The Gravitational Wave Signal of a Core Collapse Supernova Explosion of a 15M$_\odot$ Star

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by  Konstantin N. Yakunin

TheGravitationalWaveSignalofaCoreCollapseSupernovaExplosionofa15M Star
(cid:12)
KonstantinN.Yakunin1,2,3,AnthonyMezzacappa1,2,PedroMarronetti4,EricJ.Lentz1,2,3,5,StephenW.Bruenn6,
W.RaphaelHix1,3,O.E.BronsonMesser1,4,7,EirikEndeve1,2,8,JohnM.Blondin9,andJ.AustinHarris10
1DepartmentofPhysicsandAstronomy, UniversityofTennessee, Knoxville, TN37996-1200, USA
2JointInstituteforComputationalSciences,OakRidgeNationalLaboratory,P.O.Box2008,OakRidge,TN37831-6354,USA
3PhysicsDivision,OakRidgeNationalLaboratory,P.O.Box2008,OakRidge,TN37831-6354,USA
4Physics Division, National Science Foundation, Arlington, VA 22207 USA
6DepartmentofPhysics,FloridaAtlanticUniversity,777GladesRoad,BocaRaton,FL33431-0991,USA
5Joint Institute for Nuclear Physics and its Applications,
Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6374, USA
7NationalCenterforComputationalSciences,OakRidgeNationalLaboratory,P.O.Box2008,OakRidge,TN37831-6164,USA
8ComputerScienceandMathematicsDivision,OakRidgeNationalLaboratory,P.O.Box2008,OakRidge,TN37831-6164,USA
7 9DepartmentofPhysics, NorthCarolinaStateUniversity, Raleigh, NC27695-8202, USAand
1 10NuclearScienceDivision, LawrenceBerkeleyNationalLaboratory, Berkeley, CA94720, US∗
0
2 In this Letter, we report on the gravitational wave signal computed in the context of an ab initio, three-
dimensionalsimulationofacorecollapsesupernovaexplosion,beginningwitha15M starandusingstate-of-
n (cid:12)
the-artweakinteractions.ThesimulationwasperformedwithourneutrinohydrodynamicscodeCHIMERA.We
a
J discussthepotentialfordetectionofourpredictedgravitationalsignalbythecurrentgenerationofgravitational
wavedetectors.
5
2

Introduction.– The first direct detection of gravitational art weak interactions. Our signal predictions are based on
]
E wave (GW) signals from binary-black-hole mergers [1, 2] the simulation data detailed by Lentz et al. [28]. (See also
H openedanewerainobservationalastronomy. Thishassetthe Melson et al. [29] for the case of a low-mass progenitor and
stage to prepare, even more fervently, for future detections, Melson et al. [30] for the case of a massive progenitor but
.
h especially of other of the primary sources of GWs, among with modified neutrino scattering cross sections.) Because
p themcore-collapsesupernovae(CCSNe). CCSNearephysics this simulation includes all of the relevant physics, albeit in
-
o rich with many physical processes operating in conjunction some instances with some level of approximation (e.g., ray-
r toproduceasupernova. Supernovamodelsare,therefore,in- by-rayneutrinotransport),andbecauseofthesimulationout-
t
s natelycomplex. InthecaseofaGalacticevent,aGWdetec- come,thecomputedGWsignalbasedonthissimulationdata
a tion is possible [3]. Such a detection, along with a detection isunique,withimplicationsforthepredictionoftheGWsig-
[
of the SN neutrinos, would provide direct information about nalamplitudeasafunctionoftime(forbothpolarizations),its

1 theseprocessesandtheSN‘centralengine’,inturnallowing frequency distribution and evolution, and the energy emitted
v ustovalidateourmodels. Moreover,inconjunctionwithde- intheformofGWs.
5 tailedGWsignals,ourmodelswouldprovideinsightintothe
2 Methodandinitialmodels.–OurGWanalysisisbasedon
nature and role of multidimensional fluid instabilities in the
3 thedatageneratedinthe2Dand3Dcorecollapsesupernova
proto-neutron star (PNS) and supernova core, the rotation of
7 simulations performed by Lentz et al. [28]. The simulations
thestellarcore,andthestructureoftheremnantPNS,aswell
0 werebothinitiatedfromthe15M progenitorofWoosleyand
. asthePNShigh-densitynuclearequationofstate(EoS),with (cid:12)
1 Heger [34] and were carried out with the CHIMERA code,
implications for fundamental nuclear physics – e.g., nuclear
0 which includes multigroup flux-limited diffusion neutrino
forcemodels.
