Neutrinos and core collapse supernovae

Progress in Particle and Nuclear Physics PERGAMON

Progress

in Particle

and Nuclear

Physics 40 (1998) 3 140

Neutrinos and Core Collapse Supernovae

The observation of neutrinos from Supernova 1987A has confirmed the theoretical conjecture that these particles play a crucial role during the collapse of the core of a massive star. Only one per cent of the energy they carry away from the newly formed neutron star may account for all the kinetic and electromagnetic energy responsible for the spectacular display of the supernova explosion. However, the neutrinos emitted from the collapsed stellar core at the center of the explosion couple so weakly to the surrounding matter that convective processes behind the supernova shock and/or inside the nascent neutron star might be required to increase the efficiency of the energy transfer to the stellar mantle and envelope. The conditions for a successful explosion by the neutrineheating mechanism and the possible importance of convection in and around the neutron star are briefly reviewed. Neutrino-driven explosions turn out to be very sensitive to the parameters describing the neutrino emission of the proto-neutron star and to the details of the dynamical processes in the collapsed stellar core. Therefore, convectively enhanced neutrino luminosities from the nascent neutron star could be decisive for a successful explosion. The possible existence of long-lasting convective activity in the newly formed neutron star is confirmed by recent twedimensional simulations.

1

Introduction

Even after ten exciting years SN 1987A keeps rapidly evolving and develops new, unexpected an aging character. facilities

In the first few months

of the Kamiokande,

from very different

fields.

decay of light emission

the historical

IMB, and Baksan In the subsequent

in all wavelengths

detection

laboratories

months

of 24 neutrinos

caused

hectic activity

the scene was dominated

which followed the outbreak

sides like

in the underground among scientists

by the rise and slow

of the supernova

shock and

contained a flood of data about the structure of the progenitor star and the dynamics of the explosion. Now that the direct emission has settled down to a rather low level, the supernova light which is reflected

from circumstellar

information

about the latter

structures

provides

can be expected

insight

into the progenitor’s

when the supernova

evolution.

Even more

shock hits the inner ring in a few

years. The neutrino

detections

in connection

with SN 1987A were the final proof that neutrinos

up the bulk of the energy during stellar core collapse and neutron star formation. spectra of SN 1987A show clear evidence of large-scale mixing in the stellar mantle of fast moving were already

Ni clumps. present

Both might indicate

near the formation

Ol46-6410/98;$19.00 +O.OO 0 PII: SOl46-6410(98)00006-4

that

macroscopic

region of Fe group elements

1998 Elsevier Science BV. All rights reserved.

take

Light curves and and envelope and

anisotropies

and inhomogeneities

during

the very early stages of

Printed

in Great

Britain

H.-T. Janka / Prog. Part. Nucl. Phys. 40 ( 19981 31-40

32

the explosion.

Spherically

symmetric

inside the newly formed neutron unstable.

These theoretical

models had been suggesting

star and in the neutrino-heated

results

and the observational

study stellar core collapse and supernova In this article core is discussed for the supernova nascent

neutron

convective

2 2.1

overturn

explosion.

in the neutrino-heated

inside the proto-neutron milliseconds

in SN 1987A were motivation

simulations

are briefly described.

to

simulations.

region around

energy deposition

The first two-dimensional

of a few hundred

findings

with multi-dimensional

its effects on the neutrino

star for more than one second

activity

on a timescale

convective

concerning

explosions

for some time already that regions layer around it might be convectively

the collapsed

and its potential

that follow the evolution They support

stellar

importance

suggestions

star might be a crucial boost of the neutrino

of the that

luminosities

after core bounce.

