The direct localization of a fast radio burst and its host

References

Methods

Detection and precise localization of an FRB requires $\sim$arcsecond angular resolution, $\sim$millisecond time resolution, and $\sim$MHz frequency resolution. In November 2015, we conducted 10 hours of fast dump (5 ms) observations of the FRB 121102 field with the VLA at 1.6 GHz, with no burst detections. In April–May 2016, we observed for 40 hours at 3 GHz, and again detected no bursts with either our fast imaging or beam-forming pipeline (described below). Detections of FRB 121102 with the 305-m Arecibo telescope suggested that VLA detections might be sensitivity limited, leading us to conduct a simultaneous observing campaign where Arecibo would identify a burst in the time domain and contemporaneous VLA observations would precisely localize it. In practice, this proved to be unnecessary for VLA detection, but it provided a wider frequency band to characterize the burst spectra.

Arecibo observations.

VLA fast-dump observations.

The VLA fast-sampled interferometric data were recorded with 5 ms integration time, 256 channels, and bandwidth 1024 MHz centred at 3 GHz. We first detected FRB 121102 on 2016 August 23 with a signal-to-noise ratio S/N$\sim$35. Through 2016 September, we continued coordinated Arecibo and VLA observations, detecting another 8 bursts at the same location and DM. In total, we acquired $\sim$83 hrs of fast-dump interferometric observations in three sessions: 2015 November at 1.6 GHz, 2016 April-May at 3 GHz, and 2016 August-September at 3 GHz with some observing at 6 GHz.

Millisecond imaging with fast-dump visibility data.

During the coordinated campaign, all bursts were detected with real-time analysis within hours of the data being recorded by the realfast system at the VLA. The real-time processing system de-dispersed visibilities to a small range of values centred on DM = 557.0 pc cm-3. For each integration and DM value, the pipeline formed a Stokes I image on time scales from 5 to 80 ms and saved images with peak S/N greater than 7.4, a threshold based on the known false positive rate due to thermal noise.

All candidates were re-analyzed offline with improved calibration, data cleaning, and refined localization using both custom, Python-based software and CASA. We calibrated and imaged de-dispersed visibilities with a typical sensitivity ($1\sigma$) of 5 mJy in 5 ms. Extended Data Table 1 lists burst properties, and the brightest detection is shown in Figure 1. By fitting a model of the synthesized beam to an image of the burst, we measure burst locations with statistical errors better than 0.3′′. However, the locations are affected by systematic errors at the level of about 1% of the synthesized beam sizes, a modest effect that is evident when comparing the localizations of the first four VLA burst detections (beam sizes $\sim$2.5′′$\times$ 2′′) with the last five (beam sizes $\sim$1.3′′$\times$ 0.8′′). Using just the last five burst centroids (with lower residual systematics due to the narrower beam), we find that the burst locations are consistent with the persistent radio continuum conterpart centroid (Extended Data Table 3 and Extended Data Figure 1). The radio continuum counterpart location is measured from the error-weighted mean of the location measured in deep imaging from 1 to 26 GHz (see below). The error in the offset is calculated from the quadrature sum of errors in each burst and the counterpart.

Beam-forming analysis with fast-dump visibility data.

Beam-forming is complementary to millisecond imaging: instead of de-dispersing interferometric visibilities and searching for bursts in the image domain, the visibilities are summed with appropriate phasing to produce time-frequency data that can be searched for dispersed bursts. For the VLA observations, the calibration tables generated from time-averaged data (see below) were applied to the fast-dump visibility data, and custom Python software and existing CASA tools were used to extract time-frequency data per beam from a tiling of synthesized beams covering the search region. The time-frequency data from each beam were then written to PSRFITS format and run through a single pulse search pipeline that used PRESTO pulsar processing tools. Single pulse candidates from all the synthesized beams were jointly filtered to remove candidates that occurred simultaneously in many beams, as well as candidates that were narrow-band, as these were likely caused by radio frequency interference. Diagnostic plots for the remaining candidates were examined by eye for bursts. The beam-forming pipeline was used to independently verify the times and positions of each of the VLA detected bursts. For the example shown in Figure 1, the instrumental time resolution for the observations (5 ms) is much larger than both the intrinsic pulse width and the intra-channel DM smearing, leading to a pixelated appearance.

