Mapping the Cosmic-Ray Ionization Rate in the Local Galaxy with H$_3^+$

Chemistry in diffuse molecular clouds relies primarily on rapid ion-molecule reactions. Formation of the initial ions, H$^+$ and H$_2^+$, is dominated by cosmic-ray ionization of H and H$_2$, making the cosmic-ray ionization rate (denoted $ζ({\rm X})$ for species X) an important parameter for chemical modeling. We have made observations targeting absorption lines of H$_3^+$, one of the most reliable tracers of $ζ({\rm H_2})$, toward diffuse molecular cloud sight lines where the H$_2$ column density has been directly measured in the ultraviolet, detecting H$_3^+$ in 12 out of 27 sight lines. The 3D-PDR modeling method introduced by Obolentseva et al. (2024) was used to infer cosmic-ray ionization rates in the clouds along these sight lines, and our combined sample has a mean ionization rate of $5.3\times10^{-17}$ s$^{-1}$ with standard deviation $2.5\times10^{-17}$ s$^{-1}$. By associating H$_3^+$ absorption with gas density peaks derived from the differential extinction maps of Edenhofer et al. (2024) we have constructed a sparsely sampled 3D map of the cosmic-ray ionization rate in targeted regions within about 1~kpc of the Sun. Specific regions show reasonably uniform ionization rates over length scales of tens of parsecs, with the average ionization rate in each region being different. Large differences (factor of 5) in $ζ({\rm H_2})$ are found over length scales of about 100 pc. This supports a picture where the cosmic-ray ionization rate varies smoothly over small size scales, but is not uniform everywhere in the Galactic disk, likely being controlled by proximity to particle acceleration sites.

💡 Research Summary

This paper presents a comprehensive study of the cosmic‑ray ionization rate of molecular hydrogen, ζ(H₂), in the local interstellar medium using H₃⁺ absorption as a direct tracer. The authors selected 27 diffuse molecular cloud sight lines for which the H₂ column density has been measured from ultraviolet absorption. High‑resolution infrared spectra were obtained with the iSHELL spectrograph on NASA’s Infrared Telescope Facility (R≈80,000) and with CRIRES on the Very Large Telescope (R≈100,000), covering the four strongest H₃⁺ transitions near 3.7–3.9 µm. After rigorous data reduction—including flat‑fielding, wavelength calibration with atmospheric lines, telluric correction, and combination of multiple nights—the authors detected clear H₃⁺ absorption in 12 sight lines (R(1,1)ᵤ and R(1,0) in all twelve, R(1,1)ₗ in eight, and Q(1,1) only in one).

Each line was fitted with a Gaussian profile to obtain equivalent widths, central velocities, and line widths. Column densities for the (J,K) = (1,0) (ortho) and (1,1) (para) levels were derived using the standard optically‑thin relation, and the total H₃⁺ column was taken as the sum of these two states. For non‑detections, upper limits were set by using CH λ4300 Å absorption profiles as velocity templates, following the method of Obolentsev et al. (2024).

The chemistry of H₃⁺ in diffuse clouds is simple: cosmic‑ray ionization of H₂ produces H₂⁺, which reacts rapidly with H₂ to form H₃⁺; H₃⁺ is destroyed mainly by dissociative recombination with electrons. Assuming steady‑state, constant density, and co‑location of H₂ and H₃⁺, the ionization rate can be expressed analytically as

 ζ(H₂) = kₑ xₑ n_H N(H₃⁺)/N(H₂),

where kₑ is the recombination rate coefficient, xₑ the electron fraction, n_H the total hydrogen nuclei density, and N the observed column densities. This simple estimate agrees within a factor of two with full 1‑D chemical models (Neufeld & Wolfire 2017) and with the more sophisticated 3D‑PDR modeling described below.

To obtain spatially resolved ζ(H₂) values, the authors employed the 3D‑PDR code (Bisbas et al. 2012) together with the differential extinction maps of Edenhofer et al. (2024), which provide 3‑D dust‑derived gas density distributions out to ~1 kpc. The conversion from extinction gradient to hydrogen density follows n_H = 1710 (dE_GRZ/ds) cm⁻³, as used in previous work. For each sight line, the authors extracted a 1‑D density profile along the line of sight and constructed a 3‑D cloud model that reproduces the observed H₃⁺ and H₂ columns. Bayesian inference was used to adjust the cosmic‑ray ionization rate until the model column densities matched the observations.

Nine sight lines (HD 23180, HD 281159, HD 170740, HD 179406, HD 203374, HD 206165, HD 206267, HD 207198, HD 224151) plus HD 27778 (from Albertsson et al. 2014) satisfied all requirements for full 3D‑PDR treatment. The resulting ζ(H₂) values span (1–9) × 10⁻¹⁷ s⁻¹, with a mean of 5.3 × 10⁻¹⁷ s⁻¹ and a standard deviation of 2.5 × 10⁻¹⁷ s⁻¹. This mean is an order of magnitude lower than earlier H₃⁺ surveys (≈3.5 × 10⁻¹⁶ s⁻¹) because the newer density estimates from Gaia‑based extinction maps are higher, reducing the inferred ionization rate for a given H₃⁺ column.

Mapping the derived ζ(H₂) values onto the 3‑D density structure reveals that within individual regions the ionization rate is remarkably uniform over tens of parsecs, but systematic differences of up to a factor of five appear when comparing regions separated by ~100 pc. The authors interpret this as evidence that local cosmic‑ray flux is modulated by proximity to particle acceleration sites (e.g., recent supernova remnants, pulsar wind nebulae). The smooth variation on small scales suggests efficient diffusion, while the larger‑scale gradients point to spatially varying source contributions and possible magnetic‑field guided transport.

In summary, the paper introduces a novel workflow that combines high‑resolution H₃⁺ spectroscopy, CH‑based velocity templates, 3D‑PDR modeling, and Gaia‑derived extinction maps to produce the first sparsely sampled three‑dimensional map of the cosmic‑ray ionization rate within ~1 kpc of the Sun. The results refine the canonical ζ(H₂) value for the local diffuse ISM, demonstrate significant regional variations, and provide observational constraints for models of cosmic‑ray propagation and interstellar chemistry. Future extensions with a larger sample of sight lines and inclusion of denser cloud environments will further elucidate the interplay between cosmic‑ray sources, transport mechanisms, and the chemical state of the Galaxy’s interstellar medium.