An application of Galactic parallax: the distance to the tidal stream GD-1

We assess the practicality of computing the distance to stellar streams in our Galaxy, using the method of Galactic parallax suggested by Eyre & Binney. We find that the uncertainty in Galactic parallax is dependent upon the specific geometry of the problem in question. In the case of the tidal stream GD-1, the problem geometry indicates that available proper-motion data, with individual accuracy similar to 4 mas yr(-1), should allow estimation of its distance with about 50 per cent uncertainty. Proper motions accurate to similar to 1 mas yr(-1), which are expected from the forthcoming Pan-STARRS PS-1 survey, will allow estimation of its distance to about 10 per cent uncertainty. Proper motions from the future Large Synoptic Survey Telescope (LSST) and Gaia projects will be more accurate still, and will allow the parallax for a stream 30 kpc distant to be measured with similar to 14 per cent uncertainty. We demonstrate the feasibility of the method and show that our uncertainty estimates are accurate by computing Galactic parallax using simulated data for the GD-1 stream. We also apply the method to actual data for the GD-1 stream, published by Koposov, Rix & Hogg. With the exception of one datum, the distances estimated using Galactic parallax match photometric estimates with less than 1 kpc discrepancy. The scatter in the distances recovered using Galactic parallax is very low, suggesting that the proper-motion uncertainty reported by Koposov et al. is in fact overestimated. We conclude that the GD-1 stream is (8 +/- 1) kpc distant, on a retrograde orbit inclined 37 degrees to the plane, and that the visible portion of the stream is likely to be near pericentre.