A sub-arcsec localised fast radio burst with a significant host galaxy dispersion measure contribution

The relatively wide width of FRB 20210410D  suggests a repeater origin (Pleunis et al., 2021b). Consequently, we calculated the DM to optimise the structure under the burst envelope using DM_phase (https://github.com/danielemichilli/DM_phase). The DM_phase algorithm finds the structure-optimised DM of a burst by maximising the coherent power across the bandwidth (Seymour et al., 2019). We dedispersed the data over a trial DM range of $565.0\leq\rm{DM}\leq 580.0$ ${\rm pc\,cm^{-3}}$  in steps of 0.1 ${\rm pc\,cm^{-3}}$. The uncertainty on each DM estimate was calculated by converting the standard deviation of the coherent power spectrum into a standard deviation in DM via the Taylor series. We measure a structure-optimised DM of $571.2\pm 1$ ${\rm pc\,cm^{-3}}$ for FRB 20210410D. Visual inspection of the spectrum after dedispersing to the structure-optimised DM showed hints of scattering.

We performed a 2D scattering fit to the FRB using a python-based burst model software and Monte Carlo sampling methodology based on Qiu et al. (2020). We utilise a robust dynamic modelling in a higher resolution model to account for the convolved scatter broadening, dispersion smearing and intrinsic pulse width. The model also takes into account of any possible varying pulse arrival time across frequency due to incomplete dedispersionas seen in e.g Hessels et al. (2019). For FRB 20210410D, we assume a single Gaussian pulse model with scatter broadening. To avoid confusion with intrinsic pulse width and also to accurately determine scattering caused by inhomogeneous plasma, we fix the scattering index to $\alpha=-4$.

We measure a scattering time of $29.4^{+2.8}_{-2.7}$ ms at 1 GHz and an intrinsic pulse width of $1\sigma=\mathrm{2.0\pm 0.3\,ms}$. The pulse position is delayed in relation to frequency when structure maximised. This can be characterised as an excess dispersion delay of $1.8^{+0.5}_{-0.4}$ ${\rm pc\,cm^{-3}}$, which corresponds to the scattering corrected DM. The pulse position shift can also be characterised by a drift rate of $1.2\pm 0.4\ \mathrm{ms/107\ MHz}$ by measuring the two subband positions at 1444.5 MHz and 1016.5 MHz. Our relatively coarse time resolution of 306.24 $\upmu$s does not allow us to robustly distinguish between the two. We show our best-fit model and residuals in Figure 2 and the parameter posteriors in Figure 3.

The shortest integration image we could make during the 2021 April 10 observation when FRB 20210410D  was detected was 2 s. Though the standard integration time for MeerKAT imaging data is 8 s, it is possible to go to shorter integration times for certain projects. The MeerKAT open-time proposal SCI-20210212-CV-01 used an integration time of 2 s for their data, as there was a possibility of detecting repeat pulses from the target FRB 20190611B. As such, we imaged the observations into 2 s chunks. The 2 s images have a typical root-mean-square (RMS) noise of $\sim 0.7$ mJy $\mathrm{beam^{-1}}$ and a synthesised beam size of 21^′′$\times$10^′′.

To find the position of the FRB we used difference imaging. The total dispersion delay of FRB 20210410D across the MeerKAT band is $\sim$2.4 s and based on the time of detection, we expect most of the FRB to lie within a single 2 s image. We use WSClean to produce $20\times 2$ s images around the time of the MeerTRAP FRB detection. We then combined these images into an average image and subtracted this average image from each individual 2 s image. The subtracted images of the time step before, the time step of, and the time step after the FRB detection are shown in Figure 4. We can see in this figure that only the difference image at the time of the detection has a bright spot, which is $\sim$40′  from the phase centre of the images. As this source in the difference image is detected at the time that we expect to see the FRB, it is outside of the MeerTRAP coherent beam tiling as expected, it is the only source in the difference image, and there is no source in the difference images surrounding the expected FRB detection time, we determine that this source is the FRB. The FRB has a flux density of 35 mJy with a $\sim 1.8$ mJy RMS.

The position of the FRB detected in the difference image prior to astrometric correction is 21^h44^m20$.\!\!^{\rm s}$6s$\pm$0$\aas@@fstack{\prime\prime}$7 $-79^{\mathrm{\circ}}$19′04$\aas@@fstack{\prime\prime}$8$\pm$0$\aas@@fstack{\prime\prime}$3.

