The Delay Time Distribution of Tidal Disruption Flares

Abstract: Recent observations suggest that stellar tidal disruption events (TDE) are strongly overrepresented in rare, post-starburst galaxies. Several dynamical mechanisms have been proposed to elevate their TDE rates, ranging from central stellar overdensities to the presence of supermassive black hole (SMBH) binaries. Another such mechanism, introduced here, is a radial velocity anisotropy in the nuclear star cluster produced during the starburst. These, and other, dynamical hypotheses can be disentangled by comparing observations to theoretical predictions for the TDE delay time distribution (DTD). We show that SMBH binaries are a less plausible solution for the post-starburst preference, as they can only reproduce the observed DTD with extensive fine-tuning. The overdensity hypothesis produces a reasonable match to the observed DTD (based on the limited data currently available), provided that the initial stellar density profile created during the starburst, $\rho(r)$, is exceptional in both steepness and normalization. In particular, explaining the post-starburst preference requires $\rho \propto r^{-\gamma}$ with $\gamma \gtrsim 2.5$, i.e. much steeper than the classic Bahcall-Wolf equilibrium profile of $\gamma = 7/4$. For "ultrasteep" density cusps ($\gamma \ge 9/4$), we show that the TDE rate decays with time measured since the starburst as $\dot{N} \propto t^{-(4\gamma-9)/(2\gamma-3)} / \ln t$. Radial anisotropies also represent a promising explanation, provided that initial anisotropy parameters of $\beta_0 \approx 0.5$ are sustainable against the radial orbit instability. TDE rates in initially anisotropic cusps will decay roughly as $\dot{N} \propto t^{-\beta_0}$. As the sample of TDEs with well-studied host galaxies grows, the DTD will become a powerful tool for constraining the exceptional dynamical properties of post-starburst galactic nuclei.