GRB/GW association: Long-short GRB candidates, time-lag, measuring gravitational wave velocity and testing Einstein's equivalence principle

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by  Xiang Li

DraftversionAugust12,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
GRB/GWASSOCIATION:LONG-SHORTGRBCANDIDATES,TIME-LAG,MEASURINGGRAVITATIONALWAVE
VELOCITYANDTESTINGEINSTEIN’SEQUIVALENCEPRINCIPLE
XiangLi1,2,Yi-MingHu3,4,Yi-ZhongFan1,andDa-MingWei1
1KeyLaboratoryofdarkMatterandSpaceAstronomy,PurpleMountainObservatory,ChineseAcademyofScience,Nanjing,210008,China.
2UniversityofChineseAcademyofSciences,YuquanRoad19,Beijing,100049,China.
3MaxPlanckInstituteforGravitationalPhysics,AlbertEinsteinInstitute,Callinstraße38,D-30167Hannover,Germany.
6 4TsinghuaUniversity,30ShuangqingRd,Beijing,100084,China.
1
0 DraftversionAugust12,2016
2
ABSTRACT
g
u ShortdurationGRBs(SGRBs)arewidelybelievedtobepoweredbythemergersofcompactbinaries,like
A binary neutron stars or possibly neutron star-black hole binaries. Though the prospect of detecting SGRBs
withgravitationalwave(GW)signalsbytheadvancedLIGO/VIRGOnetworkispromising,noknownSGRB

1 hasbeenfoundwithintheexpectedadvancedLIGO/VIRGOsensitivityrangeforbinaryneutronstarsystem.
1 Wefind,however,thatthetwolong-shortGRBs(GRB060505andGRB060614)maybewithinthehorizon
of advanced GW detectors. In the upcoming era of GW astronomy, the merger origin of some long-short

] GRBs, asfavoredbythe macronovasignaturedisplayedin GRB060614,canbe unambiguouslytested. The
E
model-dependenttime-lagsbetweenthe mergerandthe onsetof the promptemission ofGRB are estimated.
H
The comparison of such time-lags between model prediction to the real data expected in the era of the GW
. astronomywould be helpfulin revealingthe physicalprocessestaking place at the centralengine (including
h
thelaunchoftherelativisticoutflow,theemergenceoftheoutflowfromthedensematerialejectedduringthe
p
mergerandtheradiationofgamma-rays).WealsoshowthatthespeedofGW,withorwithoutasimultaneous
-
o testoftheEinstein’sequivalenceprinciple,canbedirectlymeasuredanaccuracyof∼3×10−8cms−1oreven
r betterintheadvancedLIGO/VIRGOera.
t
s Subjectheadings:gamma-rayburst:general—stars:blackholes—stars:neutron—binaries:general
a
[

3 1. INTRODUCTION sient (i.e., GBM transient 150914) 0.4 s after GW150914
v Thecoalescenceofabinarycompactobjectsystem(eithera withafalsealarmprobabilityof0.0022(Connaughtonetal.
0 neutron-star(NS)binaryorastellar-massblackhole(BH)and 2016). If true, this is the first GW/SGRB association
8 NS binary) has been widely suggested to account for short- (see however Savchenko et al. 2016 for some arguments).
1 Lietal. (2016)comparedGBMtransient150914withother
duration gamma-ray burst (SGRB) events (Eichleretal.
0 SGRBsandfoundthatsuchaneventisremarkablydifferentin
1989; Narayanetal. 1992; Nakar 2007; Berger 2014) that
0 thepromptemissionproperties.Thebinaryblackholemerger
lasted typically shorter than 2 seconds in soft γ−ray band
. originaswellasits“distinguished”promptemissionproperty
1 (Kouveliotouetal. 1993). Since 2006, it had been sus-
suggestthatGW150914/GBMtransient150914isnotatypi-
0 pected that the compact object mergers could also produce
calGW/SGRBassociation.
6 theso-calledlong-shortGRBs(alsoknownasthesupernova-
1 less long GRBs which are apparently long-lasting but do In the absence of successful detection of the gravitational
: not show any signal of supernovae down to very strin- radiation triggered by a “normal” (S)GRB(Abadieetal.
v 2012;Aasietal. 2014a,b),a“smoking-gun”signatureforthe
gent limits) which share some properties of both long- and
i
X short-durationGRBs (Gehrelsetal. 2006;DellaValleetal. compact-binaryoriginwouldbethedetectionoftheso-called
Li-Paczynskimacronova(also called a kilonova),which is a
r 2006; Gal-Yametal. 2006; Zhangetal. 2007). The com-
a pact binary coalescence (CBC) is generally expected to be near-infrared/opticaltransientpoweredbytheradioactivede-
cay of r−process material synthesized in the ejecta that is
strong gravitational wave (GW) radiation source and are
launchedduringthemergerevent(e.g.,Li&Paczynski 1998;
prime target for some gravitational detectors like advanced
Kulkarni 2005;Metzgeretal. 2010;Barnes&Kasen 2013).
LIGO/VIRGO (Abadieetal. 2015; Acerneseetal. 2015;
Theidentificationofmacronovacandidatesintheafterglows
Belczynskietal. 2010, 2016, see also the latest LSC-Virgo
of the canonical short event GRB 130603B (Tanviretal.
white paper at https://dcc.ligo.org/LIGO-T1400054/public).
2013;Bergeretal. 2013), thelong-shortburstGRB 060614
On September 14, 2015 the two detectors of the Laser In-
(Yangetal. 2015; Jinetal. 2015) and the short event with
terferometerGravitational-WaveObservatory(LIGO) simul-
extended X-ray emission GRB 050709 (Jinetal. 2016) are
taneouslydetectedatransientgravitational-wavesignalfrom
stronglyinsupportoftheCBCoriginofsomeGRBs. Acon-
the merger of two black holes (GW150914, Abbottetal.
servative estimate of the macronova rate favors a promising
(2016)). GW150914 is the first direct detection of gravi-
detectionprospectoftheGWradiationbythe(upcoming)ad-
tational waves and the first identification of a binary black
vancedLIGO detectors(Jinetal. 2015). We anticipate that
hole merger (Abbottetal. 2016). Surprisingly, the Fermi
in the near future many compact-object-merger driven GW
Gamma-rayBurstMonitor(GBM)observationsatthetimeof
sources would be detected (Abadieetal. 2010) and a small
GW150914 claimed a detection of a weak gamma-ray tran-
fractionofsucheventswouldbeaccompaniedbysupernova-
Email:[email protected](YZF) lessGRBs(includingboththeshortandlong-shortevents).
2
The observation of a “nearby” supernova-less GRB Noneutronstar-blackhole(NS-BH)binarieshavenotbeen
provides a reliable estimate of the time, sky loca- directly observed yet (Lattimer 2012) but indirect evidence
tion and distance of a potential binary merger sig- forNS-BHmergerhasbeensuggestedinthemacronovamod-
nal. This significantly reduces the parameter space of eling (Yangetal. 2015; Jinetal. 2015). In a systematic
a follow-up GW search and consequently could be used analysis of the BH mass distribution based on 35 X-ray bi-
to reduce the effective detection threshold and effec- naries, Farretal. (2011) found strong evidence for a mass
tively increase the detectors’ sensitivity and their detec- gapbetweenthemostmassiveneutronstarsandtheleastmas-
tion rate (e.g., Kochanek&Piran 1993; Finnetal. 1999; siveblackholes,confirmingtheresultsofBailynetal. (1998)
Harry&Fairhurst 2011; Kelleyetal. 2013; Nissankeetal. andOzeletal. (2010). Forthelow-masssystems(combined
2013;Dietzetal. 2013;Williamsonetal. 2014;Clarketal. sampleofsystems),theyfoundablackholemassdistribution
2015; Bartos&Marka 2015). In this work we examine whose1%quantileliesabove4.3M (4.5M )with90%con-
⊙ ⊙
whethersomeSGRBsand/orlong-shortGRBsarewithinthe fidence.ThetypicalNS-BHbinarysystemsareexpecttohave
horizonof the advancedLIGO/VIRGO network and discuss amassratioof∼1:4,forwhichthesensitivedistanceofthe
the model-dependent time lag between the coalescence and aLIGO/AdVnetworkcanbeestimatedas
GRBs.
