On the Power to Constrain the Accretion History of Massive Black Holes
  via Spin Measurements by Upcoming X-Ray Telescopes
  The spin distribution of massive black holes (MBHs) contains rich information
on their assembly history. However, only limited information can be extracted
from currently available spin measurements of MBHs owing to the small sample
size and large measurement uncertainties. Upcoming X-ray telescopes with
improved spectral resolution and larger effective area are expected to provide
new insights into the growth history of MBHs. Here we investigate, at a proof
of concept level, how stringent constraints can be placed on the accretion
history of MBHs by the spin measurements from future X-ray missions. We assume
a toy model consisting of a two-phase accretion history composed of an initial
coherent phase with a constant disk orientation, followed by a chaotic phase
with random disk orientations in each accretion episode. By utilizing mock spin
data generated from such models and performing Bayesian Markov Chain Monte
Carlo simulations, we find that most accretion models of MBHs can be
reconstructed provided that $\gtrsim100$ MBH spins are measured with an
accuracy of $\lesssim0.1$. We also quantify the precision of the reconstructed
parameters by adopting various combinations of sample sizes and spin
accuracies, and find that the sample size is more crucial to model
reconstruction once the spin accuracy reaches $\sim 0.1$. To some extent, a
better spin accuracy will compensate for a small sample size and vice versa.
Future X-ray missions such as the Advanced Telescope for High Energy
Astrophysics and the enhanced X-ray Timing and Polarimetry mission, may provide
spin measurements of $\gtrsim100$ MBHs with an uncertainty of $\sim0.04-0.1$
and will thus put strong constraints on the MBH growth history.
