Constraining the cosmic-ray ionization rate and their spectrum with NIR spectroscopy of dense clouds -- A test-bed for JWST

Low-energy cosmic-rays (CRs) control the thermo-chemical state and the coupling between gas and magnetic fields in dense molecular clouds, the sites of star-formation. However, current estimates of the low-energy CR spectrum ($E \lesssim 1$ GeV) and the associated CR ionization rate are highly uncertain. We apply for the first time, the new method recently proposed by Bialy (2020), in which H$_2$ rovibrational lines in cold molecular clouds are used to constrain the CR ionization rate and the CR spectral shape. Using the MMIRS instrument on the MMT, we obtained deep near-infrared (NIR) spectra in six positions within four dense cores, G150, G157, G163, G198, with column densities $N_{\rm H_2} \approx 10^{22}$ cm$^{-2}$. We derive 3$\sigma$ upper limits on the H$_2$ $(1-0)$S(0) line (2.22 $\mu$m) brightness in the range $I=4.5$ to $8.3 \times 10^{-8}$ erg cm$^{-2}$ s$^{-1}$ sr$^{-1}$. Using both an analytic model and a numerical model of CR propagation, we convert these into upper limits on the CR ionization rate in the clouds' interior, $\zeta=1.0$ to $2.6 \times 10^{-16}$, and lower limits on the low-energy spectral slope of interstellar CR protons, $\alpha=-0.87$ to $-0.67$. We show that while MMT was unable to detect the H$_2$ lines due to high atmospheric noise, JWST/NIRSpec will be able to efficiently detect the CR-excited H$_2$ lines, making it the ideal method for constraining the otherwise elusive low-energy CRs, shedding light on the sources and propagation modes of CRs.