A deep HST view of the open cluster NGC 2158: binaries, mass functions, and M-dwarf discontinuity

Abstract: A significant fraction of stars in both the Galactic field and stellar clusters belong to binary systems. Understanding their properties is therefore fundamental for a comprehensive picture of stellar structure, stellar evolution, and cluster dynamics. Despite extensive work on binaries in clusters, key questions remain open, particularly concerning photometric binaries among low-mass stars. While the binary fraction among field stars shows a strong dependence on stellar mass, studies of star clusters have so far suggested an approximately constant fraction across the limited mass range explored. Moreover, the mass function (MF) of very low-mass stars remains poorly constrained in clusters older than a few hundred Myr. In this work, we use deep Hubble Space Telescope imaging of the intermediate-age open cluster NGC 2158 to investigate its binary population and derive the luminosity and MFs down to ∼ 0.14 M⊙. This dataset enables the first detailed study of binaries in this cluster. We measure a global binary fraction of 38%, consistent with that observed in other open clusters, and detect a clear mass dependence: the fraction decreases from ∼ 52% at 1.0M⊙ to ∼ 11% at 0.2M⊙. This trend mirrors that seen in the Galactic field, suggesting that binaries in NGC 2158 and field populations share similar properties. The MF of NGC 2158 is best described by three regimes: high-mass stars (α = −2.49 ± 0.19), low-mass stars (α = −1.11 ± 0.09), and very low-mass stars (α = −0.08 ± 0.07). The slope change near 1.0 M⊙ agrees with recent open cluster surveys, although we find a deficit of stars at the lowest masses (M ≲ 0.3 M⊙). Finally, we identify a discontinuity in the main sequence around M ∼ 0.3 M⊙. We explore the possibility that this feature traces the 3He-driven instability predicted by stellar models, analogous to the “Jao Gap” observed in the color–magnitude diagram of nearby field stars.