A temperate sub-Neptune transiting the M4 Dwarf TOI-210 identified by NIRPS and TESS -- Uncovering hidden M-dwarf planetary systems in the near-infrared
Super-Earths and sub-Neptunes dominate the exoplanet population, yet their compositions, formation mechanisms, and capability of retaining atmospheres remain poorly understood. M-type stars offer a unique opportunity to investigate these questions, thanks to their favorable planet-to-star radius and mass ratios and the diversity of planetary systems they host. We aim to characterise the planetary system of the M4 dwarf TOI-210, in which TESS during its primary mission identified one transiting exoplanet candidate at $P= 9.01$ days. We combine multi-technique observations, including transits from 40 sectors of TESS and ground-based follow-up with LCOGT and ExTrA, and radial velocities (RV) from NIRPS obtained as part of its Guaranteed Time Observations program. These data were analysed using a Bayesian framework to constrain stellar, planetary, and orbital parameters. We confirm TOI-210 b, a temperate sub-Neptune ($T_{\rm eq} = 368 \pm 9$ K) with a mass of 6.75 $\pm$ 1.25 M$_{\oplus}$ and a radius of 2.234 $\pm$ 0.074 R$_{\oplus}$. Its bulk density implies a volatile-rich composition, either as an extended H/He atmosphere with mass fraction of approximately 1% (gas dwarf), a substantial water reservoir comprising at least 29% of the mass (2$σ$ lower limit; water world), or a mixture of both. The NIRPS RVs show moderate evidence ($Δ\ln Z = 5.9$) for at least one non-transiting exoplanet interior to TOI-210 b. In a targeted search, we identify two Keplerian signals at 2.15 and 3.76 days, with minimum masses of 3.2 $\pm$ 0.8 M$_{\oplus}$ and 4.4 $\pm$ 1.0 M$_{\oplus}$, respectively, that provide a plausible explanation for the observed RV variations. If these signals are planets, the absence of transits in the TESS photometry implies mutual inclinations with TOI-210 b above 2.3-3.5$^{\circ}$.