Molecular fluorine chemistry in the early Universe

Early Universe chemistry (standard Big Bang chemistry, hereafter SBBC), of which hydrogen recombination is only one aspect, has been the subject of several studies in the conventional frame of a homogeneous expanding Universe. One of the most important result of these studies is that the formation of a significant number of molecules such as $H_2$ and HD plays a crucial role on the dynamical evolution of the first collapsing structures appearing at temperatures below a few hundred K.
The literature on chemistry in the post-recombination epoch has expanded considerably in the recent years. Many authors have developed studies of primordial chemistry in different contexts:

• Chemical network lep84 (); puy93 (); sta96 (); gal98 (); lep02 (); pfe03 ().

• Formation of the first objects puy96 (); abe97 (); abe00 (); shc06 (); nun06 (); hir06 (); yos06 (); puy06 ().

All these authors clearly point out that trace amounts of light molecules such as $H_2$, HD and LiH were formed during the post-recombination period of the Universe. However a key item is the question of heavier elements synthesis during the phase of primordial nucleosynthesis and the formation of the corresponding molecules during the period of recombination, because many observations suggest that heavy elements already exist in high redshifts son96 (); pic03 (); ara04 (); coh04 ().
It is known that under certain conditions, high density baryonic bubbles are created in the Affleck-Dine model of baryogenesis aff85 (), and these bubbles may occupy a relatively small fraction of space, while the dominant part of the cosmological volume is characterized by the normal observed baryon-to-photon ratio. The value of this ratio $\eta$ in the bubbles could be much larger than the usually accepted value and still be consistent with the existing data on light element abundances and the observed angular spectrum of cosmic microwave background radiation (CMBR). In this context, numerous authors investigated the possibility that non-homogeneous baryogenesis produced very high baryon density in a small fraction of the universe and in these regions some fraction of heavy elements were already synthesized during primordial nucleosynthesis app87 (); tho94 (); jed94 (); kur77 (); jed01 (). More recently mat05 () analyzed Big Bang nucleosynthesis in very high baryon density regions. They found that primordial synthesis can produce very heavy elements including proton rich nuclei such as ${}^{92}Mo$, ${}^{94}Mo$, ${}^{96}Ru$ and ${}^{98}Ru$.
Abundance of primary fluorine is below the abundances of the primordial C N O group during the Big Bang nucleosynthesis. However molecular fluorine could be more important in comparison with the molecules provided by reactions with C, N and O atoms. The first detection of interstellar hydrogen fluoride was reported by neu97 () using the long wavelength spectrometer of ISO satellite. To interpret this detection of HF, they have constructed a simple model for the steady state of chemistry of interstellar fluorine with H${}_2$ and with water. Two important factors must be considered for the formation of the molecular component in the early universe. One is the binding energy of the hydrogen atom in the molecular component considered, and the second the ionization potential of the molecule. Relative to these two criteria, the molecule of fluorine HF is an interesting candidate. Ionization potential of F ($I_F$ = 17.42 eV) is greater than that of hydrogen ($I_H$ = 13.6 eV). Thus fluorine ions must have recombined before hydrogen ions in the early Universe. Moreover the binding energy of HF, $E_{HF}$ = 5.92 eV, is greater than the binding energy of $H_2$. As such, HF could be formed in the early Universe.
In this paper we investigate the growth of molecular fluorine abundance. In Sect. 2, we introduce the standard Big Bang chemistry (hereafter SBBC). In Sect. 3, we perform a detailed analysis of the primordial chemical evolution of the atomic and molecular species of fluorine. Finally, in Sect. 5 we discuss some extensions and implications of this study.

The standard Big Bang nucleosynthesis (SBBN) model predicts the nuclei abundances, mainly those of hydrogen, helium and lithium, and their isotopes in the early Universe. The standard chemistry of the early Universe is the chemistry of these light elements and their respective isotopic forms. This chemistry is non-trivial because on one hand the universal expansion dilutes matter, so lowers the collision rates and slows down the chemical reactions, while, on the other hand, the matter and radiation temperatures drop, which decreases the molecule destruction rates, so may encourage molecule formation.
After the hydrogen recombination, the ongoing physical reactions are numerous, partly due to the presence of the cosmic microwave background radiation (or CMBR), Stancil et al. 1998. We can establish three classes of chemical reactions:

• collisional: $\xi +{\xi }^{\prime }⟷{\xi }_1+{\xi }_2$

• electronic: $\xi +e^{-}⟷{\xi }_1+{\xi }_2$

• photo-processes: $\xi +\gamma ⟷{\xi }_1+{\xi }_2$.

A comprehensive account was given of the chemistry of HF in interstellar clouds by zhu02 (), and more recently by neu05 () for the chemistry of fluorine-bearing molecules in diffuse and dense interstellar gas clouds. One very promising result was presented by rau94 () with a calculation of heavy element abundances in the context of non-homogeneous Big Bang nucleosythesis. In this paper the relative abundance of fluorine nuclei is estimated to be close to ${10}^{-15}$ which is our initial abundance. Our calculations start at the redshift $z_s=2000$ to avoid fluorine recombination. For redshifts greater than $z_s$, the fluorine chemistry is essentially dominated by the successive recombination from $F^{n+}$ to the neutral atom F.
We consider seven reactions which involve fluorine component:

• radiative association: $F+H\to HF+\gamma$.

• photodissociation: $HF+\gamma \to F+H$.

• radiative attachment: $F+e^{-}\to F^{-}+\gamma$

• photodetachment: $F^{-}+\gamma \to F+e^{-}$.

• associative detachment: $F^{-}+H\to HF+e^{-}$

• electronic collision: $HF+e^{-}\to F^{-}+H$

• neutral-neutral reaction: $F+H_2\to HF+H$.

In some cases we have estimated the reaction rate of these reactions. All of these reactions are coupled with the chemical network of the SBBC and the equations of evolution for the temperatures (matter and radiation) and the density.

HF molecules are mainly formed by the exothermic neutral-neutral reaction of atomic fluorine with $H_2$, which is confirmed by sno06 () where they reported results from a survey of neutral fluorine in the interstellar medium. They showed that the hydride of fluorine, HF, is in competition with the abundance of atomic fluorine, depending on how abundant $H_2$ is.
Primordial molecules could play an important role in the future observations of CMBR anisotropies(dub77 (); mao94 (). These authors argued that huge enhancement of the emission line intensity from the proto-objects could occur, and mentioned that molecular protoclouds at high redshift, $10<z<300$, which have a peculiar velocity relative to the CMBR, could produce spectral-spatial fluctuations through the mecanism of pure reflection of the CMBR photons due to the opacity of a proto-object in narrow spectral lines and the Doppler shift in frequency due to the peculiar velocity. In this context, molecules of fluorine HF could play an interesting role, despite the low initial abundance of fluorine compared to the abundance of lighter elements. We find (see Fig. 2), that the abundance of molecular fluorine is the third neutral molecular abundance (with $H_2$ and HD). Thus HF molecules could contribute to the process of fragmentation of large proto structures. HF molecules¹¹1where the dipole moment of HF is closed to $d_{HF}=1.8$ Debye, see mue72 (). could be an important coolant agent in collapsing proto-objects and initiate the mechanism of thermal instability as do HD and LiH Puy & Signore 1996, 1997; lip05 ().
The detection of primordial HF will be possible in the near future with instruments such as ALMA or HERSCHEL satellite mao05 (). Searching for HF could result in constraints on the fundamental process of nuclei formation during the Big Bang nucleosynthesis.