Tidal disruption of a star by a massive black hole in Fermi normal coordinates

I present a new numerical code constructed to obtain accurate simulations of encounters between a star and a massive black hole. The relativistic tidal interaction is calculated in \emph{Fermi normal coordinates} (FNC). This formalism allows the addition of an arbitrary number of terms in the tidal expansion. Although Newtonian hydrodynamics and self-gravity is assumed for the star, there are several significant terms in the expansion that should be retained. I give the relevant orbital post-Newtonian terms. The three-dimensional parallel (MPI) code includes a PPMLR hydrodynamics module to treat the gas dynamics and a Fourier transform-based method to calculate the self-gravity. Results are given for a white dwarf ($n=1.5$ polytrope) with comparisons between simulations and predictions from the linear theory of tidal encounters. The encounters are at the threshold of disruption ($\eta=1-6$) for white dwarf to black hole mass ratios $\mu \sim 10^{-5}-10^{-3}$. It is shown that the inclusion of the octupole ($l=3$) tidal term will cause the center of mass of the star to deviate from the origin of the FNC. Also shown is a relativistic suppression in the amount of energy deposited onto the star. Finally, I estimate the new orbital parameters for the star after it passes by the black hole.