Neutrino-driven supernova of a low-mass iron-core progenitor boosted by three-dimensional turbulent convection

4.8 MB·English

by  Tobias Melson

DraftversionFebruary20,2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
NEUTRINO-DRIVENSUPERNOVAOFALOW-MASSIRON-COREPROGENITOR
BOOSTEDBYTHREE-DIMENSIONALTURBULENTCONVECTION
TobiasMelson1,2,Hans-ThomasJanka1,andAndreasMarek3
DraftversionFebruary20,2015
ABSTRACT
We present the first successful simulation of a neutrino-driven supernova explosion in three dimensions
(3D), using the Prometheus-Vertex code with an axis-free Yin-Yang grid and a sophisticated treatment of
5 three-flavor,energy-dependentneutrinotransport. Theprogenitorisanonrotating,zero-metallicity9.6M(cid:12)star
1 with an iron core. While in spherical symmetry outward shock acceleration sets in later than 300ms after
0 bounce,asuccessfulexplosionstartsat∼130mspostbounceintwodimensions(2D).The3Dmodelexplodes
2 ataboutthesametimebutwithfastershockexpansionthanin2Dandamorequicklyincreasingandroughly
10% higher explosion energy of >1050erg. The more favorable explosion conditions in 3D are explained
b
by lower temperatures and thus reduced neutrino emission in the cooling layer below the gain radius. This
e
F movesthegainradiusinwardandleadstoabiggermassinthegainlayer,whoselargerrecombinationenergy
booststheexplosionenergyin3D.Thesedifferencesarecausedbylesscoherent,lessmassive,andlessrapid

9 convectivedowndraftsassociatedwithpostshockconvectionin3D.Thelessviolentimpactoftheseaccretion
1 downflowsinthecoolinglayerproduceslessshockheatingandthereforediminishesenergylossesbyneutrino

emission. We thus have, for the first time, identified a reduced mass accretion rate, lower infall velocities,
]
R andasmallersurfacefillingfactorofconvectivedowndraftsasconsequencesof3Dpostshockturbulencethat
facilitateneutrino-drivenexplosionsandstrengthenthemcomparedtothe2Dcase.
S
Subjectheadings: supernovae: general—hydrodynamics—instabilities—neutrinos
.
h
p
- 1. INTRODUCTION plosions in 3D, because it destroys the biggest convective
o
plumes, which were recognized as helful for 2D explosions
r Modeling the core-collapse supernova (SN) mechanism in
t three dimensions (3D) is still in its infancy. Generaliza- (Hanke et al. 2012; Couch 2013; Couch & O’Connor 2014;
s Dolence et al. 2013). Therefore Abdikamalov et al. (2014)
a tion from spherical symmetry (1D) to axial symmetry (2D)
are worried about even less favorable explosion conditions
[ introduces nonradial flows and hydrodynamic instabilities
when resolution shortcomings of all current 3D models can
like convection and the standing accretion shock instability
2 be overcome, and Couch & Ott (2013, 2014) advocate pre-
(“SASI”; Blondin et al. 2003) in the neutrino-heated post-
v collapse progenitor-core asymmetries as possible solution of
shock layer, which have been recognized as helpful for the
1 thedilemma.
explosion due to improved neutrino-heating conditions and
6 Here we present the first successful 3D simulation of a
buoyancyorturbulentpressurebehindtheshock(e.g.,Herant
9
neutrino-drivenSNexplosionofa9.6M iron-corestarcom-
1 etal.1994;Burrowsetal.1995;Janka&Mu¨ller1996;Mur- (cid:12)
putedfullyself-consistentlywiththeneutrino-hydrodynamics
0 phy & Burrows 2008; Murphy et al. 2013; Marek & Janka codePrometheus-Vertex. Weidentify,forthefirsttime,con-
. 2009; Mu¨ller et al. 2012a,b, 2013; Mu¨ller & Janka 2014a,b;
1 sequences of 3D turbulence in the convective gain layer that
Suwa et al. 2013; Bruenn et al. 2013, 2014; Takiwaki et al.
0 enhancetheexplosionenergyandaccelerateshockexpansion
2014;Couch&Ott2014).
5 in3Drelativeto2D.Whilesofarinmoremassiveprogenitors
Explosionsof2Dmodels, however, startlateandtheiren-
1 3Dturbulenceappearslesssupportivefortheinitiationofex-
ergiestendtobefairlylow(exceptforthoseofBruennetal.
