Collisional rate coefficients for OH-H$_2$ at high temperatures

TL;DR

This work addresses the need for reliable OH–H$_2$ collisional rate coefficients at high rotational levels and temperatures by performing close-coupling quantum scattering calculations for OH colliding with para- and ortho-H$_2$ up to $j_{ m OH}=15/2$ and $T=750$ K, using the RCCSD(T)-F12a-based Ma et al. potential. The authors compute state-to-state de-excitation cross sections for energies up to $1700~\mathrm{cm}^{-1}$ and obtain Maxwellian-averaged rate coefficients, validating convergence and employing a scaling approach to extrapolate to higher OH levels; results indicate larger rates for oH$_2$ than pH$_2$ due to the H$_2$ quadrupole moment, and reveal resonances and energy-gap dependencies that enable robust extrapolation with uncertainties around a factor of $5$. A key methodological contribution is the empirical Proca–Levine-type scaling $k_{ij}(T) = A(T) g_j \, \exp\left(-\Theta_R(T) \Delta E_{ij} / (k_B T)\right)$, applied separately to different transition classes to extend the dataset to higher $j_{ m OH}$ states. The dataset enhances non-LTE OH excitation modeling in warm interstellar and circumstellar environments and, through an illustrative GROSBETA model, demonstrates that collisions with H$_2$ dominate low-$j$ OH populations under typical warm, dense conditions, with chemical pumping mainly affecting higher-$j$ lines shortward of ~35 μm. All rate coefficients are publicly available in the LAMDA database, facilitating more accurate interpretation of JWST/MIRI OH observations and improving constraints on physical conditions in shocks, disks, and PDRs.

Abstract

OH is a cornerstone molecule in the chemistry of interstellar and circumstellar media and is ubiquitously detected in warm gas thanks to its infrared rotational lines. However, the excitation processes of OH remain poorly characterized. We provide a new set of collisional rate coefficients for OH with H$_2$, expanding the existing data to $j$ levels up to $j=15/2$ and temperatures up to 750 K. These rate coefficients are obtained from state-to-state collision cross sections calculated by means of well-converged close-coupling quantum scattering calculations for collisions of OH with para- and ortho-H$_2$ with energies up to 1700 cm$^{-1}$ ($\simeq 2450$ K). We reproduce the rate coefficients computed by Klos et al. (2017) and extend their results to higher temperatures and higher rotational levels of OH. The de-excitation rate coefficients are lower in collisions with para-H$_2$ ($j_{\rm H_2} = 0$) due to the absence of a quadrupole moment, but this difference decreases at higher temperatures. We find that the rate coefficients follow scaling relations with the energy gap between the upper and lower levels of a given transition, which allows extrapolation to higher OH rotational states $j_{\rm OH}$. As a first application, we show that under astrophysical conditions typical of warm and dense gas around nascent stars, the populations of low-$j_{\rm OH}$ states are dominated by collisions, even when chemical pumping is included. The full set of rate coefficients is made available in the LAMDA database.

Figures (6)

• Figure 1: Cross sections of OH transitions from the $F_1$ state with $j=7/2$ and parity $p=+1$ (spectroscopic parity $f$) [panels (a) and (b)] and from the $F_2$ state with $j=5/2$ and parity $p=-1$ (spectroscopic parity $f$) [panels (c) and (d)] to all lower OH levels. H$_2$ is assumed to be initially in $j=0$ for pH$_2$ and in $j=1$ for oH$_2$ and the cross sections are summed over all final states of pH$_2$ and oH$_2$, respectively. Panels (a) and (c) refer to collisions with pH$_2$, panels (b) and (d) to collisions with oH$_2$. The final states of OH are listed in order of increasing energy.
• Figure 2: Rate coefficients of OH collisions with para- and ortho-H$_2$ for the same OH transitions of which the cross sections are shown in Fig. \ref{['fig:cross']}. Panels (a), (b), (c), and (d) refer to the same transitions as in Fig. \ref{['fig:cross']}.
• Figure 3: Collisional rate coefficients normalized by the degeneracy of the lower levels at $T_K=500$ K as a function of the energy gap $\Delta E_{ij}$ between the upper and the lower state of the transition. Transitions occurring within a single $N$ state are shown as gray dots. Parity-conserving and parity-changing transitions are plotted as red and blue dots, respectively. The straight lines are fits to the parity-conserving (red) and parity-changing (blue) transitions using Eq. (\ref{['eq:ProccaLevine']}) as an ansatz and excluding $\Delta N=0$ transitions. For parity-changing transitions with pH$_2$, we restricted the fit to $\Delta E_{ij} > 510~$K.
• Figure 4: Collisional rate coefficients at a kinetic temperature of 500 K as a function of the $N$ rotational number for the $\Delta N = 0$ collision-induced transitions. These transitions correspond to the lower energy gap, and their rate coefficients do not follow the correlation observed in Fig. \ref{['fig:rate_coeff_scalings']} (see gray dots).
• Figure 5: Synthetic spectra of OH computed with GROSBETA at a spectral resolving power of $\lambda/\Delta \lambda=3000$ assuming an unresolved emission of size $\pi (10~\text{au})^2$ at 140 pc (see text for the other parameters). The red spectrum corresponds to a case where both chemical pumping and collision with H$_2$ are included. The blue spectrum neglects chemical pumping. The similarity of the spectra at long wavelength indicates that collisions with H$_2$ dominate over chemical pumping for $j \lesssim 15/2$. The upper rotational number $N$ is labelled for the pure rotational transition $\Delta N = 1$.