Neut rino-driven explosions and convective overt urn Neutrino heating and supernova explosions

Figure 1 displays at the center.

a sketch of the neutrino

The main processes

cooling and heating

of neutrino

energy

v, + n + p + e- and Y, + p + n + e+. The heating

where Y, and YP are the number

fractions

of ye or z& in 105* erg/s,

[S]

gain

shock

radius

of free neutrons

73 the radial position

R,

R”

PNS (convective)

the proto-neutron

are the charged-current

rate per nucleon

Q,’ 2 110.

the luminosity

regions outside

deposition

star

reactions

(N) is approximately

,

and protons,

(1) respectively,

in 10’ cm, and (c$s)

Lv,52 denotes

the average of the

R,

Figure 1: Sketch of the post-collapse stellar core during the neutrino heating and shock revival phase. At the center, the neutrino emitting prom-neutron star (PNS) with radius R,, is shown. The average radius where neutrinos decouple from the matter of the nascent neutron star and stream off essentially freely (“neutrinosphere”)

is denoted by R,.

supernova shock (at &)

The neutrino cooling layer and the neutrino heating region behind the

are separated by the “gain radius” R,.

Matter is accreted into the shock at a rate G and is partly advected through the gain radius into the cooling region and onto the neutron star. Convec-

tive overturn between the gain radius and the shock increases the efficiency of neutrino heating. Convective activity inside the protwneutron deposition.

star raises the neutrino luminosities and thus amplifies the neutrino energy

33

H.-T. Jankaj Prog. Part. Nucl. Phys. 40 (1998) 31-40

squared

neutrino

radiation

energy measured

field (the ‘&fluxfactor”,

propagation

relative

and 1 for radially to re-emission neutron

to the radial direction)

streaming

of neutrinos,

star potential

after accretion explosion

N

about

factor of the neutrino

0.25 at the neutrinosphere

Using this energy deposition

that

balanced

matter

2.105’ .

the gravitational

by the sum of internal

through

binding

rate, neglecting energy

loss due

of a nucleon

and nuclear recombination

the shock, one can estimate

Lv$~15) (&)

mass, At the typical

of the overlying,

plosive nucleosynthesis

outward

heating

accelerated

is even stronger

Convective

Convective

in the energies

(very approximately)

the

E,,,the

three-dimensional

gradient

simulations

of the calculations shock formation,

by Janka

of neutrino-heated,

general agreement

to the nascent

built up by neutrino

and Miiller

high-entropy

about the existence

binding

energy from exwith

Egbl. Since the gain radius, shock

in the neutrino-heated

spherically

additional

of

Eexp to

the neutrino

emission

by Eq. (2).

[6].

At about

symmetric

region

neutron

heating

[2, 3, 4, 5, 6, 7, 8, 91. Figure

the originally

(2)

of a few 10sOerg only for progenitors

on L+(cz), the sensitivity

in the layers adjacent

entropy

[erg] .

Emi,

Esb the (net) total gravitational

layers, and

contribution

than suggested

overturn

instabilities

of the negative

bubbles

timescale,

stellar

which is a significant

and At and thus also AM depend

parameters

(&) - Egb +

masses above 20 M, and which roughly compensates

main sequence

2.2

which varies between

far out.

and assuming

of the infalling

dilution

energy to be of the order

AM is the heated

radius,

neutrinos

is (roughly)

E =P

energy

in units of 15 MeV. f is the angular

which is equal to the mean value of the cosine of the angle of neutrino

star are a natural

2 shows an exemplary

170 ms after

entropy

consequence

[l] and are seen in recent

stratification

two- and

result from one

core bounce is distorted

and supernova by large, rising

gas and long, narrow inflows of cooler gas. Although of this unstable

region between the radius of maximum

there is neutrino

heating (which is very close outside the “gain radius” R,,i.e. the radius where neutrino cooling switches into net heating) and the shock position &, the strength of the convective overturn and its importance for the success of the neutrino-heating

mechanism

in driving

the explosion

of the star is still a matter

of much debate. The effect of convective overturn in the neutrino-heated region on the shock is two-fold. On the one hand, heated matter from the region close to the gain radius rises outward and at the same time is replaced neutrinos

by cool gas flowing down from the postshock

(e* capture on nucleons and thermal

and cooling

of rising plasma

reduces

processes)

region.

