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Astron. Astrophys. 354, 557-566 (2000)

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3. Nebular phase

3.1. Nebular model

The high quality late time spectrum of SN 1997D at the nebular epoch [FORMULA] d (Turatto et al. 1998) gives us an opportunity of a complementary test for the ejecta model. Our goal here is to reproduce all the strong lines observed in the spectrum, viz. H[FORMULA], [O I] 6300, 6364 Å, and [Ca II] 7291, 7324 Å using the density distribution of the hydrodynamical model. We assume that the ejected envelope consists of two distinctive regions: a core and an external H-rich envelope. The core in the nebular model is a macroscopic mixture of radioactive 56Ni, H-rich matter (component A), He-rich matter (component B), O-rich matter (component C), and the rest of metals, e.g., C, Ne, Mg (component D). The latter does not contribute noticeably to the lines we address. The density of the A, B, and D components is equal to the model local density [FORMULA], while the O-rich matter of density [FORMULA] may be clumpy with the density contrast [FORMULA]. Voids arising from the oxygen clumpiness are presumably filled in by the 56Ni bubble material.

The average gamma-ray intensity was calculated using a formal solution of the transfer equation with known distribution of 56Ni and assuming the absorption approximation with the absorption coefficient [FORMULA] cm2 g-1. The fraction of deposited energy lost by fast electrons on heating and ionization of hydrogen, helium, and oxygen was taken from Kozma & Fransson (1992). The rate of nonthermal excitation and ionization of helium in the H-rich matter was added to the hydrogen ionization rate to take account of hydrogen ionization by UV radiation produced by helium nonthermal excitation and ionization. Due to this process the H[FORMULA] intensity is insensitive to the He/H ratio. The photoionization of hydrogen from the second level by hydrogen two-photon radiation and by the Balmer continuum were taken into account as well. The Balmer continuum radiation consists of the recombination hydrogen continuum and the rest of ultraviolet radiation created by the radiation cascade of the deposited energy of radioactive 56Co. This additional component of Balmer continuum radiation was specified assuming that a fraction p of the deposited energy is emitted in Balmer continuum with the spectrum [FORMULA]. We adopted [FORMULA] according to estimates by Xu et al. (1992) for SN 1997A at the nebular epoch.

In thermal balance only the principal coolants are included: hydrogen lines, C I 2967 Å, 4621 Å, 8727 Å, 9849 Å, Mg II 2800 Å, [O I] 6300, 6364 Å, [Ca II] 3945 Å, 7300 Å, Ca II 8600 Å, and Fe II lines. For the sake of simplicity the total Fe II cooling rate of permitted and semi-forbidden lines is assumed to be equal to the cooling rate of one Mg II 2800 Å line. However, unlike for the real Mg II line collisional saturation is omitted to allow photon branching in Fe II lines. Cooling via the excitation of Fe II forbidden lines is represented by [Fe II] 8617 Å and [Fe II] 4287 Å lines, which are the most efficient coolants for the relevant temperature and electron density. We include also adiabatic cooling; it is important in the outer region of the hydrogen envelope. Metals with a low ionization potential (Mg, Ca, Fe) are assumed singly ionized.

With a specified density distribution and 56Ni mass the primary fitting parameter is the velocity at the core boundary [FORMULA], which affects line intensities via the mass of the mixed core [FORMULA] exposed to the intense gamma-rays. The amount of matter in components A, B, and C should then be determined from the spectrum fit.

3.2. Model test

Before applying the nebular model to SN 1997D it is instructive to compute the nebular spectrum of the well studied SN 1987A. We used the CTIO spectrum corrected for reddening at the epoch 339 days (Phillips et al. 1990; Pun et al. 1995). The primordial metal abundance (Z) is assumed to be 0.4 solar. The density distribution in the envelope is approximated by Eq. (1) with [FORMULA]. Compromise values of ejecta mass [FORMULA] and kinetic energy [FORMULA] erg are adopted (Woosley 1988; Shigeyama & Nomoto 1990; Utrobin 1993). Apart from the 56Ni mass (0.075 [FORMULA]), we specify the amount of metals in the core [FORMULA] (component D), in line with the expectations for an 18-22 [FORMULA] progenitor (Woosley & Weaver 1995; Thielemann et al. 1996).

A satisfactory description of line profiles and intensities of H[FORMULA], [O I] 6300, 6364 Å, and [Ca II] 7291, 7324 Å (Fig. 8) is obtained with the test model (TM) for a sound choice of parameters (Table 1). The table gives ejecta mass (M), kinetic energy ([FORMULA]), the primordial-to-solar metal abundance ratio ([FORMULA]), velocity at the outer boundary of the mixed core ([FORMULA]), oxygen density contrast ([FORMULA]), core mass ([FORMULA]), and other core components, viz. H-rich matter ([FORMULA]), He-rich matter ([FORMULA]), O-rich matter ([FORMULA]), and metals ([FORMULA]). All masses in Table 1 are given in solar masses. The amount of H-rich and He-rich matter in the mixed core inside 2000 km s-1 ([FORMULA] and [FORMULA], respectively) are in good agreement with values advocated by Kozma & Fransson (1998). The rest of newly synthesized helium ([FORMULA]) is presumably mixed with the H-rich component. The oxygen mass and density contrast were found from best "eye-fit" of flux of the [O I] doublet. The value [FORMULA] corresponds to the oxygen filling factor [FORMULA], a value earlier found by Andronova (1992).

[FIGURE] Fig. 8. Computed (thick line) and observed (thin line) emission lines in the SN 1987A spectrum on day 339 (Pun et al. 1995).


