Magnetospheric origin of a fast radio burst constrained using scintillation
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The document presents a measurement of two distinct scintillation scales in the frequency spectrum of fast radio burst (FRB) 20221022a, supporting an emission process operating within or just beyond the magnetosphere of a central compact object. This study finds the observed emission region size to be less than 30,000 kilometers, which contradicts models suggesting large radial distances. Additionally, the findings highlight the significance of scintillation in understanding FRB emission physics and progenitors.
Magnetospheric origin of a fast radio burst constrained using scintillation
- 1. 48 | Nature | Vol 637 | 2 January 2025 Article Magnetosphericoriginofafastradioburst constrainedusingscintillation Kenzie Nimmo1✉, Ziggy Pleunis2,3,4 , Paz Beniamini5,6 , Pawan Kumar7 , Adam E. Lanman1,8 , D. Z. Li9 , Robert Main10,11 , Mawson W. Sammons10,11 , Shion Andrew1,8 , Mohit Bhardwaj12 , Shami Chatterjee13 , Alice P. Curtin10,11 , Emmanuel Fonseca14,15 , B. M. Gaensler2,16,17 , Ronniy C. Joseph10,11 , Zarif Kader10,11 , Victoria M. Kaspi10,11 , Mattias Lazda2,16 , Calvin Leung18 , Kiyoshi W. Masui1,8 , Ryan Mckinven10,11 , Daniele Michilli1,8 , Ayush Pandhi2,16 , Aaron B. Pearlman10,11 , Masoud Rafiei-Ravandi10,11 , Ketan R. Sand10,11 , Kaitlyn Shin1,8 , Kendrick Smith19 & Ingrid H. Stairs20 Fast radio bursts (FRBs) are microsecond-to-millisecond-duration radio transients1 that originate mostly from extragalactic distances. The FRB emission mechanism remains debated, with two main competing classes of models: physical processes that occur within close proximity to a central engine2–4 ; and relativistic shocks that propagate out to large radial distances5–8 . The expected emission-region sizes are notably different between these two types of models9 . Here we present the measurement of two mutually coherent scintillation scales in the frequency spectrum of FRB 20221022A10 : one originating from a scattering screen located within the Milky Way, and the second originating from its host galaxy or local environment. We use the scattering media as an astrophysical lens to constrain the size of the observed FRB lateral emission region9 to ≲3 × 104 kilometres. This emission size is inconsistent with the expectation for the large-radial-distance models5–8 , and is more naturally explained by an emission process that operates within or just beyond the magnetosphere of a central compact object. Recently, FRB 20221022A was found to exhibit an S-shaped polarization angle swing10 , most likely originating from a magnetospheric emission process. The scintillation results presented in this work independently support this conclusion, while highlighting scintillation as a useful tool in our understanding of FRB emission physics and progenitors. Inhomogeneitiesintheinterstellarmediumcausetheradiowavesfrom point sources to scatter, which results in temporal broadening of the signal11 (parameterizedbythescatteringtimescaleτs atsomereference frequency).Scatteringcreatesastochasticinterferencepatternonthe signal, called scintillation, corresponding to a frequency-dependent intensitymodulation(parameterizedbythecharacteristicfrequency scale, known as the decorrelation bandwidth ΔνDC specified at some frequency)11 . Temporal broadening becomes larger towards lower frequencies,τs ∝ ν−α ,forobservingfrequencyν,andspectral‘scintles’ become wider towards higher frequencies, ΔνDC ∝ να . The index α is often close to the expectation from Gaussian density fluctuations in the scattering medium, α = 4. Moreover, scattering and scintillation areinverselyproportional12 :τs ≈ C/(2πΔνDC),withCintherangeof1–2. Scattering and/or scintillation measurements in the radio signal are a powerful probe of interstellar optics13 . Such measurements have been used to resolve emission regions in the Crab Pulsar14 ; measure relativisticmotioninCrabPulsargiantpulses15 ;constrainthesizeofa gamma-ray burst afterglow16 ; probe the circumburst environment of fastradiobursts(FRBs)17 ;andhavethepotentialtoprobethestructure of the circumgalactic medium (for example, refs. 18,19). TheCanadianHydrogenIntensityMappingExperiment(CHIME)FRB project20 recentlydiscoveredtheas-yetnon-repeatingFRB 20221022A10 , withasignal-to-noiseratio(S/N)of64.9.Theeventwasprocessedusing the CHIME/FRB baseband pipeline21 , which produced a beamformed data product containing complex voltages for both the X and the Y polarization hands, with a time and frequency resolution of 2.56 μs https://doi.org/10.1038/s41586-024-08297-w Received: 14 June 2024 Accepted: 28 October 2024 Published online: 1 January 2025 Check for updates 1 MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA. 2 Dunlap Institute for Astronomy and Astrophysics, University of Toronto, Toronto, Ontario, Canada. 3 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands. 4 ASTRON, Netherlands Institute for Radio Astronomy, Dwingeloo, The Netherlands. 5 Department of Natural Sciences, The Open University of Israel, Ra’anana, Israel. 6 Astrophysics Research Center of the Open university (ARCO), The Open University of Israel, Ra’anana, Israel. 7 Department of Astronomy, University of Texas at Austin, Austin, TX, USA. 8 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA. 9 Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA. 10 Trottier Space Institute, McGill University, Montreal, Quebec, Canada. 11 Department of Physics, McGill University, Montreal, Quebec, Canada. 12 McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA. 13 Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, NY, USA. 14 Department of Physics and Astronomy, West Virginia University, Morgantown, WV, USA. 15 Center for Gravitational Waves and Cosmology, West Virginia University, Morgantown, WV, USA. 16 Department of Astronomy and Astrophysics, University of California Santa Cruz, Santa Cruz, CA, USA. 17 David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto, Toronto, Ontario, Canada. 18 Department of Astronomy, University of California Berkeley, Berkeley, CA, USA. 19 Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada. 20 Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada. ✉e-mail: knimmo@mit.edu
- 2. Nature | Vol 637 | 2 January 2025 | 49 and 0.39 MHz, respectively. The FRB was localized10,21 to equatorial coordinates right ascension (J2000) = 03 h 14 min 31 s(22), declina- tion (J2000) = +86° 52′ 19′′(14) (where the uncertainties quoted are 1σ confidence levels), and associated with a host galaxy at a redshift of 0.0149(3) with posterior probability ≳99%. Thebeamformedbasebanddatawerecoherentlyandincoherently dedispersedtoadispersionmeasureof116.837 pc cm−3 ,measuredby maximizingthestructureintheburst10,22 .Thedatawerethenupchan- nelizedtoafrequencyresolutionof0.76 kHz(Methods),attheexpense of time resolution. This frequency resolution is the highest we can achieve before diluting the signal with noise, given the total width of the FRB (about 2 ms; Extended Data Fig. 1). This resolution is suf- ficiently high to allow us to probe the expected decorrelation band- width from the Milky Way interstellar medium (52 kHz at 600 MHz: estimated from the NE2001 Galactic electron density model23,24 ). The autocorrelation function (ACF; Methods) of the upchannelized spec- trum (that is, the flux density as a function of frequency integrated over the 2-ms burst duration), was then computed and is shown in Fig.1.Foraburstspectrumthatshowsintensityfluctuationsowingto scintillation, the expected functional form of the ACF is a Lorentzian wherethehalf-widthathalf-maximumisthedecorrelationbandwidth25 . Inaddition,theACFthatwecomputeisnormalizedsuchthatthepeak of the Lorentzian is the square of the modulation index (Methods), defined as the standard deviation of the observed spectrum divided by its mean25 . Three distinct frequency scales are evident in the ACF (Fig. 1). The approximately 30-MHz scale, which is also apparent in the burst dynamic spectrum (Extended Data Fig. 1), is not scintilla- tion, but rather introduced by reflections between the mesh and the focalline(separatedby5 m)ofthesemi-cylindricalCHIMEreflectors26 . We confirm that the other 2 frequency scales are both scintillation from 2 distinct scattering screens by computing the ACF for 8 sub- bandsacrosstheCHIMEobservingbandof400–800 MHz,containing an equal fraction of the burst energy, measuring both scales in each subband, and observing that they evolve with frequency with index α = 3.7 ± 0.6 and α = 3.2 ± 0.3 for the frequency scales ΔνDC = 6 ± 1 kHz andΔνDC = 128 ± 6 kHzat600 MHz,respectively(Fig.2andMethods). Scalingourscintillationmeasurementsto1 