Binary evolution leads to the formation of important objects that are crucial for the development of astrophysics, but the statistical properties of binary populations are still poorly understood. The LAMOST-MRS has provided a large sample of stars to study the properties of binary populations, especially for the mass-ratio distributions and binary fractions. We have devised a peak amplitude ratio (PAR) approach to derive the mass ratio of a binary system based on results obtained from its spectrum. By computing a cross-correlation function, we established a relation between the derived mass ratio and the PARs of the binary systems. By using spectral observations obtained from LAMSOT DR6 and DR7, we applied the PAR approach to form distributions of the derived mass ratio of the binary systems to the spectral types. We selected the mass ratio within the range of 0.6−1.0 to investigate the mass-ratio distribution. Through a power-law fitting, we obtained power index γ values of −0.42 ± 0.27, 0.03 ± 0.12, and 2.12 ± 0.19 for the A-, F-, and G-type stars identified in the sample, respectively. The derived γ-values display an increasing trend toward lower primary star masses, and G-type binaries tend to be twins more frequently. The close binary fractions (for P ≲ 150 days and q ≳ 0.6) in our sample for A, F, and G binaries are 7.6% ± 0.5%, 4.9% ± 0.2%, and 3.7% ± 0.1%, respectively. Note that the PAR approach can be applied to large spectroscopic surveys of stars.

Binaries consisting of a hot subdwarf star and an accreting white dwarf (WD) are sources of gravitational wave radiation at low frequencies and possible progenitors of type Ia supernovae if the WD mass is large enough. Here, we report the discovery of the third binary known of this kind: it consists of a hot subdwarf O (sdO) star and a WD with an orbital period of 3.495 hours and an orbital shrinkage of 0.1 s in 6 yr. The sdO star overfills its Roche lobe and likely transfers mass to the WD via an accretion disk. From spectroscopy, we obtain an effective temperature of Teff = 54 240 ± 1 840 K and a surface gravity of log g = 4.841 ± 0.108 for the sdO star. From the light curve analysis, we obtain a sdO mass of MsdO = 0.55 M⊙ and a mass ratio of q = MWD/MsdO = 0.738 ± 0.001. Also, we estimate that the disk has a radius of ∼0.41 R⊙ and a thickness of ∼0.18 R⊙. The origin of this binary is probably a common envelope ejection channel, where the progenitor of the sdO star is either an RGB star or, more likely, an early AGB star; the sdO star will subsequently evolve into a WD and merge with its WD companion, likely resulting in an R CrB star. The outstanding feature in the spectrum of this object is strong Ca H&K lines, which are blueshifted by ∼200 km s−1 and likely originate from the recently ejected common envelope, and we estimated that the remnant CE material in the binary system has a density ∼6 × 10−10 g cm−3.