subsequent reduction of the derived rates by Frail et al. (Reference Frail, Kulkarni, Ofek, Bower and Nakar2012), motivated Aoki et al. (Reference Aoki2014) to revisit the rates that had been reported from the 1.4 GHz Nasu Sky Survey. Although not strictly an imaging survey (transients were detected directly in drift scan fringe data), 11 extreme transients had been reported over a number of years (see Kuniyoshi et al. Reference Kuniyoshi2007; Niinuma et al. Reference Niinuma2007; Matsumura et al. Reference Matsumura2009, and others). The derived transient rate was inconsistent with other rates reported at the time. However, in the re-analysis, only a single transient passed the more rigorous thresholds applied by Aoki et al. (Reference Aoki2014), giving a rate more consistent with other projects.

The first results from the Australia SKA Pathfinder Boolardy Engineering Test Array (ASKAP-BETA; Hotan et al. Reference Hotan2014) came in 2016, with Heywood et al. (Reference Heywood2016) and Hobbs et al. (Reference Hobbs2016) publishing transient surveys covering timescales of days and minutes to hours, respectively. These surveys used the 6-dish ASKAP test array, operating at $\sim 1$ GHz. This work was followed by Bhandari et al. (Reference Bhandari2018) who conducted a pilot survey at 1.4 GHz using a 12-dish array, in the Early Science phase of ASKAP operations. None of these surveys detected any transient sources, but provided the first demonstration of ASKAP’s capabilities for transient science. In particular, the prospect of imaging of long integration observations on short timescales (Hobbs et al. Reference Hobbs2016).

A big step forward came with the Caltech-NRAO Stripe 82 Survey (CNSS; Mooley et al. Reference Mooley2016), a multi-year, sensitive (rms $\sim 40\,\mu$ Jy beam $^{-1}$ ) survey of the 270 deg $^2$ Stripe 82 region. The survey was conducted with the VLA at 3 GHz, and the Stripe 82 region was chosen for its existing multi-wavelength coverage, to improve the chances of identifying transients. By many measures this could be considered the most successful radio transient imaging survey to date, at that time. In addition to characterising the variability of the 3 GHz source population, the initial pilot survey over $50\,\mathrm{deg}^2$ detected two transients serendipitously, which were both identified – as an RS CVn binary and a dKe star. Further studies discovered a tidal disruption event (Anderson et al. Reference Anderson2020) and identified state changes in AGN (Kunert-Bajraszewska et al. Reference Kunert-Bajraszewska, Mooley, Kharb and Hallinan2020; Wołowska et al. 2021).

Another novel aspect of CNSS was a contemporaneous optical survey carried out with the Palomar Transient Factory (Law et al. Reference Law2009). This allowed a comparison of the dynamic sky in optical and radio wavebands; the main finding being that they are quite distinct, something that needs to be considered in planning for complementarity with, for example, the SKAO and Rubin Observatory (Ivezić et al. 2019) transient surveys.

4.3.6. Multi-epoch radio transient surveys (2020s)

By the start of the 2020s, roughly 50 untargeted radio transient imaging surveys had been conducted using both dedicated observations and commensal data obtained for other purposes, and yet only a handful of radio transients had been discovered via those surveys, most of which had not been conclusively classified. The main reasons for this were (i) the lack of surveys that were able to optimise the metrics presented in Equations (4) and (5) – all were limited in either sensitivity, sky coverage, or time sampling; and (ii) processing limitations meant that in many cases candidates were identified long after the event, limiting the potential for multi-wavelength follow-up.

The promise of large scale, well-sampled radio transient imaging surveys was finally (partially) realised, with the arrival of three SKAO pathfinder telescopes: ASKAP, MeerKAT and LOFAR, along with the VLA and MWA. The specifications for the major transient surveys on these telescopes are given in Section 4.4. In this section we will summarise some of the key results that have been published to date.

On ASKAP, the dedicated Variables and Slow Transients survey (VAST; Murphy et al. Reference Murphy2013, see Section 4.4.3) has both a Galactic and extragalactic component. The pilot survey, conducted at 888 MHz (Murphy et al. Reference Murphy2021), consisted of 12 min observations (with typical sensitivity of 0.24 mJy beam $^{-1}$ ), repeated with cadences of 1 day to 8 months. This survey detected 28 highly variable and transient sources including: known pulsars, new radio stars, sources associated with AGN and galaxies, and some sources yet to be identified. A pilot survey search of the Galactic Centre by Wang et al. (Reference Wang2022a ) resulted in the detection of a new GCRT (see Section 3.9).

Dobie et al. (Reference Dobie2019, Reference Dobie2022) conducted 10 observations of a single ASKAP field (30 deg $^2$ ) which covered 87% of the localisation area of the gravitational event GW190814 localisation area. They reported a single synchrotron transient, which was not associated with the neutron star-black hole merger. Further multi-wavelength observations were conducted, but are so far inconclusive (D. Dobie, private communication). Reprocessing of a subset of this data on 15-min timescales resulted in the discovery of 6 rapid scintillators in a linear arrangement on the sky (Wang et al. Reference Wang, Tuntsov, Murphy, Lenc, Walker, Bannister, Kaplan and Mahony2021a ). These were used to constrain the physical properties of a degrees-long plasma filament in our own Galaxy.

Wang et al. (Reference Wang2023) extended this short-timescale (15 min) imaging approach to 505 h of data from several ASKAP pilot surveys, with typical frequency $\sim 1$ GHz. Their search found 38 variable and transient sources, which is enough to start characterising the fraction of different source types on these timescales. They found 22 AGN or galaxies, 8 stars, 7 (known) pulsars and one unknown source, somewhat similar to the population found by Murphy et al. (Reference Murphy2021).

On MeerKAT there have also been several surveys that sample a range of timescales, often resulting from data focused on monitoring other sources (e.g. Driessen et al. Reference Driessen2020, Reference Driessen, Williams, McDonald, Stappers, Buckley, Fender and Woudt2022a ; Andersson et al. Reference Andersson2022). Rowlinson et al. (Reference Rowlinson2022) searched data from a monitoring campaign of MAXI J1820+070. There were 64 weekly observations with a typical integration time of 15 min and typical sensitivity of 1 mJy beam $^{-1}$ . This resulted in 4 AGN, a pulsar and one unidentified object. Driessen et al. (Reference Driessen2022b ) searched data from weekly observations of GX 339 $-$ 4 and identified 21 variable sources, most of which have low-level variability consistent with refractive scintillation from AGN. On shorter timescales, Fijma et al. (Reference Fijma2024) re-imaged 5.45 h of MeerKAT data, centred on NGC 5068, on timescales of 8 s, 128 s, and 1 hr, but did not find any transients.

On the VLA, the CHILES Variable and Explosive Radio Dynamic Evolution Survey (Sarbadhicary et al. Reference Sarbadhicary2021) was designed to study radio variability in the extragalactic COSMOS deep field. It had 960 h of 1–2 GHz data, observed over 209 epochs, with typical sensitivity of $\sim10\,\mu$ Jy beam $^{-1}$ . They found 18 moderately variable sources, all of which were identified as AGN or galaxies.

The VLA Sky Survey (VLASS; Lacy et al. Reference Lacy2020) is underway and producing results (see Section 4.4.5) but no general transient survey paper has been published yet. At low frequencies, the MWA Galactic Plane Monitor and LOFAR transient surveys are discussed in Sections 4.4.2 and 4.4.1.