VLA imaging observations of the persistent counterpart.

The 3 GHz VLA fast-dump observations were also averaged down to lower time resolution, calibrated using the standard VLA pipeline procedures with CASA, and imaged at each epoch. Once the persistent counterpart to FRB 121102 had been identified, we used these per-epoch images to construct the light curve of the source, as well as a deep average image of the sky (Figure 2 and Extended Data Table 2). The variability of the persistent radio counterpart is uncorrelated with the detection of bursts; the point biserial correlation coefficient between the detection (or not) of a burst and the flux density of the counterpart is $r=-0.054$, which would be exceeded by chance $\sim$75% of the time. Of the 69 sources detected within a 5′ radius, nine (including the persistent counterpart) showed significant variability, as measured by $\chi^{2}_{r}=1/(N-1)\;\Sigma_{t}(S_{t}-\bar{S})^{2}/\sigma_{t}^{2}>5.0$, where $S_{t}$ is the source flux density and $\sigma_{t}$ the image RMS at epoch $t$, and $\bar{S}$ is the epoch-averaged flux density.

We also acquired VLA imaging data covering a contiguous frequency range from 1 to 26 GHz. These observations utilized six separate receivers on the VLA: L- (1-2 GHz); S- (2-4 GHz); C- (4-8 GHz); X- (8-12 GHz); Ku- (12-18 GHz); and K-band (18-26 GHz). Observations were carried out on 2016 September 6 and 9, when the VLA was in the B-configuration, with maximum spacing between antennas of roughly 11 km (on September 9, a few antennas had been moved to their A-configuration locations). A third epoch was observed on September 28, only at C-band, with the VLA in the most extended A-configuration. Visibilities were dumped every 2 seconds, with channels of width either 1 or 2 MHz (depending on band). Calibration of the flux density scale was done using an observation of 3C 48 at all bands, and the secondary calibrator J0555+3948 was used to monitor complex gain (amplitude and phase) fluctuations as a function of time throughout each of the observations. Standard calibration was done with the VLA calibration pipeline, and subsequent imaging done in both CASA and AIPS. Final flux densities were estimated by a number of techniques to provide a cross-check, including imfit in CASA, JMFIT in AIPS, summing up CLEAN component flux density, and summing up flux density in the image pixels. Positions were measured using JMFIT. The two epochs (three for C-band) were imaged separately, and results between the two (three) were found to agree to within the uncertainties (Extended Data Figure 2), so visibility data from the two epochs (three for C-band) were combined together to make final images. Results are reported in Extended Data Table 3 and the measurements are plotted as part of the broad-band SED (Figure 3).

Very Long Baseline Interferometry with the European VLBI Network.

The European VLBI Network (EVN) observed at 1.65 GHz in five epochs (2016 February 2, 10–11, 11–12 and 2016 May 24, May 25) for about two hours per session. The array included the 100 m Effelsberg, the 76 m Jodrell Bank, the 32 m Medicina, the 25 m Onsala, the 32 m Torun, the 25 m Westerbork (single dish), and the 305 m Arecibo telescopes. The data were streamed to the EVN Software Correlator (SFXC) at the Joint Institute for VLBI ERIC (JIVE) in Dwingeloo, at a data rate of 1024 Mbit/s (512 Mbit/s for Arecibo) in real time. The individual station voltages were recorded simultaneously as well. During the first epoch, the ICRF source J0518+3306 was used as a phase-reference calibrator (separation from the field $\sim$2.9∘) and observations were alternated between the field (8 minutes) and the calibrator (2 minutes). For subsequent epochs we used J0529+3209 as phase-reference calibrator (separation $\sim$1.1∘) since it was proven to be sufficiently bright ($\sim$60 mJy) and compact for the EVN from the first epoch observations.

