Binaries in Star Clusters: NGC 2158

A large fraction of stars in both the solar neighborhood and star clusters are a part of binary systems, so developing a complete understanding of binaries is essential in order to properly describe stellar structure, stellar evolution, and the dynamical history of clusters. Despite extensive study of binaries in star clusters, key open questions still exist. In particular, photometric binaries among low mass stars are largely unexplored. While the binary fraction in field stars has a strong correlation with stellar mass, studies focused on star clusters suggest a nearly constant fraction across the limited mass range investigated to date. Additionally, the mass function of very low mass stars remains largely unconstrained among clusters older than a few hundred Myr. In this work, I analyze deep, multi-epoch images of the intermediate age open cluster NGC 2158, obtained with the Wife Field Channel of the Hubble Space Telescope Advanced Camera for Surveys. I derived high precision photometry and proper motions using software developed by Jay Anderson. This data enabled, for the first time, a detailed study of binary stars in this cluster as well as the determination of the luminosity and mass functions to ∼ 0.1M⊙. The best fit isochrone for this cluster gives an age of 1.9 Gyr and [Fe/H] = -0.03. The color magnitude diagram reveals a well defined binary sequence that is clearly distinguishable down to the lowest stellar masses. From this dataset, I measured the binary fraction over the deepest mass range investigated so far, finding a value of 19%, comparable to that observed in other open clusters. I also find a strong mass dependence: the binary fraction decreases from ∼26% at 1.08 M⊙ to ∼12% at 0.22 M⊙. This trend is consistent with that observed in the solar neighborhood and the Galactic field, suggesting that binaries in clusters and in the field share similar properties, in contrast with some earlier results. The mass function of NGC 2158 is best described by three regimes: high-mass stars (α = −2.27), low-mass stars (α = −1.24), and very low-mass stars (α = 0.03). The change in slope at log(M/M⊙) ≈ −0.05 separating the high and low mass regimes is in agreement with Cordoni et al. [2023], but there is a deficit of stars in the very low mass range. This study presents the first combined analysis of the binary fraction and mass function across such an extended mass range in this cluster, providing new insights into the binary population and very low-mass stars in open clusters.