Characterisation of TOI-406 as showcase of the THIRSTEE program: A 2-planet system straddling the M-dwarf density gap

The exoplanet sub-Neptune population currently poses a conundrum, as to whether small-size planets are volatile-rich cores without an atmosphere, or rocky cores surrounded by a H-He envelope. To test the different hypotheses from an observational point of view, a large sample of small-size planets with precise mass and radius measurements is the first step. On top of that, much more information will likely be needed, including atmospheric characterisation and a demographic perspective on their bulk properties. We present here the concept and strategy of the THIRSTEE project, which aims to shed light on the composition of the sub-Neptune population across stellar types by increasing their number and improving the accuracy of bulk density measurements, as well as investigating their atmospheres and performing statistical, demographic analysis. We report the first results of the program, characterising a new two-planet system around the M-dwarf TOI-406. We analyse TESS and ground-based photometry, together with ESPRESSO and NIRPS/HARPS RVs to derive the orbital parameters and investigate the internal composition of the 2 planets orbiting TOI-406, which have radii and masses of $R_c = 1.32 \pm 0.12 R_{\oplus}$, $M_c = 2.08_{-0.22}^{+0.23} M_{\oplus}$ and $R_b = 2.08_{-0.15}^{+0.16} R_{\oplus}$, $M_b = 6.57_{-0.90}^{+1.00} M_{\oplus}$, and periods of $3.3$ and $13.2$ days, respectively. Planet c is consistent with an Earth-like composition, while planet b is compatible with multiple internal composition models, including volatile-rich planets without H/He atmospheres. The 2 planets are located in 2 distinct regions in the mass-density diagram, supporting the existence of a density gap among small exoplanets around M dwarfs. With an T$_{\rm eq}$ of only 368 K, TOI-406 b stands up as a particularly interesting target for atmospheric characterisation with JWST in the low-temperature regime.