Non-Gaussian Error Distribution of ${}^7\mathrm{Li}$ Abundance Measurements

Abstract

We construct the error distribution of ${}^7\mathrm{Li}$ abundance measurements for 66 observations (with error bars) used by Spite12 that give $\mathrm{A}(\mathrm{Li})=2.21\pm 0.065$ (median and 1$\sigma$ symmetrized error). This error distribution is somewhat non-Gaussian, with larger probability in the tails than is predicted by a Gaussian distribution. The 95.4% confidence limits are 3.0$\sigma$ in terms of the quoted errors. We fit the data to four commonly used distributions: Gaussian, Cauchy, Student's t, and double exponential with the center of the distribution found with both weighted mean and median statistics. It is reasonably well described by a widened $n=8$ Student's $t$ distribution. Assuming Gaussianity, the observed A(Li) is 6.5$\sigma$ away from that expected from standard Big Bang nucleosynthesis given the $Planck$ observations Coc2014. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to 4.9$\sigma$, which is still significant.

24 pages, 6 figures, 4 tables

References in corpus (9)

• Improved Age Estimation for Solar-Type Dwarfs Using Activity-Rotation Diagnostics
• The Primordial Lithium Problem
• First stars VII. Lithium in extremely metal poor dwarfs
• Coupled Variations of Fundamental Couplings and Primordial Nucleosynthesis
• Lithium abundances of halo dwarfs based on excitation temperature. I. LTE
• Resonant Destruction as a Possible Solution to the Cosmological Lithium Problem
• Post-$Planck$ constraints on interacting vacuum energy
• Radio Detection of Radio-Quiet Galaxies
• Median statistics cosmological parameter values

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