Skip to main content Accessibility help
×
Home
Hostname: page-component-564cf476b6-lwxm7 Total loading time: 0.495 Render date: 2021-06-19T03:27:59.622Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Strategies for Finding Prompt Radio Counterparts to Gravitational Wave Transients with the Murchison Widefield Array

Published online by Cambridge University Press:  03 October 2016

D. L. Kaplan
Affiliation:
Department of Physics, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA
T. Murphy
Affiliation:
Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006, Australia ARC Centre of Excellence for All-sky Astrophysics (CAASTRO)
A. Rowlinson
Affiliation:
Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands ASTRON, The Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands
S. D. Croft
Affiliation:
University of California, Berkeley, Astronomy Dept., 501 Campbell Hall #3411, Berkeley, CA 94720, USA Eureka Scientific, Inc., 2452 Delmer Street Suite 100, Oakland, CA 94602, USA
R. B. Wayth
Affiliation:
ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia
C. M. Trott
Affiliation:
ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia
Corresponding
E-mail address:
Rights & Permissions[Opens in a new window]

Abstract

Wepresent and evaluate several strategies to search for prompt, low-frequency radio emission associated with gravitational wave transients using the Murchison Widefield Array. As we are able to repoint the Murchison Widefield Array on timescales of tens of seconds, we can search for the dispersed radio signal that has been predicted to originate along with or shortly after a neutron star-neutron star merger. We find that given the large, 600 deg2 instantaneous field of view of the Murchison Widefield Array, we can cover a significant fraction of the predicted gravitational wave error region, although due to the complicated geometry of the latter, we only cover > 50% of the error region for approximately 5% of events, and roughly 15% of events will be located < 10° from the Murchison Widefield Array pointing centre such that they will be covered in the radio images. For optimal conditions, our limiting flux density for a 10-s long transient would be 0.1 Jy, increasing to about 1 Jy for a wider range of events. This corresponds to luminosity limits of 1038−39 erg s−1 based on expectations for the distances of the gravitational wave transients, which should be sufficient to detect or significantly constrain a range of models for prompt emission.

Type
Research Article
Copyright
Copyright © Astronomical Society of Australia 2016 

1 INTRODUCTION

In 2015 September, the LIGO/Virgo Consortium (LVC) began its O1 science run that resulted in the first detection of gravitational waves (GWs) (Abbott et al. Reference Abbott2016c, also see Abbott et al. Reference Abbott2016a for a second event). Together with the GW analysis, the LVC sent private alerts to the electromagnetic (EM) follow-up community (Abbott et al. Reference Abbott2016b, Reference Abbott2016f) to identify coincident EM transients (e.g., Lipunov et al. Reference Lipunov2016; Evans et al. Reference Evans2016b; Troja et al. Reference Troja, Read, Tiengo and Salvaterra2016; Ackermann et al. Reference Ackermann2016; Morokuma et al. Reference Morokuma2016; Savchenko et al. Reference Savchenko2016; Connaughton et al. Reference Connaughton2016). This identification is complicated by the very large uncertainty regions for the GW events: As discussed in Singer et al. (Reference Singer2014) and Kasliwal & Nissanke (Reference Kasliwal and Nissanke2014), the error regions for these events can cover hundreds of square degrees (especially for the initial sensitivities of the detectors). Moreover, they need not be compact or simply connected. Whilst identifying an EM counterpart would greatly enhance the utility of the GW signal (e.g., Phinney Reference Phinney2009; Singer et al. Reference Singer2014; Chu et al. Reference Chu2016; Branchina & De Domenico Reference Branchina and De Domenico2016) and would enable a range of new physical and astrophysical tests, it is not a simple task (e.g., Kasliwal & Nissanke Reference Kasliwal and Nissanke2014; Cowperthwaite & Berger Reference Cowperthwaite and Berger2015).

The EM counterparts span a range of models at a range of wavelengths, see Metzger & Berger (Reference Metzger and Berger2012), Singer et al. (Reference Singer2014), Kasliwal & Nissanke (Reference Kasliwal and Nissanke2014), and Chu et al. (Reference Chu2016), amongst other recent publications. At low radio frequencies, telescopes such as the Murchison Widefield Array (MWA; Tingay et al. Reference Tingay2013), the Low Frequency Array (LOFAR; van Haarlem et al. Reference van Haarlem2013), and the Long Wavelength Array (LWA; Ellingson et al. Reference Ellingson2009) have a number of advantages over optical/infrared searches: They have fields of view of hundreds to thousands of square degrees; unlike the optical/near-infrared sky which has a large number of transients present in every field (e.g., Cowperthwaite & Berger Reference Cowperthwaite and Berger2015), the radio sky is relatively quiet at these frequencies (Karastergiou et al. Reference Karastergiou2015; Tingay et al. Reference Tingay2015; Stewart et al. Reference Stewart2016; Rowlinson et al. Reference Rowlinson2016; Polisensky et al. Reference Polisensky2016) with very few unrelated transients (e.g., Hotokezaka et al. Reference Hotokezaka2016) to distract from those associated with the GW event; and many of the low-frequency facilities have no moving elements and so in principle can respond within seconds to an external trigger.