This work is structured as follows: In Sec. 2 we dis- D∗,NS−BH ≈690Mpc(9/ρ∗). (3)
cuss/summarize the prospect of detecting GW-associated
If ∼ 1/5 of short and long-short GRBs are produced by
GRBs in the era of advanced LIGO/VIRGO and examine
NS-BHmergers,whileaLIGO/AdVaremoresensitivetothe
whetheranyrecentGRBs(eitherSGRBsorlong-shortGRBs)
heavier NS-BH system, we expect around half of the CBC
are within the horizon of the advanced LIGO/VIRGO net-
eventsmighthaveanEMcounterparthasanoriginofNS-BH
work. In Sec. 3 the model-dependenttime lags betweenthe
mergers.
mergerandGRBsarepresentedandthepossibilityofreveal-
ing the nature of merger remnants with such time delays is
As an optimistic estimate (i.e., supposing most nearby
discussed. The expectedprogressin measuringthe speed of
SGRBs can be observed by Fermi GBM-like detectors), in
GWwiththefuturedataareinvestigatedinSec. 4.Ourresults
10yearsoffullrunofaLIGO/AdVnetwork∼ 10−20GW-
anddiscussionarepresentedinSec. 5.
associatedSGRBsareexpectedandpossiblyonehalfofthem
may have an NS-BH merger origin. The statistical study of
2. THEPROSPECTSOFDETECTINGGWSIGNALASSOCIATED
such a sample, though still limited, may shed valuable light
SGRBSANDLONG-SHORTGRBS
on the physical processes taking place at the central engine
2.1. TheprospectofdetectingSGRBsassociatedwithGW
(see Sec. 3 for the details) and possibly also the fundamen-
signals
talphysics(seeSec. 4forthedetails). InadditiontoSGRBs,
The strategy of the targeted search for GWs associ- somesupernova-lesslongGRBsmayalsohaveacompactob-
ated with short GRBs has been extensively discussed in jectmergeroriginandthedetectionrateofmergereventswill
Harry&Fairhurst (2011)andWilliamsonetal. (2014). The increase.
prospectofdetectingSGRBswithGWsignalshasalsobeen
widely estimated in the literature (e.g., Williamsonetal. 2.2. “Supernova-less”GRBswithinthesensitivitydistance
2014; Wanderman&Piran 2015; Clarketal. 2015) and in ofadvancedLIGO/VIRGOnetwork
thissubsectionwesimplysummarizetheirmainconclusions.
As shown in Sec. 2.1, the detection prospect of
GW-associated SGRBs is promising for the advanced
2.1.1. BNSmergers
LIGO/VIRGO network. The nearest short burst is GRB
Thesensitivedistancecanbeapproximatedas(Clarketal. 061201. It is measured to have a redshift of z = 0.111
2015) (Berger 2014, see however D’Avanzo et al. (2014) for
D∗,BNS ≈400Mpc(9/ρ∗), (1) the uncertainty), or a distance of 520 Mpc, which is lager
than D (ρ = 9). Note that most SGRBs are expected
where ρ is the signal-to-noiseof the GW signal. When the ∗,BNS ∗
∗ to be powered by BNS mergers, hence no single SGRB
advancedLIGO/VIRGOnetworkhasreacheditsfullsensitiv-
has been found within the averaged sensitive distance of
ity,withthe‘local’SGRBdetectionrateof4±2Gpc−3yr−1
theadvancedLIGO/VIRGOnetwork(Williamsonetal. 2014;
(Wanderman&Piran 2015),thedetectionrateoftheGWsig-
Wanderman&Piran 2015). Such a result is somewhat dis-
nalassociatedSGRBforafullskyγ−raymonitorisestimated
appointing though not in significant tension with the expec-
as
tation (see eq.(2)). To better explore the situation, in this
Rfullsky(ρ∗ =9)≈1±0.5yr−1, (2) work we also take into account all “nearby” (i.e., z < 0.3)
supernova-less long GRBs, including XRF 040701 (X-ray
where all SGRBs are assumed to originatefrom BNS merg-
flash,Soderbergetal. 2005),GRB060505andGRB060614
ers. SuchanassumptionseemsreasonablesincetheBH−NS
(Fynboetal. 2006). Pleasenotethatactuallysome“SGRBs”
mergerrateisgenerallyexpectedtobejust∼ 1/10timesthat
withtheso-calledextendedemissioncanalsobeclassifiedas
oftheBNSmergerrate(Abadieetal. 2010). Pleasenotethat
supernova-lesslongGRBs,butsucheventshavealsobeenin-
theLIGO/Virgonetworkcanboostgravitationalwavedetec-
cluded in previous GW/SGRB association studies. Below
tionratesbyexploitingthemassdistributionofneutronstars
wefocusonthe“traditional”long-shortGRBsandintroduce
within BNS system, and for searches with detected electro-
theminsomedetails.
magneticcounterpartsthedetectionratemayincreaseof60%
XRF040701waslocalizedbytheWide-FieldX-RayMoni-
(Bartos&Marka 2015).
toronboardtheHighEnergyTransientExplorer(HETE-2)on
2004July1.542UT.Itischaracterizedbytheverylowpeak
2.1.2. BH-NSmergers
frequency(i.e.,< 6keV)ofthepromptemission. Soderberg
3
et al. (2005)’s foreground extinction-corrected HST detec- Redshift (z)
tion limit is ≃ 6 mag fainter than SN 1998bw, the archety- 0 0.0457 0.0925 0.1404 0.1895 0.2400 0.2921 0.3457
pal hypernova that accompanied long GRBs (Galamaetal.
060614
1998), at a redshift of z = 0.21. The analysis of the X- 100 XRF040701
ray afterglow spectra reveals that the rest-frame host galaxy
extinction is constrained to A < 2.8 mag, suggesting
V,host
10
that the associated supernova, if there was, should be at
060505
least ∼3.2 mag fainter than SN 1998bw (Soderbergetal. s] 050724
2005). Due to the lack of the sufficient multi-wavelength T [90 1 GW150910461028001905A
afterglow data, the “absence” of a bright supernova associ-
ated with XRF 040701 did not attract wide attention. The
situation changed dramatically when the supernovae asso- 0.1 150101B 050709
ciated with GRB 060505 and GRB 060614 had not been 050509B
detected down to limits hundreds of times fainter than SN
1998bw (Fynboetal. 2006). Particularly, GRB 060614, a 0.01
bright burst with a duration of ∼ 102 s at a redshift of 0 200 400 600 800 1000 1200 1400
0.125,haddensefollowupobservationswithVeryLargeTele- Luminosity Distance [Mpc]
scope and Hubble Space Telescope. The physical origin
(either a peculiar collapsar or a compact object merger) of Fig.1.— The “nearby” (i.e., z ≤ 0.3) supernova-less GRBs, including
GRB060614wasdebatedoveryears(e.g.,Fynboetal. 2006; theSGRBsandthelong-shortGRBs,andtheaveragedsensitivitydistances
Gehrelsetal. 2006; DellaValleetal. 2006; Gal-Yametal. of advanced LIGO/VIRGO network (i.e., ρ∗ ≥ 9) for binary neutron star
mergers and neutron star-stellar black hole mergers. Theopen circles are
2006;Zhangetal.2007). There-analysisoftheopticalafter-
theSGRBsdiscussedintheliterature, includingGRB050724withadura-
glowemissionofGRB060614foundsignificantexcesscom- tion T90 = 3±1s(Foxetal. 2005). Thered filled circles are thelong-
ponentsinmulti-wavelengthphotometricobservations,which shortGRBs. ThedataaretakenfromBerger (2014),Fynboetal. (2006),
can be reasonably interpreted as a Li-Paczyn´ski macronova Soderbergetal. (2005)andLevanetal. (2015).Interestingly,thelong-short
that powered by the radioactive decay of debris following burstGRB060505iswithinD∗,BNS(ρ∗ = 9). Threeshortbursts(including
GRB061211,GRB080905AandGRB150101B)andthelong-shortburst
anNS-BHmergerwhiletheweaksupernovamodeldoesnot GRB060614arewithinD∗,NS−BH(ρ∗ =9). ThoughtheNS-BHmergerrate
work(Yangetal. 2015;Jinetal. 2015). As summarizedin isexpectedtobeoneorderofmagnitudelowerthanthatoftheBNSmerg-
Xuetal. (2009), the origin of GRB 060505 at a redshift of ersandhencemostsupernova-lessGRBsshouldhaveaBNSmergerorigin,
thereissomeevidenceforanNS-BHmergeroriginofGRB060614. Hence
z=0.089islessclear.Thepropertiesofitshostgalaxyseems
theGW signals ofGRB060614-like events taking place inthe era ofad-
tobeconsistentwiththatexpectedforthelong-durationGRBs vancedLIGO/VIRGOwouldbedetectable.Theadoptedcosmologicalmodel
(Tho¨neetal. 2008) butGRB 060505is anoutlierofthe so- parametersispresentedindetailinSec.4.1. GW150914isalsoincludedin
calledAmatirelationthatholdsforlongGRBs(Amatietal. theplotforillustration.Weremindthereadersthattheobservedgravitational
waveeventisabinaryblackholecoalesce.AlthoughforO1,advancedLIGO
2007). TheHSTobservationsatt ∼ 14.4daysaftertheburst
detectorsarenotyetsensitiveenoughtodetectNS-BHeventsfromthatdis-
did not find optical emission down to a limiting AB magni- tance,thisobservationofGW150914demonstratesthatCBCeventsdohap-
tudes of 27.3th in F814W band and 27.1th in F475W band pen within the NS-BH horizon of the full sensitive advanced LIGO/Virgo
network.