We have now reached a regime where radio transient imaging surveys are detecting significant numbers of transient and highly variable objects. Equally importantly, they have sufficient time sampling and resolution, along with multi-wavelength information, to allow the class of most of the objects to be identified. We discuss these populations further in Section 6.2.

4.3.7. Low frequency surveys

In the decades leading up to the mid-2010s, a majority of radio transient imaging surveys were conducted at gigahertz frequencies, predominantly with the VLA. There were a small number of exceptions, for example Lazio et al. (Reference Lazio2010) conducted a survey at 73.8 MHz with the Long Wavelength Demonstrator Array (LWDA), finding no transients above 500 Jy, and Jaeger et al. (Reference Jaeger, Hyman, Kassim and Lazio2012), who found one (unidentified) transient source in a search of 6 archival VLA fields observed at 325 MHz.

However, the advent of three new wide-field, low-frequency telescopes – the Long Wavelength Array (LWA1; Ellingson et al. Reference Ellingson2013), the Murchison Widefield Array (MWA; Tingay et al. Reference Tingay2013) and the Low Frequency Array (LOFAR; van Haarlem et al. Reference van Haarlem2013) – opened up the possibility of more fully characterising the time domain radio sky at $\lt 300$ MHz.

The LWA1 enabled very widefield surveys at low frequencies (10–88 MHz), but with relatively poor sensitivity (10s–100s of Jy). Surveys by Obenberger et al. (Reference Obenberger2014, Reference Obenberger2015) detected fireballs from meteors, but no transients originating outside the Solar System.

The next set of results were from early surveys with the MWA and LOFAR. Bell et al. (Reference Bell2014) conducted a survey on timescales of 26 min and 1 yr with MWA at 154 MHz. They found no transients above 5.5 Jy. Carbone et al. (Reference Carbone2016) reported on a LOFAR survey of 4 fields, observed on cadences between 15 min and several months. The frequency of the observations were between 115 and 190 MHz. They found no transients above 0.3 Jy. Stewart et al. (Reference Stewart2016) reported results from a 4 month monitoring campaign of the Northern Galactic Cap as part of the Multifrequency Snapshot Sky Survey. The survey consisted of 2149 11-min snapshots, each covering 175 deg $^2$ . They reported the discovery of one transient source, with no optical or high-energy counterpart. Despite an extensive investigation, the source class was not identified, and future attempts to discover more sources from this hypothetical population were unsuccessful (e.g. Huang et al. Reference Huang, Anderson, Hallinan, Lazio, Joseph, Price and Sharma2022).

The Stewart et al. (Reference Stewart2016) transient increased the motivation for low frequency transient surveys. However, the next set of surveys yielded no new candidates. These included: Rowlinson et al. (Reference Rowlinson2016), Feng et al. (Reference Feng2017), Tingay & Hancock (Reference Tingay and Hancock2019), Kemp et al. (Reference Kemp, Tingay, Midgley and Mitchell2024) all with the MWA at 150–190 MHz; Polisensky et al. (Reference Polisensky2016) with the Jansky Very Large Array Low-band Ionosphere and Transient Experiment (VLITE) survey at 340 MHz; Anderson et al. (Reference Anderson2019) taking advantage of the wide field of view of the Owens Valley Radio Observatory Long Wavelength Array (OVRO-LWA) at $\lt$ 100 MHz and Hajela et al. (Reference Hajela, Mooley, Intema and Frail2019a ) with the GMRT at 150 MHz. Even with improved sensitivity, a significant population of low frequency transients remained elusive.

The lack of radio transients at low frequencies is partly expected from predictions of synchrotron transient rates (e.g. Metzger et al. Reference Metzger, Williams and Berger2015b ). As emission from, for example, GRBs evolves, the brightness decreases as the spectral peak moves to lower frequencies and the evolution slows, meaning they are less likely to be detectable given the sensitivity of low frequency telescopes (Ghirlanda et al. Reference Ghirlanda2014). Recently there has been a shift in focus towards searching for shorter timescale Galactic transients: these often have coherent emission mechanisms, leading to much faster variability. For example, de Ruiter et al. (Reference de Ruiter, Meyers, Rowlinson, Shimwell, Ruhe and Wijers2024) present an analysis of the LOFAR Two-metre Sky Survey (LoTSS; Shimwell et al. Reference Shimwell2017) on 8-s timescales, which resulted in the detection of a new magnetic white dwarf M-dwarf binary system (de Ruiter et al. Reference de Ruiter2025). See Sections 4.4.2 and 4.4.1 for work currently underway at low frequencies.

4.3.8. High frequency surveys

All of the surveys discussed so far have been conducted at or below frequencies of a few gigahertz. At higher radio frequencies (and in the millimetre regime), telescope fields of view are much smaller. For example, the field of view of the Australia Telescope Compact Array is $\sim2$ arcmin at 20 GHz, and the field of view of the Atacama Large Millimeter Array (ALMA; Wootten & Thompson Reference Wootten and Thompson2009) is $\sim19^{\prime\prime}$ at 300 GHz. As a result, there are very few large scale continuum surveys at frequencies $\gt10$ GHz. Two examples are the 9C survey (Waldram et al. Reference Waldram, Pooley, Grainge, Jones, Saunders, Scott and Taylor2003) covering 520 deg $^2$ at 15 GHz and the AT20G survey (Murphy et al. Reference Murphy2010) covering 20 626 deg $^2$ at 20 GHz. Two conclusions from these projects were that (i) the overall properties of the source population at high frequencies can not be extrapolated from the $\sim1$ GHz population; (ii) the high frequency radio sky has a comparable level of variability to gigahertz frequencies: ( $\sim 5\%$ of bright sources were variable on 1–2 yr timescales; Sadler et al. Reference Sadler2006).

The challenges of conducting large-scale high frequency radio surveys means that there have been a limited number of studies of high frequency radio variability. Bolton et al. (Reference Bolton, Chandler, Cotter, Pearson, Pooley, Readhead, Riley and Waldram2006) selected 51 sources from the 9C survey for further monitoring. The motivation for 9C was to identify foreground contaminants for cosmic microwave background (CMB) maps; and variability could impact the completeness of such a sample. Monitoring over 3 yr confirmed that about half of the steep spectrum objects (likely to be compact young radio galaxies), and none of the flat spectrum objects, were highly variable. There are various other high frequency monitoring programs in which sources have been selected from surveys (e.g. Franzen et al. Reference Franzen2009), however there have not been any untargeted multi-epoch imaging surveys, as such.

At even higher (millimetre) frequencies there have been a relatively small number of transient surveys using bolometric arrays on single-dish telescopes. Several of these are with the South Pole Telescope (SPT; Carlstrom et al. Reference Carlstrom2011). Whitehorn et al. (Reference Whitehorn2016) searched for transients in the SPT 100 Square Degree Survey at 95 and 150 GHz, finding a single transient consistent with an extragalactic synchrotron source. Guns et al. (Reference Guns2021) searched at 95, 150, and 220 GHz, resulting in the detection of 15 transient events including stellar flares and possible AGN activity. Other examples are Chen et al. (Reference Chen, Rachen, López-Caniego, Dickinson, Pearson, Fuhrmann, Krichbaum and Partridge2013) who searched for transients using the combined Wilkinson Microwave Anisotropy Probe and Planck epochs at 4 bands between 33 and 94 GHz; Naess et al. (Reference Naess2021), Li et al. (Reference Li2023) and Biermann et al. (Reference Biermann2025) using the Atacama Cosmology Telescope at 77–277 GHz.

