Mass Ratio Distribution of Hierarchical Triple Systems from the LAMOST-MRS Survey

Abstract

Hierarchical triple-star systems consists of three components organised into an inner binary ($M_{1}$,$M_{2}$) and a more distant outer tertiary ($M_{3}$) star. The LAMOST Medium-Resolution Spectroscopic Survey (LAMOST-MRS) has offered a great sample for the study of triple system populations. We used the Peak Amplitude Ratio (PAR) method to obtain the mass ratio ($q_\mathrm{in}$, $q_\mathrm{out}$) of a triple system from its normalised spectrum. By calculating Cross-Correlation Function (CCF), we determined the correlation between the mass ratio $q_\mathrm{out}$ ($M_{3}$/($M_{1}$+$M_{2}$)) and the amplitude ratio ($A_{3}$/($A_{1}$+$A_{2}$)). We derived $q_\mathrm{in}$ of $0.5-1.0$ and $q_\mathrm{out}$ between 0.2 and 0.8. By fitting a power-law function of the corrected $q_\mathrm{in}$ distribution, the $γ_\mathrm{in}$ are estimated to be $-0.654\pm2.915$, $4.304\pm1.125$ and $11.371\pm1.309$ for A, F and G type stars. The derived $γ_\mathrm{in}$-values increase as the mass decrease, indicating that less massive stars are more likely to have companion stars with similar masses. By fitting a power-law function of the corrected $q_\mathrm{out}$ distribution, the ${γ_\mathrm{out}}$ are estimated to be $-2.016\pm0.172$, $-1.962\pm0.853$ and $-1.238\pm0.141$ for G, F and A type stars, respectively. The ${γ_\mathrm{out}}$-values show a trend of growth toward lower primary star masses.