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OCR for page 39
The Shock Breakout in SNI987A
Modelled with the Time-Dependent Radiative Transfer
S.I. BLINNIKOV, D.K. NADYOSHIN
Institute for Theoretical and Eyperunental Physics
O.S. BARTUNOV
Sternberg Astronomical Institute
ABSTRACT
The fully implicit high-order scheme has been developed for the time
dependent multi-group radiative transfer coupled with implicit hydrody
namics. The application of this scheme to the SN1987A explosion shows
that shorter after the shock breakout a dense shell forms.
Many papers have modeled the early light curve of SNI987A in an
approximation of radiation equilibn am diffusion (e.g., Woosley et al. 198 7;
Grasberg e! al. l9g7; Arnett 1987; Shigeyama e! al. 1987~. However,
this approximation is never valid in the outermost layers of a supernova.
Moreover, at the stage of shock breakout the radiation field changes so
quickly, that it is necessary to take into account that the light speed is not
infinite (the retardation effect).
We have developed a new gasdynamic code describing the time
dependent radiation transport in the multi-group approximation with vari
able Edd~ngton factors. The method used is free of the limitation of the
equilibrium diffusion.
We assume the Newtonian mechanics and gravitation, taldug into
account the radiative force in the momentum equation, and the radiative
heating in the temperature equation The temperature of ions is assumed
to be equal to that of electrons (cf. Chevalier and Klein 1979, for the
opposite case). The time~ependent equations for the radiation energy
and the momentum include all therms of order v/c, where v is the matter
velocity and c is the light speed (Imshennik and Morozov 1981; Castor
39
OCR for page 40
40
AMERICAN AND SOVIET PERSPECTIVES
1972; Mihalas and Mihalas 1984~. The equations are closed with a space-
variable Eddington factor furs evaluated from the transfer equation by the
Feautrier (1964) method for an instantaneously static atmosphere to which
our code calls after the prescribed number of steps. Optionally, the user
may take into account the retardation effect more precisely by calculating
factors f~r,t) from the time-dependent equation of transfer (Mihalas and
Mihalas 19843 at every time step.
The ionization equilibrium is taken into account in the Saha appro~n-
mation. In the outermost rarefied layers the option for the kinetic STEP
treatment of me hydrogen ionization is provided for. The ~ne-dependent
radiation transport accounting for all the effects of the order of v/c is com-
bined with the gasdynamics in a common, fully implicit difference scheme,
which is based on the high-order predictor-corrector algorithm developed
by Gear (l971~. We calculate the flux in every energy group from the
time-dependent equations as described by FaLk and Arnett (1977) and Mi-
halas and Mihalas (1984~. Therefore, we do not encounter the problem
of the flux limiting which is the source of some ambiguity in the world;
using the static expression for the flux (Chevalier and Klein 1979; and for
the neutnno transport: Bowers and Wilson 1982; Bruenn 1985; Myra et al.
1987~.
The implicit gasdynamic part of our code was successfully tested in the
problem of strong explosion of the degenerate stellar cores with allowing
for me ld;netics of the carbon burning. The testing was also done in the
investigation of quasistatic and dynamic stages of gravitational collapse with
kinetics of beta-processes (BIirmikov and Rudzskiy 1984) and in the pureik,r
static problem of white dwarf cooling (Blinnikov 1988~.
For SN1987A, we used the model of mass 16M~, radius WRY, and
explosion energy 2x105i ergs. The initial hydrostatic model has been
constructed by the special code for initial models (Nadyozhin and Razinkova
1986) and was close to a pol,,rtrope of index n = 3.5.
We present now the main results for the simplest case: LTE-io'ii~tion;
opacity is independent of frequency and depends only on density and
temperature; and Compton scattenug is treated as pure absorption. The
run of the calculated light curse and of the effective temperature, shown
Figures 1 and 2, proves to be very close to the results of Grasberg e' al.
(1987) and Utrobin (1989~. In particular, the effective temperature reaches
the maximum value of about Sx 105K (The run on our 1 Mflops computer
uses 150 Lagrangian mass zones, 20 geometrically spaced frequency groups
and for optical depth T greater than 15-30, we switch to the equilibrium
diffusion. The results, presented in Figures 1 and 2, are obtained in ~
1 hour of CPU time. It takes about 20 hours for the next 10,000 steps,
when at about the 80th day of the supernova evolution T HI the center
OCR for page 41
HIGlI-ENERGY ASTROPHYSICS
-22
-20
-18
-16
-14
-10
-8
, _
_
Mb/
-12 _
Jet
ret
1 00 sac ~ R/c
-
-
-
1 1
.052
41
4 Y
LO
lo
3
2
1
.053
t, d
.054
FIGURE 1 The bolometac magnitude Mb and the elective temperature Teff ~ defined
as the matter temperature at T = 0.64, for the epoch of shock breakout.
becomes less than lS, and all of the lSO radial zones are treated with the
non-equilibrium radiative transfer.)
Figure 3 displays the evolution of the emergent spectrum. The spec-
trum is almost black-body, but we wish to point out that it is not assumed
to be black-body. It is the result of our calculation with the simplified
assumption of "grey" opacity and the crude treatment of the Compton
effect
The most important qualitative difference of these new calculations
from the results obtained in equill~irum diffusion approximation is the
OCR for page 42
42
AMERICAN AND SOVIET PERSPECI.IVES
-14
-12
-10
-8
._
McNaugt _ - -
, ~Zoltowski +
Jones/
it ~m- M= 18.6
V Av=0.6
. · ·
-
0 0.1 0.2 0.3
I, d
FIGURE 2 The absolute visual magnitude and the earliest observations of SN1987^
formation of a dense peak (with the density contrast of 30-100 times)
in the outermost layers of a compact star (see Figure 4~. Such a peak
was also discovered by Falk and Arnett (1977), by Chevalier and Klein
(1979) and for more extended models by Grasberg and Nadyozhin (1969~.
