$\Gamma = 3\ $ Initial Configuration
This neutron star is modeled as a $\Gamma = 3$ polytrope, which is known to produce differentially rotating ergostars. The $\Gamma = 3$ polytropic index was chosen since it produced ergostars at higher $R_p/R_e$ , i.e. with almost spheroidal geometries and at lower $T$ /|$W$| so that they are less susceptible to nonaxisymmetric instabilities. Here, $T$ and $W$ are the rotational and gravitational potential energies of the star, respectively. An additional consideration was the choice of $\hat{A} = 2.5$, where $\hat{A} = A/R_e$ determines the degree of differential rotation. The constant $A$ appears in the "j-const" law, $\ j(\Omega) = A^2(\Omega_c-\Omega)$, and has units of length. The rotational period of the star, $P_c$, corresponds to its central angular velocity, $\Omega_c$.
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