A Synoptic VLBI Technique for Localizing Non-Repeating Fast Radio Bursts with CHIME/FRB
Calvin Leung, Juan Mena-Parra, Kiyoshi Masui, Mohit Bhardwaj, P.J. Boyle, Charanjot Brar, Mathieu Bruneault, Tomas Cassanelli, Davor Cubranic, Jane F. Kaczmarek, Victoria Kaspi, Tom Landecker, Daniele Michilli, Nikola Milutinovic, Chitrang Patel, Andre Renard, Pranav Sanghavi, Paul Scholz, Ingrid H. Stairs, Keith Vanderlinde
DDraft version September 23, 2020
Typeset using L A TEX twocolumn style in AASTeX63
A Synoptic VLBI Technique for Localizing Non-Repeating Fast Radio Bursts with CHIME/FRB
Calvin Leung,
1, 2
Juan Mena-Parra, Kiyoshi Masui,
1, 2
Mohit Bhardwaj, P.J. Boyle,
3, 4
Charanjot Brar,
3, 4
Mathieu Bruneault, Tomas Cassanelli,
6, 7
Davor Cubranic, Jane F. Kaczmarek, Victoria Kaspi,
3, 4
Tom Landecker, Daniele Michilli,
3, 4
Nikola Milutinovic, Chitrang Patel,
6, 3, 4
Andre Renard, Pranav Sanghavi,
10, 11
Paul Scholz, Ingrid H. Stairs, Keith Vanderlinde,
6, 7 (CHIME/FRB Collaboration) MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA02139, USA Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA Department of Physics, McGill University, 3600 rue University, Montr´eal, QC H3A 2T8, Canada McGill Space Institute, McGill University, 3550 rue University, Montr´eal, QC H3A 2A7, Canada McGill Space Institute, McGill University, 3550 rue University, Montreal, QC H3A 2A7, Canada Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario, Canada M5S 3H4 David A Dunlap Department of Astronomy & Astrophysics, 50 St George St, Toronto, Ontario, Canada, M5S 3H4 Department of Physics and Astronomy, University of British Columbia, 325 - 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada National Research Council Canada, Herzberg Astronomy and Astrophysics Research Centre, Dominion Radio Astrophysical Observatory,PO Box 248, Penticton, British Columbia, V2A 6J9 Canada CSEE, West Virginia University, Morgantown, WV 26505, USA Center for Gravitational Waves and Cosmology, West Virginia University, Morgantown, WV 26505, USA Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada (Received September 23, 2020; Revised September 23, 2020)
Submitted to AJABSTRACTWe demonstrate the blind interferometric detection and localization of two fast radio bursts (FRBs)with 2- and 25-arcsecond precision on the 400 m baseline between the Canadian Hydrogen IntensityMapping Experiment (CHIME) and the CHIME Pathfinder. In the same spirit as very long baselineinterferometry (VLBI), the telescopes were synchronized to separate clocks, and the channelized voltage(herein referred to as ”baseband”) data were saved to disk with correlation performed offline. Thesimultaneous wide field of view and high sensitivity required for blind FRB searches implies a highdata rate—6.5 terabits per second (Tb/s) for CHIME and 0.8 Tb/s for the Pathfinder. Since suchhigh data rates cannot be continuously saved, we buffer data from both telescopes locally in memoryfor ≈
40 s, and write to disk upon receipt of a low-latency trigger from the CHIME Fast RadioBurst Instrument (CHIME/FRB). The ≈
200 deg field of view of the two telescopes allows us touse in-field calibrators to synchronize the two telescopes without needing either separate calibratorobservations or an atomic timing standard. In addition to our FRB observations, we analyze brightsingle pulses from the pulsars B0329+54 and B0355+54 to characterize systematic localization errors.Our results demonstrate the successful implementation of key software, triggering, and calibrationchallenges for CHIME/FRB Outriggers: cylindrical VLBI outrigger telescopes which, along with theCHIME telescope, will localize thousands of single FRB events to 50 milliarcsecond precision. Corresponding author: Calvin [email protected] a r X i v : . [ a s t r o - ph . I M ] S e p Leung et al.
