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ABSTRACT We present a model to estimate the average primary masses, companion mass ranges, the inclination limit for recognizing a rotational variable, and the primary mass spreads for populations of binary stars. The model fits a population’s binary mass function distribution and allows for a probability that some mass functions are incorrectly estimated. Using tests with synthetic data, we assess the model’s sensitivity to each parameter, finding that we are most sensitive to the average primary mass and the minimum companion mass, with less sensitivity to the inclination limit and little to no sensitivity to the primary mass spread. We apply the model to five populations of binary spotted rotational variables identified in ASAS-SN, computing their binary mass functions using RV data from APOGEE. Their average primary mass estimates are consistent with our expectations based on their CMD locations ($$\sim 0.75 \, {\rm M}_{\odot }$$ for lower main sequence primaries and $$\sim 0.9$$–$$1.2 \, {\rm M}_{\odot }$$ for RS CVn and sub-subgiants). Their companion mass range estimates allow companion masses down to $$M_2/M_1\simeq 0.1$$, although the main sequence population may have a higher minimum mass fraction ($$\sim 0.4$$). We see weak evidence of an inclination limit $$\gtrsim 50^{\circ }$$ for the main sequence and sub-subgiant groups and no evidence of an inclination limit in the other groups. No groups show strong evidence for a preferred primary mass spread. We conclude by demonstrating that the approach will provide significantly better estimates of the primary mass and the minimum mass ratio and reasonable sensitivity to the inclination limit with 10 times as many systems. 

ABSTRACT We examine the properties of ∼50 000 rotational variables from the ASAS-SN survey using distances, stellar properties, and probes of binarity from Gaia DR3 and the SDSS APOGEE survey. They have higher amplitudes and span a broader period range than previously studied Kepler rotators. We find they divide into three groups of main sequence stars (MS1, MS2s, MS2b) and four of giants (G1/3, G2, G4s, and G4b). MS1 stars are slowly rotating (10–30 d), likely single stars with a limited range of temperatures. MS2s stars are more rapidly rotating (days) single stars spanning the lower main sequence up to the Kraft break. There is a clear period gap (or minimum) between MS1 and MS2s, similar to that seen for lower temperatures in the Kepler samples. MS2b stars are tidally locked binaries with periods of days. G1/3 stars are heavily spotted, tidally locked RS CVn stars with periods of 10s of days. G2 stars are less luminous, heavily spotted, tidally locked sub-subgiants with periods of ∼10 d. G4s stars have intermediate luminosities to G1/3 and G2, slow rotation periods (approaching 100 d), and are almost certainly all merger remnants. G4b stars have similar rotation periods and luminosities to G4s, but consist of sub-synchronously rotating binaries. We see no difference in indicators for the presence of very wide binary companions between any of these groups and control samples of photometric twin stars built for each group.