Limits on precursor and afterglow radio emission from a fast radio burst in a star-forming galaxy

The burst was detected on 2019 October 1 UT 16:55:35.97081 at a DM of 506.92(4) pc cm^-3, during observations taken as part of the Evolutionary Map of the Universe (EMU; Norris et al., 2011) pilot survey in the frequency range of $752-1088$ MHz. EMU is an ASKAP key science project to conduct a deep radio continuum survey of the entire southern sky. The FRB was detected in beam 24 (an outer ASKAP beam) of the closepack36 beam footprint pattern (see Shannon et al. (2018)) during a $\sim$9 hr observation with 30 antennas in a 336 MHz band centred on 920 MHz. The properties of the burst are presented in Table 1. Figure 1 shows FRB 191001’s pulse profile and dynamic spectrum. The discussions of the profile are presented in Section 2.5.1.

The standard ASKAP hardware correlator integrates and writes out visibilities on a 10-s timescale — hereafter termed “low time resolution” data. The correlator was operating simultaneously, and independently of, the CRAFT FRB search. The low time resolution data were calibrated following the standard data reduction steps as presented in Bhandari et al. (2018b) and were then used for imaging. We performed difference imaging of the consecutive 10-s snapshots around the FRB arrival time derived from the CRAFT data to check for any significant source in the direction of the FRB. FRB 191001 was detected in a difference image providing a preliminary position. Once found, we performed the imaging and deconvolution of that single integration (without differencing) to obtain a better estimate of the flux density. The FRB was detected with 9$\sigma$ significance with a primary beam corrected flux density of 19.3 mJy averaged over 10 s. (see right panel of Figure 2). We note that the fluence derived from the above flux density is $\sim 1.5\times$ higher than the measured fluence of the FRB. This can be explained by high uncertainty in the measurement of FRB fluence because of an outer beam detection.

The real-time detection of FRB 191001 in online incoherent-sum data triggered the retention of 3.1 s of raw (voltage) data around the FRB event. Due to a greater-than-usual latency (2.1 s in this case) between the FRB arrival and the voltage dump trigger⁶⁶6This was caused by a software bug that has since been corrected., only half the FRB signal was captured (a center frequency of 824 MHz and bandwidth of 144 MHz), with the upper half of the FRB emission (where the dispersion delay is less) already falling outside the voltage buffer. We followed standard CRAFT procedures for calibrating and imaging both the FRB and background continuum sources (Day et al., 2020), but flagged channels in which the FRB was not present for the FRB image only.

To refine the astrometric position of FRB 191001, we compared the positions of sources identified in the CRAFT image of the FRB field with reference positions obtained from the Australia Telescope Compact Array (ATCA) at 2 GHz, which is the closest we could get compared to ASKAP’s FRB observation at 824 MHz. We did not use the full ASKAP observation as a reference due to the known arcsecond level astrometric uncertainties in ASKAP pilot data (Bhandari et al., 2018b). The process involved observation of three bright calibrators around the FRB field, namely SUMSS J212104$-$611125, SUMSS J213520$-$500652, SUMSS J220054$-$552008, and three continuum sources detected in the ASKAP image of the field generated from the 3 s of data containing the FRB, namely J2132$-$5420, J2134$-$5450 and J2140$-$5455 at 824 MHz. The phase calibration solutions were derived using each of the calibrator sources and transferred to the background continuum sources and other calibrators. Out of three calibrators, the solutions derived from SUMSS J213520$-$500652 resulted in zero positional offsets between the known and derived positions (from ATCA image) of calibrators within positional uncertainties. Thus, SUMSS J213520$-$500652 was used for the remainder of this analysis.

The position of background sources obtained from the ATCA radio image were compared with the ASKAP field source positions, and we obtain a weighted mean systematic offset (also described in Macquart et al. (2020)) of $731\pm 107$ mas in RA and $-809\pm 99$ mas in Dec. These corrections were applied to the position of the FRB and final uncertainties were obtained by taking a quadrature sum of systematic and statistical uncertainties. The FRB position is RA(J2000): 21:33:24.37(2) and DEC(J2000): $-$54:44:51.86(13).

