Quasar Parallax: A Method for Determining Direct Geometrical Distances to Quasars

Abstract

We describe a novel method to determine direct geometrical distances to quasars that can measure the cosmological constant, Lambda, with minimal assumptions. This method is equivalent to geometric parallax, with the `standard length' being the size of the quasar broad emission line region (BELR) as determined from the light travel time measurements of reverberation mapping. The effect of non-zero Lambda on angular diameter is large, 40% at z=2, so mapping angular diameter distances vs. redshift will give Lambda with (relative) ease. In principle these measurements could be made in the UV, optical, near infrared or even X-ray bands. Interferometers with a resolution of 0.01mas are needed to measure the size of the BELR in z=2 quasars, which appear plausible given reasonable short term extrapolations of current technology.