The explosion mechanism of core-collapse supernovae: progress in supernova theory and experiments

1.4 MB·English

by  Thierry Foglizzo

Publications of the Astronomical Society of Australia(PASA)
(cid:13)c AstronomicalSocietyofAustralia2015;publishedbyCambridgeUniversityPress.
doi:10.1017/pas.2015.xxx.
The explosion mechanism of core-collapse supernovae:
progress in supernova theory and experiments
Thierry Foglizzo1, R´emi Kazeroni1, J´erˆome Guilet2, Fr´ed´eric Masset3, Matthias Gonz´alez1, Brendan K.
Krueger1,∗, J´erˆome Novak4, Micaela Oertel4, J´erˆome Margueron5, Julien Faure1, No¨el Martin6, Patrick Blottiau7,
5 Bruno Peres8 and Gilles Durand1
1 1LaboratoireAIM(CEA/Irfu,CNRS/INSU,Univ.ParisDiderot),CEASaclay,F-91191GifsurYvette,Cedex,France
0 2MaxPlanckInstituteforAstrophysics,Karl-Schwarzschild-Str.1,85748Garching,Germany
2 3InstitutodeCienciasF´ısicas,UniversidadNacionalAutonomadeM´exico,P.O.Box48-3,62251Cuernavaca,Morelos,Mexico
4LUTh,CNRS/ObservatoiredeParis/Univ.ParisDiderot,5placeJulesJanssen,F-92195Meudon,France
b 5InstitutdePhysiqueNucl´eairedeLyon,Univ.ClaudeBernardLyon1,IN2P3-CNRS,F-69622Villeurbanne,France
e 6InstitutdePhysiqueNucl´eaire,IN2P3-CNRS,Univ.Paris-Sud,F-91406Orsaycedex,France
F 7CEA,DAM,DIF,F-91297Arpajon,France
8Deptd’AstronomiaiAstrof´ısica,Univ.deValencia,Edificid’Investigaci´oJ.Munyoz,C/Dr.Moliner,50,46100Burjassot,Spain
6

]
E Abstract
H Theexplosionofcore-collapsesupernovadependsonasequenceofeventstakingplaceinlessthanasecond
. inaregionofafewhundredkilometersatthecenterofasupergiantstar,afterthestellarcoreapproachesthe
h
Chandrasekharmassandcollapsesintoaproto-neutronstar,andbeforeashockwaveislaunchedacrossthe
p
stellarenvelope.Theoreticaleffortstounderstandstellardeathfocusonthemechanismwhichtransformsthe
-
o collapse into an explosion. Progress in understanding this mechanism is reviewed with particular attention
r toitsasymmetriccharacter.Wehighlightaseriesofsuccessfulstudiesconnectingobservationsofsupernova
t
s remnantsandpulsarspropertiestothetheoryofcore-collapseusingnumericalsimulations.Theencouraging
a results from first principles models in axisymmetric simulations is tempered by new puzzles in 3D. The
[
diversity of explosion paths and the dependence on the pre-collapse stellar structure is stressed, as well

2 as the need to gain a better understanding of hydrodynamical and MHD instabilities such as SASI and
v neutrino-driven convection. The shallow water analogy of shock dynamics is presented as a comparative
4 system where buoyancy effects are absent. This dynamical system can be studied numerically and also
3 experimentally with a water fountain. The potential of this complementary research tool for supernova
3 theory is analyzed. We also review its potential for public outreach in science museums.
1
0
Keywords: accretion – hydrodynamics – instabilities – shock waves – supernovae
.
1
0
5
1 INTRODUCTION events observed every year in distant galaxies, and the
1
: progress of computational power. Even if robust explo-
v The explosive death of massive stars is a key ingre-
sions are not obtained from first principles yet, numer-
i dient in stellar evolution, stellar population synthesis
X ical simulations are able to explore physical ideas in
and the chemical enrichment of galaxies. It defines the
r full 3D models, filling the gap between theoretical con-
a birth conditions of neutron stars which, if associated
cepts and observations. The multiplication of theoreti-
in a coalescing binary system, may be responsible for
calresultsmayseemdifficulttointerpretinviewofthe
short GRBs and r-process nucleosynthesis. The shock
multiplicity of physical assumptions, which range from
wave launched in the interstellar medium during a su-
simple adiabatic approximations of an ideal gas to ad-
pernovaexplosionacceleratescosmicraysandmaycon-
vanced modeling of neutrino transport and nuclear in-
tribute to triggering star formation. Understanding the
teractionsingeneralrelativity.Substantialprogresshas
mechanism of supernovae explosions has become a pri-
been achieved over the last ten years with an emphasis
ority since the detailed observation of SN1987A neutri-
ontheasymmetriccharacteroftheexplosion,whichwe
nos and the identification of its massive progenitor. It
propose to summarize in the present review.
is still a theoretical challenge despite hundreds of new
Some important observational constraints regarding
the asymmetric character of the explosion are recalled
∗present address: Los Alamos National Laboratory, NM 87545,
in Sect. 4.2. The general theoretical framework of
USA
1
2 T. Foglizzo
neutrino-driven explosions is summarized in Sect. 3. regions become visible.
In order to underline the nature of recent theoretical On a longer timescale, the shape of the inner ejecta
progress we have shown in Sect. 4 that a large set of currentlyseeninSN1987Aalsosuggestsanasymmetric
modern physical ideas were already known before 2009 explosion geometry which is not aligned with the large
andlaterconfirmedbymoreadvancedcalculations.We scalestructureofthecircumstellarmedium(Larssonet
analyze in Sect. 5 the new ideas which have driven su- al.2013).Eventhreehundredyearsaftertheexplosion,
pernova theory in the most recent years beyond the its asymmetric character can leave an imprint on the
production of better tuned models. In particular the chemical composition of the ejecta. The spatial distri-
diversity of explosion scenarios has drawn attention to butionof44TiobservedbytheNuSTARspacetelescope
the pre-collapse stellar structure and correspondingly inCassiopeaAshowsaglobalasymmetry,whichseems
increased the size of the parameter space of initial con- tofavortheregionopposedtothedirectionofthecom-
ditionstobeexplored.Thiscomplexitycallsforadeeper pact object (Grefenstette et al. 2014). This one-sided
understandingofthephysicalprocesses.Anexperimen- asymmetry seems to confirm the theoretical prediction
tal fountain based on a shallow water analogy has been of Wongwathanarat et al. (2013) where a strong one-
proposed to gain insight into one of the instabilities re- sided shock expansion is favorable to nucleosynthesis
sponsiblefortheasymmetriccharacteroftheexplosion. whilethecloserregionintheoppositedirectionattracts
The potential of this new tool is analyzed in Sect. 6, the neutron star gravitationally.