Since the production

are very temperature

the energy loss by reemission

sensitive,

of neutrinos.

reactions

of

the expansion

Moreover,

the net

energy deposition by neutrinos is enhanced as more cool material is exposed to the large neutrino fluxes just outside the gain radius where the neutrino heating rate peaks (the radial dilution of the fluxes roughly

goes as l/r*).

the pressure and therefore

there.

On the other hand, hot matter

Thus the shock is pushed

also of the net energy transfer

further

floats into the postshock

region and increases

out which leads to a growth

from neutrinos

of the gain region

to the stellar gas.

‘The latter statement is supported by the following argument (S. Woosley, private communication): Material with a specific gravitational binding energy @srav which is equal to or larger than the nuclear energy release per gram in Si burning, enuc - lO’*erg/g, is located interior to the radius where the temperatures can become high enough (T 2 5 x 10’ K) for explosive nucleosynthesis of “Ni. From @srv = GM/r 2 10lserg/g one estimates a radius of r 5 2 x lo* cm, and from ~nr3aT4 - 105’ erg with Tz 5 x 1O0K one finds r 6 4 x 1Oscm. This means that the energy release from explosive nucleosynthesis is easily able to account for the gravitational binding energy of the burning material.

H.-T. Junka/

34

Figure

2: Inhomogeneous

neutron

star

distribution

(left side, middle)

Prog. Part. Nud. P/~>x. 40 (199X) 31-40

of cool (low entropy)

and the supernova

and hot (high entropy)

gas between

shock front (bumpy, hemispheric discontinuity)

the nascent

during the

first second of the explosion. The figure shows a snapshot of the evolution about 170 ms after the formation of the supernova shock. Neutrino-heated

matter rises and expands in mushroom-like

flows down toward the neutron star in narrow streams.

bubbles, while cool gas

The radius of the semicircle is 1600 km, the shock is

at about 1400 km.

2.3

Requirements

In order to get explosions fulfilled. R,,,

Expansion

by the delayed

of the postshock

of the developing

density

for neutrino-driven

explosions

neutrino-heating

mechanism,

region requires sufficiently

mass cut. If one neglects

self-gravity

certain

according

which yield a power law index of n M 3; see also [lo]), one gets P(r) is maintained

as long as the following condition 1

EC GMplr

&,,, > (n+

l)(y-

need to be

near the radius

of the gas in this region and assumes

profile to be a power law, p(r) 0: r-” (which is well justified

outward acceleration density E holds:

conditions

large pressure gradients

0; r+-’

to numerical

for the pressure,

for the “critical”

the

simulations

internal

and

energy

3 (3)

1) = 4 ’

where use was made of the relation P = (y - 1)~. The numerical value was obtained for y = 413 and n = 3. This condition can be converted into a criterion for the entropy per baryon, s. Using the thermodynamical relation for the entropy density normalized to the baryon s = (E + P)/(nbT) - xi n;Yi where n, (i = n, p, eC, e’) are the particle chemical potentials the temperature,

and assuming

completely

disintegrated

nuclei behind

density nb, divided by

the shock so that the number

H.-T. Jarka

fractions

of free protons

and neutrons

sc(&)

In this approximate 0.5

less than

1 Prog. Part. Nud. Phys. 40

2

are YP = Y, and Y, = 1 - Y,, respectively,

15 s

expression

lR, ut

region),

nucleons

are assumed

normalized

to representative

values,

M 1.1 is measured

in lo7 cm.

Inserting

numbers

(T E 1.5MeV,

s > 15 ks/N, explode.

typical

which gives an estimate

These requirements following

of the entropy

can be coupled

considerations.

10m3 !$$)I14ut

In (1.27.

a term with a factor Y, was dropped

in the considered

A stalled

35

i 1998) 31-40 one gets

[bINI .

