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 ${\hat{I}}_{\mathrm{in}}^3$ are estimated to be $-0.654\pm 2.915$, $4.304\pm 1.125$ and $11.371\pm 1.309$ for A, F and G type stars. The derived ${\hat{I}}_{\mathrm{in}}^3$-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 ${\hat{I}}_{\mathrm{out}}^3$ are estimated to be $-2.016\pm 0.172$, $-1.962\pm 0.853$ and $-1.238\pm 0.141$ for G, F and A type stars, respectively. The ${\hat{I}}_{\mathrm{out}}^3$-values show a trend of growth toward lower primary star masses.