Abstract
Context. The high-precision parallax data of the Gaia mission allows for significant improvements in the distance determination to stellar clusters and their stars. In order to obtain accurate and precise distance determinations, systematics such as parallax spatial correlations need to be accounted for, especially with regard to stars in small sky regions. Aims. Our aim is to provide the astrophysical community with a free and open code designed to simultaneously infer cluster parameters (i.e., distance and size) and distances to the cluster stars using Gaia parallax measurements. The code includes cluster-oriented prior families and it is specifically designed to deal with the Gaia parallax spatial correlations. Methods. A Bayesian hierarchical model is created to allow for the inference of both the cluster parameters and distances to its stars. Results. Using synthetic data that mimics Gaia parallax uncertainties and spatial correlations, we observe that our cluster-oriented prior families result in distance estimates with smaller errors than those obtained with an exponentially decreasing space density prior. In addition, the treatment of the parallax spatial correlations minimizes errors in the estimated cluster size and stellar distances, and avoids the underestimation of uncertainties. Although neglecting the parallax spatial correlations has no impact on the accuracy of cluster distance determinations, it underestimates the uncertainties and may result in measurements that are incompatible with the true value (i.e., falling beyond the 2σ uncertainties). Conclusions. The combination of prior knowledge with the treatment of Gaia parallax spatial correlations produces accurate (error < 10%) and trustworthy estimates (i.e., true values contained within the 2σ uncertainties) of cluster distances for clusters up to ∼5 kpc, along with cluster sizes for clusters up to ∼1 kpc.
Highlights
Stellar clusters offer a unique opportunity to test models of the formation and evolution of stars and stellar systems
In the context of distance determination based on parallax measurements, the traditional approach consists of averaging the parallaxes of the cluster stars and inverting the resulting parallax mean
It is a statistical tool for the simultaneous inference of star cluster parameters and individual distances of its stars
Summary
Stellar clusters offer a unique opportunity to test models of the formation and evolution of stars and stellar systems Their distance is useful for the comparison of model predictions to observations when the observational uncertainties are taken into account. The authors assumed that the spatial distribution of stars in open clusters follows a spherical Gaussian distribution and they inferred the cluster distance together with its dispersion and other kinematic parameters by marginalizing the positions of individual stars. They validated their methodology on synthetic clusters with properties similar to those expected for the Gaia data. They neglect the cluster intrinsic depth, which results in underestimated distance uncertainties
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