(Ofeketal. 2007). Suchstringentlimitsarestronglyatodds
with the collapsar modelbutcan be wellconsistentwith the
BNSmergermodelaslongasther-processejectahasamass signal. Therefore we suggest that the supernova-less long-
<10−3 M (Jinetal. 2016). duration XRFs/GRBs are one of prime targets for advanced
⊙
It may be still a bit early to conclude that all “nearby LIGO/VIRGOnetworkandthenatureofsuchakindof“mys-
supernova-less” long GRBs (i.e., “long-short GRBs”) are terious”eventswouldbeunambiguouslypinneddowninthe
from compact object binary mergers. The successful iden- eraofGWastronomy.
tificationofamacronovasignalinthelong-shorteventGRB
060614,nevertheless,renderssucha possibilitymoreattrac- 3. MODEL-DEPENDENTESTIMATESOFTIMELAGBETWEEN
BINARYCOALESCENCEANDGRBONSET
tivethanbefore.IftheNS-BHmergermodelforGRB060614
is correct, the luminositydistance of this eventis D ≈ 576 Thoughextensivelystudied,sofarthelaunching,accelera-
L
Mpc, which is smaller than D as long as ρ ≤ 10.8 tionandenergydissipationoftheGRBejectaarestillheavily
∗,NS−BH ∗
(see eq.(3)). For GRB 060505, the redshift z = 0.089 cor- debated(seeZhang 2014,foradedicatedreview).Insteadof
respondsto a luminositydistance D ≈ 400Mpc, whichal- carryingoutadvancedstudy ofa specific model, in thissec-
L
most equals to D for ρ = 9 (see eq.(1)). Intriguingly, tion we adopt some widely-discussed scenarios and present
∗,BNS ∗
among the supernova-less and short events detected so far ourmodel-dependentestimatesoftime lag betweenGW co-
(note that the GBM transient 150914 is still uncertain), the alescencetimeandGRBonset(i.e.,∆tGW−GRB)andexamine
long-shortburstGRB060505andGRB060614are theonly how a statistical study of ∆tGW−GRB could help us to better
candidatesthatmightyielddetectableGWsignalforthead- understandthe physicalprocessestakingplace at the central
vancedLIGO/VIRGOnetwork(seeFig.1). . engine.
ThepresenceoftwoSwiftGRBcandidateswithintheaver- In general, ∆tGW−GRB can be divided into two parts. One
agedsensitivitydistanceoftheadvancedLIGO/VIRGOnet- is the time delay between the merger time, which could be
work for ρ ≥ 9 is indeed very encouraging for the ongo- estimated by analyzing the GW data (e.g., Fairhurst 2011;
∗
ing GW experiments. On the other hand, if the supernova- Veitchetal. 2015), and the successful launch of the ultra-
less long-duration XRFs/GRBs were from a peculiar kind relativistic ejecta (i.e., ∆tlaun). The other is the time delay
of collapsar (which is very unlikely to be the case for GRB betweenthelaunchoftheultra-relativisticejectaandtheonset
060614), we can verify it with the non-detection of GW of the gamma-ray emission (i.e., ∆tem). Below we examine
∆t and∆t separatelyunderdifferentmodelsandthenget
laun em
4
thecorrespondingestimateof could range from tens of milliseconds to a few sec-
onds (see Faber&Rasio 2012, for a recent review).
∆t =∆t +∆t .
GW−GRB laun em For instance, in the presence of strong magnetic field,
Noticethatweareusingthecoalescencetime,whentheGW the magnetic braking effect can effectively transfer
signal spikes, as a proxy to the merger moment. One might the angular-momentum in a timescale τbr ∼ Rs/VA ∼
reasonably argue that these two are not identical, but as the 0.3 s (Rs/106cm)(ρ/1015gcm−3)12(ǫ/0.3)(Bs/1013G)−1,
binary system evolve very rapidly towards the merger, they where V is the Alfven’s velocity, R is the radius of the
A s
should not differ by more than a couple of rotations around neutron star and ǫ ∼ 0.3 is the expected strength ratio be-
themerger. ForBNSsystemsthemergerfrequencyisaround tween the surface magnetic field B and the interior polorial
s
1000Hz so the difference in time can not exceed ∼ 1ms magnetic field (Sharpiro 2000). Another mechanism is
(Fairhurst 2011;Pu¨rrer 2014). the magnetorotational instability (MRI), which generates
Inthisworkwefocusonthemostwidely-adoptedhypoth- turbulenceina magnetizedrotatingfluidbodythatamplifies
esis that the SGRBs were powered quickly after the merger the magnetic field and transfers angular momentum. In the
(i.e.,∆t < 10s). Howevernoticethatasmallamount presence of MRI, an effective viscosity is likely to be gen-
GW−GRB
of SGRBs seem to have precursor emission and the precur- eratedwith the effectiveviscousparameterν ∼ α c2/Ω ,
vis vis s c
sors are likely from the same central engine activity as the where α is the viscosity parameter, c is the sound ve-
vis s
main bursts (Charisietal. 2015). In the binary mergersce- locity of the envelope of the HMNS and Ω is the angular
c
nario,themergermaylikelyhappenedbeforetheprecursor.If velocityofthecoreofthedifferentially-rotatingneutronstar
so,thetime-lagbetweentheGWsignalandtheSGRB/long- (Balbus&Hawley 1991).Thus,theviscousangularmomen-
shortGRBcanbelongto∼ 100s, whichmaylabelthelife- tumtransporttimescalecanbeestimatedasτ ∼ R2/ν ∼
MRI s vis
time of the supramassive neutron star formed in the merger 0.1s(R /106cm)2(α /0.01)−1(c /0.1c)−2(Ω /104rads−1)−1
s vis s c
or alternativelythe fall-backaccretion timescale of the frag- (Hotokezakaetal. 2013a;Siegeletal. 2013). A reasonable
mentedpartofthecompactobject.Rezzolla&Kumar (2015) estimate of the termination timescale of the differential
argued that the BNS mergers might actually take place sev- rotation is τ = min{τ ,τ } ∼ 0.1 s, after which the
eralhoursbeforetheSGRBs. TheGW/GRBassociationob- HMNSisexpdeiffctedtocollabprseM.RI
servationscaneasilydistinguishbetweensuchscenarios(i.e., The situation is even less uncertain when both finite-
∆tGW−GRB ∼ 102−104s)withandtheshortdelaycases(i.e., temperatureeffectsintheequationofstateandneutrinoemis-
∆tGW−GRB < 10 s), asshownin Tab. 1. A longtime-lagbe- sion of the central compact object have been taken into ac-
tweentheGWandGRBsignals,inprinciple,couldalsoarise count. In the numerical simulations of the merger of bi-
fromthe supluminalmovementof theGW inthe vacuumor nary neutron stars performedin full generalrelativity incor-
its higher velocity than the photons in the gravitational po- porating the finite-temperature effect and neutrino cooling,
tential. Such possibility can be precisely tested as long as a Sekiguchietal. (2011) found that the effect of the thermal
sampleofGW/GRBassociationisestablished(seeSec.4.2for energy is significant and can increase M by a factor of
max
thedetails). 20%−30% for a high-temperaturestate with T ≥ 20 MeV.
Since they are notsupportedby differentialrotation, the hy-
3.1. ∆tlaunexpectedindifferentmergerscenarios permassive remnants were predicted to be stable until neu-
3.1.1. NS-NSmergers trinocooling,withluminosityof∼3−10×1053ergs−1,hasre-
movedthepressuresupportinτ ∼ 1s(Sekiguchietal.
The maximum gravitational mass of a cold non-rotating thermal
2011).
neutronstarisknowntobe M > 2 M (Antoniadisetal.
max ⊙ For t < τ , a baryon-loadedwind is continuouslyejected
2013) and the threshold for collapse of the merger-formed w
which would bound the bulk Lorentz factor of the jet to
remnantsintoblackholescanbeestimatedroughlyasM ≈
thres Γ ∼ 5(L /1052ergs−1)(M˙ /10−3M s−1)−1, where L is
1.35M (Shibata&Taniguchi 2006)Henceatotalgravita- w jet w ⊙ jet
tionalmmaaxss&2.7M⊙islikelyrequiredforpromptcollapseto theisotropic-equivalentluminosityofthejet, M˙w isthemass
loss rate via the wind and τ is the wind duration (either
a blackhole. Such massive neutronstar binariesshouldjust w
accountforasmallfractionofmergereventsifthemassdistri- τdiff orτthermal,dependingonthemechanismthatmainlysup-
ports against the collapse). Such a low Γ is too small to
butionof“cosmic”neutronstarbinariesresembleswhatwas w
giverise to energeticGRB emission. Hence it is widely an-
observed in the Galaxy (see Lattimer 2012, for a recent re-
view).Henceusuallywedonotexpectthepromptcollapseof ticipated that no GRB is possible unless the neutrino-driven
windgetsveryweakormorerealisticallytheneutronstarhas
the merger-formedneutronstars. Insteadthe mergerformed
collapsed to a black hole. After the collapse of the HMNS,
remnantsarewidelyexpectedtobeverymassiveneutronstars
with strong differential rotation that can support against the theearlierout-movingdensewindremainstohamperthead-
vance of the jet, whose injection lifetime, t , is determined
collapseatleasttemporarily. jet
by the viscous timescale of the accretion disk (Lee et al.
