The multi-messenger picture of compact object encounters: binary mergers versus dynamical collisions

3.5 MB·English

by  S. Rosswog

Mon.Not.R.Astron.Soc.000,1–23(2012) Printed10January2013 (MNLATEXstylefilev2.2)
The multi-messenger picture of compact object encounters:
binary mergers versus dynamical collisions
S. Rosswog1,2,3(cid:63), T. Piran4† and E. Nakar5‡
1School of Engineering and Science, Jacobs University Bremen, Germany
3 2TASC, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064
1 3The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden
0 4Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
2 5Raymond and Beverly Sackler School of Physics & Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

n
a
J Accepted2012.Received2012;inoriginalform2012

9

] ABSTRACT
E
We explore the multi-messenger signatures of encounters between two neutron stars
H (ns2)andbetweenaneutronstarandastellar-massblackhole(nsbh).Wefocusonthe
. differencesbetweengravitationalwavedrivenbinarymergersanddynamicalcollisions
h
that occur, for example, in globular clusters. Our discussion is based on Newtonian
p
- hydrodynamics simulations that incorporate a nuclear equation of state and a multi-
o flavourneutrinotreatment.Forbothtypesofencounterswecomparethegravitational
r wave and neutrino emission properties. We also calculate the rates at which nearly
t
s unbound mass is delivered back to the central remnant in a ballistic-fallback-plus-
a
viscous-disk model and we analyze the properties of the dynamically ejected matter.
[
Last but not least we address the electromagnetic transients that accompany each

2 type of encounter.
v We find that dynamical collisions are at least as promising as binary mergers for pro-
0
ducing (short) gamma-ray bursts, but they also share the same possible caveats in
4
terms of baryonic pollution. All encounter remnants produce peak neutrino luminosi-
2
tiesofatleast∼1053 erg/s,someofthecollisioncasesexceedthisvaluebymorethan
6
an order of magnitude. The canonical ns2 merger case ejects more than 1% of a solar
.
4 mass of extremely neutron-rich (Y ∼ 0.03) material, an amount that is consistent
e
0 with double neutron star mergers being a major source of r-process in the galaxy.
2
nsbh collisions eject very large amounts of matter (∼ 0.15 M ) which seriously con-
1 (cid:12)
strains their admissible occurrence rates. The compact object collision rate (sum of
:
v ns2 and nsbh) must therefore be less, likely much less, than 10% of the ns2 merger
i rate. The radioactively decaying ejecta produce optical-UV “macronova” which, for
X
thecanonicalmergercase,peakafter∼0.4dayswithaluminosityof∼5×1041 erg/s.
r ns2 (nsbh) collisions reach up to 2 (4) times larger peak luminosities. The dynamic
a
ejecta deposit a kinetic energy comparable to a supernova in the ambient medium.
Thecanonicalmergercasereleasesapproximately2×1050 erg,themostextreme(but
likely rare) cases deposit kinetic energies of up to 1052 erg. The deceleration of this
mildly relativistic material by the ambient medium produces long lasting radio flares.
A canonical ns2 merger at the detection horizon of advanced LIGO/Virgo produces a
radio flare that peaks on a time scale of one year with a flux of ∼0.1 mJy at 1.4 GHz.
Collisions eject more material at higher velocities and therefore produce brighter and
longer lasting flares.
Key words: black hole physics – gravitational waves – neutrinos – nuclear reac-
tions,nucleosynthesis,abundances–radiationmechanisms:non-thermal—gamma-ray
bursts
1 INTRODUCTION
(cid:63) E-mail:[email protected]
The encounter of a neutron star (ns) with another neutron
† E-mail:[email protected]
‡ E-mail:[email protected] star or with a stellar mass black hole (bh) is a fascinating
(cid:13)c 2012RAS
2 S. Rosswog, et al.
15 0.5
14
0.4
13 1.3 Msol 1.3 Msol
]) 1.4 Msol 1.4 Msol
3
m 12
c 0.3
g/
ρ [ 11 Ye
(
1010 0.2
g
o
l
9
0.1
8
7 0
0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16
r [km] r [km]
Figure 1. Initial density and Ye profiles (in hydrostatic and β-equilibrium) of the neutron stars used in this study (1.3 and 1.4 M(cid:12),
nuclearequationofstateofShenetal.(Shenetal.1998a)).
