# Optical and X-ray luminosity of expanding nebulae around ultraluminous X-ray sources

## TL;DR

This study simulates expanding nebulae around ultraluminous X-ray sources, revealing how shock cooling and wind velocity influence optical, UV, and X-ray emissions, aiding in understanding accretion disk outflows.

## Contribution

It introduces realistic cooling in simulations of ULX nebulae, showing how shock radiative properties depend on wind velocity and providing a method to estimate outflow parameters.

## Key findings

- Forward shock becomes radiative at ~100 pc
- Optical/UV emission dominates, X-ray luminosity is low
- Wind velocity determines whether shocks are radiative or adiabatic

## Abstract

We have performed a set of simulations of expanding, spherically symmetric nebulae inflated by winds from accreting black holes in ultraluminous X-ray sources (ULXs). We implemented a realistic cooling function to account for free-free and bound-free cooling. For all model parameters we considered, the forward shock in the interstellar medium becomes radiative at a radius $\sim $ 100 pc. The emission is primarily in the optical and UV, and the radiative luminosity is about 50% of the total kinetic luminosity of the wind. In contrast, the reverse shock in the wind is adiabatic so long as the terminal outflow velocity of the wind $v_{\rm w} \sim 0.003c$. The shocked wind in these models radiates in X-rays, but with a luminosity of only $\sim 10^{35} \rm\,erg\,s^{-1}$. For wind velocities $v_{\rm w} \sim 0.001c$, the shocked wind becomes radiative, but it is no longer hot enough to produce X-rays. Instead it emits in optical and UV, and the radiative luminosity is comparable to 100% of the wind kinetic luminosity. We suggest that measuring the optical luminosities and putting limits on the X-ray and radio emission from shock-ionized ULX bubbles may help in estimating the mass outflow rate of the central accretion disk and the velocity of the outflow.