Research Projects

The study aims to explore the dynamical relaxation of dark matter haloes around galaxies into scale-invariant density profiles. Dark matter is considered collisionless systems, unlike ordinary gas, as it is composed of particles moving freely without colliding. These systems pose a challenge to equilibrium theories in physics, particularly statistical mechanics, as they struggle to achieve equilibrium in the absence of collisions. The right approach for such systems is to find a mechanism for relaxation to a phase-mixed steady state. The collisionless Boltzmann equation for the evolution of phase space density, f(x,p,t), is generally used to describe such systems. However, the system relaxes to a steady time-independent state at a volume averaged coarse-grained level, requiring a separate evolutionary equation for course-grained phase space density. The study also aims to investigate the process of virialization to establish the origin of scale-invariant profiles of dark matter haloes. The findings will be connected to a complete study of the evolution of coarse-grained phase space density, aiming to derive an appropriate relaxation term in the Boltzmann equation and understand its effects on achieving a steady state leading to scale-invariant profiles.