Fate of the remnant in tidal stripping event: repeating and non-repeating

Tidal disruption events (TDE) occur when a star ventures too close to a massive black hole. In a partial TDE (pTDE), the star only grazes the tidal radius, causing the outer envelope of the star to be stripped away while the stellar core survives. Previous research has shown that a star, once tidally stripped in a parabolic orbit, can acquire enough orbital energy for its remnant to become a high-velocity star potentially capable of escaping the galaxy. Conversely, some studies have reported that the remnant may lose orbital energy and undergo re-disruption, leading to a recurring pTDE. This study aims to uncover the physical mechanisms and determine the conditions that lead to these divergent outcomes. We find that the orbital energy change only depends on the impact factor and the stellar structure, and barely depends on the mass of the black hole or the exact mass or orbital eccentricity of the star. For a $\gamma=5/3$ (or $\gamma=4/3$) polytropic star, after a pTDE its remnant gains orbital energy when the impact factor $\beta \gtrsim 0.62$ (or $\gtrsim 1.1$) or loses energy vice versa. Additionally, we verify an analytical equation for orbital energy change that is applicable across various systems. Through hydrodynamic simulations, we also explore the structure of the stellar remnant post-tidal stripping. Our findings provide critical insights for interpreting observed pTDEs and advancing knowledge on the orbital evolution and event rate of these events.