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

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.