events that involve a large variety of different physical pro- & Janka 2011)1. The main r-process nucleosynthesis con-
cesses, see Faber (2009), Duez (2010), Shibata & Taniguchi tenders are compact binary mergers which release neutron-
(2011),Rosswog(2011)andFaber&Rasio(2012)forrecent rich matter in at least three ways. Apart from the matter
reviews on various aspects of this topic and for a guide to that is ejected dynamically via gravitational torques, there
the current literature. is an additional contribution due to neutrino-driven winds
Thedetectionofthegravitationalwaves(GWs)emitteddur- (Dessartetal.2009)andfromthelate-timedissolutionofac-
ing the inspiral of ns2 and nsbh binary mergers are prime cretiondisks(Chen&Beloborodov2007;Beloborodov2008;
targetsofground-basedgravitationalwavedetectorssuchas Metzger et al. 2008). While the initial starting point is the
LIGO,VirgoandGEO600(Willkeetal.2006;Acerneseetal. same, cold neutron star matter in β-equilibrium, the three
2008; Grote 2008; Smith 2009). In their advanced states, channelsdifferintheamountsofreleasedmatter,intheiren-
the interferometers target to detect the signals of ns2 coa- tropies,expansiontimescalesandelectronfractions.There-
lescences out to hundreds of megaparsecs, corresponding to fore they might possibly produce different nucleosynthetic
redshifts of z ≈0.1. Once detected, the gravitational waves signatures.
offertheexcitingpossibilityoffillinggapsinourunderstand- The ejecta are responsible for two types of electromagnetic
ingoftheneutronstarequationofstateinthehighdensity, transients: the decompressed neutron star matter is sub-
lowtemperatureregimethatisexperimentallyhardlyacces- ject to radioactive decays (Li & Paczyn´ski 1998; Rosswog
sible. 2005; Metzger et al.2010; Roberts etal. 2011)and at some
Compact binaries have for a long time been the prime can- stage the ejecta dissipate their kinetic energy in the am-
didates for the central engines of (short) gamma-ray bursts bient medium. The former is expected to produce an op-
(GRBs; Eichler et al. (1989); Paczyn´ski (1991); Narayan tical display not too different from a supernova, but much
et al. (1992)) and this hypothesis has survived being con- shorter, sometimes referred to as “macronova”, the latter
frontedwithawealthofobservationalresultsinrecentyears. hasbeenshowntoproducedetectable,isotropicradioemis-
Severalchallengesremain,however,andthecaseisfarfrom sion that peaks near one gigahertz and persists on a de-
being closed (Piran 2005; Nakar 2007; Lee & Ramirez-Ruiz tectable (sub-milliJansky) level for weeks out to a distance
2007; Gehrels et al. 2009). ofz≈0.1(Nakar&Piran2011).EspeciallyifthetrueGW
They are also promising sources for the heaviest elements detection rates should be near the lower end of the predic-
in the Universe that are formed via rapid neutron cap- tions,additionalelectromagneticsignatureswouldbecrucial
ture (Lattimer & Schramm 1974, 1976; Eichler et al. 1989; to confirm marginal gravitational wave detections and they
Freiburghausetal.1999;Rosswogetal.1999;Robertsetal. would therefore enhance the effective detector sensitivities
2011; Goriely et al. 2011). The textbook r-process source, (Kochanek & Piran 1993; Hughes & Holz 2003; Dalal et al.
core-collapse supernovae, have been found to be seriously 2006; Arun et al. 2009).
challenged in providing the physical conditions (high en-
tropy, low electron fraction together with rapid expansion)
that are required to produce the heavy (A > 90) r-process 1 Apossibleexceptionmaybemagnetorotationallydrivensuper-
elements (Roberts et al. 2010; Fischer et al. 2010; Arcones novajetswhereinterestinglylowelectronfractionvaluesseemto
be reachable (Winteler et al. 2012). It remains to be explored,
however, how robust this scenario is with respect to the stellar
parametersandwithrespecttoitsnucleosyntheticyields.
