The identities of the progenitors of type Ia supernova (SN Ia) has long been under study and remains an unsolved problem of astrophysics. The answer to this question will impact cosmology and subfields such as galactic evolution. To help resolve this issue and determine what systems give rise to SN Ia, the relationships between progenitor systems, their winds, and their environments are here considered, and a theoretical tool is created to model the consequences. I present theoretical semi-analytic models for the interaction of stellar winds with the interstellar medium (ISM). To investigate a wide range of possible winds and environments, I developed and employ piecewise, semi-analytical descriptions implemented in the code SPICE (Supernovae Progenitor Interaction Calculator for parameterized Environments, available on request), assuming spherical symmetry and power-law ambient density profiles. It is shown that a wide class of solutions can be found using the Buckingham Π-theorem. Semi-analytic solutions allow us to test a wide variety of configurations, their dependencies on the wind and environment parameters, and find non-unique solutions within a set of observational constraints. SPICE may be used to model such interactions in different types of Supernovae (SNe), stellar winds, as well as modeling realistic feedback in star formation and large scale galactic evolution simulations. As one of the many potential applications for SPICE, here I study pre-conditioning of the environment of Type Ia Supernovae (SNe Ia), which may originate from two merging WDs, known as the double degenerate scenario (DD), or an accreting white dwarf star (WD) from a non-degenerate companion, known as the single degenerate scenario (SD). The wind of the progenitor systems may originate from the progenitor, a donor star, or an accretion disk (AD). The environment is determined by the ISM and/or the wind of the donor star or the wind of the progenitor star during a prior epoch. The free parameters are: the a) mass loss [m with dot above] , b) wind velocity v[subscript w], c) density distributions ∝ r[superscript -s] of the ISM, and d)} the duration of the wind prior to the supernova explosion. I discuss the observational signatures with respect to light curves and high resolution spectra as tools to probe the environment of SNe Ia. The specific properties and evolution of the progenitor systems are found to leave unique imprints. During the progenitor evolution and with typical parameters in the SD scenario, the winds create a low density bubble surrounding the progenitor system and a high-density shell. It is also found that accretion disk winds dominate the environment formation. Within a distance of several light-years (ly), the densities are smaller by factors of 10²…⁴ compared to the environment. This explains the general lack of observed interaction in late time Supernova (SN) light curves for, at least, several years. The overdensities of the shells are between a factor of 4 to several hundred in case of constant density ISM and environments produced by stellar winds, respectively. The expansion velocity and width of the shell are typically 1-10% of both v[subscript w] and the contact discontinuity R[subscript C] and may produce narrow spectral lines as observed in some SNe Ia. Typically, narrow circumstellar lines of equivalent width ≈ 100 mÅ are found for uniform ISM typical in Spiral galaxies and ≈ 1 mÅ for wind environments. The outer layers of a SNe Ia expands with velocities of 10 to 30% of the speed of light and we may expect some interaction with the shells several years after the explosion. I apply the analysis to SN2014J and discuss several scenarios. For SN 2014J, the environment is likely formed by the AD wind running into a region produced by the Red Giant (RG) wind from the progenitor star prior to its WD stage. The delay times between the formation of the WD and the explosion is suggested to be short, ∼ 10⁵ yr. Finally the same analysis is repeated with other well-observed SN, including SN2001fe, PTF 11kx, SN2006X, and SN2007le.