Keywords:
Very long baseline interferometry (1769), Radio astrometry (1337), Radio transient sources(2008), Radio pulsars (1353) INTRODUCTIONFast radio bursts (FRBs, Lorimer et al. 2007; Thorn-ton et al. 2013) are brief ( ∼ ms), usually nonrepeatingradio transient events with dispersion measures in excessof that predicted by the electron column density of theMilky Way. Currently, their progenitors and produc-tion mechanism are unknown but their high luminosityand impulsive nature have generated significant interestin the astrophysics community (Platts et al. 2019). Inaddition, due to their cosmological distances (Thorntonet al. 2013), FRB pulses are strongly dispersed by theionized intergalactic medium and have the potential toprobe the large-scale structure of the universe (McQuinn2014; Masui & Sigurdson 2015; Macquart et al. 2020).The vast majority of FRBs are not observed toemit multiple bursts (Petroff et al. 2016) , and thehandful of known repeaters are observed to do sostochastically with the notable exceptions of FRB180916.J0158+65 (CHIME/FRB Collaboration et al.2020a) and possibly FRB 121102 (Zhang et al. 2018;Rajwade et al. 2020). This unpredictability makes lo-calization and followup studies extremely challenging.Since the serendipitous detection of the first FRB in2007 (Lorimer et al. 2007), two repeating FRBs havebeen studied with very long baseline interferometry(VLBI): FRB 121102 (Chatterjee et al. 2017; Marcoteet al. 2017), with optical followup performed by Ten-dulkar et al. (2017); and FRB 180906.J0158+65 (Mar-cote et al. 2020). The localization of seven oth-ers with sufficient precision to identify their respec-tive host galaxies at redshifts between z = 0 . − . b using FRBs, in-cluding the so-called “missing baryons”. This measure-ment is consistent with that of Planck Collaborationet al. (2018), experimentally evaluating the possibilityof using localized FRBs as cosmological probes (Mac-quart et al. 2020).Having detected over seven-hundred FRBs in its firstyear of operation (Fonseca et al. 2020), the CanadianHydrogen Intensity Mapping Experiment/FRB Project(CHIME/FRB Collaboration et al. 2018) has opened up See http://frbcat.org/ for the latest statistics on repeat burstsfrom known FRB sources. a window for population-level studies of the propertiesof FRBs (Josephy et al. 2019; CHIME/FRB Collabora-tion et al. 2019b,a; Fonseca et al. 2020; CHIME/FRBCollaboration et al. 2020a,b). However, CHIME/FRB’sreal-time localization pipeline, which has a precision ofarcminutes, does not yet always allow for unambigu-ous identification of an FRB’s host galaxy. For verybright FRBs with very low dispersion measure (DM), itis sometimes possible to identify a host by imposing aprior on the host galaxy’s maximum redshift.To routinely pinpoint the host galaxy of FRBs de-tected by CHIME/FRB, the CHIME/FRB collabora-tion is developing CHIME/FRB Outriggers, a set ofcylindrical telescopes at distances of one hundred toseveral thousand kilometers from the CHIME telescope.Along with CHIME, the Outriggers will perform a blindVLBI survey to localize thousands of FRBs with 50 mil-liarcsecond precision. To our knowledge, there has onlybeen one previous attempt to blindly localize FRBs withVLBI. V-FASTR was a campaign to search for FRBs inarchival data taken by the Very Long Baseline Array(Wayth et al. 2011; Burke-Spolaor et al. 2016; Wagstaffet al. 2016). None was found, highlighting the difficultyof detecting FRBs with traditional radio telescopes.In contrast, the CHIME/FRB Outriggers program willcombine CHIME/FRB’s high discovery rate with the lo-calization precision afforded by continental baselines, al-lowing astronomers to conduct detailed population-levelstudies of FRB host environments.We report here on the development of a voltage record-ing backend as a testbed for CHIME/FRB Outriggersthat was deployed on the CHIME Pathfinder, itself areduced-scale testbed for the CHIME telescope (Ban-dura et al. 2014). We demonstrate a synoptic VLBIcalibration technique for CHIME/FRB outriggers, anddemonstrate the performance of our technique on auto-matically triggered single-pulse detections of the brightpulsars B0329+54 and B0355+54. We also localize twoFRBs detected during two observing campaigns usingCHIME and the Pathfinder in October and Decem-ber 2019. Our east-west baseline allows for localiza-tion of each source in the RA direction on the sky witharcsecond-level statistical uncertainties for bright FRBs. INSTRUMENTATIONCHIME (Bandura et al. 2014) is a beamforming (Nget al. 2017) interferometer located at the Dominion Ra-dio Astrophysical Observatory (DRAO) near Penticton, ynoptic VLBI with the CHIME Pathfinder × −
800 MHz frequency band using a polyphase filterbank (Bandura et al. 2016). It is synchronized to a GPS-disciplined ovenized crystal oscillator. The channelizedvoltage data, hereafter referred to as “baseband” data,are passed to the second stage of the correlator (the X-engine) (Denman et al. 2015) at 4 real + 4 imaginary bitdepth, for all 1024 frequencies and 2048 signal chains,every 2 . µ s, for an overall rate of 6.5 Tb/s. In additionto performing real-time processing, the X-engine buffersthe baseband data in memory in a 36-s long ring buffer.If the real-time FRB search pipeline (CHIME/FRB Col-laboration et al. 2018) detects an FRB candidate, thering buffer saves the appropriate ≈
100 ms segment ofdata to disk, with the exact duration being determinedby the uncertainty in the dispersion measure (DM) es-timated by the real-time searc pipeline.The CHIME Pathfinder was built prior to CHIME andis used for ongoing technology development for projectssuch as CHIME/FRB Outriggers. It has approximatelyone eighth of the collecting area of CHIME and oper-ates on an independent clock. The effective baseline ofPathfinder is approximately 385.42 m due East, 50.43due South, and 5.17 m lower than that of CHIME.It consists of two 20-m × Figure 1. Interior of the baseband recorder back-end.
