Planet-induced Periodic Modulation of Stellar Activity in GJ~436: Insights into a Warm Neptune's Magnetic Field

Interactions between stellar and planetary magnetic fields are expected to produce observable radio and optical signals modulated by their orbital periods, but direct detections remain elusive. We analyze 17 years of spectroscopic data of the GJ 436 system. This M2.5 V star hosts a transiting Neptune-sized planet in a close-in, inclined orbit. The data shows repeated enhancements of the stellar chromospheric activity at approximately the same phase of its 8-year activity cycle modulated by a combination of the planet's orbital period and the stellar rotation. We interpret this modulation as star-planet interaction. We propose a new geometrical model to interpret these signals, then, estimate the power of the interaction and, from models, estimate the magnetic field of GJ 436 b to be between 6 and 110G. This finding opens new pathways to detect star-planet interactions and to investigate planetary magnetic fields and their implications on atmospheric retention and detectability.