7 transport with a state-of-the-art set of weak interactions and
1 ManystudiesofGWemissionincorecollapsesupernovae
an effective gravitational potential that incorporates the gen-
: (CCSNe) based on a variety of 2D/3D CCSN models were
v eralrelativisticmonopoleandcommensuratecorrections(e.g.,
performed in the past [4–15], including our studies [16, 17].
i gravitational redshift) to the neutrino transport [35]. The 3D
X Progress on multidimensional CCSN modeling has been ar-
computationalgridcomprised540(r)×180(θ)×180(φ)zones
r guablyexponential,inlightoftheincreasinglypowerfulcom-
equally distributed in the φ-direction only. The φ-resolution
a putationalresourcesavailabletomodelers,culminatinginthe
wasuniformly2◦. Theθ-resolutioninthe2Dmodelwasuni-
recent 3D modeling efforts of a number of groups [18–33].
formly 0.7◦. The θ-resolution in the 3D model varied from
A subset of these have been ab initio simulations with full
2/3◦ near the equator to 8.5◦ near the poles. The radial res-
physics (i.e., general relativistic with a complete set of neu-
olutioninbothsimulationsvariedaccordingtoconditionsof
trinointeractions)[28–31]. Inturn,asubsetofthelatterhave
the moving grid and reached 0.1 km inside the PNS. In both
reportedonexplosions[28–30].
simulations,weemployedtwoequationsofstates(EoS):Lat-
InthisLetter,wereportonourGWsignalpredictionsbased
timerandSwesty[36](incompressibilityK = 220MeV)for
on an ab initio, general relativistic, multi-physics, 3D sim-
ρ>1011 gcm−3andanenhancedversionoftheCooperstein
ulation of a CCSN of a 15M progenitor using state-of-the-
(cid:12) [37]EoSforρ<1011gcm−3. Inouterregionsweemployed
a14-speciesα-network[38]. Themodelswereevolvedin1D
during collapse and through bounce. At 1.3 ms after bounce
∗[email protected] randomdensityperturbationsof0.1%wereappliedtothemat-
2
terbetween10–30km. thePNSandgeneratethehigh-frequency,large-amplitudeex-
WecomparetheGWsignalsofthesetwomodels: C15-2D cursions evident in rh+. In the 3D case, there are a larger
and C15-3D. We employ the quadrupole approximation for numberoffunnelsfromneutrino-drivenconvection,eachac-
extracting the GW signals from the mass motions, using the cretinglessmassthanthosein2D,thatimpingeonthePNSto
expressionsdetailedin[17]. Toisolatetheimpactofdimen- inducethesamebehaviorinbothrh+ andrh×. Inperform-
sionality, all comparisons of the GW emissions in C15-2D ingacomparisonoftheamplitudesofrh+ acrossthe2Dand
and C15-3D have been performed using the same evolution 3Dcases,itisimportanttokeepinmindthepresenceoftwo
timeframe,whichisdictatedbyour3Drun(0–450ms),and polarizationsinthe3Dcase. TheoverallstructureoftheGW
thesamesamplinginterval(∆t = 0.2ms). Whilethisisnot signals, and their relationship to the phenomenology of the
particularlyimportantforcomparisonsofthewaveformsasa stellar core, is similar, and consistent (in the sense that there
functionoftime,acomparisonoftheGWspectraisnotpossi- is no physical argument as to why we should expect any of
bleunlessthetimeframeoverwhichthespectraarecomputed thephasesassociatedwiththe2DGWsignaltobeabsentin
iskeptthesame. 3D),acrossthe2Dand3Dcases. Acomparisonofthesignals
Results. – Direct comparison of the GW signal ampli- infrequency,discussedbelow,supportsthis. Boththespectra
tudes from models C15-2D and C15-3D (Fig. 1) should be and the total energy emitted are based on the complete GW
performed with cognizance of the fact that 3D admits more signals–inthe2Dcase,onthe+polarization,andinthe3D
degreesoffreedom–specifically,that3DadmitstwoGWpo- case, on both the + and × polarizations. In 3D and during
larizations (+,×) whereas 2D admits only one (+). Gossan thefirst∼450ms, westillseethreephasesofGWemission.
