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Many field stars reside in binaries, and the analysis and interpretation ofphotometric and spectroscopic surveys must take this into account. We havedeveloped a model to predict how binaries influence the scientific resultsinferred from large spectroscopic surveys. Based on the rapid binary evolutioncode BSE, it allows us to model a representative population of binaries andgenerate synthetic survey observations. We describe this model in detail, andapply it to the radial velocity variation of subgiant and giant stars in theGalactic disc, as observed by the Apache Point Observatory Galactic EvolutionExperiment (APOGEE), part of the Sloan Digital Sky Survey III. APOGEE providesan excellent data set for testing our binary models since a large fraction ofthe stars have been observed multiple times.  By comparing our model to the APOGEE observations we constrain the initialbinary fraction of solar-metallicity stars in the sample to be $f_{\rmb,0}=0.35\pm0.01$, in line with the solar neighbourhood. We find that thebinary fraction is higher at lower metallicities, consistent with otherobservational studies. Our model matches the shape of the high-velocity scatterin APOGEE, which suggests that most velocity variability above 0.5 km/s comesfrom binaries. Our exploration of binary initial properties shows that APOGEEis mostly sensitive to binaries with periods between 3 and 3000 years, and islargely insensitive to the detailed properties of the population. We can,however, rule out a population where the mass of the lower-mass star is drawnfrom the IMF independently of its companion.

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