Equations with Type la and II SNe

In general, if one wants to compute in detail the evolution of the abundances of elements produced and restored into the ISM on long timescales, the I.R.A. approximation is a bad approximation. Therefore, it is necessary to consider the stellar lifetimes in the chemical evolution equations and solve them with numerical methods. 

For models involving Sub-Chandrasekhar white dwarf masses, which have been suggested to explain subluminous Type la SNe Greggio obtains Mwd 0.6Mq and eM2je 0.15 

The masses ML = 0.8 and Mu = 100M0 define the lowest and the highest mass, respectively, contributing to the chemical enrichment. The function rTO(m) describes the stellar lifetimes. The quantity Qmi(t — rm) contains all the information about stellar nucleosynthesis for elements either produced or destroyed inside stars or both, and is defined as in Talbot Arnett (1973). 

A recent model has been suggested by Hachisu et al. (1996, 1999) and is based on the classical scenario of Whelan Iben (1973) but with a metallicity effect. It predicts that no Type la systems can form for [Fe/H] —1.0. This model seems to have some difficulty in explaining the low [a/Fe] ratios observed in Damped Lyman- a systems (DLAs) which show that even at low metallicities is present the effect of Type la SNe. Recently, Matteucci Recchi (2001) showed that there are some problems with this scenario also 

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