3.1.1 The radio sky at μJy levels: AGN or star formation?

After years of intense debate, it is now clear that while SF galaxies contribute significantly to the sub-mJy counts, they do not dominate it above ~200μJy. Recent results (e.g. Seymour et al. Reference Seymour2008; Smolčić et al. Reference Smolčić2008; Padovani et al. Reference Padovani, Mainieri, Tozzi, Kellermann, Fomalont, Miller, Rosati and Shaver2009), which are summarised in Figure 5, show that both SF galaxies and AGNs contribute significantly to the source counts. About half of these AGNs are radio-quiet, characterised by relatively low radio-to-optical flux density ratios and radio powers, as compared with radio quasars (see also Prandoni Reference Prandoni2010). Above 1 mJy, the contribution of radio-quiet objects to the source counts is insignificant, and they are dominated by radio-loud AGNs.

Figure 5. Differential fraction of SF galaxies as a function of 1.4-GHz flux density, taken from Norris et al. (Reference Norris2011b). Shaded boxes, and the two lines for Padovani et al., show the range of uncertainty in the survey results. Arrows indicate constraints from other surveys. These results show that the fraction of SF galaxies increases rapidly below 1 mJy and, at the 50 μJy survey limit of EMU/WODAN, about 75% of sources will be SF galaxies.

To probe the radio-quiet AGN component, it is therefore necessary to analyse the deepest radio fields (S ≤ 100 − 200 μJy), where most sources are typically associated with SF galaxies. Radio-quiet AGNs share many properties with SF galaxies: they have similar radio luminosities (10²²–10²⁴ W Hz⁻¹), steep radio spectra (α < −0.5), and similar infrared/radio flux ratios (e.g. Roy et al. Reference Roy, Norris, Kesteven, Troup and Reynolds1998).

In addition, radio-quiet AGNs are often associated with faint optical galaxies characterised by Seyfert-2-like spectra, containing both SF and AGN components. Even when available, if optical spectroscopy is not of sufficient quality, it can be difficult to derive reliable emission line ratios, and distinguish between starburst and Seyfert 2 spectra, through BPT (Baldwin, Phillips, & Terlevich Reference Baldwin, Phillips and Terlevich1981) diagrams (see e.g. Prandoni et al. Reference Prandoni, Morganti and Mignano2009). This makes it difficult to distinguish radio-quiet AGNs from SF galaxies, even with multiwave length information, although the availability of X-ray data can help (Padovani et al. Reference Padovani, Miller, Kellermann, Mainieri, Rosati and Tozzi2011).

Spitzer IRAC colours, when available, can be very effective in separating radio-quiet AGNs from SF galaxies as shown in Figure 6, where the well-known IRAC colour–colour plot (Lacy et al. Reference Lacy2004) is exploited for the First Look Survey (FLS) deep radio field. A fraction of sources with typical AGN IRAC colours appear to be genuine radio-quiet AGNs, and account for ~45% of the overall AGN component in the FLS.

Figure 6. IRAC colour–colour plot of the FLS radio sources with q ₂₄ = log (S ₂₄μ/S _1.4GHz > 0.6 (filled symbols), from Prandoni et al. (Reference Prandoni, Morganti and Mignano2009). Colours refer to optical spectral classification: SF galaxies (blue); narrow/broad line AGNs (green); early-type galaxies (red); galaxies with narrow emission line, which do not have a secure optical classification (magenta); sources with no optical spectroscopy available (black). Arrows indicate upper/lower limits. The lines indicate the expected IRAC colours as a function of redshift for different source types (see legend). The expected location for AGNs is highlighted in pink. For reference, we also show IRAC colours of (a) all FLS IRAC-identified radio sources (no optical identification selection applied, cyan dots); (b) the entire FLS IR-selected star/galaxy population (no radio selection applied, black dots); and (c) a sample of high-redshift obscured (type-2) quasars (Martinez-Sansigre et al. Reference Martinez-Sansigre2006), green crosses.

A number of other methods can also be used to distinguish AGNs from SF galaxies in radio surveys (e.g. Norris, Middelberg, & Boyle Reference Norris, Middelberg and Boyle2008), including

• • radio morphology (e.g. Biggs & Ivison Reference Biggs and Ivison2008; Biggs, Younger & Ivison Reference Biggs and Ivison2010),

• • radio spectral index (e.g. Ibar et al. Reference Ibar, Ivison, Biggs, Lal, Best and Green2009, Reference Ibar, Ivison, Best, Coppin, Pope, Smail and Dunlop2010),

• • radio–far-infrared ratio (e.g. Norris et al. Reference Norris2006; Middelberg et al. Reference Middelberg2008b),

• • radio–near-infrared ratio (e.g. Willott et al. Reference Willott, Rawlings, Jarvis and Blundell2003),

• • radio polarisation (e.g. C. A. Hales et al., in preparation),

• • radio variability (e.g. Norris et al. Reference Norris, Middelberg and Boyle2008; Chatterjee et al. Reference Chatterjee and Murphy2010; Murphy et al. Reference Murphy2012),

• • optical and IR colours, including the use of spectral energy distribution (SED) templates (e.g. Lacy et al. Reference Lacy2004),

• • optical line ratios (e.g. Baldwin et al. Reference Baldwin, Phillips and Terlevich1981),

• • X-ray hardness ratio (e.g. Rosati et al. Reference Rosati2002),

• • X-ray power (e.g. Padovani et al. Reference Padovani, Miller, Kellermann, Mainieri, Rosati and Tozzi2011),

• • radio source brightness measured by VLBI (e.g. Kewley et al. Reference Kewley, Heisler, Dopita, Sutherland, Norris, Reynolds and Lumsden2000; Parra et al. Reference Parra, Conway, Aalto, Appleton, Norris, Pihllström and Kewley2010; Alexandroff et al. Reference Alexandroff2012).

None of these techniques is foolproof and universal, and a combination of techniques is necessary to provide unambiguous classification. In preparation for the daunting task of classifying tens of millions of radio sources, we need to define reliable methods for classifying radio sources.

3.1.2 Composite galaxies

It is well established (e.g. Roy et al. Reference Roy, Norris, Kesteven, Troup and Reynolds1998) that the radio emission from Seyfert galaxies contains significant contributions from both AGN and SF activity, and there is growing recognition (Norris et al. Reference Norris, Middelberg and Boyle2008; Lutz et al. Reference Lutz2010; Shao et al. Reference Shao2010; Seymour et al. Reference Seymour2011) that this may also be true of high-luminosity galaxies, particularly at high redshift. Many of these galaxies are not simply ‘star-forming’ or ‘AGNs’ but include a significant contribution from both. In extreme cases (Norris et al. Reference Norris, Lenc, Roy and Spoon2012), a galaxy may appear to be ‘pure AGN’ at one wavelength and ‘pure SF’ at another.

Particularly at high redshifts, such composite AGN/SF systems constitute a significant fraction of radio sources, and so a simple classification into AGN or SF galaxy is inadequate. Instead, the contribution to the galaxy’s luminosity from both AGN and SF activity must be assessed, to measure the relative contributions from underlying physical properties such as black hole and galaxy mass, star-formation rate (SFR), environment, etc. However, the relative contribution will vary depending on the observing band, and so comprehensive multiwavelength data are required. However, such detailed information will be hard to obtain for very large samples, perhaps necessitating a simpler classification scheme, which may lead to oversimplifications or even to incorrect interpretation of the data.

It is therefore essential to develop methods which fit the SED of a given radio source with both a starburst and AGN component (e.g. Afonso et al. Reference Afonso, Mobasher, Chan and Cram2001). This approach is clearly only possible for fields with good multiwavelength data, but will inform analysis of fields with lower quality ancillary data. Observations from Spitzer and Herschel cover the bulk of the energy output of most galaxies and can be used to distinguish the starburst and AGN components. For example, the far-IR is directly related to the SFR, and, if the FIR–radio correlation remains true at all redshifts (e.g. Mao et al. Reference Mao, Huynh, Norris, Dickinson, Frayer, Helou and Monkiewicz2011a, and references therein), can be used to determine what fraction of the radio emission is due to star formation. Hence, the remaining radio emission would be due to AGN activity. The AGN bolometric luminosity can be estimated from the mid-IR component which is not necessarily proportional to the AGN emission at radio wavelengths. Once the starburst and AGN fractional contribution to individual sources are determined, it is possible to construct derived results such as luminosity functions and relative contributions by type to the source counts.

3.1.3 Are there undiscovered populations of radio sources?

The cosmic radio background (CRB) has been well studied at high frequencies by instruments such as COBE and WMAP, but is less well studied at low frequencies.

Fixsen et al. (Reference Fixsen2011) measured the background sky temperature at five frequencies between 3 and 90 GHz using an in situ calibrator on board the balloon-borne ARCADE2 experiment. These authors found an excess radio sky temperature above that due to the cosmic microwave background (CMB) below 10 GHz. The CRB was measured to have an excess of 50±7 mK at 3.3 GHz above a CMB temperature of 2.730 ± 0.004 K, which is a factor of five higher than expected from known source populations.

The ARCADE2 result is either due to an instrumental or calibration problem (e.g. incorrectly subtracting the Galactic foreground emission), or it is a startling result which will necessitate a drastic revision of our models of extragalactic radio sources. Given that Fixsen et al. (Reference Fixsen2011) appear to have taken careful steps to avoid errors, there is a prima facie case that this result is correct, and the radio-astronomical community has been galvanised to search for this putative new population. Since it is inconsistent with known radio source populations (e.g. De Zotti et al. Reference De Zotti, Massardi, Negrello and Wall2010; Padovani Reference Padovani2011), it must, if confirmed, be caused by another population. For example, the radio emission could be caused by dark matter annihilation (Fornengo et al. Reference Fornengo, Lineros, Regis and Taoso2011), in which case the emission would trace the dark matter distribution of cluster galaxies, resulting in a scale size of ~ arcmin. Other mechanisms are also possible, such as diffuse emission from clusters or haloes, or very low surface brightness emission from extended AGN radio lobes, or from a population of dwarf galaxies.

Condon et al. (Reference Condon2012) have conducted a deep survey with the VLA which shows that the ARCADE2 result cannot be caused by a population of compact objects spatially associated with galaxies. It is therefore either due to a diffuse population of objects which cannot be detected with the shortest baselines of the VLA observations, or they are due to an instrumental or calibration error. A number of observational programs continue with the VLA and ATCA to determine the cause of this result.

3.1.4 Simulations

There is widespread agreement that the SKADS continuum sky (Wilman et al. Reference Wilman2008) represents the current state of the art in simulations of the radio sky. Such simulations have two distinct functions.

• • They represent useful approximations to the real sky which can be used to test algorithms and design surveys.

• • They can be viewed as an attempt to encapsulate the current ‘best knowledge’ of the sky, and can therefore be used to test models of radio source evolution.

These two functions have different implications for future updates of the SKADS continuum sky. For example, the SKADS continuum sky was constructed from the best information then available of the radio luminosity functions (RLFs) of different populations of radio objects, and deeper and wider surveys have since become available. The SKADS simulation also assumes that sources are members of distinct populations, omitting the composite sources in which both star formation and AGN activity contribute to their radio luminosity. Such small differences from the real sky are unlikely to be important for the design of a survey, but will be important if SKADS is to be used to test theoretical models.

A useful, and relatively simple, modification to the SKADS continuum sky would be to change the assumed luminosity function for one or more of the populations in order to assess how that might influence the results of various continuum surveys. This change might be implemented in a parametric way, allowing users to specify parameters of a luminosity function.

More difficult would be an attempt to incorporate ‘best knowledge’, with the aim of producing ‘realistic’ sky images. Experience from the Herschel mission bolsters the concern that identifying and incorporating information can be extremely difficult. Similarly, incorporating polarisation information would be useful, so that one could calculate Faraday RMs, but would be quite difficult in practice because of the need to trace the geodesic of a photon in order to determine the RM. Nevertheless, there are efforts underway to insert realistic source shapes into the SKADS sky, and the SKADS team is investigating how to add the signature of the cosmic dipole.

It would be very useful to include models of more complex structures in the SKADS sky, such as those of large radio sources, diffuse cluster sources, and structures near the Galactic plane, which could potentially limit the lowest Galactic latitude to which an ‘all-sky’ survey could probe. However, as described in Section 4.3, imaging a field containing many compact sources may have similar issues as to imaging a field containing large-scale structure.

3.2.1 Measuring star formation rates from radio observations

At redshifts between 1 ≲ z ≲ 3, when galaxies were undergoing rapid evolution, the star formation activity appears to have been dominated by dusty, heavily obscured, starbursting galaxies (e.g. Chary & Elbaz Reference Chary and Elbaz2001; Caputi et al. Reference Caputi2007; Magnelli et al. Reference Magnelli2010; Murphy et al. Reference Murphy, Chary, Dickinson, Pope and Lin2011). Optical and near-infrared observations are therefore seriously hampered by dust extinction. Thus, deep radio continuum surveys provide an important tool for measuring the cosmic star formation history of the Universe.

A key result from the next generation of wide and deep radio surveys will therefore be the measurement of the radio luminosity due to star formation in a wide range of galaxies. Converting this radio luminosity to a SFR depends on a conversion factor which is principally based on the infrared/radio correlation (Yun et al. Reference Yun, Reddy and Condon2001; Bell Reference Bell2003; Seymour et al. Reference Seymour2008). However, this correlation has not yet been well determined at the high end of the luminosity function, since the number of ultraluminous IR galaxies (ULIRGs) in these papers is very small, or at high redshifts, although evidence so far suggests the correlation remains constant (Mao et al. Reference Mao, Huynh, Norris, Dickinson, Frayer, Helou and Monkiewicz2011a).

At high redshifts, however, we know that the comoving SFR density is increasingly dominated by more luminous galaxies (with naturally higher SFRs). In Figure 8, we show the comoving infrared luminosity density, a proxy for the comoving SFR density, as a function of redshift. We also separate the contribution by infrared luminosity and find that ULIRGs represent an increasing fraction of the total star formation budget above a redshift of unity. Hence, if we are to use deep radio surveys to probe the star formation history of the Universe at high redshift, we must obtain a considerably more accurate conversion of the radio luminosity to SFR for galaxies with high SFRs. This conversion factor could also depend upon other parameters such as stellar mass, environment, and metallicity.

Figure 8. The comoving infrared luminosity density of SF galaxies as a function of redshift, separated into four infrared luminosity ranges. The shaded regions are from Le Floc’h et al. (Reference Le Floc’h2005) and the bold points are derived from the analysis of faint radio sources in the 13H field (Seymour et al. Reference Seymour2008) where the SF radio luminosities have been converted to infrared luminosities using the relation of Bell (Reference Bell2003). The faint, grey points are from the compilation of Hopkins & Beacom (Reference Hopkins and Beacom2006) converted to IR luminosity density. The figure shows that ULIRGs make an increasing contribution to the total star formation budget above redshifts of unity.

3.2.2 Measuring SFRs at 10 GHz

Radio continuum emission from galaxies typically arises from two processes that are both tied to the massive SFR. At low frequencies (e.g. ≲ 2 GHz), the radio continuum is dominated by non-thermal synchrotron emission arising from cosmic-ray (CR) electrons that have been accelerated by shocks from supernova remnants and are propagating through a galaxy’s magnetised ISM. This physical link to massive star formation provides the foundation for the far-infrared (FIR)–radio correlation (e.g. Helou, Soifer, & Rowan-Robinson Reference Helou, Soifer and Rowan-Robinson1985; Condon Reference Condon1992; Yun et al. Reference Yun, Reddy and Condon2001; Murphy et al. Reference Murphy2006). However, this link is not at all direct given that there are a large number of physical processes affecting the propagation of CR electrons and the heating of dust (e.g. CR diffusion, magnetic field strength/structure, dust grain sizes and composition) that must conspire together to keep this relation intact (Bell Reference Bell2003).

High frequency (~10–100 GHz) radio emission, on the other hand, offers a relatively clean way to quantify the current star formation activity in galaxies. At these frequencies, emission is generally optically thin and dominated by free–free radiation, which is directly proportional to the ionising photon rate of young, massive stars. While this picture could be complicated by the presence of anomalous dust emission (e.g. Kogut et al. Reference Kogut, Banday, Bennett, Gorski, Hinshaw and Reach1996; de Oliveira-Costa et al. Reference de Oliveira-Costa, Kogut, Devlin, Netterfield, Page and Wollack1997; Leitch et al. Reference Leitch, Readhead, Pearson and Myers1997), which occurs at these frequencies and is thought to arise from spinning dust grains (e.g. Erickson Reference Erickson1957; Draine & Lazarian Reference Draine and Lazarian1998), it is currently unclear whether this component contributes significantly to globally integrated measurements (Murphy et al. Reference Murphy2010). Thus, higher frequency radio observations may be particularly powerful for precisely measuring the star formation history of the Universe unbiased by dust.

