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We report cosmic ray ionization rates towards ten reddened stars studiedwithin the framework of the EDIBLES (ESO Diffuse Interstellar Bands LargeExploration Survey) program, using the VLT-UVES. For each sightline, between 2and 10 individual rotational lines of OH$^+$ have been detected in its (0,0)and (1,0) $A^3\Pi-X^3\Sigma^-$ electronic band system. This allows constrainingof OH$^+$ column densities towards different objects. Results are alsopresented for 28 additional sightlines for which only one or rather weaksignals are found. An analysis of these data makes it possible to derive theprimary cosmic ray ionization rate $\zeta_p$ in the targeted diffuseinterstellar clouds. For the ten selected targets, we obtain a range of valuesfor $\zeta_p$ equal to $(3.9-16.4) \times 10^{-16}~\mathrm{s}^{-1}$. Thesevalues are higher than the numbers derived in previous detections ofinterstellar OH$^+$ in the far-infrared / sub-millimeter-wave regions and inother near-ultraviolet studies. This difference is a result of using new OH$^+$oscillator strength values and a more complete picture of all relevant OH$^+$formation and destruction routes (including the effect of proton recombinationson PAHs), and the relatively high $N$(OH$^+$) seen toward those ten targets.

The EDIBLES survey IV. Cosmic ray ionization rates in diffuse clouds from near-ultraviolet observations of interstellar OH$^+$