Large host-galaxy dispersion measure of fast radio bursts

0.2 MB·

by  Yuan-Pei Yang

Draftversion January24,2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
LARGE HOST-GALAXY DISPERSION MEASURE OF FAST RADIO BURSTS
Yuan-Pei Yang1, Rui Luo1,2, Zhuo Li1,2 and Bing Zhang1,2,3
1KavliInstituteforAstronomyandAstrophysics,PekingUniversity,Beijing100871, China;KIAA-CASFellow,[email protected];
[email protected];[email protected];
2 DepartmentofAstronomy,SchoolofPhysics,PekingUniversity,Beijing100871, China
3 DepartmentofPhysicsandAstronomy,UniversityofNevada,LasVegas,NV89154, USA;[email protected]
Draft version January 24, 2017
7
1 ABSTRACT
0 Fast radio bursts (FRBs) have excessive dispersion measures (DMs) and high Galactic latitudes,
2 whichpoint towarda cosmologicalorigin. We developa method to extractthe meanhostgalaxyDM

n ( DMHG,loc ) and the characterized isotropic luminosity (L) of FRBs using the observed DM-Flux
h i
a data. Applying a Markov Chain Monte Carlo (MCMC) method to the data of 18 FRBs, We derive
J a relative large mean host DM, i.e. DM 270 pc cm−3 with a large dispersion, and L
3 1043 erg s−1. A relatively large DM hof FHRGB,losciis∼also supported by the millisecond scattering time≃s
HG
2 of some FRBs and the relatively small redshift z =0.19273 of FRB 121102 (which gives DM =
HG,loc
210 pc cm−3). The large host galaxy DM may be contributed by the ISM or a near-source plasma in
]
E thehostgalaxy. IfitiscontributedbytheISM,thetypeoftheFRBhostgalaxieswouldnotbeMilky
Way (MW)-like, consistent with the detected host of FRB 121102. We also discuss the possibility of
H
having a near-sourcesupernova remnant (SNR), pulsar wind nebula (PWN), or HII regionthat gives
h. a significant contribution to the observed DMHG.
p Subject headings: intergalactic medium — radio continuum: general
-
o
r 1. INTRODUCTION is applied to the current FRB sample with 18 sources.
t
s Through a Markov Chain Monte Carlo (MCMC) sim-
Fast radio bursts (FRBs) are mysterious as-
a ulation, we derive a relatively large mean host galaxy
[ tronomical radio transients with short intrinsic
durations ( 1ms), large dispersion measures DM, DMHG,loc , for FRBs. We also provide two sup-
h i
1 (DM & 200∼pc cm−3), and high Galactic latitudes portingevidenceforalargevalueofDMHG: millisecond-
v (Lorimer et al. 2007; Keane et al. 2012; Thornton et al. durationofscatteringtails forsome FRBsandDMHG =
5 176 pc cm−3 for FRB 121102.
2013; Burke-Spolaor & Bannister 2014; Spitler et al.
6
2014, 2016; Masui et al. 2015; Petroff et al. 2015;
4 2. METHOD
Ravi et al. 2015; Champion et al. 2016; Keane et al.
6
2016;Ravi et al.2016; Chatterjee et al.2017). Recently, ForanFRB,theobserveddispersionmeasurehasthree
0
thanks to the precise localization and multi-wavelength contributions(e.g. Deng & Zhang 2014; Gao et al. 2014;
.
1 follow-up observations of the repeating source FRB Yang & Zhang 2016), i.e.
