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We present new MMT/Hectochelle spectroscopic measurements for 257 stars observed along the line of sight to the ultrafaint dwarf galaxy Triangulum II (Tri II). Combining results from previous Keck/DEIMOS spectroscopy, we obtain a sample that includes 16 likely members of Tri II, with up to 10 independent redshift measurements per star. To this multi-epoch kinematic data set, we apply methodology that we develop in order to infer binary orbital parameters from sparsely sampled radial velocity curves with as few as two epochs. For a previously identified (spatially unresolved) binary system in Tri II, we infer an orbital solution with period $296.0_{-3.3}^{+3.8} \rm ~ d$, semimajor axis $1.12^{+0.41}_{-0.24}\rm ~au$, and systemic velocity $-380.0 \pm 1.7 \rm ~km ~s^{-1}$ that we then use in the analysis of Tri II’s internal kinematics. Despite this improvement in the modelling of binary star systems, the current data remain insufficient to resolve the velocity dispersion of Tri II. We instead find a 95 per cent confidence upper limit of $\sigma _{v} \lesssim 3.4 \rm ~km~s^{-1}$.

We measure rotational broadening in spectra taken by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey to characterize 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 vsin i 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, ΔRVmax, 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 vsin i and ΔRVmax values. These expectations agree with the positive correlation between the maximum ΔRVmax and vsin i values observed in our sample as a function of log(g). We find that the fast rotators in our sample have a high occurrence of short-period [log(P/d) ≲ 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 ΔRVmax 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.