Quantum-state–selective electron recombination studies suggest enhanced abundance of primordial HeH+

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Science  16 Aug 2019:
Vol. 365, Issue 6454, pp. 676-679
DOI: 10.1126/science.aax5921

Enhanced abundance of primordial HeH+

Though only recently detected in space, the helium hydride ion (HeH+) is thought to be the first molecule ever to have formed in the early Universe. Novotný et al. report state-specific rate coefficients for the dissociative reaction of HeH+ with electrons, obtained using a cryogenic ion storage ring combined with a merged electron beam (see the Perspective by Bovino and Galli). They detect substantial rotational dependence and a decrease of the rates for the lowest states of HeH+, far below the values listed in astrochemistry databases and those previously applied in early-Universe models. These results suggest high abundance of this important primordial molecule at redshifts of first star and galaxy formation.

Science, this issue p. 676; see also p. 639


The epoch of first star formation in the early Universe was dominated by simple atomic and molecular species consisting mainly of two elements: hydrogen and helium. Gaining insight into this constitutive era requires a thorough understanding of molecular reactivity under primordial conditions. We used a cryogenic ion storage ring combined with a merged electron beam to measure state-specific rate coefficients of dissociative recombination, a process by which electrons destroy molecular ions. We found a pronounced decrease of the electron recombination rates for the lowest rotational states of the helium hydride ion (HeH+), compared with previous measurements at room temperature. The reduced destruction of cold HeH+ translates into an enhanced abundance of this primordial molecule at redshifts of first star and galaxy formation.

At the beginning of the Universe, only small nuclei—mainly hydrogen, deuterium, and helium—existed. When temperatures lowered to ~2500 K, their recombination with electrons led to neutral atoms. Later, primordial molecules—mainly H2, HD, HeH+, and LiH—formed by radiative association and charge-exchange reactions (1). These molecules are crucial for the formation of the first stars, because the collisional excitation of their rotational levels and subsequent radiative emission (2) can cool a gas cloud to the low temperatures required for gravitational collapse. Critical for this radiative cooling is the molecular dipole moment. The dipole moment vanishes for the most abundant molecule, H2, and is only small (0.00083 D) for the isotopically asymmetric HD molecule. However, the dipole moments are large for HeH+ (1.66 D; HeH is unstable), HD+ (0.9 D), and LiH (5.98 D) (1, 3). Because the relative D-to-He and Li-to-He elemental abundance ratios are ~10−4 and ~10−8, respectively, HeH+ moves into the focus. Although a number of astronomical searches for this elementary species have been unsuccessful (4, 5), HeH+ was very recently detected in a planetary nebula (6).

Given that the underlying cosmological parameters and the outcome of Big Bang nucleosynthesis are known with great precision, uncertainties of the reaction rate coefficients are now perceived (1) as the only limitation on our understanding of primordial gas evolution. The relevant temperatures range from ~2500 K (redshift z ~ 800) to ~20 K (z ~ 6) at the end of the cosmic reionization phase. Temperatures as low as a few kelvin also apply to astrochemistry in the interstellar medium of the contemporary Universe (7); hence, molecular ions are crucial drivers of low-temperature gas-phase astrochemistry in all eras. Their abundance is often limited by dissociative recombination (DR) with electrons (8).

In this process, the ion captures a free electron while its internal degrees of freedom undergo excitation. The resulting neutral, excited compound typically dissociates on a subpicosecond time scale. The cross section of the exothermic DR reaction is strongly system dependent, as possible excitation pathways—electronic, vibrational, or rotational—vary. Extended studies (814) were performed on cold-electron reactions with HeH+. Ion storage rings with an internal, merged electron beam target were used (1012) to measure DR of molecular ions at electron temperatures that reached below 20 K. These studies and related theoretical work (1315) revealed the strong collision energy dependence of the cross section from predissociating molecular Rydberg states, formed when the colliding electron excites vibrations and rotations of the ion core. Despite the expected strong influence of rotational excitation, all measurements to date (912) were performed for HeH+ in excited rotational levels: Through the molecular dipole moment, thermal equilibrium with the blackbody radiation in the beam enclosure led to a rotational temperature of ~300 K. The present experiment, using a cryogenic ion storage ring, can finally address this rotational dependence.

