Inverse-Compton Emission

In the case of a radio emitting system, an alternate method to produce x-ray emission is inverse-Compton scattering. If the relativistic electrons responsible for the radio emission are produced in proximity to the primary, the photons in the radiation field of the primary may be inverse-Compton scattered to x-ray and -ray energies.

For inverse-Compton production, the x-ray and radio emission are both linked to the creation of relativistic particles and one might expect that the x-ray outburst would be very nearly coincident with the radio outburst. The fact that our observations show radio and x-ray outburst peaks at nearly opposite phase contradicts this simple prediction. However, a strict coincidence of radio and x-ray emission is relaxed if the radio and x-ray flux originate from different volumes. To produce detectable, optically-thin radio emission, relativistic particles must either be produced in, or escape to, a region at large radii from the underlying Be star; where they can fill a sufficient volume to be detectable and survive against the high inverse-Compton losses that occur at smaller radii. On the other hand, inverse-Compton x-rays are most efficiently produced close to the star, where the stellar radiation energy density is high.

Paredes et al. (1990) have noted that the phase of peak radio outburst varies from cycle to cycle, lying within the boundaries 0.4 to 0.9. In figure 4 we show the distribution of phases of peak radio flux density along with a schematic of our x-ray light curve. For clarity the data have been plotted for two cycles. The open squares indicate the phase and flux density of radio peak for a complete sample of observed outbursts since the first radio detection of LSI+61 in 1977. The phase of peak flux density appears almost uniformly distributed between phase 0.4 and 1.0. Within this range there is a broad distribution of peak flux densities up to the maximum value of 300 mJy. The radio periodicity of LSI+61 is defined more by the intervals of no radio activity than by the active phase. It is striking that the duration of the high state of the x-ray light curve matches the range of phases during which the system is, on average, radio active. Taylor & Gregory (1984) noted that the radio emission from LSI+61 is optically-thin during most of the rise of the outburst (as observed during the second outburst in figure 1) and consequently there must be continued particle production during at least the rising portion of the outburst. The detection, on several occasions, of weaker bursts of emission past the main outburst (Taylor et al.1992), indicates further that relativistic particle production continues well past the time of peak flux density. The data therefore indicate a continuous period of particle production during the active radio interval (phase 0.4 - 1.0). If at least some of this particle production occurs close to the primary star, a continuous high state of inverse-Compton scattered photons would be produced during this phase range. The relative strength and timing of the associated radio activity from cycle to cycle might then depend on additional factors affecting the transport of electrons to large radii.

Can we account for the observed luminosity of x-rays in this fashion? We are developing a model that attempts to simultaneously fit the radio light curves and predict the time evolution of emission in high energy photons. The detailed explanation of the model and the fits to the light curves will appear in a future paper (Peracaula et al, 1995). We present here initial calculations we have done to determine whether sufficient high energy photon luminosity can be produced by inverse-Compton scattering. The model consider a cloud of relativistic particles with spherical symmetry, expanding adiabatically at uniform velocity and embedded in a magnetic field. The particles are injected at a constant rate for a finite period of time and with a power-law, injected energy distribution . The relativistic particles lose energy due to adiabatic expansion, synchrotron radiation and inverse-Compton scattering. For a single electron the inverse-Compton losses are given by the expression:

where is the radiation field energy density, given by

Here is the luminosity of the primary and is the distance of the electron from the primary. To calculate the inverse-Compton losses for a population of electrons we require the distribution function , which gives the number of particles at distance from the primary that have an energy at time . This function is given by the solution to the continuity equation,

The details of the solution of this equation will be presented by Peracaula et al. (1995). The total energy loss rate due to inverse-Compton scattering as a function of time is given by integrating the quantity over the volume of the expanding sphere and over the range of particle energies.

The constraints on this calculation are the observed properties of LSI+61 . The primary has 26,000 K and luminosity about erg/s (Hutchings & Crampton, 1981). From analysis of the multi-wavelengths radio observations (Taylor & Gregory 1984, Paredes et al. 1991) estimate the power-law index of the energy distribution for the injected particles , an initial size of cm, the magnetic field strength at that time and a total energy in radio-emitting, relativistic particles of a few 10 erg. The inverse-Compton luminosity also depends on the upper energy limit, , of the injected particle distribution function. To produce scattered photons with energies above 100 MeV, must be at least several ergs (see below). Taking ergs, and placing the site of particle injection at a distance equal to the semi-major axis yields a peak inverse-Compton luminosity of erg s. This luminosity is sufficient to explain the flux of high energy photons from LSI+61 above 1 MeV, however it greatly exceeds the x-ray luminosity.

The low ratio of inverse-Compton x-ray to -ray luminosity can be understood as an effect of the expansion of the plasmon of relativistic particles. A relativistic electron created at a distance from the primary, will have a lifetime to inverse-Compton scattering of

For an electron to avoid giving up its energy to inverse-Compton scattering, it must travel outward from the primary with velocity, (Taylor & Gregory 1982). This condition defines a break energy, , given by:

Electrons with energy greater than have residence times near the primary longer than the inverse-Compton lifetime, and hence suffer significant losses. Electron with energy less then escape to large radii on a time scale shorter than the inverse-Compton lifetime.

This break energy will produce a corresponding low-energy turndown in the spectrum of inverse-Compton photons. For relativistic particles, the final energy, of an inverse-Compton scattered photon is related to its initial energy, , as . At a stellar temperature of 26,000 K, the peak in the stellar photon distribution occurs at about 10 eV. The x-ray photons at energies near 1 keV therefore arises primarily from scattering off electrons with , or energies of erg. Similarly, 1 MeV photons are produced by electrons with energies erg. For the observed values of and , and cm, equation (5) yields a break energy of erg - predicting a spectral turn-down between the MeV and keV range, as observed.