Constraining Disk-to-Corona Power Transfer Fraction, Soft X-ray Excess Origin, and Black Hole Spin Population of Type-1 AGN across Mass Scales
Understanding the nature of the accretion disk, its interplay with the X-ray corona, and assessing black hole spin demographics remain open challenges in astrophysics. In this paper, we examine the predictions of the standard $\alpha$-disk model, origin of the puzzling soft X-ray excess, and measure the black hole spin parameter by applying an updated high-density disk reflection model to the XMM-Newton/NuSTAR broadband (0.3$-$78 keV) X-ray spectra of a sample of 11 Type-1 AGN. Our Bayesian analysis confirms that a variable-density relativistic disk reflection model with a broken power-law emissivity profile can simultaneously fit the soft X-ray excess, broad iron K line emission, and Compton hump in 3 out of 11 AGN. For the remaining sources, a distinct warm Comptonization component is still required, which supports a hybrid origin for the soft X-ray excess. The measured temperature and optical depth of the warm corona span nearly the entire theoretically allowed range, with median values of $0.43_{-0.18}^{+0.40}$ keV and $12.5_{-3.9}^{+3.1}$, respectively. Our first systematic calculation of the disk-to-corona power transfer fraction reveals that the fraction of power released from the accretion disk into the hot corona spans a wide range, with a sample median of $0.68_{-0.25}^{+0.25}$. The sample median values for the hot coronal plasma temperature and optical depth are $54_{-12}^{+11}$ keV and $0.98_{-0.28}^{+0.22}$, respectively. Finally, through both hard X-ray (3$-$78 keV) and broadband (0.3$-$78 keV) relativistic reflection spectroscopy, we systematically constrain the black hole spin parameter across the mass scales of $\log(M_{\rm BH}/M_{\odot}) \sim 5.5-9.0$, thereby increasing or refining the available spin measurements in the AGN population by $\sim$20%.