# Constraining the mass of accreting black holes in ultraluminous X-ray sources with ultrafast outflows

## TL;DR

This paper uses observed ultrafast outflows in ULXs to constrain black hole masses and accretion rates, supporting the idea that ULXs are stellar-mass black holes accreting above the Eddington limit with specific efficiencies.

## Contribution

It provides a self-consistent method to estimate black hole masses and accretion rates in ULXs based on ultrafast outflow properties, supporting super-Eddington accretion models.

## Key findings

- Black hole masses are constrained to less than 100 solar masses.
- Accretion rates are about ten times the Eddington limit.
- Radiative efficiency is approximately 0.01, explaining luminosity observations.

## Abstract

The nature of ultraluminous X-ray sources (ULXs) -- off-nuclear extra-galactic sources with luminosity, assumed isotropic, $\gtrsim 10^{39}$ erg s$^{-1}$ -- is still debated. One possibility is that ULXs are stellar black holes accreting beyond the Eddington limit. This view has been recently reinforced by the discovery of ultrafast outflows at $\sim 0.1$-$0.2c$ in the high resolution spectra of a handful of ULXs, as predicted by models of supercritical accretion discs. Under the assumption that ULXs are powered by super-Eddington accretion onto black holes, we use the properties of the observed outflows to self-consistently constrain their masses and accretion rates. We find masses $\lesssim 100$ M$_{\odot}$ and typical accretion rates $\sim 10^{-5}$ M$_{\odot}$ yr$^{-1}$, i.e. $\approx 10$ times larger than the Eddington limit calculated with a radiative efficiency of 0.1. However, the emitted luminosity is only $\approx 10\%$ beyond the Eddington luminosity, because most of the energy released in the inner part of the accretion disc is used to accelerate the wind, which implies radiative efficiency $\sim 0.01$. Our results are consistent with a formation model where ULXs are black hole remnants of massive stars evolved in low-metallicity environments.