Contrary to Chevalier and Klein (1979), the radiative acceleration of matter
outside the peak proves in our calculations to be fairly high, and a new
high-temperature shock is therefore absent.
In Figure 4 we present the formation of the dense shell in Eulerian
coordinates, and Figure 5 shows the structure of the outermost layers of
SN1987A in Lagrangian coordinates for the moment when the density peak
looks most prominent. The layer containing the density peak has a mass of
about 2 x 10-6 M<3 and the optical thickness ~ ~ 10. This is in excellent
agreement with the analytical estimate of the parameters of the outermost
layers, where the shock cumulation Resented by a self-similar solution has
to be cut on ~mshennik and Nadyozhin, 19%, 1989~. Thus, this calculation
gives an example for a physically correct description of the region where
the shock cumulation is saturated.
We may conclude that we have developed a workable method for the
time~ependent, multi-group radiative transfer in the continuum. The first
application of this method to SN1987A shows that the results of equilibrium
diffusion modeling are basically true. One principal feature, not obtained
with the equilibrium diffusion, is the formation of a dense shell. The
OCR for page 43
HIGH-ENERGY ASTROPHYSICS
2
o
_
4
6 _
8
43
2320
_
224
\
\
\
\
\
\1800
109 `, ~
~1 ~
1
\
\
I ~
12.4
40400 7360
1340 244 44.3
x, ~
FIGURE 3 The dimensionless spectral intensifier, labeled by the number of step. For steps
1800, MOO, and 2320 we have Teff = 16400, 2290X), 480000 K
shell is certainly Rayleigh-Taylor and thermally unstable, and it should
fragment into small blobs. Further calculations, with other parameters of
presupernova models and more accurate treatment of the Compton effect
and the influence of lines on the opacity, are expected to show how the
shell properties and the emergent spectra can vary.
The descried method has good prospects and is being used by us to
solve various problems in the dynamics of exploding supernova envelopes
and collapsing cores.
OCR for page 44
12
T
1 OsK
^~ = (v - 20)
1 03km/s
10
8
6
T 4
2
n
44
AMERICAN AND SOVIET PERSPECTIVES
25 _
20
u,
~ 15
y
o
10
5
\ 20 \ 22 ~\ 24 26 \
l ~I- 1 ~\ 1 ~1~_
2.8 3.0 3.2 3.4 3.63.8
/\
/
26 \
R/1ol2 cm
~ _9
I -10
1 -11
-12
19 p
-6
7
.,
-8 ~
cn
FIGURE 4 Densitr (solid lines) and veloaty (dashed lines) Łor steps 2000 - 2600 (labeled
by 20-26) in Eulenan coordinates.
R/1o12 cm
3.268 3.461 3.654 3.71902 3.71910 3.762
I I! 1 1
\
~ \///~\
_ /~ \
//\\
/- \
~v /
/
/
/1
3.2E-4 3.4E-5
-7
-8
3.6E-6 3.9E-7 3.8E-8 0
m (from surface)
M<,
Igp
gem-3
_9
-11
FIGURE 5 Distnbutions of density p, temperature ~ velocity v, and optical depth ~ near
the edge of SN1987A envelope at time t = 4919 s (step 2600~.
OCR for page 45
HIGH-ENERGY ASTROPHYSICS
45
REFERENCES
Arnett, W.D. 1987. Ap. J. 319: 136.
Blinnikov, S.I. 1988. Prepnnt ITEP No. 19.
Blinnikov, S.I., and M.A. Rudzsky. 1984. Pis'ma Astron. Zh. 10: 363.
Bowen, R.L, and J.R. W~lson. 1982. Ap. J. Suppl. 50: 115.
Bruenn, S.W. 1985. Ap. J. Suppl. 58: 771.
Castor, J.I. 197Z Ap. J. 178: 779.
Chevalier, RA., and R.I. Klein. 1979. Ap. J. 234: 597.
Falk, S.W., and W.D. Arnett. 1977. Ap. J. Suppl. 33: 515.
Feautrier, P. 1964. C.R. 252: 3189.
Gear, CW. 1971. Numencal initial value problems in ordinary dilierential equations. Prentis
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Grasberg, E.K, and D.K NadyozLin. 1969. Astron. Zh. 46: 745.
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Zh. 13: 547.
Imshennik, VS., and Yu.I. Morozov. 1981. Radiation relativistic gasdynamics of high
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Imshennik, V.S., and D.K Nadyozhin. 1989. Sov. Sci. Rev. Sec. F. 8: Part 1,1.
Imshennik, V.S., and D.K Nadyozhin. 1988. P~x'ma Astron. Zb. 14: 1059.
Mihalas, D., and B.W. Mihalas. 1984. Foundations of radiation hydrodynamics Oxford
University Press, New York, Oxford.
Myra, E.S., SA. Bludman, Y. Ho~man, I. Lichtenstadt, N. Sack, and KA Van Riper.
1987. Ap. J. 318: 744.
Nadiozhin, D.K, and T.L R=inkova. 1986. Nauchaye Inform. 61: 29.
Shiggyama, I, K Nomoto, M. Hashimoto, and D. Sugimoto. 1987. Nature. 328: 320.
Utrobin, V.P. 1989. Pistma Astron. Zh. 15: 99.
Woosley, S.E., P~ Pinto, and ~ Ensm~n. 1988. Ap. J. 324, 466.
Representative terms from entire chapter:
shock breakout