Following the VLA localization of FRB 121102, we re-correlated all our observations with the phase center at the FRB 121102 position. The data were analyzed with AIPS following standard procedures, and the images were made with the Caltech Difmap package. We did not detect the persistent counterpart during the first epoch due to a combination of technical failures and the distant phase calibrator. In the subsequent epochs we detected the persistent counterpart as a slightly resolved source with typical peak brightness of about 100 $\mu$Jy beam-1 and integrated flux density of about 200 $\mu$Jy, and deconvolved source size of about 5 $\times$ 3 milliarcseconds at a position angle of 140∘. The naturally-weighted beam size was about 18$\times$2.2 milliarcseconds in all cases, with a major axis position angle of $-$54∘; the noise was 7$\mu$Jy beam-1. Brightness temperature lower limits from the four successful epochs are $7\times 10^{6}$ K. (See Extended data Figure 2 and Table 3.)

Very Long Baseline Interferometry with the Very Long Baseline Array.

The NRAO Very Long Baseline Array (VLBA) observed on 2016 Sep 09, 16 with 8 hour tracks per epoch. First epoch observations were at $1.392-1.680$ GHz, with a synthesized beam size of 11.3 $\times$ 5.0 milliarcseconds at a position angle = 163.7∘. Second epoch observations were at $4.852-5.076$ GHz (beam size 2.74 $\times$ 1.43 milliarcseconds at a position angle = 174.8∘). A total recording bandwidth of 2 Gbps with dual circular polarizations was obtained for each observation. As in the EVN observations, the compact calibrator J0529+3209 was used to provide phase referencing solutions for FRB 121102. Standard interferometric calibrations were applied using AIPS. Images of the field achieved 17 and 12 $\mu$Jy beam-1 RMS at 1.5 and 5.0 GHz, respectively. The persistent counterpart to FRB 121102 was clearly detected in both observations with partially resolved compact structure. At 1.5 GHz, two-dimensional Gaussian deconvolution yields a size of 4.6$\times$3.3 milliarcseconds, while the 5.0 GHz upper limit on the deconvolved size is $<$1.73 milliarcseconds. Brightness temperature lower limits from the two epochs are $8\times 10^{6}$ and $3\times 10^{6}$ K, respectively. (See Extended data Figure 2 and Table 3.)

Atacama Large Millimeter Array observations.

The Atacama Large Millimeter and Submillimeter Array (ALMA) observed on 2016 Sep 15, using Band 6 and covering 8 GHz of bandwidth in the range $220-240$ GHz (with 2-MHz channels). We used 38 antennas in the C40-6 configuration, yielding a resolution of 0.32′′$\times$ 0.13′′. Calibration and imaging was provided by the ALMA observatory, and done using CASA via the ALMA pipeline. The image RMS noise level was 17 $\mu$Jy beam-1 and did not reveal any significant sources.

Optical and infrared imaging

The counterpart is not detected in near and mid-infrared observations from the UKIDSS and Deep GLIMPSE surveys with upper limits of $J=19.8$, $H=19.0$ and $K=18.0$ for UKIDSS and 17.8 and 17.3 for the GLIMPSE 3.6 and 4.5 $\upmu$m bands. At the location of FRB 121102, the total $V$-band absorption, as determined from the COBE/DIRBE dust maps, is 2.42 mag. We use published extinction coefficients to correct for absorption in the other bands. Published zeropoints and effective wavelengths and the IRAC Instrument Handbook v2.1.2 were used to obtain the flux density measurements and limits shown in the broadband spectrum of the persistent counterpart (Figure 3).

X-ray Imaging with XMM-Newton and Chandra X-ray Observatory

X-ray observations were done with XMM-Newton (IDs 0790180201, 0790180501, 0792382801, and 0792382901) and the Chandra X-ray Observatory (ID 18717). The cameras aboard XMM-Newton consist of one EPIC-pn and two EPIC-MOS CCD arrays. The Chandra observation used the ACIS-S3 detector in TE mode. Two XMM-Newton observations occurred in 2016 February–March, before we achieved our precise localization, with pn in Large Window mode and the MOS cameras in Full Frame mode. Two more observations were performed in 2016 September with the pn camera in Small Window mode and the MOS cameras in Timing mode. A 40 ks Chandra observation was performed in 2015 November. In the first two XMM-Newton observations, the pn data were not usable for imaging FRB 121102 as it was positioned at the edge of a CCD chip. The MOS Timing mode observations are also not usable for imaging purposes. We therefore used 41 ks of pn data from 2016 September and 60 ks of MOS data from 2016 February–March for X-ray imaging.