: plosionsthan2Dflows(cf.referencesaboveandHankeetal.
v 2013, 2014, whose results still need better explanation and
2013; Tamborra et al. 2014 for 11.2,20,27M models), we
i confirmation by detailed comparisons with other recent sim- (cid:12)
X ulations). 3D effects were hoped to improve the situation, investigateherewhether3Dcanstrengthentheexplosionaf-
r butafirstoptimisticreportbasedonparametricallytriggered tertheonsetofshockrunaway. Theconsidered9.6M(cid:12)model
a offers an ideal case for this study because it explodes at the
neutrino-drivenexplosionsbyNordhausetal.(2010)wasnot
same time in 2D and 3D. We briefly describe our numerical
supported by subsequent works (Hanke et al. 2012; Couch
approach in Sect. 2, discuss our results in Sect. 3, and con-
2013;Couch&O’Connor2014;Takiwakietal.2012,2014;
cludeinSect.4.
Mezzacappaetal.2015). Dolenceetal.(2013)andBurrows
et al. (2012) confessed an error in Nordhaus et al. (2010), 2. NUMERICALSETUPANDPROGENITORMODEL
nevertheless they still claimed a remaining positive effect in
We performed 1D, 2D, and full (4π) 3D simulations of
3D.Turbulentfragmentationbyenergycascadingfromlarge
a nonrotating, zero-metallicity 9.6M , iron-core progenitor
(cid:12)
to small scales, however, seems to disfavor and delay ex-
provided by A. Heger (private communication; Woosley &
Heger2015)andpreviouslyinvestigatedin2DbyMu¨lleretal.
1Max-Planck-Institut fu¨r Astrophysik, Karl-Schwarzschild-Str. 1,
(2013).
85748Garching,Germany
WeusedthePrometheus-Vertexhydrodynamicscodewith
2PhysikDepartment,TechnischeUniversita¨tMu¨nchen,James-Franck-
Straße1,85748Garching,Germany three-flavor,energy-dependent,ray-by-ray-plus(RbR+)neu-
3Rechenzentrum der Max-Planck-Gesellschaft (RZG), Boltzmannstr. trinotransportincludingthefullsetofneutrinoreactionsand
2,85748Garching,Germany microphysics (Rampp & Janka 2002; Buras et al. 2006) ap-
2 Melson,Janka,&Marek
Fig.1.— 3Diso-entropysurfacesat90,170,and350msafterbounce.Colorsrepresentradialvelocities.Thesupernovashockisvisiblebyathinsurrounding
line,theproto-neutronstarbyawhitishiso-densitysurfaceof1011gcm−3.Theyardstickindicatestherapidlygrowingvolume.
plied in 3D also by Hanke et al. (2013) and Tamborra et al. Here,ρisthedensity,andthevolumeintegrationisperformed
(2014),inparticularthehigh-densityequationofstateofLat- overthepostshockregionwherethetotalspecificenergy,
timer & Swesty (1991) with a nuclear incompressibility of
1 (cid:104) (cid:105)
K = 220MeV. Our simulations were conducted with a 1D e =e+ |v|2+Φ+ e (56Fe)−e , (2)
tot bind bind
gravitypotential(whichisunproblematicfornearlyspherical 2
explosions) including general relativistic corrections (Marek is positive, with e, 1|v|2, and Φ being the specific internal,
et al. 2006). For the first time we employed the newly im- kinetic, and (Newton2ian) gravitational energies. The brack-
plementedaxis-freeYin-Yanggrid(Kageyama&Sato2004). etedtermexpressesthedifferencebetweenthenuclearbind-
The implementation followed Wongwathanarat et al. (2010) ingenergiesperunitmassofallnucleonsfinallyrecombined
and posed no particular problems for the RbR+ transport. to iron-group nuclei and for the nuclear composition at a
Conservation laws are globally fulfilled with an accuracy of given time. It therefore accounts for the maximum release
∼10−3 over several 100ms for our angular resolution of 2◦. of nuclear binding energy and corresponds to an upper limit
Theradialgridhadareflectingboundaryconditionattheco- of E , while omitting this term yields a lower bound on
exp
ordinatecenterandaninflowconditionattheouterboundary E (redandbluelines, respectively, inbottomleftpanelof
exp
of109cm. Ithad400nonequidistantzonesinitiallyandwas Fig.3). Thebindingenergyofthestellarlayersaheadofthe
refined in steps up to >600 zones, providing an increasingly shockplaysonlyaminorroleintheenergybudgetoftheex-
better resolution of ∆r/r ∼0.01...0.004 around the gain ra- plosion because at t = 400ms it is only −3.5×1048erg in
pb
dius. For the neutrino transport 12 geometrically spaced en- the1Dsimulationandevenonly−9.5×1047erginourmulti-
ergybinswithanupperboundof380MeVwereused.
dimensionalsimulations.