Such remnants are called the hypermassive neutron stars
(HMNSs). The fate of the post-merger HMNSs is how- 2004). Murguia-Berthieretal. (2014) suggested that in the
ever uncertain, and is contingent on the mass limit for blackhole centralengine modelfor (short)GRBs, the black
support of a hot, differentially rotating configuration (e.g., hole formation should occur promptly as any moderate de-
Baumgarteetal. 2000;Hotokezakaetal. 2013a). Belowwe lay at the hyper-massiveneutronstar stage wouldresult in a
presentthemodel-dependentestimatesofthecollapsetimeof choked jet. The argumentthat just the mergers with a rem-
theHMNSswhichweregardas∆t . Oneexceptionwould nant collapse within a timescale ∼ tdiff ∼ 0.1 s can produce
laun
bepresentedinthelastparagraphofthissub-subsection. (short)GRBsmayjustholdinthescenarioofenergyextrac-
When M < M < M , various mechanisms could tion via neutrino mechanisms. The accretion timescale of
max thres
act to dissipate and/or transport energy and angular mo- the torus formed in binary neutron star mergers can be es-
mentum, possibly inducing collapse after a delay which timated as tacc ∼ 0.1 s (αvis/0.1)−6/5 (Narayanetal. 2001;
5
Pophametal. 1999). Following Zalamea&Beloborodov Theexpectedtimedelaybetweenthemergerofthebinary
(2011) and Fan&Wei (2011), it is straightforward to es- neutronstarsandthelaunchoftheultra-relativisticGRBout-
timate the corresponding luminosity of the annihilated neu- flow can thus be approximately summarized as ∆t ∼
laun,BNS
trinos/antineutrinosas L ≈ 1049 ergs−1(m˙/0.1 M s−1)9/4, (0.01s, 0.1 s, 1 s) for (the promptformationof black hole,
νν¯ ⊙
where m˙ is the accretion rate and the spin of the black differentialrotationsupportedHMNS, thermalpressuresup-
hole has been taken to be a = 0.78, a typical value for portedHMNS),respectively.Theminimum∆t istaken
laun,BNS
the black hole formed in binary neutron star mergers. The to be ∼ 10 ms since the mergertime is expectedto be mea-
isotropic-equivalent luminosity of the ejecta is then L ≈ sured with an accuracy better than ∼ 10 ms and the ultra-
jet
2×1051 ergs−1(m˙/0.1 M s−1)9/4(θ /0.1)−2,whichsatisfies relativisticoutflowmaybelaunchedpromptly.
⊙ jet
the condition of relativistic expansionof the jet head within In the above discussion we assume that the short GRBs
the preceding neutrino-driven wind medium (i.e., eq.(8) of are produced when the HMNSs collapse into black holes.
Murguia-Berthieretal. (2014)) as long as m˙ > m˙ ≈ There is another possibility that the differentially-rotating
jet
0.2 M s−1. The accretion disk mass is M ∼ m˙ t ∼ NSs can eject a significant material towards the rotation
⊙ disk jet acc
axis which might also produce (short) GRBs. Such a sce-
0.02 M . Suchanaccretiondiskmassisconsistentwiththat
⊙
nario has attracted wide attention since the analysis of a
foundinnumericalsimulationsofbinaryneutronstarmergers
good fraction of afterglow emission of Swift short GRBs
(Faber&Rasio 2012; Nagakuraetal. 2014), which in turn
found possible evidence for the magnetar central engine
suggests that short GRBs are possible for t ≈ t > τ if
jet acc w
(Rowlinsonetal. 2013). One possible physical scenario is
τ <0.1s,inagreementwithMurguia-Berthieretal. (2014).
w thatthedifferentiallyrotatingneutronstarwrapsthepoloidal
Ifinsteadτ ≫0.1s,therequiredM wouldbetoomassive
w disk seed magnetic field into super-strong toroidal fields (B ∼
toberealistic(Fan&Wei 2011;Liuetal. 2015). f
1017 Gauss) that may emerge from the star through buoy-
The situation is significantly different for the magnetic
ancy and then generate GRBs via magnetic energy dissipa-
process to launch the GRB ejecta. The huge amount of
tion(Kluza´niak&Ruderman 1998;Daietal. 2006). Inthis
rotational energy of the black hole can be extracted ef-
model∆t isexpectedtobethetimeneededtoamplify
ficiently via the Blandford−Znajek process and the lumi- laun,BNS
nosity of the electromagnetic outflow can be estimated by theseedmagneticfieldto Bf ∼ 1017 Gauss, i.e., ∆tlaun,BNS ∼
LBZ ≈ 6 × 1049 ergs−1 (a/0.75)2(BH/1015 G)2, where 5 ms (Bf/1017G)(ǫ/0.3)(Bs/1015G)−1(∆Ω/6000rads−1)−1,
BH ∼ 1.1 × 1015 G (m˙/0.01 M⊙ s−1)1/2(RH/106 cm)−1 where ∆Ω ≡ 2π(1/Pc − 1/Ps), and Pc and Ps are the rota-
tional periods of the differentially rotating internal part and
is the magnetic field strength on the horizon of the
black hole (Blandford&Znajek 1977). Therefore m˙ ∼ mainNS,respectively(Kluza´niak&Ruderman 1998). With
0.01 M⊙ s−1 is sufficient to launch energetic ejecta with the Bs andthe initialrotationalperiodsof the magnetarcen-
L ∼ 1052 ergs−1(θ/0.1)−2. An α ≤ 0.01 is needed to tral engine estimated in Rowlinsonetal. (2013) we have
jet j ∆t ∼10−100ms.
get a t ∼ a few seconds. Such a “small” α is still pos- laun,BNS
acc
sible (Narayanetal. 2001) and the required accretion disk
mass is also in the reasonable range of ∼ 0.01 M . Please 3.1.2. NS-BHmergers
⊙
notethatintheseestimatetheejecta“breakout”criterionsug- In this case the central engine is a stellar mass black hole
gested in Murguia-Berthieretal. (2014) has been adopted. andthe regionalongthe spin axisof the black holeis likely
In reality, the Poynting-flux jet could break out from the cleanerthanthe case of NS-NSmergers. However,the joint
“neutrino-driven wind” more easily than the hydrodynamic effects of shocksduringthe disk circularization, instabilities
jet. This is because the reverse shock that slows down the at the disk/tail interface, and neutrino absorption unbinds a
hydrodynamic jet and the collimation shock that collimates small amount (∼ 10−4 M ) of material in the polar regions
⊙
it, cannot form within the Poynting-flux-dominated jet. As (Foucartetal. 2015). Over longer timescales, the neutrino-
a result the Poynting-flux dominated jet moves much faster poweredwindsbecomeactiveandejectmaterialinthepolar
and dissipates much less energy while it crosses the pre- regions. Though the material is still negligible compared to
ceding neutrino-driven wind (Brombergetal. 2014). The thematerialejecteddynamicallyin the equatorialplanedur-
latest time-dependent 3D relativistic magnetohydrodynamic ingthedisruptionoftheneutronstar,thisejectacouldimpact
simulations of relativistic, Poynting-flux dominated jets that theformationofarelativisticjet(Foucartetal. 2015). Nev-
propagateintomediumwitha spherically-symmetricpower- ertheless, a few percents of the energy radiated in neutrinos
law density distribution has found out that some instabili- is expected to be depositedin the regionalong the spin axis
ties can leads to efficient dissipation of the toroidal mag- of the black hole through νν¯ annihilations (Setiawanetal.
netic field component and hence the propagation of such a 2006; Jankaetal. 1999). The energy deposition at a rate
“headed”magnetizedejectaislikelysimilartothatofahydro- ∼ 1051 ergs−1 mightalso be able to powershortγ-rayburst
dynamicejecta (Bromberg&Tchekhovskoy 2015). In such (Foucartetal. 2014;Lee&Ramirez-Ruiz 2007).
a case, the “breakout” criterion of Murguia-Berthieretal. As in the BNS merger scenario, the magnetic mechanism
(2014) applies. After the “breakout” of the “headed” mag- may be more promising in launching ultra-relativistic out-
netized ejecta, an evacuated funnel presents and the later flows and then giving rise to GRBs. In the recent high-
ejecta moves freely without significant magnetic energy resolution numerical-relativitysimulations for the merger of
dissipation (i.e., it is within the phase of “headless” jet BH-NSbinariesthataresubjecttotidaldisruptionandsubse-
(Bromberg&Tchekhovskoy 2015)). Therefore, a tacc ∼ a quent formation of a massive accretion torus, the accretion
few seconds may be sufficiently long to successfully pro- torus formed quickly and the magnetic-field was amplified
duce GRBs for τw ∼ τthermal ∼ 1 s. The conclusion of significantlyduetothenon-axisymmetricmagnetorotational
this paragraph is that GRB is still possible in the case of instability and magnetic winding (Paschalidisetal. 2015;
τw ∼ τthermal ∼ 1 s but the outflow should be launched via Kiuchietal. 2015). Theamplificationcanyield B ∼ 1015 G
magneticprocesses.