The baseband recorder architecture features four servergrade network cards connected via a PCIeX16 slot to twoCPU sockets, each of which can access 512 gigabytes (GB)of RAM with low latency. While awaiting a dump triggerfrom CHIME, our baseband recorder runs a custom versionof the kotekan software framework which buffers 40 secondsof complex-valued baseband data for 256 of the PathfinderF-engine’s 1024 frequency channels. Four such basebandrecorders could process the 0.8 Tb/s of data coming out ofthe Pathfinder, or an outrigger with similar data throughput.A full parts list is provided in Appendix 1. the band, at an input data rate of 204.8 gigabits persecond (Gb/s) (for details, see Appendix 1). Our ringbuffer architecture is implemented in kotekan , a flex-ible and efficient software framework written in C++for real-time data processing for digital radio astron-omy (Recnik et al. 2015). INTERFEROMETRIC LOCALIZATION3.1.
Detection at CHIME
CHIME/FRB features a real-time processing pipelinewhich coarsely estimates the DM, time of arrival,and signal-to-noise ratio of dispersed radio tran-sients (CHIME/FRB Collaboration et al. 2018). Upondetecting a sufficiently bright transient, a classificationalgorithm filters out false positives from radio frequencyinterference and known pulsars. Successful classifica-tion of a dispersed radio transient as an FRB triggersthe dump of ≈
100 ms of baseband data to disk at bothtelescopes with subsecond latency.Prior to data transfer and cross correlation, the base-band data from just the CHIME/FRB instrument are https://github.com/kotekan/kotekan Leung et al. processed to estimate the FRB’s dispersion measureand sky position. This is done by beamforming base-band data from CHIME/FRB’s 2048 correlator inputstowards a grid of sky positions around the detection po-sition, calculating the signal-to-noise ratio of the burstdetection in each beam, and then fitting a 2D Gaus-sian model to the resulting intensity map of the signal.Finally, we perform coherent dedispersion to the opti-mal dispersion measure maximizing the burst signal-to-noise ratio and form a tied-array beam to the re-fined coordinates provided by this so-called “basebandpipeline” (Michilli et al. 2020). From here on we de-note the beamformed baseband data from CHIME as F Cνbt . Here, C stands for CHIME, while ν represents thefrequency channel ( N ν = 1024) ranging from 400-800MHz. The integer b is the “beam number”, reflectingthe fact that a single dump of full-array baseband datacan be beamformed to multiple sky positions in bothpolarizations (north-south and east-west, hereafter NSand EW); b ranges from 1 , , . . . , N b where N b = 2 N p and where N p is the number of unique sky positions.Finally, t is the time index, measured in units of 2 . µ s.We calculate the flux as a function of frequency chan-nel, polarization, and time block, albeit a lower timeresolution indexed by T : S CνbT = t = T + t int (cid:88) t = T | F Cνbt | . Setting the integration time t int = 40 . µ s yields theplots in Fig. 2.3.2. FRB Cross Correlation Pipeline
Our cross correlation pipeline picks up where the base-band pipeline leaves off. Due to the reduced sensitiv-ity of the Pathfinder, we only cross-correlate the base-band data from bright FRBs. We calculate beamformedbaseband at both telescopes ( F Cνbt and F Pνbt ), and di-vide the baseband data into segments of 40 . µ s. Foreach segment we calculate the complex temperature-normalized visibility V CPνbT as a function of frequency,polarization/beam, and time block T as we did previ-ously for the flux. V CPνbT = (cid:80) t = T + t int t = T F Cνbt F Pνbt (cid:113)(cid:80) t (cid:48) = T + t int t (cid:48) = T || F Cνbt (cid:48) || (cid:80) t (cid:48)(cid:48) = T + t int t (cid:48)(cid:48) = T || F Pνbt (cid:48)(cid:48) || (1)The