Stellar multiplicity in high-resolution spectroscopic surveys. I. Application to APOGEE subgiants and giants.

Many field stars reside in binaries, and the analysis and interpretation of photometric and spectroscopic surveys must take this into account. We have developed a model to predict how binaries influence the scientific results inferred from large spectroscopic surveys. Based on the rapid binary evolution code BSE, it allows us to model a representative population of binaries and generate synthetic survey observations. We describe this model in detail, and apply it to the radial velocity variation of subgiant and giant stars in the Galactic disc, as observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE), part of the Sloan Digital Sky Survey III. APOGEE provides an excellent data set for testing our binary models since a large fraction of the stars have been observed multiple times. By comparing our model to the APOGEE observations we constrain the initial binary fraction of solar-metallicity stars in the sample to be $f_{\rm b,0}=0.35\pm0.01$, in line with the solar neighbourhood. We find that the binary fraction is higher at lower metallicities, consistent with other observational studies. Our model matches the shape of the high-velocity scatter in APOGEE, which suggests that most velocity variability above 0.5 km/s comes from binaries. Our exploration of binary initial properties shows that APOGEE is mostly sensitive to binaries with periods between 3 and 3000 years, and is largely insensitive to the detailed properties of the population. We can, however, rule out a population where the mass of the lower-mass star is drawn from the IMF independently of its companion.