Annu. Rev. Astron. Astrophys. 1981. 19: 373-410
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6.3 Interpretation of Superluminal Motion

Attempts to understand the superluminal motion have produced a flurry of imaginative phenomenological interpretations including

(a) real tachyonic motion;

(b) grossly incorrect Hubble constant or non-cosmological red shifts (Kellermann & Shaffer 1977, Burbidge 1978) or incorrect cosmological model (Segal 1979);

(c) light echoes (Lynden-Bell 1977, Lynden-Bell & Liller 1978);

(d) gravitational lenses and screens (Barnothy & Barnothy 1971, Chitre & Narlikar 1980);

(e) systematic variations in synchrotron opacity (Epstein & Geller (1977);

(f) synchrotron or curvature radiation from electrons gyrating in a fixed dipole field (Milgrom & Bahcall 1978, Sanders & Da Costa 1978, Bachall & Milgrom 1980);

(g) various kinematic illusions caused by the finite signal propagation time (Rees 1966, 1967, Cavaliere et al. 1971).

It is beyond the scope of this paper to discuss all of these models in any detail. In general, they each explain some but not all of the observed characteristics of motion and, with the exception of the last category, are not supported by the other observational data discussed in previous sections. For a complete discussion of the various models see Rees (1971, 1978), Blandford, McKee & Rees (1977), Blandford & Rees (1978), Blandford & Konigl (1979), and Marscher & Scott (1980).

In this review we concentrate on interpretations based on bulk relativistic motions. The first suggestion that this effect might be important in compact radio sources was made by Rees (1966, 1967) well before the observational discovery of superluminal motion. Rees postulated relativistically expanding sources to explain the observed rapid flux density variations (Rees & Simon 1968), but more detailed studies have since shown that short flux density outbursts cannot be satisfactorily explained in this way (Terrell 1977, Jones & Tobin 1977, Vitello & Pacini 1978). However, relativistic linear motion, which is oriented nearly along the line of sight, does lead to a satisfactory explanation of the rapid flux density outbursts, as well as the observed superluminal component motion.

Due to the finite propagation time of the signal radiated, the time scale for events seen by an external observer at rest with respect to an approaching source is shortened by a factor ~ gamma-1. (3) Thus the apparent angular size deduced from light-travel-time arguments is too small by a factor of gamma, and the corresponding brightness temperature too great by a factor of gamma2. Values of gamma ~ 10 (beta ~ 0.995) are generally adequate to reduce the apparently excessive brightness temperatures discussed in Section 4.2, although for some of the low frequency variables, uncomfortably high values gamma ~ 100 (beta ~ 0.9999) may be needed.

The apparent transverse velocity vperp of an object moving with a true velocity v is given by (Ginzburg & Syrovatskii 1969):

Equation 6 (6)

where theta is the angle between the motion and the line of sight. Figure 7a shows the observed velocity plotted as a function of theta for various values of beta. For values of theta ~ 90° the effect of finite signal propagation time is unimportant and vperp ~ v, but for values of theta ~ 1/gamma, vperp can be very large. The maximum value of vperp for a given value of beta occurs when sin theta = 1/gamma and is vm = gammav = beta gammac. We note also that, at any given angle theta, there is maximum velocity,

Equation 7 (7)

which is observed no matter how great the true space velocity. For small values of theta

Equation 8 (8)

Figure 7a
Figure 7b
Figure 7c

Figure 7. (a) Apparent transverse velocity as a function of theta for different values of beta. (b) Probability of finding one component of a double ejection aligned to within an angle, theta, of the line of sight. (c) Power radiated as a function of theta and beta relative to an isotropic source.

These results are only slightly changed if we consider two objects moving in opposite direction from a common origin. Then the velocity of separation vsperp is given by

Equation 9 (9)

which has a maximum velocity at an angle sin theta = 1/gamma beta which is vm = betac. For values of beta ~ 1, vm is nearly the same as for a single moving object. This is because the receding component "barely moves" with an apparent velocity ~ c/2.

The two cases, of oppositely directed ejection of two components, and ejection of a single component seen together with a stationary core, could be distinguished by measuring the "absolute" component positions by comparison with nearby (stationary) reference sources. Differential position measurements of the required accuracy are possible with VLB techniques (Shapiro et al. 1979). Also, high resolution maps made with sufficient dynamic range can determine the number of components and their relative motion.