attheBHpolesin∼20millisecondsafterthemergerandthe
6
correspondingBlandford-Znajekluminositycanbesufficient detectable(say,fortheNS-BHmergersatD ∼ 1Gpc),more
hightopowerGRBs. efficientemissionmaybecasedbythecollisionbetweenthe
For the role of the magnetic process in extracting the en- baryonicshellsejectedfromthesamecentralenginebutwith
ergy for the GRBs, the data of GRB 060614 likely has much different Lorentz factors. Strong internal shocks are
shed valuable light on. Such a long-short event is most generated and ultra-relativistic particles are accelerated. A
likely powered by the merger of a binary system of neutron fractionofinternalshockenergyhasbeenconvertedintomag-
star and stellar massblack hole(Yangetal. 2015;Jinetal. neticfieldandtheelectronsmovinginthemagneticfieldpro-
2015). As found in various numerical simulations, the to- duceenergeticγ−rayemission(Rees&Me´sza´ros 1994). In
tal mass of the accretion disk is expected to be not much such a model, the variability of the promptemission largely
more massive than ∼ 0.1 M . On the other hand, the du- traces the behavior of the activity of the central engine and
⊙
ration of the “long-lasting” soft γ−ray emission is ∼ 100 the onset of the “internal shock emission” is expected to be
s. Hence the time averaged accretion rate is expected to within the typical variability timescale of the prompt emis-
be just in order of m˙ ∼ 10−3 M s−1. For such a low ac- sionthatcanbe∼1−10ms(Piran 1999),i.e.,∆t ∼1−10
⊙ em
cretion rate, the neutrino mechanism is expected to be un- ms.
abletolaunchenergeticGRBoutflow(e.g.,Fanetal. 2005;
Liuetal. 2015). Instead,theBlandford−Znajekprocesscan 3.2.2. Themagneticoutflow
giverisetoPoynting-fluxdominatedoutflowwithan“intrin- In the case of the magnetic outflow, both the accelera-
sic”luminosityLBZ ≈6×1047ergs−1(a/0.75)2(BH/1014G)2 tionandthesubsequentenergy-dissipation/radiationaremore
(Blandford&Znajek 1977), which is sufficient to explain uncertain (see Kumar&Zhang 2015; Granotetal. 2015,
theobservedγ−rayluminosityofGRB060614afterthecor- for recent reviews). If the magnetic energy has been ef-
rection of a jet opening angle of the outflow θj ∼ 0.1 (see fectively converted into the kinetic energy of the outflow
Xuetal. 2009). Therefore,thesoftlong-lastinggamma-ray (Granotetal. 2015), the prompt emission of GRBs can
“tail”emissionofGRB060614likelyhasamoderatetohigh be from the magnetized internal shocks (Fanetal. 2004)
linearpolarization(Fanetal. 2005). or the photosphere with internal dissipation of energy via
Inviewofthesefacts,wesuggestthatultra-relativisticout- gradualmagnetic reconnection(Giannios 2008) and we ex-
flows may be launched within ∆tlaun,BHNS ∼10 milliseconds pect ∆tem ∼ 1 − 10 ms. Note that in the latest time-
aftertheBH-NSmergersviaeithertheneutrino-antineutrino dependent3Drelativisticmagnetohydrodynamicsimulations
annihilationormagneticprocess(es). of relativistic, Poynting-flux dominated jets that propagate
intomediumwithaspherically-symmetricpower-lawdensity
distributionhasfoundoutthatsomeinstabilitiescanleadsto
3.2. ∆temexpectedinbaryonicandmagneticoutflowmodels efficientdissipationofthetoroidalmagneticfieldcomponent
3.2.1. Thebayronicoutflow (Bromberg&Tchekhovskoy 2015), for which the onset of
thepromptemissionislikelydominatedbythephotospheric
The neutrino-antineutrinoannihilationprocesswill launch
radiationand∆t isignorablysmall.
an extremely-hot fireball. For such a kind of baryonic out- em
If the photospheric radiation is too weak to be detectable
flow, the acceleration is well understood (Piranetal. 1993;
forFermi-GBM-like detectorsdue to either the absenceof a
Me´sza´rosetal. 1993) and most of the initial thermal en-
dense wind-like medium in the direction of the black hole
ergy may have been converted into the kinetic energy of
spin or the small luminosity of the breaking out material,
the baryons at the end of the acceleration (Shemi&Piran
the observed onset of the prompt emission is likely signifi-
1990). A quasi-thermal emission component, however, is
cantlydelayed. In somemodelsmostofthe initialmagnetic
likely inevitable(see Chhotray&Lazzati 2015, andthe ref-
energy has not been converted into the kinetic/thermal en-
erences therein for the resulting spectrum). The quasi-
ergyoftheoutflowandthepromptemissionofGRBsisdue
thermal emission is mainly from the photosphere at a
to the magnetic energy dissipation at a rather large distance
radius R , which can be estimated as R ≈ 4.6 ×
ph ph R ∼ 1016 cm 1 possibly due to the breakdown of mag-
1010 cm (L/1051 ergs−1)(η/200)−3, where L is the total pro
netohydrodynamic approximation of the highly-magnetized
isotropic-equivalent luminosity of the baryonic outflow and
outflow (Usov 1994; Zhang&Me´sza´ros 2002; Fanetal.
η∼102−103istheinitialdimensionlessentropy(Paczynski
2005), or the current-driven instabilities developed in the
1990; Daigne&Mochkovitch 2002). Assuming an ini-
outflow shell (Lyutikov&Blandford 2003), or the inter-
tial launch radius of the fireball R ≈ 107 cm, at R
0 ph nal collision-induced magnetic reconnection and turbulence
the thermal radiation luminosity is expected to be L ≈
th (Zhang&Yan 2011). Correspondingly we have ∆t ≈
2.5×1049ergs−1(L/1051ergs−1)1/3(η/200)8/3(R /107cm)2/3. em
0 (1+ z)R /2η2c ≈ 2 s(1 + z)(R /1016 cm)(η/300)−2 (i.e.,
Andthequasi-thermalradiationpeaksatatemperatureT ∼ pro pro
th theradialtimescale),whichequalstothe“angulartimescale”
80keV(L/1051 ergs−1)1/4(η/200)2/3(R /107 cm)1/6. Forthe
0 oftheemission,theminimaltimescaleoftheGRBduration,
sourceswithin the advancedLIGO/VIRGO detectionranges
as long as the ejecta has an opening angle larger than 1/η
(i.e., D ≈ 300Mpc), the energyflux can be highup to F ∼
(Piran 1999). Since the angular timescale is derived for an
2×10−6ergs−1(L/1051ergs−1)1/3(η/200)8/3(R /107cm)2/3,
0 infinite-thin radiating shell, it is expected to be shorter than
whichisdetectableforSwiftorFermi-GBM.Theacceleration
the durationof the promptemission of the wholeGRB (i.e.,
timescale of the baryonicis ∼ (1+z)R0/c and the delaybe- ∆t ≤T ).
em 90
tweenthe terminationof the accelerationandthe emergence SGRB050509BandSGRB050709haveT = 0.04sand
ofthethermalphotonscanbeestimatedas∼(1+z)Rph/2η2c. 0.07s,respectively(Foxetal. 2005).Forsuch90“brief”events,
Forη≥100thelatterissignificantlysmallerthantheformer,
hence∆tem ∼(1+z)R0/c∼0.3ms(1+z)(R0/107cm),which 1 The magnetized internal shocks with significant magnetic dissipation
isignorablysmall. (Fanetal. 2004)cantakeplaceatamuchsmallerradius,say,∼1014−1015
If the photospheric quasi-thermal radiation is non- cm.
7
R ∼ 1016 cm is disfavored unless η & 2000. The η as withGWsignals(seeSec.2.1),wethinkthatintheeraofthe
pro
highas∼ 2000,however,wouldrenderthemtheoutstanding GWastronomy,reasonablylargeBNSmergerGRBsamples
outliersofthe correlationη ≈ 250(L /1052 ergs−1)0.3 hold- and NS-BH merger GRBs sample will be available and our
γ
ing for some long GRBs (Lu¨ etal. 2012; Fanetal. 2012; goalswillbe(atleastpartly)achievable.