0 121102 (Chatterjee et al. 2017; Marcote et al. 2017;
7 Tendulkar et al. 2017), the distance scale of FRBs has DMobs =DMMW+DMHG+DMIGM, (1)
1
been finally settled to the cosmological range. So far, which are from the Milk Way, the FRB host galaxy
:
v even though only FRB 121102 has a measured redshift (whichitselfincludesthecontributionsfromtheinterstel-
i z = 0.19273 (Tendulkar et al. 2017), the large DM lar medium (ISM) in the host galaxy and a near-source
X
excess of other FRBs with respect to the Galactic value plasma), and the IGM, respectively. According to the
r and their high Galactic latitudes suggest that most, if Galactic pulsar data, DM can be well constrained
a MW
not all, FRBs should have a cosmologicalorigin. (Cordes & Lazio2003), which is a strongfunction of the
The host galaxies of FRBs carry important informa- Galactic latitude b, e.g. DM . 100 pc cm−3 for
MW
tionregardingtheprogenitorofFRBs. ForFRB121102, b & 10◦ and DM| | 1000 pc cm−3 for b 0◦.
opticalimagingandspectroscopyindicateadwarfgalaxy | | MW ∼ | | ∼
Since DM can be well extractedfor a localized FRB,
with a mass of M ∼ (4 − 7) × 107M⊙ as the host one can dMefiWne the extragalactic (or excess) dispersion
galaxy. The H flux of the host galaxy suggests a star
α measure of an FRB as
formation rate of SFR 0.4M⊙yr−1 (Tendulkar et al.
∼
2017). No information about the host galaxies of other DM DM DM =DM +DM , (2)
E obs MW IGM HG
FRBs is available. One possible way to derive FRB host ≡ −
galaxyinformationistoextractthehostgalaxyDMfrom whichcanbetreatedasanobservedquantity. Theprop-
data. (Yang & Zhang 2016) proposed a method to de- erties of FRB host galaxies may be assumed to have no
rive DMHG using the measured DM and z of a sample significant evolution with redshift, i.e. hDMHG,loci ∼
of FRBs. However, the z values of most FRBs are not const, where DMHG,loc is the averagevalue ofthe rest-
h i
obtained so far. frame host galaxy DM within a certain redshift of dis-
In this paper, we further develop a method to apply tance bin. Due to cosmological time dilation, the ob-
DM and flux of FRBs to infer DMHG. This method served host DM value reads DMHG = DMHG,loc/(1 +
z) (Ioka 2003). Considering the local inhomogeneity
2 Yang et al.
of the IGM, we define a mean DM of the IGM as We apply the MCMC method to extract DM
HG,loc
h i
(Deng & Zhang 2014; Yang & Zhang 2016) fromtheobservedDM F relation. Thelikelihoodfor
E ν
the fitting parametersis−determinedbythe χ2 statistics,
DM =3cH0ΩbfIGM z fe(z′)(1+z′) dz′, i.e.
IGM
h i 3cH8π0ΩGbmfIpGMfZe0 zp+Ωzm2(11+z′3)3Ω+mΩΛ+O(z2) , χ2(L,hDMHG,loci,f)=Xi (DMσiE2,+i −σs2hyDs(Mf)Ei)2, (7)
≃ 8πGm (cid:20) (cid:18)2 − 4 (cid:19) (cid:21)
p whereirepresentsthesequenceofanFRBinthesample,
(3) σ represents the error of DM , and σ f DM is
i E,i sys E
≡ h i
the system error, and f is a fitting parameter reflecting
where fe(z) = (3/4)y1χe,H(z)+(1/8)y2χe,He(z), y1 1 the uncertainty of the model. We minimize χ2 and con-
∼
and y 4 3y 1 are the hydrogen and he-
2 1 vert it into a probability density function. We can then
≃ − ∼
lium mass fractions normalized to 3/4 and 1/4, re-
obtain the probability distribution of the fitting param-
spectively, and χe,H(z) and χe,He(z) are the ionization eters using the software emcee3.
