Chin. Astron. Astrophys. (1995)19/4,426-431 A translation of Acta Astrophys. Sin. (1995) 15/3,22&232

Copyright @ 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved

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Modelling the April 15 spectrum of

Supernova 1993 Jt

ZHANG Qing’ WANG Li-fan2 HU Jing-yao2 P. A. Mazzali3~4 WANG Zhen-ru’

UniversiZy, Nanjing 2lOUO8

2 Beijing Astronomical Observa2ory, Chinese Academy of Sciences, Beijing 100080

30sservalorio Astronomico, Via G. B. Tiepolo 11, I-34131 Triesae, Italy

4 European Southern Observatory, Garching b. Miinchen, Germany

Abstract We present the modeling of the ultraviolet and optical spectra ob-

tained simultaneously on 1993 April 15 with the HST and at Lick Observatory.

A Monte Carlo code is employed in the modeling and a comparison is made

between models reported by different groups. With an atmosphere similar to

the Sun in chemical composition, the observed spectral lines are well reproduced

by a power law density structure of index around 20 except the strong H, and

He1 X5876 lines which have peculiar absorption profiles. The photospheric veloc-

ity is found to be 9500 km/s and the blackbody temperature of the spectrum is

7990K. For H, and He1 X5876, we suggest a two-component density structure

which has a smoother layer located immediately outside the steeply decreasing

inner envelope. The power law indices are most probably 20 and 3, respectively,

with the transition point at about 13 000 km/s. Jn addition, this outer smooth

layer serves to flatten the far UV spectrum as observed.

Key words: supernovae-SN 1993 J-line formation-line identification

1. INTRODUCTION

Supernova 1993 J was discovered on 1993 March 29[‘1 and was estimated to have erupted at

March 28.0 UTi21. B ecause its spectrum showed transition from Type II to approximately

Type Ib, it was assigned Type IIb [3~‘1 . The only precedent of this type is SN 1987 Ki51. From

the spectrum of April 15, we see that the spectrum at the early stage showed strong Balmer

lines and typical iron lines. Most of the spectral lines are narrow, and the narrow lines

are mostly the weak lines such as HP, Hy and Fe11 5018 and 5169, while the strong lines

like Ha and He I 5876 are broader, and their absorption pits showed a small bump161. The

t Supported by National Education Commission Doctoral Foundation Received 1994-08-05

Modelling Supernova 1993 J 427

narrowness of the lines imply a very steep density gradient in the atmosphere, with an index

as large as 20 or more~7~al. As for the peculiar profile of the broad links, mechanisms including

asymmetry of eruption have been proposed [6~g~101, but model calculations so far, whether

LTE or NLTE[“~a~121, while fitting a great part of the narrow lines, have not produced

satisfactory results for the broad lines.

The aim of this paper is using the Monte Carlo method to fit the spectrum of April 15,

in an attempt to explain the coexistence of the broad and narrow lines.

2. MONTE CARLO METHOD

In the Monte Carlo method, the supernova atmosphere is assumed to be spherically sym-

metric and uniformly expanding, and there is no energy accumulation outside some definite

photosphere. The formation of spectral lines mainly comes from resonance scattering in the

atmosphere. Line scattering is treated with the Sobolev approximation. The advantage of

synthetic spectrum from Monte Carlo method is simplicity in the treatment of the radiative

transfer of the liens. In an expanding atmosphere, displacement of spectral lines due to bulk

motion makes line superposition a common occurrence, but in such models the superposi-

tion is naturally included. In the calculation we considered some 20 000 spectral lines. The

model uses an approximate treatment of ionization and excitation regarding departure from

LTE, and includes relativistic terms to the first order in v/c.

The model parameters for SN 1993 J are: 1) the time reckoned from the eruption, 1, 2) the

atmospheric density structure p - r-“, 3) the photometric luminosity of the supernova at

time t, and 4) the position of the photosphere, expressed by the velocity Zlph, from which the

radius can be obtained. The models defines an effective temperature Tee and a blackbody

temperature Tbb. T,tf is directly calculated according to L = 4rR2T4, while Tbb has to be

found by iteration of the radiative transfer equation.

3. FITTING THE APRIL 15 SPECTRUM

The spectrum of SN 1993 J on April 15 was obtained 18.2 days after the eruption[“l. After

flux calibration, the UBV magnitudes were found to be close to those of Richmond et a1.[131,

i.e., V = 10.89, B - V = 0.49, U - B = -0.15. Using a density structure with a power law

index of 22, the best fit shown in Fig. 1 is obtained (the position of each line in the figure is

fixed by its absorption pit).

In the model, Zlph = 9500 km/s, corresponding to a radius of the photosphere of 1.495x 1015

cm, the luminosity is 2.3x 1O35 J/s, and T,tf = 6170K. These values are close to the results

of Baron et al.lsl. The blackbody temperature of the supernova spectrum is Tbb = 7990K,

and the total mass of the atmosphere outside the photosphere is 0.12 Ma, which agrees with

the conclusion that Type IIb supernovae have only a hydrogen envelope of small massL31.

Because the radio emission appeared rather early [141, the outer boundary of the atmosphere

was taken to be 22500km/s in the calculation. The model spectrum simulated well HP, Hy,

the H and K and three infrared lines of CaII, and clearly distinguished the Fe11 5018 and

5169 lines. The absorption at 56OgA probably comes from nont,hermal excitation of He1

428 ZHANG Qing et al.

= ?000.11

&

!).I) ~1WJ ;IJOl) liolnl 8000 I uooo

l\‘a\rlength (A)

Fig. 1 Comparison between a model spectrum with power law density structure of index 22

(dashed line) and the observed spectrum (solid line)

(possibly including NaI) 141. Here, we enhanced alone the He1 5876 line and found its LTE

deviation factor to be 2~10~. We did this only for discussing the line profile. The lines

marked in the figure correspond to the location of their formation, they are always blue

shifted with respect to their rest wavelengths.

