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 |$L_{\rm x} \sim \dot{M}\sim L_{\rm bol}^{1.7}$| if the shocks are radiative or with |$L_{\rm x} \sim \dot{M}^{2} \sim L_{\rm bol}^{3.4}$| 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 |$L_{\rm x} \sim \dot{M}^{0.6} \sim L_{\rm bol}$| that matches the empirical scaling. To fit observed X-ray line profiles, we find that such radiative-shock-mixing 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 |$\dot{M}^2$|⁠. Future numerical simulation studies will be needed to test the general thin-shell mixing ansatz for X-ray emission.