Black hole accretion in gamma ray bursts

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by  Agnieszka Janiuk

Article
Black hole accretion in gamma ray bursts
AgnieszkaJaniuk1*,MichalBejger2,PetraSukova1,andSzymonCharzynski1,3
1 CenterforTheoreticalPhysics,PolishAcademyofSciences,Al.Lotnikow32/46,02-668Warsaw,Poland;
[email protected]
2 NicolausCopernicusAstronomicalCenter,PolishAcademyofSciences,ul.Bartycka18,00-716Warsaw,
Poland;[email protected]
2 ChairofMathematicalMethodsinPhysics,UniversityofWarsaw,ul.Pasteura5,02-093Warsaw,Poland
* Correspondence:[email protected]
7 AcademicEditor:name
1 Received:date;Accepted:date;Published:date
0
2 Abstract: We study the structure and evolution of the hyperaccreting disks and outflows in the

n gamma ray bursts central engines. The torus around a stellar mass black hole is composed of
a
free nucleons, Helium, electron-positron pairs, and is cooled by neutrino emission. Accretion of
J
matterpowerstherelativisticjets,responsibleforthegammaraypromptemission. Thesignificant
6
2 numberdensityofneutronsinthediskandoutflowingmaterialwillcausesubsequentformationof

heaviernuclei.Westudytheprocessofnucleosynthesisanditspossibleobservationalconsequences.
]
E We also apply our scenario to the recent observation of the gravitational wave signal, detected on
H September14th, 2015bythetwoAdvancedLIGOdetectors, andrelatedtoaninspiralandmerger
. ofabinaryblackholesystem. AgammarayburstthatcouldpossiblyberelatedwiththeGW150914
h
p eventwasobservedbytheFermisatellite. Ithadadurationofabout1secondandappearedabout
- 0.4 seconds after the gravitational-wave signal. We propose that a collapsing massive star and a
o
r blackholeinaclosebinarycouldleadtotheevent. Thegammarayburstwaspoweredbyaweak
t
s neutrinofluxproducedinthestarremnant’smatter.Lowspinandkickvelocityofthemergedblack
a
[ holearereproducedinoursimulations.Coincidentgravitational-waveemissionoriginatesfromthe

mergerofthecollapsedcoreandthecompanionblackhole.
1
v
3 Keywords: blackholephysics;accretion,accretiondisks;gravitationalwaves;neutrinos
5
7
7
0
. 1. Introduction
1
0
Gamma-ray bursts (GRBs) are energetic, transient events observed in the sky at high energies.
7
1 Their known cosmological origin requires a physical process that causes them to be a cosmic
: explosion of great power. Proposed mechanisms involve the creation of a black hole (BH) in a
v
i cataclysmic event. This may either result from the collapse of a massive rotating star, or via the
X
mergerofcompactobjects’binary,e.g. neutronstars(NSs)oraBHandaneutronstar. Theso-called
r
a ‘centralengine’ofthisprocessiscomposedofahotanddenseaccretiondiskwithahyper-Eddington
accretionrate(uptoafew M(cid:12)s−1)nearaspinningBH.
InthehyperaccretingdisksthatarepresentaroundtheBHsinthecentralengine, thedensities
and temperatures are so high, that the equation of state (EOS) can no longer be assumed to be of
an ideal gas. The pressure and chemical balance is required by the nuclear reactions that take part
betweenthefreeprotons,neutrons,andelectron-positronpairsabundantintheplasma. Thecharged
particles must satisfy the total neutrality condition. In the β reactions, neutrinos are produced in
threeflavorsandaresubjecttoabsorptionandscatteringprocesses. Thepartiallytrappedneutrinos
contribute to the pressure in the plasma, together with nucleons, electron-positron pairs, radiation,
andsynthesizedheavierparticles(Helium).
Galaxies2016,xx,x;doi:10.3390/—— www.mdpi.com/journal/galaxies
Galaxies2016,xx,x 2of11
Numerical computations of the structure and evolution of the accretion flows in the gamma
ray bursts engine were historically first carried out with the use of steady-state, and later with the
time-dependent models. These models were axially and vertically averaged, and used the classical
α-parameterprescriptionfortheviscosity(Pophametal.1999;DiMatteoetal.2002;Kohrietal.2002,
2005; Chen&Beloborodov2007; Reynosoetal. 2006; Janiuketal. 2004; 2007; 2010). Morerecently,
accretion flows are described by fully relativistic MHD computations (e.g., Barkov & Komissarov
2011;Janiuketal. 2013). Thismethodhasalsobeenappliedrecentlytodescribethecentralengineof
aputativegammarayburstwhichcouldbeassociatedwiththeeventGW150914(Janiuketal. 2017).
