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Revisiting the Rates and Demographics of Tidal Disruption Events: Effects of the Disk Formation Efficiency

Tidal disruption events (TDEs) are valuable probes of the demographics of supermassive black holes as well as the dynamics and population of stars in the centers of galaxies. In this Letter, we focus on studying how the debris disk formation and circularization processes can impact the possibility of observing prompt flares in TDEs. First, we investigate how the efficiency of disk formation is determined by the key parameters, namely, the black hole mass $M_{BH}$, the stellar mass $m_\star$, and the orbital penetration parameter $β$ that quantifies how close the disrupted star would orbit around the black hole. Then we calculate the intrinsic differential TDE rate as a function of these three parameters. Combining these two results, we find that the rates of TDEs with prompt disk formation are significantly suppressed around lighter black holes, which provides a plausible explanation for why the observed TDE host black hole mass distribution peaks between $10^6$ and $10^7M_\odot$. Therefore, the consideration of the disk formation efficiency is crucial for recovering the intrinsic black hole demographics from TDEs. Furthermore, we find that the efficiency of the disk formation process also impacts the distributions of both stellar orbital penetration parameter and stellar mass observed in TDEs.