The probability, P(theta), that one component of an oppositely directed pair of ejected sources will be aligned to within an angle, theta, of the line of sight is (1 - cos theta) (Figure 7b). For sin theta = 1/gamma and for small values of theta, (i.e. gamma >> 1), P(theta) ~ 1/2gamma2.

An important consequence of the bulk relativistic motion is that the radiation is no longer isotropic but is beamed along the direction motion within an angle of halfwidth ~ 1/gamma. The apparent flux density of a moving component, Sa(theta), in terms of the flux density, S0, of the same component at rest, is given by (Ryle & Longair 1967)

Equation 10 (10)

when viewed at angle theta, from the direction of motion. The function Sa(theta) is shown in Figure 7c for several values of beta. When sin theta = 1/gamma (i.e. vperp = vm), then (for alpha = 0)

Equation 11 (11)

For an approaching component viewed "head-on," and gamma >> 1, the apparent flux density, Sa(0)

Equation 12 (12)

while the receding component (cos theta ~ -1) is essentially invisible with an apparent flux density, Sa(180), given by

Equation 13 (13)

A detailed description of the appearance, time variations, and spectral behavior of two sources separating with relativistic velocity is given in the classical paper by Ozernoi & Sazonov (1969), which preceded the observational discovery of superluminal motion. With great perception Ozernoi & Sazonov were able to infer the double relativistic ejection from consideration of the radio source spectra and total flux variations alone.

The interpretation of the observed superluminal motion in terms of bulk relativistic motion is very attractive in that it avoids the need to resort to non-cosmological red shifts or to abandon the synchrotron radiation mechanism: at the same time it provides a natural interpretation for the rapid flux density variations, the absence of inverse Compton scattered X rays, and interstellar scintillations, as well as the general asymmetric appearance of the superluminal sources. The models also fit naturally into the general picture of extragalactic radio sources in which energy is thought to be supplied to the extended lobes by means of well-collimated beams or jets (Blandford & Rees 1974, Scheuer 1974, DeYoung 1976, Miley 1980, Fomalont 1981).

Nevertheless, the large bulk velocities of gtapprox 0.99 c do introduce a number of problems (Jones & Burbidge 1973). These are:

(a) While the apparently excessive energy requirement in the form of relativistic particles is greatly reduced, the reduction is at the expense of energy that is tied up in component motion and in the magnetic field.

(b) The superluminal radio sources are smaller than the probable dimensions of the excited clouds of gas that give rise to the narrow optical emission lines. It is normally assumed that the radio source lies at least within the emission line region, so that, depending on the energy in the relativistic component, Jones & Burbidge (1973) argue that either it should be slowed down to a velocity v << c or interaction with the gas should significantly perturb the emission line spectrum. However, because the filling factor in the emission line region is small, it might be possible for a sufficiently well-collimated relativistic beam to escape relatively unimpeded.

(c) To produce the observed superluminal motion, the motion must be closely aligned with a narrow cone along the line of sight which has an a priori probability of ltapprox 1 percent (1/2gamma); yet about half of all compact sources show evidence for superluminal motion, either from the VLBI observations or, less directly, but for a much larger sample, from the flux density variations.

(d) According to Equation (10) the flux density of the approaching component should be very much greater than that of a receding or stationary component by factors of ~ 106 and 103 respectively (for gamma ~ 5). This may be difficult to reconcile with the observations, which typically show roughly comparable component flux densities, although, as pointed out above, this may, at least in part, be an artifact of the limited dynamic range. Moreover, relativistic time dilation combined with a finite component lifetime could cause the exponent in Equation (10) to be (2 - alpha) rather than (3 - alpha), and so reduce the apparent discrepancy by an order of magnitude (Scheuer & Readhead 1979).

Problems (a), (b), and (d) may be avoided if there is no actual material moving with high velocity, but only an electromagnetic wave that "ignites" stationary matter in the manner first discussed by Rees (1971) and Lynden-Bell (1977), but problem (c) still remains in this case.

If, however, there is actual material moving, then the large fraction of sources that show evidence for superluminal motion and the apparent equality in the flux density of components might be explained as a selection effect. Only those components that are moving towards the observer and have enhanced emission due to the Doppler beaming are observed. Two variations of this model may be considered: many components may be ejected more or less isotropically, and owing to the relatively poor dynamic range of the VLBI maps, only the approaching components are strong enough to observe; or there may be a preferred axis for each source, and only those sources with axes pointed towards the observer are sufficiently strong to be observed.