Herewereportonthiswork,andinaddition,wealsopresentnewresultsonthenucleosynthesisof
heavyelementsintheaccretionflowinthisengine.
2. AccretionflowintheGRBengine
2.1. Equationofstate
In the EOS, contribution to the pressure comes from free nuclei and e+ −e− pairs, helium,
radiationandtrappedneutrinos:
P = P +P +P +P ,
nucl He rad ν
whereP includesfreeneutrons,protons,andtheelectron-positrons:
nucl
Pnucl = Pe−+Pe++Pn+Pp
with √
2 2(m c2)4 (cid:20) 1 (cid:21)
P = i β5/2 F (η,β )+ β F (η,β ) .
i 3π2 (h¯c)3 i 3/2 i i 2 i 5/2 i i
Here, F are the Fermi-Dirac integrals of the order k, and η , η and η are the reduced chemical
k e p n
potentials, η = µ /kT is the degeneracy parameter, µ denoting the standard chemical potential.
i i i
Reducedchemicalpotentialofpositronsis ηe+ = −ηe−2/βe. Relativityparametersaredefinedas
β = kT/mc2. ThetermP ,describingthepressureofradiation,scaleswiththetemperatureasT4,
i i rad
andisaddedheretogetherwiththepressureofneutrinos,P ,whichiscomputedfromthetwo-stream
ν
approximation (see details in Janiuk et al. 2007). The disk is fully opaque to photons, however the
radiationpressureisstillbyseveralordersofmagnitudesmallerthanthepressureofneutrinos. This
EOS is computed numerically by solving the balance of nuclear reactions (Yuan 2005; Janiuk et al.
2007;Janiuk&Yuan2010;seealsoLattimer&Swesty1991;Setiawanetal. 2004).
2.2. NeutrinocoolingoftheaccretionflowinGRBs
Inthehotanddensetorus,withtemperatureof∼1011 Kanddensity> 1010 gcm−3,neutrinos
are efficiently produced. The main reactions that lead to their emission are the electron/positron
capture on nucleons, as well as the neutron decay. Their nuclear equilibrium is described by the
followingreactions:
p+e− → n+ν
e
p+ν¯ → n+e+
e
p+e−+ν¯ → n
e
n+e+ → p+ν¯
e
n → p+e−+ν¯
e
n+ν → p+e−,
e
Galaxies2016,xx,x 3of11
and the forward and backward reaction rates are equal. The reaction rates are given by the
appropriateintegrals(Reddy,Prakash&Lattimer1998;seealsoAppendixAinJaniuketal. 2007).
Otherneutrinoemissionprocessesare: electron-positronpairannihilation,bremsstrahlungand
plasmondecay:
e−+e+ → ν +ν¯
i i
n+n → n+n+ν +ν¯
i i
γ˜ → ν +ν¯ .
e e
Wecalculatetheirratesnumerically,withproperintegralsoverthedistributionfunctionofrelativistic,
partiallydegeneratespecies.
The neutrino cooling rate is finally given by the two-stream approximation, and includes the
scatteringandabsorptiveopticaldepthsforneutrinosofallthreeflavors(DiMatteoetal. 2002):
Q− = 87σT4 ∑ 1 × 1 [ergs−1cm−3].
ν 34 i=e,µ,τ τa,˚2i+τs + √13 + 3τa1,˚i H
Theneutrinocoolingisself-consistenltycomputedfromthebalanceofthenuclearreactions,listedin
Section2.2,whoseratesgovernthevaluesoftheabsorptiveopticaldepthsforelectron(allreactions)
and muon or tau neutrinos (pair annihilation and bremsstrahlung reactions). Also, the neutrino
scatteringopticaldepthiscomputed,usingthevaluesofprotonandneutronnumberdensities,and
Cabbiboangleofsin2θ = 0.23(seeYuan2005,Janiuketal. 2007). Theemissivityisaveragedover
C
thediskheight,insteadoftheintegrationovertheneutrinosphere,whoseshapeisrathercomplex.