Whilst most expectations for transients associated with GW sources at radio wavelengths have concentrated on late-time radio afterglows and remnants (Metzger, Williams, & Berger Reference Metzger, Williams and Berger2015; Hotokezaka & Piran Reference Hotokezaka and Piran2015; Morsony, Workman, & Ryan Reference Morsony, Workman and Ryan2016; Hotokezaka et al. Reference Hotokezaka2016; Palliyaguru et al. Reference Palliyaguru2016), which only peak after hundreds or thousands of days at 150 MHz and can be quite faint (depending on the parameters of the explosion and the circumburst medium), there are models that predict a prompt, coherent radio transient from the GW event (e.g., Lipunov & Panchenko Reference Lipunov and Panchenko1996; Usov & Katz Reference Usov and Katz2000; Pshirkov & Postnov Reference Pshirkov and Postnov2010; Totani Reference Totani2013; Zhang Reference Zhang2014; Wang et al. Reference Wang, Yang, Wu, Dai and Wang2016; Metzger & Zivancev Reference Metzger and Zivancev2016) which may be related to the phenomenon of fast radio bursts (FRBs; Lorimer et al. Reference Lorimer, Bailes, McLaughlin, Narkevic and Crawford2007; Thornton et al. Reference Thornton2013) at least some of which may be cosmological in origin (Keane et al. Reference Keane2016, although see Williams & Berger Reference Williams and Berger2016; Vedantham et al. Reference Vedantham2016). Searches for direct connections between GW events and FRBs are proceeding largelyFootnote 1 through searches for GW events associated with individual FRBs (e.g., Abbott et al. Reference Abbott2016e) since the GW detectors have quasi-all sky sensitivity. But this strategy can be reversed: Given their wide fields of view and very fast response times (Kaplan et al. Reference Kaplan2015), low-frequency facilities might be ideal for finding such prompt emission (Chu et al. Reference Chu2016; Howell et al. Reference Howell2015) triggered instead by the GW signal. We then must optimise the follow-up procedure to maximise the prospects of a discovery without time for human-aided decision making.

Strategies to aid follow-up have been studied in the optical/near-infrared regime (Rana et al. Reference Rana, Singhal, Gadre, Bhalerao and Bose2016; Chan et al. Reference Chan, Hu, Messenger, Hendry and Heng2015) where the signals are likely to be faint, relatively short in duration, and may be quite red (Metzger et al. Reference Metzger2010; Metzger & Berger Reference Metzger and Berger2012; Barnes & Kasen Reference Barnes and Kasen2013; Metzger & Fernández Reference Metzger and Fernández2014; Kasen, Fernández, & Metzger Reference Kasen, Fernández and Metzger2015). In the optical/near-IR, the search can be aided by using prior information on host galaxies and likely distances to help reduce the search volume (e.g., Gehrels et al. Reference Gehrels2016; Singer et al. Reference Singer2016). Strategies have also been studied in the X-ray regime (e.g., Evans et al. Reference Evans2016a), looking to directly probe the association between GW events and short gamma-ray bursts.

In this paper, we present and compare concrete strategies for low-frequency radio follow-up to search for prompt radio emission from a GW transient, where we use the MWA as an example to determine the likely sensitivity and success rate. Unlike in the optical/near-infrared, where a limited time window nonetheless allows limited sky coverage (e.g., Chan et al. Reference Chan, Hu, Messenger, Hendry and Heng2015), if we are searching for a prompt (duration ≲ ms) radio signal, we are limited to only a single pointing, and so we must optimise where that is with limited information. We discuss this in the context of simulated GW error regions from the first couple of years of GW observations, using two and three detectors (based on the simulated events from Singer et al. Reference Singer2014). The MWA occupies a middle ground in the current generation of low-frequency arrays: It has a considerably wider field of view than the more sensitive LOFAR, but it is pointed, unlike the LWA which observes the whole (visible) sky. The MWA can respond on timescales of seconds to external triggers, which is currently not possible with LOFAR (A. Rowlinson 2016, personal communication) and which is not needed with the LWA’s all-sky coverage. We discuss a search that focusses on standard imaging techniques (Tingay et al. Reference Tingay2015; Kaplan et al. Reference Kaplan2015; Rowlinson et al. Reference Rowlinson2016) and not more rapid ‘beam-formed’ data (e.g., Coenen et al. Reference Coenen2014; Karastergiou et al. Reference Karastergiou2015; Tremblay et al. Reference Tremblay2015), which, although it can be more sensitive to fast signals, is much more computationally intensive to process.

2 SEARCH METRICS

To assess the success or failure of our pointing strategies, we looked at a number of different metrics and computed these for simulated GW events based on realistic expectations for the first two years of GW detector operations (Singer et al. Reference Singer2014)Footnote 2 . These simulated events included the large uncertainty region that will be communicated rapidly to EM observers, as well as the actual event locations and distances. Therefore, for a given pointing strategy, we computed the distribution of flux density and luminosity sensitivities for each simulated event. These were compared with model predictions (such as Pshirkov & Postnov Reference Pshirkov and Postnov2010; Totani Reference Totani2013; Zhang Reference Zhang2014). We also computed the separation between our pointing centre and the event location or the fraction of the total probability map covered by the observations (Abbott et al. Reference Abbott2016b, Reference Abbott2016f), but these are of limited use for a wide-field aperture array. This is because unlike optical observations with a finite but relatively uniformly covered field of view (limited slightly by vignetting), the sensitivity for an aperture array over the sky is controlled primarily by the primary beam and varies considerably over the area imaged, with some sensitivity even down to the horizon (e.g., Neben et al. Reference Neben2015).