3.1. ExplosionDynamicsandProperties: 2Dvs3D
3. SIMULATIONRESULTS In 3D convective overturn in the neutrino-heated post-
The relatively steep density gradient above the iron core shocklayerdevelopsattpb (cid:38)70ms,showingthewell-known
enables a neutrino-driven explosion of the 9.6M star at Rayleigh-Taylormushrooms(Fig.1,left)andincreasingnon-
(cid:12)
roughly300msafterbounceevenin1D(leftpanelsinFig.3), radial velocities (colors in Fig. 2). The postshock convec-
similarto(butmoredelayedthan)oxygen-neon-magnesium- tionreachesitsmaximumactivitybetweenabout100msand
core progenitors exploding as “electron-capture SNe” (Ki- 200msafterbouncewithaprominentmaximumat∼120ms,
tauraetal.2006;Jankaetal.2008;Fischeretal.2010). The at which time the shock starts its accelerated expansion (cf.
energy of such a late explosion, however, remains low, only Figs.2and3)andthepostshockflowbecomeshighlyturbu-
Eexpl ∼ 2×1049erg (Fig. 3), because it is provided mainly lent (Fig. 1, middle). At tpb (cid:38)200ms the shock and post-
bytherecombinationoffreenucleonstoα-particlesandiron- shock matter expand with ∼25,000kms−1, and the ejecta at-
groupnucleiinthegainlayer(seeSchecketal.2006)andthe tain a nearly self-similar structure (Fig. 1, right). This is the
corresponding mass at tpb > 300ms is only 2.2×10−3M(cid:12) in time when convection and turbulence behind the shock be-
1D.Ofcourse,thesubsequentneutrino-drivenwindfromthe comeweakeragain(lessintenseredinFig.2)andmassshells
proto-neutron star (PNS) will increase the power of the ex- leavingthePNSsurfaceindicatethatthecompactremnantbe-
plosion. E denotestheinstantaneous“diagnosticenergy”, ginstolosematerialinthelow-density,high-entropybaryonic
expl
whichisdefinedby winddrivenbyneutrinoheatingabovetheneutrinosphere.
In our multi-dimensional simulations the shock stagnates
(cid:90) only for ∼120–130ms and then expands to (cid:104)R (cid:105) ≈
shock
E = dV ρe . (1) 6000km at 400ms postbounce (p.b.) compared to only
expl tot
etot>0,postshock
Neutrino-drivensupernovaofalow-massprogenitorinthreedimensions 3
9 3.2 shift of the gain radius in 3D compared to 2D: R3D < R2D
gain gain
2.8 (Fig.3).
1] Consequently, the mass of the gain layer, M =
adius[cm])78 122...604 82[10cms−φ(cid:69) d(cid:82)ceRone(cid:104)gRpocaisenelhionncokdg(cid:105)fsdlMVaoynρceo,orm,lisoMvdlaaceroriloge-lsse,prswemacinitafihdllc,eticrdmoeinretrae3ibslDesp,co.atnWuhdseihengigltaehliyent,h-dmethea3efisDnsmi-t2daioDsiffsngeadiiornniefffnteRhcree0-
log(r6 01..82 2vv+θ (cid:113) agnrodwrsemtoa∆inMsgeasinse≈nt1ia.2lly×c1o0n−s3tMan(cid:12)t abfettewrweeanrd1s0.0Tmhseannudcl2e0a0rmres-
(cid:68) combinationenergyofthismassdifference,
(cid:104)Rshock(cid:105) 0.4
5 {0.1,1.3,1.35}M(cid:12) 0.0 ∆Mgain×erecomb ∼(1.6...2.0)×1049erg(cid:38)∆Ee3xDp−l2D (5)
0.2 0.1 0.0 0.1 0.2 0.3 0.4
− − for e ∼ (7...8.8)MeV/nucleon ≈ (6.76...8.49) ×
time[s] recomb
1018ergg−1 (dependingonwhetherfreenucleonsrecombine
Fig.2.—Mass-shell(radiiforchosenenclosedmasses)evolutionofthe3D
to α-particles or iron-group elements) can easily account for
explosionwithcolorsshowingrmsvaluesofthenonradialvelocity. Thered
solidlinemarkstheangle-averagedshockradius,thedashedlinesseparate the3D-2DdifferencesoftheexplosionenergyinFig.3.
regionswithmassspacingsof0.01, 0.1, 0.01, and0.001M(cid:12) (frominside Turbulentpressureinthegainlayerisunderstoodtobesup-
outwards). The3Dsimulationwasstartedfroma1Dmodelat∼10msafter
portive for the onset of neutrino-driven explosions (Murphy
bounce(verticaldottedline).