fractions for hydrogen and helium, respectively. For
The analysis results are shown in Figure 1. We
ozf<bo3th, χhey,Hdr(ozg)e≃n aχned,Heh(ezl)iu≃m 1(M, deiukesitno2f0u0ll9)i.oniTzahteiroen- have log(L/erg s−1) = 42.96+−00..2545, hDMHG,loci =
267.95+215.57 pc cm−3 and lnf = 0.8+0.23. Our re-
fore, one has fe(z) fe = 7/8. We adopt the flat −114.69 − −0.19
ΛCDMparametersre≃centlyderivedfromthePlank data: sultsshowthatFRBs mayhavealargehostgalaxyDM,
H = 67.7 km s−1Mpc−1, Ω = 0.31, Ω = 0.69, although with large dispersion. On the other hand, the
0 m Λ
luminositydistributionisquitenarrow,whichwouldsug-
and Ω = 0.049 (Planck Collaboration et al. 2015). For
b
gestapossiblecommonoriginoftheobservedFRBs. In-
the fractionofbaryonmassin the intergalacticmedium,
terestingly, we note that the fitting intrinsic luminosity
we adopt f =0.83 (Fukugita et al. 1998; Shull et al.
IGM L 1043 erg s−1 is closed to the characteristic luminos-
2012).
ity∼ofthemagnetargiantflares,e.g. L 1044 erg s−1.
For an FRB with an intrinsic frequency-dependent lu- GF
≃
On the other hand, it is possible that FRBs may have a
minosity Lν∗(ν∗), the observed flux is given by Fνdν = wide luminosity function, with the fainter ones not de-
Lν∗dν∗/4πd2L. The luminosity distance of the FRB may tectable with current telescopes.
be given by
Ourderivedrelativelylargevalueof DM issup-
HG,loc
h i
1/2 ported by two other independent pieces of evidence.
L
d , (4) First, for Galactic pulsars, the scattering time τ
L
≃(cid:18)4πνFν(cid:19) 10−3 msfor b &30◦ (e.g.Cordes et al.2016). Howeve≪r,
someFRBsw|i|th b >30◦ havemeasuredscatteringtime
whereL≡ν∗Lν∗ istheisotropicintrinsicluminosity,and ofafewmillisecon|d| (Petroff et al.2016),suggestingthat
ν 1 GHz is the characteristicfrequency ofFRBs1. For
≃ scattering happens outside the Milky Way. The scatter-
a flat universe, one has
ing contribution from the IGM is calculated to be neg-
c z 1 ligibly small, so that most the scattering would occur
d = (1+z) dz′,
L in the FRB host galaxy (Xu & Zhang 2016a). Observa-
H0 Z0 Ωm(1+z′)3+ΩΛ tions show that a larger scattering tail correspond to a
c z+z2 1p3Ωm +O(z2) . (5) larger DM, e.g. τˆ = 2.98×10−7 ms DM1.4(1+3.55×
≃H0 (cid:20) (cid:18) − 4 (cid:19) (cid:21) 10−5DM3.1) for Galactic pulsars (Cordes et al. 2016), a
fact understandable and required by turbulence theories
For z . 1, according to Eq.(3)-Eq.(5), we can ob-
(Xu & Zhang 2016b). If one assumes that the FRBs’
tain approximately DM Ad , where A
r3eHla02tΩiobnf:IGMfe/8πGmp. TIhGeMrefor≃e,oneLhastheDME−F≡ν hinogsttsimhae,veonaeswimouilladrrreeqlautiiroenD,fMorHGthe&m28il0lispeccocnmd−s3c.aTttheris-
is consistent with our derived results.
A Second, the host galaxy DM FRB 121102 can be pre-
DM L1/2ν−1/2F−1/2+ DM . (6)
h Ei≃ √4π ν h HG,loci cisely derived. FRB 121102 was localized to a ∼ 0.1
arcsecondprecision by Chatterjee et al. (2017). The ob-
As shown in Eq.(6), DME Fν−1/2 for Fν Fν,crit, served dispersion measure is DMobs = 558 pc cm−3.
and DM DMh i ∝for F F ≪, where According the location of FRB 121102, Tendulkar et al.
