Confirmation of the Long-Period Planet Orbiting Gliese 411 and the Detection of a New Planet Candidate

We perform a detailed characterization of the planetary system orbiting the bright, nearby M dwarf Gliese 411 using radial velocities gathered by APF, HIRES, SOPHIE, and CARMENES. We confirm the presence of a signal with a period near $2900$ days that has been disputed as either a planet or long-period stellar magnetic cycle. An analysis of activity metrics including $\mathrm{H_\alpha}$ and $\mathrm{log'R_{HK}}$ indices supports the interpretation that the signal corresponds to a Neptune-mass planet, GJ 411 c. An additional signal near $215$ days was previously dismissed as an instrumental systematic, but our analysis shows that a planetary origin cannot be ruled out. With a semi-major axis of $0.5141\pm0.0038$ AU, this candidate's orbit falls between those of its companions and skirts the outer edge of the habitable zone. It has a minimum mass of $4.1\pm0.6$ $M_\oplus$, giving a radial velocity amplitude of $0.83\pm0.12$ $\mathrm{m\,s^{-1}}$. If confirmed, this would be one of the lowest-amplitude planet detections from any of these four instruments. Our analysis of the joint radial velocity data set also provides tighter constraints on the orbital parameters for the previously known planets. Photometric data from $\it{TESS}$ does not show any signs of a transit event. However, the outermost planet and candidate are prime targets for future direct imaging missions and GJ 411 c may be detectable via astrometry.