Draft version May 19, 2020 Typeset using LATEX twocolumn style in AASTeX63

Implications of a “Fast Radio Burst” from a Galactic

Ben Margalit,1, ∗ Paz Beniamini,2 Navin Sridhar,3 and Brian D. Metzger4, 5

1Astronomy Department and Theoretical Center, University of California, Berkeley, Berkeley, CA 94720, USA 2Division of , Mathematics and , California Institute of Technology, Pasadena, CA 91125, USA 3Department of Astronomy, Columbia University, New York, NY 10027, USA 4Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA 5Center for Computational Astrophysics, Flatiron Institute, 162 W. 5th Avenue, New York, NY 10011, USA

ABSTRACT A luminous radio burst was recently detected in temporal coincidence with a hard X-ray flare from the Galactic magnetar SGR 1935+2154 with a time and frequency structure consistent with cosmological fast radio bursts (FRB) and a fluence within a factor of . 10 of the least energetic extragalactic FRB previously detected. Although active are commonly invoked FRB sources, several distinct mechanisms have been proposed for generating the radio emission which make different predictions for the accompanying higher frequency radiation. We show that the properties of the coincident radio and X-ray flares from SGR 1935+2154, including their approximate simultaneity and relative −5 fluence Eradio/EX ∼ 10 , as well as the duration and spectrum of the X-ray emission, are consistent with extant predictions for the synchrotron maser shock model. Rather than arising from the inner magnetosphere, the X-rays are generated by (incoherent) synchrotron radiation from thermal electrons heated at the same internal shocks which produce the coherent maser emission as ultra-relativistic flare ejecta collides with a slower particle outflow (e.g. as generated by earlier flaring activity) on a radial scale ∼ 1011 cm. Although the rate of SGR 1935+2154-like bursts in the local universe is not sufficient to contribute appreciably to the extragalactic FRB rate, the inclusion of an additional population of more active magnetars with stronger magnetic fields than the Galactic population can explain both the FRB rate as well as the repeating fraction, however only if the population of active magnetars are born at a rate that is at least two-orders of lower than that of SGR 1935+2154-like magnetars. This may imply that the more active magnetar sources are not younger magnetars formed in a similar way to the population (e.g. via ordinary supernovae), but instead through more exotic channels such as superluminous supernovae, -induced collapse or neutron mergers.

Keywords: Radio transient sources (2008) — Magnetars (992) — Soft gamma-ray repeaters (1471)

1. INTRODUCTION ized events, as well as the fact that some FRBs appear Fast radio bursts (FRBs) are bright, millisecond du- to repeat (Spitler et al. 2016; Chatterjee et al. 2017; ration pulses of coherent radio emission with disper- CHIME/FRB Collaboration et al. 2019) while others do sion measures (DM) well in excess of Galactic values not. Many theoretical models have been proposed for FRBs arXiv:2005.05283v2 [astro-ph.HE] 17 May 2020 (Lorimer et al. 2007; Thornton et al. 2013; see Petroff et al. 2019, Cordes & Chatterjee 2019 for reviews), and (see Platts et al. 2019 for a catalog). Perhaps the hence pointing to an extragalactic origin. The precise most well-studied models are those which postulate mechanisms powering FRBs remain a topic of debate, that FRBs arise from the flaring activity of strongly- in large part due to the small number of well local- magnetized neutron (NS) known as “magnetars” (Popov & Postnov 2013; Lyubarsky 2014; Kulkarni et al. 2014; Katz 2016; Metzger et al. 2017; Beloborodov 2017; Corresponding author: Ben Margalit Kumar et al. 2017). Evidence in favor of magnetars as [email protected] FRB sources include: (1) high linear polarization and ∗ NASA Einstein Fellow large rotation measures (e.g. Masui et al. 2015; Michilli et al. 2018), indicative of a strongly-magnetized cen- 2 Margalit, Beniamini, Sridhar, & Metzger tral engine and environment; (2) spatial association with sofar as it would have been detectable even in the side star-forming regions, in the two repeating events where lobes of Parkes (Tendulkar et al. 2016). Such behavior VLBI imaging enables precise sky localizations (Bassa may still be consistent with some magnetar models, e.g. et al. 2017; Tendulkar et al. 2017; Marcote et al. 2020); because of beaming of the radio emission or because the (3) statistical properties of the bursts’ repetition con- nature of the external environment (i.e. the history of sistent with those of Galactic magnetar flares (e.g. Wa- the flaring activity) plays as important of a role in gener- diasingh & Timokhin 2019; Cheng et al. 2020); (4) a ating FRB emission as the flare itself (Beloborodov 2017; sufficiently high volumetric rate of magnetar birth to Metzger et al. 2019; Beloborodov 2019). Nevertheless, plausibly explain the observed FRB rate (e.g. Nicholl skepticism regarding magnetar FRB models would only et al. 2017), unlike other models involving rare cata- continue to grow if FRB-like emission were never seen clysmic events (Ravi 2019). in association with nearby, verifiable magnetars. Despite these hints, several properties of the growing The observational situation changed abruptly with the sample of FRBs appear−at least at first glance−to be in recent discovery of a luminous millisecond radio burst tension with magnetars as a primary source. The first from the Galactic magnetar SGR 1935+2154 (Scholz repeating source, FRB 121102 (Spitler et al. 2016), has & CHIME/FRB Collaboration 2020; Bochenek et al. been bursting nearly continuously (albeit interrupted by 2020a). The double-peaked burst, detected indepen- extended “dark” periods) for over 7 years; no known dently by CHIME (Bandura et al. 2014) and STARE2 magnetar in our matches this continuous level (Bochenek et al. 2020b), was temporally coincident with of activity. One is forced to the conclusion that at an X-ray burst of significantly larger fluence (Mereghetti least the most active repeating FRB sources arise from et al. 2020a; Zhang et al. 2020a; Mereghetti et al. 2020b). magnetars which are somehow different from the Galac- This “fast radio burst” is still a factor of ∼ 10 less en- tic population, e.g. being of very young age (Metzger ergetic than the weakest FRB previously detected from et al. 2017; Beloborodov 2017), formed via alternative any localized cosmological FRB source. It nevertheless channels than ordinary core-collapse supernovae (CC- represents an enormous stride in bridging the energy gap SNe; Metzger et al. 2017; Margalit et al. 2019; Zhong between Galactic magnetars and their hypothesized ex- & Dai 2020), or possessing other atypical property such tragalactic brethren, providing new support to magnetar as an unusually long rotational period (Wadiasingh & FRB models. Timokhin 2019). Here, we explore several implications of this discovery The recurrent fast radio burst FRB 180916 was re- for the broader magnetar-FRB connection. We empha- cently shown by the CHIME/FRB collaboration to size that there exists no single “magnetar model”, but exhibit a 16 day period of unknown origin (The rather a range of models which make drastically differ- CHIME/FRB Collaboration et al. 2020). Again, al- ent predictions for the mechanism and location of the though known Galactic magnetars offer no clear expla- radio emission and the accompanying higher frequency nation for periodic behavior at this scale (with the pos- radiation, some which this discovery lend credence to sible exception of candidate magnetar 1E 1613485055 and others for which the model is placed in tension. which has a measured period of 6.7 hr; De Luca et al. This paper is organized as follows. In §2 we summa- 2006), reasonable variations in the properties of extra- rize the observational picture regarding SGR 1935+2154 galactic magnetars (e.g. extremely slow rotation, pre- and its recent radio/X-ray activity. In §3 we address sev- cession, or presence in a binary) offer a potential expla- eral broad implications of this discovery in the context nation (Lyutikov et al. 2020; Levin et al. 2020; Zanazzi of magnetar models for cosmological FRBs. In §4 we & Lai 2020; Beniamini et al. 2020; Yang & Zou 2020; discuss the implications of the coincident radio and X- Tong et al. 2020). Furthermore, several FRBs have now ray flare from SGR 1935+2154 for extant variations of been localized to host with low levels of star the magnetar model. Finally, we summarize and provide formation (Bannister et al. 2019; Ravi et al. 2019), un- bulleted conclusions in §5. characteristic of the environments of magnetars in the Milky Way as being the product of relatively typical 2. SUMMARY OF OBSERVATIONS CCSNe. 2.1. SGR 1935+2154 Perhaps most challenging to the magnetar model, un- SGR 1935+2154 is a Galactic til recently no Galactic magnetar had been observed to (SGR) first discovered by Neil Gehrels Swift Observa- produce a radio burst with an energy matching those tory’s Burst Alert Telescope (BAT) as a GRB candi- of known cosmological FRBs. An FRB-scale burst was date through a series of soft bursts from the Galac- ruled from the giant magnetar flare in SGR 1806-20 in- tic plane (Stamatikos et al. 2014; Lien et al. 2014). A Galactic FRB in the Context of Magnetar Models 3