2.3. GRMHDscheme
OursimulationsoftheaccretionflowdynamicsintheGRBcentralenginewereperformedwith
a 2D code HARM (High Accuracy Relativistic Magnetohydrodynamics; Gammie et al. 2003). Our
versionofthecodewasextendedtoincludethemicrophysics,describedinthepreviousSection. The
codeprovidesasolverforthecontinuityandenergy-momentumconservationequations:
(ρuµ) =0
;µ
Tµ =0
ν;µ
P = Kργ = (γ−1)u
where:
Tµν = Tµν +Tµν
gaz EM
Tµν = ρhuµuν+pgµν = (ρ+u+p)uµuν+pgµν
gaz
Tµν = b2uµuν+ 1b2gµν−bµbν; bµ = u ∗Fµν
EM 2 ν
whereuµisthefour-velocityofgas,uistheinternalenergydensity,bµ = 1εµνρσu F isthemagnetic
2 ν ρσ
four-vector, and F is the electromagnetic stress tensor. The metric tensor is denoted by gµν. Within
theforce-freeapproximation,wehaveE = u Fµν =0.
ν µ
HARM-2D uses a conservative numerical scheme to obtain solutions of equations of the
followingtype:
∂ U(P) = −∂ Fi(P)+S(P),
t i
where U denotes a vector of “conserved” variables (momentum, energy density, number density,
taken in the coordinate frame), P is a vector of ’primitive’ variables (rest mass density, internal
Galaxies2016,xx,x 4of11
energy), Fi are the fluxes, and S is a vector of source terms. In contrast to non-relativistic MHD,
where P → U and U → P haveaclosed-formsolution, inrelativisticMHD, U(P) isacomplicated,
nonlinear relation. Inversion P(U) is calculated therefore numerically, at every time step. The
inverse transformation requires a solution to 5 non-linear equations, done here by means of a
multi-dimensionalNewton-Raphsonroutine(see,e.g.,Nobleetal. 2006fordetails).
Theprocedureissimple,ifthepressure-densityrelationisadiabatic.However,forageneralEOS,
onemustalsocomputedp/dw,dp/dv2 and p(W,v2,D),wherew = p+u+ρdenotestheenthalpy,
√
W = γ2w, D = −gρut, and v2 = gµνuµuν. In our scheme, we have tabulated (p,u)(ρ,T) values
and then interpolate over this table. The Jacobian ∂U/∂P is computed numerically. The conserved
variablesarethenevolvedintime.
HARM-2D has been MPI-parallelized for the hydro-evolution, and also implemented with the
shared memory hyperthreading for the EOS-table interpolation. Our 2D simulations typically run
up to t=2000-3000 M (within a couple weeks of computations on the local cluster, or a few days on
Cray XC40 with 1k nodes). The computations are performed in the polar coordinate system, with
resolutionof256x256pointsintherandθdirections.
2.4. Examplesimulationresults
Parameters used in our computations are: BH mass, with a fiducial value of M = 10M(cid:12), BH
spin a = 0.6−0.98, and accretion disk mass Md ≈ 1M(cid:12), which gives the scaling for the density
in physical units, needed for the EOS computations. To describe the rotationally-supported torus
aroundaspinningBHweusetheinitialconditiongivenbytheequilibriumsolution,firstdeveloped
analytically by Fishbone & Moncrief (1976) and Abramowicz et al. (1978). We adopt the polar
coordinate system, r−θ, and use the Kerr-Schild coordinates to avoid the coordinate singularity
ontheBHhorizon. Initially,apoloidalconfigurationofthefieldisassumed,withthevectorpotential
A = (ρ/ρ ), and initial normalization of P /P = 50. Magnetic turbulences develop within
φ max gas mag
the dense matter torus and the field is advected with the infalling gas under the BH horizon. For a
rapidly-spinningBH,theopenmagneticfieldlinesformalongtherotationaxis,andthemagnetically
driven jets can be produced. Energy extracted from the rotating BH through the Blandford-Znajek
process (Blandford & Znajek 1977) gives then a substantial contribution to the jet luminosity. In
addition, annihilation of neutrino-antineutrino pairs produced in the torus is yet another source of
powertothejets.InFigure1,weshowtheresultofanexemplarysimulation,whichshowsasnapshot
takenfromevolvedrun,withthedistributionofmagneticfieldlines,magneticandgaspressureratio,
andneutrinoemissivity,intheregionclosetoablackhole.