We note that the majority of these surveys have been designed for cosmological purposes and hence have focused on high Galactic latitudes, where the transient targets are largely extragalactic synchrotron transients (although the actual discoveries often include Galactic stars). Therefore they have excluded low-latitude sources like X-ray binaries, which can show high levels of variability at millimetre frequencies associated with state transitions (e.g. Fender et al. Reference Fender, Pooley, Durouchoux, Tilanus and Brocksopp2000; Russell et al. Reference Russell2020). Future low-latitude surveys will doubtless identify more Galactic sources.

We will not discuss millimetre transient surveys further in this review. An analysis of the expected populations of extragalactic transients detectable in future CMB surveys (including long and short GRBs, tidal disruption events and fast blue optical transients) is given by Eftekhari et al. (Reference Eftekhari2022).

4.3.9. Galactic Centre and Galactic plane surveys

Parallel to the efforts to characterise variability in the extragalactic radio sky, there were a number of surveys of the Galactic Centre, Galactic bulge and the Galactic plane more generally. These surveys were motivated by the dense stellar and compact object environment in the plane (and centre) of our Galaxy, making it a likely rich source of transient events (e.g. Muno et al. Reference Muno2003; Morris & Serabyn Reference Morris and Serabyn1996; Calore et al. Reference Calore, Di Mauro, Donato, Hessels and Weniger2016). However, radio imaging of Galactic regions comes with additional challenges, including (a) producing high quality images in regions of significant diffuse emission; and (b) identifying multi-wavelength counterparts when the optical and infrared source density is high, and there is substantial extinction.

One of the first Galactic surveys was a 5-yr monitoring program of the northern Galactic plane, conducted between 1977 and 1981 with the NRAO 91m transit telescope, operating at 6 GHz (Gregory & Taylor Reference Gregory and Taylor1981, Reference Gregory and Taylor1986). This survey explored timescales from days to $\sim1$ yr. A key motivation was to find more sources like the high mass X-ray binary Cyg X-3, which had recently been discovered to have large radio outbursts (Gregory et al. Reference Gregory, Kronberg, Seaquist, Hughes, Woodsworth, Viner and Retallack1972). About 5% of the 1 274 sources monitored showed significant variability on either short or long timescales. The authors were not able to identify any of these objects, but determined that most were likely to be extragalactic.

The next major long-term Galactic centre monitoring program was conducted by Hyman et al. (Reference Hyman, Lazio, Kassim and Bartleson2002). This project used archival and new widefield images of the Galactic centre taken with the VLA at 0.33 GHz, with targeted follow-up of objects of interest at 1.4 and 4.8 GHz. They introduced the nomenclature Galactic Centre Radio Transient (GCRT) to describe these sources, as their nature was unknown. Subsequent work by Hyman et al. (Reference Hyman, Lazio, Kassim, Ray, Markwardt and Yusef-Zadeh2005, Reference Hyman, Lazio, Roy, Ray and Kassim2006, Reference Hyman, Roy, Pal, Lazio, Ray, Kassim and Bhatnagar2007, Reference Hyman, Wijnands, Lazio, Pal, Starling, Kassim and Ray2009) resulted in the discovery of three GCRTs. These sources shared some common properties (highly variable, steep spectrum, circularly polarised) but their identity has remained elusive (see Section 3.9).

The challenges presented by imaging near the Galactic region, and difficulty of identifying potential transients has limited the number of surveys with a Galactic focus. Becker et al. (Reference Becker, Helfand, White and Proctor2010) searched for transients in three epochs of the Multi-Array Galactic Plane Imaging Survey, a collection of VLA observations conducted at 4.8 GHz. The observations spanned 15 yr, with a sky area of $23.2$ deg $^2$ . They found no transients, and a number of highly variable sources (at a higher source density than found by extragalactic surveys at that time). However, they were not able to conclusively identify their object class.

Williams et al. (Reference Williams, Bower, Croft, Keating, Law and Wright2013) conducted a two-year survey with the Allen Telescope Array at 3 GHz, with weekly visits to 23 deg $^2$ in two fields in the Galactic plane. This was a substantial improvement on previous surveys, but did not detect any transient sources, pointing to lower frequencies potentially being more productive for Galactic transient discovery. The capabilities of SKAO pathfinder and precursor telescopes has seen a renewed interest in transient surveys of the Galactic centre and Galactic bulge (e.g. Hyman et al. Reference Hyman2021; Wang et al. Reference Wang2022a ; Frail et al. Reference Frail2024) as well as the re-exploration of archival data (e.g. Chiti et al. Reference Chiti, Chatterjee, Wharton, Cordes, Lazio, Kaplan, Bower and Croft2016). Some of the large-scale Galactic plane surveys currently underway are outlined in Section 4.4.

4.3.10. Circular polarisation surveys

A vast majority of radio sources are driven by synchrotron emission and so do not show significant levels of circular polarisation (Saikia & Salter Reference Saikia and Salter1988). For example, AGN, by far the most populous objects in the radio sky, are typically $\lt0.1\%$ circularly polarised (e.g. Rayner, Norris, & Sault Reference Rayner, Norris and Sault2000). However, some highly variable radio source classes do have significant fractions of circularly polarised emission, including pulsars (Section 3.8), radio stars (Section 3.5), and unusual transients like GCRTs and LPTs (Section 3.9).

Circular polarisation surveys provide an alternative way of discovering and identifying these objects. Historically, most large radio surveys have only produced total intensity (Stokes I) data products (see Table 3). For example the Westerbork Northern Sky Survey (Rengelink et al. Reference Rengelink, Tang, de Bruyn, Miley, Bremer, Roettgering and Bremer1997), SUMSS (Mauch et al. Reference Mauch, Murphy, Buttery, Curran, Hunstead, Piestrzynski, Robertson and Sadler2003) and the GMRT 150 MHz All-sky Radio Survey First Alternative Data Release (Intema et al. Reference Intema, Jagannathan, Mooley and Frail2017). The NRAO VLA Sky Survey (Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998) produced linear polarisation products (Stokes Q and U) but did not produce circular polarisation products.

When circular polarisation is available, it provides a method for easily identifying many interesting objects (e.g. Kaplan et al. Reference Kaplan2019; Wang et al. Reference Wang2021b , Reference Wang2022b ) while filtering out the non-variable sources. In the cases where sensitivity in Stokes I is limited by confusion, Stokes V can also often have better sensitivity. Finally, unlike linear polarisation no correction for Faraday rotation (Burn Reference Burn1966) is needed, which eliminates the need for multiple frequency channels and hence provides better sensitivity (cf. Brentjens & de Bruyn Reference Brentjens and de Bruyn2005) and easier processing.

The first all-sky circular polarisation survey was conducted using the MWA at 200 MHz (Lenc et al. Reference Lenc, Murphy, Lynch, Kaplan and Zhang2018). An untargeted search of this data resulted in detections of Jupiter, some known pulsars, several artificial satellites, and the tentative detection of two known flare stars. Several large survey telescopes now produce circular polarisation products by default, enabling searches for new objects via their circularly polarised emission. For example, Pritchard et al. (Reference Pritchard2021) detected 33 radio stars in the ASKAP RACS survey at 888 MHz; and Callingham et al. (Reference Callingham2023) produced a catalogue of 68 circularly polarised sources from V-LoTSS (the circularly polarised LOFAR Two-metre Sky Survey). These sources consisted of radio stars, pulsars, and several that remain unidentified. This is an area that the SKAO pathfinder and precursor surveys are opening up for discovery.

