JWST observations of cosmic-ray-excited H$_2$ in Barnard 68: spatial variations and constraints on cosmic-ray attenuation

We present James Webb Space Telescope (JWST) NIRSpec observations of the starless dark cloud Barnard 68 that reveal the spatially-resolved signature of cosmic-ray excited molecular hydrogen (CRXH$_2$) emissions for the first time. Following up on our initial detection of CRXH$_2$ emissions from B68 (Bialy et al. 2025), we now exploit JWST's sensitivity and spatial multiplexing to map CRXH$_2$ rovibrational lines across 16 sight lines through the cloud. By disentangling the CRXH$_2$ and UV-pumped H$_2$ components, we isolate the para-H$_2$-dominated spectrum attributable to cosmic-ray excitation. We find that there are significant spatial variations in the ratio of the CRXH$_2$ line intensity to the line-of-sight H$_2$ column density; these cannot be accounted for by dust extinction alone and demonstrate a clear attenuation of the cosmic-ray flux with increasing shielding column. Modeling B68 as a Bonnor-Ebert sphere, we constrain both the unshielded cosmic-ray ionization rate, $ζ_{\rm H_2}$, and how it decreases with shielding column. At a reference depth of $N({\rm H}_2) = 3 \times 10^{21}$ cm$^{-2}$, we infer $ζ_{\rm H_2} \approx 1.4 \times 10^{-16}$ s$^{-1}$, a factor of $\approx 3$ higher than the average value derived from H$_3^+$ absorption studies. These results provide the most direct probe to date of cosmic-ray penetration into cold, dense gas, offering new constraints on both the microphysics of CR-H$_2$ interactions and the attenuation of low-energy cosmic rays in molecular clouds. Our findings establish CRXH$_2$ emission as a powerful new diagnostic of the cosmic-ray environment in interstellar space.