Figure 1. Magnetisation β = Pgas/Pmag and magnetic field lines topology (left), and neutrino
emissivity distribution (right) in the evolved accretion flow. Snapshots taken at time t = 2000M.
Blackholespinisa=0.98.
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3. NucleosynthesisofheavyelementsintheGRBengine
In the astrophysical plasma, thermonuclear fusion occurs due to the capture and release of
particles(n,p,α,γ).Reactionsequenceproducesfurtherisotopes.Thenuclearreactionsmayproceed
with one (decays, electron-positron capture, photodissociacion), two (encounters), or three (triple
alphareactions)nuclei. Therefore,thechangeofabundanceofthei-thisotopeisingeneralgivenby:
Y˙ = ∑Niλ Y +∑Ni ρN YY +∑ Ni ρ2N2YY Y
i j j j j,k A j k j,k,l A j k l
j j,k j,k,l
Abundances of the isotopes are calculated under the assumption of nucleon number and charge
conservation for a given density, temperature and electron fraction (T ≤ 1MeV). Integrated
cross-sectionsdependingontemperaturekT aredeterminedwiththeMaxwell-BoltzmannorPlanck
statistics,andthebackgroundscreeninganddegeneracyofnucleonsmustbetakenintoaccount. The
setofresultingnon-lineardifferentialequationsissolvedusingtheEulermethod(Wallersteinetal.
1997).
Inourcomputations,weusedthethermonuclearreactionnetworkcode,http://webnucleo.org,and
wecomputedthenuclearstatisticalequilibriaestablishedforthefusionreactions,forwhichthedata
were taken from the JINA reaclib online database (Hix & Meyer 2006). This network is appropriate
fortemperaturesbelow1MeV,whichisthecaseattheouterradiiofaccretiondisksinGRBengines.
Themassfractionoftheisotopesissolvedforconvergedprofilesofdensity,temperatureandelectron
fractioninthedisk.
Figure 2. Volume integrated abundance distribution of elements synthesized in the accretion disk,
basedonthe2Dsimulation. Parameters: disktoBHmassratioofM /M =0.25,BHspina=0.9.
d BH
Abundanceswerecalculatedfromthedensity,temperature,andelectronfractionprofiles,asevolved
tothetimet=2000M(solidline)andt=3000M(dashedline),whilethelong-dashedlineshowsthe
distributionattimet=0.
Wefindthatthefreenucleiarepresentmostlybelow100-200gravitationalradii,andtheplasma
there is rather neutron rich. Then, most abundant heavy elements formed in the accretion tori in
GRBsareNickel, IronandCobalt, aswellasArgonium, Titatnium, Cuprum, Zinc, Silicon, Sulphur,
Clorium,Manganium,Titatnium,andVanadium.
As a consequence of the heavy element formation, the enhanced emission in the lower energy
bands, i.e., ultraviolet or optical, due to the decay of species, may accompany the GRB (the
’macronova’; e.g., Li & Paczynski 1998). Also, the radio flares, occurring months to years after the
GRBcanbeobserved(Piranetal. 2012). Furthermore,certainisotopesdecayshouldbedetectablevia
emissionlines. FortheNuSTARsatellite,sensitiveinthe5−80keVrange,it’sinprinciplepossibleto
detectthephotonsfromTi,Co,Mn,Cu,Zn,Ga,Crunstableisotopesdecays. Additionally,theEPIC
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detectoronboardtheXMM-Newton,couldbeabletoseelinesbelow15keV,e.g.,45Ti,57Mn,or57Co
(Janiuk2014). InFigure3,weplotanexampleresultofthenucleosynthesiscomputations,showing
thevolumeintegratedabundancedistributionofelements,inthefunctionoftheirmassnumber. The
input was taken from the simulation of the GRB central engine, as designed to model the putative
GRBthatcouldpossiblybeassociatedwithGW150914(seenextSection).