both for theoretical research and for public outreach. Direct constraints on the first second of the explosion
The study of neutrino and gravitational wave diagnos- areexpectedfromthefuturedetectionofneutrinos(e.g.
tics are left to the recent reviews of Janka et al. (2012), Wurmetal.2012,Mu¨lleretal.2014a)andgravitational
Janka(2012),Kotakeetal.(2012),Burrows(2013)and waves(Ott2009,Kotake2013,Mu¨lleret al. 2013)from
Kotake(2013).Particularattentionispaidtothemany aGalacticsupernova.Thefuturedetectionofthediffuse
newresultsdiscoveredoverthelasttwoyearssincethese neutrino background will globally constrain both the
reviews. physics of the explosion and the supernova rate (Bea-
com 2010). For an individual Galactic event, the time
variability of the neutrino signal from the IceCube ex-
2 OBSERVATIONAL EVIDENCE FOR
periment could directly measure the modulation of the
ASYMMETRIC EXPLOSIONS
emission due to a SASI oscillation of the shock (Lund
The observed distribution of pulsar velocities (e.g. et al. 2010, 2012, Tamborra et al. 2013, 2014).
Hobbs et al. 2005) has been a puzzle for more than 40
years because they are much faster than massive stars
3 THEORETICAL FRAMEWORK
(Gunn & Ostriker 1970). Average velocities of several
hundredsofkm/scannotbeexplainedbyaresidualor- 3.1 Neutrino-driven explosion scenario
bitalvelocitygainedthroughthedisruptionofabinary
The most promising framework to understand the ma-
system during the explosion. A pulsar kick is a natu-
jority of supernova explosions was set by Bethe & Wil-
ral outcome of an asymmetric explosion process with a
son (1985). The delayed explosion mechanism driven
significant l=1 component as seen in Sect. 4.2.1. The
by neutrino energy was initially described as a spher-
angle between the direction of the kick and the direc-
ically symmetric process. As the mass of the central
tion of the rotation axis of the pulsar contains a very
core approaches the Chandrasekhar mass (∼1.4M ),
interestingconstraintonthegeometryoftheexplosion. sol
thepressureofdegeneraterelativisticelectronsbecomes
Thedirectionoftherotationaxiscanbeaccuratelyde-
insufficienttoresistgravity.Electronpressureisfurther
termined when a pulsar wind nebula is observed, but
decreased as theyare captured by protonsand produce
this sample is still small and lacks unambiguous cases
neutrons and neutrinos. A new equilibrium is reached
where the kick is strong enough to neglect a possible
between gravity and nuclear matter essentially made
orbital contribution to the kick (Ng & Romani 2004,
of neutrons. The stellar core collapses from a radius
Wang et al. 2006). Polarimetry suggests a strong corre-
of ∼1500km to this new equilibrium of a few tens of
lation but cannot fully disentangle kick-spin alignment
kilometersinlessthanhalfasecond(Fig.1).Thegrav-
from orthogonality (Noutsos et al. 2012). This correla-
itational energy gained from this collapse seems large
tionissmearedoutbytheGalacticpotentialforpulsars
enough to be able to account for the observed kinetic
older than 10 Myr (Noutsos et al. 2013).
energy ∼1051erg of the supernova ejecta:
The asymmetric character of the explosion is also sug-
gestedbythesuddenincreaseofpolarizationofthelight GM2 (cid:18)30km(cid:19)(cid:18) M (cid:19)2
observedfromatypeII-Psupernovaexplosionafter∼90 ns ∼2×1053erg ns . (1)
R R 1.5M
days,atthemomentoftransitionfromthephotospheric ns ns sol
phase to the nebular phase (Leonard et al. 2006). This Amajordifficultyofsupernovatheoryistoexplainhow
increasecoincideswiththemomentwhentheinnermost thisgravitationalenergyistransferredtothestellaren-
PASA(2015)
doi:10.1017/pas.2015.xxx
The explosion mechanism of core-collapse supernovae 3
Although most neutrinos emerge from the neutri-
nosphere of the cooling neutron star, a fraction comes
from the neutronization of accreted matter below the
gain radius. This process decreases the entropy of neu-
tron rich matter settling in a stably stratified manner.
Betweentheshocksurfaceandthegainradius,thedom-
inanceofneutrinoabsorptionoverneutrinoemissionin-
creases the entropy of the matter. This gain region is
crucial to the success of the explosion, which relies on
theabsorptionofsufficientneutrinoenergytorevivethe
stalled shock.
Other sources of energy have been considered to pro-
duce an explosion, such as the rotational and the mag-
netic energies. The rotation period of pulsars at birth
defines a reference rotational energy E deduced from
rot
the conservation of angular momentum
(cid:18) M (cid:19)(cid:18) R (cid:19)2(cid:18)10ms(cid:19)2
E ∼2.8×1050erg ns ns (4.)
rot 1.4M 10km P
sol ns
Spin periods P ∼10−20ms at birth are considered
ns
by Heger et al. (2005) as plausible extrapolations from
the observations of young pulsars, without excluding
possibleeffectsofbinaryinteractionduringthelifetime
Figure 1.Theneutrino-drivendelayedexplosionmechanismre-
liesontheabsorptionofneutrinosbythedensepost-shockgas. of the massive star (Sana et al. 2012, De Mink et al.