(cid:13)c 2012RAS,MNRAS000,1–23
Mergers vs collisions: the multi-messenger picture 3
Recently, dynamical collisions between compact objects as 2 SIMULATIONS
they may occur in the core of globular clusters have been
The simulations of this paper make use of the Smooth Par-
studied by several authors (Kocsis et al. 2006; O’Leary
ticle Hydrodynamics (SPH) method, see Monaghan (2005)
et al. 2009; Lee et al. 2010; Kocsis & Levin 2012). Lee
and Rosswog (2009) for recent reviews. Our code is an up-
et al. (2010) concluded that collisions could produce GRBs
dated version of the one that was used in earlier studies
at a detectable rate. To demonstrate the viability as GRB
(Rosswog & Davies 2002; Rosswog & Liebendo¨rfer 2003;
engines they performed hydrodynamic simulations of com-
Rosswog et al. 2003; Rosswog 2005). We solve the follow-
pact object collisions, though without use of detailed mi-
ing evolution equations for each particle a
crophysics such as a nuclear equation of state or neutrino
(cid:18) (cid:19)
emission. d(cid:126)v (cid:88) P P
a =− m a + b +Π ∇ W +f(cid:126) +f(cid:126) (1)
The main questions that we want to address in this paper dt b ρ2 ρ2 ab a ab a,g a,GW
are: b a b
(cid:18) (cid:19)
du (cid:88) P 1 duν
a = m a + Π (cid:126)v ·∇ W − a (2)
dt b ρ2 2 ab ab a ab dt
a) In which ways do the remnants and signatures of dy- b a
namical collisions differ from those of binary mergers? dY
e,b = λ Y −λ Y , (3)
b) Towhichextentcantheirratebeconstrainedbynucle- dt PC n EC n
osynthetic yields? themassdensityiscalculatedbysummingupcontributions
c) How different are electromagnetic transients following from neighboring particles
mergers and collisions? (cid:88)
ρ = m W . (4)
a b ab
b
ToaddresstheseissuesweperformedasizeablesetofNew-
Here m is the (constant) mass of particle b and W =
tonian hydrodynamics simulations which include a nuclear b ab
W(|(cid:126)r − (cid:126)r |,h ) denotes the cubic spline kernel (Mon-
equation of state and an opacity-dependent neutrino cool- a b ab
aghan 1985) evaluated with the average smoothing length
ingscheme.Thesesimulationsaresubsequentlyexploredto
h = (h +h )/2. f(cid:126) is the additional acceleration due
predict the electromagnetic signatures of compact binary ab a b a,g
to self-gravity that we evaluate using a binary tree (Benz
encounters.Clearly,theinvestigatedsystemsarerelativistic
and ultimately General Relativity should be applied. It is, et al. 1990) and f(cid:126)a,GW results from gravitational wave
however, not gravity alone that shapes the dynamics and back-reaction. The relative particle velocity is denoted as
observable signatures of these encounters. Instead, also the (cid:126)vab =(cid:126)va−(cid:126)vb. To produce entropy in shocks artifical dissi-
remaining fundamental interactions contribute their share: pation is included via the tensor Πab. It has the standard
a)thestronginteractionviathenuclearequationofstate,b) form Monaghan (1992) but particular care has been taken
the weak interaction since it determines the neutrino emis- toavoidpossibleartifactsduetoartificialviscosity,thishas
sionratesandthustheevolutionoftheelectronfractionY been outlined in detail in Rosswog et al. (2008). The quan-
e
and c) the electromagnetic interaction which is, for exam- tity ua denotes the specific internal energy of particle a the
ple, responsible for producing radio-flares once ejected ma- evolution of which is determined by PdV-work and viscous
terial dissipates its kinetic energy in the ambient medium. heating(summationterm)andtheenergylosstoneutrinos,
Given this complexity, we consider Newtonian gravity as a duνa. The quantities
dt
tolerable approximation for the time being. The presented
Reff Reff
simulationsaremeanttoserveasbenchmarksforfuturesim- λ = PC and λ = EC (5)
PC η EC η
ulationsthatmayincludegeneralrelativityandtherelevant np pn
microphysics. are the electron and positron capture rates per neu-
WediscusstheviabilityofdynamicalcollisionsasGRBcen- tron/proton. Reff are the effective neutrino number
EC/PC
tral engines, in particular the properties of remnant disks, emissionratesandthequantitiesη /η reduceinthenon-
np pn
theirneutrinoemissionandtheprospectsformagneticfield degeneratelimittothenumberdensitiesn andn (Bruenn
n p
amplification.Wefurthercalculatethemassandthereturn 1985), for a more detailed account on the neutrino treat-
timescalesoffallbackandwepresentindetailtheproperties mentwerefertotheoriginalpaper(Rosswog&Liebendo¨rfer
ofdynamicalejectaasabasisforsubsequentnucleosynthesis 2003).Thepressureataparticleb,P (ρ ,T ,Y ),iscalcu-
b b b e,b
calculations.Basedonthesefindingswediscussthequestion lated using the Shen et al. equation of state (EOS) (Shen
“Whatistheelectromagneticsignatureofans2 andansbh et al. 1998a,b) extended to lower densities as described in
encounter?” Rosswog & Davies (2002).