For example, surveys at ν ≳ 10 GHz start to probe the rest-frame ν ≳ 30 GHz emission from SF galaxies by z≳2 for which ≳50% of the emission is thermal (free–free). This is illustrated in Figure 9, where the thermal fraction of the observed 10- and 1.4-GHz emission is shown against redshift for SF galaxies having intrinsic magnetic field strengths of 10, 50, and 100 μG while still obeying the FIR–radio correlation at z = 0. In addition to measuring higher rest-frame frequencies with increasing redshift, this calculation also accounts for the suppression of a galaxy’s non-thermal emission due to rapid cooling of CR electrons from inverse Compton (IC) scattering off the CMB, whose radiation field energy density scales roughly as U _CMB~(1 + z)⁴ (Murphy Reference Murphy2009). By z ≳ 4, nearly 80% of observed 10-GHz radio continuum is due to free–free emission for a galaxy having a large (i.e. 50 μG) magnetic field.

Figure 9. The fraction of radio emission of SFG due to thermal processes as a function of redshift. Galaxy magnetic fields of 10 (solid lines), 50 (dashed lines), and 100 μG (dotted lines) are shown. The radio emission from observations at 10 GHz is dominated by free–free processes beyond a redshift of z≳2 even for magnetic field strengths of ~100 μG, making it an ideal measure for the current SFR of high-z galaxies (Murphy Reference Murphy2009).

Additionally, we can compare the relative sensitivity requirements of surveys at 10 and 1.4 GHz to detect cosmologically important galaxies at early epochs.

This is shown in Figure 10, where we show the expected 10- and 1.4-GHz flux densities from galaxies having a range in IR (8–1000 μm) luminosities and an intrinsic magnetic field of 50 μG. This figure essentially shows the selection function of radio surveys to SF galaxy populations as a function of redshift. While higher frequency surveys need to be much more sensitive to detect the same luminosity class of galaxies at 1.4 GHz, this becomes less of a problem at higher redshifts. For example, by z≳4, the sensitivity requirement of a 10-GHz survey is less than a factor of ~2 deeper than a corresponding 1.4-GHz survey to detect the same population of SF systems. For an intrinsic magnetic field of 10 μG, this small discrepancy between point source sensitivity requirements for 10- and 1.4-GHz surveys occurs at a z≳2. Given that high-frequency observations are almost as sensitive to high-z SF galaxies as low-frequency observations, and that higher frequency observations provide a much more robust measure of star formation activity, surveys at ν≳10 GHz will be invaluable for accurately tracing the star formation history of the Universe.

Figure 10. The expected 10 GHz (solid line) and 1.4 GHz (dotted line) flux densities for galaxies of different IR luminosities assuming an intrinsic magnetic field strength of 50 μG. The depths of possible future surveys taken by the VLA, MeerKAT (MIGHTEE), and SKA are shown. Since the non-thermal emission from SF galaxies should be suppressed by increased IC scattering of CR electrons off of the CMB, the discrepancy between the point source sensitivity requirements of surveys at 1.4 and 10 GHz falls below a factor of ~2 by z ≳ 4.

Figure 10 also shows the expected depths from potential continuum surveys using the VLA, MeerKAT, and SKA. The tentative Tier 4 and 5 steps of the MIGHTEE survey plan to map 0.25 and 0.01 deg² down to an rms of 1 and 0.2  μJy at 12 GHz, respectively. Although the precise area on the sky has not yet been defined, obvious targets are the Chandra Deep Field-South and COSMOS fields. While the depth of a megasecond exposure is shown for the VLA, the area of such a survey would be restricted by the small primary beam at 10 GHz (θ_PB ≈ 4 – 5 arcmin). However, VLA surveys reaching μJy depths for entire fields such as GOODS-N at 10 GHz have already been proposed, allowing synergy with future ALMA observations. Clearly, the SKA will revolutionise any such high-frequency continuum surveys using either the VLA or MeerKAT by being ≳2 orders of magnitude deeper for the same integration times.

3.3.1 The AGN component in deep radio fields

Radio source counts at μJy levels are dominated by SF galaxies, but their contribution decreases rapidly with increasing flux density (e.g. Seymour et al. Reference Seymour2008), and AGNs contribute significantly at radio fluxes below 1 mJy (e.g. Gruppioni et al. Reference Gruppioni1999; Georgakakis et al. Reference Georgakakis, Mobasher, Cram, Hopkins, Lidman and Rowan–Robinson1999; Magliocchetti et al. Reference Magliocchetti, Maddox, Wall, Benn and Cotter2000; Prandoni et al. Reference Prandoni, Gregorini, Parma, de Ruiter, Vettolani, Zanichelli, Wieringa and Ekers2001; Afonso et al. Reference Afonso, Mobasher, Koekemoer, Norris and Cram2006; Norris et al. Reference Norris2006; Mignano et al. Reference Mignano, Prandoni, Gergorini, Parma, de Ruiter, Wieringa, Vettolani and Ekers2008; Smolčić et al. Reference Smolčić2008; Padovani et al. Reference Padovani, Mainieri, Tozzi, Kellermann, Fomalont, Miller, Rosati and Shaver2009). Recent estimates of their relative contributions are summarised in Figure 5.

Models of the sub-mJy radio population (e.g. Wilman et al. Reference Wilman2008) therefore include three main components:

• • SF galaxies,

• • The extrapolation to low flux densities of the classical radio-loud AGN population (radio galaxies and radio-QSOs),

• • A radio-quiet (or low-luminosity) AGN component.

The unexpected presence of large numbers of AGN-type sources at sub-mJy levels implies a large population of low/intermediate power AGNs, which may have important implications for the black hole-accretion history of the Universe. It will be particularly important to determine the accretion mode (see Section 3.3.2) of these low-power AGNs.

Radio and optical studies of the Australia Telescope ESO Slice Project (ATESP) sub-mJy sample (Prandoni et al. Reference Prandoni, Parma, Wieringa, de Ruiter, Gregorini, Mignano, Vettolani and Ekers2006; Mignano et al. Reference Mignano, Prandoni, Gergorini, Parma, de Ruiter, Wieringa, Vettolani and Ekers2008) have shown that at fluxes 0.4 < S < 1 mJy, a prominent class of low-luminosity (P < 10²⁴ W Hz⁻¹) AGNs associated with early-type galaxies appears. These sources have typically flat or inverted radio spectra (α> − 0.5) and compact sizes (d<10–30 kpc). This source class produces a flattening of the average spectral index at flux densities around 0.5–1 mJy. A similar flattening has been found also in deep low-frequency (350 MHz) surveys (Owen et al. Reference Owen, Morrison, Klimek and Greisen2009; Prandoni et al. Reference Prandoni, Bernardi, Vincenzo and de Bruyn2011). Radio spectral index studies (e.g. Prandoni et al. Reference Prandoni, de Ruiter, Ricci, Parma, Gregorini and Ekers2010) suggest that this class of objects is presumably associated with core-dominated self-absorbed FRI-like radio galaxies, perhaps representing a low-luminosity extension of the classical radio-loud radio galaxy population, which dominates at flux densities S≫1 mJy. On the other hand, deeper radio fields have shown that flat/inverted radio spectra become less frequent at lower flux densities (100 < S < 400 μJy) (Owen et al. Reference Owen, Morrison, Klimek and Greisen2009; Prandoni et al. Reference Prandoni, Morganti and Mignano2009), where steep-spectrum SF galaxies and radio-quiet AGNs are increasingly important.

Our current understanding of the AGN component in deep radio fields can be summarised as follows:

• • above flux densities S ~ 400 μJy, there is no clear evidence for a radio-quiet AGN component;

• • sub-mJy radio-loud AGNs are mostly low-power, compact (self-absorbed) jet-dominated systems, and seem to be a low power counterpart of the classical bright radio galaxy population;

• • at lower flux densities, radio-quiet AGNs become increasingly important and at S ~ 100 μJy they account for about 45% of the overall AGN component;

• • radio-quiet AGNs show radio/optical/IR properties consistent with radio follow-up of optically selected radio-quiet AGNs (Kukula et al. Reference Kukula, Dunlop, Hughes and Rawlings1998), compact radio sizes, steep radio spectra, luminosities of P < 10²⁴ W Hz⁻¹, and Seyfert-2 optical spectra and/or mid-IR colours.

Multiwavelength analyses of larger and deeper radio samples are needed to confirm these results, and to obtain quantitative constraints for evolutionary modelling of faint AGNs. We can expect this field to move forward significantly in the next years, thanks to the combination of wide-field and all-sky surveys (sampling large local volumes) and very deep fields (sampling low powers at high redshifts) planned with the facilities described in this paper. An example of what can be obtained is illustrated in Figure 11, where we show the AGN luminosity function at different redshifts that can be derived from the combination of EMU and MIGHTEE.

Figure 11. AGN luminosity function at different redshifts expected from the combination of ASKAP and MeerKAT deep surveys (based on models described by Prandoni, de Ruiter, & Parma Reference Prandoni, de Ruiter, Parma and Lobanov2007).

3.3.2 Accretion modes

AGN activity, and associated black-hole growth, occurs in at least two different modes, each of which may have an associated feedback effect upon the AGN host galaxy:

1. (i) A fast accretion mode (often referred to as cold-mode accretion or quasar-mode accretion) associated with quasars (Silk & Rees Reference Silk and Rees1998); this radiatively efficient accretion mode may be important in curtailing star formation at high redshifts and setting up the tight relationship between black hole and bulge masses observed in the nearby Universe (e.g. Magorrian et al. Reference Magorrian1998).

2. (ii) A radiatively inefficient slow accretion mode (often referred to as hot-mode accretion or radio-mode accretion) (Croton et al. Reference Croton2006; Bower et al. Reference Bower, Benson, Malbon, Helly, Frenk, Baugh, Cole and Lacey2006), the observational manifestation of which is low-luminosity radio sources; this mode is thought to be responsible for maintaining elliptical galaxies at lower redshifts as ‘old, red and dead’ (e.g. Best et al. Reference Best, Kaiser, Heckman and Kauffmann2006) and for preventing strong cooling flows in galaxy clusters (e.g. Fabian et al. Reference Fabian2003).

One of the most fundamental issues in understanding the role of AGNs in galaxy formation is the need to measure accurately the cosmic evolution of quasar activity and the accretion history of the Universe, and to compare this with the build-up of the stellar populations of galaxies. Do black holes and their host galaxies grow coevally, or does one precede the other? What is the primary mode of black hole growth?

Much of the growth of black holes is believed to occur in an obscured phase, and these ‘Type-2’ AGNs are difficult to identify. Even the deepest current X-ray observations do not detect the most heavily absorbed sources which cosmic X-ray background synthesis models predict exist in abundance (e.g. Gilli et al. Reference Gilli, Comastri and Hasinger2007), implying that much high-z quasar activity has yet to be detected directly. These ‘radio-quiet’ quasars are not radio-silent, and their radio luminosity distribution peaks at about L _1.4GHz≈10²³ W Hz⁻¹ (e.g. Cirasuolo et al. Reference Cirasuolo, Celotti, Magliocchetti and Danese2003). Deep radio surveys with the SKA pathfinders therefore offer an alternative route to identifying these distant AGNs, in a manner unbiased by dust and gas absorption at other wavelengths. Combined with multiwavelength data sets to separate source populations, the relative contribution of radio-quiet AGNs to the faint radio source population can be determined. This will enable investigation of the dependence of the fraction of obscured AGNs on luminosity and cosmic epoch, and thus the history of radiatively efficient accretion in the Universe to be determined.

The deep and wide radio surveys will also allow study of the role of low-luminosity radio sources in galaxy evolution. The low-luminosity radio-AGN population is dominated by a population of sources in which there is little evidence for radiative emission from an accretion disc, and the bulk of the accretion power is channelled into the expanding radio jets (e.g. Merloni & Heinz Reference Merloni and Heinz2007; Hardcastle et al. Reference Hardcastle, Evans and Croston2007; Best et al. Reference Best and Heckman2012). These jets pump energy into their environments, inflating cavities and bubbles in the surrounding intergalactic and intracluster medium (ICM), from which estimates of the mechanical energy associated with the jets can be made (e.g. Cavagnolo et al. Reference Cavagnolo, McNamara, Nulsen, Carilli, Jones and Bîrzan2010). Studies of radio AGNs in the nearby Universe have shown that the fraction of galaxies that host radio-loud AGNs (with L _1.4GHz>10²³ W Hz⁻¹) is a strong function of stellar mass (e.g. Best et al. Reference Best, Kauffmann, Heckman, Brinchmann, Charlot, Ivezić and White2005), and that the time-averaged energetic output associated with recurrent radio source activity may indeed be sufficient to control the rate of growth of massive galaxies. However, sensitivity limits of current large-area radio surveys mean that these low-luminosity sources are only observed in the nearby Universe. How does the relation between galaxy mass and radio-AGN fraction (the radio source duty cycle) evolve with redshift out to the peak epoch of galaxy formation? Out to what redshift does radio-AGN heating continue to balance cooling? What is the differential evolution of the radiatively efficient and inefficient accretion modes (cf. Best et al. Reference Best and Heckman2012), and is evidence for ‘down-sizing’ in the radio source population (e.g. Rigby et al. Reference Rigby, Best, Brookes, Peacock, Dunlop, Röttgering, Wall and Ker2011) confirmed? What drives these processes? These are all questions for the next-generation radio arrays, coupled with high-quality multiwavelength data sets. Large-area surveys are required in order to study a sufficient volume to include the full range of galaxy environments, given the very important role that large-scale environment can play in the evolution of galaxies.

3.3.3 Ultra-steep spectrum radio sources below the mJy barrier

Another exciting prospect for the upcoming generation of radio continuum surveys is that of finding complete populations of high-redshift radio galaxies (HzRGs). These are among the most luminous galaxies and seem to be associated with the most massive systems (e.g. van Breugel et al. Reference van Breugel, De Breuck, Stanford, Stern, Röttgering and Miley1999; Jarvis et al. Reference Jarvis, Rawlings, Eales, Blundell, Bunker, Croft, McLure and Willott2001a; Willott et al. Reference Willott, Rawlings, Jarvis and Blundell2003; Rocca-Volmerange et al. Reference Rocca-Volmerange, Le Borgne, De Breuck, Fioc and Moy2004; De Breuck et al. Reference De Breuck, Downes, Neri, van Breugel, Reuland, Omont and Ivison2005; Seymour et al. Reference Seymour2007) often going through a phase of violent star formation at the 1 000 M_⊙ yr⁻¹ level and showing large gas and dust reservoirs (e.g. Dunlop et al. Reference Dunlop, Hughes, Rawlings, Eales and Ward1994; Ivison Reference Ivison1995; Hughes, Dunlop, & Rawlings Reference Hughes, Dunlop and Rawlings1997; Ivison et al. Reference Ivison1998; Papadopoulos et al. Reference Papadopoulos, Röttgering, van der Werf, Guilloteau, Omont, van Breugel and Tilanus2000; Archibald et al. Reference Archibald, Dunlop, Hughes, Rawlings, Eales and Ivison2001; Klamer et al. Reference Klamer, Ekers, Sadler, Weiss, Hunstead and De Breuck2005; Reuland et al. Reference Reuland2003, Reference Reuland, Röttgering, van Breugel and De Breuck2004, Reference Reuland2007; but see Rawlings et al. Reference Rawlings, Willott, Hill, Archibald, Dunlop and Hughes2004). HzRGs are considered to be the progenitors of the brightest cluster ellipticals and have been used as beacons to identify overdensities in the distant universe, i.e. proto-cluster environments at z ~ 2.5 (e.g. Stevens et al. Reference Stevens2003; Venemans et al. Reference Venemans2007). Identifying and tracing the evolution of HzRGs offers a unique path to study galaxy and large-scale structure formation and evolution from the earliest epochs, and extensive studies will finally become possible over the next few years.

