Calculation of Primary Variables Affecting the g-mode Oscillations in Neutron Stars*

Other than black holes, neutron stars are the only known source of gravitational waves. Unlike black holes, however, neutron stars contain matter at extremely high density. Thus, studying gravitational waves from neutron stars helps us discover new forms of matter. We study particular oscillations of neutron star matter driven by chemical gradients, called g-modes, that couple to gravitational waves. Using a theoretical model for the neutron star, we derive the trends in proton fraction with mass density and the Brunt-Väisälä frequency at which the g-mode oscillates. The trends confirm published results from literature for nuclear matter. We extend this benchmark to new regimes of dense matter that include a mixed phase of quark and nuclear matter.