Uses and limitations of relativistic jet proper motions: lessons from Galactic microquasars

It is shown that the two-sided jet proper motions observed from the Galactic microquasars GRS 1915+105 and GRO J1655-40 in practice only allow us to place lower limits on the Lorentz factors of the outflows. As a consequence, it is not possible to rule out the possibility that jets from X-ray binaries are just as relativistic as those from active galactic nuclei (AGN). This results from the fact that distance estimates place the sources, within uncertainties, at the maximum distance d(max) which corresponds to an intrinsic velocity v=c. The general case is explored, for a range of intrinsic Lorentz factors and angles to the line of sight, and it is shown that a source of significantly relativistic jets will nearly always be observed close to d(max), and as a result it is unlikely that we will ever be able to measure with any accuracy the Lorentz factor of a jet from two-sided proper motions. We will generally not be able to do more than place a lower limit on the Lorentz factor of the flow, and this limit is naturally even lower in the cases where we only observe the approaching jet. On the other hand, under the assumption that any two-sided jets we see are intrinsically relativistic, we can confidently place the source at a distance dsimilar tod(max). As a result, observations of two-sided proper motions in relativistic jets from AGN would be extremely important for calibration of the cosmological distance scale. While the proper motions do not allow us to measure the Doppler shifts associated with the jets, the ratio of proper motions will correspond to the ratio of frequencies of any emission lines emitted by both jets, which will aid in searching for such lines. Furthermore, it is shown that if the jet is precessing, the product of the proper motions as a function of angle to the line of sight may be used to determine if the jet is only mildly relativistic.