Thepaperisstructuredasfollows.InSec.2webrieflysum- Compactbinarysystemsaredriventowardscoalescencevia
marize the ingredients of our simulations both in terms of the emission of gravitational waves. The corresponding ra-
physics and numerical methods. In Sec. 3 we describe the diation reaction forces for a slow-motion, weak field source
main findings. Sec. 3.1 discusses the dynamics and its im- can be calculated as the gradient of a radiation reaction
print on gravitational waves, Sec. 3.2 explores the neutrino potentialwhichcontainsthefifthtimederivativesofthere-
signal and Sec. 3.3 the differences between merger and col- ducedquadrupolemoments(Burke1971).Simplebackreac-
lision fallback. In Sec. 3.4 we discuss the properties of the tion prescriptions usually rely on reducing the order of the
dynamicallyejectedmaterialsuchasmass,electronfraction time derivatives by averaging over several orbital periods.
and velocity structure. They all shape the electromagnetic This procedure is well justified during the secular inspiral
display,whichisaddressedinSec.3.5.Ourresultsaresum- stagesofacompactbinarymerger,butithasnowell-defined
marized and discussed in Sec. 4. meaninginthecaseofaparabolicencounter.Forthisreason
(cid:13)c 2012RAS,MNRAS000,1–23
4 S. Rosswog, et al.
weignoretheexertedbackreactionforthecollisioncasesof investigatethedependenceontheblackholemass(m =3,
bh
this first study, for the merger cases we use a simple point 5and10M )whilekeepingtheimpactparameteratβ =1.
(cid:12)
mass description (Davies et al. 1994) for f(cid:126) . The pos- We consider run H with m = 1.3 M , m = 1.4 M ,
a,GW 1 (cid:12) 2 (cid:12)
sible impact of this technical shortcoming will be discussed i.e. q ≈0.923 and negligible spins (Bildsten & Cutler 1992;
below. Kochanek 1992) as the generic merger case and we will use
As a diagnostics of the dynamical evolution we will use be- itfrequentlyasareferencepointtocomparetheothercases
low the gravitational wave amplitudes as seen by an ob- against. As a somewhat academic case, we explore an ini-
server located along the binary rotation axis. Consistent tiallytidallylockedbinaryneutronstarsysteminrunG.In
with the Newtonian treatment of gravity we extract gravi- runs I and J we briefly touch upon neutron star black hole
tational waves in quadrupole approximation mergerswheretheblackholeistreatedasaNewtonianpoint
mass with an absorbing boundary at the Schwarzschild ra-
hTT = 1G (cid:0)I¨xx−I¨yy(cid:1) (6) dius.
+ dc4
The initial neutron stars are constructed from spheri-
2G
hTT = I¨xy, (7) cally symmetric, zero-temperature, β-equilibrium profiles,
× dc4
see Fig. 1. The SPH particles are placed in a close packed,
where Iij is the reduced quadrupole moment tensor evalu- hexagonal lattice configuration and they are subsequently
ated at retarded times, relaxed so that they can find their true numerical equilib-
rium state, see Sect. 3.1 of Rosswog & Price (2007). Some
(cid:88) 1
Iij = mb(xibxjb− 3δijrb2). (8) of our simulations have been run up to 0.5 s, more than an
b order of magnitude longer than existing simulations on this
The needed time derivatives can be obtained by straight topic.
forwarddifferentiationofEq.(8)sothattheamplitudescan All performed simulations are summarized in Tab. 1.
be calculated as sums involving particle masses, positions,
velocities and forces.
In the presented simulations we restrict our collision study
to parabolic orbits. The strength of such an encounter is 3 RESULTS
parametrized by the parameter
3.1 Encounter dynamics and gravitational wave
R +R emission
β ≡ 1 2, (9)
r
P Tosetthestageforlatercomparisons,westartwithabrief
where the R are the neutron star/Schwarzschild radii of descriptionofthe“standard”binarymergercase,runH.In
i
theinvolvedobjectsandr isthepericenterdistance.Thus Fig. 2 we show a 3D rendering of its temperature distribu-
P
β = 1 corresponds to a grazing impact, stronger (weaker) tion.Weonlydisplaymatterbelowtheorbitalplanesothat
impactshavelarger(smaller)values.Sincethecollisionrates thetemperaturesandflowstructuresinsidethecentralrem-
are proportional to the pericenter distance r , we consider nant can be easily grasped. About one orbital period after
P
run A with β =1 as the most likely ns2 collision case. Col- contacttwoasymmetricspiralarmshaveformed(panelone
lisions with pericenter distances β < 1 can still form tidal and two), which evolve during the next ∼ 15 milliseconds
capture binaries (Fabian et al. 1975; Lee et al. 2010) which into a nearly axisymmetric torus (panel 4). When the stars
can lead to final collisions after a sequence of pericenter come into contact a shear interface forms between them.