2013, 2014) or a significant redistribution of angular
momentum during or immediately after the pulsar
birth. The relative inefficiency of known spin-down
veloppe to reverse the infalling motion into an explo- mechanisms (Ott et al. 2006) rules out rotationally-
sion.Theinfallofsupersonicmatterontothesurfaceof driven supernovae as the generic case. According
this proto-neutron star produces a deceleration shock to Eq. (4), the rotational energy could be a major
which stalls at a radius of ∼150km. The bounce of the contributor in the particular cases where the rotation
free-falling matter v2/2∼GM/r onto the core is far rate of the stellar core is large enough to produce
ff
fromelastic,becauseasignificantfractionofthekinetic millisecond pulsars.
energy is absorbed into the dissociation of iron nuclei. Magnetic energy could also play an important role if
This can be seen by comparing the kinetic energy of a the magnetic field within the core were strong enough.
free-falling nucleon and its binding energy 8.8MeV in The main source of magnetic field amplification is the
theironatom,neglectingspecialrelativisticcorrections differential rotation within the core (e.g. Akiyama et
for the sake of simplicity: al.2003),whichisonlyafractionofthetotalrotational
energy.
1m v2 236km M
2 n ff ∼ . (2) Assuming that the rotational energy is too weak to
8.8MeV r 1.5M
sol be the dominant contributor of the most common
Stellarmatterpassingthroughtheshockisthusdissoci- explosions (i.e. P ≥10ms), most studies of core
ns
atedintofreenucleons.Thesubsonicadvectionofthese collapse have focused on the challenge of producing
nucleons towards the surface of the proto-neutron star an explosion without any rotation at all. We shall
takes place in an intense flux of neutrinos which diffuse see in Sect. 4.3 that rotation could be an important
out of the proto-neutron star and carry away most of ingredient of the explosion mechanism even if its total
the gravitational energy gained during the contraction. energy is modest.
The detection of neutrinos from SN1987A were instru- We can also expect magnetic effects to play a role
mental to confirm the premises of supernova theory set in shaping the geometry of the explosion even if the
by Colgate & White (1966). magnetic energy is modest compared to the final
Thepost-shockregionismadeoftwosuccessiveregions kinetic energy of the ejecta (e.g. Guilet et al. 2011).
defined by the direction of the reaction
Detailed numerical modeling solving the Boltzmann
p+e↔n+ν, (3)
equationtodescribeneutrinotransportandtakinginto
where the relativistic velocity of the electrons corre- account special and general relativistic effects reached
sponds to a Lorentz factor γ >(m −m )/m ∼2.5. the conclusion that the scenario proposed by Bethe &
e n p e
PASA(2015)
doi:10.1017/pas.2015.xxx
4 T. Foglizzo
Wilson (1985) is unable to power the spherically sym-
metric explosion of massive stars (Liebendoerfer et al.
2001)exceptforthelightestones.Theenvelopeofstars
in the range 8-10 M is light enough to allow for a
sol
spherical explosion of ∼1050erg in about 100ms (Ki-
taura et al. 2006). In a sense, the absence of systematic
explosions in spherical symmetry is consistent with the
observational evidence summarized in Sect. 4.2. Theo-
retical efforts over the past two decades have updated
the delayed neutrino-driven explosion scenario by tak-
ing into account its multidimensional nature.
Figure2.SASImechanismbasedonthecouplingbetweenacous-
3.2 Hydrodynamical sources of asymmetry
ticwaves(wavyarrows)andadvectedperturbations(circularar-
rows)betweenthestalledshockandtheprotoneutronstar.
3.2.1 Neutrino-driven buoyancy
In addition to the prompt convection associated with
the deceleration of the shock as it stalls, the continued
heating of the gas by neutrino absorption maintains a
radialentropygradientorientedinthesamedirectionas
vary from one progenitor to another, depending on the
gravity from the shock to the gain radius (Herant et al.
radius of the stalled shock.
1992, Janka & Mu¨ller 1996). Some gravitational energy
can be gained if the flow is able to interchange high
and low entropy layers. The Brunt-V¨ais¨al¨a frequency
3.2.2 Instability of the stationary shock: SASI
ω characterizes the timescale of the fastest motions
BV
Another source of symmetry breaking was discovered
fed by buoyancy forces. Defining the entropy S in a
by Blondin et al. (2003) who studied a simplified setup
dimensionless manner, the Brunt-V¨ais¨al¨a frequency is
where neutrino heating was neglected in order to avoid
expressed as follows:
anypossibleconfusionwithneutrino-drivenconvection.
S ≡ 1 log P/P0 , (5) TheStandingAccretionShockInstability(SASI)corre-
γ−1 (ρ/ρ )γ sponds to a global oscillatory motion of the shock sur-
0
γ−1 face with a period comparable to the advection time
ω2 ∼− ∇S·∇Φ. (6)
BV γ from the shock to the neutron star surface. This global
(l=1) and oscillatory character are distinct features
This interchange can feed turbulent motions and push
of the linear regime when perturbations grow exponen-
the shock further out, increasing the size of the gain
tially with time. In contrast, the convective instability
region and diminishing the energy losses due to disso-
is non-oscillatory and dominated by smaller azimuthal
ciation. Numerical simulations performed in the early
scales(typicallyl=5−6)comparabletotheradialsize
2000’s were disappointing though (Buras et al. 2003),
of the gain region.
both because the duration of the simulation was lim-
The mechanism responsible for SASI relies on the in-
ited to a few hundred milliseconds and as some equa-
teraction of acoustic perturbations and advected ones,
torial symmetry was assumed due to limited compu-
such as entropy and vorticity perturbations (Galletti &
tational resources. The equatorial symmetry precluded
Foglizzo2005,Ohnishi2006,Foglizzoetal.2007,Scheck
the growth of global l=1 modes. Foglizzo et al. (2006)
et al. 2008, Guilet & Foglizzo 2012). As illustrated in
pointedoutthatthenegativesignoftheentropygradi-
Fig.2,aperturbationoftheshocksurfaceproducesen-
ent is not a sufficient criterion for the convective in-
tropy and vorticity perturbations which are advected
stability in the gain region because the interchange
towards the proto-neutron star surface. Their deceler-
has to be fast enough to take place before the ad-
ation in the hot region close to the neutron star pro-
vected gas reaches the gain radius. A criterion for lin-
duces an acoustic feedback which propagates towards
ear stability compares the advection timescale to the
the shock surface, pushes it and regenerates new ad-
buoyancy timescale estimated from the Brunt-V¨ais¨al¨a
vected perturbations with a larger amplitude than the
growth rate:
first ones. This advective-acoustic cycle has been de-
(cid:90) shock dr scribed analytically in a Cartesian geometry (Foglizzo
χ≡ |ωBV||v | <3 (7) 2009, Sato et al. 2009). The same coupling mechanism
gain r is responsible for the instability of the bow shock in
Fromthiscriteriononecananticipatethatthestrength Bondi-Hoyle-Lyttleton accretion (Foglizzo 2001, 2002,
and consequences of neutrino-driven buoyancy may Foglizzo et al. 2005).
