Gravitational instability in a baryonic-dark matter system with two different distribution functions and collisional effects

In this study, we explore the gravitational instability in baryonic-dark matter systems using kinetic theory. We investigate whether the differences in the velocity distribution function for baryonic matter and dark matter affect the instability analysis. Our findings reveal that the dissimilarity in velocity distribution function can affect on the growth rate and the critical wave number of the instability. Our studied system has more stability than baryonic-dark matter system with Maxwell–Boltzmann distribution. However, it is more unstable than a system with a Tsallis distribution function for dark and baryonic matter. Furthermore, we examined the effect of collisions in a simplified manner. By solving the collisional Boltzmann equation using the relaxation time approximation (or Bhatnagar–Gross–Krook operator), we found that collision effects can decrease both the instability growth rate and the critical wave number of instability, depending on the ratio of collisional time to free fall time ([Formula: see text]). These results are applicable for analyzing the nonextensivity of self-gravitating systems and self-gravitating gaseous dynamical systems.