It is generally accepted that the emission mechanism responsible for the radio to optical emission of blazars is the synchrotron process. In objects similar to Mkn 501, which is discussed in Sect. 3, the synchrotron emission extends up to X-ray energies. It has recently emerged that a model in which the radiating relativistic electrons reside in a region of uniform magnetic field can provide a reasonable fit to observations not only of the synchrotron component, but also, via the inverse compton scattering of the synchrotron photons, to gamma-ray observations in the GeV to TeV range. In this paper, we have introduced a detailed model of the emission region including the processes of acceleration and synchrotron cooling. This should ultimately help us to assess how accurately a homogeneous region can reproduce the observed synchrotron emission. In combination with a computation of the inverse compton emission, the physical conditions and the geometry of the emission zone can be constrained.
The model used to describe acceleration is similar to that used by Ball & Kirk (1992) to describe the nonthermal radio emission of SN1987A. It involves a phenomenological division of the particle population into two groups: particles which are undergoing both acceleration and cooling and particles which merely cool. As a result, distributions are found which extend to a maximum value of the Lorentz factor, and then cut-off abruptly. The synchrotron emission from such a distribution fits well with that from the source we have discussed in Sect. 3 - Mkn 501. However, the form of the spectrum, especially in the hard X-ray region, depends on the shape of the cut-off of the electron spectrum. In our model, the sharpest possible turn-over is produced. Inhomogeneities within the source or refinements of the acceleration model result in a broader turn-over. This indicates that in the case of Mkn 501 a homogeneous model of the region in which synchrotron X-rays are emitted is a good approximation. It also confirms that a detailed model of the cut-off - which would necessarily involve additional parameters - is unnecessary. In other blazars e.g., Mkn 421 as well as in other synchrotron emitting objects e.g., SNR1006 (Mastichiadis & de Jager 1996), a broader cut-off is indicated by the observations. Our current computations suggest that if the physical situation is similar to that in Mkn 501, the broadening of the cut-off should be attributed to inhomogeneities within the source rather than an intrinsic property of the acceleration mechanism.
The variability predicted for a homogeneous source depends on the frequency of observation and the parameters of the acceleration mechanism - for relatively low frequency radiation, a characteristic pattern is produced, as pointed out by several groups. We have shown that closer to the maximum emitted frequency, this pattern should change. However, the observed variability depends not only on the intrinsic time-dependence, but also on the smoothing caused by light travel time delays across the source. We have described in detail the situation when the observer is positioned exactly on the axis of the source so that the emitting plasma moves directly towards the observer. This assumption is not as restrictive as it might at first sight appear, since the emission from a source in relativistic motion with Lorentz factor is significantly boosted when viewed from a direction which makes an angle of less than with the velocity. Intrinsic time variations within the source then appear shorter by a factor (see Sect. 2). These are also smoothed out on the timescale , where R is a typical dimension of the source perpendicular to the line of sight, provided that the angle between the source velocity and line of sight is of the order of . It is a good approximation to neglect this smoothing if the intrinsic synchrotron cooling time, measured in the rest frame of the emitting plasma, is longer than the light travel time . The same restriction applies to the size of the source along the direction to the observer. Here, however, the intrinsic variations always dominate if . The general formulae given in Sect. 2 are valid also for relativistic , but in the examples predicted, we have restricted ourselves to . Whether or not intrinsic variability dominates over light travel time effects depends on the frequency of observation. For Mkn 501, for example, we have found that the maximum timescale over which particles cool is determined by the position of the spectral break and is roughly 700 times the synchrotron cooling time at the maximum emitted frequency. Thus, depending on R, there may exist a critical frequency above which variations are smoothed out by light travel time effects, but below which the results of Sect. 3 are valid. A detailed model of the inverse Compton emission is needed to estimate this frequency.
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998