(its absolute

value being usually

to obey Boltzmann

statistics,

and,

in units of 1.1 I!&, ps in 10gg/cm3, and TV I”, z 0.3, R,,, z 1.5 . 107cm), one obtains in the heating

to the neutrino

emission

shock is converted

region when the star is going to of the proto-neutron

into a moving

star by the

one only when the neutrino

heating is strong enough to increase the pressure behind the shock by a sufficient amount. Considering the Rankine-Hugoniot relations at the shock, Bruenn [ll] derived a criterion for the heating rate per unit mass, qv, behind

the shock that guarantees

a positive 2p-

QV > Here /3 is the ratio of postshock (assumed

R, where net heating

to preshock

by neutrino

o analytical

1

velocity

(Us > 0):

121013

D3(P - 1)(-Y - 1) n& density,

to be the same in front and behind

which is a fraction

postshock

p = pr/po,

y the adiabatic

index of the gas

the shock), and 77defines the fraction

processes

11 = (R, - R&/h.

occurs:

and numerical

calculations

of the shock radius

uo is the preshock

show that typically

(Yx l/a)

velocity, of the free

fall velocity, ~0 = cr J--2GM/r. Assuming a strong shock, one has p = (y + l)/(y - 1) which becomes p = 7 for y = 4/3. With numbers typical of the collapsed core of the 15 M, star considered by Janka mass M = 1.1 Ma, one finds for the threshold

and Miiller [6], & = 200 km, 77x 0.4, and an interior luminosities

of v, and fie (separately):

L,52k~,l5)

’

M3/2 1.1

2.0

-

&1,2,0

The existence

of such a threshold

luminosity

of the order of 2. 1O52erg/s is underlined

by Fig. 3 where

the explosion energy E,c as function of time is shown for numerical calculations of the same postcollapse model but with different assumed neutrino luminosities from the proto-neutron star. E,n is defined to include the sum of internal, positive

(the gravitational

from nuclear burning

kinetic,

and gravitational

are not taken into account).

below 1.9. 105’ erg/s we could not get explosions the threshold

for the v, and fie luminosities

(see [S]). The supporting

effects of convective

even below the threshold

higher values of the explosion

For one-dimensional when the proto-neutron

overturn

energy for the same neutrino

This can clearly be seen by comparing

neutrino-driven plosion

and mean energies. explosions

star was assumed

for the spherically

luminosities,

should be self-regulated. than

a few times

static,

and

star was contracting

the solid (2D) and dashed energy is extremely

Which

symmetric

case, to

and to a faster development (1D) lines in Fig. 3.

sensitive

This holds in 1D as well as in 2D. The question

from being more energetic

energy release

with luminosities

between the gain radius and the shock described

luminosities

The results of Fig. 3 also show that the explosion luminosities

simulations

was 2.2. 1O52erg/s when the neutron

above lead to explosions of the explosion.

energy for all zones where this sum is

binding energies of stellar mantle and envelope and additional

to the neutrino

can be asked why

kind of feedback should prevent the ex1051 erg ? Certainly, the neutrino luminosities

H.-T. Janka / Prog. Part. Nucl. Phys. 40 (1998) 31-40

36

1,,,11

I

I1

I

0.2

0

I

0.4

I

I

I

I

I

I

0.6

time

I

e

I

0.8

[set]

Figure 3: Explosion energies E>e(t) for 1D (dashed) and 2D (solid) simulations and fie luminosities

(labels give values in 105’erg/s)

I 1

from the prom-neutron

with different assumed I+

star. Below the smallest given

luminosities the considered 15Ma star does not explode in 1D and acquires too low an expansion energy in 2D to unbind the stellar mantle and envelope. and gravitational

E,e is defined to include the sum of internal, kinetic, and

energy for all zones where this sum is positive (the gravitational

binding energies of stellar

mantle and envelope and additional energy release from nuclear burning are not taken into account).

in current imagine.

