A Bayesian estimation of the helioseismic solar age

Abstract

The helioseismic determination of the solar age has been a subject of several studies because it provides us with an independent estimation of the age of the solar system. We present the Bayesian estimates of the helioseismic age of the Sun, which are determined by means of calibrated solar models that employ different equations of state and nuclear reaction rates. We use 17 frequency separation ratios $r_{02}(n)=(ν_{n,l=0}-ν_{n-1,l=2})/(ν_{n,l=1}-ν_{n-1,l=1})$ from 8640 days of low-$\ell$ BiSON frequencies and consider three likelihood functions that depend on the handling of the errors of these $r_{02}(n)$ ratios. Moreover, we employ the 2010 CODATA recommended values for Newton's constant, solar mass, and radius to calibrate a large grid of solar models spanning a conceivable range of solar ages. It is shown that the most constrained posterior distribution of the solar age for models employing Irwin EOS with NACRE reaction rates leads to $t_\odot = 4.587 \pm 0.007$ Gyr, while models employing the Irwin EOS and Adelberger, et al., Reviews of Modern Physics, 83, 195 (2011) reaction rate have $t_\odot = 4.569 \pm 0.006 $ Gyr. Implementing OPAL EOS in the solar models results in reduced evidence ratios (Bayes factors) and leads to an age that is not consistent with the meteoritic dating of the solar system. An estimate of the solar age that relies on an helioseismic age indicator such as $r_{02}(n)$ turns out to be essentially independent of the type of likelihood function. However, with respect to model selection, abandoning any information concerning the errors of the $r_{02}(n)$ ratios leads to inconclusive results, and this stresses the importance of evaluating the trustworthiness of error estimates.