The source is associated with remnant (SNR) the four Interplanetary network (IPN) spacecrafts (Ko- G57.2+0.8 (Gaensler 2014). Distance estimates are un- zlova et al. 2016). This burst’s long duration ∼ 1.7 s certain, ranging from 6.6-12.5 kpc ( et al. 2011; and large fluence ∼ 2.5 × 10−5 erg cm−2 (radiated en- Pavlovi´cet al. 2013; Kothes et al. 2018; Zhou et al. 2020; ergy ∼ 1041 erg) place it in the rare class of “intermedi- Mereghetti et al. 2020b), and throughout this paper we ate” SGR flares (Mazets et al. 1999; Feroci et al. 2003; adopt a distance of d = d10 10 kpc. Subsequent discov- Mereghetti et al. 2009; G¨oˇg¨us, et al. 2011). ery of coherent X-ray pulsations of SGR 1935+2154 with The trend that the bursts from SGR 1935+2154 have the Chandra X-ray Observatory established the spin pe- become progressively more energetic in the years since riod of the magnetar, P ' 3.2 s (Israel et al. 2014, 2016). its initial discovery (Younes et al. 2017) persists with XMM-Newton and NuSTAR observations of the source the recent outburst, which is the most energetic yet during outburst in 2015 provided the magnetar’s spin- (Mereghetti et al. 2020b; Zhang et al. 2020a). Similar down rate, P˙ ' 1.43 × 10−11 s s−1, which implies a sur- behaviour has previously been observed for SGR 1806- face dipolar magnetic field B ' 2.2×1014 G, a spin-down 20, which culminated with it’s production of the most 34 −1 Lsd ' 1.7 × 10 erg s , and characteristic energetic magnetar giant flare seen to date (Younes et al. spin-down age of P/2P˙ ' 3600 years. 2015). We note, however, that the age estimate based on the SNR association, & 16 kyr, is significantly older (Zhou et al. 2020; see also Kothes et al. 2018). This discrepancy 2.2. An “FRB” from SGR 1935+2154 between the dipolar and the SNR age estimates is similar On April 10, 2020, a short soft X-ray burst was trian- to the one observed in the other magnetar associated gulated by the IPN to SGR 1935+2154 (Svinkin et al. with a SNR, Swift J1834.9–0846 (Granot et al. 2017; 2020). This was followed by a slew of bursts, extend- with a spin-down age of 4.9 kyr and a SNR age between 5 ing to hard X-rays, detected over the following couple and 100 kyr). Since the dipolar age estimate is expected of weeks (Veres et al. 2020; Ridnaia et al. 2020a; Cherry to be inaccurate in case either the surface magnetic field et al. 2020; Hurley et al. 2020; Ridnaia et al. 2020b; evolves with time (e.g. Colpi et al. 2000; Dall’Osso et al. Palmer 2020; Ricciarini et al. 2020; Marathe et al. 2020; 2012; Beniamini et al. 2019) or else the spin evolution is Ridnaia et al. 2020c; Mereghetti et al. 2020a; Ridnaia not dominated by dipolar radiation (Thompson & Blaes et al. 2020d; Lipunov et al. 2020; Younes et al. 2020; 1998; Harding et al. 1999; Beniamini et al. 2020), Granot Kennea et al. 2020). et al.(2017) concluded that for Swift J1834.9–0846 the On April 28, as part of this period of enhanced source SNR age is likely to be the more realistic case. In this activity, a bright millisecond radio burst, the first of case, both Swift J1834.9–0846 and SGR 1935+2154 are its kind, was detected from SGR 1935+2154 (Scholz & significantly (by a factor of ∼ 4 − 10) older than the CHIME/FRB Collaboration 2020). The radio burst was majority of the observed Galactic magnetar population associated with a short hard X-ray burst (Mereghetti (Beniamini et al. 2019). et al. 2020a) peaking at energies E ∼ 70 keV (Zhang Radio observations with the Parkes telescope at peak et al. 2020a; see also Mereghetti et al. 2020b). The 1.5 GHz and 3 GHz did not reveal any significant ra- detection by the CHIME/FRB backend in the 400–800 dio pulsations from SGR 1935+2154 to a limiting flux MHz band comprise two sub-burst components. The of 0.1 mJy and 0.07 mJy, respectively (Burgay et al. bursts, each ∼ 5 ms wide and separated by ∼ 30 ms 2014). NCRA/GMRT and ORT observations at ∼ 300 had a reported DM of 332.81 pc cm−3. This DM value and 600 MHz also found no radio pulses down to 0.4, is consistent with the observed ≈ 8.6 s delay of the ra- 0.2 mJy, respectively (Surnis et al. 2014, 2016), followed dio burst (at 400 MHz) with respect to the peak of the by additional 14 µJy and 7µJy limits by Arecibo (at 4.6 X-ray counterpart flare as being almost entirely due to and 1.4 GHz; Younes et al. 2017). the cold plasma time delay (Mereghetti et al. 2020a; The non-detection of periodic radio pulses from the Zhang et al. 2020b; Mereghetti et al. 2020b). An inde- source has not impaired SGR 1935+2154 from being a pendent detection of the burst was also reported from prolific X-ray burster. This magnetar has been active the STARE2 radio feeds at the 1.4 GHz band (Bochenek since its discovery with at least four outbursts on: July et al. 2020a). They report the burst arrival time and the 5th 2014; February 22nd 2015; May 14th 2016; and June DM value to be consistent with the CHIME detection, 18th 2016—each with an increasing number of bursts and constrain the peak fluence to be > 1.5 MJy ms. The extending to higher energies (Lin et al. 2020). During much lower flux detected by CHIME versus STARE2 its active outburst cycles, SGR 1935+2154 exhibited a may be at least partly attributable to the fact that the remarkably bright burst on April 12th 2015, detected by burst was detected in the sidelobes of CHIME. 4 Margalit, Beniamini, Sridhar, & Metzger

The compelling nature of this burst led to a search for track-like muon neutrino events with the IceCube ob- 181112 101 121102 servatory, with no significant neutrino signals detected 180924

) 190523 1 along its direction (Vandenbroucke 2020). Likewise, 1 r 10 10

h yr ( VLA followup of the source found no persistent or af- 1 0 1

) 6 G E 1 180916 terglow radio emission down to a flux of ∼ 50µJy (Ravi 0 15 > 10 3 G ( 1 0 17 et al. 2020a,b). , 1 G

e 0 3 t yr a

The millisecond-duration high-brightness temperature r 10 5 n o

i SGR 1935

radio burst of SGR 1935+2154 is unlike any other pul- t i 1 t 0 14 e G sar/magnetar phenomenology observed to date, with a p 7 e 10 r × (Giant Flares) luminosity exceeding that of even the most luminous 10 5 yr Crab giant pulses (e.g. Mickaliger et al. 2012) by several 10 9 orders of magnitude. Instead, the burst properties are 1034 1035 1036 1037 1038 1039 1040 1041 1042 suggestively similar to cosmological FRBs. As pointed Eradio (erg) out by Bochenek et al.(2020a), placed at the distance Figure 1. Repetition rate above a given emitted radio en- of the nearest localized FRB 180916, ' 149 Mpc (Mar- ergy as a function of energy for SGR 1935+2154 and local- cote et al. 2020), the SGR 1935+2154 outburst would ized FRBs: the repeating sources FRB 121102 (Law et al. have been potentially detectable as a > 7 mJy ms burst, 2017; Gourdji et al. 2019) and 180916 (Marcote et al. 2020; coming close to, albeit still lower than typical FRB flu- The CHIME/FRB Collaboration et al. 2020), and apparently non-repeating FRBs 180924 (Bannister et al. 2019), 190523 ences. Stated energetically, SGR 1935’s emitted radio 34 2 (Ravi et al. 2019), and 181112 (Prochaska et al. 2019). The energy is Eradio > 4×10 d10 erg, within a factor of 10 of energy of the recent radio burst from SGR 1935+2154 is a 2 the lowest-energy burst observed from any cosmological factor of ∼ 10d10 lower than the least energetic extragalactic FRB of known distance to date, ≈ 5×1035 erg (Marcote FRB of known distance. Applying the same ratio of radio to et al. 2020). This is illustrated in Fig.1. Also, at least X-ray fluence measured for SGR 1935+2154 η ∼ 10−5 (eq.1) from the standpoint of its X-ray fluence and duration, to giant magnetar flares would imply that Galactic magne- the “FRB”-generating flare from SGR 1935+2154 ap- tars are capable of powering even the most energetic cosmo- logical FRBs. However, a stark discrepancy exists between pears to be fairly typical among Galactic magnetar flares the activity (burst repetition rate) of Galactic magnetars and (Fig.2; however, see discussion in §3). The immediate the sources of the recurring extragalactic FRBs (§3). Scaling implication of all this is that magnetar activity akin to from the magnetic field and age of SGR 1935+2154 implies the burst observed from SGR 1935+2154 should be con- that magnetar progenitors of extragalactic FRBs must have tributing to the extragalactic FRB population. larger B-fields and younger ages (see §3.1 for further details).

3. SGR 1935 IN THE CONTEXT OF Here we have calculated the X-ray burst energy EX ≈ 39 −7 −2 COSMOLOGICAL FRBS 8 × 10 d10 erg using the fluence 6.8 × 10 erg cm In this section, we assume that all FRBs are produced reported by the Hard X-ray Modulation Telescope by magnetar flares, with universal properties motivated (HXMT; Zhang et al. 2020a). A similar fluence was re- by the SGR 1935 burst. Proceeding under this strong ported by INTEGRAL (Mereghetti et al. 2020b). Like- assumption, we explore the implications for FRB en- wise, we have estimated the radio energy Eradio ≈ 34 ergetics and repetition rates. We are led to conclude 4 × 10 d10 erg by adopting the 1.5 MJy ms lower limit that “ordinary” magnetars with activity-levels similar on the fluence reported by STARE2 (Bochenek et al. to SGR 1935 cannot alone explain the observed FRB 2020a) and assuming a frequency width corresponding population. to the instrument bandwidth BW ≈ 250 MHz (Boch- As discussed in §2, a contemporaneous X-ray flare enek et al. 2020b). The true value of Eradio (and hence η) was detected in coincidence with the radio burst of may be somewhat larger than this estimate because the SGR 1935. The timing coincidence and similar sub- STARE2 radio fluence is quoted as a lower limit. Fur- structure in both radio and X-ray bands implicates that thermore, the fact that the same burst was detected also the two be interpreted as counterparts (Mereghetti et al. by CHIME at lower radio frequencies (albeit at a lower 2020a; Zhang et al. 2020b; Mereghetti et al. 2020b). The reported fluence, possibly attributable to the detection ratio between the radiated energy of the radio burst and occurring in an instrumental sidelobe) suggests its spec- its X-ray counterpart is tral energy distribution is broadband, such that the true burst energy could be larger by a factor of & ν/BW ≈ 6. E η ≡ radio ∼ 10−5. (1) EX A Galactic FRB in the Context of Magnetar Models 5

The low value of η illustrates that magnetars are inef- SGR 1806-20 giant flare (2004) ficient FRB producers. Implications of this fact for spe- SGR 1935+2154 (2020) cific magnetar FRB models are discussed later (§4). Re- 6 10 1.54 tX

gardless of the emission mechanism, the active lifetime ) 2 101 of cosmological recurrent FRB sources cannot be long B 4 s m

10 u

if FRB emission is similarly inefficient for such sources. c r

f

g (

For the activity rate and radio fluences of FRB 121102 r × e

−5 1 (e.g. Law et al. 2017), the radio-inefficiency η ∼ 10 2 7

10 0

0 1 4 implies that the FRB-generating engine must be losing 0 10 G 39 −1 1 energy at a rate of ∼several ×10 erg s (itself only ) × 0 (

