TOI-3288 b and TOI-4666 b: two gas giants transiting low-mass stars characterised by NIRPS

Gas giant planets orbiting low-mass stars are uncommon outcomes of planet formation. Increasing the sample of well-characterised giants around early M dwarfs will enable population-level studies of their properties, offering valuable insights into their formation and evolutionary histories. We aim to characterise giant exoplanets transiting M dwarfs identified by TESS. High-resolution spectroscopic data are obtained in the optical and nIR, combining HARPS and NIRPS. We derive RVs via the cross-correlation function and implement a novel post-processing procedure to further mitigate telluric contamination in the nIR. The resulting RVs are jointly fit with TESS and ground-based photometry to derive the orbital and physical parameters of the systems. We confirm two gas giants transiting the low-mass stars TOI-3288 A (K9V) and TOI-4666 (M2.5V). TOI-3288 A hosts a Hot Jupiter with a mass of $2.11\pm0.08~M_{\rm Jup}$ and a radius of $1.00 \pm 0.03~R_{\rm Jup}$, with an orbital period of 1.43 days ($T_{\rm eq} = 1059 \pm 20~{\rm K}$). TOI-4666 hosts a $0.70_{-0.06}^{+0.05}~M_{\rm Jup}$ warm Jupiter ($T_{\rm eq} = 713 \pm 14~{\rm K}$) with a radius of $1.11 \pm 0.04~R_{\rm Jup}$, and an orbital period of 2.91 days. We identify a decrease in planetary mass with spectral type, where late M dwarfs host less massive giant planets than early M dwarfs. More massive gas giants that deviate from this trend are preferentially hosted by more metal-rich stars. Furthermore, we find an increased binarity fraction among low-mass stars hosting gas giants, which may play a role in enhancing giant planet formation around low-mass stars. The observed population trends agree with theoretical expectations, where higher metallicity can compensate for lower disk masses, and wide binary systems may influence planet formation and migration through Kozai-Lidov cycles or disk instabilities.