In general there is no strong evidence that the radio emission from GPS/CSS galaxies is significantly Doppler boosted. In fact, there is evidence to the contrary.
In the radio, GPS/CSS sources are the least variable class of compact extragalactic radio sources (see, e.g., Rudnick & Jones 1982; Seielstad, Pearson, & Readhead 1983; Waltman et al. 1991; Aller et al. 1992). Typically, only minor variations are seen, e.g., ~ 10% over a timescale of 1 yr. However, life is never this simple, and there are counterexamples of sources (all quasars) that are very variable, e.g., 0552+398, 1127-145, and 2134+004 (Wehrle et al. 1992). Some CSSs are observed to vary at low frequencies; however, these cases are thought to be due to extrinsic effects, e.g., refractive scintillation or ionospheric Faraday rotation (see, e.g., Mantovani et al. 1992). At this point not much is known about variability at other wave bands.
De Bruyn (1990) has used the limits on flux density variability in OQ 208 to place an interesting limit on the expansion speed of the radio source. If the turnover in OQ 208 is due to synchrotron self-absorption, then below the turnover, where the source is optically thick, the flux density is proportional to the source solid angle. The observed limits on variability at 1.4 GHz imply an expansion speed of less than 103 km s-1. This argument has been revisited by Stanghellini et al. (1997a) using improved knowledge of the milliarcsecond structure, deriving an upper limit to the expansion speed of 1.2 × 103 km s-1.
Seven sources (0108+388, 0710+439, 0711+356, 1934-638, 2021+614, 2134+004, and 2352+495) now have upper limits to component proper motion that are subluminal, ranging from 0.05c to 0.5c (Pearson, Readhead, & Barthel 1987; Conway et al. 1992, 1994; Pauliny-Toth et al. 1984; Tzioumis et al. 1989; Taylor, Readhead, & Pearson 1996a; G. Taylor 1996, private communication). The observed upper limits are generally much larger than the "expected" hot spot advance speeds of ~ 0.02c (see, e.g., Readhead et al. 1996b). Although 3C 216 has been shown to be superluminal (Barthel et al. 1988), it is now thought to be a large-scale double viewed close to the radio axis and not a true CSS (see, e.g., van Breugel et al. 1992; Taylor et al. 1995). There are a few sources that are apparently superluminal (e.g., CTA 102, Bääth 1987, Wehrle & Cohen 1989; 1946+708, Taylor & Vermeulen 1997; 3C 138, Cotton et al. 1997a; and possibly 0646+600, Akujor, Porcas, & Smoker 1996). The arm-length ratio and brightness ratios of the bidirectional jets in 1946+708 are consistent with Doppler effects. However, superluminal motion currently appears to be rare in GPS/CSS sources, unlike core-jet sources, which are very frequently found to be superluminal.
Wilkinson et al. (1994) have argued based on the similar number of CSOs (objects with radio cores) and compact doubles (i.e., CDs, objects without apparent cores) that the CSOs do not constitute a beamed subset of the CDs. Thus, all these arguments taken together are consistent with the hypothesis that the morphologies and luminosities of the GPS/CSS galaxies are not dominated by Doppler-boosted emission. This implies that these sources are intrinsically very powerful. On the other hand, there is evidence from variability that at least some of the GPS quasars are Doppler boosted.
The GPS/CSS quasars tend to be at higher redshift than the galaxies (section 8.1) and tend to have higher radio powers by roughly an order of magnitude (section 6). This is consistent with the quasar radio flux densities being moderately increased by Doppler boosting.
Fanti et al. (1990b), Saikia (1995), and Saikia et al. (1995) have considered the orientation-dependent properties of CSS sources in order to determine whether beaming is significant. Fanti et al. concluded that the radio luminosity of the CSS sources was not strongly affected by Doppler boosting and that the quasars seemed more asymmetric and distorted than expected purely on the basis of projection effects. Saikia has compared the fraction of total emission contributed by the core, projected linear size, misalignment angle, ratio of distances from the core to the lobes, and ratio of flux densities of the lobes for a sample of CSS sources and a sample of larger 3CR sources. He finds that the distributions of these orientation indicators are consistent with the differences in the CSS galaxies and quasars being due primarily to orientation, i.e., the quasars are closer to the line of sight than the galaxies. However, the CSS sources have more extreme values of these parameters than do the larger scale sources (i.e., the CSS sources are more asymmetric than the larger scale sources). Saikia suggests this is due to an additional effect - interactions with dense clouds in the environment.