On the Determination of Stellar Mass and Binary Fraction of Open Clusters within 500 pc from the Sun

Abstract: We investigated the stellar mass function and the binary fraction of 114 nearby open clusters (OCs) using the high-precision photometric data from Gaia Data Release 3 (Gaia DR3). We estimated the mass of member stars by using a ridge line (RL) that is better in line with the observed color-magnitude diagram (CMD), thus obtaining more accurate stellar mass and binary mass ratio ($q$) at the low-mass region. By analyzing the present-day mass function (PDMF) of star clusters, we found that 108 OCs follow a two-stage power-law distribution, whereas 6 OCs present a single power-law PDMF. Subsequently, we fitted the high(low)-mass index of PDMF ($dN/dm \propto m^{-\alpha}$), denoted as $\alpha_{\rm h}$($\alpha_{\rm l}$), and segmentation point $m_{\rm c}$. For our cluster sample, the median values of $\alpha_{\rm h}$ and $\alpha_{\rm l}$ are 2.65 and 0.95, respectively, which are approximately consistent with the initial mass function (IMF) results provided by Kroupa (2001). We utilized the cumulative radial number distribution of stars with different masses to quantify the degree of mass segregation. We found a significant positive correlation between the state of dynamical evolution and mass segregation in OCs. We also estimated the fraction of binary stars with $q \geq 0.5$, ranging from 6% to 34% with a median of 17%. Finally, we provided a catalog of 114 nearby cluster properties, including the total mass, the binary fraction, the PDMF, and the dynamical state.