If the x-ray emission arises from thermal processes in a hot, optically-thin
plasma, the spectral fits to the data when the x-ray flux is high indicate
kinetic temperatures of 0.8 keV = 9 K.
Such high temperatures can arise from shocked gas.
The circumstellar environments of Be stars are generally thought to contain
dense equatorial regions extending to very large distance from the underlying
star. The expansion of the radio emitting plasmon will shock this
ambient material.
For a strong, adiabatic shock, the temperature of the post-shock
gas is given approximately by
where is the velocity of the shock relative to the pre-shock gas.
Estimates of the bulk expansion velocity of the radio emitting plasmon
from VLBI observations LSI+61 (Taylor et al. 1992; Massi et al. 1993) range from
200 to 600 km s
.
An expansion velocity of
400 km s
was derived by Paredes et al.
(1991) by modelling the evolution of a radio light curve.
At
km s
, the post-shock temperature is
K,
in good agreement with the x-ray spectrum, given the uncertainty on
the velocity.
Very hot, optically-thin plasma radiates via Bremsstrahlung emission and
via line emission from highly ionized heavy elements.
At temperatures below a few K, the broad-band flux is
dominated by the line component.
However, to obtain a rough estimate of the expected x-ray luminosity from
gas shocked by the expanding radio plasmon, we restrict our discussion
to the Bremsstrahlung component.
Assuming a homogenous source with radius,
, the
Bremsstralung luminosity over the ROSAT energy band,
is,
where is the Bremsstrahlung volume emissivity given by
Waters et al. (1988) fit a conical disk, mass outflow model to the far-infrared excess emission from LSI+61 . They derive an equatorial circumstellar mass density relationship of the form
where is the distance from the Be star.
Setting
equal to the semi-major axis of the binary orbit
(7.5
cm), and taking
(Waters et al.),
yields a number density
= 7
cm
at a distance characteristic of the binary separation.
Expanding at 400 km s, the radio plasmon will
grow by 3.5
cm per day. Thus during the very early
phase of the radio outbursts, the source dimension will be at least
a few
cm, and over the approximately 4 day rise time to radio peak
(Taylor and Gregory 1984), the source will grow to dimensions of a few
cm.
For
cm,
cm
and assuming a totally ionized
hydrogen plasma with
, we obtain a luminosity,
erg s
, which agrees in order of magnitude
with the unabsorbed luminosity of LSI+61 at peak x-ray flux. Since the
luminosity depends on
, the x-ray luminosity will be highest during
the early stages of the radio outburst when the source is compact and
the ambient density is high. The x-ray flux will decline as the plasmon
reaches the larger radii at peak radio flux density.
While more detailed modelling should be carried out, these calculations show that shocked circumstellar gas from the expanding radio plasmon can roughly account for the spectral properties and luminosity of the x-ray emission, and for the timing of the x-ray peak relative to the radio outburst.