quantity V CPνbT , like the baseband data, iscomplex-valued. For geometric delays shorter than2 . µ s the information about the geometric delay iscompletely encoded in the phase of the numerator of V CPνbT . The denominator ensures that increasing the sys- tem temperature (i.e. scaling any of the F νbt by a con-stant factor) does not affect | V CPνbT | . Hence, | V CPνbT | asplotted in Fig. 3 measures the strength of the cross-correlation independently of the system temperature.The morphological similarity of | V CPνbT | in Fig. 3 and S νbT in Fig. 2 allows us to unambiguously interpret our cross-correlated baseband data as a genuine FRB detection.We cross-correlate the NS polarizations and EW polar-izations at both telescopes separately; since the two tele-scopes’ polarization axes differ by only ≈ ≈
100 ms baseband dump toreduce statistical uncertainty of the visibility phase. Inaddition, for the beams with pulsed emission, we per-form the integration with the help of a real-valued time-domain matched filter, h t , constructed from the pulse’sintensity profile as detected in CHIME autocorrelation(i.e. the curves shown in the top panel of Fig. 2). V CPνb = (cid:80) t F Cνbt h t F Pνbt (cid:113)(cid:80) t (cid:48) || F Cνbt (cid:48) || (cid:80) t (cid:48)(cid:48) || F Pνbt (cid:48)(cid:48) || (2)The filter is normalized to have (cid:104) h t (cid:105) = 0 and (cid:104) h t (cid:105) =1. The former constraint enables optimal rejection ofsteady sources of correlated voltage signals other thanthe pulse of interest, and the latter constraint ensuresthat the noise variance of the data is preserved.3.3. Synoptic Calibration Technique
Our calibration technique fundamentally relies on in-field steady sources to keep the two telescope backendssynchronized over the ∼
10 second duration of the dis-persed burst. Each array only needs to be individuallysynchronized once per day during the transit of a brightradio calibrator, to re-compensate for the slow thermalexpansion of cables between the antennas and the cor-relator. However, since CHIME and the Pathfinder areeach synchronized to independent ovenized crystal os-cillator clocks, the time difference between the two ar-rays jitters on timescales of minutes. Clock jitter anddifferences in the telescopes’ analog chains introduce anunknown instrumental phase between the two telescopeswhich must be calibrated near or during the time of ob-servation.To solve for the instrumental phase, we used the factthat the primary beams of CHIME and Pathfinder com-pletely overlap and that their large size virtually guar-antees that there will be ∼ −
10 bright NVSS (Condon ynoptic VLBI with the CHIME Pathfinder Figure 2. CHIME waterfall plot for FRB 20191219F.
At UTC 2019-12-19T16:51:34, the detection of an FRB inCHIME triggered a simultaneous dump of channelized volt-age data at CHIME/FRB and the CHIME Pathfinder. Afternulling channels containing radio frequency interference, webeamform the baseband data at the optimum position cal-culated by the baseband pipeline, and plot the flux of theburst as a function of time and frequency in the 400-800MHz band. et al. 1998) calibrators ( S . GHz > . Delay Model
For each formed beam (indexed by b ) and each fre-quency channel (indexed by ν ), our general delay model(more generally, a phase model) can be written as:Φ iνb = φ iν + (cid:126)u i ( t ) · ˆ n b + K ∆ DM (ˆ n b ) ν (3)where φ iν is a free function representing the instrumen-tal phase for the i th telescope, (cid:126)u i ( t ) is the (time depen-dent) position of the i th telescope, ˆ n b is the sky position Figure 3. Absolute magnitude of the temperature-normalized visibility between CHIME Pathfinderand CHIME/FRB, in both the north-south and east-west polarizations, calculated and as a function oftime and frequency as in Eq. 2.
