Stellar multiplicity and stellar rotation: Insights from APOGEE

We measure rotational broadening in spectra taken by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey to characterise the relationship between stellar multiplicity and rotation. We create a sample of 2786 giants and 24 496 dwarfs with stellar parameters and multiple radial velocities from the APOGEE pipeline, projected rotation speeds \vsini\ determined from our own pipeline, and distances, masses, and ages measured by Sanders \& Das. We use the statistical distribution of the maximum shift in the radial velocities, \drvm, as a proxy for the close binary fraction to explore the interplay between stellar evolution, rotation, and multiplicity. Assuming that the minimum orbital period allowed is the critical period for Roche Lobe overflow and rotational synchronization, we calculate theoretical upper limits on expected \vsini\ and \drvm\ values. These expectations agree with the positive correlation between the maximum \drvm\ and \vsini\ values observed in our sample as a function of \logg. We find that the fast rotators in our sample have a high occurrence of short-period ($\log(P/\text{d})\lesssim 4$) companions. We also find that old, rapidly-rotating main sequence stars have larger completeness-corrected close binary fractions than their younger peers. Furthermore, rapidly-rotating stars with large \drvm\ consistently show differences of 1-10 Gyr between the predicted gyrochronological and measured isochronal ages. These results point towards a link between rapid rotation and close binarity through tidal interactions. We conclude that stellar rotation is strongly correlated with stellar multiplicity in the field, and caution should be taken in the application of gyrochronology relations to cool stars.