The SPHINX M dwarf Spectral Grid. II. New Model Atmospheres and Spectra to Derive Fundamental Properties of mid-to-late type M-dwarfs

Abstract

M-dwarfs are the most dominant stars in the Galaxy. Their interiors and atmospheres exhibit complex processes including dust condensation, convective feedback, and magnetic activity-driven heterogeneity. Standard stellar characterization methods often struggle to capture these coupled effects. Part I of this series introduced SPHINX I, a validated grid of self-consistent radiative-convective model atmospheres and spectra for M-dwarfs with up-to-date molecular opacities suitable for early-to-mid M-dwarfs. Here, we present SPHINX II, which extends the model grid to cover mid-to-late type M-dwarfs, including both gray and physically motivated condensate cloud treatments and shorter convective mixing lengths. We validate SPHINX II using 39 benchmark FGK+M binary systems observed with SpeX IRTF (Mann et al. 2014) and apply it to 32 mid-to-late-type M-dwarfs from the SpeX Prism Library. SPHINX II yields improved fits that are statistically consistent with empirical benchmarks, achieving precisions of 0.078 dex in metallicity and 0.13 dex in C/O. Across the model grid, condensate cloud mass peaks between 2100-2400 K, decreasing sharply toward both cooler and hotter temperatures. We find the onset of the cloud-free regime around 2900 K, and below 2100 K, we see formation of deep/buried clouds. As a case study, we also model Trappist-1 and show that even mass-limited silicate grains subtly modify its emergent spectrum, suppressing near-infrared flux and reddening the mid-infrared slope via shallow cloud formation near 1e-2 bar. In sum, SPHINX II provides an improved framework for constraining the fundamental properties of mid-to-late M-dwarfs.

Figures (23)

• Figure 1: Schematic illustration of clouds, convection, and radiative transfer in a mid-to-late-type (T$_\mathrm{eff}$$\sim$ 2000–2900 K) M-dwarf atmosphere. The solid black curve shows a representative temperature–pressure (T-P) profile. Orange shading marks the radiative zone, blue shading the convective envelope, and the dashed black line denotes the radiative–convective (R-C) boundary. The solid black double-headed arrow indicates the approximate observable photosphere ($\tau \sim$ 1), from which emergent flux across optical (0.4-0.9$\mu$m), NIR (1-2.5 $\mu$m), and MIR (3-8 $\mu$m) arises. Purple (MgSiO$_3$), yellow (Mg$_2$SiO$_4$), and green (CaTiO$_3$) dashed curves show condensation boundaries for major silicates and titanates, with the shaded "Condensates" region marking the expected cloud-forming zone near 10$^{-1}$ bar. Upward arrows denote convective and radiative energy transport, while the orange bar ("LW Heating Zone") indicates layers influenced by long-wavelength radiative heating. Even when the cloud deck lies just below the $\tau \sim$ 1 surface, its additional opacity raises the effective photosphere to cooler layers and smooths the near- and mid-infrared continuum, producing the flux suppression and reddening characteristic of late-M dwarfs.
• Figure 4: Representative spectral fits comparing SPHINX II cloudy and SPHINX I cloud-free models. (Left) A SpeX Prism Library late-type M-dwarf (2MASS J03023398--1028223). (Right) A benchmark FGK+M companion from mann2014prospecting (2M0739+1305). Black points show observed spectra, with error bars where visible. Red curves denote cloud-free SPHINX I models with $\alpha = 1$, while blue curves include a minimal gray cloud opacity SPHINX II models ($\log \kappa = -29$) and reduced mixing length $\alpha = 0.5$. Residuals are plotted below each spectrum. The cloudy, low-$\alpha$ model improves near-infrared slopes and yields metallicities consistent with FGK primaries, whereas the cloud-free case tends to bias metallicity high.
• Figure 5: Model Inferred metallicities and C/O values for all M-dwarfs in the SpeX Database burgasser2014spex sample. We also overlay our results from part I iyer2023sphinx with values inferred for WBS + IS early-M-type targets. (Left) all targets were fitted using our fiducial SPHINX I model including cloud-free atmospheres and mixing-length value $\alpha$=1. (Right) we show fits for the same using the upgraded SPHINX II models with a fixed minimal gray cloud opacity (log$\kappa$=-29) and lower mixing-length value of convection ($\alpha$=0.5). The right panel shows how the model upgrades yield comparable [M/H] values that are more consistent with neighborhood FGK-type stars as taken from the Hypatia Catalog hinkel2014 shown in gray.
• Figure 6: Model Inferred metallicities compared to empirically derived [M/H] values from mann2014prospecting for FGKM+companion mid-to-late M-dwarfs from table \ref{['manndatatable']}. Here we show that both empirical- and model-derived values are strongly consistent with a linear function with a slope of 1.1 and intercept of 0.03 with a p-value of 1e-9. Therefore, we validate our SPHINX II model against these benchmark mid-to-late type M-dwarfs with a scatter of 0.078 dex in SPHINX II derived [M/H], consistent with the empirically calibrated values.
• Figure 7: Best fits to potentially young SpeX target 2MASSJ00013044+1010146 using four models: cloud-free + $\alpha$=1 (red), gray cloud with log $\kappa$=-29 + $\alpha$=1 (yellow), gray cloud + $\alpha$=0.5 (blue), and starspot-parameterized cloud-free + $\alpha$=1 (green). While all achieve residuals below 20% in the 0.8–2.4 $\mu$m range, the BIC strongly favors the blue (SPHINX II) and green (SPHINX II with spots) models (by $\sim$3 dex).