The flux density sensitivity of the MWA observations at the positions of the GW events was computed using the tile area at 150 MHz from Tingay et al. (Reference Tingay2013), along with a receiver temperature of 50 K. To that, we added a predicted sky temperature, computed by integrating the Global Sky Model (de Oliveira-Costa et al. Reference de Oliveira-Costa2008, interpolated to 150 MHz) over the MWA tile response. We do not account for the additional contribution of the Sun. We assume a 10 σ detection threshold with 30 MHz bandwidth over a 10-s observation. The search duration is determined from likely dispersion measures: For an event at a redshift z ≈ 0.05 which is a typical horizon for the current detectors, Ioka (Reference Ioka2003) and Inoue (Reference Inoue2004) predict an extragalactic dispersion measure DM ≈ 50 pc cm−3. This can be added to dispersion measures of 50–100 pc cm−3 from the Milky Way and the host galaxy (e.g., Cordes & Lazio Reference Cordes and Lazio2002; Keane et al. Reference Keane2016; Kaplan et al. Reference Kaplan2015) for a total of 150–250 pc cm−3. With the 30 MHz bandwidth of the MWA centred at 150 MHz, this gives an event duration of 10–20 s (Lorimer & Kramer Reference Lorimer and Kramer2004; Kaplan et al. Reference Kaplan2015; Rowlinson et al. Reference Rowlinson2016). We assume no additional loss of sensitivity due to the complex nature of the Galactic synchrotron emission, but this is likely reasonable given the short duration of the expected signals. The resulting flux density is converted to a luminosity using the simulated event distance.

3 POINTING STRATEGIES

To point the MWA, we change the delays for individual dipole antennas on each tile. The whole array (128 tiles) can be pointed together, or it can be split into subarrays, but only a single pointing is current possible for each tile. The pointing is generally done at a series of discrete steps about 7° apart. The nominal field of view is about 600 deg2 at 150 MHz (Tingay et al. Reference Tingay2013). Our first goal was to determine a pointing strategy: When a HEALPIX (Górski et al. Reference Górski2005) sky probability map is received, where do we point the MWA and do we point as a single array or use subarrays?

We consider several simple strategies:

  1. (1) Zenith pointing.

  2. (2) Point towards the maximum of the probability accessible (i.e., above the horizon) in the map.

  3. (3) Point towards the maximum of the probability weighted by cos 2 Z accessible (i.e., over the horizon) in the map, where Z is the zenith angle.

  4. (4) Maximise the overlap between the MWA primary beam pattern and the GW probability map.

The first of these serves as a benchmark. In addition, the sensitivity of the MWA is maximum at zenith and the primary beam at that pointing has been characterised considerably better than for other pointings. Finally, this strategy has the benefit that no decisions are necessary, so the MWA can repoint as soon as a GW alert is received. Moreover, meridian drift-scans are amongst the most common observational programme (e.g., for the MWA Transients Survey and the GaLactic and Extragalactic All-Sky MWA Survey; Bell et al. Reference Bell2016; Wayth et al. Reference Wayth2015), so if we did not interrupt an ongoing observation this would be the most likely result.

The second strategy is also simple. We simply identify the point in the GW probability map (which is sent along with the alert announcements) that has the highest value and which is also above the horizon. This is also relatively fast to compute, although it does require parsing of the GW probability map and not just knowledge of an alert.

The third strategy is very similar to the second, except that we account for the overall envelope of a Hertzian dipole which is the basic component of an MWA tile (Tingay et al. Reference Tingay2013; Sutinjo et al. Reference Sutinjo2015; Neben et al. Reference Neben2015). This downweights observations close to the horizon.

Finally, the fourth strategy examines the overlap between the LVC GW sky probability and the MWA’s pointing pattern. Specifically, it tries to maximise:

(1) $$\begin{equation} I_{\rm MWA}= \int d\Omega \, P_{{\rm LVC}}(\alpha ,\delta ) B_{\rm tile}(\alpha ,\delta ), \end{equation}$$

where P LVC is the normalised sky probability returned in the LVC HEALPIX map as a function of sky position (α, δ), and B tile(α, δ) is the individual tile response for the MWA, normalised to 1 at the zenith. Constructed in this way, we maximise I MWA by choosing the best discrete pointing B tile.

The implementation of the four strategies proceeds as follows. Strategy 1 is fixed to the zenith, so no computation is necessary. For the other strategies, we first compute the MWA horizon. If the integral of P LVC (weighted by cos 2 Z for strategy 3, or by B tile for strategy 4) above the horizon is less than some threshold (currently 2%), we do not consider the target worthwhile, and do not return a pointing position. Otherwise, strategies 2 and 3 return the discretised pointing closest to the maximum of P LVC (strategy 2) or P LVCcos 2 Z (strategy 3). For strategy 4, we iterate through the range of discrete tile pointings. For each one, we compute the normalised MWA tile beam pattern sampled on the HEALPIX gridFootnote 3 . We then identify the pointing position that maximises the integral of P LVC × B. If that integral is less than a threshold (again currently 2%), we again do not consider the target worthwhile, and do not return a pointing position. Otherwise, we return the optimal target position α, δ, along with (if desired) the beamformer delays and the integrated probability.