etal.2013;Couch&Ott2014;Mu¨ller&Janka2014b).How-
ever, for our low-mass SN progenitor this effect cannot be
∼2000kminthe1Dcase(Fig.3). Angle-averagedquantities
crucialfortheobserved2D-3Ddifference. Despitethefaster
X(r)arecomputedaccordingto
andmoreenergeticexplosion,the3Dmodelexhibitsalower
(cid:82)
X(r)dΩ turbulent kinetic energy in the gain layer during the crucial
(cid:104)X(r)(cid:105)≡ (cid:82) dΩ . (3) tpreibriuotdio1n0E0gmains(cid:46) =tpb(cid:82)(cid:46)(cid:104)Rs2ho0ck0(cid:105)dmVs,1vρi(svi2bl+e vb2y)tihneFniogn.r3a.diaTlakcoinng-
kin,θ,φ Rgain 2 θ φ
Positive total energies in the postshock layer develop only into account the larger mass in the gain layer, it means that
shortly after the onset of outward shock acceleration. Inter- thenonradialfluidmotionsaremuchlessvigorousinthe3D
estingly, in 3D the shock expands faster and the explosion case.
energy increases more steeply and to a higher value than in Incontrast,thenonradialkineticenergyinthecoolinglayer,
2D.Attpb =400msthediagnosticenergyreaches Ecool =(cid:82)RgaindV 1ρ(v2+v2),issmallerinthe2Dsimulation
kin,θ,φ R0 2 θ φ
E3D (400ms)∼(0.77...1.05)×1050erg (4) despitethehighermassofthislayerin2D.Thissuggeststhat
expl nonradialmotionsaremuchmoreefficientlydampedbydis-
in3Dwithanincreaseatarateof∼(0.75...1.25)×1050ergs−1 sipationinstrongerdecelerationshocksandduetosymmetry
duetothePNSwindforthecasesofminimalandmaximalen- constraints(reflectiveaxisboundaries)inthecoolinglayerof
ergy,respectively,whereasitisonly∼(0.67...0.92)×1050erg the2Dmodel.
in2DwithasimilargrowthratebythePNS-windpowerasin
3D4. 3.2. DetailedAnalysisof2D-3DFlowDifferences
While the onset of the explosion in multi-dimensions is The reason for more favorable explosion conditions in 3D
aided by buoyant convection, the steeper rise of the explo- becomesclearerthroughradialprofilesoftheturbulentaccre-
sionenergyin3Dcanbeunderstoodbyasmallernetenergy- tionflowinthegainandcoolinglayers(Figs.4and5). Here,
lossrate,Q˙ ,intheneutrino-coolinglayerduring100ms(cid:46) angularaveragesofquantities X(r)overinfallingmatter,i.e.,
cool
t (cid:46) 200ms (Fig. 3). Q˙ is evaluated between the mean overregionswithradialvelocityv <0,arecomputedaccord-
pb cool r
gain radius, R , and an inner radius R ≡ r(τ = 3), ingto
whichis(somegwaihnatarbitrarily)definedata0nopticalνedepthof (cid:82) X(r)Θ(−v )dΩ
r
3 for νe (all quantities are evaluated on angle-averaged pro- (cid:104)X(r)(cid:105)vr<0 ≡ (cid:82) Θ(−v )dΩ , (6)
files). In contrast, the integrated net neutrino-heating rate r
in the gain layer, Q˙ , and the heating efficiency, ηgain = whereΘ(x)istheheavisidefunctionwithΘ(x) = 1for x ≥ 0
Q˙ (E˙ +E˙ )−1 (wgiatinh E˙ being the direction-averagheedatlu- andΘ(x)=0otherwise.
mginaionsitνieesofνν¯eeandν¯e),doνinotexhibitanysignificant3D-2D Radial velocity profiles of vr, angle-averaged over con-
differences(Fig.3). vective downdrafts in the postshock accretion layer, ex-
The reduced energy-loss rate in the cooling layer for hibit stronger local variations with higher extrema and pro-
100ms(cid:46) t (cid:46) 200ms is associated with a systematically nounced intermittency-like behavior in 2D, whereas the
lower specpifibc internal energy, e¯cinotol ≡ (cid:18)(cid:82)RR0gaindVρe(cid:19)Mc−o1ol, asmngoloe-thavereraangdedshionwfalllesvseleoxctirteiemseiflnucthtueat3ioDnsm(Foidge.l4a,plpeefta)r.
averaged over the cooling-layer mass M = (cid:82)RgaindVρ This points to a larger number of smaller-scale convective
cool R0 structures,thusreducingthestatisticalvariance,andsuggests
(Fig. 3). This suggests lower temperatures in the cooling lessvigorousradialmassmotionsinthe3Dmodel, whichis
layer,lessefficientneutrinoemission,andthereforeaninward compatiblewiththelowernonradialkineticenergyinthegain
layerbetween100msand200msp.b.(cf.Fig.3).