models can hardly Nevertheless,

neutrino-heated

power an explosion

and therefore

Fig. 3 and Eq. (2) offer an answer

region outside

the gain radius has absorbed

a way to overpower

to the question:

it is not easy to

When the matter

roughly its gravitational

binding

in the energy

from the neutrino fluxes, it starts to expand outward (see Eq. (3)) an d moves away from the region of strongest heating. Since the onset of the explosion shuts off the m-supply of the heating region with cool gas, the curves in Fig. 3 approach and the density in the heating the neutrino

heating,

by the amount

a saturation

region decreases.

level as soon as the expansion

Thus the explosion

which scales with the V, and z& luminosities

of matter

both of which decrease

AM in the heating when the heating

energy depends and mean energies,

region and by the duration

is strong and expansion

gains momentum on the strength

happens

of

and it is limited

of the heating

(see Eq. (2)),

fast.

This also implies that neutrino-driven explosions can be “delayed” (up to a few 100 ms after core bounce) but are not “late” (after a few seconds) explosions. The density between the gain radius and the shock decreases with time because the prom-neutron star contracts and the mass infall onto the collapsed core declines steeply with time. Therefore the mass AM in the heated region drops rapidly and energetic

explosions

Moreover,

by the neutrino-heating

Fig. 3 tells us that convection

mechanism

become less favored at late times.

is not necessary

to get an explosion

and convective

overturn is no guarantee for strong explosions. Therefore one must suspect that neutrino-driven typeII explosions should reveal a considerable spread in the explosion energies, even for similar progenitor stars. Rotation in the stellar core, small differences of the core mass or statistical variations dynamical events that precede and accompany the explosion may lead to some variability.

2.4

in the

When is neutrino-driven convection crucial for an explosion?

The role of convective overturn considering the three timescales

and its importance for the explosion can be further illuminated of neutrino heating, ‘&, advection of accreted matter through

by the

H.-T. Janka/ frog.

gain radius convective

into the cooling

region and onto the neutron

star (compare

Fig. l), Tad, and growth

of

overturn,

the relative

7,“. The evolution of the shock - accretion or explosion - is determined by sizes of these three timescales. Straightforward considerations show that they are of the

same order and the destiny

of the star is therefore

a result of a tight competition

between

the different

entropy

s, (Eq. (4)),

(see Fig. 4).

processes

The heating and the heating

timescale

With a postshock

is estimated

from the initial entropy

SC -

.-SC -

Si

=

Q,+/(kBT)

!t!C-EE

(Ly/2.

where the gain radius can be determined

R, (

that the heating

(RJT) with R,,being

radius).

The growth timescale of entropy

the pro&r-neutron of convective

behavior star

instabilities

through

radius

of the temperature (roughly

to

Q; z

T(T)z

equal to the neutrinosphere

in the neutrinoheated

the growth

according

region depends

rate of Ledoux convection,

on the

(TL (g is the

Explosion

strongly aspherical

no strong u heating

(9)

($3

rate, Eq. (l), is equal to the cooling rate per nucleon,

and lepton number

Accretion

(8)

dK’

-1’4 &)-1’4f1’4

when use is made of the power-law

4MeV

is

f%o )

l-R,

timescale

as

Rg,7 g 0.4 ( 2 . $lergls) from the requirement

(7)

10s2erg/s)(e&) + 1) the advection

E 52ms.

‘1Ll

gradients

R&(TPMeV)f

Si

45ms 5kB/N

velocity of u1 = us//3 x (y - l)dm/(y Tad x

288(T/2MeV)6,

si, the critical

rate per nucleon (Eq. (1)) as

Tht =

Figure

37

Part. Nucl. Phys. 40 (1998) 31-40

lL

strong convection

I nearly I spherical I 1 I convection I not fully : developed

4: Order scheme for the dependence of the post-collapse dynamics on the strength of the neutrino

heating as a function of &(cE).

The destiny of the star - accretion or explosion - depends on the relative size

of the timescales of neutrino heating, q,t, matter advection through the gain region onto the proto-neutron star, rdTadvr and growth of convective instabilities, rev. With a larger value of Ly($)

the heating timescale as

well as r,, decrease, the latter due to a steeper entropy gradient built up by the neutrino energy deposition near the gain radius.