We corrected the astrometry in the MeerKAT images using the method described in Driessen et al. (2022). We imaged the full-time integration image of 2.25 hours to determine the astrometric correction. We first find the positions of the sources in the images using the Python Blob Detector and Source Finder¹¹1https://www.astron.nl/citt/pybdsf/ (pyBDSF). We then find Australian Telescope Compact Array (ATCA) Parkes-MIT-NRAO (PMN) (ATPMN; McConnell et al., 2012) sources within the MeerKAT FoV, excluding any sources that appear resolved in the MeerKAT images. There are 27 ATPMN sources in the FoV, 13 of which are resolved. The ATPMN positions of the unresolved sources, and the separations between the ATPMN and MeerKAT sources before and after applying the astrometric correction are shown in Table 2. The ATPMN survey has a median absolute astrometric uncertainty of 0$\aas@@fstack{\prime\prime}$4 in both Right Ascension (RA) and Declination (Dec). We use the matching ATPMN and MeerKAT point sources to solve for a transformation matrix to shift and rotate the MeerKAT sources to match the ATPMN source positions²²2The code for performing the astrometric corrections can be found on GitHub: https://github.com/AstroLaura/MeerKAT_Source_Matching. We apply the transformation matrix to all MeerKAT source positions and we combine the pyBDSF uncertainties and 0$\aas@@fstack{\prime\prime}$4 ATPMN uncertainty in quadrature. In shorter time-scale MeerKAT imaging, 2 s or 8 s images, we often do not detect many ATPMN sources. As such, we determine the astrometric correction using the sources extracted from the full integration image of the epoch and apply that correction to the sources extracted from the 2 or 8 s images. We find that the corrected position of the FRB is 21^h44^m20$.\!\!^{\rm s}$7s$\pm$0$\aas@@fstack{\prime\prime}$8 $-79^{\mathrm{\circ}}$19′05$\aas@@fstack{\prime\prime}$5$\pm$0$\aas@@fstack{\prime\prime}$5.

The FRB was detected in the $\sim 1$-hour long observation on 2021 April 10, $\sim$40′ from the phase centre. This means that the sensitivity to faint, persistent emission near the FRB was low. A 3-hour long observation on 2021 September 05 was pointed to accommodate three FRBs within the MeerKAT FoV. This meant that the position of FRB 20210410D  was $\sim$28′ from the phase centre resulting in higher sensitivity at the FRB position than in the detection observation. On 2021 September 05 a faint, $\sim 8\sigma$ (RMS = $\sim 4.8\,\mu$Jy) persistent continuum source was detected $\sim$3^′′ from the FRB position. We corrected the astrometry of the image (the offsets between the MeerKAT positions and ATPMN positions before and after correction are shown in Table 2) and found the corrected position of the persistent continuum source to be 21^h44^m19$.\!\!^{\rm s}$5s$\pm$0$\aas@@fstack{\prime\prime}$6 $-79^{\mathrm{\circ}}$19′05$\aas@@fstack{\prime\prime}$8s$\pm$0$\aas@@fstack{\prime\prime}$5 (uncorrected: 21^h44^m19$.\!\!^{\rm s}$4s$\pm$0$\aas@@fstack{\prime\prime}$4 $-79^{\mathrm{\circ}}$19′05$\aas@@fstack{\prime\prime}$4s$\pm$0$\aas@@fstack{\prime\prime}$3). The separation between the corrected FRB position and the corrected persistent continuum source position is 3$\aas@@fstack{\prime\prime}$3. The MeerKAT persistent continuum source is consistent with the position of the galaxy at $z\sim 0.4$ (see Section 4.5 for details) as shown in Figure 5 and is not a compact persistent radio source (PRS) as observed in a couple of repeating FRBs.

The FRB discovery was made while commensally observing with a MeerKAT open-time proposal that did not require polarization information. Consequently, a standard polarization calibrator was not observed. To extract the polarization information we used, in the 2 s image containing the FRB detection, J1619$-$8418 as the secondary and polarization calibrator. It is a known calibrator with very low linear ($\sim 0.4\%$) and circular ($\sim 0.03\%$) polarization³³3https://archive-gw-1.kat.ac.za/public/meerkat/MeerKAT-L-band-Polarimetric-Calibration.pdf. We mapped Stokes Q, U, and V along with Stokes I using the IDIA pipeline⁴⁴4https://idia-pipelines.github.io/. FRB 20210410D  was only detected in Stokes I and not in Stokes Q, U or V, giving us a $3\sigma$ upper limit of about $18\%$ for each of them. We used the RMsynth3D algorithm from the RM-tools⁵⁵5https://github.com/CIRADA-Tools/RM-Tools package to perform 3D RM synthesis on the image-frequency cube. The method transforms polarized intensity as a function of $\lambda^{2}$ to Faraday depth, $\phi$, representing polarized intensity for different trial RMs in the range [$-150000,+150000$]. We did not detect a peak in the maximum polarized intensity map at the position of the FRB. We do, however, detect a peak at a $6\sigma$ significance with an RM of $-77,929$ rad m^-2. This peak is not associated with any of the sources detected in the field in Figure 5. Therefore, we consider this a spurious detection.

