Absorption lines from the molecules OH ^ { + } , H _ { 2 } O ^ { + } , and H _ { 3 } ^ { + } have been observed in a diffuse molecular cloud along a line of sight near W51 IRS2 .
We present the first chemical analysis that combines the information provided by all three of these species .
Together , OH ^ { + } and H _ { 2 } O ^ { + } are used to determine the molecular hydrogen fraction in the outskirts of the observed cloud , as well as the cosmic-ray ionization rate of atomic hydrogen .
H _ { 3 } ^ { + } is used to infer the cosmic-ray ionization rate of H _ { 2 } in the molecular interior of the cloud , which we find to be \zeta _ { 2 } = ( 4.8 \pm 3.4 ) \times 10 ^ { -16 } s ^ { -1 } .
Combining the results from all three species we find an efficiency factor—defined as the ratio of the formation rate of OH ^ { + } to the cosmic-ray ionization rate of H—of \epsilon = 0.07 \pm 0.04 , much lower than predicted by chemical models .
This is an important step in the future use of OH ^ { + } and H _ { 2 } O ^ { + } on their own as tracers of the cosmic-ray ionization rate .