4. GravitationalwavesourceGW150914
Data from Fermi Gamma-ray Burst Monitor (GBM) satellite suggested that the recently
registeredgravitationalwaveeventGW150914(Abbottetal. 2016),acoalescingbinaryBHsystem,is
potentiallyrelatedtoaGRB.Theelectromagneticradiationinhighenergy(above50keV)originated
fromaweaktransientsourceandlastedforabout1second(Connaughtonetal. 2016). Itslocalization
isbroadlyconsistentwiththeskylocationofGW150914.
We speculate here on the possible scenario for the formation of a GRB accompanied by the
gravitational wave (GW) event. Even though the presence of the GRB was recently questioned by
other instruments measurements (e.g., Greiner et al. 2016), we envisage the possibility of a GRB
coincidentwiththeGWeventfromtheBHmergertobeworthexploring,inthecontextofthefuture
observations.
Our model invokes coalescence of a collapsing star’s nucleus that forms a BH, with its
companionBHinabinarysystem(Janiuketal. 2013,2017). Wefindthattherecoilvelocityacquired
bythefinalBHthroughtheGWemissionallowsittotakeonlyasmallfractionofmatterfromthehost
star, providedspecificconfigurationofthebinaryspinvectorswiththeorbitalangularmomentum.
TheGRBisproducedonthecostofaccretionofthisremnantmatterontothefinalBH.Themoderate
spin of this BH accounts for the GRB jet to be powered by a weak neutrino emission rather than
theBlandford-Znajekmechanism,andhenceagreeswiththelowpowerobservedintheFermiGRB
signal.
Thesemi-analyticaltreatmentoftheBHcorecollapseandthestar’senvelopespin-up(seeJaniuk
et al. 2008, for details) is followed by the general-relativistic simulations of the binary BH merger.
Then, the GRB central engine evolution is carried numerically, to find the energy output from the
magnetized,neutrino-cooledtorusthatpowerstheelectromagneticburst.
4.1. MergerofbinaryBHs
TheGW150914eventwasinterpretedtobeamergeroftwoBHsofthemassesof36+−54 M(cid:12) and
29+−44 (Abbott et al. 2016). The final BH parameters were estimated to be of 62+−44 M(cid:12) and 0.67+−00..0057
foritsmassandspin. Probabilitiesthattheanglesbetweenspinsandthenormaltotheorbitalplane
are between 45◦ and 135◦ are about 0.8 for each component BH. Spin magnitudes are constrained
tobesmallerthan0.7and0.8at90%probability. Assumptionofastrictco-alignmentofspinswith
theorbitalangularmomentumresultsinanupperlimitof0.2and0.3forthespins. Distancetothe
source was that of 410+160 Mpc, corresponding to a redshift of about z = 0.09 (assuming standard
−180
cosmology).
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Figure3. Visualizationofthespacetimecurvaturejustaftertheblackholemerger,describedbythe
Weylscalar ψ , whichshowstheoutgoingradiationforasymptoticallyflatspacetime(left), andan
4
exemplaryGWsignalthatcanbedetectedintheinstrument,shownbythetimedependenceofthe
realpartofthel=2,m=2componentsofψ (right).
4
We made several runs for BH mass and range of spins, constrained from the Advanced LIGO
data. InFigure3, weplottheexampleresultsfromtherunwithBHmassratioof0.82, andaligned
spinsof0.2and0.3. ThewaveformisplottedusingtheWeylscalarψ 1. ThefinalBHspinobtained
4
inthissimulationwas0.68.
TheserunswereperformedwiththeEinsteinToolkitcomputationalpackage(Loeffleretal2012).
The numerical methods used here are based on finite difference computations on a gridded mesh
and follow the inspiral, merger and ringdown phases of the binary black hole evolution, using the
techniqueoftheadaptivemeshrefinement. TheCartesiangridcoversthevolumeof48×48×48M.
In AMR we use 7 levels of refinement, and the resolution ranges from ∆x = 2.0M for the coarsest
grid to ∆x = 0.03125M for the finest grid. From the simulation runs, we constrained not only the
spin of the merger black hole (it is then used to be a parameter in the GRB engine model), but also
thevelocityofthegravitationalrecoil. Thisturnedouttobeontheorderof∼ 700km/s. Following
Kocsisetal. (2012), wearguethatitislikelythataccretionoftheaccumulatedmatterontothefinal
BHistriggeredwhileitmovestowardsthecircumbinarydiskafterthemerger.