PASA(2015)
doi:10.1017/pas.2015.xxx
The explosion mechanism of core-collapse supernovae 5
4 WHAT DID WE KNOW BACK IN 2009? ferent axisymmetric code by Nordhaus et al. (2010a,
2012) which directly followed the motion of the neu-
4.1 First successful explosions in numerical
tron star. This kick mechanism has been confirmed in
simulations from first principles
3D simulations by Wongwathanarat et al. (2010, 2013)
The discovery of the global l=1 oscillations of SASI whousedanaxis-freeYin-Yanggridratherthanspher-
emphasized the importance of performing numerical ical coordinates.
simulations over the full sphere. Using a ray by ray ap-
proximation of neutrino transport and relativistic cor- 4.2.2 Enhanced mixing triggered by asymmetric
rections to the gravitational potential, Marek & Janka shock in SN1987A
(2009) obtained the first successful explosions of 11.2 The light curve of SN1987A, together with the early
and15M progenitormodelsfromfirstprinciples.The emergence of X-ray and gamma rays suggested that
sol
explosion was more difficult to obtain with the more significant mixing disrupted the onion like structure
massive progenitor due to the intense ram pressure of of the star (McCray 1993, Utrobin 2004, Fassia &
infalling matter. It took 800ms of post-bounce evolu- Meikle 1999), probably triggered by the interaction of
tion (and three years of computation) for the axisym- the shock with composition interfaces. The efficiency
metric shock to reach an explosion after a long phase of this mixing is enhanced if the shape of the shock
of SASI oscillations. The easier explosion of 2D simu- is non-spherical, as shown by Kifonidis et al. (2006).
lations compared to radial ones was analyzed by Mur- This study considered shock deformations dominated
phy & Burrows (2008) who showed that post-shock gas by the modes l=1,2 as naturally produced by SASI
trapped in convective patterns is exposed for a longer during the first second after shock bounce. The sub-
timetotheneutrinoflux,thusaccumulatingenoughen- sequent hydrodynamical evolution of the shock across
ergy and entropy in the gain region to push the shock the stellar envelope up to the surface showed final iron
outwards. The turbulent motions induced by hydrody- group velocities up to 3300km/s, strong mixing at the
namicalinstabilitiesalsocontributetotheshockrevival H/He interface, and hydrogen mixed down to velocities
by building up a turbulent pressure in the post-shock of 500km/s. These features are closer to observations
region as observed by Burrows et al. (1995) and more than those obtained by the same team from a spherical
recently stressed by Murphy et al. (2013) and Couch & shock dominated by the smaller scale convective insta-
Ott (2014). bility (Kifonidis et al. 2003). The viability of this pro-
cessin3DwaslaterconfirmedbyHammeretal.(2010),
whofollowedtheevolutionoftheshockcalculatedin3D
by Scheck (2007), across the stellar enveloppe. They
4.2 Instabilities in the supernova core as an
found that the development of mixing instabilities is
explanation for observed asymmetries?
more efficient in 3D and allows for higher clump ve-
4.2.1 The mystery of pulsar kicks potentially locities due to the different action of drag forces. The
explained effect of the progenitor structure was recently explored
The Garching team was first to recognize the potential by Wongwathanarat et al. (2014) with a series of red
ofgloball=1deformationstoexplainpulsarvelocities and blue supergiants of 15M and 20M .
sol sol
of several hundreds of kilometers per second (Scheck et
al. 2004). The global conservation of linear momentum
4.3 First hints of a dominant spiral mode in
implies that the final momentum of the neutron star is
3D and the spin rate of neutron stars
equalinmagnitudeandopposedindirectiontothetotal
momentum of the ejecta. The asymmetric distribution As early as 2007, the first 3D simulations of the SASI
ofejectedmatterhasbeenstudiedinaseriesofaxisym- instabilitywereperformedinthesimplestadiabaticap-
metric simulations where the neutrino luminosity was proximation (Blondin & Mezzacappa 2007). Instead of
adjusted to trigger an explosion. They showed that the the sloshing oscillation l=1, m=0 ubiquitous in 2D
gravitational interaction pulls the neutron star in the axisymmetric simulations, the 3D simulations revealed
direction of the closest dense regions of post-shock gas, a dominant spiral mode l=1, m=±1 even though no
overatimescaleofseveralsecondswhichcanexceedthe angular momentum was contained in the free falling
timescaleofdirectadvectionofmomentumfromtheac- stellar matter. This opened the possibility that a non-
creted gas. Their statistical study produced a shape of rotating stellar core could give birth to a rotating neu-
the distribution of pulsar velocities in agreement with tronstar,withtheoppositeangularmomentumcarried
observationalconstraints(Schecketal.2006).Themag- away by the ejecta of the supernova. Blondin & Mezza-
nitude of the kick is a stochastic variable, while the cappa(2007)estimatedthatthefinalspinperiodofthe
explosion energies and timescales were found to be de- neutron star could be as short as 50ms. They checked
terministic in this study. The magnitude of the kicks that these dynamics were not an artifact of the inflow-
obtained has been subsequently confirmed with a dif- ing inner boundary condition by performing equatorial
PASA(2015)
doi:10.1017/pas.2015.xxx
6 T. Foglizzo
simulations with a hard surface and a cooling function Back in 2009 it was very unclear whether the pulsar
(Blondin & Shaw 2007). kickwouldreachacomparablemagnitudein3Dandin
Another spectacular result was obtained by Blondin & 2D,andwhethertheefficiencyofmixinginducedbythe
Mezzacappa(2007)byconsideringforthefirsttimethe shock propagation in the stellar enveloppe would com-
3DdevelopmentofSASIinarotatingprogenitor.They pare as favorably to SN1987A in 3D simulations as in
observedthatthespiralmodeispreferentiallytriggered 2D. As already noted in Sect. 4.2, these two questions
inthesamedirectionastheprogenitorrotation,andas later received positive answers. Launching an explosion
a consequence the angular momentum received by the from first principles, however, turned out to be even
proto-neutronstarisopposedtothatoftheparentstar. more challenging in 3D than in 2D.
