H, He-like recombination spectra I: $l$-changing collisions for hydrogen

Abstract

Hydrogen and helium emission lines in nebulae form by radiative recombination. This is a simple process which, in principle, can be described to very high precision. Ratios of He I and H I emission lines can be used to measure the He${}^{+}$/H${}^{+}$ abundance ratio to the same precision as the recombination rate coefficients. This paper investigates the controversy over the correct theory to describe dipole $l$-changing collisions ($nl\to n{l}^{\prime }=l\pm 1$) between energy-degenerate states within an $n$-shell. The work of Pengelly & Seaton (1964) has, for half-a-century, been considered the definitive study which "solved" the problem. Recent work by Vrinceanu et al.(2012) recommended the use of rate coefficients from a semi-classical approximation which are nearly an order of magnitude smaller than those of Pengelly & Seaton (1964), with the result that significantly higher densities are needed for the $nl$ populations to come into local thermodynamic equilibrium. Here, we compare predicted H~I emissivities from the two works and find widespread differences, of up to $\approx 10$%. This far exceeds the 1% precision required to obtain the primordial He/H abundance ratio from observations so as to constrain Big Bang cosmologies. We recommend using the rate coefficients of Pengelly & Seaton (1964) for $l$-changing collisions, to describe the H recombination spectrum, based-on their quantum mechanical representation of the long-range dipole interaction.

arXiv comment6 pages, 3 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

References in corpus (9)

• The 2013 Release of Cloudy
• Improved He I Emissivities in the Case B Approximation
• Corrigendum: Improved He~I Emissivities in the Case B Approximation
• Theoretical He I Emissivities in the Case B Approximation
• He~I Emission in the Orion Nebula and Implications for Primordial Helium Abundance
• J-resolved He I emission predictions in the low-density limit
• Uncertainties in Theoretical HeI Emissivities: HII Regions, Primordial Abundance, and Cosmological Recombination
• Angular momentum changing transitions in proton-Rydberg atom collisions
• Emission and recombination coefficients for hydrogen with kappa-distributed electron energies

Cited by in corpus (16)

• Carbon and hydrogen radio recombination lines from the cold clouds towards Cassiopeia A
• Low Frequency Carbon Radio Recombination Lines I: Calculations of Departure Coefficients
• H, He-like recombination spectra II: $l$-changing collisions for He Rydberg states
• Lyman-$\alpha$ feedback prevails at Cosmic Dawn: Implications for the first galaxies, stars, and star clusters
• NEBULAR: A simple synthesis code for the hydrogen and helium nebular spectrum
• H-, He-like recombination spectra III: $n$-changing collisions in highly-excited Rydberg states and their impact on the radio, IR and optical recombination lines
• The influence of continuum radiation fields on hydrogen radio recombination lines
• Inverted level populations of hydrogen atoms in ionized gas
• On the treatment of $\ell$-changing proton-hydrogen Rydberg atom collisions
• H, He-like recombination spectra IV; H, He-like recombination spectra IV: clarification and refinement of methodology for $l$-changing collisions
• Testing atomic collision theory with the two-photon continuum of astrophysical nebulae
• Spectroscopy with the Engineering Development Array: cold H${}^{+}$ at 63 MHz towards the Galactic Centre
• Efficient computation of collisional $\ell$-mixing rate coefficients in astrophysical plasmas
• Current and future development of the photoionization code Cloudy
• Thermodynamically-consistent semi-classical $\ell$-changing rates
• H-, He-like recombination spectra -- V: On the dependence of the simulated line intensities on the number of electronic levels of the atoms