10

a lower-limit if the luminosity-function is energetically- X dominated by low energy undetectable bursts; Gour- F dji et al. 2019). For FRB 180916 the repetition rate 10 2 10 1 and luminosity function point to qualitatively similar 10 2 10 1 100 101 requirements on the power output of the central en- X-ray burst duration, tx (s) gine, 5 × 1038 erg s−1 (The CHIME/FRB Collabora- & Figure 2. X-ray fluence and duration of Galactic magne- tion et al. 2020). tar flares. The SGR 1935+2154 flare associated with the If recurrent FRBs are powered by magnetars, then April 28th radio burst (, black border) is typical their active lifetime is at the very least limited by amongst Galactic magnetar flares. The grey line shows the their total magnetic energy reservoir Emag ∼ 3 × fluence–duration correlation found by Gavriil et al.(2004), 49 16 2 1.54 10 erg (B/10 ) , FX ∝ tX . Points are colored by the surface magnetic field of each magnetar (the McGill magnetar catalog†; Olausen  2 Emag B  η  & Kaspi 2014). In the event of a prolonged outburst τactive ∼ ∼ 200 yr , (2) E˙ /η 1016 G 10−5 (1 ∼ 3 months), we show only the brightest burst of a given FRB outburst. Likewise, for bursts clustered over timescales of a where B is the interior magnetic field strength and few seconds, we show the fluence corresponding to that of 34 −1 the initial peak, and not of the entire envelope of bursts. we have taken E˙ FRB ∼ 5 × 10 erg s motivated by FRB 121102 (Law et al. 2017). Even for large interior The anomalous concentration of bursts with tX ∼ 0.1 s can be attributed to instrument temporal resolution. fields B 1016 G, the maximum active lifetime is sig- & †http://www.physics.mcgill.ca/∼pulsar/magnetar/main. nificantly shorter than the 16 kyr estimated age of SGR html 1935+2154 (Zhou et al. 2020), or indeed of any other known Galactic magnetar. the duration of the burst (tX) is defined as the interval Based purely on their X-ray behavior, magnetars as of time when 5% and 95% of the total background sub- active as FRB 121102 or other repeating FRB sources do tracted counts are recorded (G¨oˇg¨us, et al. 2001). A rough not exist in our own Galaxy. These points suggest that if correlation is seen between the fluence and duration cosmological FRBs originate from magnetar progenitors, 1.54 (G¨oˇg¨us, et al. 2001), approximately satisfying FX ∝ tX at least a subset of these magnetars must be far more consistent with reports in the magnetar literature for active than SGR 1935+2154, and are perhaps formed via the bursts from single sources (Gavriil et al. 2004). Al- different mechanisms than Galactic magnetars (Margalit though the bursts from SGR 1935+2154 are bright, they et al. 2019). We further quantify this point in the next fit within this trend, and are not exceptional in terms of section by calculating the extragalactic detection rate of their fluence or overall-envelope duration with respect to SGR 1935+2154-like events. bright bursts from other Galactic magnetars. However, Before turning to extragalactic sources, we examine the burst associated with SGR 1935+2154’s radio emis- more closely the burst from SGR 1935+2154 in light sion may have exhibited a harder spectrum than other of other bursts from Galactic magnetars observed in the bursts (Mereghetti et al. 2020b), indicating that per- past ∼ 20 years. Figure2 depicts the X-ray fluence ( FX) haps this particular burst was produced via a different and the duration (tX) of the recent X-ray bursts from emission mechanism, and that this mechanism may be 1 SGR 1935+2154, alongside other bright bursts . Here, related to FRB production. In §4.2.2 we present a sce- nario in which shock-powered X-rays are generated con- 1 The duration and fluence are obtained from an extensive currently with the coherent radio emission; however, as search of NASA GCN circulars archive (https://gcn.gsfc.nasa. thermal X-rays may be produced in the magnetosphere gov/gcn3 archive.html), and The ’ Telegram (http: during flaring by other mechanisms, it is plausible that //astronomerstelegram.org/). 6 Margalit, Beniamini, Sridhar, & Metzger

STARE2 observable window SGR 1935+2154 April 22nd 2020 (Ridnaia et al. 2020b). These events fall CHIME observable window Tendulkar et al. (2016) SGR 1806-20 giant flare within the nominal STARE2 observable window, despite no reported radio detection. We note that relatively few ) 5 s 10 (a) magnetar flares have occurred over the last few years, m

y J 3 when STARE2 and CHIME have been operational, at

M 10 ( 1 a fluence that would have been detectable by these in- o

i 10 d

a 1 r 10 struments. Also note that the on-beam CHIME/FRB F

d sensitivity shown is not the relevant one for most bursts, e B t 1 c 10 s

i which will occur in the sidelobes of the telescope. u r d f

e (

r In the exceptional case of the giant flare from 3 × P

10 1

0 SGR 1806–20 (Palmer et al. 2005; Hurley et al. 2005), 1 2 4 (b) G the upper limit on radio emission (Tendulkar et al. 2016; 10 100 ) estimated based on sidelobe sensitivity of Parkes) is −5 n i 0 smaller than the predicted radio fluence (for η ∼ 10 )

m 10 L

/ by a factor of ∼ 100 (Fig.3; red triangle and square, X L respectively). As we discuss later in §4.2.2, this may be 10 2 understood in some magnetar FRB models, for different beaming properties of the radio emission relative to the 10 4 10 1 higher frequency counterpart in giant flares as opposed 2000 2003 2006 2009 2012 2015 2018 2021 to less energetic magnetar flares. More generally, the Burst epoch fact that one FRB was observed out of only a few mag- Figure 3. Properties of Galactic magnetar flares as a func- netar bursts where we might have expected a detection, tion of burst epoch. Different markers denote the same set of suggests that the FRB beaming is rather modest. The sources described in Fig.2. (a) Top Panel: the predicted flu- beaming can be directly probed in the future, once more ence of radio burst counterparts to magnetar flares, assuming X-ray bursts from SGR 1935+2154 with comparable lu- a radio-to-X-ray efficiency η ∼ 10−5 (eq.1). Hatched blue minosities are observed, by searching for a possible cor- and grey regions denote the observable windows of STARE2 and CHIME/FRB, respectively (assuming on-beam sensi- relation between FRB detectability and the rotational tivity limits). The upper limit on radio emission from the phase of the magnetar. SGR 1806–20 giant flare (red square) is shown as an upside- Using the X-ray burst fluence for each source, and down triangle (Tendulkar et al. 2016). (b) Bottom Panel: distance estimates from the McGill magnetar catalogue the luminosity of the same bursts relative to the magnetic (Olausen & Kaspi 2014)2, we estimate the intrinsic Lmin (Paczynski 1992; see also §3), a burst X-ray luminosity (LX). For the selected bursts, rough scale for the minimum luminosity burst that is capable we depict in Figure3 the value of L normalized to of driving baryonic outflows via radiation pressure. X the individual source’s “magnetic Eddington luminos- 38 12 4/3 −1 ity” Lmin = 3.5×10 (Bsurf /10 G) erg s (Paczyn- multiple sources of X-ray emission contribute to differ- ski 1992), where Bsurf is the surface dipole magnetic ent flares, or within a single burst. Nonetheless, this field strength. Lmin is a rough scale for the minimum raises the question of whether other FRBs from Galac- luminosity of a burst that can drive a mass outflow via tic magnetars should have already been observed in the radiation pressure. past? Note that the FRB-producing flare from SGR Assuming the value of η from the recent radio detec- 1935+2154 obeyed LX < Lmin (black-outlined green tion of SGR 1935+2154 is universal across all flares, we star in Fig.3) and hence would not have necessarily predict the fluence of the radio emission (Fradio) that been expected to produce a baryon-loaded outflow, at should accompany the X-ray bursts from a large pop- least via radiation pressure. This is potentially relevant ulation of Galactic magnetar outbursts over the past because some FRB models−particularly the baryonic ∼ 2 decades (the same sample shown in Fig.2). Fig- shock models (§4.2.2)−require an upstream medium into ure3(a) shows Fradio as a function of the burst date, which the shocks collide. On the other hand, other with reference to the estimated sensitivity (hatched re- mechanisms than radiation pressure (e.g. magnetic gions) of STARE2 and CHIME/FRB telescopes. We stresses) may also play a role in mass ejection, and the see that two flares preceded the April 28th FRB event from SGR 1935+2154 with higher predicted Fradio—one on April 10th 2020 (Veres et al. 2020) and another on 2 http://www.physics.mcgill.ca/∼pulsar/magnetar/main.html A Galactic FRB in the Context of Magnetar Models 7 quantity of mass in the external medium needed in the B3.2 (Dall’Osso et al. 2012; Beloborodov & Li 2016).3 synchrotron maser scenario is extremely modest. This is shown schematically with the dotted-blue con- tours in Fig.1, assuming that λ(> E)E ∼ E˙ ∝ B3.2, and scaling the B-field from ∼ 2 × 1014 G, the external 3.1. Rates: A Single Magnetar Population? dipole field of SGR 1935+2154 (note that the internal field is what sets E˙ , and thus we implicitly assume that Given the 3.6 steradian field-of-view of STARE2 the internal field is comparable to the external dipole (Bochenek et al. 2020b) and the fact that a single magne- field for this object). This assumed B-field implies an tar radio burst has been detected during the ∼ 300 day active lifetime of ∼ 70 kyr for SGR 1935 (e.g. Margalit operating period of the experiment, we estimate the rate et al. 2019, their eq. 1), consistent with the 16 kyr of SGR 1935+2154-like magnetar radio bursts (taking & source age. Contours of active lifetime (∼magnetar age) the number of active magnetars in the Galaxy to be N = are also shown in Fig.1 (grey shaded regions), scal- 29; Olausen & Kaspi 2014) to be λ ∈ [0.36, 80]×10−2 mag ing from SGR 1935’s estimated age as τ ∝ B−1.2 per magnetar per year at 95% confidence (assuming active (Dall’Osso et al. 2012). The 5 order of magnitude Poisson statistics; Gehrels 1986). higher repetition rate of FRB 180916 would thus imply The radio-burst activity (repetition) rate of SGR 1935 B ∼ (105)1/3.2B ∼ 1016 G, in agreement estimated above is plotted in Fig.1 in comparison to 180916 SGR1935 with separate lines of argument, e.g. requirements for cosmological FRBs. We show here the full sample FRB 180916 periodicity to be attributable to magnetar of published localized FRB sources, where the radio- precession (Levin et al. 2020). emitted (isotropic-equivalent) energy can be reliably cal- An alternative possibility is that the repetition rate culated: repeating FRB 121102 (yellow; Law et al. 2017; increases significantly with the periodicity (Wadiasingh Gourdji et al. 2019), the recently localized CHIME re- et al. 2020). In this case, the periodicity of 180916 (and peater FRB 180916 (purple; Marcote et al. 2020; The its high activity relative to SGR 1935+2154) may be as- CHIME/FRB Collaboration et al. 2020), and the ap- cribed to an extremely long period magnetar (Beniamini parently non-repeating FRBs 180924 (green, upper lim- et al. 2020). Interestingly, this option too, requires a its denoted by upside-down triangles; Bannister et al. large internal magnetic field, > 1016 G, at birth (see Be- 2019), 190523 (brown; Ravi et al. 2019), and 181112 niamini et al. 2020 for details). (blue; Prochaska et al. 2019). We have used quoted rates The maximum distance up to which SGR 1935+2154’s where possible (Law et al. 2017; Gourdji et al. 2019; radio flare would be detectable by typical FRB search The CHIME/FRB Collaboration et al. 2020) and oth- facilities sensitive to F ∼ 1 Jy ms fluence radio pulses erwise estimated Poissonian rates based on quoted field lim is D ≈ 12 Mpc d (F /1 Jy ms)−1/2. The birth rate exposure times, where available. Grey markers with er- lim 10 lim of “ordinary” Galactic magnetars in the local Universe rorbars show the repetition rate (from Tendulkar et al. can be estimated as a fraction f ≈ 0.1 − 1 (Be- 2016) and radio energy implied if some giant magnetar CCSN niamini et al. 2019) of of the CCSN rate, Γ ≈ flares produce radio emission with the same efficiency CCSN (0.71 ± 0.15) × 10−4 Mpc−3 yr−1 (Li et al. 2011). Thus, η ∼ 10−5 between X-ray and radio fluences. This indi- the rate of potentially-detectable FRBs produced by cates that Galactic magnetars may be energetically ca- SGR 1935+2154-like bursts is pable of powering even the most luminous FRBs, though for one particular flare from SGR 1806-20 such radio 4π R(> F ) ≈ D3 f Γ τ λ (3) emission is ruled out (Tendulkar et al. 2016). Finally, lim 3 lim CCSN CCSN active mag we note that radio pulses observed from M87 by Linscott ∈ [0.004, 1.4] sky−1 day−1 & Erkes(1980) ∼ 40yr ago, though unconfirmed by sub- f  τ   F −3/2 sequent followup, may have been the earliest recorded ×d3 CCSN active lim . 38 10 4 FRB detections, and correspond to Eradio ∼ 10 erg on 0.1 10 yr 1 Jy ms this figure. Figure1 shows that, at comparable energy, the This is much lower than the Parkes estimated FRB rate −5 +1.5 3 −1 −1 SGR 1935 radio burst is ∼ 10 less frequent than ≈ 1.7−0.9 × 10 sky day above a fluence of 2 Jy ms FRB 180916 bursts. Within the hypothesis that mag- (Bhandari et al. 2018). netars are also the progenitors of such cosmological FRB, this stark discrepancy in activity rate may be 3 Also note that activity may increase with the NS mass, because attributable to the magnetar age and internal field at sufficiently high central densities the star can cool through strength. Indeed, Margalit et al.(2019) show that mag- direct URCA reactions, which hastens the release of magnetic netar activity scales strongly with magnetic field, E˙ ∝ energy from the core (Beloborodov & Li 2016). 8 Margalit, Beniamini, Sridhar, & Metzger

