Fundamental effective temperature measurements for eclipsing binary stars -- VIII. NIRPS spectroscopy of CD-27 2812

There are very few M-dwarfs with accurate independent measurements of their mass, radius and effective temperature (T$_{\rm eff}$) that can be used to test stellar models for these low-mass stars. We aim to use high-resolution, near-infrared spectroscopy to measure the mass of M-dwarfs in eclipsing binary systems with solar-type stars and to measure the flux ratio between the two stars at near-infrared wavelengths. This information can then be combined with the analysis of the light curve, photometry, and the parallax to measure the mass, radius and T$_{\rm eff}$ for both stars. We have used the TESS light curve and spectra observed with the HARPS and NIRPS spectrographs to measure the following model-independent radii and masses for CD-27 2812, an F9 V star in an eclipsing binary with a much fainter M-dwarf companion on a short near-circular orbit (P=7.8 d) : $R_1 = 1.721 \pm 0.004 R_{\odot}$, $R_2 = 0.531 \pm 0.002 R_{\odot}$, $M_1 = 1.3597 \pm 0.0024 M_{\odot}$, and $M_2 = 0.5624 \pm 0.0006 M_{\odot}$ We show how the NIRPS spectra can be used to measure the flux ratio in the J and H bands. This information, combined with published photometry and the Gaia DR3 parallax, leads to the following effective temperature measurements: $T_{\rm eff,1} = 6197 \pm 55$ K, $T_{\rm eff,2} = 3770 \pm 28$ K. This study demonstrates that it is now feasible to use eclipsing binaries to accurately measure T$_{\rm eff}$ for M-dwarf stars for which we also have independent mass and radius measurements.