Until recently, searches for HzRGs have been limited to wide-area (and thus relatively shallow) surveys. This is appropriate as the luminosities of HzRGs are large enough to make them detectable to very high redshifts (beyond z~5) at flux densities of tens or even hundreds of mJy. For example, TN J0924−2201, the most distant known radio galaxy at z = 5.2, exhibits a 1.4-GHz flux of over 70 mJy (De Breuck et al. Reference De Breuck, van Breugel, Röttgering and Miley2000; van Breugel et al. Reference van Breugel, De Breuck, Stanford, Stern, Röttgering and Miley1999). But understanding a population, its origin and evolution, and how it fits in the overall galaxy population requires more than just the detection and study of the most extreme objects. The selection of more complete samples, over a wider redshift range, requires deeper surveys over wide areas. However, the large population of low-z (z ≲ 1–2) SF galaxies at sub-mJy levels presents a considerable difficulty for studies of HzRGs, as efficient ways of distinguishing between AGNs and SF galaxies are then necessary.

One of the most successful tracers of HzRGs relies on the relation between the radio spectral index and redshift (e.g. Tielens, Miley, & Willis Reference Tielens, Miley and Willis1979; Chambers et al. Reference Chambers, Miley, van Breugel and Huang1996). Although an ultra-steep (radio) spectrum (USS; α ≲ −1) is not a necessary condition for a high redshifts, and, in fact, the USS selection misses a possibly large fraction of HzRGs (e.g. Waddington et al. Reference Waddington, Windhorst, Cohen, Partridge, Spinrad and Stern1999; Jarvis et al. Reference Jarvis, Rawlings, Willott, Blundell, Eales and Lacy2001b, Reference Jarvis, Teimourian, Simpson, Smith, Rawlings and Bonfield2009; Schmidt, Connolly, & Hopkins Reference Schmidt, Connolly and Hopkins2006), a higher fraction of high-redshift sources can be found among those with the steepest radio spectra. The USS criterion is so effective that most of the radio galaxies known at z>3.5 have been found using it (see Miley & De Breuck Reference Miley and De Breuck2008, for an overview of the selection of HzRGs). Surprisingly, there is still no satisfactory explanation for this spectral index–redshift correlation, as neither (a) a combination of an increased spectral curvature with redshift and the redshifting of a concave radio spectrum (e.g., Krolik & Chen Reference Krolik and Chen1991) to lower radio frequencies nor (b) radio jets expanding in dense environments, more frequently observed in distant proto-clusters, which would appear with steeper spectral indices (Klamer et al. Reference Klamer, Ekers, Bryant, Hunstead, Sadler and De Breuck2006; Bryant et al. Reference Bryant, Johnston, Broderick, Hunstead, De Breuck and Gaensler2009; Bornancini et al. Reference Bornancini, O’Mill, Gurovich and Lambas2010) seem to explain the observations.

With the next generation of radio continuum surveys, the search for USS HzRGs will be extended to the whole sky and to microJansky flux levels. Although such collections have been assembled before (e.g. Bondi et al. Reference Bondi2007; Owen et al. Reference Owen, Morrison, Klimek and Greisen2009; Afonso et al. Reference Afonso, Heald and Serra2009; Ibar et al. Reference Ibar, Ivison, Biggs, Lal, Best and Green2009), only very recently has it been possible to characterise them. Using deep optical and infrared imaging of the Lockman Hole, Afonso et al. (Reference Afonso2011) have started a detailed analysis of the μJy USS radio source population, something that will be possible over a significant fraction of the sky using radio surveys such as EMU, WODAN, and LOFAR.

This first detailed analysis of the USS μJy population used the deep multiwavelength coverage of the Lockman Hole. The sample selection was made using ultra deep VLA 1.4-GHz (reaching 6 μJy rms) and GMRT 610-MHz data (15 μJy rms), and resulted in 58 sources with a spectral index of α¹⁴⁰⁰ ₆₁₀ ≤ − 1.3. The deep IR coverage at 3.6 μm and 4.5 μm provided by the Spitzer Extragalactic Representative Volume Survey (SERVS; Mauduit et al. Reference Mauduit2012) resulted in an extremely high identification rate, above the 80% level. Mid-infrared colours are compatible with a significant AGN presence among the radio-faint USS population. Spectroscopic redshifts for 14 sources and photometric redshifts for a further 19 sources were used for the redshift distribution of these sources, ranging from z~0.1 to ~2.8 and peaking at z~0.6 (see Figure 12). Twenty-five sources have no redshift estimate, including the faintest sources at infrared wavelengths, which indicates that higher redshifts are likely in this population. In this respect, they may be similar to the Infrared-Faint Radio Sources (IFRS), first identified by Norris et al. (Reference Norris2006), and which appear to be very high redshift dusty radio galaxies (Garn & Alexander Reference Garn and Alexander2008; Huynh, Norris, & Middelberg Reference Huynh, Norris and Middelberg2010; Middelberg et al. Reference Middelberg, Norris, Tingay, Mao, Phillips and Hotan2008a, Reference Middelberg, Norris, Hales, Seymour, Johnston–Hollitt, Huynh, Lenc and Mao2011a; Norris et al. Reference Norris, Tingay, Phillips, Middelberg, Deller and Appleton2007, Reference Norris2011a; Cameron et al. Reference Cameron, Keith, Hobbs, Norris, Mao and Middelberg2011; Zinn, Middelberg, & Ibar Reference Zinn, Middelberg and Ibar2011).

Figure 12. Redshift distribution for radio-faint USS sources in the Lockman Hole, from Afonso et al. (Reference Afonso2011). Filled histogram denotes sources with a spectroscopic redshift determination, while the open region refers to photometric redshift estimates. A further 25 USS sources (43% of the full sample) exist but with no redshift estimate, mostly at fainter 3.6 μm fluxes and likely to be found at higher redshifts.

A comparison with the SKADS Simulated Skies models (Figure 13) indicates that FRIs and RQ AGNs may constitute the bulk of the USS population at μJy radio flux densities (FRIIs are thought to dominate above the mJy level). According to the models, the USS technique will be as efficient for the selection of very high-z radio sources at μJy fluxes as when applied at much higher flux density levels. This raises exciting prospects for the next generation of wide-field radio surveys, as it increases the potential for detailed studies of sources at very high redshifts and understanding of the evolution of the AGN activity in the Universe.

Figure 13. Predictions from the SKADS simulated skies models for the redshift distributions of radio source populations, irrespective of their radio spectral indices, for a radio survey reaching a detection sensitivity of 100 μJy at 610 MHz over 0.6 deg², similar to the Lockman Hole radio survey considered in Afonso et al. (Reference Afonso2011). The observed redshift distribution for USS sources in that work is also displayed.

These prospects are strengthened by the recent work of Ker et al. (Reference Ker, Best, Rigby, Röttgering and Gendre2012), who have shown that redshift and spectral index are correlated in spectroscopically complete samples, and argue that this is due both to the dense intergalactic medium and the early evolutionary stage of the AGN, although they, together with Zinn et al. (Reference Zinn, Middelberg, Norris, Hales, Mao and Randall2012), also show that the redshift–spectral index correlation is weaker than other potential redshift indicators.

3.3.4 The luminosity-dependent evolution of the radio luminosity function

Section 3.3.2 described how AGN radio jets interact with the surrounding intergalactic and ICM to prevent both large-scale cluster cooling flows and the continued growth of massive ellipticals (e.g. Fabian et al. Reference Fabian2006; Best et al. Reference Best, Kaiser, Heckman and Kauffmann2006, Reference Best, von der Linden, Kauffmann, Heckman and Kaiser2007; Croton et al. Reference Croton2006; Bower et al. Reference Bower, Benson, Malbon, Helly, Frenk, Baugh, Cole and Lacey2006). Determining the evolution of the RLF is therefore important for understanding the timescales on which they impose these effects.

A key early study of radio-loud AGN by Dunlop & Peacock (Reference Dunlop and Peacock1990) found increases of two to three orders of magnitude at a redshift of two, compared with the local Universe, in the comoving number density of both flat and steep spectrum radio-loud sources. They also saw indications of a high-redshift (z~2.5) decline in density, but their work, and that of subsequent studies in this area (e.g. Shaver et al. Reference Shaver, Wall, Kellermann, Jackson and Hawkins1996; Jarvis et al. Reference Jarvis, Rawlings, Willott, Blundell, Eales and Lacy2001b; Waddington et al. Reference Waddington, Dunlop, Peacock and Windhorst2001), has been limited by the inability to probe the depth and volume necessary to probe the high-redshift behaviour. This has motivated the development of the Combined EIS–NVSS Survey of Radio Sources (CENSORS; Best et al. Reference Best, Arts, Röttgering, Rengelink, Brookes and Wall2003), which has been designed to maximise the information for high-redshift, steep spectrum sources close to the break in the RLF. CENSORS is a 1.4-GHz-selected sample and contains 135 sources complete to a flux density of 7.2 mJy. It is currently 78% spectroscopically complete (Ker et al. Reference Ker, Best, Rigby, Röttgering and Gendre2012), with the remaining redshifts estimated via either the K–z or I–z magnitude–redshift relations.

The CENSORS sample, together with additional radio data, source counts, and local RLF, is used to investigate the evolution of the steep spectrum luminosity function via a new grid-based modelling method in which no assumptions are made about the high-redshift behaviour (Rigby et al. Reference Rigby, Best, Brookes, Peacock, Dunlop, Röttgering, Wall and Ker2011). Instead, the RLF variations are determined by allowing the space densities at various points on a grid of radio luminosities and redshifts to each be free parameters, and then simply finding the best-fitting values to this many-dimensional problem. The modelling finds conclusive evidence, at >3σ significance, for a luminosity-dependent high-redshift decline in space density for the steep-spectrum sources. At low radio powers (P _1.4GHz=10²⁵–10²⁶ W Hz⁻¹) the space densities peak at z ≳ 1, but move to higher redshift for the higher powers (z ≳ 3 for P _1.4GHz>10²⁷ W Hz⁻¹). This is illustrated in Figure 14, and is similar to the ‘cosmic downsizing’ seen for other AGN populations (e.g. De Zotti et al. Reference De Zotti, Massardi, Negrello and Wall2010; Wall Reference Wall2008; Hasinger, Miyaji, & Schmidt Reference Hasinger, Miyaji and Schmidt2005; Richards et al. Reference Richards2005). These results are robust to the estimated redshift errors and to variation in the radio spectral index with redshift.

Figure 14. The dependence of the redshift of the peak in space density (z _peak) on radio power for the best-fitting steep spectrum grid, showing that the numbers of the most powerful radio sources peak at the highest redshifts (Rigby et al. Reference Rigby, Best, Brookes, Peacock, Dunlop, Röttgering, Wall and Ker2011). The shaded region and error bars give two different determinations of the spread in the measurements.

The evolution of low-luminosity radio AGNs is less well understood than that of radio-loud AGNs, with some studies finding no evidence for any evolution of the RLF for low-luminosity radio AGNs (e.g. Clewley & Jarvis Reference Clewley and Jarvis2004) and others finding that low-luminosity AGNs (LLAGNs) do evolve with redshift, although more slowly (less than a factor of 10 from z = 0 to 1.2) than their high-luminosity counterparts (Smolčić et al. Reference Smolčić2009; McAlpine & Jarvis Reference McAlpine and Jarvis2011). Best et al. (Reference Best and Heckman2012) suggest that the luminosity dependence of the evolution of the AGN RLF may be attributed to the varying fractions of hot and cold mode sources with redshift. Recent results (Mauch & Sadler Reference Mauch and Sadler2007; Sadler et al. Reference Sadler2007; Padovani et al. Reference Padovani, Miller, Kellermann, Mainieri, Rosati and Tozzi2011; Mao et al. Reference Mao2012) fail to resolve this discrepancy, with ambiguity added by factors such as evolution, cosmic variance, differences in classification, differences in terminology, and the difficulty of distinguishing LLAGNs from SF galaxies, or the bulge from the disc of a galaxy. Next-generation radio surveys using SKA pathfinders can resolve this discrepancy provided we develop reliable techniques for distinguishing the AGN component from the SF component of a galaxy.

3.3.5 Environment

Studies of galaxies in groups and clusters by Best et al. (Reference Best, von der Linden, Kauffmann, Heckman and Kaiser2007) and Wake et al. (Reference Wake, Croom, Sadler and Johnston2008) have shown that the environment of a radio galaxy has a significant effect on the radio emission. Sabater et al. (Reference Sabater, Leon, Verdes-Montenegro, Lisenfeld, Sulentic and Verley2008, Reference Sabater, Verdes–Montenegro, Leon, Best and Sulentic2012) built on this result by comparing (a) the radio AGN activity in a sample of isolated galaxies (AMIGA sample; Verdes-Montenegro et al. Reference Verdes–Montenegro, Sulentic, Lisenfeld, Leon, Espada, Garcia, Sabater and Verley2005) with that of a matched sample of galaxies in clusters (Miller & Owen Reference Miller and Owen2001; Reddy & Yun Reference Reddy and Yun2004) and (b) the optical AGN activity for the AMIGA sample with that of a matched sample of galaxies in compact groups (Martinez et al. Reference Martinez2010). The results of all these studies show that radio AGN activity is strongly influenced by the environment while this influence is less clear for optical AGN activity (Miller et al. Reference Miller, Nichol, Gómez, Hopkins and Bernardi2003).

3.3.6 Black hole spin

A further area of study from radio observations is the study of black hole physics. For a given accretion rate, as traced by the X-ray to mid-infrared SED, AGNs show a huge range of radio luminosities. This suggests that some extra parameter, independent of the accretion rate, is controlling the jet power of the AGN. The spin of the black hole is a very attractive candidate, for both observational and theoretical reasons (e.g. Wilson & Colbert Reference Wilson and Colbert1995). Spin is effectively a hidden parameter, which will barely show itself in the SED of the AGN. In addition, spinning black holes can convert rotational energy into jet power, meaning that jets can be powered with nominal efficiencies close to or exceeding unity. Observations of the most powerful radio AGNs suggests the jet power is comparable or larger than the rate of accretion of energy (e.g. Fernandes et al. Reference Fernandes2011).

Radio observations allow us to estimate the jet power, and combining these with observations at X-ray energies or optical wavelengths can allow an estimate of the accretion rate and spin. For example, Martínez-Sansigre & Rawlings (Reference Martínez-Sansigre and Rawlings2011) consider the jet powers of SMBHs with m _• ≥ 10⁸ M_⊙. The authors use a suite of semi-analytic models and general relativistic (GR) magnetohydrodynamic (MHD) simulations that predict the jet efficiencies as a function of spin, and find that these efficiencies can approximately explain the radio loudness of optically bright quasars.

Martínez-Sansigre & Rawlings (Reference Martínez-Sansigre and Rawlings2011) also find that they can explain the local RLF of high- and low-excitation galaxies independently (HEGs and LEGs, respectively), and that the HEGs and LEGs have different best-fitting spin distributions. The LEGs, modelled as advection-dominated accretion flows (ADAFs) or low-accretion rate SMBHs, have a bimodal spin distribution, with the SMBHs having typically low (â ~ 0) or high (â ~ 1) spins. The probability density of the high-spin peak is significant, typically ~33% of the total probability density. On the other hand, the HEGs, modelled as SMBHs accreting at a high fraction of their Eddington rate, are found to have typically low spins (â ~ 0 only), with a small or non-existent component of high spin. The radio LFs of HEGs and LEGs given by these spin distributions can be extrapolated to high redshift, where they correctly reproduce the total radio LF of all AGNs at z = 1. Due to the strong evolution of the high-Eddington rate SMBHs (as reflected by the evolution of the X-ray LF), this modelling also predicts that the z = 1 radio sources above a radio luminosity density ~10²⁶ W Hz⁻¹ sr⁻¹ (at 151 MHz) should show exclusively HEG spectra, while the fraction of LEGs should increase rapidly at lower radio luminosity densities.

Since the space density of HEGs increases rapidly, the typical spin of SMBHs will change with redshift. At z~0, most of the SMBHs will have the bimodal distribution inferred for the LEGs, with a high fraction of SMBHs having a high spin (Figure 15, top). At z ≳ 1, the space density of HEG radio sources is larger than that of LEG sources, so that the SMBHs will typically have the distribution of spins of the HEGs, dominated by a low-spin component (Figure 15, bottom).

Figure 15. Inferred spin distributions for SMBHs at z = 0 and 1, from Martínez-Sansigre & Rawlings (Reference Martínez-Sansigre and Rawlings2011). The vertical dashed lines mark the mean value at each redshift. Bottom: the spin distribution at z = 1 is dominated by the low-spin population, with a minor component of high-spin SMBHs. Top: at z = 0 a larger fraction of SMBHs possess a high spin, so that the mean spin is higher.