The estimate above shows that magnetars bursting Law+17, Galactic magnetars CHIME20 Gourdji+19 th at the same rate and energy as the April 28 SGR 106

1935+2154 radio burst cannot contribute noticeably to ) 1 the FRB population. However, clearly magnetar flares y a 4

d 10 span a range of energies (Fig.2), making it natural to ( ) s

ask whether SGR 1935+2154-like magnetars can repro- m

y observed rate J 102 duce the FRB rate if one extrapolates radio produc- 2 > tion with a similar efficiency to more energetic magnetar (

,

e 0 flares. t 10 a r

y

We therefore calculate the all-sky rate of FRBs above k rate from s -

l SGR 1935-like l 2 a limiting fluence threshold assuming that all magnetars a 10 magnetars repeat following a luminosity-distribution λmag(> E) ∝ −γ (E/Emin) for burst energies between Emin and Emax. 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2 luminosity function slope, We set Emax = ηEmag ∝ B dictated by the magnetic energy reservoir of the magnetar (this is consistent with Figure 4. All-sky rate of FRBs above a limiting fluence the energies of the three observed Galactic giant flares of 2 Jy ms. The black curve (and shaded uncertainty re- relative to the magnetic dipole energies of the magne- gion) shows the FRB rate that would be detected from a tars producing them, see e.g. Tanaka et al. 2007), and single population of “normal” magnetars (assumed to be fix the minimum energy to that observed for the April born at 10% the CCSN rate) with active lifetimes and ra- th 4 dio repetition-rates set by SGR 1935+2154. The repetition 28 SGR 1935+2154 flare . The magnetar birth-rate 34 rate at Emin = 2 × 10 erg is fixed to the inferred rate of Γbirth(z) is assumed to follow the cosmic star-formation SGR 1935+2154 bursts at this energy, and is extrapolated to −γ rate (Hopkins & Beacom 2006) and is anchored to 10% higher-energies by a luminosity-function λmag(> E) ∝ E . the CCSN rate at z = 0 (Li et al. 2011). The integrated For large γ the all-sky rate is dominated by weak, common rate is thus bursts at ∼ Emin and the rate falls short of the observed Z FRB rate (horizontal red; Bhandari et al. 2018) by several R(> Flim) = dV (z)Γbirth(z)τactive (4) orders of magnitude (eq.3). However, for γ . 1 the rate Z of FRBs from SGR 1935+2154-like sources (extrapolated  2  to higher energies) accommodates and even over-produces × dEλmag(E)Θ E − 4πDL(z) Flim . the observed FRB rate. The values of γ found by different studies are indicated on the top axis, including of the X- We set τactive = 24 kyr and fix λ(> Emin) to the es- timated rate of SGR 1935 radio bursts. The former is ray/gamma-ray luminosity function of Galactic magnetars. determined from the minimum SNR age estimated by Zhou et al.(2020) and scaled to our adopted distance γ) “ordinary” magnetars similar to SGR 1935+2154 to of 10 kpc. We then integrate over cosmological redshift reproduce the number of observed FRBs, this scenario and calculate the rate as a function of the slope of the falls short of explaining many other observables. In par- luminosity-function, γ. Fig.4 shows the resulting all-sky ticular, and as discussed previously—the per-source ac- rate as a function of γ (the only free variable in the cal- tivity rate for such a population would be far too low to culation). For large γ, the rate is dominated by bursts explain prolific repeaters like FRBs 121102 and 180926. of energy ∼ Emin and we recover the result of eq. (3), For the same reason, most FRB sources would be de- namely that the rate of Galactic magnetars is too low tected only once and the relative number of repeaters compared to cosmological FRBs. However, for γ < 1.5 versus apparently-non-repeaters would be very small. the rate becomes dominated by the high-energy tail of The scenario would also predict average FRB source the luminosity function, and the number of detectable distances that are far nearer than localized sources or magnetar radio bursts increases. In particular, we find DM-estimated distances. that, for γ . 1—magnetars of a similar kind to SGR 1935+2154 can account for the entire FRB rate. 3.2. Two-Component Population Although extending the luminosity function of radio To further explore the requirements on possible mag- bursts to higher energies can allow (for certain values of netar progenitors of cosmological FRBs, we extend the calculation of the previous section and model a two- component magnetar population as necessitated by the 4 Given that the luminosity function we have adopted dictates fewer bursts at higher energies (for γ > 0), it is statistically observations: magnetars with low activity levels like unlikely that the detected radio burst of SGR 1935+2154 exceed SGR 1935+2154, and magnetars that are very active. A Emin significantly. natural question this will allow us to address is whether A Galactic FRB in the Context of Magnetar Models 9

stable BNS standard the active population is consistent with an earlier evo- merger remnants SLSNe LGRBs magnetars lutionary stage (a younger version) of the same SGR 2.50

1935+2154-like population, or whether one requires a 2.25 Gourdji+19

distinct population altogether (e.g. a rare subset of mag- ,

e 2.00 allowed region netars born through unique channels). p o l s 1.75 We again calculate the all-sky FRB rate using eq. (4), n o i CHIME20 t accounting for the two populations contributing to FRB c n 1.50 u f

production. As before, the only free parameter de- y t i 1.25 s scribing the “ordinary magnetar” population is the o

