Issue |
A&A
Volume 368, Number 2, March III 2001
|
|
---|---|---|
Page(s) | 527 - 560 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361:20010012 | |
Published online | 15 March 2001 |
Conditions for shock revival by neutrino heating in core-collapse supernovae
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85741 Garching, Germany
Corresponding author: H.-Th. Janka, thj@mpa-garching.mpg.de
Received:
30
August
2000
Accepted:
12
December
2000
Energy deposition by neutrinos can rejuvenate the stalled bounce shock
and can provide the energy for the supernova explosion of a massive
star. This neutrino-heating mechanism, though investigated by numerical
simulations and analytic studies, is not finally accepted or proven as
the trigger of the explosion. Part of the problem is that different groups
have obtained seemingly discrepant results, and the complexity of the
hydrodynamic models often hampers a clear and simple interpretation
of the results. This demands a deeper theoretical understanding of the
requirements of a successful shock revival.
A toy model is developed here for discussing the neutrino heating
phase analytically. The neutron star atmosphere
between the neutrinosphere and the supernova shock can well be considered
to be in hydrostatic equilibrium, with a layer of net neutrino
cooling below the gain radius and a layer of net neutrino heating above.
Since the mass infall rate to the shock is in general different from the rate
at which gas is advected into the neutron star, the mass in the gain layer
varies with time. Moreover, the gain layer receives additional
energy input by neutrinos emitted from the neutrinosphere and the cooling
layer. Therefore the determination of the shock
evolution requires a time-dependent treatment. To this end the
hydrodynamical equations of continuity and energy are integrated
over the volume of the gain layer to obtain conservation laws for the
total mass and energy in this layer. The radius and velocity of the supernova shock can then be calculated from global properties of the gain layer as solutions of an initial value
problem, which expresses the fact that the behavior of the shock is controlled
by the cumulative effects of neutrino heating and mass accumulation in the
gain layer. The described toy model produces steady-state accretion and mass outflow
from the nascent neutron star as special cases.
The approach is useful to illuminate the conditions that can lead to
delayed explosions and in this sense supplements detailed numerical
simulations. On grounds of the model developed
here, a criterion is derived for the requirements of
shock revival. It confirms the existence of a minimum neutrino luminosity
that is needed for shock expansion, but also demonstrates the
importance of a sufficiently large mass infall rate to the shock.
If the neutrinospheric luminosity or accretion rate by the shock are too
low, the shock is weakened because the gain layer loses more mass than
is resupplied by inflow.
On the other hand, very high infall rates damp the shock expansion and
above some threshold, the development of positive total energy in the
neutrino-heating layer is prevented.
Time-dependent solutions for the evolution of the gain layer show that
the total specific energy transferred to nucleons by neutrinos is
limited by about 1052 erg
(~5 MeV per
nucleon). This excludes the possibility of very energetic explosions
by the neutrino-heating mechanism, because
the typical mass in the gain layer is about 0.1
and does not exceed a few tenths of a solar
mass. The toy model also allows for a crude discussion of the global effects of
convective energy transport in the neutrino-heating layer. Transfer of energy
from the region of maximum heating to radii closer behind the shock mainly
reduces the loss of energy by the inward flow
of neutrino-heated matter through the gain radius.
Key words: supernovae: general / elementary particles: neutrinos / hydrodynamics / accretion
© ESO, 2001
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