The NACRE Thermonuclear Reaction Compilation and Big Bang Nucleosynthesis

TL;DR

BBN predictions are limited by uncertainties in input nuclear cross sections. This study assesses the NACRE compilation and propagates rate uncertainties through a Monte Carlo BBN calculation to derive constraints on $η$ and $Ω_{\rm B} h^2$, while comparing with CMB results. The authors explore multiple error treatments (high/low, minimal, sample variance) and find that NACRE central values largely agree with prior work, but uncertainty characterizations strongly influence the inferred abundances, especially for ${}^7$Li; rate renormalizations can shift Li yields notably. The results highlight a residual tension between BBN and some CMB determinations of the baryon density, emphasizing the need for improved nuclear data and more precise observations, with upcoming MAP/PLANCK data poised to provide a decisive cross-check of cosmology.

Abstract

The theoretical predictions of big bang nucleosynthesis (BBN) are dominated by uncertainties in the input nuclear reaction cross sections. In this paper, we examine the impact on BBN of the recent compilation of nuclear data and thermonuclear reactions rates by the NACRE collaboration. We confirm that the adopted rates do not make large overall changes in central values of predictions, but do affect the magnitude of the uncertainties in these predictions. Therefore, we then examine in detail the uncertainties in the individual reaction rates considered by NACRE. When the error estimates by NACRE are treated as 1σlimits, the resulting BBN error budget is similar to those of previous tabulations. We propose two new procedures for deriving reaction rate uncertainties from the nuclear data: one which sets lower limits to the error, and one which we believe is a reasonable description of the present error budget. We propagate these uncertainty estimates through the BBN code, and find that when the nuclear data errors are described most accurately, the resulting light element uncertainties are notably smaller than in some previous tabulations, but larger than others. Using these results, we derive limits on the cosmic baryon-to-photon ratio $η$, and compare this to independent limits on $η$ from recent balloon-borne measurements of the cosmic microwave background radiation (CMB). We discuss means to improve the BBN results via key nuclear reaction measurements and light element observations.

Figures (12)

• Figure 1: Experimental data and $R$- and $S$-factor fits for four key reactions. The solid curves are our renormalized fits, with our sample variance error bands given by the short dashed curves. For the $S$-factor curves, data are given in NACRE, whose raw fits are given by the long dashed curves. a) The $R$-factor for $\hbox{${}^{3}{\rm He}$}(n,p)t$. The data are those of SKM with the addition of Brune et al. brune99. The fit is ours, as described in § \ref{['sect:rates']}. b) The $S$-factor data for $d(p,\gamma)\hbox{${}^{3}{\rm He}$}$. c) The $S$-factor data for $\hbox{${}^{3}{\rm He}$}(\alpha,\gamma)\hbox{${}^{7}{\rm Be}$}$. d) The $S$-factor data for $t(\alpha,\gamma)\hbox{${}^{7}{\rm Li}$}$.
• Figure 2: NACRE "high/low" fractional errors for the seven NACRE reactions important for BBN. Dotted curves: high/low errors; solid curves: sample variance errors; dashed curves: SKM errors which are shown for comparison.
• Figure 3: Fractional $1\sigma$ errors in the $R$- and $S$-factors for sample variance analysis, as well as Nollett & Burles nb. Solid curves: sample variance limits; dashed curves: Nollett & Burles upper limits; dotted curves: Nollett & Burles lower limits. The $p(n,\gamma)d$ reaction is not shown, as Nollett & Burles adopt a constant $1\sigma$ fractional error of 5% in this case.
• Figure 4: Light element abundances as a function of $\eta$, using NACRE rates without renormalization. a) The solid curves are the central values of the NACRE predictions, dashed curves are those of SKM. The two are extremely close, so that they often appear to overlap. b) Percent difference $100(y_i^{\rm NACRE}/y_i^{\rm 1996} - 1)$ between the NACRE and Hata et al. (1996) central values.
• Figure 5: As in Figure \ref{['fig:nacre_vs_skm_ren']}, for light element predictions with renormalization.