2023ApJ...958...14H

Hierarchical triple-star systems consists of three components organized into an inner binary (M₁, M₂) and a more distant outer tertiary (M₃) 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 (M₃/(M₁ + M₂)) and the amplitude ratio (A₃/(A₁ + A₂)). 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, γ_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 γ_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, γ_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 γ_out values show a trend of growth toward lower primary star masses.