Theoretical cosmic Type Ia supernova rates

The purpose of this work is the computation of the cosmic Type Ia supernova rates, namely the frequency of Type Ia supernovae per unit time in a unitary volume of the Universe. Our main goal in this work is to predict the Type Ia supernova rates at very high redshifts and to check whether it is possible to select the best delay time distribution model, on the basis of the available observations of Type Ia supernovae. We compute the cosmic Type Ia supernova rates in different scenarios for galaxy formation and predict the expected number of explosions at high redshift (z\u2a7e2). Moreover, we adopt various progenitor models in order to compute the Type Ia supernova rate in typical elliptical galaxies of initial luminous masses of 1010Msun,1011Msun and 1012Msun, and compute the total amount of iron produced by Type Ia supernovae in each case. In this analysis we assume that Type Ia supernovae are caused by thermonuclear explosions of C-O white dwarfs in binary systems and we consider the most popular frameworks: the single degenerate and the double degenerate scenarios. The two competing schemes for the galaxy formation, namely the monolithic collapse and the hierarchical clustering, are also taken into account, by considering the histories of star formation increasing and decreasing with redshift, respectively. We calculate the Type Ia supernova rates through an analytical formulation which rests upon the definition of the SN Ia rate following an instantaneous burst of star formation as a function of the time elapsed from the birth of the progenitor system to its explosion as a Type Ia supernova (i.e. the delay time). What emerges from this work is that: (i) we confirm the result of previous papers that it is not easy to select the best delay time distribution scenario from the observational data and this is because the cosmic star formation rate dominates over the distribution function of the delay times; (ii) the monolithic collapse scenario for galaxy formation predicts an increasing trend of the SN Ia rate at high redshifts (mainly due to the contribution by massive spheroids), whereas the predicted rate in the framework of a decreasing cosmic star formation rate, more in agreement with the hierarchical scenario, drops dramatically at high redshift; (iii) for the elliptical galaxies we note that the predicted maximum of the Type Ia supernova rate depends on the initial galactic mass. The maximum occurs earlier (at about 0.3 Gyr) in the most massive ellipticals, as a consequence of the assumed downsizing in star formation. In addition, we find that the Type Ia supernova rate per unit mass at the present time is higher in bluer ellipticals (i.e. the less massive ones)