4 Testswithdoubledangularresolutionanddifferentseedperturbations This conclusion is supported by cross-sectional cuts
revealed∼4%variationsofEe2xDpl(400ms). (Fig. 5), where narrow convective downflows in 2D possess
4 Melson,Janka,&Marek
8 1.6 2.0
0.3 Egain Q˙
8[10cm] 4567 00..120.0 0.1 4810erg] 0111....8024 Ekkcoiinno,,lθθ,,φφ gain1,η.][01]−heat11..05 −ηhggQaea˙ainictnool
Rshock(cid:105)3 [kin,θ,φ 0.6 2ergs
E 5
(cid:104)2 0.4 00.5
1
[
1 0.2 ˙Q
0 0.0 0.0
1.2 1D 8.2 m] 35 Mgain
2D M
erg] 01..80 33DD−2D 1gg]−78..80 R∆[kgain2350 −∆coRolgain
50 56Fe er −20
[10xpl 0.6 min 18[107.6 M,](cid:12)15
Ee 0.4 coole¯int7.4 30− 10
1
0.2 7.2 [ 5
M
0
0.0 7.0
0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4
t [s] t [s] t [s]
pb pb pb
Fig.3.—Explosionparametersasfunctionsofpost-bouncetime. 1Dresultsaredisplayedbydottedlines,2Dbythinsolidlines,and3Dbythicksolidlines.
Angle-averagedshockradii(upperleft);explosionenergieswithupperlimitsinred,lowerlimitsinblue(seetext)and3D-2Ddifferenceswithdashedlines
(bottomleft); kineticenergiesofnon-radialmassmotionsinthegain(red)andcoolinglayers(blue; uppermiddle); averagespecificinternalenergiesinthe
coolinglayer(lowermiddle);totalnetneutrino-heatingratesinthegain(red)andcoolinglayers(blue)andneutrino-heatingefficiencies(dashed,scaledbya
factorof10;topright);massesintheheating(red)andcoolinglayers(blue)anddifferenceofangle-averagedgainradii,−∆Rgain =−(R3gaDin−R2gaDin)(dashed;
bottomright).
higher velocities, in agreement with radial profiles of v av- symmetric(2D)downflowsisbiggerthanthevolumeencom-
r
eraged over inflows and time-averaged over 100ms≤ t ≤ passedby3Daccretionfunnels. Exactlythisisexpressedby
pb
200ms(Fig.4). Thehigherinfallvelocitiesin2Dinthegain thelargerα inthegainlayer,which,togetherwithbigger
vr<0
layer and a fair part of the cooling layer are associated with infall velocities, accounts for the higher mass-accretion rate
agreatermass-accretionratearoundthegainradius(Fig.4). in2D.
Moreover, in 2D a larger fraction of the sphere in the gain
layer is subtended by downflows, which is expressed by the 3.3. 3DTurbulenceFacilitatingExplosion
“downflowfillingfactor”, The reduced rate and less powerful infall of mass through
the gain radius is therefore the fundamental reason for more
(cid:82)
Θ(−v )dΩ favorable explosion conditions in 3D. Higher downflow ve-
r
αvr<0 ≡ (cid:82) dΩ , (7) locitiesin2Dleadtomoreviolentdecelerationoftheaccre-
tion downdrafts in shocks as they penetrate into the cooling
layer(seeFig.5andthemoredramaticdecreaseof|(cid:104)v (cid:105) |
inFig.4. Incontrast, inthecoolinglayerα2D < α3D . All in2DinFig.4). Ontheonehandthiscausesstrongergrravvri<ty0-
vr<0 vr<0
these findings are in line with higher kinetic energies of ra- waveactivitybelowR ,whichcanberecognizedbylarger
gain
dial and nonradial flows in the gain layer and slightly lower angular variations of v for the 2D model in this region in
r
nonradialkineticenergyinthecoolinglayerforthe2Dmodel Fig.5. Ontheotherhandtheimpactofdownflowsdissipates
(Fig.3). kinetic energy, for which reason the 2D simulation shows a
Atfirstglance,thehighermass-accretionratearoundR lowerkineticenergyofnonradialmassmotionsinthecooling
gain
in 2D seems to contradict the 2D-3D differences of the flow layer despite its higher nonradial kinetic energy in the heat-
geometry visible in Fig. 5: In 2D one counts one or two inglayer(Fig.3). Moreimportant,however,istheenhanced
prominent convective downdrafts, consistent with a convec- shockheatingofthecoolinglayer,whichleadstohighertem-