n 121102/180916-like i dominated Galactic magnetars luminosity-function slope γ. The second, “active”, pop- m 1.00 u l SGR 1935-like Law+17, ulation is then scaled from the former population as a 0.75 dominated function of the internal magnetic field B and relative 5 0.50 birth-rate fCCSN. 10 6 10 5 10 4 10 3 10 2 10 1 100 The magnetic field of the magnetar enters in setting fCCSN, birth-rate of high-B magnetar population 2 −1.2 Emax ∝ B , the active lifetime of sources τactive ∝ B Figure 5. A two-component magnetar population consist- (Dall’Osso et al. 2012; Beloborodov & Li 2016), and ing of: (i) “ordinary” magnetars fixed to properties of SGR the repetition-rate λmag(> Emin). The latter is pro- 1935+2154 and extrapolated as a function of the luminosity- portional to ∝ B3.2 for γ > 1 and ∝ B1.2+2γ for γ < 1.6 function slope γ, and (ii) a magnetar population whose activ- ity rate (parameterized via the internal magnetic field) and We normalized τactive and λmag(Emin) at the magnetic birth rate (a fraction f of the CCSN rate) are allowed field of SGR 1935+2154 (' 2.2 × 1014 G7) to the age CCSN to vary (the value of γ is identical to both populations). The (& 24d10 kyr) and radio repetition-rate of SGR 1935. yellow curve and shaded uncertainty region shows the al- We then integrate eq. (4) and compare the resulting rate, lowed parameter space constrained by both the all-sky FRB a function of the three free parameters {B, γ, fCCSN}, rate and the per-source activity (repetition rate). The lat- to the observed FRB rate (Bhandari et al. 2018). From ter constraint forces fCCSN  1, indicating that the second, the point of view of the all-sky rate alone, there exists “active” population of magnetars, must be volumetrically a degeneracy between the number of FRB sources in rare. This rules out the hypothesis that active cosmological repeating FRBs are younger versions of all SGR 1935+2154- the Universe (∝ f ) and the repetition-rate of each CCSN like magnetars (for which f 0.1). source (a function of B). However, this degeneracy can CCSN & be broken by constraining the observed repetition rate of prolific repeaters. with many previous studies (e.g. Nicholl et al. 2017), Figure5 shows, for values of the magnetic field and here we have extended these by adding the, possibly inevitable (though likely subdominant), contribution of B(γ, fCCSN) required to fit the observed FRB rate (and a second population of “normal magnetars”, and utiliz- its uncertainties), the region in {γ, fCCSN} parameter- space where the average repetition rate of the “active ing scaling-relations anchored to the new observations magnetar” population equals the observed repetition- of SGR 1935+2154. rate of FRBs 121102 and 180916. For this, we take a The fact that fCCSN  1 is required of the “active 38 −1 population” implies that these sources cannot be inter- fiducial value λmag(> 10 erg) = 1 hr (see Fig.1) however the uncertainties encompass a few orders-of- preted as younger-incarnations of the SGR 1935+2154- magnitude leeway in this assumed value. On the ba- like magnetar population as a whole, since this would sis of Fig.5 one can conclude that, regardless of the require the same birth-rate for both populations, i.e. luminosity-function slope γ, fitting both the all-sky FRB fCCSN ∼ 0.1. In the above we have assumed isotropic ra- rate and the activity level of repeating FRBs requires a dio emission, as we expect beaming to be modest at most (§3). If radio emission is beamed with some preferential rare class of progenitors, fCCSN  1. This is in line directionality (as in ) then the number of FRB emitting magnetars in the Universe may be larger than 5 We assume the “ordinary-magnetar” population is born at 10% implied by the observed population. By “hiding” FRB the CCSN rate, independent of the fractional birth rate fCCSN sources this way, f may be pushed to larger values. of the “active” population. CCSN 6 We note however that if bursts are instead beamed to- This is calculated based on the magnetic-field scaling of Emax and Emin, the fact that E˙ ∝ λmag(> Emin)Emin for γ > 1 and wards random directions, then the source birth rate as 3.2 λmag(> Emax)Emax for γ > 1, and that E˙ ∝ B ;(Dall’Osso estimated above will be largely unchanged. et al. 2012; Beloborodov & Li 2016; Margalit et al. 2019). To further compare the resulting population against 7 This value is based on the inferred external dipole field of SGR observational constraints, we calculate the expected 1935+2154. The internal field may in fact be larger. 10 Margalit, Beniamini, Sridhar, & Metzger number of repeating, and apparently-non-repeating, with the median distance of apparently-non-repeating FRB sources detected by a mock survey of this pop- sources detected by the mock survey). ulation. We assume a limiting fluence of Flim = 4 Jy ms As the model shows, many potential rare magnetar and average repeat-field exposure time of Texp = 40 hrs, formation channels could in principle be consistent with parameters motivated by the CHIME FRB survey. We the all-sky FRB and repeater rate constraints (Fig.5). then calculate the (Poissonian) number of sources for One way to further break this degeneracy is via host which only a single burst would be detected, galaxy demographics. A high-B (and hence potentially Z particularly slowly rotating; Beniamini et al. 2020) tail −µ Nnon−rep = dV (z)fmagΓbirth(z)τactiveµe (5) of the magnetar population should be formed in oth- erwise ordinary CCSNe and hence track star-forming where galaxies almost exclusively. Superluminous supernovae (SLSNe) and long-duration gamma-ray bursts (LGRB) 2  µ(z) ≡ λmag > 4πDL(z) Flim Texp, (6) should originate predominantly (Fruchter et al. 2006; Lunnan et al. 2015; Blanchard et al. 2016), though and summing the contribution from both active and not exclusively (e.g. Perley et al. 2017), in dwarf star- SGR 1935+2154-like populations. The number of forming galaxies. By comparison, NS mergers, white sources classified as repeaters by the same survey is sim- dwarf-NS mergers, and accretion-induced collapse (AIC) ilarly calculated as should originate from a range of star-forming and non- star-forming galaxies (Margalit et al. 2019), weighted Z  1  Nrep = dV (z)fmagΓbirth(z)τactive 1 − Γ (2, µ) more towards massive galaxies than SLSNe/LGRB. At- 2 tempts to perform an analysis along these lines are al- (7) ready underway (e.g. Margalit et al. 2019; Li & Zhang where Γ(2, µ) is the incomplete gamma-function. 2020), though it should be cautioned that without at Figure6 shows N and N as a function of rep non−rep least arcsecond localization, it is usually challenging to γ, and for a representative value of f = 10−4 that CCSN uniquely identify the host galaxy (Eftekhari et al. 2018), is consistent with the constraints on FRB 121102-like much less the local environment within the host galaxy activity and the all-sky FRB rate (Fig.5). The num- as becomes available with VLBI localization (Bassa ber of detected repeating and non-repeating sources can et al. 2017; Marcote et al. 2020). be compared to values from the CHIME FRB survey, shown as horizontal curves (V. Kaspi, private communi- 4. IMPLICATIONS FOR MAGNETAR FRB cation). The figure shows that, for values 1 . γ . 1.5, MODELS the absolute number and relative ratio of repeating and SGR 1935+2154 provides a clear link between FRBs non-repeating FRBs can be reproduced simultaneously and magnetars. Such a connection has been proposed with the all-sky rate and per-source activity rate. At and discussed extensively in the FRB literature well low values of γ the observed FRBs are dominated by prior to this discovery (e.g. Popov & Postnov 2013; the less-active “ordinary magnetar” population. This Lyubarsky 2014; Kulkarni et al. 2014; Katz 2016; Met- results in a significant reduction in the relative number zger et al. 2017; Beloborodov 2017; Kumar et al. 2017), of repeating versus non-repeating sources that is incon- leading to the development of several distinct magnetar sistent with observations. This substantiates our previ- models for FRBs. Broadly speaking, these models can ous claim that a single population of (or equivalently, a be further divided based on whether the radio emission population dominated by) SGR 1935+2154-like magne- originates from near the NS magnetosphere (the “cur- tars cannot account for the number of known repeaters. vature”, “low twist”, and “reconnection” models) or at Finally, using the cumulative distribution of detected much further distances (“synchrotron maser blastwave” events implied by eqs. (5,7), we calculate the charac- models). We also briefly discuss a couple NS-related teristic distances at which repeating and non-repeating models not specific to magnetars. In the following, we FRBs would be detected by this mock survey. The right discuss implications of the SGR 1935+2154 radio burst panel of Fig.6 shows the median distance of detected for these models, pointing out strengths and points of repeating and apparently-non-repeating FRB sources as contention between each and the combined radio and a function of γ. Confirmed repeaters are detected on- X-ray observations. average at a lower distance, broadly consistent with the 149 Mpc distance of the first localized CHIME repeater 4.1. Low Twist Models (and note that FRB 121102, at a much larger distance In the low twist models (Wadiasingh & Timokhin of 972 Mpc is detected only once by CHIME, consistent 2019; Wadiasingh et al. 2020), magnetic field disloca- A Galactic FRB in the Context of Magnetar Models 11

Law+17, Law+17, Galactic magnetars CHIME20 Gourdji+19 Galactic magnetars CHIME20 Gourdji+19 109

4 3 apparent 10 7 10 10 SGR 1935-like 121102/180916-like non-repeaters dominated dominated

105 apparent non-repeaters 3 10 CHIME non-repeaters 121102 103 )

102 c M CHIME repeaters p G I

1 M

10 ( M D L

1 D 10 repeaters 180916 102 3 10 101 repeaters # of detected FRB sources

5 10 SGR 1935-like 121102/180916-like dominated dominated

10 7 101 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 luminosity function slope, luminosity function slope,

Figure 6. Several properties of cosmological FRBs can be simultaneously reproduced by postulating the existence of a rare −4 population of magnetars (with a birth rate taken to be fCCSN = 10 of the CCSN rate in this example) with stronger magnetic fields than the Galactic magnetar population. Left: For a mock survey with parameters motivated by the CHIME/FRB experi- ment, the number of detected repeating sources (solid red) and apparently-non-repeating sources (solid blue), as a function of the power-law slope γ of the FRB luminosity function λ(> E) ∝ E−γ . The number of repeating and non-repeating sources actually detected by CHIME are shown as light blue and red dashed horizontal curves, respectively (V. Kaspi, private communication). The thin dotted curves show the contribution of the “ordinary magnetar” population to the number of detected sources. This population is subdominant for γ & 1 and dominant at low γ, where the all-sky FRB rate is over-produced (Fig.4). Right: Median distance (right axis) and corresponding DM contribution from the intergalactic medium (left axis) of sources detected as repeaters (solid red) and non-repeaters (solid blue) for the same mock survey. The distances of FRB 180916 and FRB 121102 (which from CHIME’s point of view is a “non-repeater”) are shown for comparison. tions and oscillations in the NS surface can lead to pair 4.2. Synchrotron Maser Blastwave Models cascades assuming that the background charge density In synchrotron maser models, a version of which was is sufficiently low. The latter then result in coherent first proposed by Lyubarsky(2014), FRBs are created radio emission. Since it is the same dislocation that via the coherent synchrotron maser process that is nat- supposedly results in short X-ray bursts and (in some urally produced in magnetized relativistic shocks (Gal- cases) FRBs, a prediction of this model is that all FRBs lant et al. 1992; Plotnikov & Sironi 2019). Such shocks should be associated with short magnetar bursts (but are expected to arise from relativistic flares that may be not vice versa). This is consistent with the observations ejected during magnetar outbursts. A number of vari- of SGR 1935. Another attractive feature of this model, is ants on the synchrotron maser model exist which dif- that FRBs will typically be associated with older mag- fer regarding the nature of the upstream medium and netars, consistent with the putative age of SGR 1935. the required shock properties; however, in all cases the However, the association with older ages in the model is bursts are powered by tapping into a small fraction of due to the requirement of longer periods, while the pe- the kinetic energy of the outflow and predict correspond- riod of SGR 1935+2154 is very typical as compared to ing (though differing) high-frequency counterparts to other Galactic magnetars. Similarly, the model favours FRBs. strong dipole field strengths, while the dipole field of SGR 1935+2154 does not appear to be exceptional rel- 4.2.1. Magnetar Wind Nebula (Lyubarsky 2014) ative to other magnetars. Lyubarsky(2014) propose FRB production occurs as In the low twist model, both the radio emission and the ultra-relativistic flare ejecta collides with the pulsar the X-rays arrive from the magnetosphere. As such, wind nebula. The radius of the termination shock is this model predicts a radius-to-frequency mapping lead- estimated to be ing to frequency selection, similar to the case in pul- s L sars and potentially a polarization angle that is varying r = sd , (8) s 4πpc with time (as the magnetic field orientation changes rel- ative to the observer). The X-ray burst associated with where p is the pressure inside the nebula. Taking 34 −1 −9 −3 an FRB should exhibit a standard blackbody (or dou- Lsd ' 1.7 × 10 erg s and p ∼ 10 erg cm (esti- ble blackbody) spectrum as seen in other short X-ray mated from the energy of 1051 erg of a typical supernova bursts. and the observed ∼ 20 pc size of the supernova remnant 12 Margalit, Beniamini, Sridhar, & Metzger