GHzusingthemeasuredα, weareabletocomparewiththeMilkyWayscatteringprediction(τs at 1 GHz)23 . We find that the 6-kHz scintillation scale is a factor of about 10 less than the prediction, whereas the 128-kHz scale is a factor of about 1.6 larger. Naively, one might expect 128 kHz to be the Galactic scintillationscaleowingtoitsbetteragreementwithpredictions;how- ever,itisworthnotingthatGalacticelectrondensitymodelshavelarge uncertainties(forexample,asdiscussedinref.27),especiallyforlines of sight at high Galactic latitude, b, as is the case for FRB 20221022A (b ≈ 24.6°). Measuring two scintillation scales implies that those screens are sufficiently distant from each other that the screen closest to the observer is not resolving out the farther screen. We use this to show that if both screens were in the Milky Way, coherence would not be maintained and we would not have measured a second scintillation scale(Methods).WeknowthatFRB 20221022Aisextragalacticbecause of its host-galaxy association10 with posterior probability ≳99%, con- firmingthatscreens2 isalsoextragalactic.Moreover,weplacethefol- lowingconstraintontheproductofthedistancebetweentheFRBand the extragalactic screen, ⋆ ds2 , and the observer to Galactic screen distanced⊕s1 :d d 9.1 kpc ⊕s s 2 1 2 ≲ ⋆ (Methods). Toidentifywhichscintillationscaleoriginatesfromtheextragalac- tic screen, we consider the modulation indices: m6kHz = 1.2 ± 0.1 and m128kHz = 0.78 ± 0.08, for the 6-kHz and 128-kHz scintillation scales, respectively (Methods). Over the observing band, the modulation index of both scintillation scales are consistent with being constant (Fig. 2). m6kHz is consistent with order unity, which indicates ‘perfect’ modulation from a point source. We observe that m128kHz < m6kHz. For thescreenclosesttotheobserver,amodulationindex<1wouldimply thatthescreenispartiallyresolvingthefartherscreen.Forthescreen closesttotheFRB,amodulationindex<1wouldimplythatthescreen is partially resolving the FRB emission region. We find no strong fre- quency dependence of the 128-kHz scale modulation index, and we measure a decorrelation-bandwidth frequency evolution closer to ν3 thanν4 (Fig.2),bothofwhicharemoreinsupportofthelatterscenario (Methods). We therefore place the 128-kHz screen closest to the FRB andthe6-kHzscreenclosesttotheobserver.InMethods,wealsocon- sider the case where the order of the screens is flipped, and show that Frequency lag (MHz) –0.4 –0.2 0 0.2 0.4 –0.2 0 0.2 0 0.5 1.0 1.5 2.0 2.5 –15 –10 –5 0 5 10 15 0 0.5 1.0 1.5 2.0 2.5 a b c Residuals Autocorrelation power Autocorrelation power Reduced F2 = 0.95 FRB 20221022A Triple Lorentzian J = 3.18 ± 0.04 kHz J = 60.3 ± 0.7 kHz FRB 20221022A Triple Lorentzian Fig.1|Threefrequencyscalesevidentinthefull-bandACFoftheFRB 20221022Aspectrum.a,TheACF,withafrequencyresolutionof0.76 kHz,in thelagrange−15 MHzto+15 MHz.b,Zoom-inonthecentrallagrangeoftheACF, highlightedbytheshadedblueregionina.Theblacklinerepresentsatriple Lorentzian(equation(2))fittotheACFbetween±20 MHz(a)and±0.5 MHz(b). Thelargerfrequencyscale,mostclearlyobservableina(half-widthathalf- maximumγ = 27.3 ± 0.1 MHz),isattributedtoaninstrumentalrippleexistingin CHIME/FRBdata.Thetwosmallerscales,whicharemoreclearlyobservedinb, areattributedtoscintillationwithdecorrelationbandwidthsof3.18 ± 0.04 kHz and60.3 ± 0.7 kHz:theindividualLorentziansareplottedinbinpurpleand blue,respectively.c,Theresiduals.Thereducedχ2 iscomputedwithinthelag range±0.25 MHz,highlightedbythegreendashedlines.Wereducethelag rangeastheapproximately30-MHzfrequencyscaleisnotexpectedtoshowa Lorentzianfunctionalform.Thescintillationscales,however,areexpectedto beLorentzianinform,andwefindareducedχ2 verycloseto1,implyingagood fittothedata.
- 3. 50 | Nature | Vol 637 | 2 January 2025 Article it only strengthens the constraint on the FRB emission-region size. Consequently, the FRB emission region is being partially resolved by the 128-kHz scintillation screen. This means that the angular size of theemissionregionprojectedontotheextragalacticscreenisslightly largerthanthediffractivescaleofthescreen9 .Naturally,thisintroduces adegeneracybetweentheemissionsizeandscreen–sourcedistance:a largerphysicalemissionsizewithascreenintheoutskirtsofthegalaxy orasmallphysicalemissionsizewithaverynearbyscreencouldresult inthesameprojectedangularsize.Weplottheallowablescreen–source distance and lateral emission-region size combinations in Fig. 3. FRBemissionmodelsarebroadlygroupedintotwocategories:one where the emission originates from within the magnetosphere of a compact object2–4 , and a second where relativistic shocks propagate farfromacentralengineandproducecoherentradioemissionatlarge radialdistances5–8 .Inthelatterclassofmodels,irrespectiveoftheexact FRBemissionmechanism(forexample,synchrotronmaser28 ),onecan relate the lateral emission-region size, R⋆obs, to the FRB emission site distance,d,fromthecentralcompactobject9 : ⋆ ⋆ d R γ ≈ ≈ R c t obs 2 Δ obs 2 ,where ΔtistheFRBtemporaldurationandγistheLorentzfactoroftheshock. Forthefar-awaymodels5–8 ,radialdistancesrangefrom107 kmto1011 km, whichcorrespondstoR⋆obs ≈ 105 –107 kmgivenourobservedFRBdura- tion: Δt ≈ 2 ms (Extended Data Fig. 1). We require an FRB to screen Frequency (MHz) Masked channels Burst energy Two screens resolving Gradient = (5.8 ± 3.4) × 10–4 Scallop artefact 128 kHz at 600 MHz Frequency resolution 6 kHz at 600 MHz Q3.7 ± 0.7 Q3.2 ± 0.3 6 kHz Emission region resolving 128 kHz 400 450 500 550 600 650 700 750 800 0 0.25 0.50 0.4 0.6 0.8 1.0 0.8 1.0 1.2 1.4 1.6 200 400 0 20 –2 411.2 431.2 450.2 471.1 502.5 548.1 617.2 730.8 –1 0 1 2 a b c d e f Fraction Modulation index Modulation index Frequency scale (kHz) Frequency scale (kHz) Frequency lag (MHz) Fig.2|ConfirmingtwoscintillationscalesintheFRB20221022Aspectrum, withdecorrelationbandwidths6±1kHzand128±6kHzat600MHz. a,TheACFscalculatedfor8subbandscontaininganequalfractionoftheburst energy at a frequency resolution of 0.76 kHz. Overplotted in black is a double Lorentzian fit to each ACF. b,c, Two frequency scales are measured in each subband (smaller scale in b, and larger in c), and are fit with the functional form Aνα , for constant A and index α, shown in red. The horizontal dashed greenlineinbistheresolutionandtheyellowdashedhorizontallineincisthe upchannelizationartefact.Inbandc,themeasureddecorrelationbandwidths at600MHzaremarkedwithblackdashedlines.d,e,Themodulationindicesfor the6-kHz(d)and128-kHz(e)frequencyscalesacrosstheband.Aleast-squares fit of a straight line is overplotted on d (dark green) and we fit the expected evolution of the modulation index with frequency for a screen resolving the emission-region size (light green; equation (22)) as well as the expected evolutionforthescreensresolvingeachother(pink;equation(23))tothe 128-kHzmodulationindicesine.Errorbars(1σ)areplottedforallfrequency scalesandmodulationindices,notingthattheyareoftentoosmalltodistinguish fromthemarker.Inb–e,thehigh-frequencydatapointhasbeenomittedfrom all fits, indicated by the shaded red region, owing to the ambiguity of the scintillation scale and the upchannelization artefacts. Omitting the lowest- frequency measurement for the 6-kHz scale, where the modulation index uncertaintiesarelarge,doesnotaffectthemeasurements.f,Thenumberof maskedchannelspersubband(turquoise),andthefractionoftheburstenergy persubband(purple). 10–4 10–2 100 102 102 103 104 105 Lateral emission region size (km) FRB to extragalactic screen distance (kpc) ΔQs2 = 128 ± 6 kHz, ms2 = 0.78 ± 0.08 Two-screen constraint assuming d!s1 = 0.64 kpc Apparent diameter of host galaxy Non-magnetospheric models 23.5-s pulsar (ref. 37) Fig.3|Thedegeneracybetweenthelateralemission-regionsizeandthe FRBtoextragalacticscreendistance.Forthescintillationmeasurements ν Δ = 128 ± 6 kHz s2 and m = 0.78 ± 0.08 s2 ,thegreenlinerepresentstheallowable combinationsofemissionsizeandsource–screenseparations(withthe3σ uncertaintyupperboundindicatedbythedashedgreenline,calculatedby propagatingthe ν Δ s2 and ms2 errorsusingequation(22)).Theverticalpinkline indicatesthetwo-screenconstraintonthesource–screendistance,d 14.1 kpc s2 ≲ ⋆ , assumingaGalacticscreendistanceof0.64 kpcfromNE200123 .ThisGalactic screendistanceassumptionishighlyuncertain,andweexploreitseffectonthe emissionsizeinExtendedDataFig.5.Theverticaldarkteallineindicatesthe apparentdiameteroftheFRBhostgalaxymeasuredintheoptical(11 kpc)30 . Thegreyhatchedregionshowstheextragalacticscreendistancesweruleout. Theorangeshadedregionindicatestheobservedemission sizes,R⋆obs,inferred fromtheradialdistances,d,forfar-awayshockmodels5–8 .Thepurpleshaded region indicatesthepossibleemissionsizesfor theslowestknownpulsar37 (whichthereforehasthelargestmagnetosphereofknownradiopulsars).