38

H.-T. Jankaj Prog. Part. Nrrcl. Phys. 40 (1998) 31-40

gravitational

acceleration): In (100) _(6{f[(~)~~,~~+(~)~,~~]}-1’z*50ms. rc” = -

(IO)

CL

The numerical

value is representative

of Eq. (10) is sensitive minimum),

conditions

in hydrodynamical

between

gain radius (where s develops a maximum),

is shorter

for larger values of the neutrino

both rht and 74 depend

3

for those obtained

to the detailed

strongly

luminosity

(e.g., [S]). TV

simulations

neutrinosphere

(where Y, has typically

and the shock. The neutrino L,, and mean squared neutrino

a

heating timescale energy (c:), while

on the gain radius, rd also on the shock position.

Convection inside the nascent neutron star

Convective

energy transport

considerably

inside the newly formed neutron star can increase the neutrino

[12]. This could be crucial for energizing

Sect. 2). Recent two-dimensional of the proto-neutron

simulations

star formed

corrections

for asphericities

diffusion scheme was applied The simulations nosphere

A general relativistic

show that convectively

after bounce,

al. [20], and Mezzacappa convection, and 0.9 M,,

unstable

of about

in agreement

cause of these high velocities

regions

with

with Newtonian

(equilibrium) (i.e., around

neutrino the neutri-

exist only for a short period of a few ten and Mezzacappa

[19], Bruenn

et

in a layer deeper inside the star, between

an enclosed

Convective

corresponding

and rather flat entropy

velocities

mass of 0.7Mo

region digs into the star

as high as 5.10s cm/s are reached

to kinetic energies of up to l-2.

and composition

105’ erg. Be-

profiles in the star, the overshoot

regions are large.

The coherence coherence

potential

above several 1012 g/ cm3. From there the convective

of the local sound speed),

(and undershoot)

surface-near

1O1’g/cm3)

with the findings of Bruenn

and reaches the center after about one second. (about lo-20%

1D gravitational

of more than

were performed

et al. [7]. Due to a flat entropy profile and a negative lepton number gradient,

however, also starts at densities

star for a period

The simulations

was used, Cp= @y$+(Q &, - Cpyn), and a flux-limited for each angular bin separately (“l$,D”).

and below an initial density

milliseconds

of a 15Mo

by W. Keil in this volume).

code Prometheus.

luminosities

shock [13, 14, 151 (see also

by Keil et al. [16, 171 and Keil[lS] have followed the evolution

in the core collapse

1.2 seconds (see also the contribution the hydrodynamics

the stalled supernova

lengths

of convective

structures

are of the order of 20-40 degrees

times are of the order of 10 ms which corresponds

(in 2D!) and

to only one or two overturns.

The

convective pattern is therefore very time-dependent and nonstationary. Convective motions lead to considerable variations of the composition. The lepton fraction (and thus the abundance of protons) shows relative fluctuations of several 10%. The entropy differences in rising and sinking convective bubbles are much smaller, only a few per cent, while temperature and density fluctuations are typically less than one per cent. The energy

transport

whereas convective activity

is strongest,

transport

in the neutron

star is dominated

by neutrino

plays the major role in a thick intermediate

and radiative

transport

takes over again when the neutrino

becomes large near the surface of the star. But even in the convective is only a few times larger than the diffusive

diffusion

flux.

near the center,

layer where the convective mean

layer the convective

This means that neutrino

diffusion

free path energy flux

can never be

neglected. There is an important consequence of this latter statement. The convective activity in the neutron star cannot be described and explained as Ledoux convection. Applying the Ledoux criterion for local instability, C,(r) = (p/g)02 > 0 with 0~ from Eq. (10) and Y, replaced by the total lepton fraction I& in the neutrino-opaque interior of the neutron star, one finds that the convecting region

35,

H.-T. Janka/ Prog. Part. Nucl. Phys. 40 (199X) 31-40

should actually

be stable,

despite

of slightly

below a critical value of the lepton fraction

negative

entropy

and lepton

number

gradients.