Observational constraints on FRB 121102 and its persistent counterpart.

Our observations support the conclusion that no Galactic source can explain the observed DM excess. If the compact counterpart contributes the excess DM over the maximum predicted by NE2001 along this line of sight, the requirement that it be optically thin at 1.4 GHz implies a lower limit on its size (L $>0.03$ pc), and hence the source distance. The VLBA and EVN compactness limits ($<1.7$ mas in any case, ignoring scattering contributions to angular extent) imply a minimum distance $>3.6$ Mpc, far beyond our Galaxy. The absence of an X-ray detection constrains an AGN counterpart. The fundamental plane relation between radio and X-ray luminosities and the black hole mass predicts that X-ray emission should be detected for black hole systems with $z<0.32$ and $M_{BH}<10^{9}\,M_{\odot}$. However, not all AGN follow this relationship, including radio-loud AGN and systems with jet-ISM interactions. Radio-loud AGN are likely excluded based on the low radio luminosity $L_{R}\approx 3\times 10^{41}$ erg s-1 at $z=0.32$. A $10^{6}\,M_{\odot}$ black hole, which is plausible given the $\sim 10^{9}M_{\odot}$ stellar mass upper limit, would have to accrete at $<10^{-2}$ below the Eddington rate to match the X-ray upper limit. Our observations are also inconsistent with a young radio supernova remnant, which is typically variable on a time scale of months and associated with star formation.

For a nominal Gpc distance $D$ corresponding to redshifts $z\lesssim 0.3$, the received fluence $A_{\nu}$ from each burst implies a burst energy

The unknown emission solid angle $\delta\Omega$ could be very small due to relativistic beaming, and together with a distance possibly much smaller than 1 Gpc, could reduce the energy requirement significantly. However, the total energy emitted could be larger depending on the duration of the emission in the source frame and other model-dependent details. Either way, the burst energies from FRB 121102 are not inconsistent with those that might be expected from the magnetosphere of a compact object.

Data availability.

All relevant data are available from the authors. VLA visibility data selected for times centered on each of the nine bursts (including Figure 1) are available at: https://doi.org/10.7910/DVN/TLDKXG. Data presented in Figures 2(c), 3, and Extended data Figures 1 and 2 are included with the manuscript. The observational data presented here are available from public archives under the following project codes. VLA fast dump observations: 15B-378, 16A-459, 16A-496; VLA imaging: 16B-385; ALMA: ADS/JAO.ALMA#2015.A.00025.S; VLBA: 16B-389, 16B-406; EVN: RP024; Gemini: GN-2016A-FT-5, GN-2016B-DD-2.

Code availability.

Computational notebooks for reproducing the burst position analysis are at http://github.com/caseyjlaw/FRB121102. The code used to analyse the data and observations reported here is available at the following sites: Realfast (http://realfast.io), RTPipe (https://github.com/caseyjlaw/rtpipe), SDMPy (http://github.com/demorest/sdmpy). Other standard data reduction packages (AIPS, CASA, Difmap, PyRAF, XMM SAS, HEASoft, CIAO, PRESTO) are available at their respective websites.

References

Extended Data

Extended Data Table 1: VLA detections of bursts from FRB 121102 and Arecibo constraints. Dates are all in the year 2016. Position offsets $\Delta$RA and $\Delta$Dec are measured from RA = 05h31m58s, Dec = +33∘08′52′′(J2000). Topocentric burst MJDs are reported as offsets from MJD 57620 and are dedispersed to the top of the VLA band at 3.5 GHz. The flux densities and signal-to-noise ratios are estimated from a 5 ms visibility integration, leading to an underestimate since the burst durations are typically shorter in Arecibo detections. Instantaneous beam sizes are listed. Bursts with simultaneous coverage at Arecibo at 1.4 GHz are indicated with estimated detection peak flux density in a 5 ms integration, or 5$\sigma$ upper limits for non-detections.