4.4.1. The LOFAR two-metre sky survey

The LOFAR Two-metre Sky Survey (LoTSS; Shimwell et al. Reference Shimwell2017) is a 150 MHz survey of the sky north of $\delta=0^\circ$ . Each LoTSS image is an 8-h observation, resulting in a typical sensitivity of $83\,\mu$ Jy beam $^{-1}$ and a resolution of $6^{\prime\prime}$ , with full Stokes parameters. The most recent data release covers 27% of the sky (Shimwell et al. Reference Shimwell2022), with an upcoming data release expected to cover 70% of the sky.Footnote ^l

Although LoTSS is essentially a single-epoch continuum survey, we have included it here because there is a substantial short-time scale imaging project underway that will search for transients on timescales of 8 s, 2 min and 1 h (de Ruiter et al. Reference de Ruiter, Meyers, Rowlinson, Shimwell, Ruhe and Wijers2024). The discovery of a white dwarf binary system from this survey was reported by de Ruiter et al. (Reference de Ruiter2025).

In addition, there are other LOFAR surveys underway that will be useful for transient searches, for example the LoTSS Deep Fields which consist of hundreds of hours of repeated observations of three fields (ELIAS-N1, Boötes and the Lockman Hole), with observing blocks scheduled months to years apart (Best et al. Reference Best2023; Shimwell et al. Reference Shimwell2025), with eventual sensitivities of $\approx 10\,\mu$ Jy beam $^{-1}$ .

4.4.2. The MWA Galactic Plane Monitor

The MWA Galactic Plane Monitoring program (MWA GPM; project code G0080)Footnote ^m is a transient survey being conducted at 185–215 MHz. It covers the Galactic plane south of $\delta \lt +15^\circ$ with $|b|\lt15^\circ$ , with longitude coverage changing through the year and 30 min integrations on a bi-weekly cadence. It has a resolution of $45^{\prime\prime}$ and a typical sensitivity of 10 mJy beam $^{-1}$ on 5 min timescales (Hurley-Walker, private communication).

The main scientific goal of the survey is to discover long-period transients. The survey parameters are briefly described in the Methods section of Hurley-Walker et al. (Reference Hurley-Walker2023), which reports the discovery of GPM J1839 $-$ 10, a new long period transient, and will be fully described in a paper in preparation.

4.4.3. The ASKAP VAST survey

The ASKAP Variables and Slow Transients survey (VAST; Murphy et al. Reference Murphy2013, Reference Murphy2021) is one of nine key survey projects on the ASKAP telescope. The survey is being conducted at 887.5 MHz, and produces total intensity (Stokes I) and circular polarisation (Stokes V) data products. There are two components to the survey: an extragalactic component covering 10 954 square degrees, with typical sensitivity of $220\,\mu$ Jy beam $^{-1}$ , and a Galactic component covering 2 402 square degrees with a typical sensitivity of $250\,\mu$ Jy beam $^{-1}$ . Note that the Galactic survey also includes two fields that cover the Large and Small Magellanic Clouds. The extragalactic fields are sampled with a median cadence of 2 months, and the Galactic fields are sampled with a median cadence of 2 weeks.

The survey was designed to cover a wide range of science goals, and these goals have evolved over time since the original proposal (Murphy et al. Reference Murphy2013). Results from the VAST pilot survey, a 200 h test of the observing strategy, data quality and data processing approach have confirmed the survey is effective for a number of these goals. Two examples are the multi-epoch sampling of the radio star population (Pritchard et al. Reference Pritchard, Murphy, Heald, Wheatland, Kaplan, Lenc, O’Brien and Wang2024), and the discovery of unusual Galactic transients (e.g. Wang et al. Reference Wang2021b ).

4.4.4. The Rapid ASKAP Continuum Survey

The Rapid ASKAP Continuum Survey (RACS; McConnell et al. Reference McConnell2020) was designed to produce a reference image of the entire sky visible to ASKAP ( $\delta \lt +50^\circ$ ), that would help in calibration of all ASKAP surveys. The first epoch (RACS-low1) was conducted at 887.5 MHz, starting in April 2019, with a resolution of 15 $^{\prime\prime}$ and typical rms sensitivity of 250 $\mu$ Jy beam $^{-1}$ . There have been five subsequent epochs, two in the higher ASKAP bands: RACS-mid1 at 1 367.5 MHz starting December 2020 (Duchesne et al. Reference Duchesne2023, Reference Duchesne2024); and RACS-high1 at 1 665.5 MHz, starting in December 2021 (Duchesne et al. Reference Duchesne2025); and two repeats of RACS-low starting in March 2022 and December 2023. See Table 4 for the detailed specifications of these surveys.

The RACS data products include total intensity, linear and circular polarisation (Stokes I, Q, U, V). The repeated epochs were designed to allow exploration of the time variable sky. Early results have demonstrated the effectiveness for RACS for this. For example, in the detection of late-time radio counterparts for optically detected tidal disruption events (Anumarlapudi et al. Reference Anumarlapudi2024).

4.4.5. The Very Large Array Sky Survey

The VLA Sky Survey (VLASS; Lacy et al. Reference Lacy2020) is an all-sky survey conducted at 2–4 GHz, with 2.5 $^{\prime\prime}$ resolution. It covers the entire sky above $\delta \gt -40^\circ$ , with typical rms sensitivity of 120 $\mu$ Jy beam $^{-1}$ . It was designed to have a time domain component: one of the four science goals is ‘Hidden Explosions and Transient Events’. Hence the survey has three repeated epochs separated by $\sim32$ months, with a fourth epoch partially completed. The VLASS data products include total intensity and linear polarisation images (Stokes I, Q, U) but, at the time of writing, no public circular polarisation (Stokes V).

The science goals for VLASS are outlined in Lacy et al. (Reference Lacy2020). In the time domain, the survey is best suited to search for objects that vary on timescales of $\sim$ months, such as gamma-ray burst afterglows, radio supernovae and tidal disruption events, although it will also detect bursts from radio stars and Galactic transients. Indeed, early results have demonstrated the survey’s effectiveness for finding synchrotron transients, for example: a merger-triggered core collapse supernova (Dong et al. Reference Dong2021), and a sample of radio-detected tidal disruption events (Somalwar et al. Reference Somalwar, Ravi and Lu2025b ). However, the sparse sampling has meant that extensive followup is needed to fully characterise the discoveries.

5.3.1. Source finding

The goal of source finding software is to identify astronomical objects in radio images. The typical approach to this is to identify statistically significant collections of pixels (‘sources’) and ‘extract’ them by fitting elliptical Gaussians to measure their properties: position, angular size and flux density (note that the more general radio source finding approach can consider more complex source shapes, but transients are assumed to be point sources, although they can be in complex regions).

In optical astronomy, one of the most well-used source finding packages is SExtractor (Bertin & Arnouts Reference Bertin and Arnouts1996), and many large projects use their own custom software (e.g. Masci et al. Reference Masci2019) that works in a similar way. However, the needs for radio source finding can be both more complex and simpler than in the optical. For instance, in the radio the typical noise properties of the images are different (adjacent pixels in a restored image are correlated in the radio, but not in the optical); images are usually restored with a single beam shape that is not subject to seeing variations (although there can be ionospheric effects and variations due to RFI flagging); there are often multiple simultaneous images to search (e.g. as a function of frequency or polarisation), and imaging artefacts are usually deconvolution sidelobes rather than halos, satellite trails, and cosmic rays. These limitations and differences led to the development of radio-specific source finding packages for continuum surveys.

