Solar models with protosolar accretion and turbulent mixing

¹ Department of Physics, Kurume University, 67 Asahimachi, Kurume, Fukuoka, 830-0011 Japan
² Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
³ STAR Institute, Université de Liège, Liège, Belgium

^⋆ Corresponding author: kunitomo.masanobu@gmail.com

Received: 10 April 2025
Accepted: 21 August 2025

Abstract

Context. Over the last two decades, no standard solar model (SSM) has been able to reproduce all observational data, resulting in active discussions regarding the so-called solar modeling problem. A recent study suggests that the accretion from the protosolar disk onto the proto-Sun could have left a large compositional gradient in the solar interior, in agreement with the low-metallicity (Z) solar surface and the high-Z solar core suggested by spectroscopic and neutrino observations, respectively. In addition, recent analyses have reported low lithium but high beryllium abundances on the solar surface; SSMs predict Li abundances that differ by ∼30σ from the observed value.

Aims. We develop solar models and compare them with the Li and Be abundance constraints.

Methods. We examined the effect of accretion and turbulent mixing below the base of the surface convective zone. We computed ∼200 solar evolutionary models for each case using target quantities to optimize input parameters, similar to the SSM framework.

Results. We confirm that turbulent mixing helps reproduce the surface Li and Be abundances within ∼0.6σ by boosting burning. This suppresses gravitational settling, leading to a better matching of the He surface abundance (≲0.3σ) and a smaller compositional gradient. We derive a new protosolar helium abundance, Y_proto = 0.2651 ± 0.0035. Turbulent mixing decreases the central metallicity (Z_center) by ≈4.4%; meanwhile, our previous study suggests that accretion increases Z_center by essentially the same percentage. Unfortunately, the reduction in Z_center implies that our models do not reproduce constraints on observed neutrino fluxes, with differences of 6.2σ for ⁸B and 2.7σ for CNO.

Conclusions. Including turbulent mixing in solar models appears indispensable to reproducing the observed atmospheric abundances of Li and Be. However, the resulting tensions in terms of neutrino fluxes, even in the models with protosolar accretion, show that the solar modeling problem remains, at least partly. We suggest that improved electron screening, as well as other microscopic properties, may help alleviate this problem. An independent confirmation of the neutrino fluxes as measured by the Borexino experiment would also be extremely valuable.