The observed DM of the FRB can be broken down into contributions from various components as

where $DM_{\rm ISM}$ is estimated to be $44~{}\rm pc~{}cm^{-3}$ and $31~{}\rm pc~{}cm^{-3}$ from the Galactic models of NE2001 (Cordes & Lazio, 2002) and YMW16 (Yao et al., 2017), respectively; the contributions from the Milky Way halo and the host galaxy are $DM_{\rm MW,halo}=50~{}\rm pc~{}cm^{-3}$ and $DM_{\rm host}=50/(1+z)=40~{}\rm pc~{}cm^{-3}$ respectively, following the assumptions presented in Macquart et al. (2020). This leaves the budget for DM from the intergalactic medium (IGM) to be $DM_{\rm cosmic}=373(386)~{}\rm pc~{}cm^{-3}$ using the NE2001(YMW16) models. Based on predictions from the Macquart relation (Macquart et al., 2020), we would expect $DM_{\rm cosmic}$ to be 203 pc cm^-3, which is significantly lower than the value of $DM_{\rm cosmic}$ inferred from the observed DM and assumptions for $DM_{\rm MW,halo}$ and $DM_{\rm host}$. Thus, as for FRB 190608 (Chittidi et al., 2020) and FRB 121102 (Tendulkar et al., 2017), it is likely that FRB 191001 has a larger host contribution than typical, or lies along a sightline that traces a denser-than-average path through the cosmic web (Simha et al., 2020). The host DM contribution can also be probed by optical studies. We use the relation between optical reddening $E(B-V)$ and hydrogen column density $N_{\rm H}$ from Güver & Özel (2009), together with the $DM$-$N_{\rm H}$ correlation of He et al. (2013) to estimate the DM contribution from the host of FRB 191001. We find $DM_{\rm host}=61$ pc cm^-3, which is higher than our previous assumption but still leads to an excess in the cosmic DM. A more detailed discussion of the breakdown of the excess DM for this FRB is beyond the scope of this paper, and will be considered in a future work.

We performed a high-time-resolution analysis of the FRB using the CRAFT voltage data. Data were beam-formed (i.e., coherently summed) at the position of the FRB using the delay, bandpass and phase solutions derived from the calibrator source PKS 0407$-$658. The 144 1-MHz-bandwidth ASKAP channels that contained signal from the FRB were then coherently de-dispersed at the FRB DM before being passed through a synthesis filter to reconstruct a single 144-MHz channel with $\sim$7 ns time resolution. A detailed description of the high time resolution construction process is given by Cho et al. (2020).

We determined the scintillation bandwidth ($\delta v_{d}$) using a range of time bins in the FRB dynamic spectrum (encompassing roughly the half-power points of the pulse), with frequency resolution of 7.812 kHz, by performing an auto-correlation function (ACF) analysis following Cho et al. (2020). We estimate $\delta v_{d}\sim 600$ kHz, which is consistent with expectations for diffractive scintillation (DISS) from the Milky Way along the burst line of sight at this frequency using the NE2001 model ($\sim 860$ kHz).

We fit the frequency-averaged pulse profile with scattered Gaussian pulse models using the nested sampling method presented in Qiu et al. (2020) and Cho et al. (2020) to compare the evidence for multiple pulse components as demonstrated in Day et al. (2020). Model comparison favors three scattered pulse components (TG model in Figure 3) by a Bayes Factor of $\rm{log_{10}B=20}$ to a single pulse model and $\rm{log_{10}B=5}$ to a double pulse model with significantly lower RMS error. The pulse width of components in order of appearance are $0.22\pm 0.03$, $0.4\pm 0.2$ and $9\pm 2$ ms respectively. We measure an exponential broadening of $3.3\pm 0.2$ ms at 824 MHz. The second and third pulse component occur $0.6\pm 0.2$ and $5.9\pm 1.2$ ms after the first pulse (see Figure 3). The presence of further components or frequency-dependent structure could plausibly explain the remaining structure in the residuals in Figure 3.