† The real-time analysis of events on 23 August, 02 September, and 15 September resulted in detections with S/N ratio of 35, 16, and 16, respectively. These differences are due to different calibration and flagging approaches between the real-time and offline analyses. The real-time analysis does not include flux density scale calibration, so the offline analysis gives the best estimate of their flux density.

Extended Data Table 2: VLA 3 GHz observations of the persistent counterpart to FRB 121102 over time. Most observations were acquired during array reconfigurations (C$\rightarrow$CnB; CnB$\rightarrow$B; B$\rightarrow$A). Horizontal lines denote changes in array configuration, as indicated by the changes in the synthesized beam size.

Extended Data Table 3: Flux density and position measurements of the persistent counterpart to FRB 121102. We report the VLA radio spectrum with continuous frequency coverage from 1 to 25 GHz, along with detection positions and a weighted average position that is consistent with the detected burst positions to within 0.1′′. We also list VLBA, EVN, and Gemini detection positions. Position offsets $\Delta$RA and $\Delta$Dec are measured from a nominal RA = 05h31m58s, Dec = +33∘08′52′′(J2000). The Gemini $r$-band detection position is also included. 1-$\sigma$ errors are quoted in all cases.

Extended Data Figure 1: The offset of FRB 121102 from the persistent counterpart. Five bursts detected at the VLA with the highest resolution (A-array, 3 GHz) are plotted, with epoch indicated by MJD values. The (RA, Dec) coordinate difference (burst relative to counterpart) is shown with an ellipse indicating the $1\sigma$ error calculated as the quadrature sum of errors in the two sources. VLBA and EVN positions are indicated, with $1\sigma$ errors smaller than the symbols. The centroid of the Gemini optical counterpart is shown (red dot) with an estimated $1\sigma$ error circle of 100 mas (red) from fitting and radio-optical frame tie uncertainties.

Extended Data Figure 2: VLA spectrum of the persistent counterpart to FRB 121102. The integrated flux density is plotted for each epoch of observation (listed by MJD) over a frequency range $\nu$ from 1 to 25 GHz. The spectrum is non-thermal and inconsistent with a single power law.

Aside from the Very Large Array and the Arecibo Observatory, the observational campaign reported here relied on several other telescopes and the analysis was supported by many different organizations. S.C., R.S.W., and J.M.C. acknowledge prior support from the National Science Foundation through grants AST-1104617 and AST-1008213. This work was partially supported by the University of California Lab Fees program under award number LF-12-237863. The research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP7/2007-2013). J.W.T.H. is an NWO Vidi Fellow and, along with C.G.B., gratefully acknowledges funding for this work from ERC Starting Grant DRAGNET under contract number 337062. S.P.T acknowledges support from a McGill Astrophysics postdoctoral fellowship. M.W.A. was a participant in the 2016 Research Experience for Undergraduates in Astronomy and Astrophysics at Cornell University program, supported by grant NSF/AST-1156780. V.M.K. holds the Lorne Trottier and a Canada Research Chair and receives support from an NSERC Discovery Grant and Accelerator Supplement, from a R. Howard Webster Foundation Fellowship from the Canadian Institute for Advanced Research (CIFAR), and from the FRQNT Centre de Recherche en Astrophysique du Quebec. B.M. acknowledges support by the Spanish Ministerio de Economía y Competitividad (MINECO/FEDER, UE) under grants AYA2013-47447-C3-1-P, AYA2016-76012-C3-1-P, and MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘María de Maeztu’). L.G.S. gratefully acknowledge financial support from the ERC Starting Grant BEACON under contract number 279702 and the Max Planck Society. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. S.C., J.M.C., P.D., T.J.L., M.A.M., and S.M.R. are partially supported by the NANOGrav Physics Frontiers Center (NSF award 1430284). The European VLBI Network is a joint facility of independent European, African, Asian, and North American radio astronomy institutes. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. Based on partial observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil). This research has made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with NASA. The data set used here for cross checking was made publicly available by PI S. R. Kulkarni. Portions of the results presented were based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA, and with the Chandra X-ray Observatory. This research has made use of the NASA Astrophysics Data System (ADS) and the arXiv.