Source finding is a significant focus for radio continuum surveys as we prepare for the SKAO. See, for example, the results of the ASKAP Evolutionary Map of the Universe (EMU; Norris et al. Reference Norris2011; Hopkins et al. Reference Hopkins2025) Source Finding Data Challenge (Hopkins et al. Reference Hopkins2015) and the Square Kilometre Array Science Data Challenge 1 (Bonaldi et al. Reference Bonaldi2021). However, many of the most challenging aspects (such as characterising sources that are diffuse or have a complex morphology) are not as relevant for radio transient surveys where the objects of interest are expected to be intrinsically compact.Footnote ⁿ

Nevertheless, there are some aspects of source finding of particular importance to radio transient surveys. These include:

• • Speed: if source finding is running as part of real-time processing then it needs to be computationally efficient without reducing reliability and completeness;

• • Identifying sources with negative flux density: for example in the case of circular polarisation (Stokes V) images in which sources can have either sign of polarisation;

• • Source finding in the uv-plane: an alternative to image-plane source finding that can be useful when rapid processing is needed, but requires modelled sources to subtract.

Some of the main source finding packages used in current radio transient surveys are: Selavy (Whiting & Humphreys Reference Whiting and Humphreys2012) used in the ASKAP workflow; AEGEAN (Hancock et al. Reference Hancock, Murphy, Gaensler, Hopkins and Curran2012a ; Hancock, Trott, & Hurley-Walker Reference Hancock, Trott and Hurley-Walker2018), used in GLEAM-X (Hurley-Walker et al. Reference Hurley-Walker2022a ); and PyBDSF (Python Blob Detector and Source Finder, Mohan & Rafferty Reference Mohan and Rafferty2015), used in RACS (Hale et al. Reference Hale2021) and LoTSS (Shimwell et al. Reference Shimwell2019). A summary of the main aspects of radio source finding, for example background noise estimation, island-finding and deblending (shared by many of these packages) is given by Lucas et al. (Reference Lucas, Staley and Scaife2019). A comparison of the performance of some of these packages (with a focus on continuum survey science applications) is given by Boyce et al. (Reference Boyce2023).

5.3.2. Source association

Once sources have been identified and fit in each individual epoch, the next step is associating detections of the same object throughout multiple epochs. This is done via positional cross-matching. Both the TraP and VAST pipelines cross-match using the ‘de Ruiter radius’ (de Ruiter, Willis, & Arp Reference de Ruiter, Willis and Arp1977): the angular distance on the sky between a source and its potential counterpart in the next epoch, normalised by the positional error of both sources.

To achieve optimal results in source association there are a number of issues to consider. These include how to deal with variable image quality between epochs and how to ensure unique matches in cases were multiple potential matches are identified. There are also computational challenges when scaling this up to large datasets with many repeated fields. These issues are discussed in more detail by Swinbank et al. (Reference Swinbank2015).

5.3.3. Lightcurve creation

Source association produces a lightcurve of flux density measurements with time for all epochs in which the source was detected. To make a more complete lightcurve most pipelines measure either (i) limits or (ii) forced fit parameters for each source in each epoch in which it is not detected (this is also done for optical transient surveys, e.g. Masci et al. Reference Masci2023). Limits are typically based on the local rms noise in the region of the source (a more computationally efficient but less accurate alternative is to use the overall rms noise of each image). Forced fitting involves fitting an elliptical Gaussian at the known position of the transient source. In both cases, the implementation approach depends on whether the pipelines are running in real time (and hence cannot access previously observed images, beyond a given buffer) or in an offline or batch mode.

Subsequent analysis, such as applying variability metrics, searching for periodic behaviour, or doing automatic classification, is performed on the resulting lightcurves.

5.7.1. Radio lightcurve classification

One of the primary data products of a multi-epoch survey is radio lightcurves. Radio data alone does not typically provide enough information for a firm classification for many sources types: this usually requires multi-wavelength information (e.g. Mooley et al. Reference Mooley2016; Rowlinson et al. Reference Rowlinson2022). However, the lightcurves of different source classes do have different time-dependent features, as shown in Figure 8. For example: radio supernovae have a rapid rise followed by a power-law decay; flaring stars show short, discrete bursty behaviour that is sometimes periodic; and scintillation appears as stochastic fluctuations with characteristic amplitudes and timescales. Some sources classes (e.g. syncrotron transients) also show frequency dependent time evolution, and others such as pulsars and long period transients show variability in their polarisation fraction (these dimensions are not captured in Figure 8).

Figure 8. Sketches of lightcurves for a range of radio transient source types. The lightcurves capture qualitatively different variability with rough timescales indicated. We have not attempted to capture spectral energy evolution, polarisation fraction, or the typical flux density scale. Not all source types are included; for example other synchrotron transients such as TDEs will show qualitatively the same evolution as GRB afterglows. Note that many source classes exhibit variability on multiple timescales. Most of the sketches are inspired by real data, as listed: AGN intraday variability (Bignall et al. Reference Bignall2003); AGN flaring (Hovatta et al. Reference Hovatta, Nieppola, Tornikoski, Valtaoja, Aller and Aller2008); Changing look AGN (Meyer et al. Reference Meyer2025); supernova re-brightening (Anderson et al. Reference Anderson2017); active binary star (Osten et al. Reference Osten2004); X-ray binary (Fender et al. Reference Fender2023); eclipsing binary pulsar (Zic et al. Reference Zic2024); M dwarf star (Zic et al. Reference Zic2019); extreme scattering event (Bannister et al. Reference Bannister, Stevens, Tuntsov, Walker, Johnston, Reynolds and Bignall2016); long period transient (and long period pulsars) (Wang et al. Reference Wang2025d).

As a result of the lack of suitable training data (i.e. observed, well-sampled radio lightcurves from a range of source types), the first efforts in automatic classification of radio transients used simulated datasets (e.g. Rebbapragada et al. Reference Rebbapragada, Lo, Wagstaff, Reed, Murphy, Thompson, Griffin, Hanisch and Seaman2012; Murphy et al. Reference Murphy2013). These were useful as a proof-of-concept, but the simulated lightcurves did not account for the full complexity (or the poor sampling) of real survey data.

Following this, there were various efforts that focused on specific aspects of classification. Pietka et al. (Reference Pietka, Staley, Pretorius and Fender2017) focused on the timescale of variability as a key feature in determining an initial classification for radio transient lightcurves. They automatically measured the rise rate of $\sim 800$ synchrotron flares from a range of source types to define a probability distribution of timescales for each source type. While the predictive power of a single property is naturally limited, the intention was that this would be a useful component of a more comprehensive classification process.

Along similar lines, Stewart et al. (Reference Stewart, Muñoz-Darias, Fender and Pietka2018) investigated radio versus optical flux density as a means of making a preliminary classification of radio transients. They showed that different source types do fall (broadly) into different regions of this two-parameter space. For example, quasars tend to have quite a high radio to optical flux density ratio, whereas stars typically have a much lower one. Wang et al. (Reference Wang2022b ) took this further and used radio to near-infrared (to be more robust against extinction) flux ratio versus circular polarisation fraction, showing that the locations of pulsars and stellar sources (the two main classes of sources with significant polarisation) were very different. And Wang et al. (Reference Wang2025c) compared X-ray and radio fluxes (drawing on the radio/X-ray correlation plots for accreting sources; e.g. Gallo et al. Reference Gallo, Fender and Pooley2003; Russell et al. Reference Russell2016; Ridder et al. Reference Ridder, Heinke, Sivakoff and Hughes2023), showing that LPTs occupied an extreme region of that space distinct from other potentially related populations like low-mass X-ray binaries, stars, and cataclysmic variables, but did resemble magnetars. As with the timescale of variability, these metrics alone are not enough to definitively classify objects, but would be useful parts of a classification pipeline.

