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Hydrodynamic Study of Supernova 1987A: The Phase of A Wave of Cooling and Recombination V. P. UTROBIN Institute of Theoretical and Experimental Physics ABSTRACT A dependence of the bolometnc light curve during the phase of a wave of cooling and recombination and the eDective temperature on the density distribution within a progenitor and its chemical composition is investigated. We show that the outside layers of the blue supergiant Sk-69°202 jUSt before the supernova 1987A outburst had the- density distribution very close to that of the polytropic model with the index of n=3 and the chemical composition roughly close tO that of the Sun. A mass of these layers is about llM<3. The outburst of supernova 1987A in the Large Magellanic Cloud (LMC) allows very detailed observations to be made and gives an extremely rare chance to study this extraordinary event and the stellar evolution before it carefully. A supernova outburst and a stellar evolution before it are very complicated physical phenomena and, as a consequence, are investigated only in outline. For this reason, the hydrodynamic study of supernova outburst which does not account for the properties of the collapse and subsequent explosion and the results of evolutionary calculations is of great importance. A comparison of this study with observational data allows the general properties of an explosion mechanism and a stellar structure before the outburst to be specified. The hydrodynamic models discussed below are based on the numerical integration of a set of spherically symmetrical hydrodynamic equations with radiation diffusion and self-gravitation taken into account. The radiation diffusion is treated with a flux-limited approximation. In this approximation, the radiation flux is defined by 403
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404 AMERICAN AND SOVIET PERSPECTIVES F _ fD · fL (fD + fL) where fD is the flux given by theory of the equilibnunn radiation diffusion and fr is a flux limiter. The latter is determined by CU fL = , d where ~ is a coefficient, c is the velocity of light, and U is the radiation energy density. Note that the coefficient cat is equal to ~ in optically thick regions and to 1 in a transparent medium. Shock waves are calculated by means of artificial viscosity. The set of equations is approximated by the difference equations in the implicit scheme. Initial conditions for hydrodynamic equations are the polytropic stellar model in hydrostatic equilibrium. The chemical composition of matter is taken as a mature of hydrogen, helium, and some heavy element. The ionization equilibrium of this mixture is determined with an approximate method of calculation of the multi-stage ionization of heavy elements for each time step. The Rosseland mean opacity is calculated in the hydrogen-like approximation with regard for Thomson scattering on i ree electrons. An explosion of the star is simulated by a disturbance ~ the thermal energy near the stellar center at the initial the. Now it is certain that the progenitor of supernova 1987A is me B31a type supergiant Sk-69°202 (Panagia et al. 1987; Sonnborn et al. 1987; G2moz~ et al. 1987). According to Rousseau et al. (1978), this star had the following parameters: the apparent magnitude of V = 12m.24 and the color index of B - V = ~om.04. At the LOGIC distance modulus of 18m.6 (Sandage and Command 1971), the interstellar extinction of A', = om.6 (Panama et al. 1987), the effective temperature of Tef = 16300 K, and the bolometric correction of B.C. = -lm.15 (Humphreys and McElroy 1984) these values correspond lo the progenitor radius of about WRY. We adopt the presupernova radius of 45R<~. Other basic characteristics of the computed hydrodynamic models are the stellar mass of 16M<' and the explosion energy of 2x105i erg. To account for the exponential tail observed after the maximum of the bolometnc light curve requires the amount of cobalt -56 of about 0.08M~. In calculating the hydrodynamic models, the energy of the radioactive decay of nickel -56 and cobalt - 56 is assumed to convert completely into thermal energy. The nickel is distributed uniformly over the central core mass of 0.1M,~. The parameters under investigation are listed in the Able. The first column presents the number of the model; the second the polytropic index n; the third the mass fraction of hydrogen X with that of heavy elements of Z = 0,004; the