4 EVENT EXPECTATIONS

We sought to predict our event coverage and flux density/luminosity sensitivites to actual LIGO transients using the simulated events from 2016 (including potentially both LIGO sites as well as Virgo) given at http://www.ligo.org/scientists/first2years/ (Singer et al. Reference Singer2014). There are 475 simulated signals, covering a realistic range of signal-to-noise ratio and sky position. Examples of this are shown in Figure 1. It is clear that even with a reasonable probability coverage it is possible to miss the actual transient. We see two qualitatively different results. In the first, especially where only two GW detectors see the transient, the large, elongated uncertainty region means that there is a substantial chance of missing the actual transient regardless of strategy, even with the MWA’s large field of view, but on average strategies 2–4 will see some fraction of the transients discussed below. The second type of result has a small enough uncertainty region that all pointing strategies give substantially similar results, and we are just limited by the horizon and the sensitivity of the MWA.

Figure 1. Sky probability map of simulated LVC transients from Singer et al. (Reference Singer2014). The colour is proportional to the log 10 of the probability. The black lines are the MWA horizon. The MWA half-power beams are shown by the blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). The white stars are the actual event locations. For the event on the left, the GW signal was only recovered by two detectors with a net signal-to-noise ratio of 14.7, leading to a large error region. In contrast, the event on the right the GW signal was recovered by three detectors with a net signal-to-noise ratio of 21.8, which greatly improves the localisations and leads to very similar pointings for strategies 2–4. The images are Mollweide projections of the celestial sphere, labelled in Right Ascension and Declination, and centred on the local sidereal time at the MWA. For the event on the right, we also show a zoom around the position of the event.

We show the results in Figures 2–4. In Figure 2, we plot the separation between the MWA pointing centre for each event and each strategy with the actual event location. For strategies 2 and 3, roughly 20% of the events have separations < 10°, which is the half-power point at 150 MHz. This decreases to roughly 15% of the events for strategy 4, and < 3% for strategy 1 (the control). In many cases, the pointings will be similar for strategies 2–4 (as in the right panel of Figure 1), which accounts for the very similar distribution of events at separations < 5°.

Figure 2. Cumulative histogram of θ for the simulated 2016 events, assuming observations at 150 MHz: blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). The vertical line is the half-power point for 150 MHz.

Using these results, we can also compute the expected flux density sensitivity of the MWA observations at the positions of the GW events, as described in Section 2. For the coldest parts of the sky away from the Galactic plane, we get a limiting flux density of about 0.1 Jy. However, given the influence of Galactic synchrotron emission and the limited collecting area away from zenith, only 5% of the simulated events are close to that limit. If we consider the 15% of events that are with the half-power point, a more typical limiting flux density is 1 Jy (Figure 3). This can be compared with predictions from e.g., Pshirkov & Postnov (Reference Pshirkov and Postnov2010), who claim something like S ≈ 6 Jy at a distance of 100 Mpc and a frequency of 150 MHz, so we should be able to see events like those in about 15% of the cases. Once again we see little difference between strategies 2–4.

Figure 3. Cumulative histogram of limiting flux density (in Jy) for the simulated 2016 events, assuming observations at 150 MHz: blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). This assumes a 10 σ detection over 30 MHz of bandwidth in a 10-s integration. The sky temperature has been computed by integrating the Global Sky Model (de Oliveira-Costa et al. Reference de Oliveira-Costa2008, interpolated to 150 MHz) over the MWA tile response and assumes an additional 50 K for the receiver temperature. The vertical line shows the nominal 10 σ sensitivity limit from Tingay et al. (Reference Tingay2013).

We can also compute the limiting luminosity using the simulated GW event distances, finding limits of 1038−39 erg s−1 (Figure 4). As a representative comparison, we use the signal predicted by Pshirkov & Postnov (Reference Pshirkov and Postnov2010): 6 Jy at 100 Mpc, at a frequency of 150 MHz (this assumes an intrinsic spin-down luminosity of $\dot{E}=10^{50}\,{\rm erg\,s}^{-1}$ , efficiency scaling exponent γ = 0, and that the burst is scattered to a duration of ~10 s). For roughly 30% of the events would we be able to see the such a signal. This agrees with the estimates presented in Kaplan et al. (Reference Kaplan2015), where the prompt emission predicted by various models (such as Pshirkov & Postnov Reference Pshirkov and Postnov2010; Totani Reference Totani2013; Zhang Reference Zhang2014) is compared against the sensitivity of the MWA for prompt searches. Overall, they find that the sensitivity of the MWA should be sufficient for events at a redshift of z = 0.05, given the available predictions. In Figure 5, we show the event-by-event comparison for the different strategies. Not unexpectedly, strategy 1 performs poorly. Comparing strategies 2 and 3 to 4, the spread is a lot smaller for the better events (those with luminosity limits ≲ 1039 erg s−1), since those tend to have smaller uncertainty regions that are well covered by all three strategies. For the remaining events, the results change significantly whether strategy 2/3 or 4 is used, but there is not a global preference for one or the other.

