Calculating the Escape Velocity and Lower Mass Bound of a Body within a Dark Matter Halo

Dark matter remains to be one of the most speculative and mysterious substances from our current perspective in astrophysics. This paper will aim to provide educated hypotheses on the fermionic particle which makes up dark matter, by calculating the lower bound of the particle mass in an average dwarf spheroidal galaxy. This bound can be obtained through deriving the Escape Velocity based on calculations regarding Yukawa forces between dark matter particles. This can be done using the Pauli Exclusion Principle regarding fermionic particles to determine the mass density of the galaxy. This mass density can be calculated using models of the Jeans Analysis and Stellar Kinematics employing the Poisson Equation and Newton's Shell Theorems.
Solving dark matter can answer some of our universe's most important questions. Index Terms -Jeans Equation, Yukawa Potential, Escape Velocity, Dark Matter Halo