Because of the very steep power law of the atmosphere, all the lines are narrow. Although

this is correct for the majority of the lines, we should note that for Ho, the left wing of

the absorption pit is blue shifted to 18 300 km/s, while the calculated region of formation is

only 11000 km/s. Since the model considers only pure scattering, the Monte Carlo method

is unable to simulate the emission of the Ho line.

In the ultraviolet, the model spectrum deviates from the observed one. In the range

2800-3600A, the calculated flux exceeds the observed flux, while below 2500A, the model

shows clear iron lines, unlike the smooth, observed spectrum.

A still steeper density structure will make the absorption lines of strong lines like Ho,

He15876 and CaII H and K shallower, and their blue shifts smaller. This is because, as

more matter is concentrated in the inner layers, the regions operative for the lines get closer

to the photosphere.

In order to explain the coexistence of both broad and narrow absorption lines, we con-

structed a twolayer density structure, that is, outside the steeply decreasing atmosphere, we

put a slower distribution. Fig.2 shows the result from the two-layer structure (apart from

the atmosphere, the other parameters are the same as in Fig. 1). The power law indices of

the inner and outer layers are, respectively, 22 and 2, the transition point of the density is at

12800 km/s. The other physical parameters were kept basically the same. Clearly, the more

tenuous atmosphere of the outer layer improved the profiles of Ho and He 15876, without

affecting the majority of the weak lines. Small bumps in the absorption pits of these two

lines can also be seen in the figure.

Modelling Supernova 1993 J 429

2 2000.0 Sh’l993J April IS

&

7 m

‘;

5

a 1000.0

1,

z

i.?

Fig. z Comparison between a model spectrum with a twocomponent

structure (dashed line) and the observed spectrum (solid line)

-7 ?OOO.O SNl993J April 15

k

0.0 2000 400ll GO00 8000 10000

Wavelength (A)

Fig. 3 A model spectrum (dashed line) with an extended atmosphere is compared to the observed

one (solid line)

The calculation shows that the optical thickness of weak lines such as HP or the iron

lines are basically unchanged, while the strength of Ha is increased by about 40% over the

previous model, and the blue shift is also increased. The increase in the intensity of He I5876

line is somewhat less. The two-component atmosphere also broadens the H and K lines of Ce II, resulting in a broad absorption at 3700 8. The result regarding the ultraviolet excess remained unsatisfactory.

430 ZHANG Qing et al.

We considered a third model with a more extended outer atmosphere: the inner com-

ponent had an index of 20 as before, while, beyond 13000 km/s, the density varies as rw3

and extends to a great distance from the photosphere. The mass outside the photosphere

is 0.125Mo. This model was motivated by the fact that the smoothness of the spectrum

shorter than 2500 A suggests that it has a thick envelope llll. The results from this model are

shown in Fig. 3, where we note that while the improvement in Ho and He I5876 remained

as in Fig. 2, the excess in the range 2800-3600A had vanished. The far ultraviolet beyond

2500 A became smoother, more like the observations, only the flux is now 5-10 times smaller

than the observed one. The main reason for the vanishing of the 2800-3600A excess is the

enhancement of the CaII H and K and Mg II 2800 lines. A series of strong iron lines formed

around 2400 A, which smoothed the far ultraviolet spectrum.

4. DISCUSSION

Our calculation based on the Monte Carlo method gave a fair fit to the April 15 spectrum

of SN 1993 J. Our analysis showed that the density variation is very steep in this object. A

two-component model-a thin and slowly varying distribution outside the steeply decreasing

layer-can better fit the peculiar profile of broad lines such as Ha and He 15876. Of course,

this is not the only possible interpretation of such a profile which, however, does not look

like a direct result of NLTE;- for the Monte Carlo method is approximately NLTE. It does

not look like result of blending with other lines, either. Baron et a1.1121 pointed out that

there possibly exist some iron lines in the left absorption wing of Ho, which would broaden

the line. However, we found in our calculation that even quite strong lines like SiII 6371

and 6347 are still insufficient for the observed features in Ha, although its absorption pit

does include the silicon lines (the small absorption pit in the left wing of Ha in Fig. 1).

The April 15 spectrum of SN 1993J is very flat in the far ultraviolet 1650-2900A, very

unlike the spectrum of SN 1987Al”l. After comparing with the spectra of SN 1979C and

SN 1980K at the same stage, Jeffrey et al. 1111 think that SN 1993 J has a very thick outer

envelope. Our third model shows that an extended and slowly varying outer layer can indeed

smooth out the fluctuations in the far ultraviolet, but as in the work of Baron et al.lsl, flux

deficiency will appear. A single power-law would not achieve this result. Because our model

can give the absolute flux, we find, on adopting E(B- V) = 0.15, a distance of about 3.5 kpc

for SN 1993 J, in agreement with cepheid distance of 3.6 f 0.3 Mpc found by Freedman et

a1.1161 and the distance modulus of 28.0 f 0.3 mag found by Baron et al.ls*i21.

ACKNOWLEDGMENT We than Professor R. Kirshner and Professor E. Baron for pro-

viding the spectra of April 15 of SN 1993 J.

Modelling Supernova 1993 J 431

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