Figure 4. Cumulative histogram of limiting luminosity νL ν (in erg s−1) for the simulated 2016 events, assuming observations at 150 MHz: blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). This assumes a 10 σ detection over 30 MHz of bandwidth in a 10 s integration. The sky temperature has been computed by integrating the Global Sky Model (de Oliveira-Costa et al. Reference de Oliveira-Costa2008, interpolated to 150 MHz) over the MWA tile response and assumes an additional 50 K for the receiver temperature. The dashed vertical line shows the nominal 10 σ sensitivity limit from Tingay et al. (Reference Tingay2013) at a distance of 100 Mpc, whilst the dotted vertical line shows the predicted luminosity from Pshirkov & Postnov (Reference Pshirkov and Postnov2010).

Figure 5. Comparison of limiting luminosity νL ν (in erg s−1) for the simulated 2016 events for each strategy, assuming observations at 150 MHz: left (strategy 1: zenith), middle (strategy 2: maximum probability), right (strategy 3: maximum probability weighted by cos 2 Z), all compared to strategy 4.

We explored the frequency dependence of these limits by repeating the exercise above for observations at 120, 150, and 180 MHz, which are the range where the MWA’s sensitivity is optimised. At lower frequencies, our primary beam will be larger and we will cover more of the GW error region. Conversely, at higher frequencies, the sky noise is lower, so the same observation will reach a lower limiting flux density. The 20th percentile for the limiting flux density (corresponding to a nominal 1 Jy in Figure 3) is about 40% higher at 120 MHz compared to 150 MHz, and 20% higher at 150 MHz compared to 180 MHz. However, we must also correct for the intrinsic spectral index β (with S ν∝νβ), which is predicted to vary between − 1 and − 2 (see e.g., Kaplan et al. Reference Kaplan2015). If this spectral index is steeper than − 1.5, then the lower frequencies will dominate. This leads us to a preference for lower frequency observations, but the unknown spectral index makes this preference weak.

5 DISCUSSION & CONCLUSION

In the analysis above, we found that about 15–20% of the events would be within the MWA’s half-power point. Therefore, we would require follow-up of ≳ 6 events before we have one with a relatively sensitive observation down to luminosity limits of ~1039 erg s−1. Currently, the predicted rates of neutron star-neutron star inspirals are 0.4–400 yr−1 with a mean of 40 yr−1 (Abadie et al. Reference Abadie2010; Dominik et al. Reference Dominik2015; Abbott et al. Reference Abbott2016d), so a single year of observing should be sufficient for one or more constraining observations if the rates are not too close to the most pessimistic case.

Comparing the four strategies outlined in Section 2, we can easily reject the control strategy 1 (zenith pointing), but the remaining strategies are largely comparable in performance. Individual events may be seen better with one or the other but with the limited information available from the prompt GW triggers we cannot know which will be best in advance.

Regardless of which strategy, the metrics in Section 2 rely on the MWA being sensitivity-limited rather than event-limited. In principle, we could have different tiles with different pointing locations, so as to cover the large LVC uncertainty region. However, the limited collecting area of the MWA drives us to point all of the tiles in a single subarray so as to achieve the most sensitive possible observation, rather than attempt to cover more of the GW error region at lower sensitivity (cf. Bloemen et al. Reference Bloemen, Groot, Nelemans, Klein-Wolt, Rucinski, Torres and Zejda2015). This is because, unlike in the optical regime where prompt emission from gamma-ray bursts is a known (albeit rare) phenomenon (e.g., Vestrand et al. Reference Vestrand2014), with a known luminosity function, prompt radio emission from a gamma-ray burst or a GW event has never been seen (Bannister et al. Reference Bannister, Murphy, Gaensler and Reynolds2012; Kaplan et al. Reference Kaplan2015) so we do not know if shallower observations will be adequate: In the best 30% of the cases where the MWA did cover the GW event with a reasonable sensitivity, our luminosity limits were only ~1 order of magnitude below model predictions. Splitting the MWA into subarrays would mean that all observations were less constraining. We can instead make up for the possibility of missing the GW event in a statistical sense by observing a larger number of events. At the same time, the increasing performance of the GW detectors will lead to a large number of targets with improving localisation. Therefore, we believe it best to stick with a single array, but this will be re-evaluated as the actual successes are evaluated. Similarly, we could experiment with other observational modes like splitting our 30-MHz bandpass into multiple sub-bands (as in Kaplan et al. Reference Kaplan2015), which could be advantageous if a bright but frequency-dependent signal is expected. Given the degree of uncertainty about these models that is unlikely to be preferred at least to start, but as we gain experience, we may change our procedure.

We implemented strategy 4 for the MWA during the first LIGO observing run (O1; 2015 September to 2016 January) covering the first detection, GW 150914. However, this trigger was released after a considerable delay (several days) needed for human examination of the event. Therefore, we did not require any real-time decisions about strategy but instead could use multiple pointings to tile the GW error regions (Abbott et al. Reference Abbott2016b). We expect that as the LVC improves their internal vetting and pipelines their latency will improve to 90–120 s after the GW event (Singer et al. Reference Singer2014; Cadonati, Astone, & van den Broeck Reference Cadonati, Astone and van den Broeck2014) or possibly better (Cannon et al. Reference Cannon2012; Chu et al. Reference Chu2016) and this strategy will be employed.