etal.[3]emphasizedthattheavailabilityoftwoindependent The prompt convection phase is very similar in timing and
polarizationsin3Dincreasesthechancesofdetectionby40%. amplitudetothe2Dcase. Thequiescentphaseispresent,and
startsandstopsatthesamepost-bouncetimesrelativetothe
ThepromptconvectionphaseoftheGWsignal.–Theearly
2Dcase. Thethirdphasebeginsatthesamepost-bouncetime
GWsignalisproducedbyLedouxconvectioninsidethePNS
relativetothe2Dcase,exhibitsthesamequalitativebehavior,
along with matter perturbed behind the quickly expanding
as neutrino-driven convection and the SASI develop and in-
shock. It lasts for the first 70–80 ms after bounce. Fig. 1
duce downflows onto the PNS. The fourth, explosion, phase
showsthatthe3Drh signalhasgenerallylargeramplitude
+
hasnotyetbeenobservedinthe3Dcase.
relativetothe2Dsignal. However,thedifferencelikelydoes
notariseentirelyfromthechangeindimensionality. Aswas The explosion phase of the GW signal.– Rapid shock ex-
pointed out in Yakunin et al. [17], this phase of the signal is pansion at the onset of explosion in the 3D case is delayed
verysensitivetomodelparametersandgridresolution. Usage by approximately 100 ms relative to its 2D counterpart [28].
of a constant-µ grid for the 3D model (a practical necessity Consequently,duringthe∼450msconsideredhere,wedonot
for this model given its computational cost) and a constant- observethelow-frequencytailofrh associatedwithprolate
+
θ grid for the 2D model likely contributes to the difference. or oblate explosion. In the 2D case, the tail is evident in the
3D runs to study the effect of resolution are planned for the final100msofavailabledata,andgiventhe∼100msdelayof
nearfuture. Resolutionaside,itisclearthatanearlyGWsig- explosionin3D,another∼100msbeyondtheendofthe3D
nalphaseispresentin3D,inbothpolarizations,andpossibly simulationpresentedherewouldbeneededtoseeevidenceof
morevigorousinthe+polarizationrelativetothe2Dcase. theexpectedtail.However,wedoexpectthemagnitudeofthe
The quiescent phase of the GW signal.– The quiescent tailinthe3Dcasetobesmaller. Thehigh-entropybubblethat
phase–atransitionphasebetweentheearlyandstrongsignal initiatestheoutwardaccelerationoftheshock[28]in3Dcon-
phases – is coincident (80–120 ms after bounce) in the two tains a smaller mass fraction than that in the 2D case, where
models. Moreover, the signal during this phase is similar in thehigh-entropybubbletakesupmuchofthevolumebehind
magnitudeineachmodel. Aswewilldiscuss,thefundamen- theshock.
tal difference between the C15-2D and C15-3D signals does TheGWenergyspectraandtheintegratedGWenergyemis-
notariseuntilneutrino-drivenconvectionandthestandingac- sionwithtime.–Figure3plotsthedecompositionofourC15-
cretion shock instability (SASI) [39] develop. The quiescent 2DandC15-3DGWsignals. Botharecomputedatthesame
phaseisparticularlyevidentintheplotofrh×(t)inFigure1. post-bounce time of 450 ms. Qualitatively, the GW spectra
Theneutrino-drivenconvection/SASI(i.e.,strong)phaseof areverysimilar. Afrequencyshiftintheenergyspectra,from
theGWsignal.–ThestrongestphaseoftheGWsignalstarts high(C15-2D)tolow(C15-3D)frequencies,isevidentinthe
at∼120msforbothour2Dand3Dsimulations. Thisisnot time-integrated spectral energy distribution dE/df. This re-
surprising given that the shock is still quasi-spherical at that sultsfromthelackofaxisymmetry(l=2,m=0only)in3D
time(seeFig.2),andtheangle-averagedshocktrajectoriesin thatallowsatransferofconvectiveenergyintomultiplel=2
2Dand3Dstillfollowoneanotherratherclosely[28]. How- modes (l = 2, m = −2,...,+2) that are absent in 2D. Fig-
ever, after ∼150 ms the shock behavior is very different in ure3alsoshowstheangle-averagedcharacteristicGWstrain
thetwomodels. Inthe2Dmodel,weobserveglobaloscilla- spectrah (f)[40]ofour2Dand3Dmodels,alongwiththe
char
tionsoftheshockduetotheSASI[35], buttheSASIisless broadbanddesignnoiselevelsofadvanced-generationGWin-
pronouncedin3Dduringtheinitial∼450mswindowconsid- terferometers,assumingasourcedistanceof10kpc. Mostof
ered here [28]. Global SASI oscillations in the 2D case in- the detectable emission is within 20–2500 Hz and at essen-
ducetheformationofafew,massiveaccretionfunnels. When tially the same level of ∼1-4 of 10−21 Hz−1/2. A Galactic
thesefunnelsimpingeonthesurfaceofthePNS,theyperturb event (at 10 kpc) appears to be well detectable by upcoming
3
the emitted GW energy clearly seen in our 2D model corre-
spond to sudden increases in the accretion rate. In the 2D
case, mass accretion is mediated by a few, massive funnels.
