We reinvestigate the problem of the appearance of relativistic jets when geometrical opening is taken into account. We propose a new criterion to define apparent velocities and Doppler factors, which we think being determined by the brightest zone of
the jet. We numerically compute the apparent velocity and the Doppler factor of a non homokinetic jet using different velocity profiles. We argue that if the motion is relativistic, the high superluminal velocities beta_{app} ~ gamma, expected in the case of an homokinetic jet, are only possible for geometrical collimation smaller than the relativistic beaming angle 1/gamma. This is relatively independent of the jet velocity profile. For jet collimation angles larger than 1/gamma, the apparent image of the jet will always be dominated by parts of the jet traveling directly towards the observer at lorentz factors < gamma resulting in maximal apparent velocities smaller than gamma}. Furthermore, getting rid of the homokinetic hypothesis yields a complex relation between the observing angle and the Doppler factor, resulting in important consequences for the numerical computation of AGN population and unification scheme model.
Gamma-ray binaries could be compact pulsar wind nebulae formed when a young pulsar orbits a massive star. The pulsar wind is contained by the stellar wind of the O or Be companion, creating a relativistic comet-like structure accompanying the pulsar
along its orbit. The X-ray and the very high energy (>100 GeV, VHE) gamma-ray emissions from the binary LS 5039 are modulated on the orbital period of the system. Maximum and minimum flux occur at the conjunctions of the orbit, suggesting that the explanation is linked to the orbital geometry. The VHE modulation has been proposed to be due to the combined effect of Compton scattering and pair production on stellar photons, both of which depend on orbital phase. The X-ray modulation could be due to relativistic Doppler boosting in the comet tail where both the X-ray and VHE photons would be emitted. Relativistic aberrations change the seed stellar photon flux in the comoving frame so Doppler boosting affects synchrotron and inverse Compton emission differently. The dependence with orbital phase of relativistic Doppler-boosted (isotropic) synchrotron and (anisotropic) inverse Compton emission is calculated, assuming that the flow is oriented radially away from the star (LS 5039) or tangentially to the orbit (LS I +61 303, PSR B1259-63). Doppler boosting of the synchrotron emission in LS 5039 produces a lightcurve whose shape corresponds to the X-ray modulation. The observations imply an outflow velocity of 0.15-0.33c consistent with the expected flow speed at the pulsar wind termination shock. In LS I +61 303, the calculated Doppler boosted emission peaks in phase with the observed VHE and X-ray maximum. Doppler boosting might provide an explanation for the puzzling phasing of the VHE peak in this system.
High energy gamma-rays have been detected from Cygnus X-3, a system composed of a Wolf-Rayet star and a black hole or neutron star. The gamma-ray emission is linked to the radio emission from the jet launched in the system. The flux is modulated with
the 4.8 hr orbital period, as expected if high energy electrons are upscattering photons emitted by the Wolf-Rayet star to gamma-ray energies. This modulation is computed assuming that high energy electrons are located at some distance along a relativistic jet of arbitrary orientation. Modeling shows that the jet must be inclined and that the gamma ray emitting electrons cannot be located within the system. This is consistent with the idea that the electrons gain energy where the jet is recollimated by the stellar wind pressure and forms a shock. Jet precession should strongly affect the gamma-ray modulation shape at different epochs. The power in non-thermal electrons represents a small fraction of the Eddington luminosity only if the inclination is low i.e. if the compact object is a black hole.