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HIGH-ENER~ ~TROP~ICS TABLE The main characteristics of computed models Model n X 1 3 0.7 V3 2 1.5 0.7 V3 3 4.5 0.7 V3 4 3 0.075 V3 5 3 0.01 V3 6 3 0.7 1 405 coefficient cat. In all the models, the chemical composition is homogeneous throughout the star. The instantaneous energy release in the hydrodynamic model 1 leads lo the formation of a strong shock wave which propagates towards the stellar surface. In propagating over the star, the shock wave heats the matter and accelerates it to the velocities increasing outward and exceeding the local escape velocity throughout. Approximately at the moment of o.a73 days, the shock wave arrives at the stellar surface and then heats its external layers: the effective temperature jumps to Z3 x 105 K and the luminosity rises accordingly. After this the star begins to expand, its outside layers cool rapidly, and the luminosity decreases. A narrow luminosity peak forms as a result. The peak has a width of about 0.01 days and reaches the magnitude of Moot = - 1~.6 at maximum. For the sake of clarity, it is omitted in the bolometnc light curves shown below. The further expansion of the envelope gradually creates the conditions favorable for the appearance of the specific cooling by radiation a wave of cooling and recombination (WCR). Such a layered illumination of the ejected envelope is completed by about 10 days. From this time to about 40 days, the bolometric light curve plotted In Figure 1 is mainly determined by properties of the WCR. Dunng this period, there is a good agreement between the calculated and observed bolometnc light curves (Figure 1~. After the WCR stage, the luminosity goes to increase in the following 43 days. This erect is caused by a radiation diffusion from the central region of the envelope involving the nickel. However, We internal energy of the envelope has been exhausted by some 80 days, and the expelled matter has become optically thin. As a result, the luminosity decreases abruptly to the instantaneous rate of energy input by the radioactive decay and then is
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406 AL -.' ~ U. _ . o' ,2 ~ U] o . tD US ~ _ o - U) - AMERICANAND SOVIET PERSPECTIVES . , . , . ~ . . . . . 11 _ . - - 60 7t ' Bb eb 1tC ~ ' 5t ORYS FIGURE 1 Bolometnc light curves. Solid lines are the light curves for models 1, 2, and 3. Points are the observational data for the supernova 1987A (Catchpole en al. 1987) with time reckoned from the neutnno burst detected by Kamickande II (Hirata et al. 1987) and IMB (Bionta et al. 1987) embedments. completely determined by it. For this reason the calculated light cone is consistent with the observations after 120 days. In the internal from 40 to 120 days the light cone of model 1 differs from the observed one first slightly and then increasingly (Figure 1~. It requires a more adequate treatment of both the central region of the presupernova and the mechanism of the supernova explosion than discussed above, since dunog this period the flow is created by the most internal layers of the ejected envelope. The phase of the WCR is a remarkable feature of the supernova 1987A outburst since it involves valuable information on the structure of the major portion of the progenitor. In Me case of model 1, the WCR during the period from 10 to 40 days propagators through the mass of about llM,3 apparently comparable with the total mass of the progenitor. Note that the mass of the most external layers which are irradiating in the first 10 days is only about O.1M<~. According to Grassberg and NadyozLin (19763, the photometric char- acteristics of a supernova and the regularities of the propagation of the WCR in an expanding envelope depend basically on a density distribution of matter and its chemical composition. A radial distribution of densitr