The host galaxy of FRB 191001 was identified as DES J213324.44$-$544454.18, a galaxy catalogued in the Dark Energy Survey (Abbott et al., 2018, DES). Spectroscopic observations conducted on 2019 October 4 UT using the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-South telescope established the redshift of the host to be $z=0.2340(1)$ using the H$\beta$ spectral line (see Heintz et al., 2020, for further details). On 2019 October 05 UT deep optical imaging observations were performed with the FOcal Reducer and low dispersion Spectrograph 2 (FORS2) instrument on the Very Large Telescope (VLT). The left panel of Figure 2 shows the $g$-band image of the host, which is clearly a spiral galaxy. The neighbouring galaxy, DES J213323.65$-$544453.6, is also at a similar redshift ($z=0.2339(2)$), hence the system is a double and possibly interacting pair of galaxies. Detailed optical properties of the host are described in Heintz et al. (2020).

We conducted observations with ATCA (project code C3211) in a 6-km array configuration to search for radio emission from the FRB 191001 host galaxy at 5.5 GHz and 7.5 GHz. Observations were performed in three epochs starting 2020 January 24, 2020 March 06 and 2020 March 12 at different hour angles to maximise ($u,v$)-coverage. Epoch 1 was badly affected by weather and therefore discarded. We later obtained a fourth epoch on 2020 April 16 (project code C3347) at 2 GHz, 5.5 GHz and 7.5 GHz. We combined epoch 2, epoch 3 and epoch 4 data in the 4 cm band for deep imaging. However, we use only epoch 4 data for estimating source flux densities.

We performed a search for repeats and afterglows at the position of FRB 191001. Firstly, a deep image of the field was made using ASKAP low time resolution data taken $\sim 8$ hrs prior to the FRB observation. A model of background sources was created using the CASA task TCLEAN and subtracted from all ASKAP data using UVSUB. Secondly, the visibilities were rotated in phase to the position of the FRB to extract the dynamic spectra. Finally, we obtained a light curve for $\sim$9 hrs of data (see left panel of Figure 5) by averaging baselines of the source-model-subtracted and phase-rotated data. We also subtracted the underlying host radio emission from the light curve. The peak in the light curve (Stokes I) is the emission from the FRB.

We averaged the light curve over boxcar widths of $2^{N}$, where $N$ varies from $0-9$, to search for slowly varying radio emission on timescales ranging from 10 s to 1.4 hr. The data shows red noise either due to contamination by sidelobes of poorly subtracted faint sources in the image domain, radio frequency interference (RFI), or residual emission from the host of FRB 191001 (see top panel of Figure 6), and is therefore not amenable to a chi-square test that assumes statistically independent (white) samples. By eye, we find no evidence for slowly varying radio emission at the FRB position $\sim 8$ hr before and $\sim 1$ hr after FRB 191001 above a $5\sigma$ flux density limit at respective timescales as presented in Table 3.

We also performed a search for dispersed radio emission pre/post-FRB in $\sim$3 s of CRAFT high time resolution data (presented in Section 2.5). We time-averaged the beam-formed data to 1 ms (see right panel of Figure 5) to obtain an initial time series, which was further averaged over boxcar widths $2^{N}$, where $N$ varies from $0-9$. This allowed a search for varying radio emission on timescales ranging from 1 ms – 512 ms. Analysis of the noise showed it to be Gaussian-distributed with no frequency dependence (i.e., white noise). Therefore, we performed a chi-square analysis to test the null hypothesis that there is a slow varying radio emission pre/post-FRB. The measured chi-square ($\chi^{2}_{\rm M}$) is given by

where $Y_{i}$ is the flux density for boxcar width $i$, $Y_{\rm mean}$ is the mean flux density of the time series and $\sigma_{i}$ is the standard deviation of the off-pulse time series scaled as $\sigma_{i}=\sigma_{0}/\sqrt{i}$ ($\sigma_{0}$ is the standard deviation of the subtracted FRB time series with zero boxcar width and $i=2^{N}$, where $N$ varies from $0-9$). We calculated the cumulative distribution function (CDF) and the probability $P$ of obtaining a measured chi-square ($\chi^{2}_{\rm M}$) by chance and compared it with the critical chi-square ($\chi^{2}_{\rm crit}$) for $N$ degrees of freedom. Variable radio emission exists if $\chi^{2}_{\rm M}>\chi^{2}_{\rm crit}$ for $P<0.02$ (98% confidence level). In our data, the $\chi^{2}_{\rm M}$ for each boxcar width was less than $\chi^{2}_{\rm crit}$. Therefore, we rejected the null hypothesis that varying radio emission exists at the 98% confidence level.