tive cell pattern characterized by low spherical-harmonics peraturesinthisregionin2D(Fig.4). Estimatesconfirmthat
modes, i.e., large-scale structures with few downflows. In this difference of the angle-averaged temperature of several
contrast,manymoredownflowfunnelsexistin3D,although 109K(orseveralpercentofthelocalangle-averagedtemper-
with smaller infall velocities. Nevertheless, the 2D model ature)isresponsibleforthelargernetcoolingrateofthe2D
channels more mass per time through the gain radius. Ob- model just below R (Fig. 4), because local temperature
gain
viously, thetotalvolumeoftoroidal“sheets”formedbyaxi- fluctuations are considerably bigger than the relative differ-
Neutrino-drivensupernovaofalow-massprogenitorinthreedimensions 5
0 108 0 1.0
0
2D <
1] −1 αvr0.8
−
ms tor
1 c 2 ac 0.6
− m] 80 − gf
c 1 n
r[107 [v<0r −3 wfilli 0.4
1ms]−−2 Rgain vr(cid:104)(cid:105)−4 2D wnflo 0.2
o
c R0 3D d
8
[10 108 −5 K]0.0
v<0r 3 3D 0.8 9[10 1 (cid:104)qq˙˙(cid:105)23DD
vr(cid:105)− 1] T(cid:105) (cid:104)∆(cid:105)T
(cid:104) s−(cid:12)0.6 ∆(cid:104)0 (cid:104) (cid:105)
m] M 1,]
−
−4 r[c107 ˙M[v<0r 0.4 1ggs−−1
Rgain −0.2 0er 2
20−
1
R0 [
(cid:105)
5 0.0 q˙ 3
− 0.10 0.15 0.20 0.25 106 107 (cid:104)−106 107
t [s] r[cm] r[cm]
pb
Fig.4.—Profilesofangle-averagedradialvelocitiesofinfalling(vr <0)matter,outgoingshock(sharpblue-whitediscontinuity),meangainradius,Rgain,and
innerboundaryofcoolinglayer,R0,asfunctionsofpost-bouncetimefor2D(topleft)and3Dmodels(bottomleft). Time-averaged(over0.1s≤ tpb ≤ 0.2s)
r“asduirafalcperofifillliensgoffaacntogrlse”-aovfedraogwendfldoowwsn,flαovrw<0ve(ulopcpietirersi,g(cid:104)hvtr)(cid:105);var<n0d,a(in.eg.l,eo-afvmeraatgteerdwsiptehcvifirc<n0e;tunpeupterrinmoi-dhdelaet)i;nmg/acsoso-liinnfgalrlartaetse,s(cid:104)qi˙n(cid:105),daonwdn3flDo-w2sD,Mt˙emvr<p0er(abtoutrteomdiffmeirdednlcee);,
∆(cid:104)T(cid:105)=(cid:104)T(cid:105)3D−(cid:104)T(cid:105)2D(bottomright). Thinsolidlinesshow2D,thicksolidlines3Dresults,theverticaldottedlinesindicatethetime-averagedgainradiusin
3D.
2D 0.16s 3D 2D 0.18s 3D
4 4
3 3
2 2
m] 1 1
c
7 0 0
0
1
z[ 1 1
− −
2 2
− −
3 3
− −
4 4
− 0 1 2 3 4 4 3 2 1 0 1 2 3 4 − 0 1 2 3 4 4 3 2 1 0 1 2 3 4
− − − − − − − −
x[107cm] x[107cm] x[107cm] x[107cm]
2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0
− − − − − − − −
v (r >R )[109cms 1] v (r <R )[108cms 1]
r gain − r gain −
Fig.5.—Cross-sectionalcutswithradialvelocitiesinthex-zplaneat0.16s(left)and0.18safterbounce(right)for2D(leftsemi-panels)and3Dmodels(right
semi-panels). Themeangainradius,Rgain,ismarkedbyadashedcircle. ForbettervisibilitydifferentcolorscalesareusedoutsideandinsideofRgain(leftand
rightcolorbar,respectively).
6 Melson,Janka,&Marek
encesoftheangularaveragesandneutrinoemissionratesby withasteeperriseatthebeginningoftheexplosion.
e±-capturesande+e−-pairannihilationscalewithT6 andT9, We thus presented the first successful neutrino-driven ex-
respectively. Consequently, one finds R2D > R3D during plosion in a fully self-consistent 3D simulation and, for
170ms(cid:46)t (cid:46)220ms(Fig.4,bottomleft)g.ainSincethgaeintemper- the first time, identified effects that foster and strengthen
pb
neutrino-drivenexplosionsin3Dcomparedto2D.Incontrast
atureinthegainlayerisonlymarginallyhigherin3D,thenet
totheunfavorableinfluenceof3Dturbulenceobservedinpre-
heatingratesbetweenR andshockarehardlydistinguish-
gain
vious studies of more massive stars (e.g., Hanke et al. 2012;
ablefor2Dand3D(Fig.4,bottomright).
