A deep HST view of the open cluster NGC2158: binaries, mass functions, and M-dwarf discontinuity

Abstract

A significant fraction of stars in both the Galactic field and stellar clusters are members of binary systems. Understanding their properties is therefore essential for a comprehensive view of stellar structure, evolution, and cluster dynamics. Despite extensive studies of cluster binaries, key issues remain unresolved, particularly for photometric binaries among low-mass stars. While the binary fraction in the field strongly depends on stellar mass, cluster studies have generally suggested an approximately constant fraction over the limited mass ranges explored. In addition, the mass function (MF) of very low-mass stars is still poorly constrained in clusters older than a few hundred Myr. 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 solar masses, enabling the first detailed analysis of binaries in this cluster. We measure a global binary fraction of 38%, consistent with other open clusters, and find a clear mass dependence: it decreases from ~52% at 1.0 solar masses to ~11% at 0.2 solar masses. This trend mirrors that of Galactic field stars, suggesting similar binary properties. The MF is characterized by three regimes: high-mass stars (alpha= -2.49 +- 0.19), low-mass stars (alpha= -1.11 +- 0.09), and very low-mass stars (alpha= -0.08 +- 0.07). The slope change near 1.0 solar mass agrees with recent surveys, though we find a deficit below ~0.3 solar masses. We also detect a main-sequence discontinuity around ~0.3 solar masses, possibly linked to the 3He-driven instability predicted by stellar models and analogous to the Jao Gap seen in nearby field stars.

Figures (8)

• Figure 1: $m_{\rm F814W}$ vs. $m_{\rm F606W}-m_{\rm F814W}$ CMD of NGC 2158 corrected for differential reddening (left panel). The right panel shows a zoomed-in view of the same CMD, where the best-fit isochrone from marigo2017a is overplotted.
• Figure 2: Left: Zoom-in of the left-panel CMD shown in Figure \ref{['fig:cmd']} around the region where binaries with large mass ratios can be more clearly distinguished from the bulk of single stars. Right: Simulated CMD including only single stars. Simulated cluster members and field stars are shown as black points and magenta starred symbols, respectively. The red and green lines in both panels enclose the region A of the CMD, used to infer the binary fraction. The gray shaded area delineates region B, a subregion of A that primarily hosts binaries with mass ratios larger than 0.5. Region F, populated by field stars, is the CMD area enclosed by the black dashed lines.
• Figure 3: Total binary fraction as a function of primary-star mass from offner2023a and legnardi2025a, with the addition of five new data points (red dots) derived from our study of the open cluster NGC 2158. The grey dots reproduce the literature compilation from offner2023a for the Galaxy used in the original plot, and the green diamond represents the SMC binary fraction.
• Figure 4: Left: Reproduction of the $m_{\rm F814W}$ versus $m_{\rm F606W} - m_{\rm F814W}$ CMD from Fig. \ref{['fig:cmd']}. The regions used to derive the luminosity and MFs are overplotted, with the corresponding average stellar masses indicated on the right side of each region. Right: Luminosity function (top) and MF (bottom) derived from the left-panel CMD. The straight lines show the best-fitting relations for stars in the mass intervals defined by cordoni2023a.
• Figure 5: MF slope, $\alpha$, as a function of the explored stellar mass range, compiled from a variety of Galactic and extragalactic environments. Each point represents the best-fit power-law slope derived over a specific mass interval, with horizontal error bars indicating the width of the corresponding mass range. The green crosses indicate the measurements on NGC 2158 from this work. The solid red line marks the canonical salpeter1955a IMF slope, while the dashed black lines represent the segmented IMF slopes from kroupa2001a. The green dashed line corresponds to the slopes measured by cordoni2023a for Galactic open clusters.