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
$\beta$ 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.