−2 −3 surrounding SGR 1935+2154; Kothes et al. 2018), we trinsic synchrotron maser efficiency fξ ∼ 10 − 10 15 find rs ≈ 6 × 10 cm. The light crossing timescale to (for moderate magnetization; Plotnikov & Sironi 2019) −2 this radius is rs/c ∼ 2 day. However, because the flare and a further reduction by a factor of ∼ 10 due to the ejecta and the resulting shock are also moving close to effects of induced-Compton scattering suppressing the the speed of light, radio photons from the shocked neb- low-frequency portion of the maser’s intrinsic SED (see ula could in principle still arise nearly simultaneously Metzger et al. 2019, their §3.2).9 with the X-rays, which in this model presumably must Following the methodology of Margalit et al.(2020) be generated from the inner magnetosphere.8 we can use the energy, frequency, and duration of the Looking more closely at the predictions for the ra- observed radio burst to derive the intrinsic parameters dio emission requires rescaling the results of Lyubarsky of the flare demanded by the synchrotron maser model. (2014), who considered a giant flare which carries away Adopting the observed quantities from §2, we find that a significant fraction of the magnetic energy of the star. the energy of the relativistic flare Eflare; the Lorentz The recent flare from SGR 1935+2154 was less ener- factor Γ of the shocked gas at the time the observed radio getic by a factor of ∼ 106, corresponding to a strength flux is emitted; the radius of the shock from the central of the magnetic field in the pulse smaller by a factor magnetar at this time, rsh; and the external density of 3 −3 of ∼ 10 , i.e. dimensionless constant b ∼ 10 in the the upstream baryonic shell at this location, next, are notation of Lyubarsky(2014). Following equation (8) given by of Lyubarsky(2014) for these parameters, the predicted  W 1/5 peak frequency of the maser emission from the forward E ≈ 1040 erg f −4/5 d2 , (10) flare ξ,−3 5 ms 10 shock is estimated to be νpk ∼ 10 MHz. Given the  −2/5 drop-off in the νLν spectrum of the maser from νpk to −1/15 W 1/3 −4 Γ ≈ 24 fξ,−3 d10 , (11) ∼ 100νpk by a factor of ∼ 10 (Plotnikov & Sironi 5 ms 2019), the fraction of the total radio emission in the  2/5 −4 4 −3 −4/15 W −2/3 1.4 GHz band of STARE2 would be only ∼ 10 . Given next ≈ 9.3 × 10 cm fξ,−3 d10 ,(12) an intrinsic efficiency of the synchrotron maser emission 5 ms of f ∼ 10−2 − 10−3 (see next section), the resulting  W 1/5 ξ r ≈ 1.7 × 1011 cm f −2/15 d2/3. (13) net efficiency of the radio emission of ∼ 10−6 − 10−7 sh ξ,−3 5 ms 10 is at best marginally consistent with the observations In the above we express results in terms of the 1.4 GHz if the energy of the flare ejecta were comparable to the burst duration, W , which we normalize to 5 ms mo- released X-ray fluence. tivated by the quoted CHIME burst width (Scholz & CHIME/FRB Collaboration 2020), in addition to the 4.2.2. Baryonic Shell (Metzger et al. 2019, Margalit et al. −3 maser efficiency fξ = 10 fξ,−3. 2020) From our inferred parameters, the (very) local DM In this version of the synchrotron maser model, first contributed by the immediate upstream medium ahead −3 −3 proposed by Beloborodov(2017), the ultra-relativistic of the shock is DM & nextrsh ≈ 5 × 10 pc cm , head of the magnetar flare collides not with the magne- and can exceed this value significantly if the upstream tar wind nebula, but instead with matter ejected from a medium extends to larger radii. In the context of the recent, earlier flare. Motivated by the inference from the shock model, it may be expected that DM variations radio afterglow of the 2004 giant flare from SGR 1806- could exist between radio bursts on this order of mag- 20 of a slow ejecta shell generated by the burst (Gelfand nitude or larger. Note however, that non-linear wave et al. 2005; Granot et al. 2006), Metzger et al.(2019) consider the upstream medium to be a sub-relativistic 9 The value of fξ in general decreases with increasing values of the baryon-loaded shell with an electron-ion composition. upstream magnetization, σ. Based on 1D particle-in-cell simu- The low efficiency of radio emission implied the X- lations of electron-positron plasmas, Plotnikov & Sironi(2019) ray and radio observations of SGR 1935+2154 (eq.1) find an efficiency of −4 2 is consistent with predictions of this model. The radio fξ = 7 × 10 /σ , σ  1. (9) inefficiency is attributable to a combination of the in- −5 Matching fξ = η ∼ 10 (eq.1) places a strict upper limit σ . 8. The true efficiency (and hence allowed σ) will be lower once ac- counting for 3D effects, and electron-ion composition of the up- 8 Although a burst of higher frequency (incoherent) synchrotron is stream plasma (e.g. Iwamoto et al. 2019), and suppression of the predicted in this model from the shocked electrons, for parame- radio signal from induced scattering by upstream electrons (Met- ters appropriate to SGR 1935+2154 this is predicted to occur at zger et al. 2019). This scenario therefore requires an upstream & GeV gamma-rays. plasma which is not highly magnetized. A Galactic FRB in the Context of Magnetar Models 13 interaction with the upstream plasma as well as strong upstream magnetic fields may inhibit the DM of this 103 local environment (e.g. Lu & Phinney 2019). The derived shock properties are shown in Fig.7 in comparison to those derived for cosmological FRBs 102 within the same model, for an assumed efficiency fξ = −3 10 . One important thing to note is that the flare SGR 1935 energy Eflare the model demands (based on the radio observation of SGR 1935+2154 alone) agrees remark- ably well with the independently observed X-ray energy, 1013

39 )

EX ≈ 8 × 10 erg. As we discuss below, such agree- m c ( 121102 h

ment is naturally expected if electrons heated at the s r 12 180916 shock generate the X-rays via synchrotron radiation in 10 180924 the fast-cooling regime. 190523 SGR 1935 181112 Stated more directly, the model predicts a ratio (Mar- 105 galit et al. 2019) SGR 1935

1/5 4   ) 10 Eradio 1215 me 1/5 4/5 −1/5 3

ηtheory ≡ = fe fξ (νobs · tFRB) m

2 c Eflare 512π mp (

t 103 x 1/5 −1/5 e     n −5 fe 4/5 νobs · tFRB ∼ 3 × 10 fξ,−3 , (14) SGR 1935 0.5 1GHz · ms 102 X-ray fluence

−5 which matches the observed ratio η ≡ Eradio/EX ∼ 10 1040 1041 1042 1043 1044 1045 1046 1047 Eflare (erg) (eq.1) for expected values of the maser efficiency fξ ∼ 10−3 − 10−2 (Plotnikov & Sironi 2019) provided that Figure 7. Derived properties from the SGR 1935 radio burst EX ∼ Eflare. In the above, fe is the ratio of electron to within the variation of the synchrotron maser model in which ion number densities in the upstream medium, and is the upstream medium is a baryon-loaded shell and adopting fe ∼ 1 for an electron-ion plasma as we consider. −3 a fiducial value for the maser efficiency fξ = 10 (see also The same outwardly propagating shock that generates Margalit et al. 2020). From top to bottom, the bulk Lorentz the coherent precursor radio emission (the “FRB”) in factor Γ, radius rsh, and the external upstream density next this scenario also generates incoherent synchrotron ra- of the shock at the time of the observed radio flare, all as a diation from relativistically-hot electrons heated by the function of the derived total flare energy, Eflare. The flare shock (Lyubarsky 2014; Metzger et al. 2019), somewhat energy, as derived from radio observations alone, is compara- akin to a gamma-ray burst afterglow. Using the shock ble to the detected X-ray counterpart of this burst (vertical dashed curve), in-line with predictions of the synchrotron parameters implied by the radio observations (Fig.7), maser model (§4.2.2) if the X-rays arise from thermal syn- we now assess the predicted properties of the high- chrotron radiation from the same shocks which generate the frequency counterpart, showing it to be in accord with FRB. the X-rays emission from SGR 1935+2154. The peak frequency of the “afterglow” is set by relativistic Maxwellian distribution (supported e.g. by the characteristic synchrotron frequency, which for an particle-in-cell simulations of magnetized shocks; Sironi ultra-relativistic blastwave decelerating into an effec- & Spitkovsky 2011). In the second line of equation tively stationary upstream medium of magnetization (15) we have substituted the flare energy from equa- −1 σ = 10 σ−1 is given by (Metzger et al. 2019; their tion (13) needed to reproduce the radio burst properties eqs. 56, 57) from SGR 1935+2154. Although the value of σ in the flare ejecta of a magnetar flare is uncertain theoretically,  E 1/2  t −3/2 flare 1/2 its value is nevertheless reasonably constrained: a min- Epeak ∼ hνsyn ≈ 50 keV σ−1 1039erg 5 ms −3 imum magnetization σ & 10 is required for the syn-  W 1/10  t −3/2 chrotron maser to operate in the first place, while the ≈ 160 keV σ1/2 d , (15) −1 5 ms 5 ms 10 declining efficiency of the maser emission with increasing σ places an upper limit σ 1. where t is the time since the peak of the flare and . we have assumed that 1/2 of the kinetic power dissi- pated at the shock goes into heating electrons into a 14 Margalit, Beniamini, Sridhar, & Metzger

For the same parameters, the cooling frequency is given by 100 GeV −3/2  −4  −2 121102 −3/2  next  Γ t 180916 hνc ≈ 13 keV σ−1 4 −3 10 GeV 180924 10 cm 100 ms 190523 181112  −1  −1/2 GeV −3/2 W t −1/3

