Thin-shell mixing in radiative wind-shocks and the Lx ~ Lbol scaling of O-star X-rays

Abstract

X-ray satellites since Einstein have empirically established that the X-ray luminosity from single O-stars scales linearly with bolometric luminosity, Lx ~ 10-7Lbol. But straightforward forms of the most favoured model, in which X-rays arise from instability-generated shocks embedded in the stellar wind, predict a steeper scaling, either with mass-loss rate Lx~M ~ Lbol1.7 if the shocks are radiative or with Lx~M2 ~ Lbol3.4 if they are adiabatic. This paper presents a generalized formalism that bridges these radiative versus adiabatic limits in terms of the ratio of the shock cooling length to the local radius. Noting that the thin-shell instability of radiative shocks should lead to extensive mixing of hot and cool material, we propose that the associated softening and weakening of the X-ray emission can be parametrized as scaling with the cooling length ratio raised to a power m, the 'mixing exponent'. For physically reasonable values m ≈ 0.4, this leads to an X-ray luminosity Lx~M0.6~Lbol that matches the empirical scaling. To fit observed X-ray line profiles, we find that such radiative-shockmixing models require the number of shocks to drop sharply above the initial shock onset radius. This in turn implies that the X-ray luminosity should saturate and even decrease for optically thick winds with very high mass-loss rates. In the opposite limit of adiabatic shocks in low-density winds (e.g. from B-stars), the X-ray luminosity should drop steeply with M2. Future numerical simulation studies will be needed to test the general thin-shell mixing ansatz for X-ray emission. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.