The evolution of the spin from SMBHs (with m _• ≥ 10⁸ M_⊙) can hence be described as evolving from predominantly low spins in high-Eddington rate systems at z ≳ 1, to a bimodal spin distribution at z~0, for mostly low-Eddington rate systems. At the epoch of highest accretion, the typical spin is low and at later epochs the fraction of SMBHs with high spins increases (Figure 16). This can be understood in terms of chaotic accretion (e.g. King, Pringle, & Hofmann Reference King, Pringle and Hofmann2008) spinning the accreting SMBHs down, whereas major mergers spin the SMBHs up (e.g. Rezzolla et al. Reference Rezzolla, Barausse, Dorband, Pollney, Reis-swig, Seiler and Husa2008). At earlier epochs, there is a plentiful supply of cold gas, so that accretion spins SMBHs down. As this gas disappears, however, the breaking mechanism that spins SMBHs down is removed, while some SMBHs will still experience major mergers. Hence, a population of high-spin SMBHs gradually appears.

Figure 16. Top: mean spin of SMBHs with m _• ≥ 10⁸ M_⊙, from Martínez-Sansigre & Rawlings (Reference Martínez-Sansigre and Rawlings2011). There is a gradual increase of the mean spin between z ≳ 1 and z = 0, which is most likely due to a fraction of SMBHs undergoing major mergers and subsequent chaotic accretion. Bottom: cosmological simulation of the mean spin from Fanidakis et al. (Reference Fanidakis, Baugh, Benson, Bower, Cole, Done and Frenk2011), which includes chaotic accretion and mergers, and which is in excellent agreement with the inference based on radio observations (top).

3.4.1 Radio haloes

About 40 giant radio haloes are known so far in the redshift range 0 ≤ z ≤ 0.55. The GMRT Radio Halo Survey (Venturi et al. Reference Venturi, Giacintucci, Dallacasa, Cassano, Brunetti, Bardelli and Setti2008), in combination with the NVSS and WENSS surveys, allows a statistical exploration of radio haloes in galaxy clusters in the redshift range 0 ≤ z ≤ 0.4 (Cassano et al. Reference Cassano, Brunetti, Venturi, Setti, Dallacasa, Giacintucci and Bardelli2008). The cluster radio properties were found to be bimodal: only a fraction of massive clusters host haloes, while no Mpc-scale radio emission is detected in the majority of clusters at current sensitivity levels. The radio luminosity of these ‘radio-quiet’ clusters is less than one-tenth of that of the observed radio haloes (Brunetti et al. Reference Brunetti, Venturi, Dallacasa, Cassano, Dolag, Giacintucci and Setti2007, Reference Brunetti, Cassano, Dolag and Setti2009). X-ray follow-up of these observations shows that radio haloes are found only in merging clusters while ‘radio-quiet’ clusters are systematically more relaxed systems (Cassano et al. Reference Cassano, Ettori, Giacintucci, Brunetti, Markevitch, Venturi and Gitti2010a).

The radio properties of haloes correlate with the thermal properties of the parent clusters and the radio power of haloes increases with X-ray luminosity, suggesting a direct connection between the thermal and non-thermal cluster properties (Feretti et al. Reference Feretti, Dallacasa, Govoni, Giovannini, Taylor and Klein1999, Reference Feretti, Giovannini, Govoni and Murgia2012; Bacchi et al. Reference Bacchi, Feretti, Giovannini and Govoni2003; Cassano et al. Reference Cassano, Brunetti and Setti2006; Brunetti et al. Reference Brunetti, Venturi, Dallacasa, Cassano, Dolag, Giacintucci and Setti2007, Reference Brunetti, Cassano, Dolag and Setti2009).

According to a prominent scenario for the origin of giant radio haloes, a fraction of the gravitational binding energy of dark matter haloes released during cluster mergers can be channelled into turbulence. This turbulence may in turn accelerate relativistic particles (Brunetti et al. Reference Brunetti, Setti, Feretti and Giovannini2001; Petrosian Reference Petrosian2001) explaining the connection observed between radio haloes and cluster mergers.

The source of the synchrotron electrons in these haloes is unclear, as acceleration of electrons from the thermal pool to relativistic energies by MHD turbulence in the ICM cannot provide sufficient energy (Petrosian Reference Petrosian and East2008). Instead, there must be a pre-existing population of relativistic (or supra-thermal) seed particles that are then reaccelerated by turbulent acceleration during mergers. One possibility is that the seeds are secondary electrons generated by collisions between CRs and thermal protons (Brunetti & Blasi Reference Brunetti and Blasi2005; Brunetti & Lazarian Reference Brunetti and Lazarian2011). These hybrid models predict that Mpc-scale synchrotron emission from secondary electrons (‘pure hadronic haloes’) must also be present in relaxed clusters, with a radio luminosity 10–20 times smaller than that of merging clusters (Brunetti & Lazarian Reference Brunetti and Lazarian2011). This emission should be detectable with EMU/WODAN. Figure 17 shows the 1.4-GHz RLF of radio haloes in the local Universe (z = 0.1): at higher radio luminosities, turbulent cluster haloes dominate, but at lower luminosities the RLF is dominated by ‘hadronic’ haloes in relaxed systems. Additional sources of seed supra-thermal electrons include shocks, AGNs, galaxies, and magnetic reconnection, so relaxed clusters may have an even higher radio luminosity. If EMU fails to detect radio haloes in relaxed clusters, this will provide a strong constraint on secondary particles and on the energy content of CRs in the ICM.

Figure 17. Luminosity functions at 1.4 GHz of giant radio haloes in the redshift range 0.1 ≤ z ≤ 0.2. The red dashed line marks the contribution from ‘hadronic’ haloes in relaxed clusters, while the blue dashed line marks the contribution from haloes in merging ‘turbulent’) clusters. The black solid line gives the total luminosity functions (Cassano et al. Reference Cassano, Brunetti, Norris, Röttgering, Johnston–Hollitt and Trasatti2012). The arrows show the EMU and NVSS sensitivities at that redshift.

An extrapolation of the radio power of haloes at 1.4 GHz versus the cluster X-ray luminosity indicates that clusters with L_x < 10⁴⁴ erg s⁻¹ should host haloes of power L _1.4 < 10²³ W Hz⁻¹. With a typical size of 1 Mpc, their surface brightness could be too low to be detected at 1.4 GHz. However, less powerful radio haloes should be also smaller in size (Feretti et al. Reference Feretti, Giovannini, Govoni and Murgia2012), implying that they should be easily detected by the EMU survey. A comparison between 1.4 GHz data with low-frequency data (LOFAR) will be crucial to test turbulence properties. A large number of ‘hadronic haloes’ may be detected at 1.4 GHz (see Figure 17), emphasising the importance of comparing the EMU and LOFAR surveys.

If turbulence is responsible for the origin of haloes, then the radio-emitting electrons are accelerated up to energies m_ec ²γ _m ≤ several GeV, where the synchrotron and IC losses quench the acceleration by MHD turbulence. Radio haloes will therefore steepen at a frequency ν _s ∝γ² _m b, making it difficult to detect haloes at higher frequencies (Brunetti et al. Reference Brunetti2008).

Only the few most energetic mergers in the Universe can generate giant radio haloes with ν _s ≥ 1 GHz (Cassano et al. Reference Cassano and Brunetti2005). Most mergers instead consist of major mergers between less massive systems, or minor mergers in massive systems (Cassano et al. Reference Cassano, Brunetti and Setti2006, Reference Cassano, Brunetti, Röttgering and Brüggen2010b), which will therefore have steeper spectra (smaller ν _s ). Recent Monte Carlo calculations based on turbulent acceleration in galaxy clusters predict that LOFAR, reaching rms =0.1 mJy beam⁻¹ at 120 MHz over the northern hemisphere, will detect more than 350 radio haloes at redshift z ≤ 0.6, increasing the number of known haloes by a factor of nearly ten (Enßlin & Röttgering Reference Enßlin and Röttgering2002; Cassano et al. Reference Cassano, Brunetti and Setti2006). More than half of these haloes will be ‘ultra-steep spectrum’ haloes, with ν _s < 600 MHz (Cassano et al. Reference Cassano, Brunetti, Röttgering and Brüggen2010b), providing a clear test of the importance of turbulence in particle acceleration in merging clusters.

3.4.2 Radio relics

Relics (occasionally termed radio phoenixes) are irregular, elongated diffuse sources which are generally located at the periphery of the cluster, with the linear size of 400–1 500 kpc (Giovannini & Feretti Reference Giovannini and Feretti2002). Most have a steep spectrum (α< −1), and are linearly polarised at a level of ~10%–30%. They show an asymmetric transversal profile and spectral index distribution. Current models suggest that they are caused by diffusive shock acceleration of electrons in old radio-emitting regions, triggered by a cluster merger event. Currently, ~34 clusters are known to contain at least one relic source. Eleven of these also have a radio halo and ten have a double relic.

The existence of relic sources suggest cluster-wide magnetic fields of about 0.1–1 μG and relativistic electrons of ~ GeV energies in large peripheral regions where the density of the hot ICM is low and galaxies are scarce.

Few radio relics have been well studied and few have deep high resolution radio maps, so that their size and flux density may be underestimated. Most radio spectra have been obtained with a limited frequency range and very few spectral index images have been published. Because most relics are located at the cluster periphery, they are often outside, or at the edge, of available X-ray images, making it difficult to compare radio and X-ray data. However, a few relics have been found and studied in detail (e.g. Johnston-Hollitt Reference Johnston–Hollitt2003; van Weeren et al. Reference van Weeren, Röttgering, Brüggen and Hoeft2010; Brown, Duesterhoeft, & Rudnick Reference Brown, Duesterhoeft and Rudnick2011).

A few relics show a curved shape radio spectrum and a diffuse, filamentary morphology. They often have been found near the central cD galaxy, suggesting a possible connection with a past activity of this galaxy, but in A1664 (see Figure 18) and in A548b (Feretti Reference Feretti, Bacchi, Slee, Giovannini, Govoni, Andernach and Tsarevsky2006) the relic is far from the cluster centre.

Figure 18. Radio image (contours) overlaid on X-ray images (colour) of three representative clusters: (top) the radio relic in the cluster A1664 (Govoni et al. Reference Govoni, Feretti, Giovannini, Böhringer, Reiprich and Murgia2001), (centre) the giant radio halo in A2163 (Feretti et al. Reference Feretti, Fusco-Femiano, Giovannini and Govoni2001), and (bottom) the double relic in A3376 (Bagchi et al. Reference Bagchi, Durret, Neto and Paul2006).

Figure 19 compares the radio and X-ray power of radio haloes and relics, showing that both the relic and halo power are correlated with the parent cluster X-ray luminosity, although this may be influenced by selection effects. The relics have a larger dispersion than the haloes, confirming that shocks are more efficient than turbulence in accelerating relativistic electrons or amplifying magnetic fields. This correlation confirms the link between relics and cluster mergers and shows that the SPARCS surveys will enable the study of large-scale magnetic fields in low density regions at the cluster periphery. Such correlations have recently been discussed by Feretti et al. (Reference Feretti, Giovannini, Govoni and Murgia2012).

Figure 19. Halo (blue) and relic (red) radio power at 1.4 GHz in units of W Hz⁻¹ versus cluster X-ray luminosity.

3.4.3 Tailed radio galaxies

Tailed radio galaxies include wide-angle tails (WATs) and narrow-angle tails (NATs). They are common in large clusters (Blanton et al. Reference Blanton, Gregg, Helfand, Becker and White2000, Reference Blanton, Gregg, Helfand, Becker and Leighly2001, Reference Blanton2003) and appear to represent radio-loud AGNs in which the jets are distorted by the ICM (Mao et al. Reference Mao, Sharp, Saikia, Norris, Johnston–Hollitt and Lovell2010a). Mao et al. (Reference Mao, Sharp, Saikia, Norris, Johnston–Hollitt, Middelberg and Lovell2011b) have found six tailed galaxies in the 7 deg² of the Australia Telescope Large Area Survey (ATLAS), suggesting that ~40 000 new clusters will be detected by EMU, using the tailed galaxies as tracers. With higher spatial resolution, more tailed galaxies become visible, and Dehghan et al. (Reference Dehghan, Johnston–Hollitt, Mao, Norris, Miller and Huynh2011), using high-resolution images of the same ATLAS fields, find 12 tailed galaxies in 4 deg², implying ~10⁵ tailed galaxies in EMU. Importantly, such galaxies can be detected out to high redshifts of z~ 0.5 and beyond (Wing & Blanton Reference Wing and Blanton2011; Mao et al. Reference Mao, Sharp, Saikia, Norris, Johnston–Hollitt and Lovell2010a), providing a powerful diagnostic for finding clusters.

3.5.1 The large-scale structure of the Milky Way magnetic field

Knowledge of the strength and orientation of the large-scale magnetic field in the Milky Way is crucial for studies of the origin and evolution of Galactic magnetism, but is also valuable for extragalactic topics such as ultra-high energy CRs, CMB polarisation, and magnetism in external galaxies, galaxy clusters, and intergalactic space.

Models constrained by observational RM data from pulsars, extragalactic sources, and diffuse Galactic synchrotron emission attempt to determine reversals in the spiral magnetic pattern of the Milky Way, and to measure the large-scale configurations of the field in the Milky Way disc and halo (e.g. Beck Reference Beck2011; Noutsos et al. Reference Noutsos, Johnston, Kramer and Karastergiou2008; Van Eck et al. Reference Van Eck2011; Sun et al. Reference Sun, Reich, Waelkens and Enßlin2008; Jansson et al. Reference Jansson, Farrar, Waelkens and Enßlin2009; Nota & Katgert Reference Nota and Katgert2010; Mao et al. Reference Mao, Gaensler, Haverkorn, Zweibel, Madsen, McClure-Griffiths, Shukurov and Kronberg2010b), all of which are key to understanding the evolution of galactic magnetic fields. However, controversy still exists about the existence and location of reversals, and the overall 3D configuration of the magnetic field in the Milky Way’s disc and halo.

Major constraints to these large-scale magnetic field models will come from the rotation measure grid of RMs from compact extragalactic sources, most of which probe Galactic Faraday rotation. The SKA pathfinders ASKAP, LOFAR, APERTIF, and MeerKAT have complementary programs to observe RMs of extragalactic point sources to construct an RM grid with an average density of 100 RMs per square degree over the entire sky. These efforts will provide a polarised source density two orders of magnitude higher than the recent NVSS RM catalogue (Taylor, Stil, & Sunstrum Reference Taylor, Stil and Sunstrum2009), which has already proved useful for a wide range of analyses (e.g. McClure-Griffiths et al. Reference McClure-Griffiths, Madsen, Gaensler, McConnell and Schnitzeler2010; Schnitzeler Reference Schnitzeler2010; Stil, Taylor, & Sunstrum Reference Stil, Taylor and Sunstrum2011).

3.5.2 The turbulent, magnetised interstellar medium

Magnetised turbulence in the ISM plays a major role in many physical processes such as star formation, total ISM pressure equilibrium, CR scattering, gas mixing, and radio wave propagation (Scalo & Elmegreen Reference Scalo and Elmegreen2004).

At high Galactic latitudes, in the Galactic thick disc and halo, RM variations are small, and can be observed at long wavelengths. Spectropolarimetric observations of the Galactic foreground emission at mid-latitudes around 350 MHz, made using WSRT, show a wealth of small-scale polarisation at angular resolutions down to a few arcmin (Haverkorn, Katgert, & de Bruyn Reference Haverkorn, Katgert and de Bruyn2003a, Reference Haverkorn, Katgert and de Bruyn2003b; Schnitzeler et al. Reference Schnitzeler, Katgert, Haverkorn and de Bruyn2007; Schnitzeler, Katgert, & de Bruyn Reference Schnitzeler, Katgert and de Bruyn2009). At even lower frequencies of 150 MHz, Bernardi et al. (Reference Bernardi2009) observed abundant structure in diffuse polarisation at intermediate latitudes. Therefore, LOFAR RM synthesis observations at mid- and high-latitude are expected to discover a wealth of small-scale RM structures in the magneto-ionised gas. This will be used to characterise the power spectrum of magnetic field fluctuations at high latitudes, i.e. in the Galactic gaseous halo and disc–halo connection.

In addition, calculation of the spatial gradient of diffuse polarisation can allow direct visualisation of turbulent structures in the ISM, from which we can infer fundamental properties such as Mach number and Alfvén speed (Gaensler et al. Reference Gaensler2011; Burkhart, Lazarian, & Gaensler Reference Burkhart, Lazarian and Gaensler2012).

