Inferring the distance to Westerlund 1 from Gaia DR2.

Westerlund 1 (Wd1) is potentially the largest star cluster in the Galaxy. That designation critically depends upon the distance to the cluster, yet the cluster is highly obscured, making luminosity-based distance estimates difficult. Using Gaia Data Release 2 (DR2) parallaxes and Bayesian inference, we infer a parallax of $0.31pm{0.04}$ mas corresponding to a distance of $3.2pm{0.4}$ kpc. To leverage the combined statistics of all stars in the direction of Wd1, we derive the Bayesian model for a cluster of stars hidden among Galactic field stars; this model includes both the zero-point and astrometric excess noise. We infer the exponential length scale, $L$, for field stars; $L = 0.84_{-0.03}^{+0.02}$ kpc. This is ~1.7 times smaller than the models used for Bailer-Jones et al. (2018). Previous estimates for the distance to Wd1 ranged from 1.2 to 5.5 kpc, although values around 5 kpc have usually been adopted. The Gaia DR2 parallaxes reduce the uncertainty from a factor of 3 to 15% and rules out the most often quoted value of 5 kpc with 99% confidence. This new distance allows for more accurate mass and age determinations for the stars in Wd1. For example, the previously inferred initial mass at the main sequence turnoff was around 40 $M_{odot}$; the new Gaia DR2 distance shifts this down to about 25 $M_{odot}$. This has important implications for our understanding of late stages of stellar evolution, including the initial mass of the magnetar and the LBV in Wd1. Similarly, the new distance suggests that the total cluster mass is about three times lower than previously calculated.