Spectroscopic data of BD+40 2790 (TOI-2076)

BD+40 2790 shows an activity-induced scatter larger than 30m/s in the radial velocities. We employed different methods to measure the stellar radial velocities, along with several models to filter out the dominant stellar activity signal to bring to light the planet-induced signals, which are expected to have semi-amplitudes that are lower by one order of magnitude. We evaluated the mass loss rate of the planetary atmospheres using photo-ionisation hydrodynamic modeling, accounting for the temporal evolution of the stellar high-energy flux through the adoption of different models for X-rays and EUV irradiation.

The dynamical analysis confirms that the three sub-Neptune-sized companions (with our radius measurements of R_b_=2.54+/-0.04, R_{c}=3.35+/-0.05, and R_d_=3.29+/-0.06R_{Earth}_) have masses that situate them in the planetary regime. We derived 3{sigma} upper limits below or close to the mass of Neptune for all the planets in our sample: 11-12, 12-13.5, and 14-19M_{Earth}_ for planets b, c, and d, respectively. In the case of planet d, we found promising clues that the mass could be between ~7 and 8M_{Earth}_, with a significance level between 2.3-2.5{sigma} (at best).

This result must be further investigated using other analysis methods and techniques or using high-precision near-infrared (nIR) spectrographs to collect new radial velocities, which could be less affected by stellar activity. Atmospheric photo-evaporation simulations predict that BD+40 2790 b is currently losing its H-He gaseous envelope and that it will be completely lost at an age within 0.5-3Gyr if its current mass is lower than 12M_{Earth}_.

Furthermore, BD+40 2790c could have a lower bulk density than b and might be able to retain its atmosphere up to an age of 5Gyr. For the outermost object, planet d, we predicted an almost negligible evolution of its mass and radius, induced by photo-evaporation.