The question of how supermassive black holes (SMBHs) grow over cosmic time is a major puzzle in high-energy astrophysics. One promising approach to this problem is via the study of tidal disruption flares (TDFs). These are transient events resulting from the disruption of stars by quiescent supermassive black holes at centers of galaxies. A meter-class X-ray observatory with a time resolution $sim$ a millisecond and a spectral resolution of a few eV at KeV energies would be revolutionary as it will facilitate high signal to noise spectral-timing studies of several cosmological TDFs. It would open a new era of astrophysics where SMBHs in TDFs at cosmic distances can be studied in similar detail as current studies of much nearer, stellar-mass black hole binaries. Using Athena X-ray observatory as an example, we highlight two specific aspects of spectral-timing analysis of TDFs. (1) Detection of X-ray quasi-periodic oscillations (QPOs) over a redshift range and using these signal frequencies to constrain the spin evolution of SMBHs, and (2) Time-resolved spectroscopy of outflows/winds to probe super-Eddington accretion. SMBH spin distributions at various redshifts will directly allow us to constrain their primary mode of growth as higher spins are predicted due to spin-up for prolonged accretion-mode growth, while lower spins are expected for growth via mergers due to angular momentum being deposited from random directions. A meter-class X-ray telescope will also be able to characterize relativistic TDFs, viz., SwJ1644+57-like events, out to a redshift greater than 8, i.e., it would facilitate detailed spectral-timing studies of TDFs by the youngest SMBHs in the Universe.
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