4.2 Superluminal Motion in Radio Jets

The term ``superluminal motion'' describes proper motion of source structure (traditionally mapped at radio wavelengths) that, when converted to an apparent speed v<sub>a</sub>, gives v<sub>a</sub> > c. This phenomenon occurs for emitting regions moving at very high (but still subluminal) speeds at small angles to the line of sight (Rees 1966). Relativistically moving sources ``run after'' the photons they emit, strongly reducing the time interval separating any two events in the observer's frame and giving the impression of faster than light motion (Appendix A).

Typical proper motions observed with Very Long Baseline Interferometry (VLBI) are in the range 0.1 to 1 milliarcsecond yr^-1 and imply apparent velocities up to ~ 30 c/(H₀/50) (Vermeulen and Cohen 1994). The majority of superluminal sources are FSRQ and BL Lacs, although this is in part a selection effect since these objects have the brightest cores and so are more easily observed with VLBI. Blazars do tend to have the largest apparent velocities (Ghisellini et al. 1993; Vermeulen and Cohen 1994), in agreement with the idea that their jets are more aligned with the line of sight than other classes of radio-loud AGN.

Detection of superluminal motion does not necessarily imply that the source of radiation is moving at near-relativistic speeds. For example, the tip of a rotating beam of light moves faster than light at a distance r > c/, where is the angular speed. If the beam ionizes material that re-emits the radiation, the observer will detect superluminal motion even though the ionized material is not moving at all. (Of course, a simple rotating-beam model would predict some cases of superluminal contractions, i.e., negative values of v_a, contrary to observation; Vermeulen and Cohen 1994). Apparent superluminal motion requires only a relativistic phase or pattern speed, which could be different from the bulk velocity of the radiating plasma itself.

Whether the pattern speed inferred from superluminal motion differs from the bulk motion of the plasma, as predicted by jet models that include relativistic shocks (Lind and Blandford 1985), is a matter of current debate (Ghisellini et al. 1993; Vermeulen and Cohen 1994; Kollgaard 1994). There is an observed correlation between the apparent superluminal velocity and the Doppler beaming factor (Ghisellini et al. 1993), thus connecting superluminal motion directly to bulk relativistic motion (Sec. 6.3). A particularly nice local laboratory has been found by Mirabel and Rodriguez (1994), who discovered a Galactic superluminal source for which both jet and counter-jet are seen and the two expansion velocities and luminosities are measured. In this case the pattern and bulk velocity are probably quite similar, with _bulk / _pattern ~ 0.8 (Appendix B; Bodo and Ghisellini 1995). A second galactic superluminal source has since been discovered, with similar bulk velocity and lying roughly in the plane of the sky, but with significant intrinsic jet asymmetries (Tingay et al. 1995; Hjellming and Rupen 1995).