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, a new method for constraining the CR ionization rate and the CR spectral shape using H$_2$ rovibrational lines from cold molecular clouds. 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 $I = 5.9 \times 10^{-8}$ to $1.2 \times 10^{-7}$ erg cm$^{-2}$ s$^{-1}$ sr$^{-1}$ for the different targets. 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, $\zeta = 1.5$ to $3.6 \times 10^{-16}$ s$^{-1}$, and lower limits on the low-energy spectral slope of interstellar CR protons, $\alpha = -0.97$ to $-0.79$. 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.