Closer to the Galactic plane, the larger RM values will cause partial or complete depolarisation of low-frequency emission, but are well suited to observations with ASKAP, APERTIF, and MeerKAT. The RM grid allows statistical analysis of interstellar magnetised turbulence as a function of position (Haverkorn et al. Reference Haverkorn, Brown, Gaensler and McClure-Griffiths2008), while RM synthesis of the diffuse polarised emission allows disentangling of synchrotron emitting and Faraday rotating layers (Brentjens Reference Brentjens2011). It will also be possible to map out magnetic field strength and structure in discrete structures such as supernova remnants, planetary nebulae, superbubbles, H ii regions, Galactic chimneys, and high-velocity clouds (see, e.g., Beck & Gaensler Reference Beck and Gaensler2004).

3.5.3 Faraday screens

At 1.4 GHz, the diffuse polarised sky typically bears little resemblance to the total intensity sky (e.g. Landecker et al. Reference Landecker2010). A widely accepted interpretation for this characteristic is that the detected polarised features are the signature of Faraday rotation rather than structure in the Galactic synchrotron emission. The exceptions are supernova remnants (Section 3.8.3) and pulsar wind nebulae (Section 3.8.4).

Observations have shown that the synchrotron emission of external galaxies is very smooth and the WMAP results have confirmed that for our Galaxy too. However, at lower radio frequencies, surveys show a lot of small-scale structure caused by Faraday rotation. A typical radio telescope operating in the 1.4-GHz wavelength range proves to be more sensitive to the Faraday rotation of an ionised and magnetised medium than to its bremsstrahlung signature.

The Faraday rotation structures we find in linear polarisation images are called ‘Faraday Screens’. These Faraday Screens are still not well understood. Questions about these features we have to answer include:

• • Are those features created by variation of the magnetic field or the free electron distribution (or a combination of both)?

• • Can we correlate (or anti-correlate) these features with other tracers of the ISM?

• • How can we explain features that do not correlate with anything?

• • Can RM synthesis help to reveal the characteristics of these features?

• • Can we relate these features with structures seen in the RM distribution determined from extra-galactic point sources?

A large wide-field survey such as POSSUM will help to better understand these features and reveal their true nature

3.5.4 Nearby galaxies

Spiral galaxies have typical magnetic field strengths of the order of 10 μG. They typically show ordered field patterns consistent with the spiral pattern in the plane, a higher level of magnetic turbulence in the arms themselves, and an X-shaped configuration in the high-latitude regions. A concise review of the properties of magnetic fields in galaxies is provided by Beck (Reference Beck2009).

The WSRT–SINGS Survey has investigated the global magnetic field properties across a small sample of nearby galaxies with diffuse polarised emission (Braun, Heald, & Beck Reference Braun, Heald and Beck2010). This work showed that azimuthal patterns in polarised intensity and RM (Heald, Braun, & Edmonds Reference Heald, Braun and Edmonds2009) are consistent with a magnetic field configuration consisting of an axisymmetric spiral in the disc and a quadrupolar poloidal pattern away from the plane, as predicted by the dynamo theory of magnetic field amplification (e.g. Widrow Reference Widrow2002). A critical component of the model is that turbulent magnetic fields in the SF disc depolarise synchrotron radiation from the far side of the disc (see Burn Reference Burn1966, for a description of this Faraday dispersion effect). In face-on galaxies this effect, together with trailing spiral arms, results in the observed patterns. At higher and lower radio frequencies, the effects of Faraday dispersion will be reduced and enhanced, respectively, giving rise to different patterns in the polarised synchrotron radiation.

The polarisation surveys planned with ASKAP and LOFAR will thus be complementary in that they will trace ordered magnetic fields in significantly different volumes within nearby galaxies. Although depolarisation by Faraday dispersion is much stronger at LOFAR frequencies, this is mitigated by the fact that CR electrons that have diffused far from their acceleration sites (i.e. regions of massive star formation) will have lower energies because of synchrotron losses. Thus, synchrotron radiation from this aged CR population will peak at LOFAR frequencies, and should trace ordered fields in the far outer regions of galaxies. At the other end of the spectrum, high-frequency observations with MeerKAT and the VLA can ‘see through’ the SF disc, and trace the fields in the SF regions directly. The suite of SKA pathfinders can thereby provide complementary polarimetric studies leading to an ‘onion-peel’ polarimetric view of diffuse synchrotron emission in nearby galaxies.

3.5.5 Magnetic field evolution in galaxies

Beyond the nearby Universe, SKA pathfinder telescopes have insufficient angular resolution to map the synchrotron radiation across discs of galaxies. However, Stil et al. (Reference Stil, Krause, Beck and Taylor2009) have shown that polarised radiation with a preferred, and wavelength-independent, orientation will be detected in unresolved galaxies. Thus statistical studies of the magnetic fields in distant galaxies will be possible. These same sources are also expected to be excellent background probes in the RM grid.

Within the picture of the turbulent dynamo, the amplitude of the regular magnetic fields in galaxies is expected to decrease at higher redshift. The variation of galactic magnetic field strength with epoch may be reflected in the redshift dependence of the FIR/radio correlation (see Murphy Reference Murphy2009).

3.5.6 Galaxy clusters

The ICM of galaxy clusters consists not only of hot thermal gas (T~10⁷–10⁸ K) emitting in the X-ray domain, but also of magnetic fields and relativistic particles that may give rise to synchrotron radio emission. The most direct evidence for the presence of magnetic fields are the so-called radio haloes and radio relics (see Section 3.4). Other evidence for cluster magnetic fields comes from the Faraday rotation of radio sources that lie within or behind the cluster along our line of sight (e.g. Clarke, Kronberg, & Bohringer Reference Clarke, Kronberg and Bohringer2001; Johnston-Hollitt & Ekers Reference Johnston–Hollitt and Ekers2004).

Magnetic fields are thought to play an important role in the development of large-scale structure in the Universe, but their origin and evolution are still poorly understood. Cosmological simulations indicate that the magnetic field strength resulting from the adiabatic compression of the gas falling into the cluster potential well cannot account for more than 1% of the magnetic field strength that is inferred from observations, so that other amplification mechanisms are required (Dolag et al. Reference Dolag, Bykov and Diaferio2008). Cosmological simulations also predict that processes related to the cluster formation, such as merger events and shear flows, can in principle amplify the magnetic field up to the observed values. Hence, measurements of the ICM magnetic field, such as the power spectrum and radial profile, are necessary to test these predictions, and to measure the amplification of the magnetic field during cluster formation. Magnetic fields may also affect thermal conduction in the ICM, and so measuring the magnetic field strength is crucial to understand the origin of the relativistic particles responsible for the radio halo and relic emission.

3.5.7 Faraday rotation measures and ICM magnetic fields

A powerful method to constrain the magnetic field properties in the ICM is to study the Faraday rotation of sources that are within or behind the cluster along our line of sight (e.g. Krause et al. Reference Krause, Alexander, Bolton, Geisbüsch, Green and Riley2009). Recently, Bonafede et al. (Reference Bonafede, Feretti, Murgia, Govoni, Giovannini, Dallacasa, Dolag and Taylor2010) have constrained the magnetic field in the Coma cluster by observing seven sources at different projected distances from the cluster centre. The resulting RM images have been compared with the mock RM images obtained with the FARADAY code (Murgia et al. Reference Murgia, Govoni, Feretti, Giovannini, Dallacasa, Fanti, Taylor and Dolag2004) for different magnetic field configurations. The magnetic field that best reproduces the Coma observations has a central value B ₀ = 4.7 μG, and declines with the gas density profile n according to B(r) = n(r)^0.5. Murgia et al. (Reference Murgia, Govoni, Feretti, Giovannini, Dallacasa, Fanti, Taylor and Dolag2004), Govoni et al. (Reference Govoni, Murgia, Feretti, Giovannini, Dolag and Taylor2006), and Vogt & Enßlin (Reference Vogt and Enßlin2005) have achieved similar results on smaller samples. These studies require deep multi-frequency observations of several sources located at different projected distances from the cluster centre, so only a small number of clusters have been studied. The sensitivity of current radio telescopes is insufficient to study a large number of galaxy clusters with many RM probes per cluster, but the next generation of radio telescopes will make this possible.

3.5.8 Fractional polarisation of radio sources and magnetic field in the ICM

When synchrotron emission from a cluster or background source crosses the ICM, regions with similar intrinsic direction of the polarisation plane, Ψ_int, going through different paths, will be subject to differential Faraday rotation. If the magnetic field in the foreground screen is tangled on scales smaller than the observing beam, radiation with similar Ψ_int but opposite orientation will be averaged out, and the observed degree of polarisation will be reduced (beam depolarisation). In the central region of a cluster, B and n are higher, resulting in a higher RM, and lower fractional polarisation F_P . Sources at larger radii experience a lower RM, and so suffer from less depolarisation.

Bonafede et al. (Reference Bonafede, Govoni, Feretti, Murgia, Giovannini and Brüggen2011) selected a sample of massive galaxy clusters and used the NVSS data (Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998) to analyse the polarisation of radio sources as a function of the projected distance from the cluster centre. They find that, statistically, the fractional polarisation decreases with the cluster projected distance. By comparing this trend with that predicted by magnetic field models, they estimate the magnetic field in the cluster centre to be ~5 μG. The advantage of this approach is that it does not need multi-frequency observations. This effect can be investigated with radio surveys at a single frequency in full polarisation mode. Although such studies do not provide detailed information on magnetic fields in specific clusters, they allow us to understand the average properties of magnetic fields in the ICM, and potentially even on larger scales.

3.5.9 The origin of cosmic magnetism

Galaxies and the ICM can only account for about one-third of the baryon density in the local Universe expected from a concordance cosmology. The majority of the missing matter is likely to reside in a warm–hot intergalactic medium (WHIM), which in turn is expected to reside in the cosmic web of the large-scale structure. Detection of the magnetic field found in this cosmic web, or placing stringent upper limits on it, will provide powerful observational constraints on the origin of cosmic magnetism.

Various mechanisms have been suggested for the origin of magnetic fields in our Universe. One possibility is that the fields are truly primordial and that a seed field formed prior to recombination in the very early Universe (Banerjee & Jedamzik Reference Banerjee and Jedamzik2003). Alternatively, fields could have been produced via the Weibel instability, a small-scale plasma instability formed at structure formation shocks (Medvedev et al. Reference Medvedev, Silva, Fiore, Fonseca and Mori2004). Both of these mechanisms occurred early in cosmic history, prior to galaxy formation, and are therefore referred to as early-type mechanisms. In contrast, possible late-type mechanisms are processes where the field was injected into the WHIM via the action of jets from AGNs and other outflows such as galactic winds (e.g. Kronberg Reference Kronberg2004).

The SKA pathfinder polarisation surveys will together generate a rich data set from which a wide, high-density, broad bandwidth RM grid may be built, and weak magnetic fields in intergalactic filaments may be detected for the first time. A lower limit for the intergalactic magnetic field has been determined (10⁻¹⁵ G; Dolag et al. Reference Dolag, Kachelriess, Ostapchenko and Tomàs2011).

In the filamentary structures of the cosmic web, field strengths are expected to be far more sensitive to the origin of the magnetic fields than in larger gravitationally bound structures where turbulent amplification will have led to saturation of the field. Specifically, the strength and penetration of magnetic fields in filaments is expected to be much lower if the field arises from a ‘late’ astrophysical source (AGNs, galactic winds, etc.), compared with that arising from a primordial one, and simulations have demonstrated that the strength of these turbulently amplified early-type seed fields range typically between 0.1 and 0.01 μG (Ryu et al. Reference Ryu, Kang, Cho and Das2008). Consequently, observations of the filamentary cosmic web are invaluable for inferring the origin of cosmic magnetism. Although the predicted field strengths are extremely low, such RMs are observationally accessible with the SKA pathfinder telescopes.

In addition, the rotation of emission from background radio sources through the large-scale structure filaments within e.g. superclusters of galaxies can also be used to infer the origin of cosmic magnetism. A statistical analysis of these RMs to measure the power spectrum of the magnetic field of the cosmic web (Kolatt Reference Kolatt1998), using cross-correlations with other large-scale structure indicators, will also provide stronger constraints than individual RMs. These measurements will also probe the distribution and density of thermal gas at the interface between clusters and the cosmic web, which has important consequences for a number of related areas in astrophysics and will be highly complementary to X-ray and Sunyaev–Zel’dovich studies of these structures. However, because of the low temperatures of these regions, RM measurements may provide the only way to probe them.

3.5.10 High-redshift rotation measures

Studies of high-redshift objects (e.g. Kronberg et al. Reference Kronberg, Bernet, Miniati, Lilly, Short and Higdon2008, who examined the redshift dependence of the spread of RMs) suggest that the amplification of magnetic fields occurred more rapidly than the expectations of mean-field dynamo theory. The conclusions of this type of work are so far limited by small samples, together with uncertainties in the removal of the Milky Way foreground RM structure. SKA pathfinders will provide RM grids that will enable this kind of study to be done with significantly lower uncertainty. A better comparison with the predictions of dynamo theory (see e.g. Arshakian et al. Reference Arshakian, Beck, Krause and Sokoloff2009) will thus become possible.

3.6.1 Calculating probe predictions

Here we consider the measurements of the three probes discussed above (source count correlations, cosmic magnification, and ISW) and calculate the resulting constraints obtained with the LOFAR, WODAN, and EMU surveys (see Raccanelli et al. Reference Raccanelli2011 for details about the surveys and the assumed distributions and bias).

To predict the redshift distribution for these surveys, we use the latest empirical simulations developed for the SKA continuum survey (Wilman et al. Reference Wilman2008). This simulation provides different prescriptions for the redshift evolution of the various populations which dominate the radio source counts at five different radio frequencies: 150, 610, 1 400, 4 860, and 18 000 MHz. Catalogues are generated from the S ³ database,Footnote ³ using the radio flux-density limits of different surveys, and we perform our analysis by extracting a catalogue from the database with cuts at the 10 σ detection levels of the forthcoming surveys.

The S ³ simulation provides us with a source catalogue in which sources are identified by type (e.g. SB, SFG, FRI, FRII, and RQQ). The bias is computed separately for each galaxy population using the formalism of Mo & White (Reference Mo and White1996), in which each population is assigned a dark matter halo mass chosen to reflect the observed large-scale clustering. With this framework, the increasing bias b(z) with redshift would lead to excessively strong clustering at high redshift, so the bias for each population is held constant above a certain cut-off redshift (see Wilman et al. Reference Wilman2008, for details).

We calculate the angular power spectra for each of the probes, i.e. source-source, radio background–optical foreground, and source CMB. Each of these is a projection of the density power spectrum, see Raccanelli et al. (Reference Raccanelli2011) for details. For instance, the ISW cross-power spectrum is given by

where W^g _ℓ and W^T _ℓ are the galaxy and CMB window functions, respectively, and Δ²(k) is the logarithmic matter power spectrum today.

The galaxy window function, which enters all three power spectra, is written as

where dN/dz)dz is the mean number of sources per steradian with redshift z within dz, brighter than the flux limit, b(z) is the bias factor relating the source to the mass overdensity, D(z) is the linear growth factor of mass fluctuations, j _ℓ(x) is the spherical Bessel function of order ℓ, and η(z) is the conformal lookback time. Similar window functions exist for the CMB and foreground elements for the different power spectra.

We can write corresponding correlation functions as a function of the angular separation θ:

where L _ℓ are the Legendre polynomials of order ℓ.

3.6.2 Predictions for the pathfinders

We have calculated correlation functions or power spectra for the ISW, cosmic magnification, and source counts for the forthcoming radio surveys. For example, in Figure 20 we show our result for the CMB–LSS cross-correlation using the predicted redshift distributions and bias for the LOFAR Tier 1 survey, where we assume the standard ΛCDM+GR model and the shaded areas are cosmic-variance errors, calculated via

where f _sky is the sky coverage of the survey; C^gg _ℓ and C^TT _ℓ are the auto-correlations density–density and temperature–temperature, and contain shot noise and detector noise; the errors are then converted to real space as

Figure 20. Predicted correlations of the CMB with the LOFAR Tier 1 survey data. As a comparison, we also show error bars from current NVSS measurements. Note the improvement we obtain with one of the pathfinders over current constraints on all scales.

Now we wish to predict the combined cosmological measurements that the SKA pathfinders should allow. In order to do this, we perform a joint analysis including CMB+SNIa priors, ISW, cosmic magnification, and the auto-correlation of radio sources. We test deviations from the standard ΛCDM+GR model for two cases: we first parameterise modifications of the theory of gravity; and then alternatively, we assume GR to be the correct model to describe gravity and consider a dynamical dark energy model.