Our measurements were performed in the recently completed electrostatic cryogenic ion storage ring, CSR (16), at the Max Planck Institute for Nuclear Physics, Heidelberg, Germany. Its vacuum chamber walls and all beam-guiding electrodes were cooled to ~6 K. HeH+ ions from a discharge ion source were accelerated to 250 keV and injected into the cryogenic ring with four bending corners and interjacent linear sections (Fig. 1). The ions, circulating collision-free for hundreds of seconds (1618), are merged in one of the linear sections with a quasi-monoenergetic electron beam with the same or a slightly detuned velocity [electron energy E0=27.32±0.06 eV (±SEM) at matched velocities]. DR in the ~1-m-long overlap region leads to neutral H and He atoms that separate from the electrostatically deflected ions and impinge on a position-sensitive, multihit counting detector (19). At the electron beam energy Ee=E0, the HeH+ ions collide with electrons of thermal energy spread (~2 meV). Choosing, however, Ee>E0, the collision energy is detuned to Ed=(Ee1/2E01/2)2 and easily variable. This yields (19) the energy-dependent DR rate coefficient αDR(Ed).

Fig. 1 Dissociative recombination in the cryogenic storage ring, CSR.

(A) Scheme of the CSR ring structure with the injected and stored HeH+ ion beam (red), merged electron beam (blue), reaction products (green), and particle detector. (B) Reaction scheme and position-sensitive detection of coincident fragments. (C) Equilibrium rotational state populations of HeH+ for previous studies (300 K) and the estimated radiation field in the CSR.

As demonstrated recently (17, 18), rotationally excited hydride ions stored in the CSR relax by spontaneous emission of infrared photons along the energy ladder EJ=BJ(J+1) in steps of JJ1, where J is the angular momentum quantum number and B is the rotational constant. For HeH+, B/kB = 48.2 K (kB is the Boltzmann constant). From a comprehensive line list (2), we set up a radiative model for the HeH+ rotational level populations as functions of ion storage time t. The radiation field in CSR is approximated by two components, 99% of the spectral energy density at the molecular transitions representing the 6 K wall temperature, and 1% of it representing inevitable radiation leaks from the outer (300 K) environment (19). In such conditions, the population of the HeH+ J = 0 level at equilibrium (t10 s) is 92%. In the earlier room temperature studies (912) of HeH+, the equilibrium population was only ~15% for J = 0, and higher J levels were more strongly populated (Fig. 1).

In the CSR, >50% population in J = 0 is reached at t > 8 s of storage. Vibrational excitation (v) relaxes much more quickly; consistent with previous storage-ring work (1012), a pure v = 0 population is ensured for t > 0.1 s. The CSR result for the energy-dependent DR rate coefficient αDR(Ed) at 10 s < t < 50 s is compared with the previous storage-ring results in Fig. 2, thus displaying the effect of reducing the rotational excitation. At 20% uncertainty in the overall scaling of our data, there are minor deviations between the CSR data and previous storage-ring results between ~0.07 and 1 eV. Strong deviations, however, occur at lower energies. For the rotationally cold ions, the DR rate first assumes a sharp resonant maximum at Ed0.044 eV (Ed/kB530 K). Below Ed0.02 eV (Ed/kB260 K), the DR rate becomes much smaller (by a factor up to ~8) than that for room temperature conditions and remains nearly as low down to Ed0.001 eV (Ed/kB12 K).

Fig. 2 DR for rotationally cold HeH+.

(A) Blue circles indicate the merged-beams rate coefficient αDR as a function of the detuning energy Ed after relaxation to >50% J = 0 (this experiment, 10 s < t < 50 s, mean ± SD); absolute scaling uncertainty ±20% (SEM). Red symbols represent room temperature data from (11) (squares, absolute scaling uncertainty ±10% SEM) and from (12) [triangles, scaled to (11) at 0.03 eV]. (B) Fragment distance distribution projected into the detector plane for Ed = 0 (blue) with fit (19) for isotropic angular distribution (red). (C) Projected fragment distance distribution for Ed = 0.044 eV (blue) with fit (19) for a |Y10|2 angular distribution of the fragments (red). The angular dependences in (B) and (C) are indicated schematically. arb., arbitrary units.