The morphology of thepulse as it appears in cross-correlation matches that detectedat CHIME/FRB , revealing the detection of FRB 20191219Fin cross-correlation between the two telescopes. of a source in the b th formed beam, and where the dis-persive delay due to the ionosphere is a free function∆ DM (ˆ n b ) and where the dispersion measure constantis taken to be K = 1 / (2 . × − ) s MHz pc − cm .This simple model takes into account the time-variablegeometric delay and ionospheric delays; for simplicity weneglect small corrections such as tidal deformation thatbecome necessary over long baselines. From here on, wesuppress the time dependence of the telescope positions (cid:126)u i ( t ). Also, since CHIME and Pathfinder are approxi-mately co-located, the ionospheric delay only varies asa function of sky angle (ˆ n b ) and not of position ( (cid:126)u i ).While Eq. 3 could in principle be fitted directly tothe visibilities with a least-squares algorithm, in prac-tice it is helpful to slow down, or “fringestop”, the rapidphase variation of the visibility versus frequency to nomore than a few radians over the telescope bandwidthusing fiducial estimates for (cid:126)u i and ˆ n b . This improvesthe robustness and convergence of the fit especially inthe presence of noise. We denote these estimates withan additional subscript 0. First, we remove the geo-metric delay due to the nominal baseline ( (cid:126)u C − (cid:126)u P ),an estimate which is accurate to within a meter. Wecalculated the (uncalibrated) visibilities V CPνb , reducingour dataset to a set of ∼ complex numbers, oneper frequency channel per formed beam. The phase ofthe uncalibrated visibilities after fringestopping can be Leung et al. modeled as φ CPνb = Φ
Cνb − Φ Pνb = φ CPν +( (cid:126)u C − (cid:126)u P ) · ˆ n b − ( (cid:126)u C − (cid:126)u P ) · ˆ n b, (4)where φ CPν represents the differential instrumental phasebetween CHIME and Pathfinder, where ( (cid:126)u C − (cid:126)u P ) is thetrue baseline, where ˆ n b are the true positions, and wherethe last term encodes our fringestopping using nominalestimates of the sky positions and baseline. Note thatthe ionosphere term in Eq. 3 is identical for each tele-scope and does not appear in Eq. 4. Since the differen-tial instrumental phase is independent of sky pointing,we designate two reference beams ( B ) to use as phasereferences for the NS and EW polarizations of the tele-scope. We remove the differential instrumental phaseby calculating V νb ≡ V νb /V νB . We define σ νb to be theuncertainty on V νb , and denote the amplitude and phaseof V νb as A νb and ϕ νb ≡ φ νb − φ νB respectively.3.5. Fringe Fitting
After applying this calibration procedure, the phaseof the fringestopped and calibrated visibilities which wefit to our delay model is ϕ CPνb = ( (cid:126)u C − (cid:126)u P ) · (ˆ n b − ˆ n B ) − ( (cid:126)u C − (cid:126)u P ) · (ˆ n b, − ˆ n B, ) (5)With a good guess of the baseline offset, Eq. 5 variesslowly as a function of frequency and can be fitted toextract sky localizations and baseline information, asshown in Fig. 4. First, using ∼
10 auxiliary 100 mssnapshots similar to those shown in Fig. 5, each target-ing ≈ n b = ˆ n b, ) at a wide range of sky positions, we determinethe remaining baseline offset δ(cid:126)u ≡ ( (cid:126)u C − (cid:126)u P ) − ( (cid:126)u C − (cid:126)u P ).Next, fixing δ(cid:126)u , we can determine the unknown sources’offsets from their nominal positions, denoted by δ ˆ n b ≡ ˆ n b − ˆ n b, . Note that our approximately east-west base-line make us insensitive to the declination of sources inthe sky, and that the sky positions of sources we are ob-serving (all close to the local meridian) make our datainsensitive to east-west baseline errors.The parameters δ(cid:126)u and δ ˆ n b are estimated by maximiz-ing the likelihood L using an expression that does notdepend on the intrinsic emission spectra of any of thesources. Since only the phase of the visibility is sensitiveto astrometric quantities, we can analytically marginal-ize over the amplitude A νb of the calibrated visibilitieswithout losing phase information. We suppress the su-perscript in Eq. 5, treating it as a free function ϕ bν of skypositions and baseline parameters which we collectivelyrefer to as λ . Assuming a uniform prior and applyingBayes’s theorem we can write the posterior distributionof λ with a χ maximum likelihood estimator. Integrat-ing over the amplitude of the visibility A νb simplifies our Figure 4. Top: Successful fringe fit for FRB20191021A . We plot the slowly-varying phase ϕ CPbν of theCHIME–Pathfinder visibility as a function of frequency inthe NS and EW polarizations. To guide the eye, we bin overfrequency channels with a resolution of 16 MHz, and overlaythe corresponding best-fit delay model (solid line).