Table 1. Parameters of nebular models

The oxygen mass estimate is hampered somewhat by the uncertainty arising from the poorly known fraction of oxygen cooled via CO and SiO emission. In SN 1987A the mass of cool oxygen in the CO dominated region is estimated as 0.2 [FORMULA] (Liu & Dalgarno 1995). With a comparable oxygen mass hidden in the SiO region we thus miss about 0.4 [FORMULA] of oxygen. Therefore the total oxygen mass must be [FORMULA] in rough agreement both with the estimate from the HST spectrum at nonthermal excitation phase (Chugai et al. 1997) and predictions of stellar evolution models for an 18-22 [FORMULA] progenitor (Woosley & Weaver 1995; Thielemann et al. 1996).

Omitting details, we conclude that the test of nebular model in the case of SN 1987A is successful and demonstrates that the model is able to recover reliable values of important parameters.

3.3. SN 1997D: low and high-mass models

Now we turn to the nebular spectrum of SN 1997D at [FORMULA] d. First, the 6 [FORMULA] case based on the hydrodynamical model (Sect. 2.4) will be considered. Some refinement of the hydrodynamical model is needed, however, to apply it to nebular epoch. The amount of metals in the mixed core is specified assuming that masses of metals and oxygen are equal. This is a reasonable assumption for a low-mass pre-SN. The oxygen abundance in He-rich matter (component B) was assumed one tenth cosmic, while a carbon abundance of 0.03 is adopted for He-rich matter in the 6 [FORMULA] model. We then also consider the 24 [FORMULA] case based on the model by Turatto et al. (1998) with the composition taken from Nomoto & Hashimoto (1988).

The low-mass nebular model of SN 1997D fits the observed spectrum fairly well (Fig. 9a) with the optimal choice of parameters represented by model M1 (Table 1). The [Ca II] 7300 Å profile was reproduced for the core velocity [FORMULA] km s-1. This parameter is of primary importance, since it determines the absolute mass of the core components with the adopted density structure. We failed to fit the absolute flux of this line with a cosmic primordial abundance adopted for the model M2 (Table 1 and Fig. 9b), while the primordial abundance 0.3 of cosmic in model M1 provides an excellent fit. The oxygen doublet intensity is determined primarily by the mass of the O-rich matter, although some 20% come from He and H-rich matter. The value of 0.035 [FORMULA] is corrected for the unseen cool oxygen assuming that we see 3/4 of all the pure oxygen in the [O I] doublet as in SN 1987A. A strong oxygen overdensity is not required. We found that [FORMULA] in model M1 provides somewhat better agreement with the observed ratio of [O I] doublet components than [FORMULA]. The amount of He-rich matter is a lower limit for the mass of the He shell in the pre-SN. One may admit up to 1 [FORMULA] of helium mixed microscopically with the H-rich envelope without a notable effect on line intensities.

[FIGURE] Fig. 9a and b. Computed (thick line) and observed (thin line) emission lines in SN 1997D spectrum on day 296. Model M1 a with primordial metal abundance 0.3 of cosmic describes [Ca II] doublet better than the model M2 b with the cosmic abundance.

Unfortunately our nebular model is not applicable to the earlier nebular spectrum of SN 1997D on day 150. The reason is the significant optical depth in the Paschen continuum predicted by the model. In such a situation the multilevel statistical equilibrium must be solved together with a full radiation transfer, which is beyond the scope of this paper. Moreover, we found that the observed H[FORMULA] profile at this epoch is odd exhibiting a significant redshift of unclear origin. A prima face explanation assuming 56Ni asymmetry cannot accommodate to the late time nebular spectrum ([FORMULA] d) lacking such an asymmetry.

To evaluate the uncertainty related with the assumption of the same fraction (1/4) of cool O-rich gas as in SN 1987A, we compared parameters relevant to molecular formation (density and temperature) in the O-rich matter at a similar nebular epoch. We found that the density of O-rich gas in SN 1997D is lower, while the temperature is somewhat higher compared to SN 1987A. Both parameters suggest therefore that formation of molecules in SN 1997D cannot be more efficient than in SN 1987A, which means that the fraction of unseen pure oxygen in SN 1997D does not exceed that in SN 1987A. With the uncertainty of the core velocity the estimated range of pure oxygen mass in SN 1997D is 0.02-0.07 [FORMULA].

We applied the nebular model to the high-mass case ([FORMULA]). Due to the large mass of the He/O core the velocity of the core boundary is too high and inconsistent with the observed [Ca II] doublet profile. Mixing all the freshly synthesized helium with the hydrogen envelope (which is very unlikely) reduces the core velocity but not sufficiently to resolve this controversy (Fig. 10a). Another serious problem is a high [O I] doublet flux and wrong doublet ratio. The five-fold reduction of amount of line-emitting oxygen, for example, due to molecular formation and cooling or due to fall-back onto a black hole (if any), alleviates the problem of total flux in the [O I] doublet. However, this does not resolve the problem of high [FORMULA] ratio in the high-mass model (Fig. 10b).

[FIGURE] Fig. 10a and b. Computed nebular spectrum (thick line) in the high-mass case along with the observed (thin line) emission lines in SN 1997D spectrum on day 296. a - model M3 without reduction of oxygen line-emitting mass; b - the same model but with five-fold reduction of the oxygen line-emitting mass. Neither of the model spectra fits the data.

Summing up, we found that the hydrodynamical model of moderate mass ejecta ([FORMULA]) which contains low amount of freshly synthesized oxygen (0.02-0.07 [FORMULA]) is consistent with the nebular spectra of SN 1997D. The model of high-mass ejecta as such is incompatible with the observed nebular spectra.

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© European Southern Observatory (ESO) 2000

Online publication: February 9, 2000