The low masses of M dwarfs create attractive opportunities for exoplanet radial-velocity (RV) detections. These stars, however, exhibit strong stellar activity that may attenuate or mimic planetary signals. We present a velocimetric analysis on one such M dwarf, GJ 3998 ($d=18.2\,\text{ pc}$), with two published short-period super-Earths: GJ 3998 b and GJ 3998 c. We use additional data from the HARPS-N spectrograph to confirm these two planets and to look for more. We carry out joint modelling of: (i) RV planetary signals, (ii) stellar rotation in RV and activity indicators through Gaussian processes, (iii) long-term trends in RV and activity indicators. We constrain the rotational period of GJ 3998 to $P_\text{ rot}=30.2\pm 0.3\,\text{ d}$ and discover long-term sinusoidal imprints in RV and FWHM of period $P_\text{ cyc}=316^{ +14}_{ -8}\,\text{ d}$. We confirm GJ 3998 b and GJ 3998 c, and detect a third planet: GJ 3998 d, whose signal had been previously attributed to stellar activity. GJ 3998 d has an orbital period of $41.78\pm 0.05\,\text{ d}$, a minimum mass of $6.07^{ +1.00}_{ -0.96}\,\text{ M}_\oplus$ and a mean insolation flux of $1.2^{ +0.3}_{ -0.2}\,\Phi_\oplus$. This makes it one of the few known planets receiving Earth-like insolation flux.
Categories: astro-ph.EP astro-ph.SR