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Nature | Vol 637 | 2 January 2025 | 51 distance of ⋆ d ≳ 144 kpc s2 to have emission sizes consistent with the non-magnetosphericmodels(Fig.3).Itisunlikelythatthescreenisat suchlargedistances,faroutinthecircumgalacticmediumofthehost galaxy.Thisisbecause(1)theimplieddensities(ne ≈ O(10−3 cm−3 ),calcu lated using equations (4) and (5) from ref. 9) are at least an order of magnitude higher than the current best estimate for the Milky Way circumgalacticmediumatthesamedistance29 ;(2)fromthetwo-screen constraintsmentionedearlier,theGalacticscreendistancewouldhave tobe≲63 pctosatisfytheinequality(ExtendedDataFig.5);and(3)the FRBsourcewouldneedtobeoutsideofthehost-galaxydisktoexplain whywedonotmeasurescatteringorscintillationfromthedisk(where thedensitiesarehigher).Followingthesearguments,wefindthatitis mostplausiblethattheextragalacticscreenisconstrainedtobewithin the host-galaxy disk, allowing us to place the conservative constraint on ⋆ ds2 from the apparent diameter of the host galaxy as observed in opticallight(11 kpc)30 .Itisworthnotingthattheelectrondistribution extends farther than the optical diameter of the galaxy; however, the inclination of the galaxy as well as the low inferred host dispersion measure10 imply that the FRB is not traversing through the full length of the galaxy and therefore 11 kpc is a highly conservative upper limit onthescreendistance.Withthisupperlimitonds2⋆,weconstrainthe observed emission size of R⋆obs ≲ 3 × 104 km (Fig. 3). TheFRBemissionsizeconstraintspresentedheresupportanemis- sionprocessthatoccurswithin,orjustbeyond15,31 ,themagnetosphere ofacompactobject.Ourfindingsindependentlysupporttheconclu- sionsdrawnonFRB 20221022Ainref.10.Theretheauthorsobservedan S-shapedpolarizationpositionangleswingacrosstheburstduration, oftenseeninpulsarpulsesandattributedtoanemissionbeamsweep- ingacrossthelineofsight,indicativeofamagnetosphericoriginofthe emission. The discovery of subsecond periodicity in an FRB32 , (sub) microsecond timescales in some repeating FRBs33,34 , and magnetar spin-down glitches coinciding with FRB-like emission35 support the magnetosphericclassofFRBemissionmodels.However,thediversity of spectro-temporal properties observed, even for a single repeating source36 ,sparksdebatesaboutwhethermultipleemissionmechanisms are at play. This work highlights incredible potential for similar scin- tillation studies in the future to explore both the emission physics of FRBsandthepropertiesoftheirimmediateenvironments,whichhold valuable clues to their sources and progenitors. Onlinecontent Anymethods,additionalreferences,NaturePortfolioreportingsumma- ries,sourcedata,extendeddata,supplementaryinformation,acknowl- edgements, peer review information; details of author contributions andcompetinginterests;andstatementsofdataandcodeavailability are available at https://doi.org/10.1038/s41586-024-08297-w. 1. Petroff, E., Hessels, J. W. T. & Lorimer, D. R. Fast radio bursts at the dawn of the 2020s. Astron. Astrophys. Rev. 30, 2 (2022). 2. Kumar, P., Lu, W. & Bhattacharya, M. Fast radio burst source properties and curvature radiation model. Mon. Not. R. Astron. Soc. 468, 2726–2739 (2017). 3. Lyutikov, M. & Popov, S. Fast radio bursts from reconnection events in magnetar magnetospheres. 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- 5. Article Methods Scintillationanalysis To measure scintillation, the coherently dedispersed baseband data were first upchannelized to a frequency resolution of 0.76 kHz. The upchannelization process was as follows: first the complex voltage dynamic spectrum was divided into time blocks of length 512 bins; for each polarization hand, frequency channel and time block, a fast Fourier transform was performed, creating an array that has a single polarization hand, a single time bin and 512 frequency channels; the result was a complex voltage dynamic spectrum with 2 polarization hands,2.56 × 512 μstimeresolution,and0.390625/512-MHzfrequency resolution, where 0.390625 MHz is the original channelization of the baseband data: 400 MHz over 1,024 channels. This frequency resolu- tionwaschosentoprobetheexpecteddecorrelationbandwidthfrom the Milky Way interstellar medium, estimated using NE2001 (44 kHz at600 MHz;usingτs,1GHz ≈ 0.46 μsfromrefs.23,24andtherelationship τs ≈ 1/(2πΔνDC)). Intheupchannelizeddataproduct,thetimeresolutionissufficiently coarsesuchthattheburstisunresolvedintime.Theon-burstspectrum is then taken to be the maximum S/N time bin. An off-burst spectrum isalsocomputedforcalibrationpurposes.ThefastFouriertransform usedtoupchannelizethebasebanddataintroducesascallopingarte- factthatrepeatsevery0.390625 MHz(thatis,thewidthofthechannels oftheoriginalchannelizationofthebasebanddata).Tocorrectforthis artefact, the off-burst spectrum was folded to determine an average 0.390625-MHz scallop shape, which was then divided out from the on-burst spectrum (Extended Data Fig. 2). We attributed channels in the off-burst spectrum that exceed an S/N of 3 to radio frequency interference (RFI), and we masked both the on-burst and off-burst spectra.TheACFsofboththeon-burstandtheoff-burstspectrawere then computed using ∑ ν S ν S S ν ν S N S S ACF(Δ ) = ( ( ) − )( ( + Δ ) − ) ( − ) , (1) i i i ν Δ noise 2 following ref. 28. We only sum over indices i that give non-masked values for the S/N measurements S(νi) and S(νi + Δν) at a given i. NΔν is the total number of unmasked overlapping frequency channels that are used to compute the ACF for a given frequency lag Δν. The ACF calculatedusingequation(1)isnormalizedsuchthattheamplitudeof acharacteristicfrequencyscalepresentintheACFisthesquareofthe modulationindexofthatfrequencyscale,wherethemodulationindex is defined as the standard deviation of the observed burst spectrum divided by its mean25 . InFig.1,weshowtheon-burstACFforFRB 20221022Afortheentire observing bandwidth, with the zero lag noise spike masked and with three clear frequency scales visible by eye. There is a 27.3-MHz fre- quency scale arising from CHIME’s instrumental design20 , which we can see by eye in the dynamic spectrum (Extended Data Fig. 1). We fit the ACF out to a lag of 20 MHz with a triple Lorentzian function m ν γ m ν γ m ν γ 1 + (Δ / ) + 1 + (Δ / ) + 1 + (Δ / ) , (2) 1 2 1 2 2 2 2 2 3 2 3 2 forfrequencylagΔν,theLorentzianhalf-widthathalf-maximumγi and modulationindexmi.WenotethataLorentzianistheexpectedfunc- tional form of the ACF, with the decorrelation bandwidth defined as thehalf-widthathalf-maximumoftheLorentzian,tomathematically obtain a temporal exponential decay from scatter broadening25 . We notethataquasi-periodicspectralstructurewasobservedinspectra of FRB 20121102A and was suggested to arise from diffractive lens- ing38 . As we know that the instrumental ripple is not scintillation, we do not necessarily expect that it should adopt the functional form of a Lorentzian. The exact functional form we fit to the instrumental ripplescaleisunimportantaslongaswecapturetheamplitudeofthe modulation. This is because the frequency scale is orders of magni- tude different from the other two scales evident in the ACF, and so only the amplitude of the modulation at the frequency lags relevant for the smaller frequency scales (that is, around the peak) is impor- tant to return reliable modulation indices (the difference between, for example,aLorentzianorGaussianatsuchsmallfrequencylagsis indistinguishable). We consider correlated uncertainties in the