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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
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
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
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
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.
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) £or 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~.
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 Hall, Englewood Cli~s. Grasberg, E.K, and D.K NadyozLin. 1969. Astron. Zh. 46: 745. Grasberg, E.K, V.S. Imshennik, D.K Nadyozhin, and V.P. Utrobin. 1987. Pis'ma Astron. Zh. 13: 547. Imshennik, VS., and Yu.I. Morozov. 1981. Radiation relativistic gasdynamics of high temperature phenomena. (In Russian.) Atomizdat, Moscow. 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.