Annu. Rev. Astron. Astrophys. 1998. 36: 17-55 Copyright © 1998 by Annual Reviews. All rights reserved

4.4. Spectra

Synthetic spectrum calculations that assumed LTE but were otherwise detailed and self-consistent were carried out by Harkness (1991a, b). He found that the spectra of model W7 closely resembled those of the normal SNe Ia 1981B (Figure 13) and concluded that the ejected ⁵⁶Ni mass needs to be in the range 0.5-0.8 M, with the W7 value, 0.6 M, appearing to be optimum. Recently, detailed nonlocal thermodynamic equilibrium (NLTE) spectrum calculations have begun to be made (e.g. Baron et al 1996, Pauldrach et al 1996). Höflich (1995) compared synthetic spectra of delayed-detonation models with spectra of SN 1994D and found that models having M_Ni 0.6 provided the best fits. Nugent et al (1995a, 1997) found that W7 models provided good fits to the spectra of SNe 1981B, 1992A, and 1994D (Figure 14). Nugent et al (1995c) adopted the W7 composition structure and varied just the effective temperature to generate a sequence of maximum-light spectra that resembled the sequence of observed maximum-light spectra all the way from SN 1991bg through SN 1986G and normal SN Ia to SN 1991T (Figure 1, left panel). This means that the differences between the maximum-light spectra of SNe Ia, like the differences between the spectra of stars, are mainly due to differences in temperature. The root cause of the temperature range in real SNe Ia presumably is a range in M_Ni, and the whole composition structure surely also varies along the sequence in a way that has yet to be determined.

Figure 13. Local thermodynamic equilibrium (LTE) spectra calculated for model W7, 14 days after explosion, with no mixing (top) and mixing for v > 11,000 km s-1 (center), are compared with the maximum-light spectrum of SN 1981B (bottom). From Harkness (1991a).

Figure 14. NLTE spectra calculated for model W7 are compared to spectra of SN 1994D at maximum light and SN 1992A 5 days after maximum light. From Nugent et al (1997).

Höflich et al (1997), Nugent et al (1997) also calculated spectra of helium-ignitor models and found that they did not give satisfactory fits to the spectra of SNe Ia. The exploration of helium-ignitor models was well motivated on physical grounds (Livne 1990, Woosley & Weaver 1994a), so the interesting question about them is why do we not see them? It should be acknowledged here that on the basis of their calculations of late nebular spectra of explosion models, Liu et al (1997a, b) favored sub-Chandrasekhar mass ejection for normal SNe Ia and even SN 1991T; Ruiz-Lapuente (1996) did not. The calculation of nebular spectra is hampered by a lack of reliable atomic data, although the situation is improving (Liu et al 1997c). In any case, it is not clear why sub-Chandrasekhar C-O white dwarfs that lack the deadly surface helium layer of the helium-ignitor models should explode. Another issue with respect to the nebular phase is that there are indications from light-curve shapes (Cappellaro et al 1998, Colgate et al 1997, Milne et al 1998) that at late times, positrons from Co⁵⁶ decay are not completely trapped, as is usually assumed.

Detailed NLTE spectrum calculations are invaluable for falsifying hydrodynamical models, but since the number of parameterized hydro models that can be imagined is infinite and the number of spectra that can be calculated in NLTE is limited by computational complexity, a much more empirical approach to SN spectroscopy also is useful. Fisher et al (1997) used a fast, parameterized spectrum synthesis code to study a high-quality spectrum of the normal SN Ia 1990N that was obtained 14 days before maximum light by Leibundgut et al (1991a). Fisher et al (1997) suggested that the absorption observed near 6040 Å, which had been attributed to 6355 of Si II, actually was produced by 6580 of C II in a high-velocity (v > 26,000 km s^-1) carbon-rich region. Such a layer would be consistent with published delayed-detonation models. A Fisher, D Branch, K Hatano, and E Baron (manuscript in preparation) suggest that in the peculiar SN 1991T, the "Si II" absorption is dominated by C II 6580 before and perhaps even at maximum light. On the basis of the empirical constraints on the composition structure of SN 1991T together with estimates of the luminosity of SN 1991T, which must be checked with a Cepheid distance, Branch (1998) and Fisher et al (manuscript in preparation, noted above) suggest that peculiar events like SN 1991T are superluminous, usually extinguished, substantially super-Chandrasekhar mergers from the youngest populations that are able to produce SNe Ia in this way, ~ 10⁸ years (Tutukov & Yungelson 1994).