3.6.3 Modified gravity constraints

We want to test deviations from GR using the {η, μ} parameters, which are defined via

where Δ is the gauge-invariant comoving density contrast: in General Relativity η(a, k) = μ(a, k) = 1, while in alternative models they deviate from this value, and can also be functions of time and scale (e.g. Zhao et al. Reference Zhao, Giannantonio, Pogosian, Silvestri, Bacon, Koyama, Nichol and Song2010).

We model the time evolution of μ and η as (see Zhao et al. Reference Zhao, Giannantonio, Pogosian, Silvestri, Bacon, Koyama, Nichol and Song2010 for details)

In Figure 21 (top panel), we show predictions for how well we can constrain the modified gravity parameters using the EMU survey. Also displayed are the 68% confidence level for current surveys (SNe, WMAP, and SDSS; Raccanelli et al. Reference Raccanelli2011). We use the current best-fit model as our fiducial model; note that if this current best fit remains the best fit, the standard GR+LCDM model would be excluded with forthcoming radio surveys at high significance. In any case, the surveys impressively reduce the permitted parameter space.

Figure 21. Predicted constraints on parameters using EMU+WODAN. The outer dotted ellipse shows the current constraints and the innermost grey ellipse shows the constraints available using EMU+WODAN with the three probes described. Bottom panel: dark energy parameters, showing current and predicted 68% CL constraints. Top panel: modified gravity parameter constraints.

3.6.4 Constraints on dark energy evolution

To study how well the SKA pathfinders will constrain the evolution of dark energy we use the {w ₀, w_a } parameterisation (Linder Reference Linder2003) of the dark energy equation of state:

In Figure 21 (bottom panel) we show predictions for the constraints on the parameters {w ₀, w_a }, using the EMU survey. Again, the constraints are substantially improved over the currently permitted region of parameter space.

3.6.5 Bias

To obtain constraints on cosmological parameters from continuum surveys, the redshift distribution and bias of radio sources needs to be known. Here we suggest a method for measuring the bias of radio sources at high redshift. We cross-match FIRST radio sources (Becker et al. Reference Becker, White and Helfand1995) with SDSS-DR7 data (Abazajian et al. Reference Abazajian2009) and use photometric redshifts in the DR7 catalogue to obtain an estimate of the redshift distribution of the optically identified sources. To probe the high-z radio continuum population, we assume that the z-distribution of all FIRST sources is given by the SKADS simulation (Wilman et al. Reference Wilman2008) and we subtract off the distribution of the optically identified sources to estimate the z-distribution of the unidentified sources. By measuring the angular correlation function of the unidentified sources and comparing this with predictions for dark matter clustering, we will then be able to estimate the bias at z ~ 0.7. Some initial results using this technique are presented in Passmoor et al. (Reference Passmoor, Cress, Faltenbacher, Johnston, Smith, Ratsimbazafy and Hoyle2013).

If SKA pathfinder surveys are to be used to measure cosmological parameters, it will be important to continue and extend this work to obtain a better estimate of bias for different classes of radio source, and also to understand the sensitivity of the derived cosmological parameters to uncertainty in the value of the bias parameter.

3.6.6 The effect of redshifts on cosmological tests

The cosmology discussion to this point makes the conservative assumption that no redshifts are available for individual radio sources, although we do know the redshift distribution of the different classes of source, and the already impressive results shown in Figure 21 are calculated using this assumption. While less than about 1% of radio sources in SPARCS surveys are likely to have spectroscopic redshifts at the time of the data releases, photometric and statistical redshift information is likely to be available for ~50% of sources, as described in Section 4.7.

Camera et al. (Reference Camera, Santos, Bacon, Jarvis, McAlpine, Norris, Raccanelli and Röttgering2012) have explored the impact of photometric redshifts on the cosmological measurements from EMU and WODAN. Using only the galaxy clustering angular power spectrum and dark energy constraints, they find that even approximate photometric redshifts obtained from SDSS and SkyMapper yield a significant improvement to the constraints provided by the radio data alone.

An alternative approach has been suggested by Norris et al. (Reference Norris2011b), using radio data alone. Sources with detected polarisation in the POSSUM survey (see Section 2.4) are virtually all AGNs, with an expected median redshift of 〈z〉~1.8, while the remaining unpolarised EMU sources will be a mixture of AGNs and SFGs, with an expected median redshift of 〈z〉~1.1. The unpolarised sources can therefore be treated as a separate population from the polarised sources for the purposes of the cosmological tests described above, giving two radio source samples at different redshift ranges, thus potentially yielding a measurement of the time-dependent component of the dark energy and modified gravity parameters. However, modelling is required to establish whether this technique yields a significant improvement over other techniques.

3.6.7 Weak lensing

Weak gravitational lensing by large-scale dark matter in the Universe distorts the images of faint background galaxies. Measurements of this ‘cosmic shear’ effect as a function of redshift can provide powerful constraints on dark energy and its evolution over cosmic time (e.g. Albrecht et al. Reference Albrecht2006; Peacock et al. Reference Peacock, Schneider, Efstathiou, Ellis, Leibundgut, Lilly and Mellier2006). The measurements require a large number of well-resolved galaxies to reduce the ‘shape noise’ associated with the intrinsic variety of galaxy shapes. Most cosmic shear studies to date have therefore been at optical wavelengths. Radio measurements have typically been less effective because of smaller number densities and poorer spatial resolution. Chang, Refregier, & Helfand (Reference Chang, Refregier and Helfand2004), however, made a statistical detection of cosmic shear in the VLA FIRST survey, and Patel et al. (Reference Patel, Bacon, Beswick, Muxlow and Hoyle2010) used VLA and MERLIN data to explore radio weak lensing techniques.

Measuring weak lensing at radio wavelengths potentially offers a number of advantages over optical surveys in terms of minimising instrumental and astrophysical systematic effects. For example, radio telescopes have highly stable and well-understood point-spread functions (PSFs), which makes them particularly suited for measuring the small distortions caused by weak lensing. In addition, a future weak lensing survey conducted with the SKA could yield redshifts for a significant fraction of the lensed galaxies through the detection of their H i emission lines (e.g. Blake et al. Reference Blake, Bacon, Fluke, Kitching, Miller, Power and Wilman2007). Uncertainties and biases associated with photometric redshift errors would consequently be greatly reduced with an SKA lensing survey.

A major astrophysical cause of systematic error in weak lensing measurements is the intrinsic alignment in galaxy shapes, caused by tidal torquing during the galaxy formation process. Cleanly separating these from the extrinsic alignments caused by weak lensing will be crucial for interpreting precision weak lensing measurements in the future. Brown & Battye (Reference Brown and Battye2011a) showed that polarisation, which is routinely measured at radio wavelengths can, in principle, discriminate between the lensing distortions and intrinsic alignments.

Blake et al. (Reference Blake, Bacon, Fluke, Kitching, Miller, Power and Wilman2007) have explored the potential of the SKA to perform a precision weak lensing survey. The potential advantages described above would make such a survey highly complementary to future large-scale optical lensing surveys. The SKA pathfinders offer excellent opportunities to develop the field of radio weak lensing and to demonstrate the above techniques and advantages on real data. For example, large-area surveys with arcsec resolution with LOFAR can test weak lensing techniques on large radio data sets. Moreover, the e-MERLIN telescope offers an exciting opportunity to perform deep sub-arcsec radio imaging over a large FOV which will be an ideal testbed for investigating radio lensing techniques. This potential has recently been recognised with the award of ~ 800 h of e-MERLIN legacy survey time for the Supercluster Assisted Shear Survey (SuperCLASS), which will image a 1.75 deg² region of sky containing a supercluster to a depth of 4 μJy beam⁻¹ with 0.2-arcsec resolution, including polarisation information. This study is expected to detect ~1–2 galaxies per square arcmin, which will be used to map the dark matter distribution in the vicinity of the supercluster (Brown & Battye Reference Brown and Battye2011b).

3.8.1 H ii regions

The high sensitivity of the planned wide-field 1.4-GHz surveys such as EMU and WODAN allows access to all stages of the evolution of H ii regions, even though free–free emission near 1.4 GHz will be optically thick for the very dense ultra- and hyper-compact H ii regions (UCHII and HCHII, respectively), which are too small to be resolved by a 10-arcsec beam, unless they are very nearby. UCHII and HCHII represent a very young phase in the development of an H ii region (Churchwell Reference Churchwell2002).

Expected flux densities at 1.4 GHz for the most compact H ii regions are displayed in Figure 22. The separation between ultra-compact and hyper-compact H ii regions is at a diameter of about 0.02 pc. Hence, EMU will be able to detect all ultra-compact H ii regions and also many hyper-compact objects. There is still confusion about what a hyper-compact H ii region actually is. Are they just extremely compact ultra-compact H ii regions or a new class of objects? There is evidence that HCHIIs have somewhat different spectral characteristics than the UCHIIs, which might be explained by a density gradient within the ionised gas (Kurtz Reference Kurtz2005). So far only a small number of HCHIIs are known. A more complete census of these objects with a sensitive wide-field survey is required to get a more complete picture of the evolutionary process of H ii regions. Follow-up observations at higher radio frequencies or a comparison with high radio frequency surveys is then required to determine physical characteristics which will help to unravel the true nature of these objects.

Figure 22. Predicted peak radio flux density of unresolved UCHIIs and HCHIIs at 1.4 GHz as a function of distance from the sun. UCHIIs and HCHIIs with different diameters are displayed. We assumed a constant electron temperature of 8 000 K, a homogeneous distribution of material, and high optical depth (τ ≫ 1.0).

We can also probe the magnetic field inside H ii regions by either studying the RM signature of polarised point sources ‘shining through’ the object (e.g. Harvey-Smith, Madsen, & Gaensler Reference Harvey-Smith, Madsen and Gaensler2011) or by studying overlapping or even related diffuse polarised emission (e.g. Foster et al. Reference Foster, Kothes, Sun, Reich and Han2006).

3.8.2 Planetary nebulae

Planetary nebulae (PNe) are the most abundant compact Galactic sources in the NVSS (Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998). Condon & Kaplan (Reference Condon and Kaplan1998) identified 680 NVSS radio sources brighter than 2.5 mJy with planetary nebulae. Assuming a detection limit of 50 μJy, EMU will be able to detect unresolved PNe up to seven times farther away than NVSS, potentially leading to a significant increase of the number of PNe detected at radio frequencies. PNe can be very useful tools for measuring extinction and probing SFRs of stars not massive enough to produce supernovae or H ii regions (Condon & Kaplan Reference Condon and Kaplan1998; Condon, Kaplan, & Terzian Reference Condon, Kaplan and Terzian1999). Identification of these PNe, however, will be difficult.

The ionised low-density circumstellar material of nearby planetary nebulae, released during the Asymptotic Giant Branch (AGB) wind phase of the central stellar object, is illuminated by background linear polarised emission through Faraday rotation. Free thermal electrons embedded in a magnetised medium rotate background linear polarisation emission to create an RM signature observable at 1.4 GHz. A typical radio telescope operating in this wavelength range proves to be more sensitive to the Faraday rotation of a plasma region than to its bremsstrahlung signature. Linear polarisation studies of nearby planetary nebulae can reveal important information about the mass loss history of old AGB stars or white dwarfs that cannot be obtained easily any other way (e.g. Ransom et al. Reference Ransom, Uyanıker, Kothes and Landecker2008, Reference Ransom, Kothes, Wolleben and Landecker2010).

3.8.3 Supernova remnants

Only 274 supernova remnants (SNRs) have been discovered so far in our Galaxy (Green Reference Green2009).Footnote ⁴ However, the estimated population of SNRs is much higher (maybe 500–1 000; Helfand et al. Reference Helfand, Becker, White, Fallon and Tuttle2006). This discrepancy is mainly caused by a strong bias towards bright extended objects. These are the mature SNRs expanding into a medium- to high-density environment. There are two groups of missing SNRs. The compact, presumably very young, objects were missed by previous wide-field surveys, because they are either confused by other nearby objects or mistaken for extragalactic sources if they are not resolved. The second group of missing SNRs are low surface brightness SNRs. A population of more than 1 000 SNRs for our Galaxy can also be extrapolated using the Canadian Galactic Plane Survey (CGPS; Taylor et al. Reference Taylor2003) and its supernova remnant catalogue (Kothes et al. Reference Kothes, Fedotov, Foster and Uyanıker2006). The CGPS is a radio continuum and H i survey of the Outer Galaxy. Since the distance to the edge of the Galaxy, and hence to every object in the survey, is very short, the ~1 arcmin resolution at 1 420-MHz radio continuum (≤1 pc) is sufficient to resolve any SNR—even those which are very young.

EMU and POSSUM will have a very similar spatial resolution than the CGPS but much higher sensitivity. The 10-arcsec beam translates to about the same spatial resolution at the most distant edge of the Galaxy through the inner part of the Milky Way (≈20 kpc) than the CGPS beam does towards the Outer Galaxy. Hence, we would expect to detect a similar number density of SNRs. This indicates that EMU in conjunction with POSSUM could discover more than 500 new SNRs. Resolved SNRs can be easily distinguished from extragalactic sources and Galactic H ii regions by an analysis of structure and spectral and polarisation signatures.

Radio polarisation observations of SNRs can also be a powerful tool to probe the magnetic field into which these objects are expanding. SNRs act as magnifying glasses of ambient magnetic fields, since they freeze and compress it into the expanding shell of the swept up material. Radio polarisation and RM studies can reconstruct the 3D ambient magnetic field, as demonstrated in the studies by Uyanıker, Kothes, & Brunt (Reference Uyanıker, Kothes and Brunt2002), Kothes & Brown (Reference Kothes and Brown2009), and Harvey-Smith et al. (Reference Harvey-Smith, Gaensler, Kothes, Townsend, Heald, Ng and Green2010). Radio polarisation studies of SNRs with EMU and POSSUM can probe the large-scale magnetic field of the Inner Galaxy, detect potential field reversals, and probe the transition from the Galactic plane to the halo.

3.8.4 Pulsars and their wind nebulae

Pulsars generate magnetised relativistic particle winds, inflating an expanding bubble called a pulsar wind nebula (PWN), which is confined by the expanding supernova ejecta. Electrons and positrons are accelerated at the termination shock some 0.1 pc distant from the pulsar and interact with the magnetic field to produce synchrotron emission across the entire electromagnetic spectrum. At GHz frequencies, the flat spectrum PWNe stand out from steep spectrum SNRs and can be distinguished from H ii regions by their linear polarisation signal.

The high resolution and sensitivity of the proposed wide-field 1.4-GHz surveys will enable us to built a more complete census of Galactic pulsar wind nebulae down to unprecedented levels.

The number of pulsars at high Galactic latitudes is poorly constrained since most surveys concentrate on a narrow band along the Galactic plane. Out of the 1 433 pulsars with measured 1 400-MHz fluxes listed in the ATNF Pulsar Catalogue (Manchester et al. Reference Manchester, Hobbs, Teoh and Hobbs2005), 1 410 have integrated fluxes above 50 μJy. Only 310 of those have Galactic latitudes |b| > 5°. Sensitive high-resolution radio continuum surveys will enable us to get a more complete picture of the pulsar distribution in the Milky Way and their RMs will help to constrain the configuration and strength of the large-scale Galactic magnetic field.

Pulsars should be distinguishable from other point-like radio sources because of their steep radio continuum spectra, their polarisation, and artefacts caused by short-term variability. These observational signatures will be complemented by the variability and transient surveys discussed in Section 3.7.

3.8.5 Radio stars

Radio stars emit a tiny fraction of their total luminosity in the radio band. For example, the quiet Sun has a radio luminosity of 10¹⁴ W, which is only ~10⁻¹² of its bolometric luminosity. Nevertheless, in many cases, radio observations of stars and stellar systems have revealed astrophysical phenomena, not detectable by other means, that play a fundamental role in our understanding of stellar evolution and of physical processes that operates in stellar atmospheres.

Generally, the brightest stellar radio emission appears to be associated with magnetically induced phenomena, such as stellar flares, related to the presence of a strong and/or variable stellar magnetic field (high brightness temperature) or with enhanced mass loss (large emitting surface).

Among the brightest radio sources are active stars and binary systems, including flare stars, RS CVns, and Algol binary systems, characterised by strong magnetic activity which drives high energy processes in their atmospheres. Their radio flux density is highly variable and it usually shows two different regimes: quiescent periods, during which a basal flux density of few mJy is observed, and active periods, characterised by a continuous strong flaring which can last for several days (Umana et al. Reference Umana, Trigilio, Tumino, Catalano and Rodonó1995).