≈ 5.6 keV σ−1 d10 , (16) k a

5 ms 5 ms e 100 MeV p E −1/2 where the particular temporal scaling ∝ t is derived 10 MeV 0 assuming a radially-constant density profile (n ∝ r ). SGR 1935 ext model MeV The fact that νc . νsyn on timescales t ∼ 5 ms of interest shows that the post-shock electrons are fast- SGR 1935 100 keV measured cooling and hence a large fraction of the flare energy, 1040 1041 1042 1043 1044 1045 1046 1047 Eflare, is emitted as hard X-rays of energy Epeak ∼ Eflare (erg) 10 − 100 keV. The predicted X-ray spectrum is thus Figure 8. The synchrotron maser model predicts that FRBs fast-cooling sychrotron emission from relativistically-hot be accompanied by hard radiation counterparts, the prop- electrons with a thermal Maxwellian energy distribution erties of which can be derived by modelling the observed (see Giannios & Spitkovsky 2009, their Fig. 3), result- radio emission alone. Above, we show the peak energy of 1/2 ing in an ordinary fast-cooling spectrum νLν ∝ ν this counterpart as a function of flare energy, derived for a between νc and νsyn and an exponential cut-off at an sample of cosmological FRBs and the SGR 1935+2154 radio energy ∼ νsyn. Indeed, modeling of bright magnetar burst, assuming a uniform magnetization σ = 0.1 for the up- flares, suggests that they can be well fit by a cut-off stream medium. The emitting electrons are fast cooling and power-law spectrum in the X-rays (van der Horst et al. therefore Eflare roughly corresponds to the radiated fluence at Epeak. The observed Epeak and fluence of the contempo- 2012). raneous X-ray burst associated with SGR 1935+2154’s radio Extending the same model to the shock properties emission agree remarkably well with the model prediction. derived for the observed populations of cosmological FRBs predicts that the afterglow emission for these relation (for fixed σ) more energetic bursts will occur at much higher energies Epeak MeV-GeV in the gamma-ray band (Fig.8). Un- 1/2 −3/2 & Epeak ∝ FX tX , (17) fortunately, gamma-ray satellites like Swift and Fermi are generally not sensitive enough to detect this emis- between the spectral energy peak, burst fluence and sion to the cosmological distances of most FRB sources some measure of the burst duration tX. (Metzger et al. 2019; Margalit et al. 2020; Chen et al. For X-ray bursts from the Galactic magnetar SGR 2020). We furthermore emphasize that this predicted J1550-5418, van der Horst et al.(2012) report a correla- short (∼milliseconds duration) gamma-ray signal from tion between the fluence and “emission” time, τ90 ∝ 0.47 the shocks is distinct from the longer-lasting and typ- FX . Taking tX ∝ τ90 then equation (17) predicts −0.2 ically softer gamma-ray emission observed from giant Epeak ∝ FX , which is close to but slightly shallower −0.44 Galactic magnetar flares (e.g. Palmer et al. 2005; Hur- than the correlation Epeak ∝ FX found by van der ley et al. 2005), which is instead well explained as a Horst et al.(2012) using the entire burst sample. How- pair fireball generated by dissipation very close to the ever, note that the most energetic bursts studied by van NS surface. The latter being relatively isotropic com- der Horst et al.(2012) exhibit a flatter or even positive pared to the relativistically-beamed radio emission from correlation of Epeak with fluence. A correlation very −0.44 the ultra-relativistic shocks (hypothesized to accompany close to Epeak ∝ FX is also predicted from equation 1.54 the beginning of the flare; Lyubarsky 2014; Beloborodov (17) using the empirical relationship FX ∝ tX found 2017) might explain the non-detection of FRB-like emis- between the bursts from different magnetars (Gavriil sion from the 2004 giant flare of SGR 1806-20 (Ten- et al. 2004; see Fig.2). Thus, we advance the radical dulkar et al. 2016). hypothesis that hard X-ray emission in even ordinary If the X-rays from magnetar flares are attributable magnetar flares can be generated by internal shocks in to thermal synchrotron shock emission, this may be im- baryon-loaded outflows. printed in correlations between X-ray observables. Since Scaling the shock model to the lower values of rsh, Γ electrons behind the shock are fast-cooling, the X-ray than derived for SGR 1935+2154 above, would also have fluence FX should scale linearly with the flare energy potential consequences for the X-ray spectrum. In par- Eflare, from which one predicts from equation (15) a cor- ticular, the synchrotron spectrum could in some X-ray A Galactic FRB in the Context of Magnetar Models 15 counterparts of Galactic magnetar flares become opaque to pair creation. Following Lithwick & Sari(2001); Be- niamini & Giannios(2017) we calculate the pair cre- ation opacity corresponding to the model parameters described above, and find the external shock to be opti- cally thin to pair creation. Pair creation could however become important for somewhat lower values of rsh, Γ, which could be realized if the dissipation is due to inter- nal shocks at a radius that is much lower than rsh. For example, keeping Eflare fixed and reducing the Lorentz factor to Γ ∼ 3, will lead to a pair-creation cutoff at the internal shock site at ∼ 40 keV. We speculate that this might explain why the “high temperature” of X- Figure 9. Optical R-band and 6/22 GHz radio flux due to ray bursts described by a double black-body spectrum thermal synchrotron afterglow emission of the X-ray/FRB- typically peak at energies . 40keV. generated shock as a function of time in hours (bottom axis) Finally, the explanation provided here for the X-ray as it propagates to larger radii. Shown for comparison are spectra of Galactic magnetar short bursts might apply upper limits from Ravi et al.(2020a). In this simple estimate most robustly only to the smaller sub-set of bright SGR we have assumed a radially-constant density of the external bursts which are luminous enough to drive radiation- medium; if the external medium does not extend so far then the predicted flux would be lower than these estimates. Syn- driven outflows (i.e. large values of L /L , see Fig.3). X min chrotron self-absorption, which affects the radio light curves, In this regard it is interesting that the brightest bursts has been included in an approximate way. analyzed by van der Horst et al.(2012) exhibit a dif- ferent correlation between their peak energy and flux to duced scattering at this time, and only escapes at a time the rest of the bursts, consistent with the idea that the t ∼burst-width later. physical mechanism driving these bursts is different. As shown in Figure9, the shock model predicts that Returning to the radio burst emission, Metzger et al. the X-ray emission should be accompanied by longer- (2019) predict a downwards drift in frequency10 as the lived synchrotron emission at lower frequencies as the shock decelerates and the (Lorentz boosted) synchrotron shock propagates to larger radii, again similar to a maser emission sweeps from high to low frequencies. GRB afterglow (Sari et al. 1998). For frequencies be- The presence (or lack of) this feature in the SGR low ν and ν , the peak flux will rise as F ∝ ν1/2 as 1935+2154 burst would therefore provide a helpful diag- syn c ν ν ∝ t−α decreases in time until reaching the observing nostic of FRB models and a probe of the density profile syn frequency, where α = 3/2 during the relativistic phase in this specific burst (see Margalit et al. 2020 for appli- and α = 3 once the blastwave transitions to become non- cation to CHIME repeaters). In addition to the in-band relativistic. Thus, if ν is passing through the X-ray drift that may potentially be detectable by CHIME (al- syn band (ν ∼ 10 keV) on a timescale of t ∼ 0.1 s, it will though the non-trivial frequency response of the CHIME X X reach the optical band on a timescale of seconds and the sidelobes may hinder this), the same process could man- radio band (ν ∼ 10 GHz) on a timescale of less than ifest as a small arrival time-delay between the STARE2 R an hour. For an external medium with a radially con- detection at 1.4 GHz and the CHIME detection at lower stant density, the flux density F at peak (ν ∼ ν ) is frequencies. ν obs syn constant during the relativistic phase and thus approx- The relative delay between the observed radio emis- imately equal to that achieved initially at the higher sion (corrected for DM) and it’s hard-radiation coun- frequencies. Using as a proxy for the latter the X-ray terpart observed at peak (Fig.8) should be, at most, fluence of F ∼ 7×10−7 erg/cm2 of the FRB-generating comparable to the radio burst duration ( 5 ms in the X . flare from SGR 1935+2154, we predict a peak radio af- case of SGR 1935+2154’s April 28th burst). This re- terglow flux density F ∼ F /(ν · t ) ∼ 0.3 Jy (al- sults from the fact that the high-frequency photons are radio X X X though self-absorption severley mitigates this estimate; optically thin at the shock deceleration radius (when the see Fig.9). After peak, the predicted flux will decay emission peaks), while the radio is optically-thick to in- exponentially as the synchrotron emission occurs from electrons on the Wien tail of the thermal Maxwellian. 10 This phenomena, which is now well cataloged for many repeating Thus, such an afterglow is consistent with upper lim- FRB sources, has been termed the “sad trombone” (Hessels et al. its on radio afterglow emission of 0.05 mJy taken on a 2019; CHIME/FRB Collaboration et al. 2019). timescale of a few days (Ravi et al. 2020a,b). Also note 16 Margalit, Beniamini, Sridhar, & Metzger that the radius sampled by the shock at these late times model, push the high-energy thermal synchrotron coun- −2 is a factor & 30 times larger than at the time of the terpart to lower frequencies (νsyn ∝ fe ), leading to earlier radio emission and there is no guarantee that the an “afterglow” peaking optical/UV band (Beloborodov dense medium extends that far from the magnetar. 2019) instead of the x-ray/gamma-ray band predicted in Finally, the ejection of the baryonic outflow is pre- the baryonic model (Fig.8). In this scenario, as in the dicted to result in a small decrease in the spin frequency magnetar wind nebula case (§4.2.1), the X-rays from the of the magnetar due to the temporary opening up of flare must be created by a process which is not directly field lines by the mass-loaded wind (Thompson & Blaes related to the FRB mechanism. 1998; Harding et al. 1999; Beniamini et al. 2020). The magnitude of the spin frequency change increases with 4.3. Additional Models the luminosity of the baryonic wind and its duration, In curvature models, the FRB is produced by curva- both of which are highly uncertain. However if the X- ture radiation from bunched electrons streaming along ray burst concurrent with the FRB produced such an the magnetic field lines of the magnetar (e.g. Kumar outflow, then there are at least two other bursts within et al. 2017; Lu & Kumar 2018). These models predict the latest outburst, with even larger (Veres fluence ratios η ∼ 1 in all bands (Chen et al. 2020), et al. 2020; Ridnaia et al. 2020b) that may have also and thus cannot explain properties of the observed X- produced an outflow. Taking for example the brightest ray burst of SGR 1935+2154 (whose fluence ratio is of these bursts, that occurred on April 22nd, we can cal- η ∼ 10−5  1, but also in terms of X-ray spectrum) culate a lower limit on the spin frequency decrease of 1/2 as a bona fide FRB counterpart. This shortcoming can ∆Ω = 2 × 10−8L t1/2 s−1 (Beniamini et al. 2020). 