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

Hierarchical triple-star systems consists of three components organized into an inner binary (M 1, M 2) and a more distant outer tertiary (M 3) star. The LAMOST Medium-Resolution Spectroscopic Survey has offered a great sample for the study of triple-system populations. We used the peak amplitude ratio method to obtain the mass ratio (q in, q out) of a triple system from its normalized spectrum. By calculating the cross-correlation function, we determined the correlation between the mass ratio q out (M 3/(M 1 + M 2)) and the amplitude ratio (A 3/(A 1 + A 2)). We derived a q in of 0.5-1.0 and a q out between 0.2 and 0.8. By fitting a power-law function of the corrected q in distribution, gamma in is estimated to be -0.654 +/- 2.915, 4.304 +/- 1.125, and 11.371 +/- 1.309 for A-, F-, and G-type stars. The derived gamma in values increase as the mass decreases, 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 out distribution, gamma out is estimated to be -2.016 +/- 0.172, -1.962 +/- 0.853, and -1.238 +/- 0.141 for G-, F-, and A-type stars, respectively. The gamma out values show a trend of growth toward lower primary star masses.