6.2 Physical Basis and Self-Calibration

The standard model for a Type Ia supernova is the thermonuclear disruption of a carbon-oxygen white dwarf that has accreted enough mass from a companion star to approach the Chandrasekhar mass (Woosley and Weaver 1986; Wheeler and Harkness 1990 and references therein). The nuclear energy released in the explosion unbinds the white dwarf and provides the kinetic energy of the ejected matter, but adiabatic expansion quickly degrades the initial internal energy and the observable light curve is powered by delayed energy input from the radioactive decay of ⁵⁶Ni and ⁵⁶Co. This model brings with it a self-calibration of the peak luminosity. Arnett (1982a) predicted on the basis of an analytical model that the SN Ia peak luminosity would be equal to the instantaneous decay luminosity of the nickel and cobalt, in which case the peak luminosity follows directly from the ejected nickel mass and the rise time to maximum light. The rise time can be inferred from observation but owing to uncertainties in the physics of the nuclear burning front (e.g. Woosley 1990) the amount of synthesized and ejected ⁵⁶Ni cannot yet be accurately predicted by theory. Sutherland and Wheeler (1984) and Arnett et al. (1985) outlined how the nickel mass can be estimated indirectly from spectra and light curves. The more nuclear burning, the more ⁵⁶Ni and kinetic energy, and the greater the blueshifts in the spectrum and the faster the decay of the light curve. Arnett et al. (1985) argued from the blueshifts in the spectra that the nickel mass must be in the range 0.4 to 1.4 M and favored a value of 0.6 M (as in the particular carbon deflagration model W7 of Nomoto et al. (1984)). Adopting a rise time to maximum of 17 ± 3 days and distributing the luminosity according to the observed ultraviolet-deficient flux distribution of SNe Ia, Arnett et al. estimated M_B = -19.5^+0.4_-0.9) at bolometric maximum, which corresponds to M_B = -19.6 with limits of -19.2 and -20.5 at the time of maximum blue light a few days earlier.

Harkness (1990) finds that LTE synthetic spectra for carbon-deflagration models are very sensitive to the amount (and location in mass coordinate) of the ⁵⁶Ni in the ejecta; other models do not fit the observed spectra nearly as well as model W7 of Nomoto et al. (1984). He concludes that a nickel mass of 0.6 M may be optimum and that the upper limit is 0.8 M. From computed light curves for carbon-deflagration models Woosley (1990) favors 0.8 or 0.9 M with a lower limit of 0.4 or 0.5 M. If we accept 0.6 ± 0.2 M as the best present estimate, then following Arnett et al. we have M_B = -19.6 ± 0.5. The recent discovery of SN 1990N 17 ± 1 days before maximum light (Leibundgut et al. 1991) raises the possibility that the rise time is longer than 17 days. If the characteristic rise time should prove to be 20 days, for example, then the peak luminosity would be lowered by 0.16 mag.

Very recent investigations of the ejected nickel mass and the peak absolute magnitude, on the basis of the standard SN Ia model, are in good mutual agreement. Using an extension of the approach of Arnett et al. (1985) Branch (1992) finds an ejected nickel mass of 0.6 (+0.2, -0.1) M and M_B = -19.44 ± 35, Leibundgut and Pinto (1992) calculate the theoretical light curve of model W7 over the interval 60-130 days after explosion and use the observed SN Ia light curve to find a peak M_B = -19.6, and Ruiz-Lapuente et al. (1992) fit theoretical spectra to a 245-day observed spectrum of SN 1972E to find a nickel mass of 0.5-0.6 M. Ruiz-Lapuente et al. also find 0.4 M for the peculiar and possible subluminous SN 1986G.