Title:Empirical H- and K-band Limb Darkening for 31 CHARA Stars: A Near-Infrared Benchmark for Stellar-Atmosphere Models

Abstract:Limb darkening, the decrease in stellar intensity from the disk center to the limb, encodes the temperature structure and opacity of stellar atmospheres. Direct spatially resolved measurements of this center-to-limb variation remain scarce, especially in the near-infrared. We present interferometric limb-darkening measurements for 31 stars observed simultaneously in the $H$ and $K$ bands with the CHARA Array. The sample spans spectral types F--M and luminosity classes IV--I. The targets are well resolved in $H$ and, for most targets, also in $K$. This coverage constrains the visibility curvature associated with limb darkening in joint $H+K$ fits. We fit the combined $H{+}K$ squared visibilities with four analytic limb-darkening laws and compare the resulting coefficients with bandpass-matched predictions from five stellar-atmosphere grids (Kurucz, MPS1, MPS2, Stagger, and spherical SATLAS, with reported coefficients placed on the Rosseland-radius convention) spanning one-dimensional plane-parallel, three-dimensional radiation--hydrodynamic, and spherical low-gravity models. The associated limb-darkened angular diameters are measured with median formal precisions of $\simeq 0.2$--0.3\%. The CHARA results show expected weaker limb darkening at longer wavelengths and also with increasing $T_{\rm eff}$. The clearest discrepancy with the atmosphere grids is in the wavelength dependence: the median fractional decrease in the power-law coefficient from $H$ to $K$ is $\simeq 39\%$ in the CHARA sample, compared with only $\simeq 17$--$22\%$ with model predictions. Relative to the MPS2 comparison, the empirical coefficients are higher by $\simeq 21\%$ in $H$ and lower by $\simeq 5\%$ in $K$. These results provide multi-band interferometric limb darkening as a near-infrared benchmark for stellar-atmosphere models.