Bottom:Maximum likelihood χ statistic as a function of RA. The log-likelihood function (negative of Eq. 6) shows a clearminimum at the best-fit position of the FRB. Though weare fitting N ≈
512 visibilities, systematic effects such asa differential beam phase and confused calibrators preventthe χ statistic from reaching its expected value of ≈ full χ likelihood to its form in Eq. 6. P ( λ |V νb ) ∝ P ( V νb | λ ) ∝ exp (cid:32) − (cid:88) νb ||V νb − A νb exp( iϕ νb ( λ )) || σ νb (cid:33) ∝ exp (cid:32) − (cid:88) νb Im[ V νb exp( − iϕ νb ( λ )) /σ νb ] (cid:33) . log L ∝ − (cid:88) ν,b Im[ V νb exp( − iϕ νb ( λ )) /σ νb ] . (6)Intuitively, this can be understood as follows. If thedelay model allows us to perfectly derotate the V νb tothe real axis of the complex plane, the imaginary part of V νb , normalized by its standard deviation, will be min-imized and will be a zero-mean, unit-variance Gaussianrandom variable. Hence, the sum of squares follows a χ distribution with N b × N ν degrees of freedom, andminimizing χ allows us to recover the best fit param-eters λ without ever explicitly fitting any spectra. OurFRB localizations are summarized in Table 1.Statistical uncertainties are estimated by jack-knifingour data over frequencies: we can divide our cali- ynoptic VLBI with the CHIME Pathfinder Figure 5. Sky maps of the four fields we observed ,with a ‘+’ denoting the approximate position of the pul-sar/FRB, and bright NVSS calibrators with S . GHz > . brated visibilities V νb into 9 different “frequency combs”,spaced evenly across our band. By leaving out one combat a time and repeating our χ analysis, we can inspectthe resulting likelihood curves and reject frequency-localRFI, which would show up as a discrepancy between dif-ferent jack-knifed realizations of our analysis. We esti-mate the statistical error on our localizations using ourjack-knifed samples in accordance with McIntosh (2016).3.6. Systematic Errors
Over short baselines, most radio sources remain unre-solved and there is no shortage of calibration sources inthe sky. While our database of NVSS sources serves asan abundant calibrator network, it also means that theprobability of having two sources within a formed beam(FWHM ∼ . ) is non-negligible. While we filteredout bright calibrator candidates that are too close toeach other, we are forced to assume that the remainingcalibrators are true point sources. For example, we can-not eliminate the possibility that the emission of sourcesat low frequencies (400-800 MHz) is offset from the cat-alogued survey position at 1 . n b ) and the de-lay center (ˆ n B ).To quantify the systematic offsets in our RA measure-ments, we conducted triggered observations of pulsars,which are also summarized in Table 1. We added rulesto the event classifier in the real time FRB detectionpipeline to allow bright pulses from known pulsars totrigger a baseband dump, in the same way that an FRBwould. In this way, we collected baseband data for threebright single pulses from PSR B0329+54 and one fromPSR B0355+54, and localized the pulsars as if they wereFRBs. We estimated the systematic errors in our lo-calization analysis using the discrepancy between ourresults and the pulsars’ known position, corrected fortheir proper motion.We phase reference the pulsar position to the 7 in-beam NVSS calibrators, whose sky positions are as faras 60 degrees away from the pulsar. We plot the as-trometric localization error against the angular distancebetween the pulsar and the delay center in Fig. 6. Wefind that the astrometric discrepancy is roughly linearlyproportional to the on-sky distance to the calibrator,and that using the nearest on-sky calibrator minimizesdiscrepancies from the catalogued positions of pulsarseven with truly simultaneous phased-array observationsthrough the same ionosphere. We attribute this dis-crepancy chiefly to a static baseline determination errorcorresponding to time delays of less than a nanosecond.To estimate the magnitude of systematic uncertainty inour FRB localizations, we find the intersection of theupper edge of the shaded area in Fig. 6 with the on-skydistance to the nearest calibrator to each FRB.In addition to an unknown static baseline error, theeffective phase center of a beamforming telescope driftsslightly every day. The effective phase center positionis the centroid of active antenna positions weighted bytheir sensitivity, and the centroid drifts from day to dayon the order of ∼ cm because a slightly different set ofantennas are flagged (i.e. nulled) every day due to fac-tors like rain causing increased noise in certain antennas.We take this effect into account during tied-array beam-forming, but the current baseline positions are not yetconstrained at a level to measure this day-to-day drift inastronomical data. Using a larger sample of pulsars ata wide range of declinations for baseline determination,not just validation, will reduce our systematic error floor Leung et al.