passages. Collisions with β < 1, however, become compu- Such Kelvin-Helmholtz unstable interfaces have long been
tationally increasingly cumbersome due to the discrepancy known to emerge in neutron star mergers, see, for example,
between orbital and internal dynamical time scales. There- Ruffertetal.(1996);Rosswogetal.(1999);Rasio&Shapiro
fore we only consider collisions with β (cid:62) 1. To keep the (1999).Theresultingvorticeshavealsobeenfoundtolocally
explored parameter space under controle, all investigated amplifypre-existingmagneticfields(Price&Rosswog2006;
nsbhcollisionspossessafixedimpactstrengthofβ =1and Anderson et al. 2008; Obergaulinger et al. 2010) and inside
we only vary the black hole mass. of them the (SPH particle) temperatures can temporarily
It has long been known that the ns mass distribution pos- reach values in excess of 60 MeV. The somewhat academic
sessesanarrowpeaknear1.35M (Thorsett&Chakrabarti case of an initially tidally locked binary shows more pro-
(cid:12)
1999). Recent studies find an additional broader peak nounced tidal tails (due to larger angular momentum), but
around 1.5-1.7 M (Kiziltan et al. 2010; Valentim et al. similartemperatures.Bothdoubleneutronstarmergercases
(cid:12)
2011)forneutronstarswithwhitedwarfcompanions.There produce reasonably well-defined massive tori of 0.25 M in
(cid:12)
maybeanadditionallow-masspeaknear1.25M produced theirrotational“standard”caseand0.30M fortidallock-
(cid:12) (cid:12)
by electron capture supernovae (Podsiadlowski et al. 2004; ing, see Tab. 2.
van den Heuvel 2004; Schwab et al. 2010). The mass dis- The collision cases in contrast can suffer several close en-
tributions for neutron stars of different evolutionary paths countersbeforefinallymergingintoasingleobjectanddur-
have recently been discussed in O¨zel et al. (2012). In our ing these passages the neutron stars are efficiently tidally
simulations we restrict ourselves conservatively to masses spun up. In the β =1 case a single object only forms after
nearthe1.33M peakthatthelatterauthorsfindfordou- the third close encounter, see Fig. 3. In the first, grazing
(cid:12)
ble neutron star systems. impact the stars’ obital energy is used to spin up the stars
In ns2 collision cases we use masses of 1.3 and 1.4 M and toclosetotheirbreakupperiod,e.g.panel2,andnowthey
(cid:12)
explorethedependenceontheimpactstrengthparameterβ. form an eccentric tidal capture binary. The next encounter
For nsbh collisions we use a neutron star of 1.3 M and we near t = 8 ms is more central and again produces strong
(cid:12)
(cid:13)c 2012RAS,MNRAS000,1–23
Mergers vs collisions: the multi-messenger picture 5
Table 1.Overviewovertheperformedsimulations.Theimpactstrengthparameterβ isdefinedinEq.(9).
Run m1 [M(cid:12)] m2 [M(cid:12)] β NSPH[106] tend [ms] objects/comment
Collisions
A 1.3 1.4 1 2.7 21.2 ns-ns
B 1.3 1.4 2 8.0 9.0 ns-ns
C 1.3 1.4 5 2.7 13.2 ns-ns
D 1.3 3.0 1 1.3 127.5 ns-bh
E 1.3 5.0 1 1.3 143.6 ns-bh
F 1.3 10.0 1 1.3 540.3 ns-bh
Mergers
G 1.3 1.4 n.a. 2.7 20.3 ns-ns,corot.
H 1.3 1.4 n.a. 2.7 19.1 ns-ns,nospins
I 1.4 5.0 n.a. 0.2 138.7 ns-bh,nospins
J 1.4 10.0 n.a. 0.2 139.3 ns-bh,nospins
Kelvin-Helmholtz vortices at the interface in which (SPH for the inner, high density disk (ρ > 1011 gcm−3, r < 120
particle) temperatures locally exceed 80 MeV. The stars km) and 0.22 M if also the outer disk (ρ > 108 gcm−3,
(cid:12)
separate once more, with the 1.3 M star now transferring r <700 km) is counted. The dynamics of the 1.4 M (ns) -
(cid:12) (cid:12)
massinadirectimpactphaseintotheprimary,seepanel4. 10 M (bh) system proceeds in a similar manner, here after
(cid:12)
Thefinalencounteroccursaroundt≈12ms,againforming 15 orbital revolutions the neutron star is finally disrupted
a string of Kelvin-Helmholtz vortices (panel 5) and finally andleavesa0.20M disktogetherwitharapidlyexpanding
(cid:12)
shedding mass from the secondary neutron star (panel 6). one armed spiral structure. All the numerically determined
During the encounter the density never exceeds the initial mass trasnfer durations must be considered as robust lower
value (≈3.6×1014 gcm−3). limits on the true values (Dan et al. 2011).