E HG,loc ν ν,crit
F h A2iL/≃4πνh DM i 2. ≫ (2017) identified an extended source coincident with the
ν,crit ≡ h HG,loci burst, which is a host galaxy at z = 0.19273. Adopting
One can numerically solve Eq.(3)-Eq.(5), and use the
thePlankcosmologicalparametersandf =0.83,one
observedDM F relationtofitthecurrentsampleof18 IGM
FRBs. We taEk−e thνe FRB data from the FRB Catalogue dDeMrive DM2IG1M8p≃c1c6m4−p3cincmth−e3d.irTehcteioMnW(Chcoanttterribjeuetieotnails.
of Petroff et al. (2016)2. For the repeating FRB, FRB MW ≃
2017). So one can derive
121102,we take the brightest pulse as its peak flux.
DM =DM DM DM 176pc cm−3 (8)
1 Strictly peaking, a proper k-correction is needed to derive a HG obs− MW− IGM ≃
more rigorous dL. However, the FRB spectral shape is not well and
constrained. SincetheFRBemissionseemstopeakaround1GHz
andsincetheFRBredshiftisnotveryhigh,ourapproximatetreat- DMHG,loc =(1+z)DMHG 210 pc cm−3 (9)
mentisjustified. ≃
2 http://www.astronomy.swin.edu.au/pulsar/frbcat/ 3 http://dan.iel.fm/emcee/current.
Large host-galaxy DM of FRBs 3
log(L) = 42.96−+00..5254
800 <DMHG,loc> = 267.95−+121145..6597
> 600
MHG,loc 400
D
3)m−103 < 200
c
M/pcE 0.6 ln(f) = −0.80−+00..1293
D
Log( 0.0
ln(f) −0.6
−1.2
102
41.4 42.0 42.6 43.2 200 400 600 800 −1.2 −0.6 0.0 0.6
10-1 100 101 102 103
Log(Flux/Jy) log(L) <DMHG,loc> ln(f)
Fig. 1.—Left: ThebestfittotheobservedDME−Fν relation. TheblueFRBdatapointsarefromtheFRBCatalogue. Thegreenline
denotes the MCMC best fitting curve. Right: Two-dimensional projections of the posterior probability distributions of the model fitting
parameters. Data points are shown as grayscale points with contours. Contours are shown at 0.5, 1, 1.5, and 2σ significance levels. The
bestfittingvaluesareshownontopofeach1Ddistribution.
forFRB121102. Suchavalueisalsoconsistentwithour the SNR during an observation time ∆t is given by
fitting results.
Mυ
∆DM = ∆t
SNR 2πµm R3
3. DISCUSSION p
M R −3
The above results suggest that the FRB host galaxies =16.7 pc cm−3
have a relatively large value of DM. There could be two M⊙ (cid:18)0.1 pc(cid:19)
possible contributions to such a large DM: the ISM in υ ∆t
the host galaxy and the near-source plasma. , (11)
For the case of a host ISM, one immediate inference is ×(cid:16)3000 km s−1(cid:17)(cid:18)1 yr(cid:19)
that the type of the host galaxies of most FRBs would where υ (3000 30000) km s−1 is the characterized
not be MW-like disk galaxies. The reason is that for ∼ −
SNR velocity. The age of the SNR may be estimated as
disk galaxies, FRBs would be most likely emitted from
T R/υ (3 30) yr(R/0.1 pc). In principle, it is
Galactichighlatitudes,whichgivesrisetonegligibleDM. ≃ ≃ −
possible to expect that the host DM is dominated by a
Indeed,thehostgalaxyofFRB121102wasidentifiedasa
supernovaejecta. However,therearetwocaveatsforthis
dwarfgalaxy(Tendulkar et al.2017),whichisconsistent
possibility: 1. The thin shell model predicts an observ-
withourexpectation. However,ourinferredvalueisstill
ableDMvariationoverthedecade-longtimescale,which
somewhatlarger than the simulated host galaxy DM for
is inconsistent with the non-variationDM of the repeat-
various types of galaxies (Xu & Han 2015), suggesting
ing FRBs during the approximately four-year period of
that a near-source plasma may be needed.