ACF, following ref. 39 and the implementation in scintools40 , which are propagated into the fitting procedure. We compute the reduced-χ2 statisticbetweenlags±0.25 MHz,relevantforthe2smallerfrequency scales,whichprobablycouldbescintillation,andfindthat3Lorentz- ians fit well to the data with a reducedχ2 of 0.95. The potential decor- relation bandwidths, defined as the half-width at half-maximum of theLorentzian,aremeasuredtobe3.18 ± 0.04 kHzand60.3 ± 0.7 kHz, with modulation indices m ≈ 1.3 and m ≈ 0.89, respectively (Fig. 1; that is, in the ACF of the full CHIME bandwidth). We note that these frequency scales are smaller than the decorrelation bandwidths we measureinthefrequency-resolvedACFs(seefollowingparagraphand Fig. 2) owing to the burst having a larger S/N in the lower half of the band (where the decorrelation bandwidth is smaller): that is, these values are S/N weighted. Residual upchannelization artefacts as well as RFI can introduce misleadingfrequencystructureinthespectrumACF.Totestthatthe frequencyscalesthatwemeasureintheon-burstACFacrosstheentire CHIMEbandareconsistentwithscintillation,wedividethe400-MHz total bandwidth into 8 subbands, containing an equal fraction of the burst energy, and compute the ACF per subband to explore the fre- quencydependenceoftheputativescintillation.Asdescribedabove, we normalize the ACF using the mean of the spectrum. For the sub- banded ACFs, we normalize using the mean of the spectrum within each subband, which coarsely corrects for a frequency-dependent burstfluence.Wemeasurebothfrequencyscalesinalleightsubbands using a double Lorentzian fit per subband (Fig. 2). The uncertainties ontheACFfitparametersareaquadraturesumofthefituncertainties with the finite-scintle error, following the implementation in scin- tools40 .AsshowninFig.2,weperformaleast-squaresfitofafunction oftheformAνα tothehalf-widthathalf-maximameasuredfromthetwo Lorentzians fit to the ACF, for constant A and index α. To confirm the frequencyscalesobservedarescintillation,weexpectα ≈ 4,whereas an instrumental artefact or RFI should not evolve with frequency in the same manner. It is noted that we omit the high-frequency data point, as it cannot be distinguished from the 390-kHz upchanneliza- tion artefact (Fig. 2). For the smaller frequency scale, we measure α = 3.7 ± 0.6, and for the larger scale we measure α = 3.2 ± 0.3. The 6-kHz frequency scale shows a frequency dependence consistent with the ν4 scaling for refractive scattering, whereas the frequency dependence of the 128-kHz scale is shallower (but within the range observedforpulsarscintillation41 ).Wethereforeattributebothscales toscintillationfromtwoscatteringscreensalongthelineofsightfrom FRB 20221022Atotheobserver.Wereportdecorrelationbandwidths of6 ± 1 kHzand128 ± 6 kHzat600 MHz,whichwemeasurefromtheAνα fits,andwithuncertaintiesdeterminedusingthestandarddeviation of the fit residuals. It is worth noting that decorrelation-bandwidth measurements of individual bursts from a single source at the same observing epoch can have large scatter, for example, ref. 42. This is a resultofvaryingS/NperburstandlownumberofscintlesO(10),which isencompassedintheverylargeuncertaintiesforthesebursts.Inthis work, FRB 20221022A is at the high end of the S/N ratios reported in ref. 42, with O(1000) scintles, resulting in smaller uncertainties on the decorrelation bandwidth. Asnotedearlier,thefrequencyscalesthatwemeasureinthefull-band ACF are markedly smaller than those we measure in the subbanded analysis.Thisisowingtothefactthattheburstisbrighterinthelower partofthebandwherethedecorrelationbandwidthissmaller,aswell
- 6. as the fact that there are more scintles in the bottom part of the band comparedwiththetop.Itispossiblethattheseeffectsarestillskewing our decorrelation-bandwidth measurements within each subband, affecting both the decorrelation bandwidth and frequency evolu- tion. To explore what effect, if any, this has on our measurements, we simulate an FRB spectrum with measured decorrelation bandwidth 104 kHzat600 MHz,andfrequencyindexα = 3.95.Wethensimulate100 spectrawiththesameinputparameters,applythesameRFImaskand dividethebandintothesame8subbandsasweapplytotherealdata. We then perform the same analysis: ACF per subband, then fit Aνα to thehalf-widthathalf-maximaoftheACFs.Wefindthatthesimulations areconsistentwithintheuncertaintiesofourmeasurements(Extended DataFig.3).WethereforeconcludethatthesubbandingandRFImask- ing is not significantly skewing our measurements. TheNE2001decorrelation-bandwidthprediction23,24 at1 GHzinthis lineofsightisabout400 kHz.Wescaleourdecorrelationbandwidths usingthemeasuredfrequencyscalingindexα,givingΔνDC,1GHz ≈ 40 kHz and ΔνDC,1GHz ≈ 656 kHz. The 6-kHz and 128-kHz decorrelation band- widths are a factor of about 10 lower and about 1.6 higher than the NE2001 prediction, respectively. In addition to measuring the modulation index in the entire band ACF, we also measure the modulation indices across the burst profile intimeandacrosstheobservingband.InExtendedDataFig.1,weplot themodulationindexmeasuredacrosstheburstprofileintimebinsof width 164 μs. These modulation indices are measured by computing the ACF of the spectra (averaged over 164 μs of time) with frequency resolution 24 kHz, and taking the square root of the peak subtracting a constant offset (introduced by the instrumental ripple). We choose this frequency resolution to ensure that the 6-kHz frequency scale is unresolved and reducing its influence on the modulation index measurements.ItisnotedthatinExtendedDataFig.1,weplotonlythe modulationindexmeasurementswheretheS/Nwithinthe164 μstime intervalwas>8.Themodulationindexbroadlyappearstobeconstant over the burst duration, with a mean of 0.76 ± 0.06. Two-screenconstraints We consider a two-screen system as shown in Extended Data Fig. 4, with the observer, ⊕, an astrophysical point source (here, FRB 20221022A),⋆,andtwoscreens:s1 (closesttotheobserver)ands2 (clos- esttothesource).Wearefollowingtheformalismderivedinrefs.17,43 foranextragalacticsource,butderivingitgenerallytoallowforaGalac- tic source (see, for example, ref. 44). The temporal broadening time- scale of an FRB at distance d⊕⋆, scattered by the screen s2 at distance d⊕s2 from the observer, and distanceds2⋆ from the FRB source, is τ θ c d d d = , (3) s s 2 ⊕ ⊕s s 2 2 2 2 ⋆ ⋆ whereθs2 istheangular-broadenedsizeoftheFRBscatteredbyscreen s2 andcisthespeedoflight43 .Thecoherencelengthoftheradiowaves incident on screen s1 is ≃ ⋆ ⋆ l λ θ λ d d τ c d 2π = 2π , (4) c s ⊕ ⊕s s s 2 2 2 2 forobservingwavelengthλ.Scatteringfromscreens2 canweakenscin- tillationfroms1 ifthecoherencelengthisreducedbelowthesizeofthe Galactic scattering projected onto s1: ≃ ≃ ⋆ ⋆ l d θ τ c d d d . (5) cone ⊕s s s s ⊕s ⊕ 1 1 1 1 1 Withameasurementofscatteringorscintillation(atleastonescintil- lation scale is required) from both screens in the two-screen system, this sets the condition that lc ≳ lcone, yielding: ≲ ⋆ ⋆ ⋆ τ τ ν d d d d d 1 (2π ) . (6) s s 2 ⊕ 2 ⊕s s s ⊕s 1 2 2 1 2 1 Usingtherelationbetweenthescatter-broadeningtimescale,τ,and decorrelationbandwidthfromscintillationΔνDC:τ = C ν 2πΔ DC withC ≈ 1–2, we derive the general two-screen equation: ⋆ ⋆ ⋆ ν ν C C ν d d d d d Δ Δ ≳ . (7) s s s s 2 s s ⊕s ⊕ 2 ⊕s 1 2 1 2 1 2 1 2 The high posterior probability (>99%)10 of the host-galaxy associa- tion confirms that FRB 20221022A is extragalactic. We must consider whetherthetwoscreensweobservearebothGalactic,orifoneofthe screensisextragalactic.Withourtwomeasuredscintillationscalesin hand, we consider both of these cases below. OneextragalacticscreenandoneGalacticscreen First,letusassumethatthescreens2 isextragalactic,ands1 isascreen within the Milky Way. In this situation, we have the approximations d d d (8) ⊕ ⊕s s 2 1 ≃ ≃ ⋆ ⋆ and so we can simplify equation (7) to ν ν C C ν d d d Δ Δ ≳ . (9) s s s s 2 s ⊕s ⊕ 2 1 2 1 2 2 1 ⋆ ⋆ It is noted that typically there is a (1 + z) factor here45 , which we do not include as the redshift of FRB 20221022A is sufficiently small (z = 0.0149)10 that it does not affect the results. GivenourscintillationmeasurementsforFRB 20221022A:6 kHzand 128 kHz,assumingC C = = 1 s s 1 2 ,whichisthemostconservativevaluein this case, and taking the distance to the identified host galaxy in ref. 10, d⊕⋆ = 65.189 Mpc, we get the constraint: ≲ ⋆ d d 9.1 kpc (10) ⊕s s 2 1 2 UsingNE200123,24 ,wecanestimated⊕s1 fromthedistancewherethe wavenumber spectral coefficientCn 2 peaks (which can be thought of as a quantity resembling the amount of turbulence): d ≈ 0.64 kpc ⊕s1 . This gives us the constraintd 14.1 kpc s2 ≲ ⋆ . It is worth noting that this prediction of d⊕s1 is highly uncertain, and we consider its impact on ⋆ ds2 and ultimately our emission-region size constraints later. Furthermore, the decorrelation-bandwidth measurement can be usedtoplacealimitontheindividualscreendistances46 .Startingwith equation (47) in ref. 46 and assuming Kolmogorov turbulence47 , we derive ν ν l R Δ ≈ π , (11) s diff F 2 2 where ldiff is the diffraction length, or the length through the screen over which the phase changes by 1 radian, and ⋆ R cd ν = / F s2 is the Fresnel radius. Equation (19) in ref. 48 gives the relationship between ldiff and the phase change across the screen ϕ l ϕ l L l ≈ , (12) diff −6/5 max max 3/5 for the thickness of the screen L and the maximum eddy size in the scattering medium lmax. ϕ is directly proportional to the dispersion measure of the screen (column depth within the thickness of the screen),DMs2 , with the relationship equation (17) in ref. 48
- 7. Article ϕ ν = 2.6 × 10 DM . (13) 7 s GHz 2 Combining all of these relationships into equation (11), we arrive at (see also equation (57) in ref. 46): ν ν d l L L d DM ≈ 3 × 10 pc cm Δ 1 pc . (14) s 4 −3 s −5/12 GHz 11/6 s 5/12 max 1/3 5/6 2 2 2⋆ Substituting in our measured decorrelation bandwidth ν Δ = s2 128 kHz, observing frequency νGHz = 0.6, and taking the ratio of maxi- mumeddysizeoverscreensizetobelmax/L ≈ 10−4 (consistentwithwhat is seen from Milky Way turbulence): ⋆ ⋆ d L d DM ≈ 4 pc cm 1 pc . s −3 s 5/12 s 5/6 2 2 2 The contribution of the total dispersion measure attributed to the host galaxy was estimated in ref. 10 asDM 14 pc cm host −14 +23 −3 ≲ . We therefore estimate the following: ⋆ ⋆ d L d (0−37) pc cm ≳ DM ≈ 4 pc cm 1 pc −3 s −3 s 5/12 s 5/6 2 2 2 and so ≲ ⋆ ⋆ d L d 1 pc 210 pc . s s −2 2 2 Ifweassumethat ⋆ ≈ 1 L ds2 ,wehaveatightconstrainton ⋆ d < 210 pc s2 . However, ⋆ ≈ 1 L ds2 is not always a fair assumption, with values inferred ≪1forsomepulsars49–51 .Thistherefore,unfortunately,doesnottightly constrain the distanceds2⋆. TwoGalacticscreens Now we assume that the source is extragalactic, at a distance10 of d⊕⋆ = 65.189 Mpc, but both screens s1 and s2 are within the Milky Way. Given this situation, we can make the approximations: ≃ ≃ ⋆ ⋆ ⋆ d d d . s s ⊕ 1 2 Underthisapproximation,theassumptionthatC C = = 1 s s 1 2 andusing our decorrelation-bandwidth measurements, equation (7) gives the constraint: d d ν ν C C ν Δ Δ ≈ 2 × 10 . (15) ⊕s ⊕s s s s s 2 −9 1 2 1 2 1 2 ≲ Even if we force d⊕s2 to be the isophotal diameter of the Milky Way, about 27 kpc (ref. 52), this restricts d⊕s1 to be ≲0.0001 pc: it is highly unlikely that there is a screen within such close proximity to us. It is worth noting that FRB 20221022A is about 64° off the ecliptic, and therefore one of the scintillation scales coming from the solar wind can be easily ruled out. If we change d⊕s2 to be smaller, the condition in equation (15) forces d⊕s1 to be even smaller, supporting that this outcome is highly unlikely. We note that if we consider the case where both screens are extra- galactic, the problem is symmetric and the same constraint applies. Suppose the farther screen is 50 kpc from the source, out in the host galaxy’s halo, then the nearby screen would need to be <0.0001 pc. Althoughpulsarsareknowntoscintillatefrombowshocksveryclose tothesource53 ,thisconfigurationismuchmorefine-tunedandthere- fore more unlikely than the case where one of the screens is Galactic. Throughoutthissection,wehaveimplicitlyassumedthatthescreens are two-dimensional and isotropic. The ACF in Fig. 1 is well fit with a double Lorentzian function. We therefore find no deviations from theexpectationsoftheisotropicscreenassumption.Deviationsfrom these expectations, however, can be subtle, and so we explore below thepossibilityofone-dimensionalanisotropicscreensandtheimplica- tions for our conclusions. One-dimensional anisotropic screens Throughout this paper, the implicit assumption we make is that the scintillationscreensareisotropicandtwo-dimensional.Thisassump- tion means that the angular broadening of the source owing to the screen closest to the observer is equivalent to the size of the source as seen by the farther screen. However, if the screens are sheet-like19 (that is, the normal vector of the ‘sheet’ is perpendicular to the line of sight, rather than parallel in the case of the thin-screen model), the angularbroadeningisdirectiondependent,introducingadependence on the angle between the one-dimensional screens. The condition lc ≳ lcone from the subsection above, becomes lc ≳ lconecos(θ), where θ is the angle between the two sheet-like screens projected onto the line-of-sight plane. ForthetwoGalacticscreensdescribedabove,equation(15)becomes ≲ d d θ ν ν C C ν cos ( ) Δ Δ ≈ 2 × 10 . (16) ⊕s ⊕s 2 s s s s 2 −9 1 2 1 2 1 2 Forreasonabled⊕s1 andd⊕s2 ,thisinequalitycanbesatisfiedbyinvok- ing a cos(θ) ≪ 1, or equivalently making the one-dimensional screens almost perfectly perpendicular. This is very tightly constraining the geometry of the scattering media, which is fine-tuned in reality and thereforeunrealistic.Inaddition,asdiscussedinthefollowingsection, forthelargerscintillationscale,withmodulationindex<1,wefindthe decorrelationbandwidthandmodulationindexfrequencydependence to agree more with the emission size being resolved than the screens resolvingeachother.Thesefrequencydependenciesarenotaffected by the cos(θ) term and therefore add further doubt to the scenario of anextragalacticsourcewithtwoalmostperpendicularone-dimensional Galactic screens. Inref.19,itisshownthatonecanobserveasuppressionofthemodu- lation index for the larger scintillation scale if the finer scintillation scale is unresolved by the telescope frequency resolution. However, this situation does not apply to this work as we have resolved both scintillation scales in our analysis. Suppressedintensitymodulation Thecasestudiespresentedabovesupporttheextragalacticnatureof thesecondscreen,s2.Thetwo-screenconstraintsinequation(10)place the second screen likely within the host galaxy. We observe no clear frequency or time evolution of the modulation index of the 128-kHz scintillation scale (Fig. 2 and Extended Data Fig. 1). The modulation indexforFRB 20221022Awasobservedtodecreaseovertheburstpro- file(whichisdominatedbyanexponentialscatteringtail)owingtothe twoscreenspartiallyresolvingeachother44 .Inthecasepresentedhere, we are not resolving the scattering timescale, and so it is not surpris- ing that we do not observe an evolution of the modulation index with time. We explore the possibility that the modulation index m128kHz < 1 observediseitherowingtothescreensresolvingeachotherorowing to the emission-region size being resolved. We note that in the case of weak scintillation25 , one can expect mweak ≈ 0.1–0.3, which is lower than our measurement of m128kHz ≈ 0.78. When the source or screen is resolved,differentscintillationpatternsareeffectivelybeingaveraged. This has the effect of smearing the scintillation pattern in frequency and suppressing the amplitude of the intensity modulation. For this
- 8. reason, in both of these cases we expect different modulation index and decorrelation-bandwidth frequency dependencies, which we derive below. First we derive the relationship for the case where the observed emission-region size is being partially resolved. The physical size of the extragalactic screen, s2, is L θ d = , (17) s s s 2 2 2⋆ where θs2 is the angular size of screen s2 from the perspective of the FRB source, and ⋆ ⋆ θ cτ d c ν d = 2 = πΔ , (18) s s s s s 2 2 2 2 2 wherewerelatethescatteringtimescaleanddecorrelationbandwidth through the relation τ ν ≈ 1/(2πΔ ) s s 2 2 . Substituting equation (18) into equation (17) yields: ⋆ L cd ν = πΔ . (19) s s s 2 2 2 The physical resolution of the screen is then ⋆ ⋆ χ λ L d ν cd ν = 1 2π = 1 Δ 2π , (20) s s s s s 2 2 2 2 2 where the 1 2 π is a model-dependent factor12 . Substituting equation (20) into13 ⋆ m = 1 1 + 4 , (21) R χ s 2 2 obs s2 whereR⋆obs istheobservedemission-regionsize,wederivetherelation- shipbetweenthelateralemission-regionsizeandthedistancebetween the source and extragalactic screen: R c d ν ν ν m = Δ ( ) 8π 1 − 1 . (22) obs s s 2 s 2 2 2 2 ⋆ ⋆ Following a similar line of reasoning, we derive an equivalent rela- tionshipforthecasewherethetwoscreensarepartiallyresolvingeach other: m = 1 1 + (23) ν d d d ν ν ν ν s 2 8 Δ ( )Δ ( ) 2 s1s2 s2 ⊕s1 s1 s2 ⋆ In Fig. 2, we plot the least-squares fit of the modulation indices as a functionoffrequencywiththeirexpectedrelationships:equation(22) for the partially resolved emission-region size, and equation (23) for the two screens partially resolving each other. It is evident that in the caseofthetwoscreensresolvingeachother,weexpectastrongerfre- quency dependence than what is observed, suggesting that the data aremoreinagreementwiththecaseoftheemissionregionbeingpar- tiallyresolved(althoughneitherfitdescribesthedatawithourmeas- ured reduced χ2 > 1: quantitatively we measure reduced χ ≈ 139 ν 2 for the resolving screens, and reduced χ ≈ 97 ν 2 for the emission region beingresolved).Wenotethatthesefunctionalformscanbecomemore complex by invoking a complicated morphological structure of the scattering material, which is one reason why the fits may be poor. Another reason could be that the modulation index of the 128-kHz scintillationscaleissuppressedbyanaspectoftheanalysisperformed, for example, during the upchannelization artefact removal process. We additionally consider the case where the modulation index is 1; however, as we show later, this is less conservative for the emission- region size constraints than using the m ≈ 0.78 s2 measurement. For both scenarios, we now derive the decorrelation-bandwidth frequency dependencies. From equation (46) in ref. 13 ν σ τ = 1 + 4 2π , (24) scint 1 2 s where σ R χ = / 1 obs s2 ⋆ for the case where the emission region is being resolved (see equation (21)), and σ L χ = / 1 s s 2 1 for the case where the screen is being resolved. First let us consider a partially resolved emissionregion.Inthiscase, χ ν ∝ s2 (seeequation(20)),whichinturn means that σ1 ∝ ν−1 . From equation (24), this then gives the following frequency dependence: ν Aν Bν ∝ + (25) scint 8 6 for constants A and B. In the case where the screen is being resolved, L ν ∝ s −2 2 (see equation (19)), χ ν ∝ s1 (from equation (20)), which then results in σ1 ∝ ν−3 . From equation (24), this then gives the following frequency dependence: ν Cν Dν ∝ + . (26) scint 8 2 for constants C and D. For completely unresolved emission, the first term in both equations (25) and (26) dominates, and we arrive at the ν4 frequencyscalingforthedecorrelationbandwidth.However,ifthe scintillationis(partially)resolved,thesecondtermdominates.Forthe emissionregionbeingresolved,thefrequencydependencebecomes νscint ∝ ν3 and for the screens resolving each other we arrive at νscint ∝ ν. Our measured frequency scaling of α = 3.2 ± 0.3 for the 128-kHz scin- tillation scale (Fig. 2) supports that the emission-region size is being partially resolved. α = 4, that is, the case where the emission region is unresolved, is >3σ inconsistent. Emissionsizeconstraints As outlined in ref. 9, a measurement of scintillation from a screen in the FRB host galaxy can be used to constrain the size of the FRB emis- sion region, which in turn could be used to distinguish between FRB emission models. The 128-kHz modulation index frequency evolu- tionanddecorrelation-bandwidthfrequencyrelationsupportingthe emission-regionsizebeingpartiallyresolvedsuggeststhatthe128-kHz scintillation scale is a result of the extragalactic screen, s2. The high reducedχ2 ofthemodulationindexversusfrequencyfit,aswellasthe inconsistencywiththeNE2001prediction,asmentionedearlier,means thatwecannotruleoutthescenariowhereneithertheemissionregion nor the screen is being partially resolved. We, therefore, consider all caseshere:(1)128-kHzscintillationscalefromtheextragalacticscreen, thatispartiallyresolvingtheemissionregion,m128kHz = 0.78;(2)128-kHz scintillation scale from the extragalactic screen, with an unresolved emission region, m128kHz ≈ 1; and (3) 6-kHz scintillation scale from the extragalactic screen, with an unresolved emission region, m6kHz ≈ 1. In Fig. 3, we plot the lateral emission size as a function of the extra- galactic screen distance for case 1: which is the case our data agrees with most, while also being the most conservative constraint on the emission-region size. There is a clear degeneracy between the lateral emission-region size and the FRB to extragalactic screen distance, which naturally arises as the m ≈ 0.78 s2 measurement fixes the pro- jected size of the emission region on the screen. As shown earlier, we haveaconstraintonthescreendistance, ⋆ d < 14.1 kpc s2 (equation(9); assuming d = 0.64 kpc ⊕s1 , from NE200123 ). With this limit, we can see from Fig. 3 that the lateral emission size upper limit is lower than the estimated size for the non-magnetospheric models5–8 . However, this
- 9. Article hinges on the Galactic screen distance we have assumed from the NE2001estimate,whichcanbehighlyuncertain.Tohaveconsistency withnon-magnetosphericmodels,werequireanextragalacticscreen distance of ≳144 kpc (Fig. 3), and a Galactic screen distance of ≲63 pc (ExtendedDataFig.5).Thisscreenconfigurationisextremelyunlikely for three main reasons: (1) using equations (4) and (5) from ref. 9, we estimatetheelectrondensityatadistanceof144 kpcgivenourscintil- lation measurements to be O(10−3 ) cm−3 , which is at least an order of magnitude larger than current best estimates of the Milky Way at the same distance29 ; (2) it is unlikely for the Galactic screen to be within 63 pc (for example, ref. 54) and there are no known H ii regions or nearby stars that could explain the nearby screen; and (3) we would havetoinvokeanFRBsourcelivingoutsideofthegalaxydisktoexplain why we do not measure scattering or scintillation from the disk itself, which has higher densities. We, therefore, place an upper limit on the FRBtoscreendistanceof11 kpc,whichistheapparentdiameterofthe hostgalaxy30 .Itisworthnotingthatthisapparentdiameterisderived fromopticalobservations,whereastheelectrondistributionwillextend farther; however, the inclination of the galaxy with respect to the line of sight, as well as the low inferred host dispersion measure10 make it highly unrealistic that FRB 20221022A propagated through the full extentoftheGalacticdisk,makingthisupperlimitveryconservative. Withthisupperlimitonthescreendistance,weplacetheconservative constraint on the lateral emission-region size of R⋆obs ≲ 3 × 104 km. It is worth noting that there are two foreground stars55 at distances of about 0.5 kpc and about 0.8 kpc (broadly consistent with the d = 0.64 kpc ⊕s1 estimate from NE2001) coincident with the FRB posi- tion and host galaxy, identified in ref. 10. These stars could create a scintillation screen from their stellar winds, as has been observed for hot stars56 extending out to about 2 pc: the projected area on the sky would encompass the entire host galaxy and FRB localization region. The two foreground stars in the FRB 20221022A field, however, are lower temperature than those observed in ref. 56 and so would have a lowermasslossrateandthesurroundingswouldhavealowerdensity. Astellarwindscreencouldexplaintheinferredlargerdensitythanthe NE2001 prediction for the case where the 6-kHz scintillation scale is the Galactic scale, which is about 10 times lower—that is, an approxi- mately10timeshigherscatteringtimescale—comparedwithNE2001. However,withoutverylongbaselineinterferometry(VLBI)toconstrain theGalacticscreendistanceandgeometry,wecannotconfirmthatthe stellar wind is causing the Galactic scintillation here. Finally,letusconsidercases(2)and(3)above.Inbothofthesecases, we assume m ≈ 1 s2 , which tells us that the emission region is a point source as viewed from the extragalactic screen. This, therefore, con- strains only a minimum distance between the FRB and extragalactic screen for a given source size (Extended Data Fig. 6). The allowable lateralemission-regionsizeandscreendistancecombinationsareshown in Extended Data Fig. 6 in green and blue for case 2 and case 3, respec- tively.Tohaveanemission-regionsizeconsistentwiththeshockmodel7 , we required > 12 Mpc s2⋆ and ⋆ d > 250 Mpc s2 for case 2 and case 3, res pectively.AstheFRBisatadistanceof65 Mpc,thenon-magnetospheric model cannot work for case 3. There is no obvious nearby galaxy with a halo that could conceivably intersect the FRB line of sight, and so a scattering screen >12 Mpc from the FRB is highly unlikely. Moreover, thisrequiresaGalacticscreendistance≲1 pcgivenourtwo-screencon- straints (equation (9)), which is unreasonably close, especially as FRB 20221022A is about 64° off the ecliptic, and therefore we can rule outtheGalacticscintillationscalearisingfromthesolarwind. Given our observed emission-region size constraints, our observa- tions disfavour the non-magnetospheric FRB models (for example, refs. 5–8). Our results are more consistent with the magnetospheric classofFRBemissionmodels9 oremissionoriginatingjustbeyondthe lightcylinderofaneutronstar(forexample,refs.15,31).Thissupports thefindingsofref.10,wherewemeasureapolarizationangleS-shaped swinginFRB 20221022A,whichhasbeenattributedtoabeamsweeping across the observers line of sight, therefore tying the emission site to the rotation of an object. Assuming an emission-region size comparable to those observed in pulsars (100–1,000 km; refs. 15,57), motivated by the pulsar-like polarization angle swing10 , we infer an extragalactic screen distance from the source of 0.1–12 pc (Fig. 3), consistent with the size of the Crab Nebula58 . EuropeanVLBINetworkimaging Ifweassumeanemissionsizetypicalforpulsaremission,100–1,000 km (refs. 15,57), we infer an extragalactic screen distance of 0.1–12 pc (Fig. 3), comparable in scale to the size of the Crab Nebula58 . Three repeating FRBs in the literature have been observed associated with compactpersistentradiosources(PRSs)59–63 .Thenatureoftheseradio counterparts is debated in the literature, with one of the competing theoriesbeingmagnetizednebulaesurroundingtheFRBprogenitor64 . Motivatedbythepossibilitythatthescintillationscaleiscomingfrom asurroundingnebula,weobservedthefieldofFRB 20221022Awiththe EuropeanVLBINetwork(EVN)tosearchforanycompactradioemission (project ID RN002). These observations were conducted during an e-VLBIsession,wherethedatawerecorrelatedinreal-timeusingSFXC65 attheJointInstituteforVLBIERIC(JIVE).WeobservedwiththeEVNfrom 9April202422:01:55 UTto10April202404:22:30 UT,withthefollowing participatingstations:JodrellBankMark2,Effelsberg,Medicina,Noto, Onsala(On-85),Tianma(T6),ToruńandIrbene.Thecentralobserving frequencyofourobservationsis1.6 GHz,withabandwidthof128 MHz. The interferometric data were correlated with time and frequency integration of 2 s and 0.5 MHz, respectively. We correlated the target data at the position right ascension (J2000) = 03 h 14 min 17.4 s, dec- lination (J2000) = 86° 52′ 01′′, which is consistent with the centre of FRB 20221022A’s associated host galaxy10 . In addition to the target scans, we observed J0217+7349 as the flux and bandpass calibrator, J0213+8717asthephasecalibrator(ataspatialseparationof0.89°from thepointingcentre)andJ0052+8627asthechecksource.Traditional phase-referencing observations were conducted with a cycle time of 6.5 min: 5 min on target, 1.5 min on the phase calibrator. In total, we observed the field of FRB 20221022A for 4 hours. We note that we did notgettargetdatawithOn-85owingtothehighelevationofthesource. Raw voltage data were recorded from each participating telescope withcircularpolarizationfeedsand2-bitsamplinginVDIF66 format.The correlatedvisibilitieswerecalibratedandimagedusingstandardpro- ceduresintheAstronomicalImageProcessingSystem67 andDIFMAP68 . First,usingtheresultsoftheautomaticEVNpipeline(https://evlbi.org/ handling-evn-data), we performed amplitude calibration using the gaincurvesandindividualstationsystemtemperaturemeasurements, appliedthebandpasscalibration,andperformedsomebasicflagging. We then performed some additional manual flagging of the fringe finder, before removing the instrumental delay. The final step of the calibration was to correct the phases for the entire observation, as a function of time and frequency, by performing a fringe fit using the calibratorsources.Throughout,weuseEffelsberg,themostsensitive telescope in our array, as the reference antenna. After calibration, we imaged the check source to confirm that we detected it as a point source, as expected, and at the correct sky position. We then performed a grid search ±102 arcseconds around the target phase centre. This grid search comprised making dirty maps of 2 × 2 arcseconds spanning the entire 102 × 102 arcsecond grid, and reporting the peak of each dirty map. We made dirty maps using both natural and uniform weighting, resulting in beam sizes of 3.6 × 6.9 mas and 2.2 × 4.6 mas, respectively. The resulting root mean square (rms) noise levels are 42 μJy per beam and 63 μJy per beam for the natural and uniform weighted images, respectively. Given our shortest baseline (Irbene-to-Toruń; approximately 452 km), we are resolving out radio emission with size larger than approximately 82 mas.
- 10. Owing to time and frequency smearing, we can expect to lose sen- sitivity as we move farther from the phase centre. Across the extent of the host galaxy, we expect to lose at most 10% of the sensitivity, whereas at the edge of the 1σ FRB baseband localization10 we lose around30%.Wedidnotdetectanypersistentcompactradioemission inoursearch,downtoaluminositylimitofL1.6GHz < 2 × 1027 erg s−1 Hz−1 (7σ). There is a possible 6.6σ candidate at the edge of the FRB 3σ localization region that is not detected in the The Very Large Array Sky Survey (VLASS)69 . Confirming the astrophysical nature of this candidate is deferred to future work, but given its 3σ offset from the FRB position, and large offset from the host galaxy, it seems unlikely to be related to FRB 20221022A. We confirm that the National Radio Astronomy Observatory VLA Sky Survey (NVSS) source reported in ref. 10, NVSS J031417+865200, co-located with the centre of the FRB host galaxy is resolved out on our long base- lines. This supports their conclusion that it is from star formation in the host galaxy. With our sensitivity, we could have detected all three known PRSs with a significance ranging from approximately 15σ to >1,000σ. Our upper limit is in agreement with the proposed PRS luminosity–rotation measure relation70 , given the relatively low measured rotation measure for FRB 20221022A (rotation measure −40 rad m−2 )10 . Effelsbergsingle-dishFRBsearch AlthoughFRB 20221022Aisanas-yetnon-repeatingFRB,werecorded high-time-resolutionsearchdatawithEffelsberginparalleltosearch for possible repeat bursts. These search data was recorded at Effels- berg during the target scans in psrfits format using the Effelsberg Direct Digitization backend, with a time and frequency resolution 49.2 μs and 0.12 MHz, respectively. The bandwidth of these data is from 1.5 GHz to 1.75 GHz, that is, an observing band of 250 MHz. The totalintensitypsrfitsdatafromtheEffelsbergDirectDigitizationback- end were converted to filterbank format using digifil71 , conserving the time and frequency resolution of the psrfits data. This was done to be compatible with Heimdall (https://sourceforge.net/projects/ heimdall-astro/), which we use for the single-pulse search. Before performingtheburstsearch,wemaskedfrequencychannelsthatwere foundtocontainRFI.Single-pulsecandidatesaboveanS/Nthreshold of7identifiedbyHeimdallwerethenclassifiedusingFETCH(modelsA andH,withaprobabilitythresholdof0.5)72 .TheFETCHcandidatesas wellastheHeimdallcandidateswithdispersionmeasuresintherange of115–118 pc cm−3 wereinspectedbyeye.WefoundnopromisingFRB candidatesaboveanS/Nof7.Usingtheradiometerequation73 ,taking thetypicalEffelsbergsystemtemperatureandgainvaluesas20 Kand 1.54 K Jy−1 , respectively, and assuming a burst width of 1 ms, we arise at the fluence upper limit of 0.1 Jy ms for this observation. Owing to the sporadic activity behaviour of repeating FRBs (for example, ref. 74), our non-detection cannot confirm that FRB 20221022A will never repeat in the future. Riseanddecaytimes Asdiscussedinref.10,theburstshowsnoclearevidencefortemporal broadening owing to multi-path propagation, with an upper limit of τs < 550 μs at 400 MHz. The decorrelation-bandwidth measurements presentedinthisworkareconsistentwiththisupperlimit:thesmallest decorrelation bandwidth, 6 kHz, corresponds to the larger temporal broadening scale through the relation τs ≈ C/(2πΔνDC), which gives a scatter-broadening timescale of approximately 112 μs at 400 MHz. Thisconfirmsthattheburstmorphologyisdominatedbytheintrinsic burst decay time, as opposed to the exponential decay from scatter broadening, as indicated by the scattering upper limits presented in ref. 10. Both the rise and decay times can be important quantities for probing the burst emission physics46 . 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- 11. Article 72. Agarwal, D., Aggarwal, K., Burke-Spolaor, S., Lorimer, D. R. & Garver-Daniels, N. FETCH: a deep-learning based classifier for fast transient classification. Mon. Not. R. Astron. Soc. 497, 1661–1674 (2020). 73. Cordes, J. M. & McLaughlin, M. A. Searches for fast radio transients. Astrophys. J. 596, 1142–1154 (2003). 74. Lanman, A. E. et al. A sudden period of high activity from repeating fast radio burst 20201124A. Astrophys. J. 927, 59 (2022). 75. Nimmo, K., Magnetospheric origin of a fast radio burst constrained using scintillation Dataset. Zenodo https://doi.org/10.5281/zenodo.13954067 (2024). Acknowledgements We thank B. Marcote for help with the EVN observations; R. Karuppusamy for help with the pulsar backend recording at Effelsberg; D. Jow for discussions about anisotropic screens; J. Cordes and S. Ocker for answering questions about NE2001; and J. Hessels for discussions. K.N. is an MIT Kavli Fellow. Z.P. was a Dunlap Fellow and is supported by an NWO Veni fellowship (VI.Veni.222.295). P.B. is supported by a grant (number 2020747) from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel by a grant (number 1649/23) from the Israel Science Foundation and by a grant (number 80NSSC 24K0770) from the NASA astrophysics theory programme. P.K. is supported in part by an NSF grant AST- 2009619 and a NASA grant 80NSSC24K0770. M.W.S. acknowledges support from the Trottier Space Institute Fellowship programme. A.P.C. is a Vanier Canada Graduate Scholar. The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. B.M.G. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant RGPIN-2022-03163, and of the Canada Research Chairs programme. V.M.K. holds the Lorne Trottier Chair in Astrophysics and Cosmology, a Distinguished James McGill Professorship, and receives support from an NSERC Discovery grant (RGPIN 228738-13), from an R. Howard Webster Foundation Fellowship from CIFAR, and from the FRQNT CRAQ. C.L. is supported by NASA through the NASA Hubble Fellowship grant HST-HF2-51536.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. K.W.M. holds the Adam J. Burgasser Chair in Astrophysics and is supported by NSF grants (2008031 and 2018490). A.P. is funded by the NSERC Canada Graduate Scholarships – Doctoral programme. A.B.P. is a Banting Fellow, a McGill Space Institute (MSI) Fellow, and a Fonds de Recherche du Quebec – Nature et Technologies (FRQNT) postdoctoral fellow. K.S. is supported by the NSF Graduate Research Fellowship Program. FRB research at UBC is supported by an NSERC Discovery Grant and by the Canadian Institute for Advanced Research. The baseband recording system on CHIME/FRB is funded in part by a CFI John R. Evans Leaders Fund grant to IHS. We thank the directors and staff at the various participating EVN stations for allowing us to use their facilities and running the observations. The European VLBI Network is a joint facility of independent European, African, Asian and North American radio astronomy institutes. Scientific results from data presented in this publication are derived from the following EVN project code: RN002. Author contributions K.N. led the data analysis, interpretation and writing of the paper. Z.P. guided the analysis, and contributed to the interpretation and writing. P.B. and P.K. suggested the search for scintillation in CHIME FRBs, and contributed to the emission physics interpretation. A.E.L., D.Z.L., R.M. and M.W.S. provided substantial guidance regarding the analysis strategy, the mathematical framework and the interpretation of the results. S.A., M.B., S.C., A.P.C., E.F., B.M.G., R.C.J., Z.K., V.M.K., M.L., C.L., K.W.M., R.M., D.M., A.P., A.B.P., M.R.-R., K.R.S., K. Shin, K. Smith and I.H.S. contributed to the discovery of the FRB source and acquisition of data through the building or maintenance of the CHIME telescope and commented on the paper. Competing interests The authors declare no competing interests. Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41586-024-08297-w. Correspondence and requests for materials should be addressed to Kenzie Nimmo. Peer review information Nature thanks Casey Law and Di Li for their contribution to the peer review of this work. Peer reviewer reports are available. Reprints and permissions information is available at http://www.nature.com/reprints.
- 12. ExtendedDataFig.1|FRB20221022Aburstdynamicspectrum(panelc), profile(panelb),spectrum(paneld)andmodulationindex(panela).The burstisdedispersedtoadispersionmeasure10 of116.837 pc cm−3 andisplotted withtimeandfrequencyresolution40.96 μsand6.2MHz,respectively.The riseanddecaytimearehighlightedusingtheshadedredregionsinb.Boththe on-bursttime-averagedspectrumandoff-burstspectrumareshownind.For each163.84μstimebin,wecomputetheACF(equation(1))acrossfrequency (ACFiscomputedforspectrawithafrequencyresolutionof24kHz),and measurethemodulationindexastheheightoftheLorentzianfittotheACF aroundzerolag.Weonlyplotmodulationindicesfor163.84μstimebinsthat haveaS/N>8(a).Themeanofthemeasuredtimeresolvedmodulationindices forthe128kHzscintillationscaleisshownwiththeredlineina,andismeasured tobe m = 0.76±0.06,consistentwiththefrequency-resolvedmodulationindex measured forthisscintillationscale.
- 13. Article ExtendedDataFig.2|On-burstandoff-burstspectraacrosstheCHIME observingbandfrom400–800MHz(panelsa,c,e).Azoom-inaround 472–477MHz(theyellowbarina,c,e)isplottedinb,d,f.Panelsaandbarethe spectraofthebasebanddatawithfrequencyresolution0.39MHz(1024channels across the entire observing band). The upchannelized spectra (frequency resolution:0.76kHz)areshownincanddbefore correctingforthescalloping introduced by the FFT. The model we use to correct the scalloping is showninpurpleind.Panelseandfshowthespectraaftercorrectingfor theupchannelizationscalloping,andapplyingadditionalRFImasking.
- 16. ExtendedDataFig.5|Thelateralemissionregionsizeasitdependsonthe Galacticscreendistance,d⊕s1,throughtherelationshipshownonFig.3 andthetwo-screenconstraintinequation(9).Thegreenshadedregion showstheallowablelateralemissionregionsizes andGalacticscreendistance combinationsforourmeasuredscintillationparametersat600MHz:Δνs2 = 128kHzandms2 =0.78.TheblackverticallineindicatestheNE2001prediction23 : d⊕s1 =0.64kpc.Theorangeshadedregionshowstheemissionregionsizes estimatedfornon-magnetosphericmodels5–8 .Thegreyhatchedregionshows theparameterspaceweruledoutbasedontheapparentdiameterofthehost galaxy(seeFig.3).