2023ApJ...946...91L

The cosmic-ray ionization rate (CRIR, ζ₂) is one of the key parameters controlling the formation and destruction of various molecules in molecular clouds. However, the current most commonly used CRIR tracers, such as ${{\rm{H}}}_{3}^{+}$, OH⁺, and H₂O⁺, are hard to detect and require the presence of background massive stars for absorption measurements. In this work, we propose an alternative method to infer the CRIR in diffuse clouds using the abundance ratios of OH/CO and HCO⁺/CO. We have analyzed the response of chemical abundances of CO, OH, and HCO⁺ on various environmental parameters of the interstellar medium in diffuse clouds and found that their abundances are proportional to ζ₂. Our analytic expressions give an excellent calculation of the abundance of OH for ζ₂ ≤ 10^–15 s^–1, which are potentially useful for modeling chemistry in hydrodynamical simulations. The abundances of OH and HCO⁺ were found to monotonically decrease with increasing density, while the CO abundance shows the opposite trend. With high-sensitivity absorption transitions of both CO (1-0) and (2-1) lines from Atacama Large Millimeter/submillimeter Array, we have derived the H₂ number densities (${n}_{{{\rm{H}}}_{2}}$) toward 4 lines of sight; assuming a kinetic temperature of T_k = 50 K, we find a range of (0.14 ± 0.03-1.2 ± 0.1) × 10² cm^–3. By comparing the observed and modeled HCO⁺/CO ratios, we find that ζ₂ in our diffuse gas sample is in the range of ${1.0}_{-1.0}^{+14.8}$ × 10${}^{-16}\mbox{--}{2.5}_{-2.4}^{+1.4}$ × 10^–15 s^–1. This is ∼2 times higher than the average value measured at higher extinction, supporting an attenuation of CRs as suggested by theoretical models.