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

TL;DR

The study uses H$_3^+$ as a direct tracer of the H$_2$ cosmic-ray ionization rate to map $\zeta({\rm H_2})$ in the local Galaxy. By combining high-resolution infrared spectroscopy with Gaia-derived 3D dust extinction maps and 3D-PDR modeling, the authors localize H$_3^+$ absorption to individual clouds within ~1 kpc and derive a mean ionization rate of $\zeta({\rm H_2}) = 5.3\times10^{-17}$ s$^{-1}$ with $\sigma = 2.5\times10^{-17}$ s$^{-1}$. They find regional uniformity over tens of parsecs but variations by factors up to ~5 on ~100 pc scales, indicating spatially smooth yet non-uniform Galactic ionization rates linked to proximity to particle-acceleration sites. The results align with a Voyager-like low-energy cosmic-ray spectrum and show consistency with revised gas-density estimates that reduce previous ionization-rate values. Overall, the work presents a sparsely sampled but spatially resolved map of local cosmic-ray ionization, highlighting regional structure and the need for expanded surveys to map Galactic-scale variations more robustly.

Abstract

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.

Figures (37)

• Figure 1: Spectra in the left panel are focused on the $R(1,1)^u$ and $R(1,0)$ transitions of H$_3^+$, while spectra in the right panel are focused on the $R(1,1)^l$ transition. All spectra are normalized, and have been shifted vertically for clarity. Dashed vertical lines above spectra mark the expected location of H$_3^+$ absorption, based on previous observations of absorption from different molecular and/or atomic species along these sight lines. All wavelengths have been shifted into the LSR frame. The large noise feature near 3.6676 $\mu$m is due to a strong atmospheric CH$_4$ absorption line. Orange shaded regions show the gaussian fits to the H$_3^+$ absorption lines. Spectra in the right panel lacking orange regions were not fit due to either high noise levels or known contamination of the $R(1,1)^l$ transition.
• Figure 2: Same as Figure \ref{['fig_h3p_spectra']}, but showing sight lines where H$_3^+$ absorption is not detected. Gaps in spectra indicate regions where high noise levels caused by strong atmospheric absorption have been masked out. The bottom five spectra are from VLT/CRIRES observations made in 2011-2012.
• Figure 3: The top panel shows a normalized spectrum of HD 149757 near the $A$-$X$(0,0) transition of CH at 4300.308 Å in black, observed using UVES at the VLT. The red curve is a fit to the CH absorption line. The bottom panel shows normalized spectra of HD 149757 near the $R(1,1)^u$, $R(1,0)$, and $R(1,1)^l$ transitions of H$_3^+$ in black, with spectra shifted in the vertical direction for clarity. Solid red curves show the gaussian fits with line center and line width fixed to the results of the CH fit, as described in Section \ref{['sect_spectral_analysis']}. Dashed red curves show the gaussian fits plus 1$\sigma$ uncertainties, and the integrated areas defined by the dashed curves correspond to the upper limits on equivalent widths given in Table \ref{['tbl_upperlimits']}.
• Figure 4: These panels compare the observed H$_2$ and H$_3^+$ column densities in a given sight line to column densities predicted by models of that sight line with different cosmic-ray ionization rates. There are two panels for each sight line, with the top panel showing H$_2$ and the bottom panel showing H$_3^+$. Horizontal red lines and blue shaded regions mark the observed column densities and 1$\sigma$ uncertainties. Blue circles connected by lines show the column densities returned by the model as a function of $\zeta({\rm H_2})$. In the bottom panel for each sight line, black circles mark the "corrected" H$_3^+$ column density, accounting for the difference between observed and predicted H$_2$ column density as described in Section \ref{['sec_sim3DPDR']}. The intersection of the black curve and red line marks the inferred cosmic-ray ionization rate for each cloud, and is the value reported in Table \ref{['tbl_zeta']}. Note that for HD 281159 (top row, second panel) the simulation is for the cloud at $\sim300$ pc, and it assumes a contribution to the total H$_3^+$ column density from the cloud at $\sim150$ pc equal to that measured in the nearby HD 23180 sight line (see Section \ref{['sec_sim3DPDR']}). This is why the modeled $N({\rm H_3^+})$ for HD 281159 approaches the observed HD 23180 $N({\rm H_3^+})$ as the cosmic-ray ionization rate (in the far cloud) approaches zero.
• Figure 5: The left panel compares cosmic-ray ionization rates inferred from equation (\ref{['eq_crir']}) using gas densities derived from C$_2$ to those inferred using the 3D-PDR model. The center panel compares cosmic-ray ionization rates inferred from equation (\ref{['eq_crir']}) using peak gas densities derived from the edenhofer2024 differential extinction map to those inferred using the 3D-PDR model. The right panel is the ratio of the ionization rates in the left panel as a function of distance to the gas cloud. Filled circles are from obolentseva2024 while filled diamonds are from this work. The dashed red diagonal lines indicate a one-to-one correlation.