Flares, Rotation, Activity Cycles, and a Magnetic Star–Planet Interaction Hypothesis for the Far-ultraviolet Emission of GJ 436

Variability in the far ultraviolet (FUV) emission produced by stellar activity affects photochemistry and heating orbiting planetary atmospheres. We present a comprehensive analysis of FUV variability GJ 436, field-age, M2.5V star ($P_\mathrm{rot}\approx44$ d) orbited warm, Neptune-size planet ($M \approx 25\ M_\oplus$, $R 4.1\ R_\oplus$, $P_\mathrm{orb}\approx2.6$ d). Observations at three epochs from 2012 to 2018 span nearly full cycle, sample two rotations orbital periods planet, reveal multitude brief flares. Over 2012-2018, star's $7.75\pm0.10$ yr cycle largest observed variations, $38\pm3$% summed flux major lines. In 2018, due rotation was $8\pm2$%. An additional $11\pm1$% scatter 10 min cadence, treated as white noise fits, likely has both instrumental astrophysical origins. Flares increased time-averaged 15% over 0.88 d cumulative exposure, peaking high 25$\times$ quiescence. interpret these flare values lower limits given that flares too weak or infrequent have been exist. 436's frequency distribution (FFD) wavelengths is unusual compared other field-age M dwarfs, exhibiting statistically-significant dearth energy ($>4\times 10^{28}$ erg) events we hypothesize be result magnetic star-planet interaction (SPI) triggering premature If an SPI present, 436 b's field strength must $\lesssim$100 G explain statistically insignificant increase orbit-phased emission. *Erratum Pending:* Due arithmetic error, published limit on incorrect. The correct $\lesssim$10~G.