Studying the small scale ISM structure with supernovae

Aims. In this work we explore the possibility of using the fast expansion of a type Ia supernova photosphere to detect extra-galactic ISM column density variations on spatial scales of similar to 100 AU on time scales of a few months. Methods. We constructed a simple model which describes the expansion of the photodisk and the effects of a patchy interstellar cloud on the observed equivalent width of Na I D lines. Using this model we derived the behavior of the equivalent width as a function of time, spatial scale and amplitude of the column density fluctuations. Results. The calculations show that isolated, small (<= 100 AU) clouds with Na I column densities exceeding a few 10(11) cm(-2) would be easily detected. In contrast, the effects of a more realistic, patchy ISM become measurable in a fraction of cases, and for peak-to-peak variations larger than similar to 10(12) cm(-2) on a scale of 1000 AU. Conclusions. The proposed technique provides a unique way to probe the extra-galactic small scale structure, which is out of reach for any of the methods used so far. The same tool can also be applied to study the sub-AU Galactic ISM structure.