Liangetal. 2015) and possibly also the short burst GRB
090510ifitsη&1200,asarguedinAckermannetal. (2010), 4. MEASURINGTHEVELOCITYOFTHEGRAVITATIONALWAVE
whereL istheγ−rayluminosityoftheGRB.Moreover,un- ANDTESTINGTHEEINSTEIN’SEQUIVALENCEPRINCIPLE
γ
lessthereisthefinetuningthatthecentralengineshutdown 4.1. MeasuringtheGWvelocity: the“canonical”approach
almost at the same time as the outflow breaks out the dense
According to general relativity, in the limit in which the
material, the central engines of these two very-short bursts
wavelength of gravitational waves is small compared to the
should be (promptly-formed) black holes and ∆t <
GW−GRB radiusof curvatureof the backgroundspace-time, the waves
T is expected. For SGRB 050709 the modeling of the
90 propagatewiththevelocityofthelight,i.e.,c(seeWill 1998,
macronova signal favors a NS-BH merger origin (Jinetal.
andthereferences).Inothertheories,thespeedv coulddiffer
2016), which is in supportof our currentargument(i.e., the g
fromc. Letusdefinetheparameter
centralengineofSGRB050709wasablackhole).
ς ≡(c−v )/c. (4)
g
3.3. Expectedrelationshipbetween∆tGW−GRB andT90
WesummarizeinTable1thesuspected∆t (i.e.,the Ifthe gravitationalwave velocityis subluminal(i.e., ς > 0),
GW−GRB
sum of ∆t and ∆t ), where the case of R ≪ 1016 cm thencosmicrayslosetheirenergyviagravitationalCherenkov
laun em pro radiationsignificantly.Thedetectionofultra-highenergycos-
includes the scenarios of photospheric radiation and regular
mic rays thus imposes a stringent constraint 0 ≤ ς ≤ 2 ×
(magnetized) internal shock radiation. Clearly, the shortest
delayisexpectedinthecasesofpromptBHformationinthe 10−15 (oreven2×10−19) (i.e., the “subluminal constraint”),
NS-NS mergers or the NS-BH mergers if the onset of the dependingontheGalacticorextragalacticoriginofsuchpar-
prompt emission is governed by the photosphere or regular ticles(Caves 1980;Moore&Nelson 2001). However,there
internalshocks(i.e.,R ≪1016cm)andsucheventswillbe isnotheoreticalargument(orpathology)againstGWsprop-
pro agating faster than light (see Nishizawa&Nakamura 2014;
valuable in imposing very stringent constraint on the differ-
Blasetal. 2016, and the references therein) and the weak
encebetweentheGWandthespeedoflight(seeSec.4forthe
bounds from radiation damping in binary systems are ς >
details).
−0.01 (Yagietal. 2013). The time-lag of arrival times be-
InSec.3.1.1wehavealreadymentionedthatthepromptfor-
tweentheGWandthesimultaneouslyradiatedphotonsis
mationofBHinBNSmergersislikelyuncommon. Aslong
as Rpro ≪ 1016 cm, one naturally expects that (1) for BNS 1 zo c
mergers∆t issignificantlylongerthanthatoftheNS- δt = (1+z) −1 dl
GW−GRB o
BH mergers, i.e., ∆tGW−GRB(NS−BH) ≪ ∆tGW−GRB(BNS); c Z0 vg !
(2) for NS-BH mergers, usually ∆tGW−GRB is expected to be 1 zo ς dt
shorter than T , i.e., ∆t (NS−BH) < T . While = , (5)
for R ∼ 109106 cm, weGWex−GpReBct that ∆t 9s0hould be H0 Z0 1−ς! ΩM(1+z)3+ΩΛ
pro GW−GRB
comparablewithT forbothBNSandNS-BHmergerpow- p
90 wheredl=cdz/[(1+z)H Ω (1+z)3+Ω ]isthedifferen-
ered SGRBs (Note that for some very-shortly lasting events 0 M Λ
suchasSGRB050509BandSGRB050709,R ∼ 1016 cm tialdistancethephotonshapvetraveled.Notethatinthiswork
pro wetaketheflatcosmologicalmodel(i.e.,Ω +Ω =1),Ω =
is most-likely disfavored). Therefore, with reasonable large M Λ M
0.315 and H ≈ 70 kms−1Mpc−1 is the Hubble’s constant
BNS mergerGRB sample andNS-BH mergerGRB sample, 0
(Adeetal. 2014;Riessetal. 2011). Ingeneral,ς maybea
thestatisticaldistributionof∆t andT foreachsam-
GW−GRB 90 functionoftheGWfrequency(f)andespeciallywhengravi-
pleoralternativelythedistributionof∆t forthecom-
GW−GRB tonmassisnon-zero(i.e.,m >0)thatgivesς≈m2c4/2h2f2,
binedsamplecouldshedvaluablelightonthecentralengine g g
physics. wherehisthePlanck’sconstant. Forsimplicityweassumea
constantς andfocusontheGW/electromagneticcounterpart
Are BNS mergers and NS-BH merger events distinguish-
able in the era of advanced LIGO/VIRGO? It is known that associationatredshiftsz ≪ 1. Henceeq.(5) yields(see also
GW observations can efficiently measure the binary’s chirp Will 1998;Nishizawa&Nakamura 2014)
mass M ≡ (m m )3/5/(m + m )1/5, which however leaves
1 2 1 2 200Mpc δt
the individual masses undetermined, where m1 and m2 are ς≈5×10−17 o . (6)
thegravitationalmassesofthebinarystars,respectively(e.g. D !(cid:18)1s(cid:19)
Bartosetal. 2013; Hannametal. 2013). Moreover,the ac-
Inrealityusuallythephotonsandthecoalescencearenotsi-
curacyofthereconstructionofthemassesisdecreasedbythe
multaneousand we have δt = (1+z)∆t −∆t , where
additionalmass-ratio-spin degeneracy. Fortunately, in many o e GW−ph
∆t and∆t arethedifferencesinarrivaltimeandemis-
cases the nature of the binary system can be determined. GW−ph e
siontime, respectively,of the GW andthe photons. Inmost
For instance, considering non-spinningcompact objects and
cases, it is rather hard to get a priori value for ∆t . Assum-
aρ ≈ 10,aM & 2.8M impliesthatoneofthebinarycom- e
∗ ⊙ ing ∆t = 0 (i.e., the GW and the electromagnetic counter-
pact objects has to have a mass > 3.2 M , above M for e
⊙ max partswereemittedsimultaneously;seeNishizawa (2016)for
anyreasonableNSmodels,whileaM . 1.2M suggestthat
⊙ amoregeneraldiscussion),weconstraintheabsoluteampli-
the mass of both compact objects need to be < 2M unless
⊙ tudeofςas
oneoftheNSsissmallerthan1M ,inwhichcasethelimitto
⊙
2th0e1h3e).avTioegreothbejercwtiisth3tMhe⊙e(xBpaerctotesdedteatle.ct2io0n13r;atHeaonfntahmeGetRaBl.s |ς|<5×10−17 200Mpc ∆tGW−ph . (7)
D ! 1s !
8
TABLE1
ExpectedtimedelaybetweenthecoalescenceandtheGRBonset(i.e.,∆tGW−GRB)a.
Mergers PromptRemnant Rpro≪1016cm Rpro∼1016cmb
BH ∼10ms ∼2s(1+z)(Rpro/1016cm)(η/300)−2
BNS DRSbHMNS ∼100ms ∼0.1s+2s(1+z)(Rpro/1016cm)(η/300)−2
TPSbHMNS ∼1s ∼1s+2s(1+z)(Rpro/1016cm)(η/300)−2
GRB−DiffNSc ∼10−100ms ∼0.1s+2s(1+z)(Rpro/1016cm)(η/300)−2
NS−BH BH ∼10ms ∼2s(1+z)(Rpro/1016cm)(η/300)−2
aNotethatinsomespecificcases∆tGW−GRB∼102−104sarepossible(e.g.Charisietal. 2015;Rezzolla&Kumar 2015),whichcanbeeasilydistinguished
fromthescenariossummarizedinthistableaslongasasampleofGW/GRBassociationhasbeenestablished.
bNotethatingeneralT90≥2s(1+z)(Rpro/1016cm)(η/300)−2.ForSGRs,unless(Rpro/1016cm)(η/300)−2≪1,∆tGW−GRBisexpectedtobecomparablewith
T90.
cDRSistheabbreviationof“Differentialrotationsupported”andTPSistheabbreviationof“Thermalpressuresupported”.
d GRB−DiffNSrepresentsthecaseofthatdifferentially-rotating NSdirectlylaunchesGRBoutflow(seethelastparagraphofSec.3.1.1forthediscussionon
suchakindofpossibility).ThiscaseisdifferentfromthefirstthreescenariosinwhichtheGRBejectaisassumedtobelaunchedwhenthegravitationalcollapse
takesplace.