Substantial rotational dependence for predissociating Rydberg resonances has been predicted (14, 15) for αDR(Ed) in this energy range. We studied this concept through the storage-time dependence of the DR rate coefficient, αDR(Ed,t). The rotational populations from the radiative cooling model reveal how the J distribution is dominated by increasingly lower levels as the storage time advances (Fig. 3A). The αDR(Ed,t) data were analyzed in time slices adapted to some of the lower J levels (time slices I to IV for J = 3 to 0; see Fig. 3B). Although in slice I the DR rate at low collision energies is similar to the room temperature results, this level decreases as the ions cool rotationally. Moreover, later slices with dominating J = 2 or 1 indicate energy-shifted resonances below the strong peak of time slice IV.

Fig. 3 DR during the rotational relaxation of HeH+.

(A) Relative rotational level populations as functions of ion storage time t from the radiative model (starting temperature: 3000 K; CSR radiation field: 99% at 6 K, 1% at 300 K) for J as given and with time slices I to IV in which the dominant J varies from 3 to 0. (B) Rate coefficient αDR(Ed) measured in the marked time slices (mean ± SD).

All time-varying DR rates represent linear combinations of the time-invariant DR rates αDRJ(Ed) for individual J levels, weighted by the average relative level populations in the various time slices. Using the data for eight separate intervals between 0.1 and 45 s and the respective average level populations from the radiative model, we deduced (19) state-resolved rate coefficients αDRJ(Ed) up to J = 2 and the average DR rate from the J ≥ 3 levels contributing at early storage times (mainly J = 3 and 4). These data (Fig. 4A) show the dominance of a single near-Lorentzian peak for J = 0. Similar peaks with maxima downshifted in Ed are seen for J ≥ 1, where an increase of the width points to unresolved peak structure. Moreover, starting from J = 2 the rate at Ed < 0.01 eV grows. Recent theory, such as figure 13a of (14), predicts a similar J-dependent peak structure at ~0.01 to 0.07 eV but predicts rates up to 10 times those of the experiment at lower energy, especially for J = 0.

Fig. 4 Rotational-state selective DR rates for HeH+.

(A) Merged-beams rate coefficients αDRJ(Ed) for J ≤ 2 and average for J ≥ 3 (mainly 3 and 4; mean ± SD). The dashed lines mark the shift of the maximum as J increases. (B) Solid lines indicate single-J plasma rate coefficients αDR,plJ(Tpl) for J ≤ 2 and average (av) for J ≥ 3 (mainly 3 and 4; mean with shaded areas denoting ±SD). The dotted line represents the fully thermal rate coefficient αDR,therm(Trot=Tpl). Dashed-dotted lines indicate values applied in early-Universe models (21, 22) and astrochemistry databases (2325). See (19) for further discussion, numerical fitting functions, and parameters.

These energy- and state-resolved DR rates enable us to derive plasma rate coefficients for individual J levels or fully thermal ensembles. We deconvolved (19, 20) the merged-beams DR rate coefficients αDRJ(Ed) to yield DR cross sections in narrow energy bins. Subsequently, we reconvolved these J-specific cross sections to obtain plasma rate coefficients αDR,plJ(Tpl) (see Fig. 4B) for Maxwellian electron energy distributions of kinetic temperature Tpl. These results can be state-population weighted to obtain a rate coefficient for specified rotational temperatures Trot or even for fully thermalized conditions [see αDR,therm(Trot=Tpl) in Fig. 4B]. Our results for J = 0 and J = 1 at <80 K are lower than the values (19) presently applied in early-Universe models (21, 22) and those listed in astrochemistry databases (2325) by factors of 15 to 80. Compared with these previous data, even the enhanced J = 2 and J ≥ 3 average rates are lower.