observations; 2. For an age-independent event rate (the
For the case of a near-source plasma, we consider the
timedelaybetweenSNandFRBisuniformlydistributed
contributions from a SNR, PWN, or HII region. First,
for FRBs), the cumulative distribution of DMs of FRBs
in a thin shell approximation, the DM value through a
should satisfies N(> DM) DM−1/2 if the observed
young SNR may be estimated by (see also Katz 2016; ∝
DMisdominatedbytheSNRsassociatedwiththeFRBs.
Piro 2016; Metzger et al. 2017)
However,thestatisticalresultsoftheobservedFRBsob-
viously deviate from this relation (Katz 2016).
M
DM = ∆R Next, we consider the DM contribution from a PWN.
SNR 4πµmpR2∆R Some authors suggested an association of FRBs with
M R −2 youngpulsars(Cordes & Wasserman2016;Connor et al.
=272 pc cm−3 , (10) 2016), while some others suggested an association of
M⊙ (cid:18)0.1 pc(cid:19) FRBs with magnetar giant flares (Popov & Postnov
2010; Kulkarni et al. 2014). While these mod-
whereM,Rand∆RaretheSNRmass,radiusandthick- els are greatly constrained by available observations
ness, respectively, and µ = 1.2 is the mean molecular (Tendulkar et al. 2016; Lyutikov 2017), we nonetheless
weight. Note that the SNR dispersion measure does not consider the DM contribution from a pulsar/magnetar
depend on ∆R of the thin shell. The DM variation of wind. The classical Goldreich-Julian number density is
4 Yang et al.
given by (Goldreich & Julian 1969) where n is the gas number density in the HII region,
N is the rate of ionizing photons from a star, α is the
ΩB u
nGJ(r)=2πec recombination rate, and Rs ≡ 3Nu/4παn2 1/3 is the
≃7×1012 cm−3(cid:18)10B14pG(cid:19)(cid:16)106rcm(cid:17)−3(cid:18)1Ps(cid:19)−1, SsTttar=ro¨m1in0g4rHeKnII,raraendgdiiuotsnh.,esWSoterto¨hamastgsurαemne=rat(cid:0)2hd.ai6uts×tihs1eR0−tsh1=3erc(cid:1)e5m.4is3psa−cn.1WOfo5er
note that the Stro¨mgren radius is much larger than the
(12)
projectedsizeof.0.7pcofFRB121102radiopersistent
where B is the polar-cap magnetic field strength, and emission source (Marcote et al. 2017).
p
P is the rotation period. A relativistic electron-positron In summary, we show that the current FRB ob-
pair plasma is expected to stream out from the magne- servations imply large host galaxy DM values, e.g.,
tosphere. The DM of the pulsar/magnetarwind may be DM & 200 pc cm−3. Such a large DM may be
HG,loc
h i
estimatedusingthe pairfluxnearthe lightcylinder(e.g. contributed by the host ISM or a near-source plasma.
Cao et al. 2017) SucharesultposesrequirementstoFRBprogenitormod-
els.
DMPWN 3ΓLµ±nGJ(RLC)RLC In the total host galaxy DM, the contribution from
≃
µ 2/3 B 4/3 the near-source plasma also plays an essential role
124 pc cm−3 p to identify the progenitor systems of FRBs. The
≃ (cid:16)106(cid:17) (cid:18)1014 G(cid:19) various models have a wide DM distribution. For
P −11/3 models invoking young energetic pulsars and mag-
, (13) netars (e.g. Connor et al. 2016; Cordes & Wasserman
×(cid:18)0.3 s(cid:19)
2016;Yang et al.2016;Piro2016;Murase et al.2016a,b;
where R is the radius of the light cylin- Metzger et al. 2017; Kashiyama & Murase 2017) or col-
LC
der, µ± is multiplicity parameter, ΓL lapse of new-born supra-massive neutron star (e.g.