It is worth noting that the first published GW signal is from a binary black hole system (Abbott et al. Reference Abbott2016c), which is not expected to have any EM signature (Abbott et al. Reference Abbott2016b, but see Connaughton et al. Reference Connaughton2016). The rates of similar events will likely be quite high once LIGO reaches its full design sensitivity, approaching 1 d−1. If this is the case, then we will certainly have the opportunity to cover a sufficient number of error regions to search statistically for any associated EM emission, although the greater distances to the more massive systems will limit our sensitivity.

As discussed in Kaplan et al. (Reference Kaplan2015) and Chu et al. (Reference Chu2016), the expected delay of the radio signal relative to the GW transient is tens of seconds up to several minutes, based on the simulated distances of the transients and the expected extragalactic plus galactic dispersion measures. The actual time of any prompt radio signal may also be shifted by up to tens of seconds (e.g., Zhang Reference Zhang2014), potentially in either direction. Given the fast, ≈ 16 s response time that the MWA can achieve (Kaplan et al. Reference Kaplan2015), we can easily repoint to catch any prompt emission as long as the GW latency improves. Overall, we emphasise the need to transmit the trigger and react, as soon as possible, preferably well within 1 min.

We have demonstrated that the MWA can respond quickly to GW transients and cover a reasonable fraction of events with good sensitivity. The strategies outlined here are specifically applicable to the MWA, in that we have made use of the MWA’s location and primary beam pattern in assessing the follow-up prospects. They can be adapted for other facilities, but there other considerations may lead to different strategies. For instance, with a considerably smaller field of view but better instantaneous sensitivity splitting into subarrays may be more viable. This will also evolve as new data and new models for prompt emission become available. Overall, we believe that the MWA has a good combination of field of view, sensitivity, and operational flexibility that enables this science: The MWA has a much larger field of view compared to most pointed radio telescopes (e.g., Chu et al. Reference Chu2016; Abbott et al. Reference Abbott2016b), but is more sensitive than some all-sky facilities (e.g., Ellingson et al. Reference Ellingson2009). With roughly 1 yr of sensitive GW observations, we should be able to answer unambiguously which if any of the models for prompt emission are real.

ACKNOWLEDGEMENTS

We thank an anonymous referee and editor for helpful comments. DLK and SDC were supported by NSF grant AST-1412421. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All- sky Astrophysics (CAASTRO), through project number CE110001020. CMT is supported by an ARC Discovery Early Career Researcher Project Grant, DE140100316.

Footnotes

1 Even without a direct connection, current and future population studies (Keane & Petroff Reference Keane and Petroff2015; Law et al. Reference Law2015; Rane et al. Reference Rane2016; Li et al. Reference Li, Huang, Zhang, Li and Li2016) may be able to argue statistically for or against a connection (e.g., Thornton et al. Reference Thornton2013; Zhang Reference Zhang2016; Callister, Kanner, & Weinstein Reference Callister, Kanner and Weinstein2016).

3 For speed, we can resample the LVC HEALPIX grid from the initially fine resolution down to a coarser resolution suitable for the MWA. For example, often the LVC maps are returned with NSIDE = 2048, corresponding to a pixel size of 0.029°. This is often smaller than a single MWA pixel, and with 50 × 106 pixels, the calculation can be slow. Instead we resample (conserving probability) down to NSIDE = 64, corresponding to a pixel size of 0.92° (and 49 152 pixels).

