TESS photometry of the pulsating hot subdwarf star V585 Peg

We report on the first space-based observations of the bright, high-amplitude hybrid pulsator V585 Peg (Balloon 090100001). TESS observed V585 Peg for 28 d during Sector 56 from which we detect 14 g-mode pulsations, 20 p-mode pulsations, and 26 combination frequencies. These pulsations are unusual and interesting in a number of ways; V585 Peg is a rare hybrid pulsator where both regions have many (>10) pulsations, the p-mode pulsations have clear frequency multiplets and overtone spacings while the g-mode pulsations do not, its multiplets have shown changes in splittings between years, and it appears to have two stochastic pulsations while most are stable. From p-mode multiplets, we find an average rotation period of 6.91 +/- 0.83 d in which the different l and m indices indicate latitudinal differential rotation. Unresolved g-mode multiplets limit rotation periods to be longer then 9.3 d for dipole modes, indicating V585 Peg to also be a radially differential rotator. We detect one secure p-mode overtone of 950 mu Hz and four less sure ones of 314, 410, 440, and 554 mu Hz. Two frequencies show stochastic properties indicating mode lifetimes of 3.5 and 6.2 h, which would be the shortest yet discovered.