The most comprehensive attempt to classify radio transient lightcurves to date is that by Sooknunan et al. (Reference Sooknunan2021), based on an approach presented by Lochner et al. (Reference Lochner, McEwen, Peiris, Lahav and Winter2016) for optical lightcurves. They addressed the limitations of the currently available data in several ways: (1) they interpolated a set of real lightcurves (from Pietka et al. Reference Pietka, Fender and Keane2015 and Dobie et al. Reference Dobie2018) so they have equivalent sampling; (2) they augmented this set of lightcurves to produce a larger, more balanced training set; and (3) they incorporated some external contextual information, such as whether the object is in the Galactic plane, and the object’s optical flux density. The classifier achieved $\sim 75\%$ accuracy for a 5-class problem (AGN, GRBs, XRBs, Novae and SNe), a promising result, but with significant room for improvement.

Automatic classification of radio transients is on the cusp of becoming a reality for large surveys. The machine learning techniques are well-established in optical time domain surveys, and some of the additional challenges presented by radio surveys have been investigated in isolation. With the much larger datasets resulting from current surveys, it should be possible to train pipelines that work effectively, at least to provide an initial classification that can be further investigated manually.

5.7.2. Anomaly and outlier detection

One of the aims of radio transient surveys is to detect rare classes of objects, or unusual examples of existing classes. Anomaly detection is a type of unsupervised machine learning that involves searching for data points that do not conform to the normal properties of a given dataset (often called outliers), making it well suited to this task. The methods for identifying anomalies range from well-established statistical techniques, through to more sophisticated algorithms. For a comprehensive review of anomaly detection techniques and applications in science, engineering and business, see Chandola et al. (Reference Chandola, Banerjee and Kumar2009). For a review of anomaly detection methods applied to time series data, see Blázquez-Garca et al. (Reference Blázquez-Garca, Conde, Mori and Lozano2021).

In time-domain astronomy, anomaly detection approaches have been demonstrated on a range of tasks. For example, searching for unusual objects in Kepler light curves (Giles & Walkowicz Reference Giles and Walkowicz2019; Martnez-Galarza et al. Reference Martinez-Galarza, Bianco, Crake, Tirumala, Mahabal, Graham and Giles2021). Both of these projects were motivated by the serendipitous discovery of Boyajian’s star KIC 8462852 (Boyajian et al. Reference Boyajian2016), and the need to prepare for, and capitalise on, the increased discovery potential for unusual objects that will come with the Vera Rubin Observatory 10-yr Legacy Survey of Space and Time (LSST; Ivezić et al. Reference Ivezić2019).

Lochner & Bassett (Reference Lochner and Bassett2021) present a general framework for anomaly detection aimed at astronomy applications. It incorporates active learning, with the ability for the expert user to rank and categorise the results. Their approach is demonstrated on a set of 50 000 simulated lightcurves that represent typical (99%) and outlier (1%) sources. Andersson et al. (Reference Andersson2025) is the first group to apply this approach to observed radio transient lightcurves. Using data from ThunderKAT, they were able to recover interesting outlier sources (as defined by citizen science volunteers – see Section 5.7.3) with some success, giving results that are complementary to other approaches. This area of research shows promise for future, larger, radio transient surveys.

5.7.3. Citizen science projects

Citizen science projects (one of the first, and most influential of which, was SETI@HOME; Werthimer et al. Reference Werthimer2001) are designed to leverage the enthusiasm of members of the public to help complete large scale scientific data collection and classification, either using only their personal computer facilities (as in the case of SETI@HOME) or using the citizens themselves to help analyse data. In astronomy, a pioneering project in this space was Galaxy Zoo (Lintott et al. Reference Lintott2008) which invited the general public to visually inspect and classify the morphology of nearly a million galaxies from the Sloan Digital Sky survey (Lintott et al. Reference Lintott2011). The success of the initial Galaxy Zoo project led it to broaden its remit to the Zooniverse. This platform, and other similar approaches, have been applied to a wide range of classification tasks including gravitational wave glitch identification (Zevin et al. Reference Zevin2017), exoplanet discovery (Christiansen et al. Reference Christiansen2018), and radio galaxy classification (Lukic et al. Reference Lukic, Brüggen, Banfield, Wong, Rudnick, Norris and Simmons2018).

The first (and, to date, only) citizen science project for classifying image domain radio transients is the ‘Bursts From Space’ project on MeerKAT (Andersson et al. Reference Andersson2023). They had $\sim 1\,000$ volunteers who provided $\sim 89\,000$ classifications of sources using images and lightcurves. Sources were classified into five classes: Stable, Extended Blobs, Transients/Variables, Artefacts and Unsure. From this, 142 variable sources were identified, most of which the authors conclude are likely to be AGN. The amount of data available from current and future radio surveys should allow similar projects with more detailed classification schema.

6.1.1. Basic metrics

For surveys with a small number of epochs, the simplest way of measuring the variability of a source is to take the maximum difference between the observed flux density values at different times. For example, Carilli et al. (Reference Carilli, Ivison and Frail2003) used:

(6) \begin{equation} \Delta S = |S_1 - S_2|\end{equation}

the absolute change in flux density, S, between two pairs of two epochs (in their case, 19 days and 17 months apart). To determine if this difference was significant, they compared the value of $\Delta S$ to the $5\sigma$ image rms noise. Sources that exhibited the most extreme variability of 100%, would be detected in one epoch and not the other. These have typically been referred to as transients in the literature (but see Section 1.3 for a discussion of terminology).

This approach was also used by Levinson et al. (Reference Levinson, Ofek, Waxman and Gal-Yam2002) in their search for orphan afterglows between the FIRST and NVSS surveys. When the two epochs have significantly different sensitivity limits, additional care is required. Levinson et al. (Reference Levinson, Ofek, Waxman and Gal-Yam2002) chose a flux density cutoff designed to exclude (most) persistent sources fluctuating around the sensitivity limit.

A related approach is the fractional variability V used by Gregory & Taylor (Reference Gregory and Taylor1986):

(7) \begin{equation} V = \frac{S_\mathrm{max}-S_\mathrm{min}}{S_\mathrm{ max}+S_\mathrm{min}},\end{equation}

where $S_\mathrm{min}$ and $S_\mathrm{max}$ are the minimum and maximum flux density, respectively. This metric is only appropriate for data with a small number of measurements. However, the modulation index below can be considered a more sophisticated version of this metric.

Rather than consider a difference between values, de Vries et al. (Reference de Vries, Becker, White and Helfand2004) looked at the ratio between two flux densities $S_1$ and $S_2$ , which they called the variability ratio, VR:

(8) \begin{equation} VR = S_1/S_2\end{equation}

This was modified to account for the varying noise levels in the different epochs, which could be functions of the flux densities themselves (most appropriate for bright sources).

All of these metrics are inherently limited, and for surveys with many observations of each source, a more sophisticated approach is preferred.