Both quiescent and flaring radio emission show spectral and polarisation characteristics consistent with non-thermal radio emission, probably driven by the magnetic activity manifested at other wavelengths. In this scenario, the radio flux is due to gyrosynchrotron emission (Guedel Reference Guedel2009), caused by the interaction of the stellar magnetic field with mildly relativistic particles. A similar mechanism causes the radio emission from pre-main sequence (PMS) stars and X-ray binaries. Non-thermal radio emission is also seen from shocks of colliding winds in massive binaries.

Stellar radio flares can occur also as narrow band, rapid, intense, and highly polarised (up to 100%) radio bursts, which are particularly common at low frequency (<1.5 GHz). They are believed to be the result of coherent emission mechanisms, requiring a strong magnetic field (which may be variable) and a source of energetic particles. Coherent burst emission has been observed in RS CVns, flare stars, brown dwarfs (BD), and chemically peculiar stars (CPs) (Slee, Wilson, & Ramsay Reference Slee, Wilson and Ramsay2008; Berger Reference Berger2002; Trigilio et al. Reference Trigilio, Leto, Leone, Umana and Buemi2000). Coherent emission has been detected in just a few tens of stars, because of the limited sensitivity of the available instruments.

Stellar radio emission often exhibits significant circular polarisation (Trigilio et al. Reference Trigilio, Leto, Umana, Buemi and Leone2011; Ravi et al. Reference Ravi2010). While some extragalactic sources do exhibit circular polarisation (e.g. Rayner, Norris, & Sault Reference Rayner, Norris and Sault2000), the degree of polarisation is small (typically ~ 0.01%), compared with the levels up to 100% seen in radio stars. It is therefore important, for the purposes of distinguishing stars from extragalactic objects, that surveys record circular as well as linear polarisation.

Thermal emission (bremsstrahlung emission) is expected from winds associated with WR and OB stars, shells surrounding PNe, and novae and jets from symbiotic stars and class 0 PMS stars (Guedel Reference Guedel2002). In all these cases, radio continuum emission is an important diagnostic to understand the underlying physics. For example, radio continuum observations are the most precise way yet to determine the mass loss of stellar winds. This is particularly important when other diagnostics cannot be used, such as in the case of dust-enshrouded objects (Umana et al. Reference Umana, Buemi, Trigilio and Leto2005).

Since no sensitive survey for radio stars has yet been conducted, little statistical information on stellar radio emission is available. Forecasts of the number of sources detectable with SPARCS surveys rely on radio observations of small samples of stellar sources, usually selected on the basis of observed peculiarities at other wavelengths. Assuming typical radio luminosities for each type of radio star, we conclude that stellar winds and non-thermal radio emission from many active binaries, flares stars, PMS will be easily detected with an rms sensitivity of 10 μJy beam⁻¹ (EMU), while SKA (1 μJy beam⁻¹ rms) will be able to detect a quiescent Sun at 10 pc (see Figure 23).

Figure 23. Typical radio spectrum of several classes of radio emitting stars. Fluxes have been derived from the radio luminosity (Seaquist, Krogulec, & Taylor Reference Seaquist, Krogulec and Taylor1993; Guedel Reference Guedel2002; Umana, Trigilio, & Catalano Reference Umana, Trigilio and Catalano1998; Trigilio et al. Reference Trigilio, Leto, Umana, Buemi and Leone2008; Berger Reference Berger2006) assuming an appropriate distance for each type of radio star (10 pc for flare stars, 100 pc for active binary systems, 1 kpc for supergiants, OB and WR, 500 pc for CP stars). The bandwidth and sensitivity of EMU have also been indicated.

Until now, targeted observations of well-known radio stars have constituted the best approach to investigate their radio emission mechanisms (e.g. flare development, spectral and polarisation evolution, emission mechanism, etc.). An all-sky survey would significantly enlarge the known stellar radio emitting database, free from selection effects. Results from such a survey would provide new insights into the physics of active stellar systems and plasma processes.

Two areas of stellar radio emission will particularly benefit from SKA and SPARCS surveys. One is the study of gyrosynchrotron stellar flares, where multi-epoch, multi-frequency observations will enable the detection of serendipitous flaring activity, allowing the derivation of a typical behaviour (occurrence rate, variation amplitude, etc.) from a statistical study of a larger source population. Moreover, detailed studies of a large number of stellar coronae will be possible, allowing us to understand the nature of energy release in the upper atmospheres of stars of different mass and age and to investigate the correlation between radio and X-ray emission and thus on the Neupert effect (Guedel Reference Guedel2009). The expected sensitivity will also test the presence of superflares on solar-type stars, and search for correlations with an orbiting hot Jupiter (Maehara et al. Reference Maehara2012).

The other important area is related to the study of coherent emission. The EMU plus WODAN surveys will offer the best opportunity yet to determine how common coherent radio emission is from stellar and sub-stellar systems. The detection of coherent emission from a large fraction of surveyed stars will have immense implications for our understanding of both stellar magnetic activity and the dynamo mechanism generating magnetic fields in fully convective stars and brown dwarfs (Hallinan et al. Reference Hallinan, Antonova, Doyle, Bourke, Lane and Golden2008; Ravi et al. Reference Ravi, Hallinan, Hobbs and Champion2011). Coherent emission observed in active and BD stars shares several characteristics with that observed in CP stars (Trigilio et al. Reference Trigilio, Leto, Leone, Umana and Buemi2000), since both require a large-scale magnetosphere and are similar to the low frequency coherent radio emission observed from the magnetised planets in our solar system (Trigilio et al. Reference Trigilio, Leto, Umana, Buemi and Leone2011). The well-known topology of CPs magnetic fields, independently derived from optical observations, makes this kind of object an excellent laboratory for stellar magnetosphere studies. Matching of predicted emission with that observed yields parameters of the radio source, such as the surface magnetic field, the number density of the emitting electrons, and the energy spectrum of the electrons. In turn, this provides clues to the acceleration process, the size of the magnetosphere (Alfvén radius) and the inclination of the rotational axis.

If coherent emission is present in many radio active stars, with the same characteristics, it will constitute an excellent diagnostic for star magnetospheres, and a powerful probe of magnetic field topology. In one CP star (CU Vir) the coherent emission is stable on a timescale of years, and has been used to time the rotation of the star, revealing a likely change of its period (Trigilio et al. Reference Trigilio, Leto, Umana, Buemi and Leone2008; Ravi et al. Reference Ravi2010). The discovery of other similar radio lighthouses will enable high-precision studies of the rotation period, and thus angular momentum evolution, in different classes of stars.

4.4.1 Existing algorithms

Two distinct approaches are being pursued in the community to correct for wide-field and direction-dependent effects, which can be classified as (a) projection algorithms and (b) faceting algorithms (Bhatnagar Reference Bhatnagar2009).

Projection algorithms are based on physical modelling of the various direction-dependent (DD) terms of the measurement equation and incorporating them as part of the forward and reverse transforms. These algorithms therefore do not require assumptions about the source brightness distribution. This allows them to take advantage of the FFT algorithm for Fourier transforms, as well as integrate well with advanced deconvolution techniques for scale-sensitive wide-band imaging.

Faceting algorithms, on the other hand, are based on data partitioning in such a way that standard direction independent techniques can be applied to the partitions (Nijboer & Noordam Reference Nijboer and Noordam2007; Mitchell et al. Reference Mitchell, Greenhill, Wayth, Sault, Lonsdale, Cappallo, Morales and Ord2008; Smirnov Reference Smirnov2011). This approach is phenomenological by design requiring no physical understanding or modelling of the DD term in the measurement equation. They can however suffer from non-optimal use of the available signal-to-noise ratio (due to data partitioning), curse of dimensionality (too many degrees of freedom) and computational load. To alleviate some of these problems, in addition to the problem of degrees of freedom, assumptions about the structure of the brightness distribution typically have to be made.

The W-Projection algorithm (Cornwell, Golap & Bhatnagar Reference Cornwell, Golap and Bhatnagar2008) incorporates the effects of non-coplanar baselines and corrects for its effects during imaging. The A-Projection algorithm (Bhatnagar et al. Reference Bhatnagar, Cornwell, Golap and Uson2008) similarly accounts for the time, frequency, and polarisation dependence of the antenna primary beams modelling the antenna aperture illumination patterns (or the measured illumination patterns). The combined AW-Projection algorithm therefore can be used at low frequencies where the effects of the W-Term as well as that of antenna primary beams limit the imaging performance. Antenna pointing errors are thought to limit the imaging performance at high frequencies and in mosaic imaging at all frequencies. Using A-Projection for forward and reverse transforms, the Pointing SelfCal algorithm (Bhatnagar, Cornwell, & Golap Reference Bhatnagar, Cornwell and Golap2004) solves for the time-dependent antenna pointing errors. The pointing solutions are then incorporated as part of the A-Projection to correct for the effects of antenna pointing errors.

The Multi-Scale Clean (Cornwell Reference Cornwell2008) and Asp-Clean (Bhatnagar & Cornwell Reference Bhatnagar and Corwnell2004) algorithms are advanced image deconvolution techniques for imaging fields with extended emission. The MS-MFS algorithm (Rau & Cornwell Reference Rau and Cornwell2010) for wide-band multi-frequency synthesis not only deals with the deconvolution of extended emission, but also accounts for spatially resolved spectral index variation across the FOV. The combination of AW-Projection and MS-MFS algorithms can therefore be used to account simultaneously for all the dominant wide-field wide-band effects which are expected to limit the imaging performance with SKA pathfinder telescopes.

The algorithmic design of the combined AW-Projection and MS-MFS algorithm is such that it falls in the category of embarrassingly parallel algorithm. To mitigate the fundamentally higher computing load, work is in progress to deploy these combined advanced algorithms on high-performance computing (HPC) platforms, typically consisting of a cluster of computers with multi-core CPUs and high bandwidth interconnect (Bhatnagar, Ye, & Schiebel Reference Bhatnagar, Ye and Schiebel2009).

Since these algorithms also need to iterate over a large volume of data, computing clusters connected to a parallel file system (e.g. the Lustre file system) and using multi-threaded I/O techniques are currently being used. Tests with up to a few Terabytes of data show close to linear scaling in computing with number of computing nodes, although this is subject to the achievable compute-to-I/O ratio. Work is in progress to address the problem of improving this ratio while keeping the resulting memory footprint in reasonable limits. For SKA-sized data sets, iterating over the entire data set might not be feasible. Work is in progress to devise computing schemes and algorithms that may eliminate or at least reduce the number of iterations involving the entire data.

4.4.2 Development of new deconvolution algorithms

In the last few years, the theory of compressed sensing (CS; Donoho Reference Donoho2006; Candès, Romberg & Tao Reference Candès, Romberg and Tao2006) has been developed by the signal/image processing community, and may be applicable to radio-astronomical image deconvolution.

The theory of CS mostly addresses random sampling, sparse signals, and coarse-grained dictionaries. In radio interferometry, sampling is usually structured, astronomical images are not sparse, and dictionaries must be fine-grained to adequately represent the images. Theoretical CS results therefore do not usually improve estimates of astrophysical sources from interferometric data. However, a key ingredient of the CS framework, sparse representations (Mallat Reference Mallat2008), has demonstrated significant improvements in radio-astronomical deconvolution, and has been used as a tool for deconvolution of extended and diffuse sources in the image plane (Wiaux et al. Reference Wiaux, Jacques, Puy, Scaife and Vandergheynst2009a; Li et al. Reference Li, Cornwell and de Hoog2011a; Dabbech, Mary, & Ferrari Reference Dabbech, Mary and Ferrari2012) as well as in Faraday depth (Li et al. Reference Li, Brown, Cornwell and de Hoog2011b).

Sparse representation theory (Fornassier Reference Fornassier2010) may be seen as a generalisation of ideas exploited in clean (e.g. Högbom Reference Högbom1974; Wakker & Schwarz Reference Wakker and Schwarz1988; Cornwell Reference Cornwell2008). clean performs an iterative deconvolution by using a dictionary of shifted PSFs to construct a sparse dictionary of point sources. Sparse representation theory aims to construct a dictionary of more complex geometrical features than point sources, addressing three fundamental issues of astronomical image restoration. First, the sparsity of the dictionary reduces the indeterminacy and instability caused by the zeros of the transfer function of an interferometer. Second, the theory allows flexible and sophisticated models that can cope with complex astrophysical sources. Third, it offers computationally efficient optimisation techniques to solve the resulting deconvolution problem.

Sparse representations can take either of two approaches: synthesis and analysis (Elad et al. Reference Elad, Starck, Querre and Donoho2005).

In the synthesis approach, the unknown intensity distribution x (of size (N, 1), say) is assumed to be sparsely synthesisable by a few atoms of a given full rank dictionary S of size (N, L). Hence, we write x as x = S ± bγ, where ±bγ (the synthesis coefficients vector) is sparse. In contrast, the analysis approach assumes that x is not correlated with some atoms of an analysis dictionary A of size (N, L): A ^T x is sparse.

Since real images can often be approximated by a linear combination of a few elementary geometrical features, the synthesis approach is more intuitive and has been the focus of more research. Its design simplicity has also made it popular in image processing applications such as compression, de-noising, and in-painting. However, because a synthesis-based deconvolved image is restricted to a subspace of the synthesis dictionary, the resulting astrophysical images may be too rough to be realistic. On the other hand, since the signal is not built from a small number of atoms, the analysis approach may be more robust to ‘false detections’. However, the number of unknowns in the synthesis approach (the number of atoms in the dictionary) may be much larger than in the analysis approach. Thus, while analysis-based optimisation strategies may be computationally and qualitatively more efficient for large dictionaries (Starck, Murtagh, & Fadili Reference Starck, Murtagh and Fadili2010), the question of which approach is best remains open (Gribonval & Schnass Reference Gribonval and Schnass2009, and references therein).

Regardless of the approach chosen, a sparsity-based deconvolution method still requires a dictionary, chosen from a class of images (Mallat Reference Mallat2008). Astronomical wavelet dictionaries are widely used, but sometimes fail to represent asymmetric structures adequately. In such cases, it may be necessary to use other transforms designed for specific classes of objects, such as curvelets, which are optimum for curved, elongated patterns such as planetary rings or galaxy arms, and shapelets, which are often optimum for galaxy morphologies. Modelling complex images may require several dictionaries to be concatenated into a larger dictionary (Chen, Donoho & Saunders Reference Chen, Donoho and Saunders1998; Gribonval & Nielsen Reference Gribonval and Nielsen2003), although computational issues limit the size of dictionaries, especially for radio synthesis images containing hundreds of thousands of Fourier samples.

Several deconvolution methods that combine these approaches have recently been suggested (e.g. Suksmono Reference Suksmono2009; Wiaux et al. Reference Wiaux, Jacques, Puy, Scaife and Vandergheynst2009a, Reference Wiaux, Puy, Boursier and Vandergheynst2009b; Vannier et al. Reference Vannier, Mary, Millour, Petrov, Bourguignon and Theys2010; Wenger et al. Reference Wenger, Darabi, Sen, Glassmeier and Magnor2010; McEwen & Wiaux Reference McEwen and Wiaux2011)), including successful simulations of SKA pathfinder observations. Li et al. (Reference Li, Cornwell and de Hoog2011a) present a classical synthesis approach with an IUWT (Isotropic Undecimated Wavelet Transform) synthesis dictionary, Carillo, McEwen, & Wiaux (Reference Carrillo, McEwen and Wiaux2012) used an analysis approach using a concatenation of wavelet bases, and Dabbech et al. (Reference Dabbech, Mary and Ferrari2012) defined a hybrid analysis-by-synthesis approach.

While the theoretical results of CS have not yet generated tools which can be used routinely for synthesis imaging, they have brought new perspectives from the domain of sparse representations: improved sparsity models and improved optimisation algorithms. The increased research effort on fundamental models for sparse representations (analysis/synthesis/hybrid models) leads to improved models and thus to improved reconstruction. Research in sparse representations is active and growing, and promises valuable future developments in radio-astronomical deconvolution algorithms.

4.5.1 Compact source extraction

Two main areas of recent focus have been investigations into the impact of background and noise estimation on the detection of compact sources, and a rigorous comparison of existing source finding software tools. The first of these focuses on source detection, where the background and noise levels in an image are characterised (Huynh et al. Reference Huynh, Hopkins, Norris, Hancock, Murphy, Jurek and Whiting2012).