Wecalltheaboveprocessasthe“canonicalapproach”ofmea-
suring the GW velocity directly, in which the graviton and 18
photon are assumed to have the same journey (i.e., the Ein-
19
stein’s equivalence principle (EEP) is guaranteed). The ad-
vantage is that as long as a GW/GRB association is estab-
20
lishedonecanconstrain|ς|directly. InSec.4.2weoutlinean
approachofmeasuringtheGWvelocitywithasimultaneous de 21 ZTF
u
testofEEP. nit
ag 22
Some widely discussed electromagnetic counterparts of m
a
compact object mergers include (Metzger&Berger 2012): Veg 23
(a)the(short)gamma-rayburstsandX-rayflares;(b)theaf-
LSST
terglowemissionofthe(off-beam)gamma-rayburstoutflows; 24
(c)themacronova/kilonovaemissionofthesub-relativisticr- 25 GGRRBB 005500772049
processmaterialejectedduringthemerger;(d)theradioradi- GRB 060505
GRB 060614
ationofthe forwardshockdrivenbythe sub-relativisticout- 26 GRB 061201
GRB 080905A
flow launched during the merger. These scenarios hold for
0.01 0.1 1 10
bothNS-NSandNS-BHmergers(pleasenotethatforsystems Time since trigger (days)
withverymassiveBHs,theNSswouldbeswallowedentirely
andnobrightelectromagneticcounterpartsareexpected). To Fig.2.—Ther-bandafterglowemissionofnearbySGRBsandlong-GRBs
constrain|ς| (see eq.(7)), the time delay between the merger if they took place at a luminosity distance ∼ 400 Mpc. The initial data
andthe“emergence”oftheelectromagneticcounterpart(i.e., areadoptedfromCovinoetal. (2006),Malesanietal. (2007),Ofeketal.
(2007),Xuetal. (2009),andFongetal. (2015).
∆t )isneeded.
GW−GRB
The intense gamma-rayemission is expected to be within
cuss the radio afterglow from SGRBs and long-short GRBs
secondsafterthemerger(seeTable1forthemodel-dependent
sincetheywererarelydetected(seeFongetal. 2015,andthe
estimate,where∆t isthesameasthe∆t needed
GW−GRB GW−ph references). If the GRB outflow is “off-beam” with an an-
in eq.(7)). The X-ray flares may appear within tens seconds
andsometimesmaylast∼103sorevenlonger.Thechallenge gleseparation∆θ, theforwardshockemissionwon’t“enter”
the line of sight until its bulk Lorentz factor has dropped to
ofdetectingthe“orphan”softX-raysignalisthelackofX-ray
≈ 1/∆θ (Jankaetal. 2006). The off-beam timescale is re-
detector(s)withawidefieldofviewuntilthesuccessfulper-
lated to the on-beamone as dt ≈ (1+Γ2∆θ2)dt . On the
formance of Einstein Probe (http://ep.bao.ac.cn;Yuanetal. off on
2014)after2022.SinceadvancedLIGO/VIRGOareexpected otherhand,wehaveΓ ≈ 7 Ek1,/581n−−12/8to−n3,/d8, whereEk,51 isthe
in full run in 2019, here we just focus on the detectors that kineticenergyoftheGRBoutflowinunitof1051ergs−1,n
−2
may (still) work at that time and hence will not discuss the is the numberdensity of the circum burstmediumin unitof
X-raysignalanylonger. 10−2 cm−3 and t is the timescale in unit of day. Hence the
d
If the ultra-relativistic outflow is “on-beam”, the opti- peak emission time of the “off-beam” relativistic ejecta can
cal/radioafterglowarerelativelylong-lastingandthepeakof be estimated as t ∼ 10 day E1/3n−1/3(∆θ/0.2)8/3. At such a
the forward shock optical emission is expected to be within k,51 −2
latetime,theforwardshockopticalemissionislikely(much)
102−103 secondsafterthemerger,mainlydependingonthe
dimerthan22th magforasourceatadistanceof∼ 400Mpc
initial bulk Lorentz factor of the outflow. The optical after-
(seeFig.2)andthedetectionprospectisnotverypromising.
glow emission of some on-beam GRBs, but missed by the
The radio emission caused by the sub-relativistic outflow
gamma-raydetector(s),areexpectedtobedetectableforZTF
isexpectedtopeakinyearsafterthemerger(Nakar&Piran
andLSST2 iftheburstsarewithinthesensitivitydistanceof
2011), too late to be of our interest. As for the macronova
advancedLIGO/VIRGOnetwork(seeFig.2). Wedonotdis-
emission, in ultraviolet/optical band peak is likely in a few
2 In2017theZwickyTransientFacility(ZTF)withaninstantaneousfield
ofview∼ 470degreesandanr-bandsensitivity ∼21thmagwillhavefirst 9.6deg2fieldofviewthatcanimageabout10,000squaredegreesofskyin
light at Palomar Observatory (http://www.ptf.caltech.edu/ztf). In one full threeclearnightsdowntolimitof∼24thmagnitude(Vegasystem)inr-band
nightthesurveyfieldofviewisexpectedtobe∼2.4×104 squaredegrees, areexpectedtoplayanimportantroleindetectingthenearbyGRBafterglow
almosthalfofthesky. TheLargeSynopticSurveyTelescope(LSST)witha andeventhemacronovae(Ivezic´etal. 2008).
9
which the Shapiro time-delay can be well approximated by
10-10
BNS (Longo 1988;Sivaram 1999;Misneretal. 1973;Wuetal.
NS-BH 2016)
10-12 ∆t ≈∆γGMMW ln D
gra c3 (cid:18)b(cid:19)
M ln(D/b)
10-14 ≈1.7×107s∆γ MW , (8)
| 6×1011M⊙! 4ln10
V|
where M ≈ 6×1011 M is the massof MilkyWay, D is
10-16 MW ⊙
thedistanceofthecosmologicaltransienttotheEarth,andbis
theimpactparameteroftheparticlepathsrelativetotheMilky
10-18 Waycenter, andwe havenormalizedln(D/b)tothevalueof
4ln10toaddressthefactsthatD∼100Mpcintheadvanced
LIGO/VIRGOeraandd ∼10kpc.
10-20 Asinthe“canonicalapproach”,weassumethatvgisacon-
GRB on-beam afterglow macronova stant. Then the observed time delay consists of three parts,
i.e.,
∆t =∆t −δt +∆t . (9)
Fig.3.—ExpectedconstraintsonthedifferencebetweentheGWpropaga- GW−ph e o gra
tionvelocityandthespeedoflight(i.e.,|ς|)inthecasesofdifferentkinds where δt ≈ 2 × 1016 s ς(D/200 Mpc). In the specific
ofelectromagneticcounterparts. Thesolidanddashedrectanglesareforbi- o
naryneutronstarmergersandneutronstar-stellar-massblackholemergers, modelof“DarkMatter Emulators”theGWs areexpectedto
respectively. arrive earlier than the simultaneously-emitted GRB photons
by ∼ 103 days (Desaietal. 2008). While in reasonable as-
days while the infrared emission may peak in one or two
trophysical models the GW signal should precede the GRB
weeks(seee.g.Li&Paczynski 1998;Barnes&Kasen 2013;
for a given source. Hence an almost simultaneous arrival
Hotokezakaetal. 2013b, for the theoretical predictaions;
of the GW/GRB signals requires a subluminal GW with a
Please see Jin et al. 2015 for the first observed multi- ς ∼ 4×10−9(D/200Mpc), whichviolatesthe“submuminal
epoch/band macronova lightcurve). As shown in Jinetal.
constraint”setbytheultra-highenergycosmicrays(i.e.,0 <
(2016), macronova emission are likely to have a very-
ς<2×10−15)andinturnrulesouttheDarkMatterEmulators
promising detection prospect and can serve as ideal electro-
but favors the dark matter model (see also Kahya&Desai
magneticsignal of the mergerevents. The typicaldiscovery
(2016) for the discussion on the possible GW150914/GBM
timescaleislikely∼1−10days.
transientassociation).