6.1.2. $\chi^2$ probability

Another way of measuring overall variability is to calculate the $\chi^2$ value for a model where the source remained constant over the observing period:

(9) \begin{equation} \chi^2_\mathrm{lc} = \sum_{i=1}^{n} \frac{(S_i - \bar{S})^2}{\sigma^2_i} \end{equation}

where $S_i$ is the ith flux density measurement with variance $\sigma^2_i$ within a source light curve, and n is the total number of flux density measurements in the light curve. $\bar{S}$ is the weighted mean flux density defined as:

(10) \begin{equation} \bar{S} = \sum_{i=1}^n \frac{S_i}{\sigma_i^2} / \sum_{i=1}^n \frac{1}{\sigma_i^2}\end{equation}

This has been used for a number of variability monitoring programs, for example Kesteven et al. (Reference Kesteven, Bridle and Brandie1976), Gaensler & Hunstead (Reference Gaensler and Hunstead2000), Bell et al. (Reference Bell2014). Kesteven et al. (Reference Kesteven, Bridle and Brandie1976) considered a source ‘variable’ if the probability $p(\chi_\mathrm{lc}^2)$ of exceeding the observed $\chi_\mathrm{lc}^2$ by chance is $\le 0.1\%$ and ‘possibly variable’ if $0.1\% \le p \le 1\%$ . Care must be taken to consider the number of sources measured (effectively a ‘trials factor’), since with 1 000 sources a single-source probability of 0.1% becomes insignificant (e.g. Bannister et al. Reference Bannister, Murphy, Gaensler, Hunstead and Chatterjee2011).

The probability p is independent of the number of data points, so this method can be used to compare lightcurves with different numbers of observations. However, as identified by the authors, a limitation of this metric is that it is independent of the order of the flux density measurements, and hence is not sensitive to slowly increasing or decreasing variability with time, much less more complex behaviour (cf. Leung et al. Reference Leung, Murphy, Lenc, Edwards, Ghirlanda, Kaplan, O’Brien and Wang2023).

6.1.3. Modulation index

Together with $\chi^2$ , a popular statistic is the modulation index, which is the standard deviation of the flux density divided by the (weighted) mean (e.g. Narayan Reference Narayan1992; Rickett Reference Rickett1990). This can also be written as

(11) \begin{equation} V = \frac{1}{\bar{S}} \sqrt{\frac{N}{N-1}(\overline{S^2}-\bar{S}^2)}, \end{equation}

with

(12) \begin{equation} \overline{S^2} = \sum_{i=1}^n \frac{S_i^2}{\sigma_i^2} / \sum_{i=1}^n \frac{1}{\sigma_i^2},\end{equation}

and where the use of $N-1$ in the denominator means we are using the unbiased estimator of the sample variance. This has been used extensively in radio transients analysis (for example, see Gaensler & Hunstead Reference Gaensler and Hunstead2000; Bannister et al. Reference Bannister, Murphy, Gaensler, Hunstead and Chatterjee2011; Swinbank et al. Reference Swinbank2015; Rowlinson et al. Reference Rowlinson2019). The modulation index, which is also called the ‘coefficient of variation,’ is often written as V, but also as m (especially in the literature around scintillation). It is an extension of the fractional variability that makes use of more than two measurements. Different authors also use weighted or unweighted means.

Yet another variant on this is also seen: a ‘debiased’ variability index (Akritas & Bershady Reference Akritas and Bershady1996; Barvainis et al. Reference Barvainis, Lehár, Birkinshaw, Falcke and Blundell2005; Sadler et al. Reference Sadler2006):

(13) \begin{equation} V_d = \frac{1}{\bar{S}} \sqrt{\frac{\sum (S_i - \bar{S})^2 - \sum \sigma_i^2}{N}},\end{equation}

which also has extensive use in the X-ray literature (e.g., Green et al. Reference Green, Cram, Large and Ye1999; Vaughan et al. Reference Vaughan, Edelson, Warwick and Uttley2003; Markowitz & Edelson Reference Markowitz and Edelson2004). This is similar to Equation (11) in presenting fractional variability. It typically has not used weighted sums, but attempts to account for the range in individual measurement error through the subtraction of the per-observation variance inside the radical. A downside to this is that the factor inside the radical can easily be negative for non-variable sources (rather than deal with this issue directly, other authors use a ‘normalised excess variance’ which is $V_d^2$ ; e.g. Nandra et al. Reference Nandra, George, Mushotzky, Turner and Yaqoob1997; Vaughan et al. Reference Vaughan, Edelson, Warwick and Uttley2003). Barvainis et al. (Reference Barvainis, Lehár, Birkinshaw, Falcke and Blundell2005) and Sadler et al. (Reference Sadler2006) handle this in slightly different ways. They generally allow $V_d$ to be negative when the factor inside the radical is negative, and then present the results either as a negative value or use the range of small negative and positive values to define a minimum threshold for variability, and assign this value to all numbers below it. However, we note that $\sum (S_i - \bar{S})^2$ is distributed as a scaled $\chi^2$ distribution for $N-1$ degrees-of-freedom. For well-detected sources but with minimal excess variability, the fraction of values that have the factor inside the radical negative is $\gt50$ %. Also, as discussed extensively in the literature the exact value of this metric will depend on how the cadence of the observations compares to a typical variability timescale (when known), so in some cases more explicit parameterisations or functional forms could be used (Section 6.1.5).

Figure 9. Standard $\eta$ -V plot for identifying variable sources, following Swinbank et al. (Reference Swinbank2015). The data here were simulated and consist entirely of Gaussian noise with constant amplitude. The distribution of source brightnesses are a power-law with cumulative distribution $N(\gt S)\propto S^{-1.5}$ , appropriate for standard candles in a Euclidean universe (e.g. Hoyle & Narlikar Reference Hoyle and Narlikar1961; Longair & Scott Reference Longair and Scott1965), with SNR ranging from 6 to 2000. The points are coloured by SNR (with a colour-scale to the right). We also show marginal distributions for $\eta$ (top) and V (right), along with theoretical predictions (solid orange lines). Finally, we show the line $V_\mathrm{max}=\sqrt{\eta}/\mathrm{SNR}_\mathrm{min}$ which bounds the top of the distribution (red dashed line).

6.1.4. $\eta$ -V parameters

It has become standard to consider both the reduced $\chi^2$ :

(14) \begin{equation} \eta = \frac{1}{N-1} \chi^2_\mathrm{lc}\end{equation}

(where there are $N-1$ degrees of freedom) and the modulation index V together in finding variables which would have high values of $\eta$ , V, or both (e.g. Swinbank et al. Reference Swinbank2015; Rowlinson et al. Reference Rowlinson2019).

Both of these statistics are based on the second moments of the flux density (i.e. variance or standard deviation), and both are independent of data order. So they should convey some similar information. However, while correlated, the outliers in $\eta$ or V are not always the same. As discussed by Rowlinson et al. (Reference Rowlinson2019), sources with high $\eta$ usually are brighter, have some large flares or similar excursions from the mean, and have low uncertainties relative to the mean. Such lightcurves are statistically distinguishable from a constant value, although this relies on accurate calibration and error analysis at high signal-to-noise, which is not always reliable. In contrast, sources with high V typically have lower average flux densities.

This is illustrated in Figure 9, which consists entirely of simulated data with Gaussian noise and a range of signal-to-noise ratios (SNRs)Footnote ^o but no transients or variables beyond those expected from the noise realisations. As expected, at high V the data are dominated by low SNR sources that just happened to have slightly higher noise realisations. The trend with $\eta$ is harder to see, but at a constant V there is a trend toward higher $\eta$ at higher SNR. We also show the theoretical predictions for the marginal distributions. In the case of $\eta$ it is a scaled $\chi^2$ distribution (as expected), which indeed resembles a log-normal distribution as discussed by Rowlinson et al. (Reference Rowlinson2019). For V the distribution is largely just the distribution of $1/\mathrm{SNR}$ , which will depend on the underlying flux density distribution: since in this simulation S has a power-law distribution and $\mathrm{SNR}\propto S$ (constant noise), V also has a power-law distribution up to the maximum value but with an inverted index, $N(\gt V)\propto V^{1.5}$ . This can change in other samples, though. Finally, we also see a cutoff at high V that depends on $\eta$ as $V_\mathrm{ max}=\sqrt{\eta}/\mathrm{SNR}_\mathrm{min}$ : such cutoffs are observed in real data (e.g. Rowlinson et al. Reference Rowlinson2019; Murphy et al. Reference Murphy2021).

