A Bayesian estimation of the helioseismic solar age
Abstract
Context. 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.
Aims: 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.
Methods: We use 17 frequency separation ratios r_{02}(n) = (ν_{n,l = 0}ν_{n1,l = 2})/(ν_{n,l = 1}ν_{n1,l = 1}) from 8640 days of lowℓBiSON 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.
Results: 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_{⊙} = 4.587 ± 0.007 Gyr, while models employing the Irwin EOS and Adelberger, et al. (2011, Rev. Mod. Phys., 83, 195) reaction rate have t_{⊙} = 4.569 ± 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.
Conclusions: 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.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 August 2015
 DOI:
 10.1051/00046361/201526419
 arXiv:
 arXiv:1507.05847
 Bibcode:
 2015A&A...580A.130B
 Keywords:

 Sun: helioseismology;
 Sun: oscillations;
 equation of state;
 nuclear reactions;
 nucleosynthesis;
 abundances;
 methods: statistical;
 Sun: interior;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 4 pages, three Tables, A&