Size distribution of supernova remnants and the interstellar medium: the case of M 33

The size distribution of supernova remnants (SNRs) can help to clarify the various aspects of their evolution and interaction with the interstellar medium (ISM). Since the observed samples of SNRs are a collection of objects with very different ages and origin that evolve in different conditions of the ISM, statistical Monte Carlo methods can be used to model their statistical distributions. Based on very general assumptions on the evolution, we have modeled samples of SNRs at various initial and environmental conditions, which were then compared with observed collections of SNRs. In the evolution of SNRs the pressure of the ISM is taken into account, which determines their maximum sizes and lifetimes. When comparing the modeled and observed distributions, it is very important to have homogeneous observational data free from selection effects. We found that a recently published collection of SNRs in M 33 satisfies this requirement if we select the X-ray SNRs with hardness ratios in a limited range of values. An excellent agreement between distributions of this subset of SNRs and the subset of modeled SNRs was reached for a volume filling-factor of the warm phase of the ISM (partly ionized gas with nH ~ 0.2−0.5 cm-3; T ~ 8000−10 000 K) in M 33 of ~90%. The statistical distributions constructed in this way, which reproduce practically all the statistical properties of observed SNRs, allowed us to obtain one of the important parameters of M 33: the birthrate is one SNR every 140−150 yr, and the total number of SNRs with a shock Mach number Ms ≥ 2 is larger than ~1000.