41 potentially be dismissed by arguing that the same mag- 4.2.3. Spin-Down Powered Wind (Beloborodov 2017, 2019) netar activity leading to particle bunching, acceleration, Beloborodov(2017, 2019) argue that the upstream and FRB emission, also produces “normal” short X-ray medium into which the relativistic flare collides is an bursts. However, this scenario makes no prediction as electron/positron plasma from a spin-down powered to the quantitative relationship between the radio and component to the pulsar wind. Given the low spin-down X-ray burst properties, and the observed fluence ratio of power of SGR 1935+2154 however, this scenario might η ∼ 10−5 is ad-hoc within this framework. These consid- be somewhat disfavored. erations apply also to models where FRBs are produced The observed radio fluence at ν = 1.4 GHz in by reconnection in the outer magnetosphere (Lyubarsky this model can be estimated from equation 91 of Be- 2020), or indeed to any magnetospheric models. If true, loborodov(2019), and re-expressed as a function of the a testable prediction of the scenario (and one that would spin-down power Lsd and pair multiplicity M, be in tension with synchrotron-maser models) may be large variations in the value of η for future events. E ∼ 3 × 1031 erg L1/12 M2/3. (18) radio sd,34 3 Another class of FRB models discussed in the litera- In the above we have assumed the flare energy is 1040 erg ture power FRBs by the kinetic energy of an outflow in- motivated by the X-ray counterpart of SGR 1935+2154, teracting with the magnetosphere of a NS (Zhang 2017, and we have omitted scaling with nuisance parame- 2018; Ioka & Zhang 2020). The outflow in these “cosmic ters for clarity. For the spin-down power of SGR comb” models has been suggested to range from AGN- 1935+2154 and standard pair-multiplicity of 103, this driven winds, to GRB jets, or winds from a binary com- fluence is ∼three orders of magnitude lower than the panion to the NS. None of the above are likely to be ap- observed energy of SGR 1935+2154’s radio burst. plicable in the context of SGR 1935+2154’s radio burst, This tension may be alleviated by an enhancement of in tension with predictions of this model (although see the magnetar-wind (because of e.g. opening of field lines Wang et al. 2020). by the magnetar flare) or an increased pair-multiplicity A final class of NS-related models we discuss are “spin- shortly preceding the flare (Beloborodov 2019). From down models”, in which the radio bursts are powered by equation (18) we find that a pair-multiplicity of ∼ 5 × rotational energy of the NS (Cordes & Wasserman 2016; 107 would be required to fit the observed fluence. This Connor et al. 2016; Mu˜nozet al. 2020). Though in prin- is much higher than pulsar pair multiplicities, though ciple applicable to magnetars, these models typically en- it has been suggested that much larger values  103 vision normal pulsars as progenitors. Indeed, consider- may be attainable for magnetars immediately preceding ing the very low spin-down power of SGR 1935+2154 in a flare (Beloborodov 2019). comparison to pulsars, and the fact that the latter are The high pair-loading in this version of the syn- & 100 times more common than Galactic magnetars (in chrotron maser model, as in the Lyubarsky(2014) terms of their effective active lifetime), it seems unnatu- A Galactic FRB in the Context of Magnetar Models 17 ral that a spin-down-powered “FRB” would be first de- only the subset produced by shocks would be ex- tected for SGR 1935+2154. A prediction of this model pected to emit coherent radio bursts. would be a change in NS spin period due to the released burst energy. Accounting for the radiated energy of SGR • Applying the same fluence ratio η to giant mag- 1935+2154’s burst, including it’s associated X-ray coun- netar flares would imply that Galactic magnetars −6 −1 2 are capable of powering even the most energetic terpart, we find that a change ∆Ω ≈ −4 × 10 s d10 in the angular velocity of SGR 1935+2154 need to have cosmological FRBs (Fig.1). However, a stark dis- occurred. A reduction in the spin frequency is also ex- crepancy exists between the activity (burst repe- pected in the Metzger et al.(2019) version of the syn- tition rate) of Galactic magnetars and the sources chrotron maser model due to opening of magnetic field of the recurring extragalactic FRBs. If universal, −5 lines by the baryonic outflow, however this effect is much the low efficiency η ∼ 10 also places strong up- smaller (§4.2.2). The Beloborodov(2019) synchrotron per limits on the magnetar active lifetime in the maser model (§4.2.3) also necessitates some level of pe- latter case, much shorter than the ages of Galactic riod change due to a significant enhancement of pulsar- magnetars (eq.2). wind required immediately preceding the FRB, however • The estimated rate of radio bursts similar to that this too would be expected to be smaller than ∆Ω es- observed from SGR 1935+2154 is insufficient to timated above. Future timing of SGR 1935+2154 may contribute appreciably to the observed extragalac- help test this prediction of the spin-down model. tic FRB rate (eq.3). Depending on the luminos- ity function of the Galactic flares, the all-sky FRB 5. CONCLUSIONS rate (including also giant flares) can be reproduced We have explored implications related to the pop- by “ordinary” Galactic magnetars similar to SGR ulation of FRB sources and to theoretical models of 1935+2154 (Fig.4). However, such a model fails to FRBs in light of the recent detection of a luminous mil- simultaneously explain the large (per-source) rep- lisecond radio burst from the Galactic magnetar SGR etition rate of known repeaters or the large DMs 1935+2154 (Scholz & CHIME/FRB Collaboration 2020; of the FRB population. Bochenek et al. 2020a). The large energy of this burst makes it unique amongst any previously observed pul- • Instead, considering a two-component model— sar/magnetar phenomenology, and bridges the gap to we add a second population of magnetars whose extragalactic FRBs (Bochenek et al. 2020a). birth-rate is a free-parameter, and whose ac- Our conclusions may be summarized as follows. With tivity level and lifetime are scaled from SGR regards to general implications for extragalactic magne- 1935+2154 as a function of the population’s mag- tar populations: netic field strength. This model allows to broadly replicate the observed properties of the FRB pop- • Broadly speaking, the discovery of a highly lumi- ulation (Fig.6), however only if the birth-rate of nous millisecond-duration radio burst coincident the “active” magnetar population is  than the with the X-ray flare of the Galactic magnetar SGR CCSN rate (Fig.5; in line with previous work, e.g. 1935+2154 supports magnetar models for extra- Nicholl et al. 2017). galactic FRBs. • This implies that the population of “active” mag- • The X-ray properties of the flare are fairly typ- netars cannot be interpreted as an earlier evolu- ical of Galactic magnetar flares in terms of flu- tionary state of SGR 1935+2154-like magnetars ence and overall duration (Fig.2), however it’s which are born in a large fraction of CCSNe. In- X-ray spectrum may have been harder than usual stead this population may form through more ex- (Mereghetti et al. 2020b). Furthermore, with the otic channels such as SLSNe, AIC, or binary NS notable exception of the giant flare from SGR mergers (Metzger et al. 2017; Margalit et al. 2019). 1806-20, relatively few such flares would have pre- viously been detected at radio wavelengths for a In addition to the general implications summarized −5 similar low ratio η ≡ Eradio/EX ∼ 10 of radio to above, we also address implications for specific FRB X-ray fluence (Fig.3). This suggests that a sizable magnetar models. We stress that there is no single fraction of Galactic magnetar flares may be accom- “magnetar model” for FRBs, and that many distinct panied by luminous radio bursts, although we cau- models have been suggested in the literature, and these tion that multiple emission mechanisms may be at differ in the requisite magnetar properties, the FRB play in producing magnetar X-ray flares, and that emission mechanism, and predictions for (of lack of) 18 Margalit, Beniamini, Sridhar, & Metzger multi-wavelength counterparts (§4). In this context, we shocks. This model predicts a power-law spec- find that: trum with an exponential cut-off, and correlations between the peak energy of the burst and other • Magnetospheric models (“curvature”, “low twist”, burst properties (e.g. duration and fluence), which and “reconnection” models) predict either no high- are broadly consistent with observations (van der energy counterpart, or weak counterparts of com- Horst et al. 2012). parable energy to the radio emission (η ∼ 1). This is in tension with the observed X-ray counterpart • The baryon shell synchrotron maser shock model in SGR 1935+2154, where η ∼ 10−5. This short- (Metzger et al. 2019; Margalit et al. 2020) makes coming can be dismissed by interpreting the X- several predictions testable by future Galactic or ray counterpart as a “normal” short X-ray burst. extragalactic FRBs: (1) Although X-ray/gamma- However this scenario makes no predictions of the ray emission can arise from magnetar flares with- spectral or energetic properties of the X-ray flare out an accompanying FRB (e.g. if the X- and the η ∼ 10−5 radio-to-X-ray fluence ratio is rays/gamma-rays do not arise from shocks), the ad-hoc within this framework (§4.3). opposite is not true. Any FRB-like burst should be accompanied by X-ray/gamma-ray emission • Synchrotron maser models, which involve relativis- −1 4 with an energy at least a factor η & 10 tic flare ejecta colliding with an external medium, larger than the emitted radio energy (eq. 14); (2) provide a promising alternative. However, these scaling up to cosmological FRBs, the equivalent models differ in the nature of the upstream prompt synchrotron counterpart should peak in medium and their predicted multi-wavelength af- the & MeV-GeV gamma-rays band (Fig.8); (3) terglow. Galactic FRBs may be accompanied by longer lived optical/radio emission on a timescale of sec- • Models in which the upstream is the magnetar onds/minutes (Fig.9), the details of which how- wind nebula (Lyubarsky 2014; §4.2.1) may have ever depend on the extent of the external medium an efficiency issue and predict associated afterglow surrounding the magnetar on larger radial scales in the GeV range. Likewise, models in which the than probed by the hard X-rays. upstream is a rotational-powered pulsar wind (Be- loborodov 2017, 2019) are strained and predict a lower frequency counterpart (§4.2.3). ACKNOWLEDGMENTS • The baryonic shell version of the synchrotron maser model naturally explains the value of η We thank Bryan Gaensler and George Younes for help- (compare eqs.1 and 14) in addition to the tim- ful insight. BM is supported by NASA through the ing11 and spectral features of the observed X-ray NASA Hubble Fellowship grant #HST-HF2-51412.001- emission (Fig.8). The model requires substantial A awarded by the Space Telescope Science Institute, mass ejection to accompany the flares, which may which is operated by the Association of Universities for be in tension with the relatively low luminosity of Research in Astronomy, Inc., for NASA, under contract the flares if the outflows are driven by radiation NAS5-26555. The research of PB was funded by the pressure (Fig.3). On the other hand, the require- Gordon and Betty Moore Foundation through Grant ment for mass ejection—and the sensitivity of the GBMF5076. NS is supported by the Columbia Univer- radio emission to the detailed properties of the up- sity Dean’s fellowship and through the National Science stream medium—could help explain why not all Foundation (grant# 80NSSC18K1104). BDM is sup- magnetar flares are accompanied by a luminous ported in part by the Simons Foundation through the FRB. Simons Fellowship program in Mathematics and Physics (grant #606260). • The latter model suggests a new paradigm in which X-ray emission of magnetar flares arises from thermal synchrotron radiation from internal

11 Note that the X-rays and radio are predicted to arrive con- temporaneously in this model, contrary to arguments made by Mereghetti et al.(2020b), who did not account for relativistic time-of-flight effects. A Galactic FRB in the Context of Magnetar Models 19

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