Anticipating the Sun's heavy-element abundance

Much of our understanding of the internal structure of the Sun derives from so-called standard theoretical solar models. Unfortunately, none of those models agrees completely with observation. The discrepancy is commonly associated with chemical abundance, and has led to what is now called the solar abundance problem, the resolution of which has previously been out of sight. But now the Borexino Collaboration, who recently announced measurements of the pp-chain solar neutrinos, are optimistic that %in future they will be able to measure the flux $\Phi_{\rm CNO}$ of the neutrinos emitted by the relatively weak CNO cycle. Since C, N and O constitute the majority of the heavy elements, that measurement will permit a crucial determination of the heavy-element abundance $Z_{\rm c}$ in the Sun's energy-generating core, thereby shedding important light on the problem. To accomplish that determination, a robust relation between $Z_{\rm c}$ and $\Phi_{\rm CNO}$ will be required. That relation is $Z_{\rm c}= 0.400\, \Phi_{\rm CNO}$, where $\Phi_{\rm CNO}$ is in units of $10^{10} {\rm cm}^{-2}{\rm s}^{-1}$.