Here we consider the viability of detecting FRBs as image-plane transient in 10-s snapshot images with ASKAP. A $5\sigma$ detection in a 10-s ASKAP snapshot would be very difficult to confirm. We use $10\sigma$ or flux density greater than 20 mJy (robust=0.5 weighting) as a reasonable threshold, which should lead to minimal false positives. Of the CRAFT sample of 25 FRBs discovered in fly’s-eye mode (Shannon et al., 2018; Bhandari et al., 2019; Qiu et al., 2019), 3 have flux densities greater than 20 mJy, when diluted to 10 s integration time. Thus, three out of 25 FRBs would have been detected as reliable image plane transients. Scaling the ASKAP all-sky rate, R($>26$ Jy ms $(\rm w/1.26~{}\rm ms)^{-1/2})$ of 37 sky^-1 day^-1 (Shannon et al., 2018), we derive an FRB rate, $R(>20~{}\rm mJy,10~{}\rm s)$ of $4.4$ FRBs sky^-1 day^-1 or $0.00011$ deg^-2 day^-1. We compare this rate with other slow transients in Table 4. A scaling of $N\propto S^{-3/2}$ has been used to scale the rate of various slow transients above a flux density threshold of 0.3 mJy in Mooley et al. (2016) to the ASKAP flux density limit of 20 mJy. The FRB transients are more common than all other slow transients except the AGN(ISS) and the only transients expected on 10-s timescale.

How useful is a 10-s search of ASKAP data? The 10-s data search is affordable as compared to searching at different DM trials. However, DM searching would not be possible to confirm candidates as the dispersion delay is typically $\ll 10$ s for FRBs less than a DM of $\sim 2000~{}\rm pc~{}cm^{-3}$ at 920 MHz. Additionally, the existing incoherent sum (ICS) CRAFT search system can find FRBs more effectively. The S/N in the 10-s data is improved by $\sqrt{N}$, where $N$ is the number of antennas, but diluted by $\sqrt{\rm(10~{}s/FRB\_width)}$. For instance, a $100\sigma$ FRB of width $1$ ms in ICS mode with $N=36$ antennas will be a $6\sigma$ detection in ASKAP low-time-resolution imaging mode; hence ICS mode is significantly more sensitive than the ASKAP imaging mode. Nevertheless, we encourage searches for transients at shorter timescales at other interferometric sites which lack CRAFT-like system for potential FRB detection.

Wang & Lai (2020) have predicted radio afterglows for models involving a NS, WD or BH as the central engines, finding that sub-mJy level afterglows for non-repeating FRBs peak around 10 days post-burst at 1 GHz. For a binary NS merger scenario, the $\upmu$Jy level peak of the radio afterglow light curves of the jet (at different viewing angles) and isotropic ejecta at 1.4 GHz from a source at $z=0.5$ may vary on time scales of a few days to years (Lin & Totani, 2020). For a magnetar produced in a binary NS merger and AIC of a white dwarf, a late-time radio emission (from months/years to decades depending on the triggering mechanism) is anticipated (Margalit et al., 2019).

Most of these models predict FRB afterglows on timescales of months to years, longer than our observations probe. More interestingly for our study, Yi et al. (2014) present light curves for both forward- and reverse-shock afterglows on timescales of seconds to days post-burst. They used the standard fireball model for GRB afterglows to estimate luminosities of FRB radio afterglows for a range of assumed total kinetic energies and redshifts. Their models predict radio emission with post-burst flux densities $<1$ mJy for burst redshifts between 0.01 to 0.5 at 1 GHz. Our 920 MHz ASKAP data probe these timescales but the predicted fluxes are well below our search threshold of 10 mJy for a $5\sigma$ detection of radio emission from an FRB at $z=0.2340(1)$, consistent with our non-detection of afterglows in low time resolution data spanning the hour after the FRB.

Our luminosity limits are presented in Table 3. Detection of energetic and low redshift FRBs ($z=0.1-0.01$) in commensal ASKAP-CRAFT observations will place stronger constraints on the radio radiative efficiency of this model or could lead to detection. Constraints on long-lasting, persistent or variable radio emission associated with FRBs will require a long term monitoring program of FRB host galaxies on a day to year timescales.