Tidal Stablization of Neutron Stars and White Dwarfs

What happens to a neutron star or white dwarf near its maximum mass limit when it is brought into a close binary orbit with a companion? Such situation may occur in the progenitors of Type Ia supernovae and in coalescing neutron star binaries. Using an energy variational principle, we show that tidal field reduces the central density of the compact object, making it more stable against radial collapse. For a cold white dwarf, the tidal field increases the maximum stable mass only slightly, but can actually lower the maximum central density by as much as $30\%$. Thus a white dwarf in a close binary may be more susceptible to general relativistic instability than the instability associated with electron capture and pycronuclear reaction (depending on the white dwarf composition). We analyse the radial stability of neutron star using post-Newtonian approximation with an ideal degenerate neutron gas equation of state. The tidal stablization effect implies that the neutron star in coalescing neutron star-neutron star or neutron star-black hole binaries does not collapse prior to merger or tidal disruption.