The more central encounters form a single object after two For the neutron star black hole collision cases we only ex-
(β = 2) and just one encounter (β = 5). In both cases plore the dependence on the black hole mass and keep the
strongshocksforminwhichthe(SPHparticle)temperatures impact strength (β =1) and neutron star mass (m =1.3
ns
reachvaluesinexcessof80MeV.Insuchshockstheneutron M ) constant. During the first pericenter passage of the
(cid:12)
starsaresubstantiallycompressed,tovaluesof≈4.52×1014 m = 3 M case, run D, the neutron star survives as
bh (cid:12)
gcm−3(β =2)and≈5.55×1014 gcm−3(β =5).Inasuper- a tidally spun up (close to break up, P ≈ 0.95 ms) self-
position of rapid rotation and violent, stellar-radius ampli- gravitatingobject,butshedssomeofitsmassinatidaltail.
tudeoscillations,thecentralobjectsproduceamultitudeof When the neutron star passes the black hole after about 5
interactingshocksinastringofmasssheddingepisodes,see ms for a second time another tidal tail is produced. Once
Fig. 4. The oscillations are also imprinted on the neutrino more,thecoreoftheneutronstarsurvivesasagravitation-
signal, see below. allyboundobject.Itisonlycompletelydisruptedduringthe
For the neutron star black hole cases we also begin with thirdandfinalpericenterpassageatt≈11ms.After127ms
binary mergers as a reference point. Since they have been theremnantconsistsofthebhwith3.98M ,surroundedby
(cid:12)
exploredindetailbefore(Rosswogetal.2004;Rosswog2005; a massive disk (≈0.15 M , see Tab. 2) which is externally
(cid:12)
Rosswog2007b),werestrictourselvestoabriefsummary.In fedbythreespiralarms.Qualitatively,them =5M case
bh (cid:12)
the case of a 1.4 M ns and a 5 M bh (run I) the neutron evolvesinasimilarmanner,seeFig.5,butnowtheneutron
(cid:12) (cid:12)
star starts transferring mass into the hole after 1.5 orbital starcoresurviveseventhethirdpassage.Atthetimewhen
periods. Consistent with our earlier studies this does not wehavetostopthesimulation(t=144ms),thecoreis,ac-
lead to the disruption of the neutron star on a dynamical cording to its radial velocity, unbound from the black hole.
timescale.Instead,self-gravityovercomestidalforcesagain Theneutronstarcore,however,isembeddedintothedebris
and the neutron star enters a long-lived phase of episodic gas and might therefore be further braked during its subse-
mass transfer during which it transfers mass periodically quentevolutionsothatitwillpossiblyfallbacktowardsthe
towardstheholewhilesheddingmassthroughitsouterLa- bh. In the m = 10 M case the neutron star is already
bh (cid:12)
grangepoint2.Thisphasecontinuesforasmanyas25orbital completely disrupted during the second pericenter passage.
revolutionsbeforetheneutronstarisfinallycompletelydis- Consistent with the findings of Lee et al. (2010), all nsbh
rupted.Theremnantattheendofthesimulation(t=138.7 encounters have in common that they all leave behind a bh
ms)consistsofa“diskinsideadisk”withamassof0.16M with a massive remnant disk (see Tab. 2) and one tidal tail
(cid:12)
per close encounter.
Theorbitaldynamicsisimprintedonthegravitationalwave
2 Phasesofstablemasstransferarenotrestrictedtothecaseof (GW) signal, for its calculation see Sec. 2. For the neutron
Newtoniangravity.Astiffequationofstate(Rosswogetal.2004), star mergers (run G and H) the gravitational wave ampli-
smallmassratiosandlargebhspinparametersmakesystemspar- tudes h (times the distance to the source d as measured
+
ticularly prone to stable mass transfer, see Shibata & Taniguchi
in code units of 1.5 km) are shown in Fig. 6, upper left
(2011)forafurtherdiscussion.
