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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.