The phase of SASI instability may thus decelerate a
neutron star to a lower spin than naively deduced from
5 WHAT IS NEW SINCE 2009?
the conservation of angular momentum. They showed
that a rotating massive star may even give birth to a The progress of supernova theory in the last 5 years
counter rotating neutron star. These results were con- hasgonemuchfurtherthanconfirmingpreviousresults
firmed by Yamasaki & Foglizzo (2008) using a pertur- with improved computational power. New constraints
bativeapproachinacylindricalgeometry.Inparticular have been obtained from the determination of neutron
the growth rate of SASI was shown to depend linearly star masses. New ideas have emerged concerning the
ontheangularmomentumoftheprogenitor.Rotationis diversity of explosion paths and their sensitivity to the
able to destabilize the prograde mode of SASI through structure of the progenitor above the iron core includ-
thedifferenceofrotationratesbetweentheshockradius ing its angular momentum, magnetic field and initial
and the inner radius, even when the rotation rate is so asymmetries.
small that the centrifugal force is negligible.
Theexistenceofaphysicalmechanismcapableofmod-
5.1 A better constrained equation of state
ifying the angular momentum of the neutron star dur-
ing the collapse revived the debate about the compari- The equation of state of neutron rich matter at nuclear
son between the angular momentum in the stellar core densities is an important ingredient of the dynamics of
inferred from stellar evolution and the angular momen- core-collapse,whichsetstheradiusoftheproto-neutron
tum of pulsars at birth inferred from observations. The star and thus the depth of the gravitational potential.
studyofHegeretal.(2005)hadconcludedthatthespin Most simulations have used a parametrized equation
ratesof10-15msofthemostcommonpulsarswerecom- of state provided by Lattimer & Swesty (1991), Hille-
patible with stellar evolution with plausible magnetic brandt & Wolff (1985) or Shen et al. (1998). The de-
field strengths deduced from dynamo action, without scription of matter properties at nuclear densities is
theneedtoinvokeanymagneticbrakingduringorafter extrapolated from the properties of nuclei available in
the explosion. Alternate scenarios are possible though, terrestrial experiments, as well as measurements of the
since the transport of angular momentum in the 1-D mass and to a lesser extent the radius of neutron stars.
codes of stellar evolution relies on uncertain prescrip- The measurement of the mass of a neutron star with
tions based on debated dynamo action (Spruit 2002, a mass of 1.97±0.04M by Demorest et al. (2010) is
sol
Zahn et al. 2007). In particular the distribution of an- accurate enough to rule out a series of alternate mod-
gularmomentumcouldalsobeaffectedbytheactionof els and significantly reduces the uncertainty associated
internal gravity waves (e.g. Lee & Saio 1993, Talon & to the equation of state. A second neutron star in this
Charbonnel2003,Pantillonetal.2007,Leeetal.2014). mass range has been discovered by Antoniadis et al.
(2013), with a mass of 2.01±0.04M for the pulsar
sol
PSR J0348+0432. Exotic forms involving a transition
4.4 The uncertainties of a non-axisymmetric
toquarkmatter(Sagertetal.2009,Fischeretal.2011)
explosion scenario
can produce significant dynamical consequences dur-
The non-axisymmetric shock geometry observed in the ing core collapse, but involve phenomenological mod-
first 3D simulations by Blondin & Mezzacappa (2007) elswithparametersadjustedtoreproducetheobserved
castdoubtsonalltheconclusionsdrawnintheaxisym- massive neutron stars. In particular, the properties of
metric hypothesis and urged new 3D simulations incor- quarkmatterattherelevantdensitiesareneitheracces-
porating non-adiabatic processes. Would the third di- sibletoexperimentsnortoanytheoreticaldevelopment
mensionbeakeyingredientforrobustsuccessfulexplo- from first principles.
sions? Contrasting with the ample deformations of the Staying in the classical framework, some improvements
shock found in the idealized simulations of Blondin & are necessary to account for the latest advances in nu-
Mezzacappa (2007), the first non-adiabatic simulations clear physics. Several statistical models have been de-
by Iwakami et al. (2008) suggested that the asymme- veloped accounting for the entire distribution of nuclei
triesinducedbySASImaybeweakerin3Dthanin2D. (Hempel&Schaffner-Bielich2010,Raduta&Gulminelli
PASA(2015)
doi:10.1017/pas.2015.xxx
The explosion mechanism of core-collapse supernovae 7
2010, Buyukcizmeci et al. 2013) in contrast to the ap- sensitive to the radial structure of the envelope sur-
proximation of a single representative heavy nucleus rounding the central core.
and α-particles within the classical EoS (Lattimer &
Swesty 1991, Shen et al. 1998). Except in some small
density and temperature regions, the effects on global 5.3.1 The parameter χ and the relative roles of
thermodynamics remains small and the effect on core neutrino-driven convection vs SASI
collapsesimulationsismodest(Steineretal.2013).The The numerical simulations performed at MPA and
effectontheneutrinointeractionsandspectracouldbe ORNL confirmed the diversity of hydrodynamical pro-
more important (Arcones et al. 2008). cesses ruling the multidimensional evolution during
For progenitors with masses above ∼25M , the tem- the last hundreds of milliseconds before the explosion.
sol
peraturesanddensitiesreachedduringcorecollapsecan Neutrino-driven buoyancy seems to govern the post-
become so high that a traditional description in terms shock dynamics of the progenitor of 11.2 M . The
sol
ofelectrons,nuclei,andnucleonsisnolongeradequate. global oscillations of SASI are clearly dominant for the
Several EoS have been developed incorporating addi- 27 M progenitor (Mu¨ller et al. 2012b), while both
sol
tional particles, such as hyperons and pions (Oertel instabilities seem to be entangled in the evolution the
et al. 2012, Gulminelli et al. 2013, Banik et al. 2014). 15M progenitor. Such differences can be understood
sol
Amongtheconsequences,thetimenecessarytocollapse from the comparison of the advection time and the
to a black hole is reduced (Peres et al. 2013). buoyancy times in these systems. A short advection
time is both favorable to SASI (Foglizzo et al. 2007,
Scheck et al. 2008), and stabilizing for neutrino-driven
5.2 Confirmed axisymmetric explosions from
convection (Foglizzoetal. 2006).Byadjusting theneu-
first principles for a wider set of
trino luminosity and the rate of dissociation at the
progenitors
shock,Fernandezetal.(2014)wereabletocharacterize
A series of paper by Suwa et al. (2010), Mu¨ller et al. each instability separately and compare the properties
(2012a, 2012b, 2013), and Bruenn et al. (2013) con- of the buoyant bubbles and turbulence induced before
firmed the viability of the neutrino-driven explosion the explosion.