(cid:13)c 2012RAS,MNRAS000,1–23
6 S. Rosswog, et al.
Figure2.3Drenderingofthetemperaturedistributioninthestandardneutronstarmergercase(1.3and1.4M(cid:12),nospin;runH).The
upperhalfofthematterdistributionhasbeen”choppedoff”toallowforaviewintothestars.Toenhancethecontrast,theupperlimit
ofthecolourbarhasbeenfixedto20MeV.InthevariousvorticesthatemergeduetoKelvin-Helmholtzinstabilitiespeaktemperatures
inexcessof60MeVaretemporarilyreached.
panel. Both cases show the characteristic “chirp”, up to as long as ∼ 60 ms.
≈ 3 ms for the non-spinning and up to ≈ 6 ms for the TheGWamplitudespikesproducedbythecloseencounters
tidally locked case, and the subsequent “ringdown” phase coincide with peaks in the neutrino luminosities, see below.
of the non-axisymmetric central object. The amplitudes of Although the GWs from collisions are comparable in am-
the ns2 collisions are displayed in panel two of Fig. 6. Each plitude to those from mergers, the large diversity and the
close encounter produces a pronounced GW spike, for ex- lack of a “standard waveform” will make the detection of
ample in the β = 1 case, run A, the encounters produce collision signals by current and future ground-based gravi-
spikesatt=2.3,8.4and12.4ms.Thecasesinvolvingblack tational wave detectors extremely challenging.
holes show substantially longer activity after the first en-
counter.Inthemergercases,runIandJ,theepisodicmass
3.2 Neutrino emission
transfer is visible for tens of orbits until the neutron star
is finally disrupted. The nsbh collision cases are essentially We discuss the neutrino properties of one example of each
“GW-quiescent” (only a small contribution from the close- encounterclass(ns-ns:mergersandcollisions;nsbh:mergers
to-breakuprotationoftheneutronstarcore)whentheneu- and collisions) in some detail, an overview over the proper-
tronstarisrecedingfromthebh,butproduceanotherGW ties of all cases is provided in Tab. 3. Again, we use the
burst at the next close encounter. For the case with the 5 non-spinning neutron star merger case, run H, as a refer-
M(cid:12)bh(runE)thelongestencounteredquiescentphaselasts encepointtogaugetheotherresults.Here,theluminosities
(cid:13)c 2012RAS,MNRAS000,1–23
Mergers vs collisions: the multi-messenger picture 7
Figure 3. 3D rendering of the temperature distribution during the grazing impact of two neutron stars (1.3 and 1.4 M(cid:12), β =1; run
A).Itisonlyinthethirdcloseencounter(panel5)thatfinallyasingleobjectforms.IneachcloseencounteraslewofKelvin-Helmholtz
vortices forms at the interface between the stars. For display reasons only matter below the orbital plane is shown and the colour bar
hasbeenrestrictedtovaluesbelow20MeV.
(cid:13)c 2012RAS,MNRAS000,1–23
8 S. Rosswog, et al.
Figure4.DensitycutthroughtheorbitalplaneattheendofsimulationrunB(neutronstarswith1.3and1.4M(cid:12),β=2).Therotating
andpulsatingcentralobjectundergoesasequenceofmasssheddingepisodes,therebyproducingvariousinteractingshocksaroundthe
centralremnant.
Table 2.Massdistribution:tana isthetimeatwhichweanalyzethesimulationdata,mdisk istheresulting
disk mass, mfb is the mass in fallback material, mesc is the dynamically ejected mass and Ekin the corre-
spondingkineticenergy.ConsistentwithourapproachinSect.3.5wecappedthenumericalvelocitiesinthe
calculationofE at0.75c.
kin,esc
Run tana [ms] mdisk [M(cid:12)] mfb [M(cid:12)] mesc [M(cid:12)] Ekin[1051erg] (cid:104)vesc(cid:105)[c] comment
Collisions
A 21.2 0.27 0.10 0.060 1.15 0.13 ns-ns
B 9.0 0.40 0.10 0.009 0.97 0.22 ns-ns
C 13.2 0.32 0.03 0.030 3.61 0.28 ns-ns
D 127.5 0.24 0.11 0.142 5.70 0.19 ns-bh
E 143.6 0.14 0.04 0.172 10.68 0.24 ns-bh
F 540.3 0.05 0.04 0.134 8.73 0.24 ns-bh
Mergers
G 20.3 0.30 0.06 0.050 1.15 0.15 ns-ns,corot.
H 19.1 0.25 0.04 0.014 0.23 0.12 ns-ns,nospins
I 138.7 0.16/0.22 0.04 0.024 0.61 0.15 “diskindisk”,inner/bothdisks
J 139.3 0.21 0.03 0.049 1.82 0.18 ns-bh,nospins
(cid:13)c 2012RAS,MNRAS000,1–23
Mergers vs collisions: the multi-messenger picture 9
Figure 5.DensitycutthroughorbitalplaneofrunE.Panelone(numberingofthepanelsisfromlefttoright,fromuptodown)shows
asnapshotjustafterthefirst,paneltwoafterthesecondandpanelfivejustafterthethirdpericenterpassage.Eachpericenterpassage
producesatidaltail.Notethattheneutronstarcoresurviveseventhethirdpericenterpassage.Attheendofthesimulationitstillhas
a mass of ∼ 0.1 M(cid:12) and moves on a close-to-parabolic orbit away from the black hole. Note that the scales are changing between the
differentsnapshots.
(cid:13)c 2012RAS,MNRAS000,1–23
10 S. Rosswog, et al.
0.5 0.5
0.4 0.4 ns13, ns14, β= 1
ns13, ns14, merger, no spins ns13, ns14, β= 2
0.3 ns13, ns14, merger, corot. 0.3 ns13, ns14, β= 5
0.2 0.2
0.1 0.1
+ +
h 0 h 0
d d
-0.1 -0.1
-0.2 -0.2
-0.3 -0.3
-0.4 -0.4
-0.5 -0.5
0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 22
t [ms] t [ms]
1.75
1.25
ns14, bh5, β=1 1.5 ns13, bh3, β= 1
1 ns14, bh10, β= 1 1.25 ns13, bh5, β= 1
0.75 1 ns13, bh10, β= 1
0.75
0.5
0.5
0.25
0.25
+ +
h 0 h 0
d d
-0.25
-0.25
-0.5
-0.5
-0.75
-0.75 -1
-1 -1.25
-1.5
-1.25
-1.75
0 20 40 60 80 100 120 140 0 10 20 30 40 50 60 70 80 90 100
t [ms] t [ms]
Figure 6. Gravitational wave amplitudes h+ (times distance to source; code units = 1.5 km). The upper two panels show neutron
starneutronstarencounters(mergersleft,collisionsright),thelowertwopanelsshowneutronstarblackholeencounters(mergersleft,
collisionsright).
increase smoothly and peak about 6 ms after contact (at the mean neutrino energies: (cid:104)E (cid:105) > (cid:104)E (cid:105) > (cid:104)E (cid:105). The
νX ν¯e νe
t≈7.7ms)withatotalof1.3×1053 erg/s,seeupperpanel heavy lepton neutrinos are predominantly produced in hot,
of Fig. 7. The tidally locked case, run G, produces similar very dense regions and in the exceptional case, run F, the
results, but due to the larger disk mass, see Tab. 2, slightly densities have already dropped substantially below nuclear
higher luminosities. Since the debris is extremely neutron- matterdensity(ρ <1010 gcm−3)attheendofthesimu-
max
rich, the neutrino luminosities are dominated by electron lationwhenthemeanneutrinoenergies(asgiveninTab.3)
anti-neutrinos, followed in importance by electron neutri- are measured.
nos and heavy lepton neutrinos (collectively referred to as Even the most gentle ns2 collision with β = 1, run A,
“ν ”), consistent with earlier findings (Ruffert et al. 1997; produces a neutrino luminosity that is approximately three
X
Rosswog & Liebendo¨rfer 2003). In a recent 2D neutrino- times larger than the standard double neutron star merger
hydrodynamics calculation starting from the matter distri- case (run H). The merger neutrino lightcurves are rather
butionthatresultedfroma3Dsimulation(Price&Rosswog smooth, the collision cases, in contrast, show a much larger
2006) Dessart et al. (2009) found that our leakage scheme variability with luminosity changes of up to a factor of two
underestimates the heavy lepton neutrino emission, since it on the dynamical time scale of the central object, ≈ 1 ms,
does not account for the nucleon-nucleon bremsstrahlung see Fig. 7 middle panel. The more central collisions, run B
process. Therefore our heavy lepton neutrino emission re- and C, produce neutrino luminosities of about an order of
sults are robust lower limits on the true luminosities. In all magnitude larger than the reference case, see Tab. 3.
cases apart from run F we find the following hierarchy in Asdiscussedearlier,wefindlong-lived,episodicmasstrans-
(cid:13)c 2012RAS,MNRAS000,1–23