Tidal capture of stars by supermassive black holes: implications for periodic nuclear transients and quasi-periodic eruptions

Stars that plunge into the center of a galaxy are tidally perturbed by a supermassive black hole (SMBH), with closer encounters resulting in larger perturbations. Exciting these tides comes at the expense of the star's orbital energy, which leads to the naive conclusion that a smaller pericenter (i.e., a closer encounter between the star and SMBH) always yields a more tightly bound star to the SMBH. However, once the pericenter distance is small enough that the star is partially disrupted, morphological asymmetries in the mass lost by the star can yield an \emph{increase} in the orbital energy of the surviving core, resulting in its ejection -- not capture -- by the SMBH. Using smoothed-particle hydrodynamics simulations, we show that the combination of these two effects -- tidal excitation and asymmetric mass loss -- result in a maximum amount of energy lost through tides of $\sim 2.5\%$ of the binding energy of the star, which is significantly smaller than the theoretical maximum of the total stellar binding energy. This result implies that stars that are repeatedly partially disrupted by SMBHs many ($\gtrsim 10$) times on short-period orbits ($\lesssim$ few years), as has been invoked to explain the periodic nuclear transient ASASSN-14ko and quasi-periodic eruptions, must be bound to the SMBH through a mechanism other than tidal capture, such as a dynamical exchange (i.e., Hills capture).