Finding the most compact configuration of neutron stars

We reproduce past solutions of the Tolman-Oppenheimer-Volkoff equations to estimate the maximum mass of a neutron star for two models of the equation of state (EoS), and begin to estimate a maximal-density constraint on the EoS. We use an EoS for a non-interacting ideal Fermi gas of pure neutrons, finding a maximum mass $M_{\max}\approx0.71\,\mathrm{M_{\odot}}$ and a corresponding radius $R\approx9.0$ km, agreeing with past studies. This procedure is repeated for an EoS modified to include the strong interaction. From this we find $M_{\max}\approx2.22\,\mathrm{M_{\odot}}$ and $R\approx10.0$ km, in agreement with past studies as well. Upon reproducing these results, we construct a piecewise EoS with a large portion of minimal sound speed $c_s=0$, tuning the transition point between $c_s=0$ and $c_s=1$ until it yields $M_{\max}\approx2.0\,\mathrm{M_{\odot}}$, the lower constraint from astronomical observations. The next step of this project will be to explore the set of piecewise EoS models that minimizes pressure $p(\epsilon_i)$ for each $\epsilon_i$ in energy density $\epsilon$ and satisfies the condition $M_{\max}\approx2.0\,\mathrm{M_{\odot}}$.