Helioseismology and p+p → d + e+ + νe in the sun

Abstract

By using a phenomenological field theory of nucleon-nucleon interactions, Oberhummer et al. found a cross section of p+p → d + e + + �e about 2.9 times that given by the potential approach and adopted in Standard Solar Model calculations. We show that a solar model with S = 2.9SSSM is inconsistent with helioseismic data, the difference between model predictions and helioseismic determinations being typically a factor ten larger than estimated uncertainties. We also show that, according to helioseismology, S cannot differ from SSSM by more than 15%. The rate of the initial reaction in the pp chain is too low to be directly measured in the laboratory (even in the solar center this rate is extremely small, of the order of 10 −10 yr −1 consistently with the solar age) and it can be determined only by using the theory of low energy weak interactions, together with the measured properties of the deuteron and of the proton-proton scattering. In terms of the astrophysical factor, S(E), what really matters is its zero energy value, which for brevity will be indicated simply as S. While we refer to [1–3] for updated reviews, we remark that the calculated values are all in the range (3.89–4.21) 10 −25 MeV b, i.e. they differ from their mean by no more than 3%. In summary, as input of Standard Solar Model (SSM) calculations, one takes [2]: SSSM = 3.89 � 10 −25 (1 ± 0.01) MeV b .