The2D-3Ddifferencesintheconvectivepostshocklayer,in Couch2013;Couch&O’Connor2014;Takiwakietal.2012,
2014;Abdikamalovetal.2014),thedecreaseofthemassin-
particular higher downflow velocities and larger mass-infall
ratein2D,canbeattributedtowell-knowndifferencesof2D flowratethroughthegainradiusandreducedneutrino-energy
lossinthecoolinglayerbelowR haveahealthyinfluence
and 3D turbulence discussed previously (e.g., Hanke et al. gain
ontheexplosioninour9.6M progenitorin3D.
2012;Burrowsetal.2012;Dolenceetal.2013;Couch2013; (cid:12)
It is difficult to speculate whether these effects could play
Couch&O’Connor2014;Dolenceetal.2013;Abdikamalov
an important role also for more massive stars, in particular
et al. 2014): Turbulent energy cascading leads to fragmen-
when convection dominates the postshock dynamics (Bur-
tation of large-scale flows to smaller-scale vortices in 3D,
rows et al. 2012; Murphy et al. 2013) and current numerical
whereas the inverse energy cascade in 2D tends to enhance
resolutiondeficiencies(see,e.g.,discussionsbyRadiceetal.
kinetic energy on the largest possible scales. The turbulent
2015;Abdikamalovetal.2014;Hankeetal.2012)havebeen
fragmentation (e.g. through Kelvin-Helmholtz instability) of
the postshock accretion flow affects the flow characteristics overcome. We emphasize that our present grid resolution is
insufficient to achieve convergence and to capture fully de-
most strongly near the gain radius, for which reason 2D-3D
differences of M˙ increase as the infalling gas approaches velopedturbulence. However,weattributeour2D-3Ddiffer-
vr<0 ences to generic differences of convective downflow dynam-
R (Fig.4). Becauseofenhancedturbulentenergyinsmall-
gain
ics, which are likely to remain valid even for higher resolu-
scale vortices, the 3D flow becomes less coherent, and tur-
tion. Wehaveidentifiedturbulentfragmentationof3Dflows
bulentsmall-scalestructureskeepmassinthegainlayerand
reduce M˙ , while in 2D the mass-infall rate continues to inthegainlayerashelpfulforstrongerexplosionsthanin2D,
vr<0 insharpcontrasttodisadvantageousconsequencesof3Def-
growallthewaytowardsR .
gain
fects for the onset of explosions reported for more massive
4. CONCLUSIONS progenitorsinpreviousworks. Higherresolutionmighteven
enhanceourdescribedeffectsandtheirexplosion-facilitating
Performing simulations of neutrino-driven explosions for
consequencesratherthanendangeringthem.
a 9.6M star with the Prometheus-Vertex code in 1D and
(cid:12)
multi-D,wefoundsignificant2D-3Ddifferencesoftheaccre-
tion flow in the convective postshock layer. Turbulent frag- We thank R. Bollig, J. von Groote, F. Hanke, B. Mu¨ller,
mentation to small-scale vortices keeps more matter in the E. Mu¨ller, A. Wongwathanarat, E. Erastova, and M. Rampp
gain layer in 3D and decreases the rate and velocity of mass for support and discussions and J. Guilet for careful read-
accretionintothecoolinglayer. Thisreducesthedissipation ing and comments. Funding by Deutsche Forschungsge-
of kinetic energy in the cooling region, lowers the temper- meinschaft through grants SFB/TR7 and EXC 153 and by
ature there and decreases the energy loss by neutrino emis- the European Union through grant ERC-AdG No. 341157-
sion. Thecorrespondinginwardshiftofthegainradiusleads COCO2CASA and computing time from the European
toanincreaseofthemassinthegainlayer,whosehighernu- PRACEInitiativeonSuperMUC(GCS@LRZ,Germany)and
cleon recombination energy accelerates shock expansion in CURIE(GENCI@CEA,France)areacknowledged. Postpro-
3D and boosts the explosion energy by (cid:38)10% to >1050erg cessingwasdoneonHydraofRechenzentrumGarching.
