Estimating the feasibility of `standard speed-gun' distances

In a previous paper, we demonstrated a single-rung method for measuring cosmological distances in active galactic nuclei (AGN) that can be used from low redshift (z < 0.1) to high redshift (z > 3). This method relies on the assumption that the variability seen in AGN is constrained by the speed of light during a flare event and can therefore be used to estimate the size of an emitting region. A limitation of this method is that previously, the Doppler factor was required to be known. In this paper, we derive an extension of the `standard speed-gun' method for measuring cosmological distances that depends on the maximum intrinsic brightness temperature that a source can reach, rather than the Doppler factor. If the precise value of the intrinsic brightness temperature does not evolve with redshift and flares are statistically independent, we can in principle improve the errors in measurements of the matter content of the universe (in a flat LambdaCDM model) statistically. We then explored how well a future observing program would constrain cosmological parameters. We found that recovering the input cosmology depends critically on the uncertainty of the intrinsic brightness temperature and the number of flares observed.