Table 1. Localization of Known Pulsars and Fast Radio Bursts Detected by CHIME/FRB.
We report the DM,nominal sky position, and observing epoch during which we collected baseband data on each source. For pulsars, the nominalRA and DEC (in degrees) are taken from the ATNF catalog (Manchester et al. 2005). For FRBs, we instead report the nominalRA and DEC at which the FRB was detected by CHIME/FRB’s real-time pipeline. We report the measured RA from ourlocalization pipeline with statistical uncertainties and systematic offset of each source from its true position. For the pulsars,the systematic offset is known, and for the FRBs, the systematic offsets are extrapolated from those of pulsars (see text andFig. 6). We are unable to unambiguously identify a single host galaxy with our current localization precision.Source DM RA (nominal) DEC (nominal) Epoch (MJD) RA (measured) ± Stat Offset (deg)PSR B0329+54 26.776 53.24770 54.57860 58772.412 53 . ± . − . . ± . . . ± . . . ± . . .
92 46 .
39 58777.595 124 . ± . ± ∼ . .
92 85 .
44 58836.702 226 . ± . ± ∼ . Figure 6. Deviation of the localized positions ofB0329+54 and B0355+54 from their true positionsalong the RA direction as calculated by using dif-ferent NVSS calibrators as delay centers.
The dis-crepancy in degrees is quantified as the coordinate offset∆RA × cos(DEC) and is plotted with 3 σ statistical errorbars. We compute localizations for the same pulsar usingdifferent phase centers to study the effect of using differentdelay centers on the same transient. The shaded gray bandis drawn to guide the eye and allows us to estimate the sys-tematic localization offset of the two FRBs, whose closestcalibrators are 0.8 and 8 degrees away respectively. and improve our ability to phase reference our observa-tions to calibrators far away on the sky. DISCUSSION AND CONCLUSIONWe have developed baseband recording hardware andsoftware capable of handling the high data rate ofwideband, multi-element radio interferometers such asCHIME for VLBI observations (Section 2). Also, wehave demonstrated a calibration technique that exploitsCHIME’s wide field of view to localize several radiotransients detected by CHIME/FRB and the CHIME Pathfinder in the same spirit as VLBI (Section 3). Inan automatically triggered ≈
100 ms duration basebandcapture at CHIME and Pathfinder, we can simultane-ously detect a single FRB in cross correlation betweenCHIME and Pathfinder, as well as multiple calibratorsfor phase referencing our telescopes.We have developed efficient maximum likelihood esti-mators to perform fringe fitting in the absence of knowl-edge about the FRB spectrum(Section 3.5), and have lo-calized FRB 20191021A and FRB 20191219F with sta-tistical uncertainties of 1 . ∼
50 milliarcseconds. Thisprecision is roughly matched to that of the best opti-cal telescopes, and will allow for detailed followup stud-ies of FRB host environments within their host galax-ies. To achieve our goal, we anticipate a very differ-ent set of challenges from those presented here. Overlong baselines, the ionospheric phase shift can vary byas much as ∆DM ∼ − (corresponding to a time delayof ∼
200 ns as a function of sky position at sub-gigahertzfrequencies). Achieving high astrometric precision willrequire removing this effect with observations of calibra-tion sources close to the FRB on the sky. The relativelyuncharted territory of low-frequency VLBI calibratorsposes a major challenge for scaling CHIME/FRB VLBIobservations to continental baselines.One option is to use bright pulsars for phase referenc-ing observations with CHIME/FRB Outriggers, espe-cially for hour angles close to the Galactic plane where ynoptic VLBI with the CHIME Pathfinder −