FRB 20210410D is approximately $1\degr$ away from the position of FRB 20190611B and $0.7\degr$ away from FRB 20190102C, both of which were observed as part of the open-time proposal with MeerKAT. The MeerTRAP backend was used to piggy-back these imaging observations to look for any repeat bursts from FRB 20190611B, FRB 20190102C and consequently, from FRB 20210410D in real-time. No other radio bursts (whether repeat bursts from the known FRBs in the field or completely unassociated) were detected in our beamformed data down to a fluence limit of $0.09$ Jy ms in a total of 7.28 h of time spent on the FRB source with MeerKAT.

In addition, we performed follow-up observations of the FRB 20210410D source using the ultra-wideband low (UWL) receiver at the 64-m Murriyang (formerly known as Parkes) radio telescope. The observations spanned a bandwidth of 0.7–4 GHz and were centred at 2368 MHz. We observed the FRB source for a total of 1.9 h on 2022 January 29 and 1.1 h on 2022 July 19. We searched the Parkes data for repeat bursts using the GPU-based single-pulse search software Heimdall (Barsdell, 2012) and utilized the neural-network trained model Fetch (Agarwal et al., 2020) for the classification of candidates. We employed a tiered sub-band strategy as described in Kumar et al. (2021) to search the wide-band Parkes data in the DM range of 100–1100 pc cm^-3. In these searches, we did not find any significant repetition candidate above an S/N of 8. Using the radiometer equation and assuming a nominal burst width of 1 ms, we can constrain the detectable fluence of the repeat bursts. Our search pipeline was sensitive up to $\sim$1 Jy ms, assuming the repeat bursts are narrowband $\sim 64$ MHz and $\lesssim$ 0.15 Jy ms for a burst spanning the entire UWL band.

We also observed FRB 20210410D for a total of $\sim$5.7 hrs over four separate epochs in 2022 (September 3, October 6, October 15, and October 22) with DSS-43, a 70-m diameter dish located at the Deep Space Network’s (DSN) complex in Canberra, Australia. These observations were carried out simultaneously at S-band (centre frequency of 2.3 GHz) and at X-band (centre frequency of 8.4 GHz). The data were recorded in both left and right circular polarization modes using the resident pulsar backend in filterbank search mode, where channelized power spectral density measurements are recorded with 1 MHz channel spacing and a time resolution of 512 $\mu$s. The S-band system spans roughly 120 MHz of bandwidth, while the X-band system spans a bandwidth of 400 MHz.

The data processing procedures followed the same steps outlined in previous DSN studies of pulsars and FRBs (e.g. Majid et al., 2021). Datasets in each observing band were first corrected for bandpass slope. We excised bad frequency channels corrupted by radio frequency interference (RFI) using PRESTO’s rfifind package. To remove any long-timescale temporal variability, we subtracted a 5-s moving average from each data point. Datasets from the two orthogonal polarizations were then summed in quadrature.

The cleaned data were then dedispersed with the nominal DM value of 578.78 ${\rm pc\,cm^{-3}}$. The resulting time series were searched for FRBs using a matched filtering algorithm by convolving individual time series with logarithmically-spaced boxcar functions of widths ranging between 1-300 times the intrinsic time resolution of the pulsar backend. We did not detect any candidate bursts above a S/N threshold of 7 in either frequency band, corresponding to a flux threshold of 0.33 Jy at S-band and 0.19 Jy at X-band for a 1 ms duration burst.

