H$_2$ Ortho-Para Spin Conversion on Inhomogeneous Grain Surfaces. II. impact of the rotational energy difference between adsorbed ortho-H$_2$ and para-H$_2$ and implication to deuterium fractionation chemistry

TL;DR

This work analyzes how H$_2$ ortho-to-para conversion on dust grains (NSC on grains) and the rotational energy difference between adsorbed ortho- and para-H$_2$ influence deuterium chemistry in star-forming environments. By treating the surface energy gap $\Delta E_{ m op,s}$ as a free parameter and implementing a multi-site, three-phase model, the study shows that NSC on grains can substantially shorten the H$_2$ OPR evolution timescale at $n_{ m gas} \gtrsim 10^4$ cm$^{-3}$ and $T \lesssim 14$--$16$ K, thereby enhancing deuterium fractionation in prestellar cores and outer protostellar envelopes. Importantly, the steady-state H$_2$ OPR is only weakly sensitive to $\Delta E_{ m op,s}$ because competing surface- and gas-phase effects largely cancel; the main impact is on the approach to steady state. Integrating NSC on grains into the Rokko gas–ice astrochemical model elevates deuteration of H$_3^+$ isotopologues and reduces the dependence on initial H$_2$ OPR, producing results that better align with observed H$_2$D$^+$ OPRs in protostellar environments and offering refined insights into the link between interstellar H$_2$ spin states and molecular deuterium enrichment.

Abstract

We investigate how the H$_2$ ortho-to-para ratio (OPR) and dueterium fractionation in star-forming regions are affected by nuclear spin conversion (NSC) on dust grains. Particular focus is placed on the rotational energy difference between ortho-H$_2$ (o-H$_2$) and para-H$_2$ (p-H$_2$) on grain surfaces. While the ground state of o-H$_2$ has a higher rotational energy than that of p-H$_2$ by 170.5 K in the gas phase, this energy difference is expected to become smaller on solid surfaces, where interactions between the surface and adsorbed H$_2$ molecules affect their rotational motion. A previous study by Furuya et al. (2019) developed a rigorous formulation of the rate for the temporal variation of the H$_2$ OPR via the NSC on grains, assuming that adsorbed o-H$_2$ has higher rotational energy than adsorbed p-H$_2$ by 170.5 K, as in the gas phase. In this work, we relax the assumption and re-evaluate the rate, varying the rotational energy difference between their ground states. The re-evaluated rate is incorporated into a gas-ice astrochemical model to study the evolution of the H$_2$ OPR and the deuterium fractionation in prestellar cores and the outer, cold regions of protostellar envelopes. The inclusion of the NSC on grains reduces the timescale of the H2 OPR evolution and thus the deuterium fractionation, at densities of >10$^4$ cm$^{-3}$ and temperatures of <14-16 K (depending on the rotational energy difference), when the ionization rate of H$_2$ is 10$^{-17}$ s$^{-1}$.

Figures (9)

• Figure 1: The steady-state value of the H2D+/H3+ abundance ratio as functions of the gas temperature, varying in the H2 OPR in the range between 10$^{-7}$ and 3 (solid lines). Dashed lines show the H2D+/H3+ ratio assuming a thermalized value for the H2 OPR. i.e., $9\exp(-170.5/T_g)$. The gas-phase CO abundance is assumed to be zero in the left panel, while it is assumed to be 10$^{-4}$ in the right panel. These two cases correspond to the minimum and maximum limits of CO abundance, and in reality, the CO abundance would fall between these extremes.
• Figure 2: Energy level diagram for p-H2 ($J=0$) and o-H2 ($J=1$) rotational states in the gas phase and on solid surfaces when the surface potential is given by $V(z,\theta)=V_0(z)+V_2P_2(\cos \theta)$, where $P_2(\cos \theta)$ is the second order Legendre polynomial, and $V_0(z)$ and $V_2$ are the isotropic surface potential and the degree of anisotropy, respectively. The number of lines in each level means the rotational degeneracy. Schematic illustrations show the probability distribution of the molecular axis for the respective states, $|Y_{0,0}|^2$, $|Y_{1,0}|^2$, $|Y_{1,1}|^2$, and $|Y_{1,-1}|^2$, where $Y_{J,m}$ is the spherical harmonics. See Appendix for more details.
• Figure 3: Temporal evolution of the H2 OPR in the gas phase, on the surface, and in desorbing gas from the surface. Dashed lines show the model with $\Delta E_{\rm op,\,s} = 170.5$ K, while solid lines show the model with $\Delta E_{\rm op,\,s} = 85$ K. The H2 gas density is 10$^4$ cm$^{-3}$ in top panels, while it is 10$^6$ cm$^{-3}$ in lower panels. The temperature is from 10 K, 14 K, and 16 K in the left, middle, and right panels, respectively. Note that in the model with $\Delta E_{\rm op,\,s} = 170.5$ K, the OPRs on the surface and in the desorbing gas are similar, and the lines for them are partially overlapping in the figure. Arrows on the right margin indicate $6\exp(-170.5/T)$ (black) and $\gamma_s$ (blue).
• Figure 4: The parameter $\eta_{\rm op}$ as functions of the temperature in the case when $\Delta E_{\rm op,\,s} = 170.5$ K (blue), and $\Delta E_{\rm op,\,s} = 120$ K (orange), and $\Delta E_{\rm op,\,s} = 120$ K (green). As the density dependence of $\eta_{\rm op}$ is very weak, the values only at the H2 density of 10$^4$ cm$^{-3}$ are plotted here.
• Figure 5: Conversion timescale of o-H2 to p-H2 via the NSC on grain surfaces when $\Delta E_{\rm op,\,s}=170.5$ K (red solid lines) and when $\Delta E_{\rm op,\,s}=85$ K (red dashed lines) as functions of the gas density. Black solid line indicates the free-fall timescale ($\tau_{\rm ff}$). The blue area indicates the conversion timescale of o-H2 to p-H2 via the gas-phase proton exchange reaction with the upper and lower ends corresponding to the CO abundance of 10$^{-4}$ and 10$^{-6}$, respectively. The blue solid line indicates the case when the CO abundance is given by 10$^{-4}\exp(-\tau_{\rm ff}/\tau_{\rm freeze})$, where $\tau_{\rm freeze}$ is the freeze-out timescale of CO onto dust grains, with the minimum CO abundance of 10$^{-6}$. Gas and dust temperatures are the same and assumed to be 10 K, 14 K, and 16 K in the left, middle, and right panels, respectively.