An Alternate Pathway for H$_2$ Formation in the Early Universe: A physical process to account for the presence and coevolution of the luminous galaxies and supermassive black holes at the high redshifts

Abstract

Molecular hydrogen (H$_2$) and hydrogen deuteride (HD) are key coolants in primordial gas and regulate the formation of the first stars and proto-galaxies. Recent results from the James Webb Space Telescope provide striking insights into galaxies detected at high redshifts, which are found to be significantly more abundant and luminous than expected from galaxy formation models, thus suggesting a gap in our understanding of the early Universe. Standard pathways for H$_2$ formation in the early Universe proceed through the H$^-$ and H$_2^+$ intermediates, both of which are strongly suppressed at high redshift by the cosmic microwave background. We propose an additional pathway for H2 and HD formation that could be active as early as the end of the epoch of recombination and could enable the formation of the first stars earlier than the current prediction at redshift z ~ 30 - 20. The proposed pathway relies on the manifestation of Jahn-Teller dynamical coupling between electronic states of H$_3^+$. This coupling induces transient three-body recombination in H$^+$, H and H, and charge exchange within the charged atom-dimer complex that directly creates ground-state H$_2$ (and HD), bypassing the fragile intermediates that limit the standard primordial pathways. Our analysis shows that this mechanism could occur under the thermodynamic conditions of the post-recombination epoch, also suggesting that it might be playing a role in the active galactic nuclei feedback processes, regulating the formation rates of the first stars and the accretion rates of the first black holes. Though the global impact on galaxy formation and black-hole growth is not yet determined and will require quantitative assessment in future modeling, the mechanism offers an additional chemical route for H$_2$ and HD formation, with substantial cosmological relevance for primordial chemistry and early structure formation.

Figures (8)

• Figure 1: $\vert$Jahn-Teller coupling in H$_3^+$ states. (a) Schematic diagram of two hydrogen atoms, H$(1s)$, and a H$^+$ ion, interacting in a three-body collision via Coulomb forces. (b) Equilateral triangle geometry (ETG) for three H$^+$ nuclei along with the cuts to the two singlet potential energy surfaces (PESs) of the two-electron H$_3^+$ system, $S1$ and $S2$, depicted as functions of the internuclear separation, varying from left to right. In a collision, when the nuclei reach an ETG, the two singlet surfaces $S1$ and $S2$ cross each other through Jahn-Teller coupling. (c) At the geometries other than ETGs, $S1$ and $S2$ usually don't intersect, preventing curve-crossing reactions. The grey arrows on top of $S_1$ and $S_2$ represent movements of the nuclei guided by the PESs. (d) Two cuts to a PES of H$_3^+$. The curve labeled ETG represents the seam of the JT-coupled singlet states where $S1$ and $S2$ are degenerate. The other curve depicts the potential energies along the minimal energy configuration (MEC) and is representative of the geometries accessed by the colliding H$^+$, H$(1s)$, and H$(1s)$. JT coupling will be accessed in collisions only in the region where MEC is identical to the ETG, satisfying the primary constraint for the JT-induced reaction, i.e., TTBR and CE. (e) The possibility of CE is further controlled by the requirement that $S1$ and $S2$ be reciprocally associated with H$_2^+$ and H$_2$ dimers.
• Figure 1: $\vert$ H$_3^+$ geometries. (a) Three H$^+$ cores labeled as 1, 2, 3, and the set of internal coordinates $R_{12}$, $R_{23}$, $\theta$ ($\angle$123). (b) The atom-dimer triangle geometry (ADTG), belonging to the $C_{s}$ point group, with $R_{12}$ fixed to a given value $R_{12}^c$. (c) The isosceles triangle geometry (ITG) belonging to the $C_{2v}$ point group, with $R_{12} = R_{23} \equiv R$ for a given $\theta$.
• Figure 2: $\vert$H$_3^+$ asymptotic limits and states. (a) For H$^+$, H$(1s)$, H$(1s)$ system in ITG, six H$_3^+$ states are represented in $C_{2v}$ point group and have a common asymptotic limit at $E=0$ cm$^{-1}$, representing $R_{12} = R_{23} \rightarrow \infty$. (b) six H$_3^+$ states in $C_s$ point group, associated with four ADTG asymptotes H$_2 (g/u)$$+$H$^+$(i.e. $l_2$ and $l_3$, resp.) and H$_2^+ (g/u)$$+$H$(1s)$ (i.e. $l_1$ and $l_4$, resp.) for a given dimer size belonging in Region B, ($2.5$a$_0 < R_{12}^c < 10.7$a$_0$, and $l_1 < l_2 < l_3 < l_4$), with $R_{23} \rightarrow \infty$.
• Figure 3: $\vert$ADTG asymptotic limits. Energies of $l_1$, $l_2$, $l_3$, and $l_4$, as a function of the dimer size, $R_{12}^c$, with atom-dimer distance, $R_{23} \rightarrow \infty$. Three Regions, A, B, and C, are identified based on the energy ordering of the ADTG asymptotic limits. The inset shows the onset of Region C where both ADTG asymptotes associated with ionic dimers, H$_2^+ (g/u)$, (i.e., $l_1$ and $l_4$), become lower than the ones associated with neutral ones, H$_2 (g/u)$ , (i.e., $l_2$ and $l_3$).
• Figure 4: $\vert$H$_3^+$ states in ADTG and ITG. Three singlet and three triplet states of H$_3^+$ in ADTG and ITG for $\theta=60$° associated with the first fully atomized limit, H$^+$$+$H($1s$)$+$H($1s$). ADTG states are presented for $R_{12}^c = 2.00 a_0$ (corresponds to Region A, Extended Data Fig. \ref{['fig:h2adtgasymp']}), and for $R_{12}^c = 3.00 a_0$ (Region B, Extended Data Fig. \ref{['fig:h2adtgasymp']}), in Extended Data Fig. \ref{['fig:h3pecs']} (a) and (b), respectively. The energy ordering change of the ADTG asymptotes ($l_1$, $l_2$, $l_3$, $l_4$) is also indicated. ITG H$_3^+$ states, which are identical in both panels, all dissociate to H$^+$$+$H($1s$)$+$H($1s$). Vertical lines at $R_{23} = 2.00 a_0$ in Extended Data Fig. \ref{['fig:h3pecs']}(a) and $R_{23} = 3.00 a_0$ in Extended Data Fig. \ref{['fig:h3pecs']}(b) mark the geometries where the JT-coupling condition is met, i.e., $R_{23} = R_{12}^c$, $\theta = 60$° (the ETG). Circles highlight observed JT couplings in the second and third singlet, $2^1A'$ & $3^1A'$; $S1$ and $S2$ of Fig. \ref{['fig:JTsch']}, and first and second triplet, $1^3A'$ & $2^3A'$, H$_3^+$ states. The corresponding singlet ITG states, $1^1B_2$, $2^1A_1$, that are degenerate at $\theta = 60$°, represent the seam of the JT-coupling in $S1$ and $S2$, shown in Fig. \ref{['fig:JTsch']}(d). For the triplet JT-coupled pairs, these are $1^3B_2$, $1^3A_1$ states.