Superluminal motion statistics and cosmology

This paper has three parts. First, we give an up-to-date overview of the available apparent velocity βₐpp_) 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 (γ) can be estimated from the first-ranked βₐpp_ in samples as small as 5. Using 25 core-selected quasars, we find that the dependence of γ on redshift differs depending on the value of q₀_: γ 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 γ or observational constraints on the full distribution of γ in each of several redshift bins, as could be derived from the βₐpp_ statistics in larger samples. We investigate several modifications to the simple relativistic beam concept, and their effects on the βₐpp_ statistics. There is likely to be a spread of γ over the sample, with relative width W. There could also be a separate pattern and bulk γ, which we model with a factor r = γₚ_/γb_. The values of W and r are coupled, and a swath in the (W, r) -plane is allowed by the βₐpp_ data in core- selected quasars. Interestingly, γₚ_ could be both smaller and larger than γb_ 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 βₐpp_ 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 γ, but that only one value is observed per jet, as given by Doppler favoritism. The βₐpp_ 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 γ-selection mechanism. However, for randomly oriented samples, such as lobe-selected quasars, the effects of an internal range of γ can be confused with the angle cutoff in unification scenarios. This might greatly complicate using βₐpp_ in lobe-selected quasars either to constrain such unification models or to determine the cosmological parameters H₀_ and q₀_.