A Rotating Hollow Cone Anisotropy of Tev Emission from Binary Systems

We show that TeV γ-ray emission produced via interactions of high-energy particles with anisotropic radiation field of a massive star in binary systems should have a characteristic rotating hollow cone anisotropy pattern. The hollow cone, whose axis is directed away from the massive star, rotates with the period equal to the orbital period of the system. We note that the two maxima pattern of the TeV energy band lightcurve of the γ-ray loud binary LS 5039 can be interpreted in terms of this rotating hollow cone model. Adopting such an interpretation, we are able to constrain the geometry of the system – either the inclination angle of the binary orbit, or the elevation of the γ-ray emission region above the orbital plane. Subject headings: gamma rays: theory — radiation mechanisms: non-thermal — binaries: general Introduction. γ-ray-loud binary systems are a newly identified class of sources in which either accretion onto the compact object (a neutron star, or a black hole), or interaction of an outflow from the compact object with the wind and radiation from a massive companion star leads to the production of very-high energy (VHE) γ-ray emission. Three such systems, PSR B1259-63, LS 5039 and LSI +61 303, have been firmly detected as persistent or regularly variable TeV γ-ray emitters (Aharonian et al. 2005, 2006; Albert et al. 2006). The VHE γ-ray emission from the γ-ray-loud binaries is variable on the orbital period (or shorter) time scale. This implies that the emission region is located close to the binary system, in a highly inhomogeneous and anisotropic particle and photon background produced by massive companion star. In what follows we show that if the γ-ray emission from such a region is produced in interactions of isotropically distributed VHE particles with photons from the massive star, it should have a characteristic “rotating hollow cone” anisotropy, i.e. most of the photons are emitted at a certain angle ζ0 with respect to a symmetry axis directed radially away from the massive star. Orbital motion of the emission region around the massive star leads to the rotation of the emission cone. Rotation of the hollow cone on the orbital time scale leads to the appearance of 0, 1, or 2 maxima in the orbit-folded lightcurve in the VHE band, occurring at the phases when the line of sight is inclined at an angle ζ0 with respect to the cone axis, i.e. at the moments of passage of the of the cone through the line of sight (similarly to the hollow cone models of period-folded lightcurves of pulsars, see e.g. (Lyne & Graham-Smith 2005)). The orbital modulation of the γ-ray flux, related to the passage of the hollow cone through the line of sight could be most clearly detected if there are no additional sources of the modulation, related e.g. to the ellipticity Electronic address: [email protected] Electronic address: [email protected] of the binary orbit, absence of spherical symmetry of the wind/radiation from the companion star etc. Among the three γ-ray-loud binary systems mentioned above, the system LS 5039 is characterized by the lowest ellipticity of the orbit. In this system the compact object orbits a O6.5V star which emits isotropic stellar wind (contrary to the other two systems in which the massive star is of the Be type). Below we investigate this system in more details. We calculate the angular brightness profile of the hollow cone in LS 5039, and find that the observation of the two maxima of the orbit-folded lightcurve constrains the inclination of the binary orbit to be i > 40◦, if the emission is produced in the vicinity of the compact object. This result can be stated also in an opposite way: if the inclination of the binary orbit is i < 40◦, the two maxima structure of the orbit-folded lightcurve can be explained only if the VHE γ-ray emission region is displaced from the position of the compact object. This can be the case if the emission is produced in a jet. In this latter case, we show that the existence of the twomaxima of the lightcurve constrains the elevation of the emission point above the orbital plane. Anisotropy of VHE γ-ray emission in a central photon field. Consider the γ-ray emission produced by interactions of VHE particles X (e.g. protons or electrons) with the soft photon field in the vicinity of a massive star. Assume for simplicity that the size of the emission region is much less than the distance from the region to the center of the star and that the VHE particles in the region have isotropic velocity distribution. In spite of the isotropy of the VHE particle distribution, the γ-ray emission will be anisotropic. The anisotropy arises because of the Doppler effect which leads to the decrease (increase) of the rate of interaction of the VHE particles co-moving with (moving oppositely to) the soft photon field of the massive star. The interaction rate of particles X with momenta PX with soft photons with momenta p∗ is given by 2 Neronov & Chernyakova (Landau & Lifshitz 1980)