We performed a Probabilistic Association of Transients to their Hosts (PATH; Aggarwal et al., 2021) analysis to estimate posterior probabilities for the host galaxy candidates of FRB 20210410D. Our analysis adopts the revised priors for FRBs (Shannon et al. in prep), specifically with an exponential scale length of 1/2 the effective radius. Furthermore, we focused the analysis on the SOAR/Goodman $r$-band image. Assuming an unseen prior of $P(U)=0$, i.e. the host is detected in our relatively deep image, we calculate the posterior probabilities listed in Table 3. It is evident that the galaxy J214420.69$-$791904.8 which lies closest to the FRB has a very high posterior probability ($P(O)>99.5\%$). We, therefore, assign it as the host with high confidence. The offset of FRB 20210410D’s position from the galaxy core is not uncommon, as in most cases the FRB localisations are significantly offset from the host galaxy centres (Bhandari et al., 2022b).

We performed longslit spectroscopy with the Gemini-South GMOS spectrograph (Hook et al., 2004; Gimeno et al., 2016) towards FRB 20210410D as part of programs GS-2021B-Q-138 and GS-2022A-Q-143 (PI Tejos). Given the relative positions of the sources of interest, we used the 1^′′ slit with two position angles (PAs). On UT 2021 October 14 we used a PA=102 $\deg$ covering the FRB host, Source 3 and the (northwestern) outskirts of Source 1, and obtained $3\times 1000$ s exposures using the R400 grating centred at $700$ nm. On UT 2022 June 07 we used a PA=10 $\deg$ covering the centers of Source 1 and Source 2 and obtained $4\times 600$ s exposures using the R400 grating centred at $700$ and $750$ nm (two exposures each).⁶⁶6The use of two central wavelengths was needed in order to cover a CCD gap produced by a reported failure in one of the GMOS-South CCD amplifiers. A $2\times 2$ binning was used in all the exposures.

We reduced these data with the PypeIt pipeline (Prochaska et al., 2020) using standard recipes. For the host galaxy, we established a secure redshift of $z=0.1415$ from several emission lines present in the spectrum (H$\alpha$, H$\beta$, [N ii], S ii). For Source 1 we could only identify a single emission line and thus the redshift is not secure; given its observed wavelength we deem this line to be H$\alpha$ at $z=0.4$ (background). For Sources 2 and 3 we could not identify any strong emission line. We note that Source 3 appears spatially unresolved and thus it may well be a star.

These results have been recently confirmed by subsequent VLT/MUSE integral field unit (IFU) observations obtained on UT 2022 October 25 (e.g. Bernales et al. in prep.), which securely confirm the H$\alpha$ identification of Source 1 (and thus its redshift); furthermore, these data have securely established that Source 2 is also background to J214420.69$-$791904.8.

To understand the stellar population properties of the host galaxy J214420.69$-$791904.8, we used the Bayesian inference code Prospector (Johnson et al., 2021) with a continuity non-parametric star formation history (SFH, Leja et al., 2019). Prospector performs stellar population synthesis by jointly fitting photometric and spectroscopic data using the python-fsps stellar population synthesis library (Conroy et al., 2009; Conroy & Gunn, 2010). The models were then sampled using the dynamic nested sampling routine dynesty (Speagle, 2020). Additionally, we implement the Kroupa (2001) IMF, Kriek & Conroy (2013) dust attenuation curve, the Gallazzi et al. (2005) mass-metallicity relationship, and a ratio on dust attenuation from young and old stars. To model the spectroscopy, we use a 12th-order Chebyshev polynomial to fit the observed spectrum to the model spectrum. Further, spectroscopic priors include a spectral smoothing parameter, a pixel outlier model to marginalize over noise, and a noise inflation model to ensure a good fit between the observed and model spectrum. Several selected stellar population parameters are presented in Table 1.

The DM contribution of the host galaxy may be independently estimated from its $\rm{H}_{\alpha}$ emission by converting the $\rm{H}_{\alpha}$ flux density, $F_{\rm{H\alpha}}=1.5\times 10^{-16}$ erg s^-1 cm^-2 to a ${\rm{H}}\alpha$ surface brightness of $S({\rm{H}}\alpha)=2.74\times 10^{-16}$ erg s^-1 cm^-2 arcsec^-2 assuming an angular size $\phi=0.5\hbox{${}^{\prime\prime}$}$. The $\rm{H}_{\alpha}$ surface brightness has been obtained by correcting the flux by Galactic extinction. For a temperature $T=10^{4}$ $T_{4}$ K, we express the emission measure, (EM = $\int{n_{e}^{2}\,dl}$) in the source frame,

The host DM in the source frame derived from EM (Cordes et al., 2016; Tendulkar et al., 2017) is given by,