A recent study (22) (Fig. 2) shows that, at redshifts z < 15, the only reactions essential for the abundance of HeH+ are radiative association of H+ and He for production and DR for destruction. Hence, the HeH+ abundance from model calculations is inversely proportional to the applied DR rate coefficient. At these redshifts, a radiation temperature T ~ 40 K requires the J ≤ 1 levels to dominate, whereas the gas temperature is Tpl ≤ 10 K (26). Comparing for Tpl = 10 K the DR rate used by Bovino et al. (22) with our J = 0 and J = 1 rates, population-averaged for T = 40 K, the estimated peak HeH+ abundance at z ~ 15 increases by a factor of at least 20 above the previously calculated value (22) (Fig. 4). This strengthens the role of HeH+ as a potential coolant in primordial star formation and also increases the chance to observe HeH+ from the postrecombination era at low redshifts. Furthermore, higher abundance predictions for HeH+ indicate that the role of HeH+ in smearing out the cosmic microwave background should be reexamined (27). For the HeH+ observation in planetary nebula (6), high kinetic temperatures of Tpl104 K are relevant. The absolute HeH+ DR rate of 3.0 × 10−10 cm3 s−1 used to interpret that observation (6) is compatible with our findings (19).

Considering the importance of resonant processes, our energy- and state-selective rate coefficients αDRJ(Ed) offer a particularly clean, hitherto unavailable view on the mechanism of low-energy DR. We analyzed the emission velocities of the He and H fragments at the prominent resonance at 0.044 eV, using the position resolution of our coincidence detector, and compared them to the Ed = 0 behavior. Distributions P(D) of the fragment distances D projected into the detector plane (Fig. 2, B and C) reflect the energy and the angular characteristic of the H and He atoms emitted in a DR reaction (19). For both Ed, the end points of P(D) at D ~ 27 mm indicate an emission energy near 1.55 eV and confirm the well-known (28) fragmentation pathway into the atomic states 11S (ground state) for He and n = 2 for H. The shapes of P(D), however, reveal different angular characteristics. At Ed = 0 (Fig. 2B), there is no distinct electron impact direction and the fragments are emitted isotropically. In contrast, at Ed = 0.044 eV (Fig. 2C), the collision direction is aligned with the beam axis and the data reveal a pure low-order multipole (|Y10|2) around this axis for the fragment directions. Based on the well-established axial-recoil approximation (29), this pure low-order multipole also applies to the DR cross section with respect to the internuclear axis, as well as to the electron partial wave that drives the DR process (30). We find the DR resonance of J = 0 HeH+ ions at 0.044 eV to be mostly driven by an electronic partial wave with angular and magnetic quantum numbers l = 1, m = 0 (pσ symmetry), whose importance was raised theoretically (15).

Our new accurate rate coefficient measurements consolidate the gas-phase chemical data on HeH+ that govern its abundance in the postrecombination era of the early Universe. Moreover, the ability to obtain state-selective laboratory data for fundamental molecular reactions is particularly timely, considering the imminent launch of the James Webb Space Telescope (31). Its search for the first luminous objects and galaxies after the Big Bang will benefit greatly from reliable predictions on early-Universe chemistry. Our data show that the rotational excitation can make a substantial difference in low-temperature reaction rates of small molecules.

Supplementary Materials

Materials and Methods

Figs. S1 and S2

Table S1

References (3338)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: This article comprises parts of the Ph.D. thesis works of P.W., S.S., and D.P., submitted or to be submitted at the Ruprecht-Karls-Universität Heidelberg, Germany. Funding: This work was supported by the Max Planck Society, the Weizmann Institute of Science, the German Science Foundation (DFG Wo 1481/2-1 and DFG GE 2183/3-1), and the European Research Council (Starting Grant StG 307163). Author contributions: K.B., D.Z., and A.W conceived the original idea. K.B., S.G., H.K., D.Z., and A.W. provided financial support. O.N. and A.W. led the preparations, modeling, measurements, and analysis. O.N., P.W., D.P., Á.K., S.S., C.K., M.G., and A.W. performed the measurements and analyzed the data. O.N., P.W., D.P., C.K., D.A.O., M.R., A.S., A.S.T., S.V., and A.W. contributed to the design and realization of the CSR electron cooler and photocathode electron gun. O.N., S.S., A.B., C.K. and A.W. contributed to the design and realization of the detector. All other authors contributed to development and realization of further tools and methodology, as well as to preparatory measurements directly relevant for this work. O.N., H.K., and A.W. wrote the manuscript. All authors commented on the final manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: The underlying data are available in the supplementary materials and Edmond, the Max Planck Society repository (32).

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