mechanism in the axisymmetric hypothesis. Successful Besides a few examples in the parameter space, we do
explosions have been obtained from first principles for not have a clear picture of the dependence of the χ pa-
progenitor masses ranging from 8.1 to 27M , both by rameter on the main sequence mass yet. It should be
sol
the MPA group and the Oak Ridge group. One may noted that the development of SASI is not a sufficient
regret that the explosion times and energies measured criterion for a successful explosion. The axisymmetric
by these two groups are not yet fully compatible with simulation of a 25M progenitor is a clear example of
sol
each other, and neutrino transport still relies on some strongSASIactivitywithoutanexplosion(Hankeetal.
numerical approximations, but these recent studies are 2013).
still very encouraging steps towards a consensus. Both
groupsusearay-by-raymethodwhichsolvestheBoltz-
mannequationineachradialdirectionassuminganax- 5.3.2 The compactness parameter ξ2.5 and black
isymmetric distribution of neutrinos along each radial hole vs neutron star formation
ray. It is interesting to note that the Princeton group A systematic study performed by Ugliano et al. (2012)
didnotobtainanexplosionusingadifferentcodewhere used some educated prescription to account for multi-
neutrinotransportisapproximatedwithamulti-group, dimensionalevolutionusing1Dsimulationsoverawide
flux-limited diffusion method (Dolence et al. 2014). range of progenitor masses from 10 to 40 solar masses.
Although these explosions are an immense success in Theoutcomeofthecorecollapsecaneitherbeasuper-
view of the decades of failed numerical attempts, the nova explosion with the formation of a neutron star, a
mechanism cannot be qualified as robust enough yet, failed supernova with the formation of a black hole, or
since the final explosion energy seems significantly too a supernova with the delayed formation of a black hole
low compared to observations. It is not clear whether through the fall back of enough ejecta. The diversity
thesolutiontothispuzzlewillcomefromimprovingthe of mass loss processes during the life of a star results
modeling of progenitor models, or including 3D effects in a non-monotonous relation between its mass at the
from rotation and magnetic fields, or something else. moment of core-collapse and its mass on the main se-
quence. In addition to stressing this labeling confusion,
the study of Ugliano et al. (2012) showed that the pro-
5.3 The diversity of explosion paths
ductionofaneutronstarorablackisalsoveryvariable
Despite the universality of the Chandrasekhar mass forprogenitorsmoremassivethan15M .Aninterest-
sol
defining the initial conditions of core collapse, the past ing indicator is based on the compactness parameter
five years have taught us that the explosion process is ξ defined by O’Connor & Ott (2011), measuring the
2.5
PASA(2015)
doi:10.1017/pas.2015.xxx
8 T. Foglizzo
radius of the innermost 2.5M : M progenitorandobservedthattheexplosiontimeis
sol sol
shorter and the explosion is more vigorous in 2D than
M/M
ξ2.5 ≡ R(M)/10s0o0lkm. (8) in 3D. Similar conclusions were reached by Couch &
O’Connor (2014) with a multi species leakage scheme
Although this indicator is not strictly deterministic, a for progenitors of 15 and 27 M . Let us note that the
sol
threshold ξ2.5 >0.3 seems very favorable to black hole stochastic nature of the dynamical evolution and the
formation in the calculations of Ugliano et al. (2012). prohibitive cost of 3D simulations make it difficult to
Fromaseriesof101axisymmetricsimulationsfrom10.8 achieve numerical convergence. Beside the possible in-
to 75Msol with IDSA neutrino transport, Nakamura fluence of numerical artifacts (e.g. Ott et al. 2013 com-
et al. (2014a) found that a high compactness param- paredtoAbdikamalovetal.2014),partofthedifference
eter corresponds to a later explosion time, a stronger between 2D and 3D simulations could be related to a
neutrino luminosity and explosion energy, and a higher more efficient energy cascade from large scales to small
Nickel yield. scalesin3Dthanin2D(Hankeetal.2012,Couch2013,
Couch & O’Connor 2014).
5.3.3 The possible influence of pre-collapse
convective asymmetries
The structure of the progenitor may also influence the
asymmetry of the explosion mechanism through the 5.4.2 SASI does exist in 3D models of core collapse
convective inhomogeneities associated with thermonu- According to the mechanism proposed by Guilet et al.
