Parallax is defined as the reciprocal of distance. But when we measure a parallax, this measurement is always noisy, and its simple reciprocal is not necessarily a good estimate of the distance. In fact, it has been known for some time that once the fractional parallax error is more than about 20%, the reciprocal parallax is a rather poor and biased estimate of the distance. This is an issue for Gaia, because about 80% of all stars which Gaia observes will have fractional parallax errors larger than 20%.
This fact can be seen in the above plots, which both show the cumulative distribution of fractional parallaxes. The black line in the right panel shows the fraction of Gaia stars (vertical axis) which are expected to have a fractional parallax error below the value given on the horizontal axis. This was calculated using the GUMS catalogue and the sky-averaged, post-launch, Gaia astrometric accuracy model assuming five years of observations. The red line is for the actual fractional parallax errors from the Hipparcos mission. Hipparcos generally has a larger fraction of stars with a smaller given fractional error than Gaia, but Hipparcos observed a far smaller absolute number of stars and with larger absolute parallax errors. The left panel shows the same information but on a logarithmic scale.
Given the large number of Gaia parallaxes with large fractional uncertainties, determining meaningful distances is both an important and non-trivial issue. In a tutorial article which has just appeared in the Publications of the Astronomical Society of the Pacific, Coryn Bailer-Jones examines the issues involved. The article investigates how robust distance estimates can be obtained using both the parallax and the parallax uncertainty.
Credits: C. Bailer-Jones