∼
(Lsd/4πRL2Cµ±nGJ(RLC)mec3)1/3 is relativistic wind Falcke & Rezzolla2014;Zhang2014),anear-sourceSNR
Lorentz factor at the light cylinder, and L is or PWN may give an important contribution to the ob-
sd
the pulsar/magnetar spin-down luminosity. The pul- servedDM.Alsoirregularstar-forminggalaxies(e.g. the
sar/magnetarwindcanprovideasignificantcontribution hostgalaxyofFRB121102)donothaveadisk-likestruc-
to DM if µ is large enough. ture, and may provide a relatively large host DM. For
Recently, Zhang (2017) proposed a unified interpre- themodelsinvokingcompactobjectmergers(e.g.Totani
tation of FRBs in the so-called “cosmic comb” model, 2013; Zhang 2016; Wang et al. 2016), the contribution
which invokes the interaction between an astrophysical fromanear-sourceplasmamaynotbeimportant. These
plasma stream and a foreground regular pulsar. Since systemsmayalsohavealargeoffsetfromthehostgalaxy.
cosmic combs more easily happen in slow (P 1 s) However, elliptical or early-type host galaxies that har-
and low-field (B 1012 G) pulsars, the DM∼ con- borthese eventsmayalsoprovidelargefree electroncol-
∼ umnneededtoaccountforthelargeDM inferredfrom
tribution from the near-source plasma is DM HG
PWN
0.003pc cm−3. Therefore,inthecosmiccombmodel,th∼e the data.
large host galaxy DM might result from the host galaxy
ISM or the near-source plasma of the stream source in
front of the pulsar towards Earth.
At last, we consider the DM contribution from a HII
region in the host galaxy, assuming that an FRB is em-
bedded in a Stro¨mgren sphere. The DM contributed by
WethankZi-GaoDai,YanHuang,Tian-QiHuangand
a Stro¨mgren sphere may be estimated as
Su Yao for helpful discussions. This work is partially
1/3 supported by the Initiative Postdocs Supporting Pro-
3N n
DM =nR = u gram (No. BX201600003), the National Basic Research
HII s
(cid:18) 4πα (cid:19) Program (973 Program) of China (No. 2014CB845800),
N 1/3 n 1/3 the National Natural Science Found (No.11273005) and
=540 pc cm−3 u , Project funded by China Postdoctoral Science Founda-
(cid:18)5 1049 s−1(cid:19) (cid:16)100 cm−3(cid:17) tion (No. 2016M600851). Yuan-Pei Yang is supported
×
(14) by a KIAA-CAS Fellowship.
REFERENCES
Burke-Spolaor,S.,&Bannister,K.W.2014,ApJ,792,19 Cordes,J.M.,Wharton,R.S.,Spitler,L.G.,Chatterjee, S.,&
Cao,X.-F.,Yu,Y.-W.,&Dai,Z.-G.2017,ArXive-prints, Wasserman,I.2016,ArXive-prints,arXiv:1605.05890
arXiv:1701.05482 Deng,W.,&Zhang,B.2014, ApJ,783,L35
Champion,D.J.,Petroff,E.,Kramer,M.,etal.2016,MNRAS, Falcke,H.,&Rezzolla,L.2014,A&A,562,A137
