Thin-shell mixing in radiative wind-shocks and the Lx-Lbol scaling of O-star X-rays. (arXiv:1212.4235v1 [astro-ph.SR])

Thin-shell mixing in radiative wind-shocks and the Lx-Lbol scaling of O-star X-rays. (arXiv:1212.4235v1 [astro-ph.SR]):
X-ray satellites since Einstein have empirically established that the X-ray
luminosity from single O-stars scales linearly with bolometric luminosity, Lx ~
10^{-7} Lbol. But straightforward forms of the most favored 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 ~ Mdot ~ Lbol^{1.7} if
the shocks are radiative, or with Lx ~ Mdot^{2} ~ Lbol^{3.4} if they are
adiabatic. This paper presents a generalized formalism that bridges these
radiative vs. 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 ~ Mdot^{0.6} ~ Lbol that matches the empirical scaling. To
fit observed X-ray line profiles, we find 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 Mdot^2. Future numerical
simulation studies will be needed to test the general thin-shell mixing ansatz
for X-ray emission.