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Superluminal motion is caused by the jets traveling very near the speed of light at a small angle towards the observer. Because the high-velocity jets are emitting light at every point of their path, the light they emit does not approach the observer much more quickly than the jet itself. This causes the light emitted over hundreds of years of the jet's travel to not have hundreds of light-years of distance between its front end (the earliest light emitted) and its back end (the latest light emitted); the complete "light-train" thus arrives at the observer over a much smaller time period (ten or twenty years), giving the illusion of faster-than-light travel. Superluminal motion is often seen in two opposing jets, one moving away and one toward Earth. If Doppler shifts are observed in both sources, the velocity and the distance can be determined independently of other observations.
This explanation depends on the jet making a sufficiently narrow angle with the observer's line-of-sight to explain the degree of superluminal motion seen in a particular case. Superluminal motion of up to 6c has been observed in the inner parts of the jet of M87. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from our line-of-sight. However, evidence suggests that the jet is in fact at about 43° to our line-of-sight. The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded. Suggestions of turbulence or "wide cones" in the inner parts of the jets have been put forward to try to counter such problems, and there seems to be some evidence for this.
The model identifies a difference between the information carried by the wave at its signal velocity c, and the information about the wave front's apparent rate of change of position. If a light pulse is envisaged in a wave guide (glass tube) moving across an observer's field of view, the pulse can only move at c through the guide. If that pulse is also directed towards the observer, he will receive that wave information, at c. If the wave guide is moved in the same direction as the pulse, the information on its position, passed to the observer as lateral emissions from the pulse, changes. He may see the rate of change of position as apparently representing motion faster than c when calculated, like the edge of a shadow across a curved surface. This is a different signal, containing different information, to the pulse and does not break the second postulate of special relativity. c is strictly maintained in all local fields.
Derivation of the apparent velocity
A relativistic jet coming out of the center of an active galactic nucleus is moving along AB with a velocity v. We are observing the jet from the point O. At time a light ray leaves the jet from point A and another ray leaves at time from point B. Observer at O receives the rays at time and respectively. The angle is small enough that the two distances marked can be considered equal.
Apparent transverse velocity along ,
The apparent transverse velocity is maximal for angle ( is used)
If (i.e. when velocity of jet is close to the velocity of light) then despite the fact that . And of course means that the apparent transverse velocity along , the only velocity on the sky that we can measure, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal.
In 1966 Martin Rees pointed out that "an object moving relativistically in suitable directions may appear to a distant observer to have a transverse velocity much greater than the velocity of light". In 1969 and 1970 such sources were found as very distant astronomical radio sources, such as radio galaxies and quasars, and were called superluminal sources. The discovery was the result of a new technique called Very Long Baseline Interferometry, which allowed astronomers to set limits to the angular size of components and to determine positions to better than milli-arcseconds, and in particular to determine the change in positions on the sky, called proper motions, in a timespan of typically years. The apparent velocity is obtained by multiplying the observed proper motion by the distance, which could be up to 6 times the speed of light.
In the introduction to a workshop on superluminal radio sources, Pearson and Zensus reported
The first indications of changes in the structure of some sources were obtained by an American-Australian team in a series of transpacific VLBI observations between 1968 and 1970 (Gubbay et al. 1969). Following the early experiments, they had realised the potential of the NASA tracking antennas for VLBI measurements and set up an interferometer operating between California and Australia. The change in the source visibility that they measured for 3C 279, combined with changes in total flux density, indicated that a component first seen in 1969 had reached a diameter of about 1 milliarcsecond, implying expansion at an apparent velocity of at least twice the speed of light. Aware of Rees's model, (Moffet et al. 1972) concluded that their measurement presented evidence for relativistic expansion of this component. This interpretation, although by no means unique, was later confirmed, and in hindsight it seems fair to say that their experiment was the first interferometric measurement of superluminal expansion.
In 1994, a galactic speed record was obtained with the discovery of a superluminal source in our own galaxy, the cosmic x-ray sourceGRS 1915+105. The expansion occurred on a much shorter timescale. Several separate blobs were seen to expand in pairs within weeks by typically 0.5 arcsec. Because of the analogy with quasars, this source was called a microquasar.
^Biretta, John A.; Junor, William; Livio, Mario (1999). "Formation of the radio jet in M87 at 100 Schwarzschild radii from the central black hole". Nature. 401 (6756): 891. Bibcode:1999Natur.401..891J. doi:10.1038/44780. ; Biretta, J. A.; Sparks, W. B.; MacChetto, F. (1999). "Hubble Space TelescopeObservations of Superluminal Motion in the M87 Jet". The Astrophysical Journal. 520 (2): 621. Bibcode:1999ApJ...520..621B. doi:10.1086/307499.
^Biretta, J. A.; Sparks, W. B.; MacChetto, F. (1999). "Hubble Space Telescope Observations of Superluminal Motion in the M87 Jet". The Astrophysical Journal. 520 (2): 621. Bibcode:1999ApJ...520..621B. doi:10.1086/307499.
^Biretta, John A.; Junor, William; Livio, Mario (1999). "Formation of the radio jet in M87 at 100 Schwarzschild radii from the central black hole". Nature. 401 (6756): 891. Bibcode:1999Natur.401..891J. doi:10.1038/44780.
^Cohen, M. H.; Cannon, W.; Purcell, G. H.; Shaffer, D. B.; Broderick, J. J.; Kellermann, K. I.; Jauncey, D. L. (1971). "The Small-Scale Structure of Radio Galaxies and Quasi-Stellar Sources at 3.8 Centimeters". The Astrophysical Journal. 170: 207. Bibcode:1971ApJ...170..207C. doi:10.1086/151204.
^Whitney, AR; Shapiro, Irwin I.; Rogers, Alan E. E.; Robertson, Douglas S.; Knight, Curtis A.; Clark, Thomas A.; Goldstein, Richard M.; Marandino, Gerard E.; Vandenberg, Nancy R. (1971). "Quasars Revisited: Rapid Time Variations Observed Via Very-Long-Baseline Interferometry". Science. 173 (3993): 225-30. Bibcode:1971Sci...173..225W. doi:10.1126/science.173.3993.225. PMID17741416.
^Moffet, A.T.; Gubbay, J.; Robertson, D.S.; Legg, A.J. (1972). Evans, D.S (ed.). External Galaxies and Quasi-Stelar Objects : IAU Symposium 44, held in Uppsala, Sweden 10-14 August 1970. Dordrecht: Reidel. p. 228. ISBN9027701997.
^Pearson, Timothy J.; Zensus, J. Anton (1987). J. Anton Zensus; Timothy J Pearson (eds.). Superluminal Radio Sources : proceedings of a workshop in honor of Professor Marshall H. Cohen, held at Big Bear Solar Observatory, California, October 28-30, 1986. Superluminal Radio Sources. Cambridge New York: Cambridge University Press. p. 3. Bibcode:1987slrs.work....1P. ISBN9780521345606.