# Self-Consistent Black Hole Accretion Spectral Models and the Forgotten Role of Coronal Comptonization of Reflection Emission

## TL;DR

This paper develops a self-consistent spectral modeling framework for black hole accretion that incorporates coronal Comptonization of reflection emission, revealing its significant impact on inferred parameters and accretion physics.

## Contribution

It introduces a photon-conserving model that jointly fits continuum and reflection spectra, emphasizing the importance of coronal Comptonization effects in black hole spectral analysis.

## Key findings

- Accounting for Comptonization increases reflection fraction estimates.
- Downscattering can mimic relativistic Fe line features.
- Constraints on accretion rate challenge large disk truncation in bright hard states.

## Abstract

Continuum and reflection spectral models have each been widely employed in measuring the spins of accreting black holes. However, the two approaches have not been implemented together in a photon-conserving, self-consistent framework. We develop such a framework using the black-hole X-ray binary GX 339-4 as a touchstone source, and we demonstrate three important ramifications: (1) Compton scattering of reflection emission in the corona is routinely ignored, but is an essential consideration given that reflection is linked to the regimes with strongest Comptonization. Properly accounting for this causes the inferred reflection fraction to increase substantially, especially for the hard state. Another important impact of the Comptonization of reflection emission by the corona is the downscattered tail. Downscattering has the potential to mimic the relativistically-broadened red wing of the Fe line associated with a spinning black hole. (2) Recent evidence for a reflection component with a harder spectral index than the power-law continuum is naturally explained as Compton-scattered reflection emission. (3) Photon conservation provides an important constraint on the hard state's accretion rate. For bright hard states, we show that disk truncation to large scales (R much larger than the ISCO radius) is unlikely as this would require accretion rates far in excess of the brightest soft states. Our principal conclusion is that when modeling relativistically-broadened reflection, spectral models should allow for coronal Compton scattering of the reflection features, and when possible, take advantage of the additional constraining power from linking to the thermal disk component.