Kalkayotl: A cluster distance inference code

Context: Stellar clusters are benchmarks for theories of star formation and evolution. The high precision parallax data of the Gaia mission allows significant improvements in the distance determination to stellar clusters and its stars. In order to have accurate and precise distance determinations, systematics like the parallax spatial correlations need to be accounted for, especially for stars in small sky regions. Aims: Provide the astrophysical community with a free and open code designed to simultaneously infer cluster parameters (i.e. distance and size) and the distances to its stars using Gaia parallax measurements. It includes cluster oriented prior families and is specifically designed to deal with the Gaia parallax spatial correlations. Methods: A Bayesian hierarchical model is created to allow 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. 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 2$\sigma$ uncertainties) of clusters distances for clusters up to ~5 kpc, and cluster sizes for clusters up to ~1 kpc.