2013MNRAS.429.3379O

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_x ∼{dot}M∼L_bol^1.7 if the shocks are radiative or with L_x ∼{dot}M^2 ∼L_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_x ∼{dot}M^0.6 ∼L_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.