Tracers of the ionization fraction in dense and translucent molecular gas: II. Using mm observations to constrain ionization fraction across Orion B

TL;DR

This study maps the ionization fraction $f_ ext{e}$ across the Orion B molecular cloud by combining IRAM 30 m mm-wave observations with analytical predictions for $f_ ext{e}$ based on line ratios. It distinguishes dense and translucent gas using $A_V$ and analyzes how $f_ ext{e}$ scales with gas density $n$ and the FUV field $G_0$, finding $f_ ext{e}\npropto n^{-0.227}$ in dense gas and $f_ ext{e} propto n^{-0.3}$ in translucent gas, with $f_ ext{e}$ increasing with $G_0/n$. The dense-gas tracers CN/N$_2$H$^+$, $^{13}$CO/HCO$^+$, and C$^{18}$O/HCO$^+$ yield upper and lower bounds on $f_ ext{e}$, while translucent-gas tracers such as C$_2$H/HNC (and related ratios) trace $f_ ext{e}$ effectively, consistent with the C$^+$/CI/CO transition in PDRs. The results show regional variation tied to local radiation fields and density, with implications for chemical networks and magnetic coupling, and provide practical tracer recommendations for mapping $f_ ext{e}$ across molecular clouds. Overall, the work demonstrates that mm-line ratios can robustly constrain ionization fractions across diverse ISM environments on cloud-wide scales.

Abstract

The ionization fraction ($f_\mathrm{e}=n_\mathrm{e}/n_\mathrm{H}$) is a crucial parameter of interstellar gas, yet estimating it requires deep knowledge of molecular gas chemistry and observations of specific lines, such as those from isotopologs like HCO$^+$ and N$_2$H$^+$, which are detectable only in dense cores. Previous challenges in constraining $f_\mathrm{e}$ over large areas stemmed from the limitations of observational tracers and chemical models. Recent models have identified molecular line ratios that can trace $f_\mathrm{e}$ in different environments within molecular clouds. In this study, we analyze various molecular lines in the 3-4 mm range to derive the ionization fraction across the Orion B giant molecular cloud. We focus on dense and translucent gas, exploring variations with gas density ($n$) and the far-ultraviolet (FUV) radiation field ($G_0$). Our findings show that the ionization fraction ranges from $10^{-5.5}$ to $10^{-4}$ in translucent gas and $10^{-8}$ to $10^{-6}$ in dense gas. Notably, $f_\mathrm{e}$ is sensitive to $G_0$ in dense, UV-illuminated regions, decreasing with increasing volume density ($f_\mathrm{e} \propto n^{-0.227}$ for dense and $f_\mathrm{e} \propto n^{-0.3}$ for translucent gas) and increasing with $G_0$. In translucent gas, differing line ratios yield consistent fe values, indicating the importance of electron excitation of HCN and HNC. For dense gas, we recommend using the CN(1-0)/N$_2$H$^+$(1-0) ratio for upper limits on fe and C$^{18}$O(1-0)/HCO$^+$(1-0) for lower limits. In translucent environments, CCH(1-0)/HNC(1-0) effectively traces $f_\mathrm{e}$. The higher fe values in translucent gas align with the C$^+$/CI/CO transition, while values in dense gas are adequate for coupling with the magnetic field.

Figures (19)

• Figure 1: The ratio of the strength of FUV radiation field and volume density ($G_0/n$) in Orion B, and the distribution of pixels in dense and translucent gas. In the top panel, we show $G_0/n$ at 40 arcseconds (0.08 pc at the distance of the source) across Orion B, where $G_0$ is in Habing's units and $n$ in units of cm$^{-3}$. Black contour corresponds to $^{13}$CO integrated intensity of 0.5 K km s$^{-1}$, indicating the boundaries of a GMC. Dashed contours correspond to values of $G_0/n$ of 1 cm$^3$ (orange) and 20 cm$^3$ (dark red). We divide Orion B in six different regions. The bottom panels show histograms of normalized distribution of pixels having specific dust extinction (left panel), mean volume density (left panel) and $G_0/n$ (right panel). Orange and purple shaded regions correspond to values of pixels from translucent and dense medium, respectively.
• Figure 2: Ionization fraction computed using the $W$(CN)/$W$(N$_2$H$^+$) ratio as a function of volume-weighted mean volume density, $n$. Contours correspond to the density of points of 1, 5, 25, 50, and 75 percent (from the most outer to the most inner contour). Colored dots are the binned trends of pixels from the different regions in Orion B (top panel of Fig. \ref{['fig:histograms']}). The error bars show the weighted standard deviation of the points within each bin.
• Figure 3: The same as in Fig. \ref{['fig:cn_n2hp_n']}, but here we show binned trend of all data points except for NGC 2024 region. The purple line shows the linear fit and its uncertainty.
• Figure 4: The same as in Fig. \ref{['fig:cn_n2hp_n']}, but $f_{\rm e}$ is shown as a function of $G_0/n$.
• Figure 5: Ionization fraction in dense gas derived from intensity ratios of CN and N$_2$H$^{+}$, $^{13}$CO and HCO$^{+}$ and C$^{18}$O and HCO$^{+}$ as a function of $G_0/n$ in six dense regions in Orion B. We show binned trends by $G_0/n$, and the errorbars correspond to the 25th and 75th percentiles.