SUPERLUMINAL MOTION STATISTICS AND COSMOLOGY

This paper has three parts. First, we give an up-to-date overview of the available apparent velocity (beta(app)) data; second, we present some statistical predictions from simple relativistic beaming models; third, we discuss the inferences which a comparison of data and models allows for both relativistic jets and cosmology. We demonstrate that, in objects selected by Doppler-boosted flux density, likely Lorentz factors (gamma) can be estimated from the first-ranked beta(app) in samples as small as 5. Using 25 core-selected quasars, we find that the dependence of gamma on redshift differs depending on the value of q0: gamma is close to constant over z if q0 = 0.5, but increases with z if q0 = 0.05. Conversely, this result could be used to constrain q0, using either theoretical limits on gamma or observational constraints on the full distribution of gamma in each of several redshift bins, as could be derived from the beta(app) statistics in larger samples. We investigate several modifications to the simple relativistic beam concept, and their effects on the beta(app) statistics. There is likely to be a spread of gamma over the sample, with relative width W. There could also be a separate pattern and bulk gamma, which we model with a factor r = gamma(p)/gamma(b). The values of W and r are coupled, and a swath in the (W, r)-plane is allowed by the beta(app) data in core-selected quasars. InterestinglY, gamma(p) could be both smaller and larger than gamma(b), or they could be equal, if W is large, but the most naive model (0, 1)-the same Lorentz factor in all sources and no separate pattern motions-is excluded. A possible cutoff in quasar jet orientations, as in some unification models, causes a sharp shift toward higher beta(app) in randomly oriented samples but does not strongly affect the statistics of core-selected samples. If there is moderate bending of the jets on parsec scales, on the other hand, this has no significant impact on randomly oriented samples, but it can have surprisingly varied results in core-selected quasars. It could be that individual jets incorporate a broad range of gamma, but that only one value is observed per jet, as given by Doppler favoritism. The beta(app) statistics in core-selected quasars are a poor indicator of any such internal range. Furthermore, at small angles to the line of sight, Doppler favoritism is actually not a good gamma-selection mechanism. However, for randomly oriented samples, such as lobe-selected quasars, the effects of an internal range of gamma can be confused with the angle cutoff in unification scenarios. This might greatly complicate using beta(app) in lobe-selected quasars either to constrain such unification models or to determine the cosmological parameters H-0 and q0.