Extinction correction for type ia supernova rates - I. The model

In this paper, we present and discuss a new Monte Carlo approach aimed at correcting the observed supernova (SN) rates for the effects of host galaxy dust extinction. The problem is addressed in a general way and the model includes SN position distributions, SN light-curve and spectral library and dust properties and distribution as input ingredients. Even though the recipe we propose is in principle applicable to all SN types, in this paper, we illustrate the use of our model only for Type Ia. These represent, in fact, the simplest test case, basically due to their spectroscopic homogeneity, which to a first approximation allows one to treat them all in the same way. This test case shows that the final results do not depend critically on the spiral arm dust geometry, while the total amount of dust, its properties and the size of the Galactic bulge do have a strong effect. With the availability of more complete spectral libraries and a more accurate knowledge of SN spatial distribution, the method we propose here can be easily extended to core collapse events.