The second focuses on source characterisation, where islands of pixels are described or fit in some well-defined manner (Hancock et al. Reference Hancock, Murphy, Gaensler, Hopkins and Curran2012). The most common way to describe a source in radio astronomy is as a group of Gaussian components.

The process of background characterisation has been explored by Huynh et al. (Reference Huynh, Hopkins, Norris, Hancock, Murphy, Jurek and Whiting2012), who tested the steps of background and noise measurement, and of the choice of a threshold high enough to reject false sources yet not so high that the catalogues are significantly incomplete. This analysis explored the results from testing the background and thresholding algorithms as implemented in the SExtractor, Duchamp/Selavy, and sfind tools on simulated data. The result of this analysis shows clearly that it will be crucial to first develop and then implement an automated algorithm for establishing the appropriate scale size on which to estimate the ‘local’ background and rms noise values for each image, and that this may not be common to all images. This analysis also suggests that the false discovery rate approach (Hopkins et al. Reference Hopkins2002) to thresholding may be the most robust, optimising for both completeness and reliability.

The source characterisation stage has been found to have its own distinct issues (Hancock et al. Reference Hancock, Murphy, Gaensler, Hopkins and Curran2012). For a selection of commonly used source finding tools (sfind, SExtractor, imsad, and Selavy) there are significant differences in the way that islands of sources are divided into components and subsequently fit. This is exacerbated with examples of sources which are blended or adjacent, especially when there is a large difference in the relative flux densities (even though the fainter component(s) may in their own right be very high signal-to-noise ratio objects). Such behaviour has particular implications for variable objects. If one such source were variable or transient, this behaviour could be missed if a source finding program is not able to correctly decompose the island. If a source finder’s ability to decompose an island into components is related to the clipping limit, or background noise, then a source of constant flux could be interpreted as transient or variable due to irregularities in the source characterisation process.

These issues have triggered the development of new algorithms (e.g. Hancock et al. Reference Hancock, Murphy, Gaensler, Hopkins and Curran2012; Hales et al. Reference Hales, Murphy, Curran, Middelberg, Gaensler and Norris2012) that aim to determine the correct number of components within an island, and to generate an initial parameter set for the fitting of multiple Gaussian components. Hancock et al. (Reference Hancock, Murphy, Gaensler, Hopkins and Curran2012) use a Laplace transform, to identify regions of negative curvature in the pixel intensity profiles, combined with the map defined from the islands of pixels above a threshold, to automate the process of identifying the numbers of components in each island, and their initial position and peak flux density estimates.

Another clear requirement that has developed from these analyses is the need to quantify the false detection rate of sources as a function of signal-to-noise ratio level, and perhaps other image or telescope parameters, in order to assess the likelihood that any detected source is actually real. The impact of even a 0.1% false detection rate when catalogues of many tens or hundreds of millions of sources are being anticipated is clearly large.

These initial steps have demonstrated that while source finding has been ubiquitous in radio astronomy for many decades, there is still scope for optimising and quantifying the process, and that careful attention will need to be paid to these details in the lead up to the new generation of radio telescopes. There will be many lessons to be learned in order to ensure that source measurement using the SKA, ultimately, can be made as robust as possible.

4.5.2 Extended source extraction

Many of the feature recognition algorithms widely applied in fields such as optical character recognition, machine vision, or medical imaging are absent from the repertoire of techniques routinely employed by astrophysicists. However, the increasing complexity and scale of astronomical data are driving an interest in more advanced feature extraction techniques for astronomical contexts. In particular, radio surveys on next-generation telescopes will generate image data containing tens of millions of astronomical sources, many of which will be extended.

Localised kernel transforms, such as the wavelet transform, are often used for astronomical purposes, including diffuse source detection (e.g. detection of diffuse X-ray emission in the COSMOS field; Finoguenov et al. Reference Finoguenov, David, Zimmer and Mulchaey2006). They are created either by modifying a conventional kernel transforms, or by using exotic basis functions, and are supplemented by a localisation algorithm to allow the target to be located. The success of these methods relies on ‘matching’ the basis function to the problem at hand. Given the variety of source morphologies in astronomical images, no single transform will adequately detect all sources. Localised kernel transforms work best in cases where a single class of objects can be matched to a suitable set of basis functions, and can also be used to separate diffuse from point source components using curvelet, ridgelet, or á trous transforms (e.g. Figure 24).

Figure 24. Feature extraction in the HST image of Abell 370 from Starck, Donoho, & Candés (Reference Starck, Donoho and Candés2003). The top left panel shows the original HST image, top right shows the co-added image from the ridgelet and the curvelet transforms which extract extended features, bottom left shows the reconstruction from the à trous algorithm which responds to point sources, and bottom right shows the addition of the results of all three transforms.

Compressive processes rely on the fact that pixels in an image are not independent, so it is possible to encode the patterns in the image rather than the pixel-by-pixel information. This provides a more efficient ‘compressed’ representation of the information by providing a ‘model’ of the image. Object detection is then applied to this ‘model’ rather than to the real data, greatly reducing the complexity of the problem. Compression attempts to preserve the information inherent in the original image but does not attempt to abstract geometric or semantic information. Compressive techniques therefore preserve large-scale noise features in addition to diffuse sources. The use of compressive sampling for deconvolution has been discussed in Section 4.4.2.

Template matching is a process where an image is correlated with a target object of known form, and is similar to ‘matched filtering’. This technique has been used in radio astronomy for pulsar timing prediction (van Straten Reference van Straten2006; Oslowski et al. Reference Oslowski, van Straten, Hobbs, Bailes and Demorest2011), transient source detection (Trott et al. Reference Trott, Wayth, Macquart and Tingay2012), and to remove radio point source contaminants from diffuse source backgrounds (Pindor et al. Reference Pindor, Wyithe, Mitchell, Ord, Wayth and Greenhill2011). Two disadvantages of template matching are that (a) it is hard to control the required number of filters, resulting in a greater number than for localised kernel transforms, and (b) each template must fit a range of orientation and scaling. Even when the computational complexity of template matching is reduced by combining it with a scale-invariant transform such as the Mellin transform, orientation must still be calculated making this technique very computationally expensive. On the other hand, it has the advantages that (a) the templates do not have to be precise, and cartoon-like models suffice; (b) the method is robust against artefacts; (c) it can be applied in either the image or Fourier domains; and (d) it returns the size, orientation, location type of detected sources.

Hough transforms can find and characterise geometrical objects such as lines, circles, and ellipses. In general, the Hough transform is equivalent to template matching for some geometric shape, although it inherently incorporates scaling and orientation constraints. Circle or elliptical Hough transforms are particularly relevant to astronomical source detection to determine questions such as the size and location of a circle/ellipse, and have the advantage that the geometrical abstraction limits the number of filters required (e.g. different types of objects contain circular and arc-like features). The circle Hough transform (CHT) can find partial circular objects and is robust to noise. The CHT inputs an image and outputs a 3D array in which two dimensions represent the possible locations for the centres of circles and the third dimension spans the set of possible circle radii. Peaks in this so-called ‘Hough space’ therefore correspond to circles in the input image. In its simplest form, the circle Hough transform is computationally challenging, with both computational effort and memory consumption scaling as O(n ³) when transforming an n×n pixel image. Recently, the transform has been recast via a convolution approach which reduces the complexity to O(n ²)log n (Hollitt Reference Hollitt2009, Reference Hollitt2012). Although this is not the fastest approach for astronomical source detection, it has been applied as a source detection method for a variety of extended radio sources with arc-like features including supernova remnants, tailed radio galaxies, and radio relics (Hollitt & Johnston-Hollitt Reference Hollitt and Johnston–Hollitt2009, Reference Hollitt and Johnston–Hollitt2012). For example, Figure 25 shows the detection of a supernova remnant. Hough transforms return semantically useful information such as position, size, orientation, and eccentricity, but will produce somewhat less information than a full template matching process. For example, it cannot distinguish between a supernova remnant and a tailed radio galaxy.

Figure 25. Application of the circle Hough transform to detect radio supernova remnants in the Molonglo Galactic Plane Survey. Left to right: the original image of G315.4−2.3, the location and size of the remnant as found by the CHT, the original image with ten times the Gaussian noise and the response of the CHT in the noise case (yellow) compared with the original (black), which demonstrates the robustness of CHTs to noise (Hollitt & Johnston-Hollitt Reference Hollitt and Johnston–Hollitt2012).

Segmentation methods assume nothing about a source but rather seek to group pixels together based on differences with the background. Three main classes of segmentation methods are used in astrophysics: region growing, edge detection, and waterfalling. The simplest version of a segmentation method is to set a threshold and assume everything above that threshold is a target. In practice, adjoining pixels above the threshold are grouped together as a single target. This approach is usually too simplistic and requires an extension via one of the three subclasses above. Region growing, which includes floodfilling techniques, compares adjacent pixels at the edge of a target and groups them together based on some tolerance in pixel value (e.g. Duchamp and BLOBCAT; Whiting Reference Whiting2012; C. A. Hales et al., in preparation). This technique alone is poor at dealing with disjointed areas, although it may be heuristically augmented to define nearby areas as one object. Another method, edge detection, uses thresholds to find the borders between different ‘types’ of pixel. This is rarely useful in astronomy because sources have ‘soft’ edges. Waterfalling involves considering the image as a topographic surface and calculating the intensity gradient, pixels with the lowest gradient denoting watershed lines which are used to bound regions. An advantage of segmentation methods is their speed, making them good for large area surveys. One of the downfalls of segmentation methods is that no semantic information is returned. An additional classifier step is required to be applied to the output of segmentation algorithms to determine semantic properties.

While algorithms for the detection of point sources are well established, automatic detection and characterisation of diffuse sources presents a significant challenge to large radio surveys. While methods such as local kernel transforms, template matching, and Hough transforms have been demonstrated to detect and characterise diffuse sources, they are too computationally expensive to apply to large images. The favoured approach at present is therefore a combination of segmentation algorithms with heuristics to extract diffuse source catalogues. This combined process is not likely to be sufficient for future survey science goals and some combination of techniques, possibly applied on different resolution scales, will be required.

4.6.1 The likelihood ratio technique for radio source cross-identification

The likelihood ratio (LR) technique (e.g. Richter Reference Richter1975; Sutherland & Saunders Reference Sutherland and Saunders1992; Cilegi et al. Reference Ciliegi, Zamorani, Hasinger, Lehmann, Szokoly and Wilson2003) can be used to identify optical/near-infrared counterparts with sources selected from low resolution survey data. Smith et al. (Reference Smith2011) discuss a recent application of this Bayesian technique to identify 2 423 optical counterparts to 6 621 sources from the Herschel-Astrophysical TeraHertz Large Area Survey (Herschel-ATLAS; Eales et al. Reference Eales2010), selected at 250 μm.

The LR technique relies on the brightness and astrometric properties of the input catalogues in general, and each individual source in particular, to determine the ratio of the probability that two objects are related, to the probability that they are unrelated. After using an empirical method to account for the fraction of sources which are not detected in the optical/near-infrared catalogue, we can determine the reliability of each association, with values ranging from 0 (not related) to 1 (a match).

The likely positional uncertainties, coupled with the probable optical/near-infrared catalogues that will be available for identifying counterparts to the new catalogues that these surveys will generate, suggest that, apart from the problem of radio sources with multiple components, the problem will be very similar to that addressed using the LR technique in the Herschel-ATLAS.

McAlpine et al. (Reference McAlpine, Smith, Jarvis, Bonfield and Fleuren2012) have begun detailed investigations based on existing deep radio survey data and new near-infrared data from the VISTA VIDEO survey to quantify how effective the LR technique will be for these purposes, and how it will be affected by using data of different sensitivity and spatial resolution.

4.6.2 Bayesian approaches

Budavári & Szalay (Reference Budavári and Szalay2008) propose Bayesian hypothesis testing for cross-identification. Given a set of detections, one can ask directly whether the measured directions are consistent with a common single object. This hypothesis is tested against its complement using the Bayes factor, which is the likelihood ratio

where the likelihoods are calculated as a sum over all possible model parameters, e.g., the true position of the source. Assuming that the astrometric uncertainty is well approximated with a normal distribution, the derivation is analytic. For example, in the case of two detections of point sources with high-precision circular uncertainties and an all-sky prior on the true position where ψ is the angular separation of the detections and σ _i are the uncertainties, all in radians. When this dimensionless quantity is larger than 1, the data support the association. The higher the value, the greater is the evidence. The probability is analytically given in terms of B and the prior of the hypothesis, which is a function of the source densities of the input data sets. The approach is applicable to different kinds of data, such as fluxes or polarisation. The corresponding Bayes factors are computed independently and simply multiplied together. The method’s firm statistical foundation along with its explicit dependence on the geometry and physical modelling provides a clean framework for catalogue associations at all wavelengths and straightforward extensions. Such examples include the association of stars with unknown proper motions (Kerekes et al. Reference Kerekes, Budavári, Csabai, Connolly and Szalay2010) or transient events (T. Budavári, in preparation).

4.8.1 Stacking and data-intensive research

Stacking is used to explore the properties of a class of objects which are below the detection limit of a survey. For example, the radio flux of RQQs can be measured by averaging the measured radio flux at the position of each RQQ in a radio survey, even though each individual RQQ has a flux well below the detection limit.

More generally, the process of stacking involves combining (typically by taking a censored mean or median) the data at the position where such objects are expected in the survey. The noise tends to cancel, while any low level of flux density in the sources adds, resulting in a detection threshold very much lower than that of the unstacked survey. Stacking at radio wavelengths has been used very successfully (e.g. Boyle et al. Reference Boyle, Cornwell, Middelberg, Norris, Appleton and Smail2007; White Reference White, Helfand, Becker, Glikman and de Vries2007; Ivison et al. Reference Ivison2007, Reference Ivison2010; Dunne et al. Reference Dunne2009; Messias et al. Reference Messias, Afonso, Hopkins, Mobasher, Dominici and Alexander2010; Bourne et al. Reference Bourne, Dunne, Ivison, Maddox, Dickinson and Frayer2011) on high-resolution data for the purpose of studying faint populations which are below the detection threshold of the radio image, and has proved to be a powerful tool for studying SFRs, AGN activity, radio-infrared correlation, and measuring the fraction of the extragalactic background contributed by various source populations. Jack-knifing techniques are currently being explored to provide more information about the flux density distribution of stacked sources than is available from a simple mean or median (Rees et al., in preparation).

The unprecedented area-depth product of SPARCS surveys makes them very suitable for stacking. For example, stacking a sample of a million optically selected galaxies in the EMU data will result in a noise level of ~10 nJy. Because of the wide area of the EMU, WODAN, and LOFAR surveys, even rare classes of sources can be stacked, and it should also be possible to create stacked images of extended sources, such as clusters. However, the extent to which such deep stacking will be successful will depend on the extent to which imaging artefacts are cancelled by stacking. Stacking is also not without its hazards, and can be biased by a number of effects such as failure to account for the PSF, particularly in the presence of confusion and in highly clustered fields (Bourne et al. Reference Bourne, Dunne, Ivison, Maddox, Dickinson and Frayer2011; Greve et al. Reference Greve2010; Penner et al. Reference Penner2011; Chary, Cooray, & Sullivan Reference Chary, Cooray and Sullivan2008; Béthermin et al. Reference Béthermin, Dole, Beelen and Aussel2010).

Other examples of data-intensive research include:

• • Identification of sources which do not fit into known categories of radio source, and so are likely to be artefacts or exciting new classes of source, as discussed in Section 3.9.

• • Extraction of low surface brightness radio emission to detect the WHIM synchrotron emission from cosmic filaments or sheets, by cross-correlating with optical galaxies selected from other surveys.

• • Cross-correlation of low-redshift galaxies with high-redshift galaxies, or the CMB, to test cosmology and fundamental physics as discussed in Section 3.6.

4.8.2 Survey versus pointed data

Since surveys compete for observing time with conventional ‘pointed’ observations, it is useful to consider their role compared with projects doing detailed science on particular sources or fields. Clearly both modes are valuable and complementary. Surveys provide source lists for follow-up observations of particular sources, as well as finding and characterising calibrators for other radio observations. However, the huge volume of data from the new radio surveys will trigger a shift in the way astronomers ‘observe’. The ingenuity currently applied to devising a key experiment, and crafting a successful proposal, will be applied to devising novel ways of mining the data. To some extent, this is already happening, and about three times as many citations are delivered by results from the HST/STScI archive than from the papers written by PIs. The surveys discussed here will also have an enormous legacy value, since they will be hard to improve on until the technology makes a further major step forward.