clearburningintheSiliconandOxygenshells(Arnett& (2010) and checked on the axisymmetric simulations of
Meakin 2011). The quantitative impact of this process Fernandez & Thompson (2009), the saturation ampli-
hasbeenestimatedbyCouch&Ott(2013),whoshowed tude of SASI oscillations is not expected to be very dif-
anexamplewheretheseasymmetrieshadaneffectcom- ferentin2Dand3D.Thewavesofentropyandvorticity
parabletoa2%increaseoftheneutrinoluminosityand created by the oscillations of the shock are expected to
couldbeenoughtoturnafailedexplosionintoasuccess- lose their large scale l=1 coherence when disrupted
ful one. Elaborating in this direction, the recent study by the parasitic growth of Rayleigh-Taylor and Kelvin-
of Mu¨ller & Janka (2014b) pointed out that the most Helmholtz instabilities. This description, however, ig-
efficient effect of pre-collapse asymmetries comes from nores the interaction of SASI with small scale turbu-
inhomogeneities with the largest angular scale l=1,2. lence, whose properties may differ in 2D and 3D. Even
though the first 3D simulations performed by Blondin
& Mezzacappa (2007) in an adiabatic approximation
5.4 The unexpected difficulties of 3D
showed well defined spiral shock patterns on a large
explosions
scale, subsequent 3D simulations with less idealized se-
5.4.1 3D explosions are not easier than 2D tupssuggestedweakeramplitudesthanin2D(Iwakami
Using a simplified model of neutrino interactions with etal.2008,Burrowsetal.2012).Thecleardominanceof
cooling and heating functions, Nordhaus et al. (2010b) non-oscillatory convective motions in some simulations
hadclaimedthattheneutrinoluminosityneededtoob- even led Burrows et al. (2012) to draw general conclu-
tain an explosion was lower in 3D than in 2D, in a sions such that SASI would be an artefact of simplified
comparableproportionasmeasuredbyMurphy&Bur- physicswhichdoesnotexistinrealistic2Dsimulations,
rows (2008) between 2D and 1D. This raised the hope and even less in 3D. This reasoning missed the diver-
that the weak explosions obtained in 2D axisymmet- sity of explosion paths later explored in a parametric
ric simulations could become more robust once com- manner by Fernandez et al. (2014) in 2D or Iwakami et
puter ressources would allow first principle calculations al. (2014a) in 3D, and exemplified by the axisymmetric
including neutrino transport in 3D. A careful check simulation by Mu¨ller et al. (2012) of the 27 M pro-
sol
by Hanke et al. (2012) and Couch (2013) showed that genitor. The evolution of this progenitor was computed
theneutrinoluminositythresholdintheidealizedsetup in 3D from first principles by Hanke et al. (2013) who
studiedbyNordhausetal.(2010b)isactuallyverysimi- confirmedthepresenceoftheSASImodewithanampli-
larin3Dand2D.ThemisleadingresultsofNordhauset tude which can exceed even the amplitude observed in
al.(2010b)happenedtobeduetosomenumericalerrors 2D. Nevertheless, the explosion did not take place dur-
inthetreatmentofgravityintheirCASTROcode,later ing the first 400ms of evolution, whereas it did explode
corrected and acknowledged by Burrows et al. (2012). in 2D on this timescale. It is interesting to note the
Despite these corrections, the convergence between the sensitivity of the dynamics to small differences in the
different codes is not yet fully satisfactory (Dolence et equation of state and possibly GR effects between the
al. 2013). axisymmetric results of Hanke et al. (2013) and those
Using the IDSA approximation of neutrino transport, of Mu¨ller et al. (2012), where less than 200ms were suf-
Takiwaki et al. (2014) studied the evolution of a 11.2 ficient for an explosion.
PASA(2015)
doi:10.1017/pas.2015.xxx
The explosion mechanism of core-collapse supernovae 9
5.5 Rotation and magnetic fields & Mezzacappa (2007), and the linear stability analysis
of Yamasaki & Foglizzo (2008) indicated that this ef-
Theangularmomentumofthestellarcoreanditsmag-
fectofdifferentialrotationcanbesignificantevenifthe
netic field are two physical ingredients which definitely
centrifugal force is weak. The 3D simulations of sta-
affect the birth properties of the neutron star and may
tionary accretion by Iwakami et al. (2009) confirmed
also influence the explosion mechanism.
thattheamplitudeoftheprogradespiralmodeofSASI
is enhanced by rotation. Iwakami et al. (2014b) grad-
5.5.1 SASI effect on the pulsar spin
ually increased the angular momentum of the infalling
The spectacular conclusions regarding the pulsar spin
gas to measure the influence of rotation on the explo-
obtained by Blondin & Mezzacappa (2007) with a 3D
sion threshold. According to the few points in their
adiabatic setup were naturally followed by more realis-
Fig. 1, the change in the threshold of neutrino lumi-
tic 3D simulations. Fernandez (2010) was able to con-
nosity required to obtain an explosion seems to be a
firm the angular momentum budget when the progeni-
linear function of the angular momentum with a lumi-
tor does not rotate, with a setup similar to Blondin &
nosity variation of ∼10% for an angular momentum of
Shaw (2007) but in 3D. By contrast, the spiral mode theorderof∼5×1015cm2s−1.Moresimulationswould
did not appear easily in the non-rotating simulation
be necessary to check whether this effect really scales
of Iwakami et al. (2009) who considered a stationary
linearly with the rotation rate as expected. According
accretion flow incorporating the buoyancy effects due
toatentativelinearextrapolation,rotationeffectswith
to neutrino heating and a more realistic equation of an angular momentum of ∼1015cm2s−1 could induce
state. Significantly slower pulsar spin periods of the or-
a 2% shift of the neutrino luminosity, i.e. a similar
der of 500-1000ms were estimated by Wongwathanarat
order-of-magnitude effects as the pre-collapse asymme-
et al. (2010) who considered the collapse of a 15M
sol tries described by Couch & Ott (2013). For reference,
progenitorwithneutrinocoolingandheating,selfgrav- 1015cm2s−1 istheequatorialangularmomentumatthe
ity and general relativistic corrections of the monopole,
surfaceofapulsarwitharadiusof10kmandaspinpe-
andaYin-Yanggrid.Similarskepticalconclusionswere
riod of 6ms. The uncertain effect of mixing instabilities
reachedbyRantsiouetal.(2011),whopointedoutthat
inside the neutron star remains to be evaluated. Com-
themasscutduringtheexplosionprocessmightnotco-
pared to the models of stellar evolution by Heger et al.
incide with the separation of positive and negative an- (2005),avalueof1015cm2s−1 istwiceaslargeasthees-
gular momentum produced by SASI. A larger sample
timated angular momentum at 2000km with magnetic
of non-rotating progenitors was considered by Wong- fields (∼5×1014 cm2s−1), and 20 times smaller than
wathanaratetal.(2013),includinga20Msol progenitor, without magnetic fields (∼2×1016 cm2s−1).
and measured final spin periods of 100ms to 8000ms.
