tokens: separately for the stellar subset (H ipparcos and Tycho-2 stars) and the quasars. Table 1 , experiment 1, presents the median value of the parallax errors (estimated minus true), the uncertainty of the median calculated using the bootstrap method, and the RSE 4 dispersion of the parallax errors for each of the subsets. The different columns give statistics for selections based on the individual formal standard uncertainties of the parallaxes. The median obtained for the quasar subset agrees with the corresponding stellar value to within a few as, independent of the selection of sources. Table 1 Simulation results of three different experiments comparing the parallax median between the stellar subset and the quasars. Notes. “Stars” refers to the combined subset of H ipparcos and Tycho-2 sources. In each subset, statistics are given for the selection of 90% of the sources with the smallest individual formal uncertainties and for all sources together. The values given are the median (and its uncertainty from the bootstrap method) and the RSE dispersion of the parallax errors (estimated minus true). 3.2. Spurious proper motion from variable source structure Variation in the source structure of quasars can lead to shifts of their photocentres up to the milliarcsecond level (e.g. Popović et al. 2012 ; Porcas 2009 ; Taris et al. 2011 ). Linear trends of these shifts might lead to spurious proper motions measured for quasars and stable over years to decades. Titov et al. (2011) fitted long-term proper motions for 555 quasars from VLBI observations. The total proper motion in as yr in their catalogue can be described by a log-normal distribution with mean 1.9 dex and standard deviation 0.61 dex. It is impossible to say whether these measurements give an optimistic or conservative characterization of spurious quasar proper motions on the much shorter time baselines of our simulations. Additionally, the morphology of the host galaxy might lead to a statistical increase in the centroiding error, and photometric variability of the nucleus together with the stable photocentre of the host galaxy might lead to an effect similar to “variability-induced movers” in binaries ( Wielen 1996 ). Physically all of these effects are expected to be random and therefore should only increase the dispersion of the results but not the median values themselves. We use the statistical properties of the results by Titov et al. (2011) as the basis for simulations, but apply a factor of 10 to provide a conservative assumption on the total spurious motion. The individual components of the proper motion are computed as where is a random position angle and is taken from a normal distribution with mean value 2.9 dex and standard deviation 0.61 dex. The median value of the resulting is about 800 as yr. While this spurious proper motion increases the RSE of the solution for the quasar subset, the agreement of median parallax between the quasars and the stellar subset remains at the
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