In fact,

= 0.148 for p = 1013 g/cm3 and T = 10.7 MeV)

(e.g., &,c

changes sign and becomes positive because of nuclear the thermodynamical derivative (@/a&,),,~ and Coulomb forces in the high-density equation of state. Therefore negative lepton number gradients should stabilize

against

convection

in this regime.

vection is not fulfilled in the situations and, in particular, negligible.

considered

However,

an idealized

here: Because of neutrino

lepton number exchange between convective

Taking the neutrino

rion [18, 171, one predicts

transport

instability

elements

assumption

where convective

energy exchange

and their surroundings

effects on I;,,, into account in a modified

exactly

of Ledoux con-

diffusion,

action happens

are not

Quasi-Ledouz

crite-

in the two-dimensional

simulation.

4

Conclusions

Convection

inside the proto-neutron

ms after core bounce

star can raise the neutrino

(Fig. 5). In the considered

collapsed

luminosities

within

core of a 15 MO star L,

a few hundred and LD. increase

by up to 50% and the mean neutrino energies by about 15% at times later than 200-300 ms post bounce. This favors neutrino-driven explosions on timescales of a few hundred milliseconds after shock formation.

Also, the deleptonization

luminosities

relative

Ye in the neutrino-heated the early epochs

flux determined

emission

times of the convective

from the cooling proto-neutron

10’

tend to be smaller)

has very interesting

mass accretion consequences,

radiation

problem

raising the v, fraction

of N = 50 nuclei during

due to convection of neutrinos.

in the neutron

The angular

variations

are of the order of 5-10% (Fig. 5). With the structures,

however,

star is certainly

the global anisotropy

of

less than 1% (more likely only

and kick velocities

and rotation

in excess of 300 km/s

can

of the forming neutron star were included.

e.g., leads to a suppression

of convective

motions

near

km”‘“““““‘“““1

6 100

accelerated,

not be explained.

In more recent simulations, Rotation

star is strongly

mass motions

by the 2D simulations

O.l%, since in 3D the structures definitely

[16]. Anisotropic

wave emission and anisotropic

typical size and short coherence the neutrino

neutron

during this time. This helps to increase the electron

ejecta and might solve the overproduction

of the explosion

star lead to gravitational of the neutrino

of the nascent

to the tie luminosities

0

0.2

0.4

0.6

t I.1

0.6

1

1.2

0.901

1

1

60

60

1050

1 ms

100 0

1 120

[“I

Figure 5: Left: Luminosities L,(t) and mean energies (c”)(t) o f v, and 0, for a 1.1 Ma proto-neutron star without (“1D”; dotted) and with convection (“2D”; solid). Time is measured from core bounce. Right: Angular variations of the neutrino flux at different times for the 2D simulation.

H.-T. Jankaj Prog. Pmt. Nucl. Phys. 40 (19981 31-40

40

the rotation

axis because

which can be understood gravitating

objects.

Future

state on the presence the neutrino transport the nuclear formation

medium

of a stabilizing by applying

stratification

of the specific

the Solberg-Hoiland

simulations

criterion

angular

momentum,

for instabilities

of

of convection in nascent neutron stars. Also, a more accurate treatment in combination with a state-of-the-art description of the neutrino opacities

of of

to confirm

and to study its importance

the existence

of a convective

for the explosion

mechanism

of the nuclear

self-

equation

is needed

will have to clarify the influence

an effect

in rotating,

episode

of type-II

during

neutron

star

supernovae.

Acknowledgments The author

would like to thank S.E. Woosley for interesting

for a fruitful

and enjoyable

collaboration.

Support

and the “SFB 375-95 fiir Astro-Teilchenphysik”

conversations

and W. Keil and E. Miiller

by the DFG (Deutsche

Forschungsgemeinschaft)

is acknowledged.

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