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

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 $v_{\mathrm{w}}\sim 0.003c$. The shocked wind in these models radiates in X-rays, but with a luminosity of only $\sim 10^{35}\mathrm{erg}{\mathrm{s}}^{-1}$. For wind velocities $v_{\mathrm{w}}\sim 0.001c$, 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.

arXiv comment11 pages, 7 figures

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