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

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 ∼ 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 vw & 0.003c. The shocked wind in these models radiates in X-rays, but with a luminosity of only ∼ 1035 erg s−1 . For wind velocities vw . 0.001c, the shocked wind becomes radiative, but it is no longer hot enough to produce Xrays. 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