4.2. WeakGRBpoweredbyneutrinoemission
TheFermiGRBcoincidentwiththeGW150914eventhadadurationofabout1secandappeared
about 0.4 seconds after the GW signal. Within the limit of uncertainty of the Advanced LIGO and
Fermi detectors’ capabilities it could also be associated spatially. The GRB fluence in the range 1
keV-10 MeV, is of 2.8×10−7 erg cm−2. The implied source luminosity in gamma rays equals to
1.8+1.5×1049erg/s.
−1.0
We modeled the GRB engine, constrained by the post-merger conditions. Using the code
HARM-2D, with the numerical EOS and neutrino cooling implemented into MHD evolution, we
estimated the neutrino and Blandford-Znajek luminosities available to power the GRB jet in this
source.Inparticular,themassoftheaccretingtorus,createdfromthecircumbinarymatter,wastuned
to produce adequately low neutrino luminosity for a weak GRB. Example parameters for the BH
massof M = 62M(cid:12),theBHspinofa = 0.7,anddiskmass Md = 15M(cid:12) areconsistentwittheweak
GRBluminosity. Assuminglowefficienciesofconversionbetweenneutrinoannihilation, andweak
conversion between the jet kinetic and radiative power, this scenario is able to meet quantitatively
thelimitsputbytheFermidata. Thediskmassisherejustanorderofmagnitudeestimate. Wefirst
1 Curvatureofspacetimeisdescribedbycurvaturetensor-theRiemmantensor(20independentcomponents),whichcan
bedecomposedintosumofRiccitensor(10independentcomponents)andWeyltensor(10independentcomponents).
ForvacuumsolutionsofEinsteinequationsRiccitensorvanishes,socurvatureisdescribedbyWeyltensoronly. Inthe
Newman-PenroseformalismcomponentsofWeyltensorareencodedasfivecomplexWeylscalarsΨ0,... ,Ψ4. Theseare
differentcomponentsofcurvaturetensor,whichhavedifferentphysicalinterpretation.Ψ4describestheoutgoingradiation
foranasymptoticallyflatspacetime.
Galaxies2016,xx,x 8of11
checked,thatamuchlargermass,ontheorderofthemassofthemergedblackhole,istoolargetobe
consistentwiththeobservedlimitationsforluminosity. Ontheotherhand,thesupernovaexplosion
whichmighthavelefta30Solarmassblackhole,shouldhaveoriginatedfromatleast80Solarmass
star on zero-age main sequence, in a low-metallicity environment (Abbott et al. 2016b, Spera et al.
2015). Evenifasignificantamountofthestar’smasswasejectedduringtheevolutionandexplosion,
someremnantofthisorderisplausible.
Figure4. PoweravailableintheGRBenginethroughtheneutrinoemission(right),andthroughthe
magneticfieldadvectedundertheBHhorizon(left).
The luminosity L , emitted in neutrinos is simply equal to their volume integrated emissivity.
ν
TocomputetheenergyfluxthroughthehorizonoftheBHandtheBlandford-Znajekluminosity,L ,
BZ
weneedtheelectromagneticpartofthestresstensor,
b2
Tµν = b2uµuν+ gµν−bµbν, (1)
EM 2
where the four-vector bµ with bt ≡ g Biuµ and bi ≡ (Bi +uibt)/ut. We then evaluate the radial
iµ
energyfluxasthepoweroftheBlandford-Znajekprocess:
L ≡ E˙ =2π(cid:90) π dθ(cid:112)−gF (2)
BZ E
0
where F ≡ −Tr. This can be subdivided into a matter F(MA) and electromagnetic F(EM) part,
E t E E
althoughintheforce-freelimitthematterpartvanishes(McKinney&Gammie2004).
In Figure 4, left panel, we plot the values of L as it varies with time for various simulations,
BZ
depending on the black hole spin. In the right panel, we show the corresponding evolution of the
neutrinoluminosity.Themaximumoftheneutrinoluminosityobtainedinoursimulationsisreached
about0.4secondsafteranequilibriumtorus, prescribedbyourinitialconditions, hadformed. This
maytentativelygivethelowerlimitforthetimescalewhenthejetappearsaftertheBHmerger. The
Blandford-Znajekluminosityisontheorderof1050−1051ergs/s,andonlyoccasionallynon-zerofor
low spins (the jet is powered by magnetic field only episodically). We find therefore, that the GRB
luminosity inferred from our simulations can be reconciled with the observational upper limits, for
moderatespinsofthefinalBH(a =0.6−0.8).
