Shocked Gas

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.