New assignments of the CaH $A^{2}Π-X^{2}Σ^{+}$ transitions in the sunspot umbral spectrum and effective temperature estimation using molecular lines
High-resolution spectroscopy observations of sunspots offer a unique natural laboratory for detailed molecular spectroscopy. Calcium monohydride (CaH) is a vital spectroscopic tracer in cool stellar and solar environments, where its electronic transitions are used for line identification and temperature diagnostics, yet its high-excitation transitions remain poorly characterized. Using high-resolution sunspot umbral spectra obtained with the Brault Fourier-transform spectrometer at the McMath-Pierce telescope (Wallace et al. 1999), we investigated the $A^2Π\;-\;X^2Σ^+$ electronic transition of CaH in the $\rm{14400-14900\;cm^{-1}}$ region. We report the assignment of 224 spectral lines spanning vibrational bands with $v^{\prime}, v^{\prime\prime} = 0\text{-}3$; notably, 75 lines in the (3-3) band are reported here for the first time, and the identification of the remaining bands was extended to significantly higher rotational quantum numbers ($J\rm{ _{max}\approx 49.5}$) compared to previous studies. Incorporating these new identifications into spectral simulations that account for overlapping TiO features, we aimed to reproduce the observed umbral spectrum and found modest but measurable improvement in the agreement between the simulated and observed spectra. Minimizing the residuals between observed and simulated spectra, we estimated an effective umbral temperature range of around 4000 K. We compare this effective temperature against those inferred from independent methods to show that molecular features primarily form in the cool umbral cores of the sunspots. This study demonstrates the utility of solar observations in studying the high-energy transitions that are challenging to reproduce in laboratory settings and the potential of molecular lines as sensitive "thermometers" for cool astronomical objects.