# Spectra of Black Hole Accretion Models of Ultra-Luminous X-ray Sources

## TL;DR

This paper uses relativistic radiation MHD simulations to model super-Eddington accretion onto black holes, reproducing ULX spectra and luminosities, and analyzing the effects of magnetic fields, spin, and viewing angle on observed properties.

## Contribution

It introduces comprehensive simulations of super-Eddington accretion that account for magnetic field configurations and black hole spin, providing new insights into ULX spectral types and radiative efficiencies.

## Key findings

- Models produce apparent luminosities >10^40 erg/s for pole-on views.
- Angle-integrated luminosities rarely exceed 2.5×10^39 erg/s, indicating radiative inefficiency.
- Spectral types match observed ULX spectra, including disk-like and hard states.

## Abstract

We present general relativistic radiation MHD simulations of super-Eddington accretion on a $10M_\odot$ black hole. We consider a range of mass accretion rates, black hole spins, and magnetic field configurations. We compute the spectra and images of the models as a function of viewing angle, and compare them with the observed properties of ultraluminous X-ray sources (ULXs). The models easily produce apparent luminosities in excess of $10^{40}~{\rm erg\,s^{-1}}$ for pole-on observers. However, the angle-integrated radiative luminosities rarely exceed $2.5\times10^{39}~{\rm erg\,s^{-1}}$ even for mass accretion rates of tens of Eddington. The systems are thus radiatively inefficient, though they are energetically efficient when the energy output in winds and jets is also counted. The simulated models reproduce the main empirical types of spectra --- disk-like, supersoft, soft, hard --- observed in ULXs. The magnetic field configuration, whether MAD ("magnetically arrested disk") or SANE ("standard and normal evolution"), has a strong effect on the results. In SANE models, the X-ray spectral hardness is almost independent of accretion rate, but decreases steeply with increasing inclination. MAD models with non-spinning black holes produce significantly softer spectra at higher values of $\dot{M}$, even at low inclinations. MAD models with rapidly spinning black holes are quite different from all other models. They are radiatively efficient (efficiency factor $\sim10-20\%$), super-efficient when the mechanical energy output is also included ($70\%$), and produce hard blazar-like spectra. In all models, the emission shows strong geometrical beaming, which disagrees with the more isotropic illumination favored by observations of ULX bubbles.