Constraints on the Cosmic-Ray Ionization Rate in the $z\sim2.3$ Lensed Galaxies SMM J2135$-$0102 and SDP 17b from Observations of OH$^+$ and H$_2$O

Cosmic rays are predominantly accelerated in shocks associated with star formation such as supernova remnants and stellar wind bubbles, so the cosmic-ray flux and thus cosmic-ray ionization rate, ζ H, should correlate with the star formation rate in a galaxy. Submillimeter bright galaxies (SMGs) are some of the most prolific star-forming galaxies in the universe, and gravitationally lensed SMGs provide bright continuum sources suitable for absorption line studies. Abundances of OH+ and H2O+ are useful for inferring ζ H when combined with chemical models, and have been used for this purpose within the Milky Way. At redshifts z ≳ 2 transitions out of the ground rotational states of OH+ and H2O+ are observable with ALMA, and we present observations of both molecules in absorption toward the lensed SMGs SMM J2135−0102 and SDP 17b. These detections enable an exploration of ζ H in galaxies with extreme star formation and high supernova rates, both of which should significantly enhance cosmic-ray production. The observed OH+ and H2O+ absorption is thought to arise in massive, extended halos of cool, diffuse gas that surround these galaxies. Using a chemical model designed to focus on the reaction network important to both species, we infer cosmic-ray ionization rates of ζ H ∼ 10−16–10−14 s−1 in these extended gaseous halos. Because our estimates come from gas that is far away from the sites of cosmic-ray acceleration, they imply that cosmic-ray ionization rates in the compact regions where star formation occurs in these galaxies are orders of magnitude higher.