20 milliarcsecond level, includingless precisely localized pulsars in the calibrator networkof CHIME/FRB Outriggers will improve astrometric lo-calizations of those pulsars as observations accumulateover time.For hour angles where pulsars are sparse, phase ref-erencing after the real-time detection of an FRB canbe done by using a dense network of steady-sourceVLBI calibrators all over the northern sky, particularlynear the celestial pole in the constant-coverage area ofCHIME’s primary beam.Following pioneering low-frequency VLBI surveysby Garrett et al. (2005) and Lenc et al. (2008), the ad-vent of the International LOFAR Telescope has madesystematic surveys of the low-frequency sky possible.The LOFAR Snapshot Calibrator Survey (Mold´on et al.2015) has demonstrated that high quality, compactVLBI calibrators at low frequencies tend to be brightat 328 MHz ( S = 0 . − ∼ − . Whilethe LBCS covers even lower frequencies than those rel-evant for CHIME/FRB Outriggers, an understandingof promising low-frequency calibrators on long base-lines will be crucial for future VLBI observing cam-paigns with CHIME/FRB Outriggers. The instrumen-tation and analysis techniques developed in this paper,combined with a dense network of pulsars or compactlow-frequency VLBI calibrators, will pave the way fortransformative studies of FRB host environments andof the intergalactic medium over long baselines withCHIME/FRB Outriggers. Software: numpy (Oliphant 2006), scipy (Virtanenet al. 2020), matplotlib (Hunter 2007) ACKNOWLEDGMENTSWe thank the CHIME Collaboration for use of thePathfinder, and the staff at the Dominion Radio As-trophysical Observatory and Ev Sheehan for their hos-pitality and efforts to ensure the smooth deploymentof our instrumentation. C. L. was supported by theU.S. Department of Defense (DoD) through the Na-tional Defense Science & Engineering Graduate (ND-SEG) Fellowship. M.B. is supported by an FRQNT Doc-toral Research Award. This research is funded in partby the Gordon and Betty Moore Foundation and theNEC Corporation Fund for Research in Computers andCommunication. FRB research at UBC is supportedby an NSERC Discovery Grant and by the CanadianInstitute for Advanced Research. V.M.K. holds a Dis-tinguished James McGill Chair and the Lorne TrottierChair in Astrophysics & Cosmology and receives sup-port from an NSERC Discovery Grant and HerzbergAward, from an R. Howard Webster Foundation Fellow-ship from the Canadian Institute for Advanced Research(CIFAR), and from the FRQNT Centre de Rechercheen Astrophysique du Quebec. D. M. was supported bythe Banting Postdoctoral Fellowships Program. P.S. isa Dunlap Fellow and an NSERC Postdoctoral Fellow.The Dunlap Institute is funded through an endowmentestablished by the David Dunlap family and the Univer-sity of Toronto. The CHIME/FRB baseband recordingsystem was funded in part by a CFI John R. EvansLeaders Fund award to I.H.S.APPENDIX BASEBAND RECORDER PARTS LISTOur recorder uses 1 terabyte of RAM to buffer ap-proximately 40 seconds of baseband data correspondingto dispersion measures of up to ≈ uponreceiving a trigger from CHIME/FRB’s real-time detec-tion pipeline. A photograph of the inside of the nodeis shown in Fig. 1, and a full parts list is given in Ta-ble 2. Future recorders may feature an auxiliary bufferor GPUs for real-time beamforming capabilities (Nget al. 2017), which will facilitate longer integration timeson fainter calibrators, though this technical capability isnot necessary for our bright calibrators.REFERENCES Bandura, K., Addison, G. E., Amiri, M., et al. 2014, inGround-based and Airborne Telescopes V, ed. L. M.Stepp, R. Gilmozzi, & H. J. Hall, Vol. 9145, InternationalSociety for Optics and Photonics (SPIE), 738 – 757,doi: 10.1117/12.2054950 Bandura, K., Bender, A. N., Cliche, J. F., et al. 2016,Journal of Astronomical Instrumentation, 05, 1641005,doi: 10.1142/S2251171716410051 Leung et al.
Table 2. Components used in the prototype baseband recorder for CHIME/FRB Outriggers.
The total cost ofthe recorder was less than $20k USD in Spring 2019 and was dominated by the cost of the high-density RAM.Parts Part Number Specifications (each)Motherboard 1 × TYAN Tempest EX S7100-EX 4 × PCIeX16, 3 × PCIeX8, 2 socketsCPU 2 × Intel Xeon Silver 4116 12 cores (hyperthreaded) × × HYNIX HMAA8GR7A2R4N-VN 128 GBNetwork 4 × Silicom PE 31640G2QI71/QX4 2 × × ynoptic VLBI with the CHIME Pathfinder11