The rates of type Ia supernovae

Abstract

The aim of this paper is to provide a handy tool to compute the impact of type Ia SN (SNIa) events on the evolution of stellar systems. An effective formalism to couple the rate of SNIa explosions from a single burst of star formation and the star formation history is presented, which rests upon the definition of the realization probability of the SNIa event (A Ia ) and the distribution function of the delay times ( f Ia (τ)).It is shown that the current SNIa rate in late type galaxies constrains A Ia to be on the order of 10 −3 (i.e. 1 SNIa every 1000 M of gas turned into stars), while the comparison of the current rates in early and late type galaxies implies that f Ia ought to be more populated at short delays. The paper presents analytical formulations for the description of the f Ia function for the most popular models of SNIa progenitors, namely Single Degenerates (Chandrasekhar and Sub-Chandrasekhar exploders), and Double Degenerates. These formulations follow entirely from general considerations on the evolutionary behavior of stars in binary systems, modulo a schematization of the outcome of the phases of mass exchange, and compare well with the results of population synthesis codes, for the same choice of parameters. The derivation presented here offers an immediate astrophysical interpretation of the shape of the f Ia functions, and have a built in parametrization of the key properties of the alternative candidates. The important parameters appear to be the minimum and maximum masses of the components of the binary systems giving rise to a SNIa explosions, the distribution of the primary mass and of the mass ratios in these systems, the distribution of the separations of the DD systems at their birth. The various models for the progenitors correspond to markedly different impact on the large scales; correspondingly, the model for the progenitor can be constrained by examining the relevant observations. Among these, the paper concentrates on the trend of the current SNIa rate with parent galaxy type. The recent data by Mannucci et al. (2005, A&A, 433, 807) favor the DD channel over the SD one, which tends to predict a too steep distribution function of the delay times. The SD scenario can be reconciled with the observations only if the distribution of the mass ratios in the primordial binaries is flat and the accretion efficiency onto the WD is close to 100%. The various models are characterized by different timescales for the Fe release from a single burst stellar population. In particular the delay time within which half of the SNIa events from such a population have occurred, ranges between 0.3 and 3 Gyr, for a wide variety of hypothesis on the progenitors.

A simple and general method for solving detailed chemical evolution with delayed production of iron and other chemical elements

“…It is therefore fundamental to properly take into account the Type Ia SN contribution in a theoretical model of chemical evolution. A useful formalism to compute the Type Ia SN rate in galaxies was developed by Ruiz-Lapuente & Canal (1998), by originally introducing the concept of DTD in the theoretical framework (see also Strolger et al 2004;Greggio 2005). In this formalism, the Type Ia SN rate is defined as the convolution of the galaxy star formation rate (SFR) with a suitable DTD, as follows.…”

“…According to Greggio (2005), the so-called "double degenerate scenario" -in which Type Ia SNe originate from binary systems of electron degenerate CO white dwarfs losing angular momentum via gravitational wave emission -can be modeled by assuming DTDIa(τ ) ∝ 1/τ (see also Totani et al 2008), which provides almost the same final results for the Type Ia SN rate in galaxies as the DTD proposed by Schönrich & Binney (2009) and recently assumed by Weinberg et al (2016).…”

Abundance ratios in the hot ISM of elliptical galaxies

“…We also present a model that considers the double degenerate (DD) wide scenario (see Greggio 2005;and Valiante et al 2009, for details). We note that when this scenario is constrained to reproduce the present day SNIa rate, the total number of SNIa (hence the total mass of synthesized Fe) is lower than that in the fiducial case by a factor of four.…”

The Chemical Enrichment of the ICM from Hydrodynamical Simulations

“…For a comprehensive review of analytical formulations we refer to the paper by Greggio (2005). Following Greggio and Renzini (1983), we assume here that SN Ia arise from stars belonging to binary systems, having mass in the range 0.8-8 M .…”