Theaddition,orloss,ofsuchafunnelwouldbeaccompanied
byasignificantchangeinthemassaccretionrate.Onthecon-
trary, the jumps in the emitted GW energy are absent in the
3Dcase,withthisenergygrowingsmoothlywithpost-bounce
time. In the 3D case, mass accretion onto the PNS is medi-
ated by numerous, lower-mass accretion funnels. The addi-
tion,orloss,ofsuchafunnelwouldnotresultinasignificant
changeinthemassaccretionrate. FrombothGWspectraand
frequency-integratedGWenergyemission,weseethatthenu-
merous downflows we observe in our 3D model produce a
responseofthePNSsimilartothefewer,moremassivedown-
flowsobservedinour2Dmodel.Thus,onemayconcludethat
thecharacteristicfrequencyoftheGWsignalsdependonthe
internal properties of the PNS (e.g., its high-density nuclear
equation of state and the associated radius, density profile,
etc.),whoseevolutionissimilarinC15-2DandC15-3D.
FIG.1. Top: Therh componentsoftheGWsignalsproducedin
+
theC15-2DandC15-3Dmodels. Bottom: Therh componentof
×
theGWsignalproduceintheC15-3Dandtherh componentofthe
+
GWsignalfromtheC15-2Dforcomparison.Bothcomponentsseen
by an equatorial observer. Inset: The first 150 ms of gravitational
waveformsproducedintheC15-2DandC15-3Dmodels.
FIG.2.EntropydistributionsfortheC15-2Dmodel(left)andforthe
equatorialsliceoftheC15-3Dmodel(right)at120msafterbounce.
FIG. 3. Frequency analysis of the GW signals from C15-2D and
detectors.
C15-3Dmodels. Top: Spectralenergydensitydistributionsfor2D
Thetotal,frequency-integratedGWenergyemittedisplot- and3Dmodels.Bottom:Characteristicspectralstrainh (f)f−1/2
char
tedinFigure4. TheemittedGWenergyinC15-2DandC15- of 2D and 3D models at a distance of 10 kpc compared with the
(cid:112)
3D follow one another closely. However, the fundamentally design noise levels S(f) of Advanced LIGO in the broadband
different character of the mass accretion onto the PNS be- zero-detuninghigh-powermode(aLIGOZD-HP),KAGRA,andAd-
vancedVirgoinwidebandmode(AdVWB).
tween the 2D and 3D cases is imprinted here. The jumps in
4
aremadetotheaxialvectorcouplingconstantintheneutral-
current scattering cross sections. In all four cases, these au-
thorsfindnosignificantGWproductionforthefirst∼175ms
afterbounce. Thedifferencesbetweenourpredictionsforthe
early GW signal and the predictions of the Garching group
will need to be explored further. However, for non-rotating
(spherical) progenitors, we do not expect to see significant
differencesinthe2Dand3Dcases,whichiswhatweobserve
(seeYakuninetal.[17]forthe2Dcase).Theconditionsinthe
inner regions of the PNS at these earliest times after bounce
simplydonotdiffersignificantlyaswemovefrom2Dto3D.
In contrast, the 3D predictions of Andresen et al. [41] differ
fromtheGarchinggroup’spredictionsinthe2Dcase[8]for
the same progenitor masses within the same set of progeni-
tors(e.g.,WHW02vs. WH07). Ofcourse,itisnotclearhow
productive a comparison of the early signal obtained by dif-
ferentgroupsisinthecaseofnon-rotating(spherical)progen-
itors. Amuchmorerobustearlysignalwillbeobtainedinthe
context of first-principles simulations with rotating progeni-
FIG.4. EnergyemittedintheformofGWsduringthefirst440ms
ofCCSNexplosionfortheC15-2D,andC15-3Dmodels. Thestep- tors,whichwillproducestrongsignalsatbounce. Moreover,
likebehaviorofE intheC15-2Dmodel(see,forinstance,300ms thebouncesignalswillbelesssensitivetosimulationdetails
GW
and400ms)reflectstheevolutionofthesingledominantaccretion (numericalmethods,gridresolution,etc.) and,rather,willde-
downflowinthismodel,incontrasttothemultipledownflowsinthe pendonthephysicalinitialconditionsassumed.Atlatertimes
3Dmodel. afterbounce,duringthedominantphaseofGWemissionas-
sociatedwithneutrino-drivenconvectionandtheSASI,wedo
Summary, Discussion, and Outlook.– Our ab initio, multi- seeareductionoftheamplitudeofthestraininthe3Dcase,
physics, 3D simulation of a CCSN explosion allowed us to relative to the 2D case, for the + polarization, but in 3D the
computethedetailedtimedependenceoftheGWsignalsfor emissionissharedbetweenthe+and×polarizations,making
boththeh andh polarizations. Forthetimewindowcon- a comparison difficult. We do not see significant differences
+ ×
sidered here, which is approximately the first half second in the GW energy emitted as a function of time between the
of evolution after stellar core bounce, we provide the corre- two cases, and, for the first ∼450 ms, the 3D GW spectrum
sponding spectral decomposition of the total signal, as well exhibitsasimilarstructurerelativetothe2Dcase,includinga
as the total energy emitted in GWs (from matter) as a func- peakinthespectrumat∼1000Hz.
tionofpost-bouncetime. Quantitatively,the3Dsignalsdiffer WhiletheGWsignalpredictionspresentedherearebased
fromthesignalsobtainedinour2Dcounterpartmodelforthe onabinitiomodelsthatexhibitanoteworthylevelofrealism,
reasons covered above, but they confirm the existence of the future models can and should develop in obvious ways:
first 3 phases of the GW signal accessible in this study: a (1) While the use of the “ray-by-ray” neutrino transport
prompt convection phase followed by a quiescent phase fol- approximation may be a better approximation in 3D than
lowed by the dominant GW emission phase from neutrino- in 2D [42], definitive 3D models will require 3D neutrino
drivenconvectionandtheSASI.Thefinal,explosionphaseis transport. (2) The use of the GR monopole correction to the
notaccessibleatthistimegiventhesimulationpresentedhere Newtonian self-gravitational potential should be replaced by
coversonlythefirsthalfsecondafterbounce. Theresultspre- a more sophisticated treatment of GR, such as the Confor-
sentedherearequalitativelyconsistentwiththepredictionof mally Flat Approximation (CFA) [43], or a full BSSNOK
a4-phasesignalfirstpresentedbyMurphyetal.[5]. Clearly, treatment[44]. (3)Tofullyresolveturbulentcascadesin3D
our understanding of the GW signals from (neutrino-driven) CCSN simulations, which is relevant for GW predictions,
corecollapsesupernovae–thedetailsofthesignalsandtheir one requires angular grid resolutions of less than 1◦ and
association with the underlying CCSN phenomenology – is radialresolutionsinsidethePNSoflessthen0.1km[45,46].
maturing. (4) Future 3D CCSN models will need to begin with 3D
Equally important, the predicted signals presented here progenitor models. Recent studies have demonstrated that
were shown to be detectable by LIGO and other extant GW the impact of improved initial conditions on CCSN mod-
observatoriesforaGalacticCCSNevent. Foradetailedstudy elsandtheirpredictedoutcomesispotentiallysignificant[26].
ofthedetectabilityofsuchanevent,wereferthereadertothe
workbyGossanetal.[3]. This research was supported by the U.S. Department of
Recently,Andresenetal.[41]documentedtheirpredictions Energy Offices of Nuclear Physics and Advanced Scien-
for the GW signatures from several of their 3D models, al- tific Computing Research, the NASA Astrophysics Theory
thoughfordifferentprogenitorsthantheonesconsideredhere. and Fundamental Physics Program (grants NNH08AH71I
Three of the four models presented by Andresen et al. [41] and NNH11AQ72I), and the National Science Foundation
donotexplode. Onemodeldoesexplodewhenmodifications PetaAppsProgram(grantsOCI-0749242, OCI-0749204, and
5
OCI-0749248)andGravitationalPhysicsProgram(grantGP- (ALCF),whichareDOEOfficeofScienceUserFacilitiessup-
1505933). This research was also supported by an award portedundercontractsDE-AC05-00OR22725andDE-AC02-
of computer time provided by the Innovative and Novel 06CH11357,respectively. P.M.issupportedbytheNational
Computational Impact on Theory and Experiment (INCITE) ScienceFoundationthroughitsemployeeIR/Dprogram. The
Program at the Oak Ridge Leadership Computing Facility opinionsandconclusionsexpressedhereinarethoseoftheau-
(OLCF) and at the Argonne Leadership Computing Facility thorsanddonotrepresenttheNationalScienceFoundation.
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