11. Differential Equations in Estimating the Mass of a Galaxy

Abstract

We are attempting to estimate the mass of a galaxy by solving jeans equation, a mass estimator created from the Boltzmann equation. When solving this we discovered that the equation states that the orbital velocities decrease as the radius of the galaxy increases. Furthermore, there is physical evidence stating that the orbital velocities do not decrease as the radius increases, mainly due to dark matter. Dark matter is matter that does not give off light, therefore we are unable to detect dark matter. We assume that dark matter makes up the vast majority of the mass of a galaxy and spans well beyond the visual terminal of a galaxy. Our goal is to rearrange this equation to make the orbital velocity display as a constant not depending on the radius of a galaxy. However, this is challenging because there are two parts of a galaxy where the velocities differ. Matter close to the center has a velocity that increases greatly due with respect to its radius, then after a threshold the velocity is relatively constant throughout the rest of the galaxy. We must adjust the mass estimator and change it from a Boltzmann equation, which is used better to measure the mass of things such as a solar system, to be able to accurately measure the mass of a galaxy.

Key Words

Jean's Equation

Differential Equation

Velocity Dispersion

Circular Orbits

Dark Matter