This demonstration serves several purposes. Firstly, the use of both $\eta$ and V, while common, is not necessarily optimal since they are related to each other as a function of SNR. A better second metric in addition to $\eta$ or V might be something optimised for detecting short-timescale variability such as the result of an outlier search or a matched filter, or some other metric that incorporates information about the order of the data. Secondly, the background distribution of $\eta$ should follow a $\chi^2$ distribution, while that of V depends on the range of SNRs considered, and both can be used to determine thresholds for investigation.

6.1.5. Other variability metrics

The metrics discussed in the previous section are related: they are both second-order statistics that depend on the degree of variability but ignore any shape/ordering of the lightcurve. Hence a number of other metrics or analyses have been used in different cases.

Perhaps the simplest is the temporal gradient $\nabla_F \equiv dS/dt$ used by Bell et al. (Reference Bell2019), who also divided the gradient by its uncertainty, $\nabla_S \equiv \nabla_F/\sigma_F$ to identify statistically significant changes. They also found that higher-order polynomial changes were not needed to describe the data.

More general parameterisations use the autocorrelation function:

(15) \begin{equation} ACF(\tau) = \langle S(t+\tau)S(t)\rangle,\end{equation}

which is sometimes replaced by the autocovariance function (also ACF):

(16) \begin{equation} ACF(\tau) = \langle [S(t+\tau)-\overline{S}][S(t)-\overline{S}]\rangle,\end{equation}

where the means are subtracted before calculation. Both of these determine the ACF as a function of lag $\tau$ . The autocorrelation function can be used to study the timescale of variations (Rickett Reference Rickett1977), especially for diffractive scintillation in pulsars. A similar concept is the structure function:

(17) \begin{equation} D(\tau) = \langle [F(t+\tau) - F(t)]^2 \rangle\end{equation}

for all measurements in some bin with lag $\tau$ , where F can be the raw flux density measurements (Hughes et al. Reference Hughes, Aller and Aller1992; Kumamoto et al. Reference Kumamoto2021), but also measurements with the mean subtracted and then normalised by the standard deviation (Gaensler & Hunstead Reference Gaensler and Hunstead2000), or just normalised by the mean (Rickett & Lyne Reference Rickett and Lyne1990; Kaspi & Stinebring Reference Kaspi and Stinebring1992; Lovell et al. Reference Lovell2008). This is commonly used to study variability in AGN (Hughes et al. Reference Hughes, Aller and Aller1992; Lovell et al. Reference Lovell2008; Gaensler & Hunstead Reference Gaensler and Hunstead2000) and pulsars (Rickett & Lyne Reference Rickett and Lyne1990; Kaspi & Stinebring Reference Kaspi and Stinebring1992; Kumamoto et al. Reference Kumamoto2021) which can be compared against the predictions for refractive scintillation (e.g. Hancock et al. Reference Hancock, Charlton, Macquart and Hurley-Walker2019). Using expectations for the behaviour of the structure function with lag, it can be used to give a better definition of the modulation index and its associated timescale (e.g. Kaspi & Stinebring Reference Kaspi and Stinebring1992). In both cases effort must be taken to do this correctly for irregularly-sampled data (Edelson & Krolik Reference Edelson and Krolik1988; Kreutzer et al. Reference Kreutzer, Gillen, Briegal and Queloz2023).

These functions are also intrinsically related to the Fourier power spectrum and its extension for irregularly-sampled data, the Lomb-Scargle power spectrum (Scargle Reference Scargle1982, Reference Scargle1989). Such power spectra can be estimated directly when searching for explicitly periodic emission, such as from eclipsing pulsar systems (e.g. Zic et al. Reference Zic2024; Petrou et al. Reference Petrou2025). There are also many refinements to these broad techniques such as Gaussian processes (Aigrain & Foreman-Mackey Reference Aigrain and Foreman-Mackey2023), but in the cases of radio lightcurves with only a few tens of data-points for most examples, the differences between the techniques are small.

Furthermore, Fourier techniques can be seen as matched filters with sine/cosine kernel functions with unknown period. This can be explored further with more specific kernels that are appropriate to specific transient types. For example, Leung et al. (Reference Leung, Murphy, Lenc, Edwards, Ghirlanda, Kaplan, O’Brien and Wang2023) designed a matched filter around the expected shape of a GRB afterglow, especially orphan afterglows, parameterised as a power-law lightcurve with an optional break. Compared to selection via a standard techniques selecting sources compared to a constant model (effectively the $\chi^2_\mathrm{lc}$ in Equation 9), none of the five selected sources from that paper would have passed a more basic $3\sigma$ threshold due to their slow evolution. Such a strategy can of course be adopted for an arbitrary light-curve shape, such as a generic burst. All of these techniques, though, require richer data sets with at least tens (if not more) samples, which are only becoming common with the latest generation of surveys.

6.1.6. Burst detection

In time-domain surveys with small numbers of temporal samples (observing epochs or otherwise), there is in general no need for explicit burst detection beyond the variability analysis presented above. But as the number of samples grows, especially with short integrations from longer images (Section 5.1), the need for explicit burst detection grows.

Historically, there has not been a large focus on burst detection from radio images, largely due to the small number of samples available. This is in contrast to the significant literature in finding and classifying bursts in other domains such as FRBs (e.g. Rajwade & van Leeuwen Reference Rajwade and van Leeuwen2024) or XRBs and GRBs (e.g. Barthelmy et al. Reference Barthelmy2005; Meegan et al. Reference Meegan2009). Those cases are made further difficult by the need to examine large data-sets in real time – leading to efficient hardware implementations, machine learning classifiers, and distributed architectures – something which radio imaging surveys are only now starting to confront.

Beyond initial approaches using the metrics above or variants, there can be techniques that segment the data into ‘background’ and ‘burst’. At the simplest level, iterative sigma clipping (e.g. Leroy & Rousseeuw Reference Leroy and Rousseeuw1987) is often used for outlier excision (Vallisneri & van Haasteren Reference Vallisneri and van Haasteren2017), but can be used for outlier identification as well. More complex approaches can be taken to the same problem (e.g. Hogg, Bovy, & Lang Reference Hogg, Bovy and Lang2010) with robust statistical models that attempt to assign probabilities to each data point regarding whether it is part of the background or not. However, these approaches may be limited in that they consider each observation independently. If the burst duration is less than the sampling time that is fine, but if bursts can last longer then techniques which take into account the temporal relation between data points may be preferred.

The basic techniques used in those cases are typically variants of matched filtering (also see Section 5.2), which is also commonly used for FRB detection (after dedispersion). Typically a Gaussian or boxcar filter (if there is a priori knowledge that the burst shape should be different that could of course be used instead, or a more complex basis like wavelets if there are enough samples) of a given width is convolved with the data to identify bursts, and then this is repeated for a range of widths. And as with the outlier detection metrics above, a more formal Bayesian approach can be taken here too. For instance, Scargle et al. (Reference Scargle, Norris, Jackson and Chiang2013) offer an efficient algorithm that can identify segments of arbitrary length which differ from the background, and which can be applied to data arriving in real time and to data which have already been collected. This algorithm achieves similar sensitivity to the theoretical limit.