References

Abadie, J., et al. 2010, CQGra, 27, 173001 CrossRefGoogle Scholar
Abbott, B. P., et al. 2016a, PhRvL, 116, 241103 Google Scholar
Abbott, B. P., et al. 2016b, ApJ, 826, L13 CrossRefGoogle Scholar
Abbott, B. P., et al. 2016c, PhRvL, 116, 061102 Google Scholar
Abbott, B. P., et al. 2016d, LRR, 19, 1a Google Scholar
Abbott, B. P., et al. 2016e, PhRvD, 93, 122008 Google Scholar
Abbott, B. P., et al. 2016f, ApJS, 225, 8 CrossRefGoogle Scholar
Ackermann, M., et al. 2016, ApJ, 823, L2 CrossRefGoogle Scholar
Bannister, K. W., Murphy, T., Gaensler, B. M., & Reynolds, J. E. 2012, ApJ, 757, 38 CrossRefGoogle Scholar
Barnes, J., & Kasen, D. 2013, ApJ, 775, 18 CrossRefGoogle Scholar
Bell, M. E., et al. 2016, MNRAS, 461, 908 CrossRefGoogle Scholar
Bloemen, S., Groot, P., Nelemans, G., & Klein-Wolt, M. 2015, in ASP Conf. Ser., Vol. 496, Living Together: Planets, Host Stars and Binaries, eds. Rucinski, S. M., Torres, G., & Zejda, M. (San Francisco: ASP), 254Google Scholar
Branchina, V., & De Domenico, M. 2016, arXiv:1604.08530Google Scholar
Cadonati, L., Astone, P., & van den Broeck, C. 2014, The LSC-Virgo White Paper on Gravitational Wave Searches and Astrophysics, Tech. Rep. T1400054-v7, LIGO, https://dcc.ligo.org/LIGO-T1400054/public Google Scholar
Callister, T., Kanner, J., & Weinstein, A. 2016, ApJ, 825, L12 CrossRefGoogle Scholar
Cannon, K., et al. 2012, ApJ, 748, 136 CrossRefGoogle Scholar
Chan, M. L., Hu, Y.-M., Messenger, C., Hendry, M., & Heng, I. S. 2015, e-prints, arXiv:1506.04035Google Scholar
Chu, Q., et al. 2016, MNRAS, 459, 121 CrossRefGoogle Scholar
Coenen, T., et al. 2014, A&A, 570, A60 Google Scholar
Connaughton, V., et al. 2016, ApJ, 826L, 6CGoogle Scholar
Cordes, J. M., & Lazio, T. J. W. 2002, ArXiv Astrophysics e-prints, astro-ph/0207156Google Scholar
Cowperthwaite, P. S., & Berger, E. 2015, ApJ, 814, 25 CrossRefGoogle Scholar
de Oliveira-Costa, A., et al. 2008, MNRAS, 388, 247 CrossRefGoogle Scholar
Dominik, M., et al. 2015, ApJ, 806, 263 CrossRefGoogle Scholar
Ellingson, S. W., et al. 2009, IEEEP, 97, 1421 Google Scholar
Evans, P. A., et al. 2016b, MNRAS, 460, L40 Google Scholar
Evans, P. A., et al. 2016a, MNRAS, 455, 1522 CrossRefGoogle Scholar
Gehrels, N., et al. 2016, ApJ, 820, 136 CrossRefGoogle Scholar
Górski, K. M., et al. 2005, ApJ, 622, 759 CrossRefGoogle Scholar
Hotokezaka, K., et al. 2016, ApJ, accepted, arXiv:1605.09395Google Scholar
Hotokezaka, K., & Piran, T. 2015, MNRAS, 450, 1430 CrossRefGoogle Scholar
Howell, E. J., et al. 2015, PASA, 32, e046 CrossRefGoogle Scholar
Inoue, S. 2004, MNRAS, 348, 999 CrossRefGoogle Scholar
Ioka, K. 2003, ApJ, 598, L79 CrossRefGoogle Scholar
Kaplan, D. L., et al. 2015, ApJ, 814, L25 CrossRefGoogle Scholar
Karastergiou, A., et al. 2015, MNRAS, 452, 1254 CrossRefGoogle Scholar
Kasen, D., Fernández, R., & Metzger, B. D. 2015, MNRAS, 450, 1777 CrossRefGoogle Scholar
Kasliwal, M. M., & Nissanke, S. 2014, ApJ, 789, L5 CrossRefGoogle Scholar
Keane, E. F., et al. 2016, Nature, 530, 453 CrossRefGoogle Scholar
Keane, E. F., & Petroff, E. 2015, MNRAS, 447, 2852 CrossRefGoogle Scholar
Law, C. J., et al. 2015, ApJ, 807, 16 CrossRefGoogle Scholar
Li, L., Huang, Y., Zhang, Z., Li, D., & Li, B. 2016, arXiv:1602.06099Google Scholar
Lipunov, V. M., et al. 2016, arXiv:1605.01607Google Scholar
Lipunov, V. M., & Panchenko, I. E. 1996, A&A, 312, 937 Google Scholar
Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J., & Crawford, F. 2007, Science, 318, 777 CrossRefGoogle Scholar
Lorimer, D. R., & Kramer, M. 2004, Handbook of Pulsar Astronomy (Cambridge: Cambridge University Press)Google Scholar
Metzger, B. D., & Berger, E. 2012, ApJ, 746, 48 CrossRefGoogle Scholar
Metzger, B. D., & Fernández, R. 2014, MNRAS, 441, 3444 CrossRefGoogle Scholar
Metzger, B. D., et al. 2010, MNRAS, 406, 2650 CrossRefGoogle Scholar
Metzger, B. D., Williams, P. K. G., & Berger, E. 2015, ApJ, 806, 224 CrossRefGoogle Scholar
Metzger, B. D., & Zivancev, C. 2016, MNRAS, 461, 4435 CrossRefGoogle Scholar
Morokuma, T., et al. 2016, PASJ, 68, L9 CrossRefGoogle Scholar
Morsony, B. J., Workman, J. C., & Ryan, D. M. 2016, ApJ, 825, L24 CrossRefGoogle Scholar
Neben, A. R., et al. 2015, RaSc, 50, 614 Google Scholar
Palliyaguru, N. T., et al. 2016, ApJ, submitted, arXiv:1608.06518Google Scholar
Phinney, E. S. 2009, in Astronomy, Vol. 2010, astro2010: The Astronomy and Astrophysics Decadal Survey, arXiv:0903.0098Google Scholar
Polisensky, E., et al. 2016, ApJ, submitted, arXiv:1604.00667Google Scholar
Pshirkov, M. S., & Postnov, K. A. 2010, Ap&SS, 330, 13 Google Scholar
Rana, J., Singhal, A., Gadre, B., Bhalerao, V., & Bose, S. 2016, ApJ, submitted, arXiv:1603.01689Google Scholar
Rane, A., et al. 2016, MNRAS, 455, 2207 CrossRefGoogle Scholar
Rowlinson, A., et al. 2016, MNRAS, 458, 3506 CrossRefGoogle Scholar
Savchenko, V., et al. 2016, ApJ, 820, L36 CrossRefGoogle Scholar
Singer, L. P., et al. 2016, ApJ, submitted, arXiv:1603.07333Google Scholar
Singer, L. P., et al. 2014, ApJ, 795, 105 CrossRefGoogle Scholar
Stewart, A. J., et al. 2016, MNRAS, 456, 2321 CrossRefGoogle Scholar
Sutinjo, A., et al. 2015, RaSc, 50, 52 Google Scholar
Thornton, D., et al. 2013, Science, 341, 53 CrossRefGoogle Scholar
Tingay, S. J., et al. 2013, PASA, 30, 7 CrossRefGoogle Scholar
Tingay, S. J., et al. 2015, AJ, 150, 199 CrossRefGoogle Scholar
Totani, T. 2013, PASJ, 65, L12 CrossRefGoogle Scholar
Tremblay, S. E., et al. 2015, PASA, 32, e005 CrossRefGoogle Scholar
Troja, E., Read, A. M., Tiengo, A., & Salvaterra, R. 2016, ApJ, 822, L8 CrossRefGoogle Scholar
Usov, V. V., & Katz, J. I. 2000, A&A, 364, 655 Google Scholar
van Haarlem, M. P., et al. 2013, A&A, 556, A2 Google Scholar
Vedantham, H. K., et al. 2016, ApJ, 824, L9 CrossRefGoogle Scholar
Vestrand, W. T., et al. 2014, Science, 343, 38 CrossRefGoogle Scholar
Wang, J.-S., Yang, Y.-P., Wu, X.-F., Dai, Z.-G., & Wang, F.-Y. 2016, ApJ, 822, L7 CrossRefGoogle Scholar
Wayth, R. B., et al. 2015, PASA, 32, e025 CrossRefGoogle Scholar
Williams, P. K. G., & Berger, E. 2016, ApJ, 821, L22 CrossRefGoogle Scholar
Zhang, B. 2014, ApJ, 780, L21 CrossRefGoogle Scholar
Zhang, B. 2016, ApJ, 827, L31 CrossRefGoogle Scholar
Figure 0