Nakamura et al. (2014b) considered the collapse of the
Theynotedthatthekickandspindonotshowanyobvi-
stellar core of a 15M progenitor with a shell type
sol
ous correlation regarding their magnitude or direction. rotation profile: Ω(r)=Ω /(1+r2/R2) with R =2×
0 0 0
Theiranalysisclarifiedanimportantdifferencebetween 108cm and Ω =0, 0.1π, and 0.5π rad s−1 correspond-
0
the kick and spin mechanisms: the spin up takes place
ing to an initial angular momentum at 2000km of 0,
duringthephaseofaccretionontotheneutronstarsur- 6×1015cm2s−1,and3×1016cm2s−1.Theymeasureda
face because it is dominated by the direct accretion of
reductionofthethresholdofneutrinoluminosityofthe
angular momentum. By contrast, the kick can grow on
orderof10%forΩ =0.1π,whichisconsistentwiththe
0
a longer time scale, even when accretion has stopped,
resultsofIwakamietal.(2014b).Theyemphasizedthat
through the action of the gravitational force. Using an-
the direction of the explosion is preferentially perpen-
alyticarguments,Guilet&Fernandez(2014)estimated
dicular to the spin axis but did not take into account
the maximum spin of a neutron star born from a non-
the asymmetry of neutrino emission induced by rota-
rotatingprogenitorbymeasuringtheamountofangular
tion, which may favour the axial direction.
momentum which can be stored in the saturated spiral
mode of SASI. They obtained spin periods compatible 5.5.3 The growth of magnetic energy without
to those measured in the simulations of Wongwatha- differential rotation
narat et al. (2013). Endeve et al. (2010, 2012) used an adiabatic setup to
show that even when the initial rotation of the core is
5.5.2 Rotation effects on the shock dynamics neglected, the magnetic energy can grow from the tur-
The effect of a moderate rotation on the dynamics of bulent motions induced by SASI to reach 1014G at the
the collapse has received little attention so far, despite surfaceoftheneutronstar.Thegrowthofthismagnetic
the fact that interesting correlations between the kick field, however, did not significantly affect the dynam-
and spin directions would be expected in this regime. ics of the shock. Obergaulinger et al. (2014) addressed
Indeed,thegrowthofaprogradespiralSASImodeisex- the same question in a more realistic setup including
pected from the early numerical simulations of Blondin neutrino-driven convection and a M1 approximation of
PASA(2015)
doi:10.1017/pas.2015.xxx
10 T. Foglizzo
neutrino transport. They confirmed the lack of signif-
icant effects on the shock evolution except if the field
is initially very strong. They found evidence for an ac-
cumulation of Alfven waves at the Alfven point as de-
scribedbyGuiletetal.(2011),butdidnotfindasignif-
icant contribution to the field amplification or heating.
5.5.4 Magnetic field amplification with fast rotation
Fast differential rotation provides a large energy reser-
voirformagneticfieldamplification,suchthatmagnetic
effects cannot be neglected beyond a certain angular
momentum. The shearing of a poloidal magnetic field
intoatoroidaloneprovidesalinearamplification,which
would be relevant only if the initial poloidal magnetic
field were large enough. If the initial poloidal magnetic
field is weak, the exponential growth of the magnetoro-
tational instability (MRI) is a more promising mech-
anism of magnetic field amplification (Akiyama et al.
2003).Ameaningfuldescriptionofthisprocessrequires
3D simulations with a very high resolution, due to the
Figure 3.Theshapeoftherotatinghydraulicjumpobservedin
veryshortwavelengthoftheMRIgrowingonaweakini-
the non-linear regime in the SWASI experiment (right) is sim-
tial field. The prohibitive computing time required has
ilar to the shape observed in the shallow water approximation
led researchers to use axisymmetric simulations with (left) and the shape of the SASI in the numerical simulations of
artificial assumptions such as a strong initial poloidal cylindricalgasaccretionwithlocalneutrinocooling(top).
field mimicking the outcome of some amplification pro-
cesses (e.g. Moiseenko et al. 2006, Burrows et al. 2007,
Takiwaki et al. 2009, Takiwaki & Kotake 2011). In this
framework, they obtained powerful magnetorotational estimate that a stable stratification decreases the effi-
explosions, with jets launched along the polar axis due ciency of magnetic field amplification only slightly, but
to the winding of the initial poloidal magnetic into a significantlyimpactsthestructureofthemagneticfield.
very strong ((cid:38)1015G) toroidal field. The progress of Neutrino radiation, neglected in most numerical simu-
computational power has opened new perspectives to lations, can slow down the MRI growth through an ef-
address this problem in 3D. Winteler et al. (2012) sug- fective neutrino viscosity deep inside the proto-neutron
gestedthatsuchmagnetorotationalexplosionscouldbe star or through a neutrino drag near its surface (Guilet
animportantsourceofr-processelements.The3Dsim- et al. 2014). Further local simulations will be useful to
ulations of M¨osta et al. (2014) highlighted the role of a study the MRI in this new growth regime, and ulti-
non-axisymmetric instability of the toroidal magnetic mately global simulations (only achieved in 2D so far
field which can break the jet structure and prevent (Sawai et al. 2013, Sawai & Yamada 2014)) will be
such magnetorotational explosions, a non-runaway ex- needed to assess the magnetic field geometry and its
pansion of the shock being observed instead. impact on the explosion.
In parallel progress is being made in understanding the
magneticfieldamplificationduetotheMRIinthepro-
6 AN EXPERIMENTAL APPROACH TO
toneutron star. Buoyancy driven by radial gradients of
SUPERNOVA DYNAMICS
entropy and lepton fraction has a strong impact on the
dynamics, though the thermal and lepton number dif- In order to make the SASI phenomenon more intuitive,
fusion due to neutrinos allows for fast MRI growth, as Foglizzoetal.(2012)designedashallowwateranalogue
shown by the linear analysis of Masada et al. (2006, of the gas motion in the equatorial plane of the stel-
2007). The study of the non-linear phase of the MRI lar core. Surface gravity waves in water play the role
requires 3D simulations, which have been undertaken of acoustic waves in the stellar gas and participate in
in local and semi-global models that describe a small an unstable cycle with vorticity perturbations. Solving
fraction of the protoneutron star. Taking into account numerically the 2D system of shallow water equations
globalgradientsresponsibleforbuoyancyhas,however, revealed the similarity between SASI and its shallow
proven difficult in this framework because of boundary wateranalogue.Theabsenceofbuoyancyeffectsinthis
effects(Obergaulingeretal.2009)orcoarseradialreso- shallow water formulation is theoretically instructive,
lution(Masadaetal.2014).AlocalmodelintheBoussi- as will be shown further. The first laboratory analogue
nesq approximation allowed Guilet & Mu¨ller (2015) to of SASI dynamics was obtained using a water fountain
PASA(2015)
doi:10.1017/pas.2015.xxx