# Smoking Gun of the Dynamical Processing of the Solar-type Field Binary Stars

## TL;DR

This study analyzes the binary star properties in the solar neighborhood, revealing how dynamical processing in star clusters influences binary fractions and mass-ratio distributions across different stellar populations.

## Contribution

It introduces a hierarchical Bayesian model to connect binary properties with metallicity and primary mass, highlighting the impact of early dynamical processing on binary star evolution.

## Key findings

- High-$\gamma$ populations have lower binary fractions and are more affected by dynamical processing.
- Binary fractions correlate with metallicity in high-$\gamma$ groups and with primary mass in low-$\gamma$ groups.
- Dynamical processing preferentially destroys binaries with smaller mass and wider separation.

## Abstract

We investigate the binarity properties in field stars using more than 50\,000 main-sequence stars with stellar mass from 0.4 to 0.85\,$M_\odot$ observed by LAMOST and {\emph Gaia} in the solar neighborhood. By adopting a power-law shape of the mass-ratio distribution with power index of $\gamma$, we conduct a hierarchical Bayesian model to derive the binary fraction ($f_{b}$) and $\gamma$ for stellar populations with different metallicities and primary masses ($m_1$). We find that $f_b$ is tightly anti-correlated with $\gamma$, i.e. the populations with smaller binary fraction contains more binaries with larger mass-ratio and vice versa.The high-$\gamma$ populations with $\gamma>1.2$ have lower stellar mass and higher metallicity, while the low-$\gamma$ populations with $\gamma<1.2$ have larger mass or lower metallicity. The $f_b$ of the high-$\gamma$ group is anti-correlated with [Fe/H] but flat with $m_1$.Meanwhile, the $f_b$ of the low-$\gamma$ group displays clear correlation with $m_1$ but quite flat with [Fe/H]. The substantial differences are likely due to the dynamical processing when the binaries were in the embedded star clusters in their early days. The dynamical processing tends to destroy binaries with smaller primary mass, smaller mass-ratio, and wider separation. Consequently, the high-$\gamma$ group containing smaller $m_1$ is more effectively influenced and hence contains less binaries, many of which have larger mass-ratio and shorter period. However, the low-$\gamma$ group is less affected by the dynamical processing due to their larger $m_1$. These are evident that the dynamical processing does effectively work and significantly reshape the present-day binary properties of field stars.