REFERENCES
Abdikamalov,E.,Ott,C.D.,Radice,D.,Roberts,L.F.,Haas,R.,Reisswig, Herant,M.,Benz,W.,Hix,W.R.,Fryer,C.L.,&Colgate,S.A.1994,ApJ,
C.,Moesta,P.,Klion,H.,&Schnetter,E.2014,eprintarXiv:1409.7078 435,339
Blondin,J.M.,Mezzacappa,A.,&DeMarino,C.2003,ApJ,584,971 Janka,H.-Th.&Mu¨ller,E.1996,A&A,306,167
Bruenn,S.W.,Mezzacappa,A.,Hix,W.R,Lentz,E.J.,Bronson,M.O.E., Janka,H.-T.,Mu¨ller,B.,Kitaura,F.S.,&Buras,R.2008,A&A,485,199
Lingerfelt,E.J.,Blondin,J.M.,Endeve,E.,Marronetti,P.,&Yakunin, Kageyama,A.,&Sato,T.2004,Geochem.Geophys.Geosys.,5
K.N.2013,ApJ,767,L6 Kitaura,F.S.,Janka,H.-T.,&Hillebrandt,W.2006,A&A,450,345
Bruenn,S.W.,Lentz,E.J.,Hix,W.R,Mezzacappa,A.,Harris,J.A.,Bronson, Lattimer,J.M.,&Swesty,F.D.1991,Nucl.Phys.A,535,331
M.O.E.,Endeve,E.,Blondin,J.M.,Chertkow,M.A.,Lingerfelt,E.J., Marek,A.&Janka,H.-T.2009,ApJ,694,664
Marronetti,P.,&Yakunin,K.N.2014,eprintarXiv:1409.5779 Marek,A.,Dimmelmeier,H.,Janka,H.-T.,Mu¨ller,E.,&Buras,R.2006,
Buras,R.,Rampp,M.,Janka,H.-T.,&Kifonidis,K.2006,A&A,447,1049 A&A,445,273
Burrows,A.,Hayes,J.,&Fryxell,B.A.1995,ApJ,450,830 Mezzacappa,A.,Bruenn,S.W.,Lentz,E.J.,Hix,W.R,Harris,J.A.,Bronson,
Burrows,A.,Dolence,J.C.,&Murphy,J.W.2012,ApJ,759,5 M.O.E.,Endeve,E.,Blondin,J.M.,Marronetti,P.,&Yakunin,K.N.2015,
Couch,S.M.2013,ApJ,775,35 eprintarXiv:1501.01688
Couch,S.M.&O’Connor,E.P.2014,ApJ,785,123 Mu¨ller,B.&Janka,H.-T.2014a,ApJ,788,82
Couch,S.M.&Ott,C.D.2013,ApJ,778,L7 Mu¨ller,B.&Janka,H.-T.2014b,eprintarXiv:1409.4783
Couch,S.M.&Ott,C.D.2014,eprintarXiv:1408.1399 Mu¨ller,B.,Janka,H.-T.,&Heger,A.2012a,ApJ,761,72
Dolence,J.C.,Burrows,A.,Murphy,J.W.,&Nordhaus,J.2013,ApJ,765, Mu¨ller,B.,Janka,H.-T.,&Marek,A.2012b,ApJ,756,84
110 Mu¨ller,B.,Janka,H.-T.,&Marek,A.2013,ApJ,766,43
Fischer,T.,Whitehouse,S.C.,Mezzacappa,A.,Thielemann,F.-K.,& Murphy,J.W.&Burrows,A.2008,ApJ,688,1159
Liebendo¨rfer,M.2010,A&A,517,A80 Murphy,J.W.,Dolence,J.C.,&Burrows,A.2013,ApJ,771,52
Hanke,F.,Marek,A.,Mu¨ller,B.,&Janka,H.-T.2012,ApJ,755,138 Nordhaus,J.,Burrows,A.,Almgren,A.,&Bell,J.2010,ApJ,720,694
Hanke,F.,Mu¨ller,B.,Wongwathanarat,A.,Marek,A.,&Janka,H.-T.2013, Radice,D.,Couch,S.M.,&Ott,C.D.2015,eprintarXiv:1501.03169
ApJ,770,66 Rampp,M.&Janka,H.-T.2002,A&A,396,361
Scheck,L.,Kifonidis,K.,Janka,H.-T.,&Mu¨ller,E.2006,A&A,457,963
Neutrino-drivensupernovaofalow-massprogenitorinthreedimensions 7
Suwa,Y.,Takiwaki,T.,Kotake,K.,Fischer,T.,Liebendo¨rfer,M.,&Sato,K. Tamborra,I.,Hanke,F.,Janka,H.-T.,Mu¨ller,B.,Raffelt,G.G.,&Marek,A.
2013,ApJ,764,99 2014,ApJ,792,96
Takiwaki,T.,Kotake,K.,&Suwa,Y.2012,ApJ,749,98 Wongwathanarat,A.,Hammer,N.J.,&Mu¨ller,E.2010,A&A,514,48
Takiwaki,T.,Kotake,K.,&Suwa,Y.2014,ApJ,786,83 Woosley,S.E.&Heger,A.2015,ApJ,submitted