Rapid Rotation of Low-Mass Red Giants Using APOKASC: A Measure of Interaction Rates on the Post-main-sequence

We investigate the occurrence rate of rapidly rotating ($v\sin i$$>$10 km s$^{-1}$), low-mass giant stars in the APOGEE-Kepler (APOKASC) fields with asteroseismic mass and surface gravity measurements. Such stars are likely merger products and their frequency places interesting constraints on stellar population models. We also identify anomalous rotators, i.e. stars with 5 km s$^{-1}$$<$$v\sin i$$<$10 km s$^{-1}$ that are rotating significantly faster than both angular momentum evolution predictions and the measured rates of similar stars. Our data set contains fewer rapid rotators than one would expect given measurements of the Galactic field star population, which likely indicates that asteroseismic detections are less common in rapidly rotating red giants. The number of low-mass moderate (5-10 km s$^{-1}$) rotators in our sample gives a lower limit of 7% for the rate at which low-mass stars interact on the upper red giant branch because single stars in this mass range are expected to rotate slowly. Finally, we classify the likely origin of the rapid or anomalous rotation where possible. KIC 10293335 is identified as a merger product and KIC 6501237 is a possible binary system of two oscillating red giants.