We therefore conclude that if the electromagnetic coun-
If two events of GW/electromagnetic counterpartassocia-
terpartsare (promptGRB emission, on-beamforwardshock
tion are observed (which are marked by subscript 1 and 2,
emission,macronovaemission),
respectively),wehave
∆tGW−ph ∼0.01−1s, 0.01−1day, 1−10days, ∆γ=5.5×10−7 MMW −1 D2∆tG′W−ph,1−D1∆tG′W−ph,2,
Freisgp.3e.ctPivoeslsyib.lyTihneaefxewpeycteeadrs,co|ςn|s<tra1i0n−ts18oisnaςchaierevasbhleo.wn in 6×1011 M⊙! D2ln(Db11)−D1ln(Db22)
(10)
and
4.2. MeasuringtheGWvelocitywithasimultaneoustestof
Einstein’sequivalenceprinciple 100Mpc ln(D2)∆t′ −ln(D1)∆t′
Inthissubsection,weconsiderasimultaneousconstrainton ς =10−16 h b2 GW−ph,1 b1 GW−ph,2i,
D ln(D /b )−D ln(D /b )
thedepartureofGWvelocityfromthespeedoflightandthe 2 1 1 1 2 2 (11)
possibleviolationdegreeofEEPwithasetofGW/GRBasso- where ∆t′ ≡ ∆t − ∆t and ∆t′ ≡
ciation data. Within the framework of parameterized post- GW−ph,1 GW−ph,1 e,1 GW−ph,2
∆t −∆t (Note that the relationship ∆t ≥ ∆t ,
Newtonian approximation (PPN), deviations from EEP are GW−ph,2 e,2 GW−ph e
as expected in general relativity, may be invalid for current
described by the parameter γ, which is 1 in general relativ-
modelassumption).ForasetofGWsignalswithelectromag-
ity (Will 2014). In general, the Shapiro time-delay is cal-
neticcounterparts,the (∆t , D, b)areavailableandthe
culated bytgra = −1c+3γ rroeU r(t);t dr, where the integration main uncertainty on constGraWin−pinhg ς and ∆γ are the accuracy
isalongthepathoftheRphoto(cid:16)nemi(cid:17)ttedformthesourceatr of estimating ∆t . Here we do not simply take ∆t as zero
e e e
andreceivedatr ,andU r(t);t isthegravitationalpotential and focuson the events of SGRBs or short-longGRBs with
o
associatedGWsignals,forwhich∆t canberelativelyreason-
(Shapiro 1964). IfthePP(cid:16)Npar(cid:17)ameterγarevariablefordif- e
ablyestimated(seeTable1). Inparticular,forNS-BHmerger
ferentspeciesofneutralparticles,twokindsofparticlesemit-
GRBs we expect that ∆t ≤ T (unless T is significantly
ted simultaneously from the source would arrive at different e 90 90
shorter than ∆t (∼ 10 ms) that has not been recorded by
times,andthecorrespondingtime-lagisgovernedby∆t = laun
gra Swiftyet).
−∆c3γ rroeU r(t);t dr(Longo 1988;Krauss&Tremaine 1988; Theconservativeconstraintson|∆γ|and|ς|are
SivarRam 1(cid:16)999;S(cid:17)hapiro 1964). Inthisworkwefocusonthe
Shapirotime-delaybetweenphotonsandGWscausedbythe |∆γ|≤5.5×10−7 MMW −1
gravitationalpotentialoftheMilkyWay(seeSivaram(1999) 6×1011 M⊙!
for the brief idea and Wu et al. (2016)for the dedicated in- |D ∆t −D ∆t |+|D ∆t −D ∆t |
2 GW−GRB,1 1 GW−GRB,2 2 e,1 1 e,2
vestigation). Moreover,weadopttheKeplerianpotential,for ,
|D ln(D /b )−D ln(D /b )|
2 1 1 1 2 2
10
(12) skycontinuallytogettheaccurateinformationoftheprompt
emissionproperties.
and IntheeraoftheadvancedLIGO/VIRGO,reasonablylarge
BNS merger GRB samples and NS-BH merger GRB sam-
|ς|≤10−16 ples are establishable (see Sec.2). Motivated by such a
ln(D2)|∆tGW−GRB,1−R∆tGW−GRB,2|+|∆te,1−R∆te,2|, fact,wehaveexaminedthepossibledistributionof∆tGW−GRB
b2 |100DM2pcln(D1/b1)− 100DM1pcln(D2/b2)| panled. thAesresluatmiomnabrieztewdeeinn TTa90b.and1,∆itnGWth−eGRcBasfeoroefacRh sam≪-
pro
(13) 1016 cm that represents the scenarios of photospheric ra-
diation and regular (magnetized) internal shock radiation,
respectively,whereR≡ln(D /b )/ln(D /b ).Ifinthefuture
1 1 2 2 it is expected that (1) for BNS mergers ∆t is sig-
data people can identify two or more NS-BH merger GRBs GW−GRB
nificantly longer than that of the NS-BH mergers, i.e.,
associated with GW signals, as a conservative estimate we
∆t (NS−BH)≪∆t (NS−NS);(2)forNS-BH
takeintoaccountthefactthat|∆t −R∆t |< ∆t +R∆t GW−GRB GW−GRB
e,1 e,2 e,1 e,2 mergers,usually∆t isexpectedtobeshorterthanT ,
and further replace ∆t by T . For D ≥ 1.5D , b ∼ b , GW−GRB 90
e 90 2 1 2 1 i.e., ∆t (NS−BH) < T . While forR ∼ 1016 cm,
∆t ≈ ∆t and T ≈ T , the above two GW−GRB 90 pro
GW−GRB,1 GW−GRB,2 90,1 90,2 weexpectthat∆t shouldbecomparablewith T for
constraints(on|∆γ|and|ς|)furtherreduceto GW−GRB 90
both BNS and NS-BH merger powered SGRBs. The com-
parison with future real data will be helpfulin revealingthe
M −1 ∆t +T
|∆γ|<6×10−8 MW GW−GRB,1 90,1, (14) centralenginephysics.Wewouldliketoalsopointoutthatin
6×1011 M⊙! [ln(D1/b1)/4ln10] somespecificastrophysicalornewphysicsscenarios,theGW
may precedethe GRB signal significantly (i.e., ∆t >
GW−GRB
and 10 s). If such large time-lags indeed presents in the future
data, the statistical study of the distribution of ∆t >
(∆t +T ) ln(D /D ) GW−GRB
|ς|<10−17 GW−GRB,1 90,1 2 1 . 10scandistinguishbetweentheastrophysicalmodel(forex-
[ln(D1/b1)/4ln10] [(D2−D1)/100Mpc] ample the model proposed in Rezzolla&Kumar (2015) for
(15)
someBNSmergersbutnotforNS-BHmergers)andthenew
Interestingly,suchconstraintscanbeastightastheboundson
physics(e.g.,thesupluminalmovementoftheGW).
∆γor|ς|setbyexcludingeithertheEEPtestorthedeparture Totightlyconstrainthe differencebetweentheGW veloc-
ofvgfromc. ityandthespeedoflight,theshorter∆t thebetter(see
GW−ph
Sec.4). If the electromagnetic counterpart of GW signal is
5. DISCUSSION GRB,wehave∆tGW−ph = ∆tGW−GRB. Theshortest∆tGW−GRB
isexpectedforthepromptBHformationintheNS-NSmerg-
SGRBs arewidely believedto be poweredbythe mergers
ers or the NS-BH mergers if the onset of the prompt GRB
ofcompactobjectbinaries.NotethattheBH−NSmergerrate
emission is governed by the photosphere or regular internal
isgenerallyexpectedto be∼ 1/10timesthatof theNS−NS
mergerrate(Abadieetal. 2010).HencemostSGRBsareex- shocks (i.e., Rpro ≪ 1016 cm), in such a case the constraint
pected to be from NS−NS mergers and a small fraction of |ς|<10−16oreventighterispossible(IftheGW150914/GBM
events may be due to NS−BH mergers. Though in the up- transient 150914 association is intrinsic, |ς| < 10−17 is in-
comingeraofadvancedLIGO/VIRGOnetworktheprospect ferred, as shown in Lietal. (2016) and Ellisetal. (2016)).
of detecting GW-associated SGRBs is promising, none of WithtwoGW/GRBassociationeventsthatareexpectedtobe
the nearby (i.e., z < 0.2) SGRBs are found within the sen- availableinthenearfuturewecanmeasuretheGWvelocity
sitivity distance of the upcoming advanced LIGO/VIRGO with a simultaneous test of EEP. Intriguingly, in such treat-
network D ≈ 400 Mpc (9/ρ ) for ρ ≥ 9. Such a ments very accurate measurements/tests are still achievable
∗,BNS ∗ ∗
non-identification,thoughstillunderstandable(seeeq.(3)),is (seeSec.4.2).
somewhatdisappointing. Interestingly,wefindoutthatGRB
060505,onesupernova-lesslongevent(alsoknownas long- ACKNOWLEDGMENTS
shortGRB), ifpoweredbya NS-NSmerger,is likelywithin We thank the anonymous referee for helpful suggestions,
the distance of D (ρ ≈ 9). The other long-short burst Tsvi Piran for the discussion, Chris Messenger and Imre
∗,BNS ∗
GRB 060614, accompanied with a macronova signal that is Bartos for the comments. This work was supported in
plausiblypoweredbyaNS−BHmerger,iswithinthedistance part by National Basic Research Programme of China (No.
of D (ρ ≈ 9). ThereforeintheeraofGWastronomy, 2013CB837000 and No. 2014CB845800), NSFC under
∗,NS−BH ∗
the compact object binary merger origin of some long-short grants11525313(i.e.,FundsforDistinguishedYoungSchol-
GRBs, as favored by the macronova signature displayed in ars),11361140349,11273063and11433009,theFoundation
GRB 060614,willbe unambiguouslytested. We hencesug- forDistinguishedYoungScholarsofJiangsuProvince,China
gest that both SGRBs and long-short GRBs are prime tar- (GrantNo. BK2012047)andtheStrategic PriorityResearch
gets of the advanced LIGO/VIRGO network and γ−ray de- Program(GrantNo. XDB09000000).
tectorswithwidefieldofviewsareencouragedtomonitorthe
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