2020AJ....160...12D

Main-sequence stars exhibit a clear rotation-activity relationship, in which rapidly rotating stars drive strong chromospheric/coronal ultraviolet and X-ray emission. While the vast majority of red giant stars are inactive, a few percent exhibit strong ultraviolet emission. Here we use a sample of 133 red giant stars observed by Sloan Digital Sky Survey APOGEE and Galaxy Evolution Explorer to demonstrate an empirical relationship between near-UV (NUV) excess and rotational velocity (v sin i). Beyond this simple relationship, we find that NUV excess also correlates with rotation period and with Rossby number in a manner that shares broadly similar trends to those found in M dwarfs, including activity saturation among rapid rotators. Our data also suggest that the most extremely rapidly rotating giants may exhibit so-called supersaturation, which could be caused by centrifugal stripping of these stars rotating at a high fraction of breakup speed. As an example application of our empirical rotation-activity relation, we demonstrate that the NUV emission observed from a recently reported system comprising a red giant with a black hole companion is fully consistent with arising from the rapidly rotating red giant in that system. Most fundamentally, our findings suggest a common origin of chromospheric activity in rotation and convection for cool stars from main sequence to red giant stages of evolution.