460,L30 Fukugita,M.,Hogan, C.J.,&Peebles,P.J.E.1998,ApJ,503,
Chatterjee,S.,Law,C.J.,Wharton,R.S.,etal.2017,ArXiv 518
e-prints,arXiv:1701.01098 Gao,H.,Li,Z.,&Zhang, B.2014,ApJ,788,189
Connor,L.,Sievers,J.,&Pen,U.-L.2016,MNRAS,458,L19 Goldreich,P.,&Julian,W.H.1969, ApJ,157,869
Cordes,J.M.,&Lazio,T.J.W.2003,ArXivAstrophysics Ioka,K.2003,ApJ,598,L79
e-prints,astro-ph/0301598 Kashiyama,K.,&Murase,K.2017,ArXive-prints,
Cordes,J.M.,&Wasserman,I.2016,MNRAS,457,232 arXiv:1701.04815
Large host-galaxy DM of FRBs 5
Katz,J.I.2016,ApJ,818,19 Ravi,V.,Shannon, R.M.,&Jameson,A.2015,ApJ,799,L5
Keane,E.F.,Stappers,B.W.,Kramer,M.,&Lyne,A.G.2012, Ravi,V.,Shannon, R.M.,Bailes,M.,etal.2016,Science, 354,
MNRAS,425,L71 1249
Keane,E.F.,Johnston,S.,Bhandari,S.,etal.2016,Nature,530, Shull,J.M.,Smith,B.D.,&Danforth,C.W.2012,ApJ,759,23
453 Spitler,L.G.,Cordes,J.M.,Hessels,J.W.T.,etal.2014,ApJ,
Kulkarni,S.R.,Ofek,E.O.,Neill,J.D.,Zheng,Z.,&Juric,M. 790,101
2014, ApJ,797,70 Spitler,L.G.,Scholz,P.,Hessels,J.W.T.,etal.2016,Nature,
Lorimer,D.R.,Bailes,M.,McLaughlin,M.A.,Narkevic,D.J., 531,202
&Crawford,F.2007, Science,318,777 Tendulkar,S.P.,Kaspi,V.M.,&Patel,C.2016,ApJ,827,59
Lyutikov,M.2017,ArXive-prints,arXiv:1701.02003 Tendulkar,S.P.,Bassa,C.G.,Cordes,J.M.,etal.2017, ApJ,
Marcote,B.,Paragi,Z.,Hessels,J.W.T.,etal.2017, ApJ,834, 834,L7
L8 Thornton,D.,Stappers, B.,Bailes,M.,etal.2013,Science, 341,
Masui,K.,Lin,H.-H.,Sievers,J.,etal.2015,Nature,528,523 53
Meiksin,A.A.2009, ReviewsofModernPhysics,81,1405 Totani,T.2013,PASJ,65,L12
Metzger,B.D.,Berger,E.,&Margalit,B.2017,ArXive-prints, Wang,J.-S.,Yang,Y.-P.,Wu,X.-F.,Dai,Z.-G.,&Wang, F.-Y.
arXiv:1701.02370 2016,ApJ,822,L7
Murase,K.,Kashiyama,K.,&M´esz´aros,P.2016a, MNRAS,461, Xu,J.,&Han,J.L.2015,ResearchinAstronomyand
1498 Astrophysics,15,1629
Murase,K.,Meszaros,P.,&Fox,D.B.2016b,ArXive-prints, Xu,S.,&Zhang,B.2016a, ApJ,832,199
arXiv:1611.03848 —.2016b, ArXive-prints,arXiv:1610.03011
Petroff,E.,Bailes,M.,Barr,E.D.,etal.2015,MNRAS,447,246 Yang,Y.-P.,&Zhang,B.2016,ApJ,830,L31
Petroff,E.,Barr,E.D.,Jameson,A.,etal.2016,PASA,33,e045 Yang,Y.-P.,Zhang, B.,&Dai,Z.-G.2016, ApJ,819,L12
Piro,A.L.2016,ApJ,824,L32 Zhang,B.2014,ApJ,780,L21
PlanckCollaboration,Ade,P.A.R.,Aghanim,N.,etal.2015, —.2016, ApJ,827,L31
ArXive-prints,arXiv:1502.01589 —.2017, ArXive-prints,arXiv:1701.04094
Popov,S.B.,&Postnov, K.A.2010,inEvolutionofCosmic
Objects throughtheirPhysicalActivity,ed.H.A.
Harutyunian, A.M.Mickaelian,&Y.Terzian,129–132