Figure 1. Sky probability map of simulated LVC transients from Singer et al. (2014). The colour is proportional to the log 10 of the probability. The black lines are the MWA horizon. The MWA half-power beams are shown by the blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). The white stars are the actual event locations. For the event on the left, the GW signal was only recovered by two detectors with a net signal-to-noise ratio of 14.7, leading to a large error region. In contrast, the event on the right the GW signal was recovered by three detectors with a net signal-to-noise ratio of 21.8, which greatly improves the localisations and leads to very similar pointings for strategies 2–4. The images are Mollweide projections of the celestial sphere, labelled in Right Ascension and Declination, and centred on the local sidereal time at the MWA. For the event on the right, we also show a zoom around the position of the event.

Figure 1

Figure 2. Cumulative histogram of θ for the simulated 2016 events, assuming observations at 150 MHz: blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). The vertical line is the half-power point for 150 MHz.

Figure 2

Figure 3. Cumulative histogram of limiting flux density (in Jy) for the simulated 2016 events, assuming observations at 150 MHz: blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). This assumes a 10 σ detection over 30 MHz of bandwidth in a 10-s integration. The sky temperature has been computed by integrating the Global Sky Model (de Oliveira-Costa et al. 2008, interpolated to 150 MHz) over the MWA tile response and assumes an additional 50 K for the receiver temperature. The vertical line shows the nominal 10 σ sensitivity limit from Tingay et al. (2013).

Figure 3

Figure 4. Cumulative histogram of limiting luminosity νL ν (in erg s−1) for the simulated 2016 events, assuming observations at 150 MHz: blue lines (strategy 1: zenith), red dashed lines (strategy 2: maximum probability), green dotted lines (strategy 3: maximum probability weighted by cos 2 Z), and thick magenta lines (strategy 4: maximum I MWA). This assumes a 10 σ detection over 30 MHz of bandwidth in a 10 s integration. The sky temperature has been computed by integrating the Global Sky Model (de Oliveira-Costa et al. 2008, interpolated to 150 MHz) over the MWA tile response and assumes an additional 50 K for the receiver temperature. The dashed vertical line shows the nominal 10 σ sensitivity limit from Tingay et al. (2013) at a distance of 100 Mpc, whilst the dotted vertical line shows the predicted luminosity from Pshirkov & Postnov (2010).

Figure 4

Figure 5. Comparison of limiting luminosity νL ν (in erg s−1) for the simulated 2016 events for each strategy, assuming observations at 150 MHz: left (strategy 1: zenith), middle (strategy 2: maximum probability), right (strategy 3: maximum probability weighted by cos 2 Z), all compared to strategy 4.

You have Access
16
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Strategies for Finding Prompt Radio Counterparts to Gravitational Wave Transients with the Murchison Widefield Array
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Strategies for Finding Prompt Radio Counterparts to Gravitational Wave Transients with the Murchison Widefield Array
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Strategies for Finding Prompt Radio Counterparts to Gravitational Wave Transients with the Murchison Widefield Array
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *