Is GRB 110715A the Progenitor of FRB 171209?

Home , Magnetar

arXiv:2004.12050v1 [astro-ph.HE] 25 Apr 2020 3 4 5 6 2 1 colo srnm n pc cec,NnigUniversity, Nanjing Science, Space and Astronomy of School rmasnl oe-a pcrmfo H o26 to GHz 1 from deviates spectrum ( that power-law GHz single spectrum a non-thermal from 121102, a FRB showed with coincident which spatially be to discovered ot-etr nttt o srnm eerh unnUn Yunnan Research, Astronomy for Institute South-Western en soitdwt n R (e.g., FRB any with transient associated multi-wavelength confirmed being no is there (GRB) magnetar hand, burst gamma-ray young a or a ( (SN) supernova with a associated in from born nebula originates source shocked emission a radio persistent a such of luminosity with 2019 FRBs (e.g., few extragalactic a 2007 are of they the galaxies that and host suggest contribution the Galactic of the localizations of precise excess in are DMs eateto hsc n srnm,Uiest fNvd L Nevada of University Astronomy, and Physics of Department anse ta.2019 al. et Bannister 2019 al. et Petroff ahmtc n hsc eto,GagiUiest fChi of University Guangxi Section, Physics and Mathematics X-ACCne o srpyisadSaeSine,Nanni Sciences, Space and Astrophysics for Center GXU-NAOC Sch Astrophysics, [email protected] Relativistic China; for Laboratory Key Guangxi rgtestmeaue n ag iprinmeasures (e.g., dispersion high (DMs) large extremely and temperatures durations, brightness millisecond with transients uaee l 2016 al. et Murase rpittpstuigL using 2020 typeset 28, Preprint April version Draft atrdobrt FB)aemseiu radio mysterious are (FRBs) bursts radio Fast in-a Wang Xiang-Gao ; ; act ta.2020 al. et Marcote htejee l 2017 al. et Chatterjee hrtne l 2013 al. et Thornton n htoeFBeet R 729 icvrdb h akste at Parkes the 110715A by GRB discovered long-duration 171209, from historical FRB event, associations FRB spatial one that GRB-FRB engin find central m for possible Young searching a unknown. systematically be is to by suggested (FRBs) been bursts have radio (GRBs) fast bursts of origin physical The yayugsproarmatascae ihteGB vrl,th Overall, GRB. the with b associated can (2 remnant which supernova medium, young intergalactic a dispersio the by extragalactic by contributed The that magnetar. of millisecond excess a by powered being ihln Rscnb h rgntr fa es oeFRBs. some least at of progenitors the Keywords: be can GRBs long with . 28 oie ta.2007 al. et Lorimer − 2 1. . 55) ; L ; non-thermal tr am-a us tr atrdobrt-sa:magneta star: - burst radio fast star: - burst gamma-ray star: INTRODUCTION 1,2 ods&Catre 2019 Chatterjee & Cordes eze ta.2017 al. et Metzger σ ; A ∼ T ogLi Long , fteascaini nedpyia,orrsl ugssta the that suggests result our physical, indeed is association the If . rcak ta.2019 al. et Prochaska E tl ATX .1.0 v. 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FRB OF PROGENITOR THE 110715A GRB IS 1,2,3 htejee l 2017 al. et Chatterjee ; − hrtne l 2013 al. et Thornton unPiYang Yuan-Pei , 1 tafwGzwas GHz few a at .O h other the On ). oie tal. et Lorimer erffe al. et Petroff ; aie al. et Ravi .Their ). z o fPyia cec n ehooy unx University Guangxi Technology, and Science Physical of ool ogMiQin Song-Mei 0 = 4 ajn 103 China 210093, Nanjing eeMdcn,Nnig53001,China Nanning Medicine, nese ABSTRACT vriy umn 550 hn;[email protected] China; 650500, Kunming iversity, i-e Luo Jia-Wei , sVgs V814 S;[email protected] USA; 89154, NV Vegas, as g500,China 530004, ng ; ; . 2 h fego fGB101Ai ossetwith consistent is 110715A GRB of afterglow The 82. tl nnw.TecretFBmdl a edi- be can is models FRBs categories FRB of two current into origin The vided physical the unknown. still FRBs, with respect sociated with delay long ( a a have itself as event may (such the SN) event to a catastrophic or a young GRB a from from born emitted FRBs magnetar than e.g., longer time, is observation FRB the the and transient multi-wavelength o,eg,frtpclprmtr,teFBafterglows FRB ( the faint parameters, very typical are for are e.g., FRBs of low, counterparts multi-wavelength the of fluxes 2017 prompt itself the FRB e.g., the detector, with ( a associated than of emission shorter high-energy resolution be time may the transient multi-wavelength the 2018 2019 al. et Collaboration MAGIC 2015 age l 2019b al. et Yang 1 akn ofimdmliwvlnt rninsas- transients multi-wavelength confirmed Lacking 6 opeels fFBpoeio oescnb enin seen be can models progenitor FRB of list complete A ). The 1. reasons: main three be might There ). ; 5 igZhang Bing , alse ta.2016 al. et Callister fFB.W etsc hypothesis a such test We FRBs. of e ecp ssailycicdn iha with coincident spatially is lescope nepee sbigcontributed being as interpreted e infiac fteascainis association the of significance e 1 Rsad14 Rs We GRBs. 1440 and FRBs 110 geasbr rmgamma-ray from born agnetars esr fFB110 sin is 171209 FRB of measure n ie l 2014 al. et Yi ;3 h iedlybtenthe between delay time the 3. ); 5 aBnLin Da-Bin , uaee l 2016 al. et Murase aito mechanisms: radiation - r 1 antr associated magnetars aatohcmdl (e.g., models catastrophic : ; ;2 h uainof duration The 2. ); hn hn 2017 Zhang & Zhang 1,2 nWiLiang En-Wei , ; ; ann 530004, Nanning , igy&Yang & Tingay eze tal. et Metzger 1,2 , ; 2

Kashiyama et al. 2013; Totani 2013; Falcke & Rezzolla evidence of having a magnetar central engine, but these 2014; Zhang 2014, 2016; Wang et al. 2016) and observations did not lead to detection of any FRB from non-catastrophic models (e.g., Murase et al. 2016; these remnants during a total of ∼ 20h of observations. Metzger et al. 2017; Zhang 2017, 2020; Dai et al. In this work, we adopt a different approach to test 2016; Margalit & Metzger 2018; Wang et al. 2020; the hypothesis that GRBs can be the progenitor of Ioka & Zhang 2020). The former suggested that an FRB FRBs. We systematically search for GRB-FRB asso- is directly associated with a catastrophic event, and the ciation events based on the precise localization of GRB time delay between the FRB and the catastrophic event afterglows, allowing a few years of time delay between a is short. The latter usually involved a compact star, GRB and an FRB. Observationally, GRBs are typically e.g., a neutron star or a black hole, that was born in a localized by the Neil Gehrels Swift Observtory, i.e. the catastrophic event as the progenitor of an FRB. Since burst is detected by Swift/BAT and quickly localized by the compact star can exist for a much longer time, the Swift/XRT with a several-arcsecond error bar, and later time delay between the FRB and the catastrophic event further localized by Swift/UVOT or groundbased tele- is allowed to be relatively long. scopes to sub-arcsecond precision. Based on the archival GRBs are the most luminous catastrophic events, and Swift/XRT and optical observational data, we search are produced by core collapse of massive stars or binary for possible GRB-FRB spatial association candidates. compact star mergers (Mészáros 2006; Zhang 2018b). We detect one possible association between FRB 171209 Although GRBs are much rarer than FRBs, the follow- (Oslowski et al. 2019) and GRB 110715A at z = 0.82 ing reasons have been raised to suggest that a fraction (Sánchez-Ram´ırez et al. 2017). This paper is organized of FRBs could be associated with GRBs: 1. an FRB as follows. In Section 2, we present the search method might occur when a supermassive magnetar born in a and result. The GRB 110715A - FRB 171209 associ- GRB collapses to a black hole, so called “blitzar” sce- ation is discussed in Section 3 in detail. The results nario (Falcke & Rezzolla 2014; Zhang 2014); 2. an FRB are summarized with discussion in Section 4. Through- might be related to the merger of a binary neutron star out the paper, we adopted a concordance cosmology −1 −1 which produces a short GRB (Totani 2013; Wang et al. with parameters H0 = 71 kms Mpc , ΩM = 0.30, 2016); 3. a GRB as the source of astrophysical stream ΩΛ = 0.70, and temporal and spectral slopes of GRB could interact with the magnetosphere of a neutron star afterglow emission are defined as F ∝ t−αν−β. More- n to produce an FRB (Zhang 2017); 4. a GRB could pro- over the convention Q = 10 Qn is adopted in cgs units. duce a young magnetar that emits FRBs at a much later 2. SEARCH FOR GAMMA-RAY BURSTS epoch (e.g., Metzger et al. 2017; Margalit et al. 2019; ASSOCIATED WITH FAST RADIO BURSTS IN Wang et al. 2020). In the first three scenarios, an FRB ARCHIVAL SWIFT /XRT AND OPTICAL could occur from milliseconds before to a few thousand OBSERVATIONAL DATA seconds after the GRB. The fourth scenario allows a much longer delay of FRBs with respect to the GRB. Since the discovery of the first FRB (Lorimer et al. Related to this, recently Eftekhari et al. (2019) discov- 2007), 110 FRBs have been reported in the lit- 2 ered a radio source coincident with the SLSN PTF10hgi, erature as of February 2020 (e.g., Petroff et al. similar to the persistent radio emission of FRB 121102 2015; CHIME/FRB Collaboration et al. 2019; (Chatterjee et al. 2017), about 7.5 years post-explosion, Casentini et al. 2019). Meanwhile, up to now there which might be emitted by the magnetar born in the are 1440 GRBs that have afterglow detections, in- SLSN. However, no FRB was detected from the source cluding 845 GRBs with optical detections and 595 3 yet. with Swift/XRT detections only. Among them, the In general, the searches for GRB-FRB associ- numbers of long and short duration GRBs are 1320 and ations have so far given no confirmed results 120, respectively. Figure 1 shows the sky distribution (e.g., Bannister et al. 2012; Palaniswamy et al. of our samples (110 FRBs and 1440 GRBs) in celestial 2014; DeLaunay et al. 2016; Scholz et al. 2016; coordinates. The GRBs in our sample show a large-scale Yamasaki et al. 2016; Zhang & Zhang 2017; Xi et al. isotropic distribution, which is well known from the 2017; Guidorzi et al. 2019; Yang et al. 2019a; BATSE observations (Briggs et al. 1996). Although the Cunningham et al. 2019; Tavani et al. 2020). In sample size of FRBs is smaller than that of GRBs, the particular, Men et al. (2019) recently performed dedi- FRBs in our sample also show an isotropic distribution, cated observations of the remnants of six GRBs with consistent with their cosmological origin. As shown

2 Platts et al. (2019). http://www.frbcat.org(Petroﬀ et al. 2016). 3 https://swift.gsfc.nas.gov/archive/grb table/ 3

ter the BAT trigger, respectively (Kuin & Sonbas 2011; Evans & Sonbas 2011). It was also followed up by ground-based optical telescopes GROND (Updike et al. 2011) and AAVSO (Nelson 2011); submm telescopes APEX (de Ugarte Postigo et al. 2011) and ALMA (Sánchez-Ram´ırez et al. 2017); and the radio telescope ATCA (Hancock et al. 2011). The position of GRB 110715A, defined by its optical afterglow, is (RAJ2000.0, h m s ◦ ′ ′′ Figure 1. Sky celestial coordinate distributions of 110 FRBs DECJ2000.0) = (15 50 44 .09, −46 14 06 .53), with and 1440 GRBs in our sample. The FRBs and GRBs are an estimated uncertainty of 0.56 arc sec (radius, marked with blue and green circles, respectively. The posi- 90% confidence) (Kuin & Sonbas 2011). The red- tions of GRB 110715A and FRB 171209 are highlighted with a red circle. shift of GRB 110715A was measured to be z = 0.82 (Piranomonte et al. 2011). On the other hand, FRB 171209 (Oslowski et al. 2019) was detected 2338 days (∼6.4 yr) after the GRB 110715A trigger. It was the first FRB detected as part 1 S of the commensal search during PPTA observations, h m s with a position (RAJ2000.0, DECJ2000.0) = (15 50 25 , −46◦10′20′′), with an uncertainty of 7.5 arcmin (radius, 2.355σ confidence). The DM value is 1457.4±0.03 cm−3 11 N pc and the DM value contribution from the Milky Way −3 is DMgal = 235 cm pc (Oslowski et al. 2019). Using −3 a simple DM-z relation DMIGM ∼ 855pc cm z (Zhang 2018a), one can estimate the maximum redshift of FRB 1 1 −3 1 1 1 1 171209, which is ∼ (DM − DMgal)/855pc cm =1.43. S Due to the existence of large-scale structures, the un- Figure 2. The log N − log S distribution of the FRBs in our certainty of the DM contributed by the IGM is about −3 sample. σIGM ∼ 300 pc cm . Thus the maximum redshift is constrained in the range of z < (1.08 − 1.78). This is in Figure 2, the distributions of the FRB fluence larger than the redshift of GRB 110715A. (log N − log S)4 show a tendency with N(>S) ∝ S−3/2 To calculate of chance possibility for the putative at high S values. The deviation from the 3/2 power GRB 110715A - FRB 171209 association, we assume law is evident at low S values, which may be related that the spatial distribution of GRBs is isotropic and to the spatial inhomogeneity effect and likely also the number of GRBs within a specific sky area and time observational biases and instrumental effects. interval satisfies the Poisson distribution. The chance We perform a systematic search for GRBs that sat- probability of having at least one GRB in the error cir- isfy the following three criteria: (1) the GRB position is cle of one FRB can then be written as 0 consistent with that of an FRB; (2) the GRB occurred P1 =1 − λ exp(−λ)/0!=1 − exp(−λ), (1) earlier than the FRB if a position coincidence is discovered; (3) the redshift of the GRB is lower than the where λ = ρS is the expected number of GRBs in the maximum FRB redshift derived from its DM. FRB error region S. The surface number density of ≈ ≈ 2 We found only one GRB that is located at the po- GRBs is ρ 1440/41252.96 0.035/deg . For a cir- sition of an FRB, i.e. the GRB 110715A - FRB cular region with a radius δR (in unit of deg), we can ≈ − 171209 spatial association. GRB 110715A was trig- derive its area S [41252.96(1 cos δR)]/2. gered by the Swift/BAT on 2011 July 15 (UT dates To estimate the p-value of the chance coincidence, we adopt two approaches. First, for a conservative esti- are adopted) at 13 : 13 : 50 (T0), with T90 = 13 s (Sonbas et al. 2011; Ukwatta et al. 2011). It was also mate, we use the uncertainty of 7.5 arcmin defined by ◦ detected by the Konus-wind (Golenetskii et al. 2011). the error bar of the FRB position, i.e. δR =0.125 . We The Swift/XRT and Swift/UVOT began observing its obtain the chance probability of having at least one (out X-ray and optical afterglows at 90.9 s and 99 s af- of 1440) GRB whose distance to FRB 171209 is smaller ◦ than 0.125 , which gives P1 ≈ 0.0017. The chance probability of having only one such association for all 110 110 4 The fluence (S) values are obtained from FRBs can be estimated as P =1 − (1 − P1) ≈ 17.1%. http://www.frbcat.org. We verify this simple estimate through Monte Carlo sim- 4

200 ulations. We randomly generate 1440 GRBs and 110 FRBs in the sky. Based on 105 simulations, the chance 200 probability of having a GRB/FRB pair with a separa- 150 tion smaller than 0.125◦ is 17.4%, consistent with the 150 analytical estimate. 100 100

One also needs to consider two other criteria for an Counts Ep [KeV] Ep association, i.e. the timing criterion (the GRB needs to 50 occur before the FRB) and the redshift criterion (the 50 maximum redshift derived from the FRB DM is larger 0 than that of the GRB). To do this, we use the observed 0 distributions of the detection time and redshift for both 0 5 10 15 20 GRBs and FRBs to perform the simulations. Since most Time [Seconds]

GRBs were detected earlier than FRBs (FRBs were dis- Figure 3. The BAT lightcurve (blue line) and its Ep (black covered much later than GRBs), adding the timing crite- circle) evolution of GRB 110715A. The isotropic γ-ray energy ± × 53 4 rion does not reduce the chance probability significantly, is Eγ,iso = 1.06 0.10 10 erg in the 1-10 keV band. i.e. ∼ 14.1%. However, since the average redshift of 53 4 GRBs is higher than the average maximum redshift of energy Eγ,iso = 1.06 ± 0.10 × 10 erg in the 1-10 FRBs, adding the redshift criterion reduces the chance keV band. The results from the time-resolved spectral probability significantly to ∼ 2.3%, which corresponds analysis show the “flux-tracking” pattern for Ep. To fit to a significance of 2.28σ. the GRB 110715A afterglow lightcurves, we employed Second, since GRB 110715A is well located inside the a broken power-law function error circle of FRB 171209,one may use the angular dis- 1 2 1/ω t ωα t ωα tance between the centers of the error boxes of the two F = F1 + , (2) events, 0.0836◦, as δR5 One can obtain the chance prob- tb tb ability of having at least one (out of 1440) GRB whose where F1 is the flux normalization, α1 and α2 are distance to FRB 171209 is smaller than 0.0836◦, i.e. the afterglow flux decay indices before and after the P1 ≈ 0.0007. We also randomly generate 1440 GRBs break time (tb), respectively, and ω is a smoothness pa- and 110 FRBs in the sky. Based on 105 simulations, the rameter which represents the sharpness of the break. chance probability of having one GRB/FRB pair with Figure 4 shows the X-ray and optical light curves of a separation smaller than 0.0836◦ is 7.6%. Consider- GRB110715A. The X-ray light curve can be well fit- ing the timing criterion, we obtain P = 6.3%. When ted by a broken power-law function, with the best-fit +0.04 the redshift criterion is also considered, the final chance power-law slope αX,1 =0.70−0.05 (shallow decay) before +0.4 +0.11 probability is 1.1%, which corresponds to a 2.55σ confi- the break (tb = T0 +2.0−0.3 ks) and αX,2 = 1.60−0.09 dence level for the GRB 110715A/FRB 171209 associa- (normal decay) after the break, respectively. There is a ∼ +0.4 tion. re-brightening component appearing at T0 +50−0.3 ks. For the optical light curve, there is an early steep decay 3. IS GRB 110715A ASSOCIATED WITH FRB phase, which may be interpreted as the reverse shock 171209? emission as the ejecta is decelerated. This is followed by +0.13 Even though statistically one cannot establish a firm a shallow decay phase (with αO,1 =0.70−0.12) breaking +0.15 association between GRB 110715A and FRB 171209, it at tb and further decays with αO,2 = 1.60−0.11. The is nonetheless interesting to investigate whether physi- re-brightening component also appeared in the optical cally such an association makes sense. afterglow. The result of the temporal analysis suggests that the X-ray and optical afterglow show an achromatic 3.1. Magnetar as central engine of GRB 110715A behavior (Wang et al. 2015). The Swift/BAT time-integrated spectrum of We also analyze the spectral energy distributions GRB 110715A can be well fitted with a Band function (SEDs) of GRB 110715A afterglow, by jointly fit- (Band et al. 1993), with Epeak = 92.8 ± 18.1 keV, ting the optical and XRT data with the Xspec pack- α = −1.23 ± 0.12, and β = −2.05 ± 0.19 and χ2=0.98 age (Arnaud 1996) and the optical data that are cor- (as shown in Figure 3). We obtained the isotropic γ-ray rected for Galactic extinction based on the burst direc- tion, with AV = 0.030, AR = 0.119 and AI = 0.016 (Schlafly & Finkbeiner 2011). The extinction in the 5 This approach was adopted by the IceCube team host galaxy is also taken into account assuming an ex- to claim a possible association between the neutrino trigger event IceCube-170922A and the blazar TXS 0506+056 tinction curve similar to that of Small Magellanic Cloud (IceCube Collaboration et al. 2018). (SMC) with its Standard value of the ratio of total to se- 5

XRT XRT XRT XRT

white white white white

10 v v b b

u v u -1

0 u

10 keV -1

-1

10 s -2

-2

=1.69 (0.2-0.5 ks) 10

-3

=1.70 (3-8 ks) Photons cm

-4

=1.87 (20-100 ks)

-5

=1.89 (200-1000 ks)

-6

-3 -2 -1 0 1

10 10 10 10 10

Energy (keV)

Figure 4. Lightcurves of X-ray and optical afterglows of Figure 5. The SED analysis of GRB 110715A. Joint spectral GRB 110715A. The light curves are decomposed into mul- fits of the X-ray and optical afterglows in four selected time tiple components (dashed or dash-dotted lines). The solid intervals. The solid lines show the intrinsic power-law spec- lines represent the best fit to the data. The vertical blue tra derived from the joint fits. Different spectral bands are dashed lines mark the break time between the shallow decay denoted in different symbols: XRT data (circle), white band phase to the normal decay phase. The grey zones represent (square), b-band (prismatic), v-band (triangle), and u-band the time slices for the afterglow SED analysis. (star). The photon indices Γ in different time intervals are also marked in different colors. lective extinction Rv,SMC =2.93 (Pei 1992). The equivalent hydrogen column density of our Galaxy is NH = rameters. The results are shown in Figure 4. One × 21 −2 4.33 10 cm . The equivalent hydrogen column den- can see that the model can well reproduce the data. host ± × 21 sity of the host galaxy NH = (4.22 2.95) 10 −2 The best fitting parameters are: the isotropic kinetic cm is derived from the time integrated XRT spec- 53 energy EK,iso = 2 × 10 erg, the initial Lorentz fac- trum. We fix these values in our time-resolved spectral tor Γ0 = 45, the fraction of shock energy to elec- fits. We subdivided the broadband data into four tem- trons ǫe = 0.268, the fraction of shock energy to mag- poral ranges (as marked in Figure 4). The SEDs of the −6 netic fields ǫB = 1.1 × 10 , wind density parameter joint optical and X-ray spectra can be well fitted with a 50 A∗ =0.25, the energy injection luminosity L0 =1×10 single absorbed power-law function. The photon indices erg s−1, and the duration of energy injection t = 2000 s. − b Γ (the spectral index β =Γ 1) are 1.69, 1.70, 1.87 and The fitting parameters are consistent with the statistical 1.89 for the Slice 1 (T0 + [200, 500] s), Slice 2 (T0 + properties of a large sample of GRBs (e.g., Wang et al. × 3 × 3 × 4 × 5 [3 10 ,8 10 ] s), Slice 3 (T0 + [2 10 ,1 10 ] s), and 2015). × 5 × 6 Slice 4 (T0 + [2 10 ,1 10 ] s), respectively. There Since the energy injection q = 0 is well consistent with is no obvious spectral evolution observed in the after- the magnetar spin-down model, we can derive the mag- glow phase. The temporal slopes of the normal de- netar parameters of GRB 110715A based on the data. cay phase (αX,II and αO,II) are well consistent with the The maximum energy is the total rotational energy of a − closure relations (α β) of the fireball external shock millisecond magnetar and is defined as model α = 3β/2+0.5= 1.54 ± 0.08, which are lo- 1 cated in spectral regime (νm <ν<νc) in the wind 2 ≃ × 52 2 −2 Erot = IΩ0 2 10 erg M1.4R6P0,−3, (3) stellar medium (e.g. Gao et al. 2013). For the shal- 2 low decay phase closure relation α = q/2+(2+ q)β/2 where I is the moment of inertia, P0 is the initial spin pe- (Zhang et al. 2006), we obtained the energy injection pa- riod, Ω0 =2π/P0 is the initial angular frequency of the +0.04 +0.13 rameter q = 0 for αX,I =0.70−0.05 and αO,I =0.70−0.12, neutron star, M1.4 = M/1.4M⊙, and R is the radius of which is consistent with the energy injection from the the magnetar. The isotropic γ-ray and kinetic energies spin-down of a millisecond magnetar (Dai & Lu 1998; are larger than this value, suggesting that the outflow Zhang & Mészáros 2001). Çıkınto˘glu et al. (2019) also is beamed, with a beaming factor fb =1 − cos θj < 0.1, argued that the millisecond magnetar could be the cen- where θj is the half opening angle of the jet. Based on tral engine of GRB 110715A. the characteristic spin down luminosity L0 and the spin- We further investigate the afterglow data with the down timescale τ of a magnetar as shown in Equation standard forward shock model with energy injection (6) and (8) in Zhang & Mészáros (2001), one can cal- (q = 0). A Markov Chain Monte Carlo (MCMC) culate the surface polar cap magnetic field strength Bp method is adopted to search for the best fitting pa- and the initial spin period P0: 6

and the local DM from the host galaxy is

−3 −1/2 −1 −3 Bp,15 =2.05(I45R6 L0,49 τ3 ) G, (4) DMhost = (1+ z)(DME − DMIGM) ≃ 950 pc cm 1/2 −1/2 −1/2 (10) P0,−3 =1.42(I45 L0,49 τ3 ) s. (5) − −3 Observationally, the spindown luminosity L0 can be gen- where DME = DM DMgal = 1222.4 pc cm is the erally written as (Lü& Zhang 2014) extragalactic DM of FRB 171209 (Oslowski et al. 2019). At z = 0.82, the uncertainty of the IGM DM is L0 = [LX,iso + EK,iso(1 + z)/tb]fb, (6) −3 σIGM ∼ 200 pc cm (McQuinn 2014). Meanwhile, where LX,iso is the X-ray luminosity due to internal dis- since the host galaxy of GRB 110715A is similar to that sipation of the magnetar wind, which is negligible in our of FRB 121102, we take the DM contribution from the −3 case. interstellar medium (ISM) as DMISM . 200 pc cm Since no jet break is observed in GRB 110715A,we can (Sánchez-Ram´ırez et al. 2017; Tendulkar et al. 2017). use the epoch of the last observational data point to set Therefore, even considering the large-scale structure o a lower limit on θj (Wang et al. 2018b), i.e. θj > 6.2 . fluctuation and a possible large DM from the ISM, there 53 47 −1 ∼ −3 Using EK,iso =2×10 erg, LX,iso =3.28×10 erg s , is still a large DM excess DMloc 550 pc cm . This and τ = tb/(1+z) = 2000/(1+0.82)= 1099 s, we obtain DM excess is likely contributed by the GRB-associated 15 ≃ P0 < 3.59 ms and Bp < 4.95 × 10 G, respectively. SN occurred t 6.4 yr before FRB 171209. In the free- These parameters fall into the regime of typical young expansion phase, the DM provided by a young SNR with magnetars for GRB central engines. Such a magnetar is mass M and kinetic energy ESN can be estimated as believed to power repeating FRBs when the environment (e.g., Piro 2016; Yang & Zhang 2017) becomes clean (Murase et al. 2016; Metzger et al. 2017; 2 ηM −3 Margalit & Metzger 2018). DMSN = 2 = 630 pc cm 8πµmmpESNt 3.2. Is the magnetar the progenitor of FRB 171209? 2 −2 −1 × M t ESN η 51 (11) As reported by Oslowski et al. (2019), FRB 171209 M⊙ 6.4 yr 10 erg ∼ has a duration of ∆t 0.138 ms and a fluence of where µ =1.2 is the mean molecular weight for a solar ∼ m fν & 3.7 Jy ms at ν 1 GHz. If FRB 171209 is indeed composition in the SNR ejecta, and η is the ionization associated with GRB 110715A, according to the red- fraction of the medium in the SNR. We can see that shift z =0.82 of GRB 110715A, the luminosity distance for a typical SN with a few times solar masses, the cor- ≃ is dL 5 Gpc. The isotropic energy of FRB 171209 responding DM contribution could reach the required ∼ 2 × 41 is about EFRB 4πdLνfν & 1.1 10 erg. If this host-galaxy DM of FRB 171209. One should check the energy is provided by the magnetic energy of the un- the free-free absorption in the SN. For a young SNR, the derlying magnetar, one may place a most demanding free-free optical depth through the ejecta shell is constraint on the strength of the magnetic field of the −3/2 underlying magnetar assuming isotropic FRB radiation. −3/2 2 −2 T τff ≃ (0.018T Z n n ν g¯ff )L≃ 3600 The emission radius can be approximately estimated as e i 104 K 6 − − re ∼ c∆t ≃ 4.1 × 10 cm. The magnetic field strength 9/2 5/2 5 −2 × M ESN t ν at re should satisfy 51 , M⊙ 10 erg 1 yr 1 GHz 2 B 4π 3 (12) r & EFRB, (7) 8π 3 e where ne and ni are the number densities of electrons where B = B (r /R)−3. Therefore, the observation of p e and ions, respectively, and ne = ni and Z = 1 are FRB 171209 demands that the surface polar cap mag- assumed for an ejecta with a fully ionized hydrogen- netic field strength is dominated composition, L∼ r ∼ vt is the ejecta thick- 3 1/2 ness, andg ¯ff ∼ 1 is the Gaunt factor. If the SNR ejecta 6Ere 12 Bp & ≃ 6.8 × 10 G, (8) is transparent for FRB, i.e., τ . 1, one gets the SNR R6 ff age (e.g. Yang et al. 2019b) which is consistent with the observation constraints de- 9/10 −1/2 rived from the afterglow emission of GRB 110715A. M ESN t & 5 yr 51 , (13) According to the redshift z = 0.82 of GRB 110715A, M⊙ 10 erg the DM contribution from the IGM is given by (Zhang where ν ∼ 1 GHz and T ∼ 104 K are taken. This 2018a), is consistent with the 6.4 yr time delay between FRB −3 −3 DMIGM ≃ 855 pc cm z ≃ 700 pc cm , (9) 171209 and GRB 110715A. 7

4. SUMMARY AND DISCUSSIONS 110715A and FRB 171209. FRB 171209 so far does Lacking multi-wavelength observational data of FRBs, not show a repeating behavior. Its lightcurve shows it is hard to constrain their physical origin. It has been one single pulse without a noticeable temporal struc- suggested that at least some FRBs may be physically as- ture (Oslowski et al. 2019). The intrinsic duration is sociated with GRBs (Zhang 2014; Metzger et al. 2017). sub-millisecond. In principle, the burst could be an one- The GRB may leave behind a long-lived magnetar, off event. If it is associated with GRB 110715A, it may which may produce FRBs through ejecting magneto- be related to the collapse of the supramassive neutron sphere upon collapse Falcke & Rezzolla (2014), or more star at such a late epoch (Falcke & Rezzolla 2014; Zhang likely, produce repeated bursts through crust crack- 2014). However, contrived conditions are needed to al- ing or magnetic reconnection (e.g. Popov & Postnov low the collapsing time to be at such a late stage after 2010; Katz 2016; Beloborodov 2017; Kumar et al. 2017; the spindown timescale. More likely, FRB 171209 may Yang & Zhang 2018; Wang et al. 2018a). be one of many repeating bursts powered by the mag- We searched for possible GRB-FRB associations based netar harbored in GRB 110715A (Murase et al. 2016; on the localization data of 110 FRBs and the precise lo- Metzger et al. 2017). Searching for repeating bursts calization data of 1440 GRB afterglows. We found that from FRB 171209 would be essential to test this pos- the long-duration GRB 110715A is within the error box sibility. of FRB 171209 and the redshift of the GRB 110715A Observationally, no SN was reported for GRB is lower than the maximum redshift derived from the 110715A (Sánchez-Ram´ırez et al. 2017). This is not sur- DM of the FRB 171209. Taking the factors of spatial prising, since GRB 110715A is not nearby and is a high- location, time of occurrence, and the redshift criterion, luminosity long GRB with a bright optical afterglow. we derive a chance probability of 2.3% to 1.1%, corre- The SN signature is likely outshone by the afterglow. It sponding to a 2.28σ to 2.55σ confidence level for the is well known that essentially every long GRB is accom- association. panied by a Type Ic SN (Woosley & Bloom 2006), so Even though the chance coincidence probability can- that invoking a SN to account for the extra DM from not establish a firm association between GRB 110715A FRB 171209 is justified. and FRB 171209, we nonetheless investigated whether there exists a self-consistent physical picture to make XGW, DBL and EWL acknowledges support a connection between the two. We modeled the after- from the National Natural Science Foundation of glow of GRB 110715A and identified a shallow-decay China (grant No.11673006, U1938201, 11533003, signature, which is consistent with energy injection by 11773007), the Guangxi Science Foundation (grant a millisecond magnetar with P0 < 3.59 ms and Bp < No. 2016GXNSFFA380006, 2017GXNSFBA198206, 4.59 × 1015 G. With the Milky Way and IGM contribu- 2018GXNSFFA281010, 2017AD22006, 2018GXNS- tions subtracted, the observed DM of FRB 171209 has FGA281007), the One-Hundred-Talents Program of an excess of ∼ 950 pc cm −3, which is consistent with Guangxi colleges, and High level innovation team and the DM contribution of a young (∼ 6.4 yr old) SNR as- outstanding scholar program in Guangxi colleges. BZ sociated with GRB 110715A with a few solar masses and and JWL acknowledge the UNLV Top-Tier Doctoral 51 kinetic energy ESN ∼ 10 erg. The requirement that Graduate Research Assistantship (TTDGRA) grant the free-free optical depth τff . 1 suggests that FRBs for support. We also acknowledge the use of public can be observable only a few years after the explosion, data from the Swift data archives and the FRB catalog consistent with the observed 6.4 yr delay between GRB (http://frbcat.org).

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