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The helioseismic determination of the solar age has been a subject of severalstudies because it provides us with an independent estimation of the age of thesolar system. We present the Bayesian estimates of the helioseismic age of theSun, which are determined by means of calibrated solar models that employdifferent equations of state and nuclear reaction rates. We use 17 frequencyseparation ratios$r_{02}(n)=(\nu_{n,l=0}-\nu_{n-1,l=2})/(\nu_{n,l=1}-\nu_{n-1,l=1})$ from 8640days of low-$\ell$ BiSON frequencies and consider three likelihood functionsthat 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 aconceivable range of solar ages. It is shown that the most constrainedposterior distribution of the solar age for models employing Irwin EOS withNACRE reaction rates leads to $t_\odot = 4.587 \pm 0.007$ Gyr, while modelsemploying 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. ImplementingOPAL 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 thesolar system. An estimate of the solar age that relies on an helioseismic ageindicator such as $r_{02}(n)$ turns out to be essentially independent of thetype of likelihood function. However, with respect to model selection,abandoning any information concerning the errors of the $r_{02}(n)$ ratiosleads to inconclusive results, and this stresses the importance of evaluatingthe trustworthiness of error estimates.

A Bayesian estimation of the helioseismic solar age