Spectral Hardening in Black Hole Accretion: Giving Spectral Modelers an f

TL;DR

This study investigates how spectral hardening factors in black hole accretion disks vary with physical parameters, using synthetic spectral models, and finds that Compton scattering dominates the spectral shape, with moderate variation of the hardening factor.

Contribution

The paper provides a robust estimation of the spectral hardening factor from synthetic spectra and explores its dependence on black hole mass and accretion rate, clarifying conditions for significant spectral hardening.

Findings

Spectral hardening factor f typically ranges from 1.4 to 2.

f increases with accretion rate but weakly with black hole mass.

Significant spectral hardening occurs only under specific low surface density conditions.

Abstract

By fitting synthetic spectral models computed via the TLUSTY code, we examine how the spectra from thin accretion disks are expected to vary in accreting black hole systems. We fit color-corrected blackbody models to our synthetic spectra to estimate the spectral hardening factor f, which parameterizes the departure from blackbody and is commonly used to help interpret multitemperature blackbody fitting results. We find we can define a reasonably robust f value to spectra when the effects of Compton scattering dominate radiation transfer. We examine the evolution of f with black hole mass and accretion rate, typically finding a moderate variation (f ~ 1.4-2) for accretion rates between 1% and 100% of the Eddington rate. Consistent with most previous work, we find f tends to increase with accretion rate, but we also infer a weaker correlation of f with black holes mass. We find that f is rarely much larger than 2 unless the disk becomes photon starved, in contention with some previous calculations. Significant spectral hardening (f > 2) is only found when the disk mass surface density is lower than expected for alpha-disk models unless alpha is near unity or larger.