The constant position angles which have been observed for the multiple outbursts in 3C 120 and 3C 279 and the presence of well-defined position angles which are found in many sources over a wide range of dimensions make it difficult to accept the isotropic models. In the models involving a preferred axis, symmetrically ejected components, or pairs formed by the stationary nucleus and one ejected component, are expected to suffer the effects of differential Doppler beaming. Scheuer & Readhead (1979) suggest that the appearance of an expanding double may be due to a bright knot in the approaching jet, seen together with radio emission from matter moving out from a stationary nucleus, but the absence of the large expected flux inequality is still contrived. It is also possible that the expanding double is formed by two components ejected along the same track at somewhat different velocities. The radiation from the slower component is less sharply beamed, and Cohen et al. (1979) have shown that when viewing at the appropriate angle an observer may see an appreciable differential velocity from components with comparable flux densities.

Scheuer & Readhead (1979) have made the interesting suggestion that the relativistic beaming models may account for those quasars that are radio quiet, as they would then represent the large fraction of objects with emission which is not beamed towards the observer within a small angle theta ~ 1/gamma. In this model, the radio emission from the quasars is intrinsically weak, and the quasars have luminosities comparable to the nuclei of nearby elliptical galaxies, but they appear brightened by a factor ~ 103 (for gamma ~ 7) as a result of Doppler beaming. Scheuer & Readhead also point out that the fraction of quasars they expected to be observed as strong radio sources is ~ 1/gamma2, and furthermore that the number of quasars detected as radio sources is expected to increase only very slowly with decreasing flux density. Both of these predictions are qualitatively consistent with the observations of radio quiet quasars (Sramek & Weedman 1978, Smith & Wright 1980, Strittmatter et al. 1980), but there remain problems with reconciling all of the observational material with the model, at least in its simplest form.

(a) More recent observations of bright optically selected quasars show a much larger fraction of detections than previously found (Condon et al. 1980, D.B. Shaffer et al., unpublished, Smith & Wright 1980). Relativistic beaming cannot be important in the ~ 30 percent of the optically bright that appear to be strong radio sources, because, with the required broad beam, the relativistic enhancement is only about a factor of 2.

(b) Some sources, such as 4C 39.25, show no evidence for relativistic motion, yet have apparent luminosities comparable with the superluminal sources. Thus, unless this is interpreted as a fortuitous case of two components moving with the same velocity, or that theta << 1/gamma, the radiation must be isotropic and the intrinsic luminosity large.

(c) High resolution observations of extended symmetric double radio sources show that a large fraction contain bright compact components that are coincident with the associated optical object (Schilizzi 1976, Preuss et al. 1977, Owen et al. 1978, Potash & Wardle 1979, Gopal-Krishna et al. 1980). The extended doubles are expected to be randomly oriented in space. Since, in those cases where data exist, the compact components are aligned with the extended ones, they too must be randomly oriented, and their apparent flux densities cannot be significantly enhanced by Doppler beaming (Kellermann 1978, Readhead et al. 1978a, Schilizzi et al. 1979, Kellermann et al. 1981, Linfield 1981, Preuss et al. 1980).

(d) As discussed in the next section, optically selected quasars and compact radio sources appear to have a very different spatial distribution, so the Scheuer-Readhead interpretation would apparently require that the probability of a favorable alignment, or the distribution of y's, be a function of red shift.

(e) It is not clear how sources such as CTD 93, which are well-separated doubles with nearly equal component fluxes and no evidence of a jet, fit into this picture.

(f) 3C 273 is the brightest quasar in the sky at optical, X-ray, and gamma-ray wavelengths and shows superluminal motion (Pearson et al. 1981). The a priori probability of finding an apparent value gamma ~ 10 is about one percent. Since 3C 273 is unique on the basis of its bright optical or X-ray emission alone, it is not possible to appeal to relativistic beaming of the radio emission to explain this apparently fortuitous coincidence. Doppler beaming of the nonthermal continuum does not help, as the emission-line strength alone makes 3C 273 a unique object, and there is no evidence that the emission-line region is moving relativistically.

Some of these problems, which were recognized by Scheuer & Readhead, can be understood by appealing to more sophisticated models, for example, with the value of gamma correlated with the presence of extended emission, optical luminosity, and red shift, but then the model loses much of its simplicity, and to these reviewers, its attractiveness.


3 gamma = (1 - beta2)-1/2, beta = v/c. Back.

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