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HIGH-ENERGY ASTROPHYSICS 4~;)7 p in the ejected envelope is mainly determined by a structure of the pro- genitor. The smaller a polytropic index n, the greater an effective index q = -blnp/blur in the initial model and, as a consequence, ~ the ejected envelope. An increase of the effective index q at the level of the WCR prop- agating through the envelope of the homogeneous chemical composition leads to a rise in the luminosity rate. This is confirmed by the bolometric light curve calculated with the different polytropic index n (Figure 1~. The slope of the light curve during the phase of the WCR increases with the decreased polytropic index n (models 3, 1, and 2~. It weakly depends on the rest of the parameters of hydrodynamic models (Utrobin 1989~. For the first 40 days, the light curve of model 1 fits the observed light curve well Figure 1~. We may draw a conclusion that the density distribution of the B31a type supergiant Skew 202 before the supernova 1987A outburst is very close to that of the polytropic model with the index of n = 3 over the outside layers of about filmy. Together with the bolometric light cube, the observations of the super- nova 1987A have provided a tune dependence of the effective temperature (Catchpole et al. 1987; Hamuy et al. 1g88~. The effective temperature dur- ing the phase of the WCR is determined by the chemical composition of matter. The smaller the mass fraction of hydrogen and the greater the mass fraction of helium the higher the effective temperature. This is verified by models 1, 4, and 5 with the mass fraction of hydrogen of X = 0.7, 0.075, and 0.01 respectively (Figure 2). Whereas the density distribution ~ the progenitor, its mass, radius, and the explosion energy do not affect the effective temperature (Utrobin 1989~. This fact allows the mass fraction of hydrogen within the progenitor to be estimated by the effective temperature observed for the phase of the WCR In addition to the chemical composition, the effective temperature calculated with the flux-limited approximation depends on the coefficient a. The transition from the limit of optically thick regions (model 1) to that of transparent medium (model 6) leads to rising in He effective temperature (Figure 3~. it is to be noted that the value of ~ = 1 is relevant sow an aim of the flux-limited approximation is to improve the equil~num radiation diffusion in transparent regions. In this case, the time dependence of the effective temperature agrees well with that observed (Figure 3~. Thus, the effective temperature of He supernova 1987A during the phase of the WCR shows that the outside layers of about llM:> in the blue supergiant Sk~9°202 had the chemical composition roughly close to that of the Sun.
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408 a, AMERICAN AND SOVIET PERSPECTIVES o'er . tb 2b ~ 3b fib sb ~ ~ 7b ' sb sb To DRYS FIGURE 2 Time dependence of the effective temperature. Solid lines represent models 1, 4, and 5. Points show the observational data for the supernova 1987A (Catchpole et al. 198T). o So - 2 1 It o' 1b 2b ~_= - - + ~+.+ 3b Rb 5t ' 6t ' 7b eb eb 1bo ORtS FIGURE 3 Time dependence of the effective temperature. Solid lines represent models 1 and 6. Points are the observational data of Catchpole et al. (,19~ and crosses correspond to those of Hamlet et al. (19883.
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HIGH-ENERGY ASTROPHYSICS 409 REFE:RENCES Bionta, R.M., G. Blewitt, CB. Bratton, et al. 1987. Phys. Rev. Letters. 58:1494. Catchpole, RM., J.M. Menzies, NS. Monk, et al. 1987. Monthly Not. Roy. Astron. Soc. 229:15. Gilmozzi, R. A~ Cassatella, J. Clavel, et al. 19g7. Nature. 328:318. Grassberg, E.K, and D.K Nadyozhin. 1976. Astrophys. and Space Sci. 44:429. Ham~, M., N.B. Suntzell, R. Gonzalez, and G. Martin. 1988. Astron. J. 95:63. H~ata, K, T. Kajita, M. Koshiba, et al. 1987. Phys. Rev. Letters. 58:1490. Humphreys, RM., and D.B. McElroy. 1984. Astrophys. J. 284: 565. Menzies, J.M., R.M. Catchpole, G. van Vuuren, et al. 1987. Monthly Not. Roy. Astron. Soc. 227:39. Panagia, N., R Gilmozi, J. Oavel, et al. 1987. Astron. and Astrophy~ 117:L25. Rousseau, J., N. Martin, L" Prevot, et al. 1978. Astron. and Astrophys. Suppl. Ser. 31:243. Sandage, ^, and GN ~mmann. 1971. Astrophys. J. 167: 293. Sonneborn, G., B. Altner, and RP. Kinhner. 1987. Astrophys. J. (Letters) 323:135. Utrobin, V.P. 1989. Sov. Astron. Lettem. 15:99.
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