The SPHINX M-dwarf Spectral Grid. I. Benchmarking New Model Atmospheres to Derive Fundamental M-dwarf Properties

About 70%-80% of stars in our solar and Galactic neighborhood are M dwarfs. They span a range of low masses and temperatures relative to solar-type stars, facilitating molecule formation throughout their atmospheres. Standard stellar atmosphere models primarily designed for FGK stars face challenges when characterizing broadband molecular features in spectra of cool stars. Here, we introduce SPHINX—a new 1D self-consistent radiative-convective thermochemical equilibrium chemistry model grid of atmospheres and spectra for M dwarfs in low resolution (R ∼ 250). We incorporate the latest precomputed absorption cross sections with pressure broadening for key molecules dominant in late-K, early/main-sequence-M stars. We then validate our grid models by determining fundamental properties (T _eff, log g, [M/H], radius, and C/O) for 10 benchmark M+G binary stars with known host metallicities and 10 M dwarfs with interferometrically measured angular diameters. Incorporating the Gaussian process inference tool Starfish, we account for correlated and systematic noise in low-resolution (spectral stitching of SpeX, SNIFS, and STIS) observations and derive robust estimates of fundamental M-dwarf atmospheric parameters. Additionally, we assess the influence of photospheric heterogeneity on inferred [M/H] and find that it could explain some deviations from observations. We also probe whether the adopted convective mixing length parameter influences inferred radii, effective temperature, and [M/H] and again find that may explain discrepancies between interferometric observations and model-derived parameters for cooler M dwarfs. Mainly, we show the unique strength in leveraging broadband molecular absorption features occurring in low-resolution M dwarf spectra and demonstrate the ability to improve constraints on fundamental properties of exoplanet hosts and brown-dwarf companions.