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OCR for page 403
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
OCR for page 404
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
OCR for page 405
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
OCR for page 406
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
OCR for page 407
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.
OCR for page 408
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.
OCR for page 409
HIGH-ENERGY ASTROPHYSICS
409
REFE:RENCES
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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.
OCR for page 410
Representative terms from entire chapter:
represent models