The connection of our computation to the particular event GW150914 and the corresponding
Fermi GRB is arguable because of several facts. At first, the flare produced by our simulation is
longerthanthereportedveryshortdurationoftheGRB(1s). However,theobservedburstwasclose
to the sensitivity limit of the instrument, so it is likely that it could observe just the very top of the
flareandlefttherestoftheburstundetected. Moreover,ifourlineofsightisoffsetwithrespecttothe
jet axis and we can see only the edge of the jet, the detailed shape of the flare would be affected by
thebehaviourofthepropagatingjet. Thetimedelaybetweentheburstandgravitationalsignalcan
Galaxies2016,xx,x 9of11
besignificantlylonger,ifthereisamassivestarremnant,throughwhichthejethastopropagate. The
state of the remnant matter after the second BH collapse is very uncertain and needs to be studied
in details in future works. However, we can speculate that the collapse and subsequent orbiting of
the two BHs is violent enough to destroy the star, expel part of the matter away and form a dead
circumbinarydiscoftheremnantmatter,inwhichtheaccretionhasstopped,aroundtheBHbinary.
Thenafterthemergerthenewbornblackholecanreceiveasubstantialkicktowardsthecircumbinary
disc (see our BH merger simulations in Section 4.1), can meet the matter in fraction of second and
producetheburst. Inthatcase, thereisonlylittlematerialleftalongtheaxis, throughwhichthejet
hastopropagate, andsothetimedelaycanbequiteshort, ontheorderofasecond. However, this
speculative scenario needs both more theoretical modeling and mainly more future observations of
coincidentgravitationalandelectromagneticsignals,whicharewellabovetheinstrumentallimits.
5. Conclusions
• We have carried out numerical GR MHD simulations of the magnetized torus accreting onto
BHintheGRBcentralengine. TheEOSisnolongerassumedtobeofanidealgas,butaccounts
forthepropermicrophysicsandneutrinocoolingoftheGRBengine.
• Theneutrinoemissionandabsorptionprocessesaccountforanadditionalpressurecomponent
intheplasma,andthespeciesarepartiallydegenerate. Theresultingdensityandtemperature,
as well as the electron fraction, are then taken into account when determining the nuclear
equilibriumconditions.
• We determine the abundances of heavy elements (above Helium, up to the mass number of
∼ 100), which are synthesized in the accretion disk in GRB engine, and in the winds that are
magnetically launched from its surface. The observational signatures of radioactive decay of
some of the unstable isotopes can be, for instance, the emission lines seen in the X-rays (in
principle,intheNuSTARrange),andalsointhefaintemissioninlowerenergybandcontinuum
(i.e. ’kilonova’or’macronova’scenario).
• We compute and compare the efficiencies of the GRB jet powered through the neutrino
annihilation,andtheBlandfrod-Znajekmechanism. Wefindthattheconstraintsofamoderate
BH spin and a small disk mass to the BH mass ratio, are in tentative agreement with the
AdvancedLIGOandFermidata,ifthelatterwasreallycoincidentwiththeGWevent.
• A definite answer and a test for our scenario will be possible if further searches for the GW
eventswillprovidemoredata,alsofortheirelectromagneticcounterparts,inbothgammarays
andlowerenergies.
Weclaim,thateventhoughtheobservationsarestillsubjecttodebate,thepossibleGRB-BBHmerger
coincidence is worth to investigate. The timescales obtained in our scenario are possibly more
plausible for a lonng gamma ray burst scenario than for a short one (see also Perna et al. 2016;
Loeb2016),unlesstheFermiburstitselfwasmuchlonger,butbelowthedetctionlimit. Ontheother
hand, the model proposed by Zhang (2016) can satisfy the duration and delay timsecales, but the
intepretaionofachargedblackholeanditsobservationalsignaturesalsoneedsfurtherinvestigations.
Acknowledgments: This work was supported in part by the grants no. DEC-2012/05/E/ST9/03914 and
UMO-2014/14/M/ST9/00707fromthePolishNationalScienceCenter. Wealsoacknowledgesupportfromthe
InterdisciplinaryCenterforMathematicalModelingoftheWarsawUniversity,throughthecomputationalgrant
G53-5.
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