Solar models with protosolar accretion and turbulent mixing

TL;DR

The paper tackles the solar modeling problem by combining protosolar accretion with shallow turbulent mixing below the base of the convection zone in solar models. Using MESA, about 200 evolutionary sequences per scenario are computed and calibrated against three target constraints via a Nelder–Mead optimization, with extended diagnostics to test deeper aspects of the structure. Turbulent mixing successfully reproduces surface Li and Be within $0.6\sigma$ and the present-day He abundance within $0.3\sigma$, and yields a new protosolar helium abundance of $Y_{\mathrm{proto}} = 0.2651 \pm 0.0035$, but it decreases the central metallicity by $\approx 4.4\%$, which lowers the predicted neutrino fluxes to tensions of $\sim$ $6\sigma$ for $^{8}$B and $\sim$ $2.7\sigma$ for CNO even with variable accretion. This indicates that, although the mixing mechanism is essential for Li/Be, additional physics (e.g., electron screening, updated reaction rates, winds) or new constraints are needed to fully reconcile all observational probes. The work thus narrows the viable parameter space for solar interior models and highlights the need for independent neutrino measurements to resolve the residual discrepancies.

Abstract

(abridged) Recent analyses have reported low lithium but high beryllium abundances on the solar surface; however, standard solar models (SSMs) predict Li abundances that are ~30$σ$ away from the observed value. In this study, we aim to develop solar models and compare them with the Li and Be abundance constraints. We examine the effect of protosolar accretion and turbulent mixing below the base of the surface convective zone. We compute ~200 solar evolutionary models for each case to optimize input parameters using target quantities, similar to the SSM framework. We confirm that turbulent mixing helps reproduce the surface Li and Be abundances within ~0.6$σ$ by enhancing burning. It suppresses gravitational settling, leading to a better matching of the He surface abundance ($\lesssim$0.3$σ$) and a smaller compositional gradient. We derive a new protosolar helium abundance $Y_{\rm proto}=0.2651\pm0.0035$. Turbulent mixing decreases the central metallicity ($Z_{\mathrm{center}}$) by $\approx$4.4%, even though accretion increases $Z_{\rm center}$ by $\approx$4.4%, as suggested by our previous study. Unfortunately, the reduction in $Z_{\rm center}$ implies that our models do not reproduce constraints on observed neutrino fluxes by $6.2σ$ for $^8{\rm B}$ and $2.7σ$ for CNO. Including turbulent mixing in solar models appears indispensable to reproduce the observed atmospheric abundances of Li and Be. However, the resulting tensions in terms of neutrino fluxes, even in the models with the 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 measured by the Borexino experiment would also be extremely valuable.

Figures (9)

• Figure 1: Schematic illustration showing the structure evolution (panel a; so-called Kippenhahn diagram) and the $D_\mathrm{mix}$ profile at the solar age (panel b) of our fiducial model "K2-MZvar-TM" (see Table \ref{['tab:chi2']}). The convective zones are depicted as a cloudy region. The color of the shade in panel a shows $Z_{\mathrm{accretion}}$. The two lines at the stellar surface and center also illustrate metallicity by color. The two green dashed lines indicate the locations at temperatures $T=2.5\times10^6$ and $3.5\times10^6$ K, indicative of Li and Be burning, respectively.
• Figure 2: Evolution of the surface abundances of helium (panel a), lithium (b), and beryllium (c). The red and blue lines show the models with variable and steady $Z_{\mathrm{accretion}}$, respectively. The solid and dashed lines show the models with and without turbulent mixing, respectively. The dotted lines show the models from Kunitomo+22 (with Asplund+09 abundances, without turbulent mixing but with overshooting). See Table \ref{['tab:chi2']} for more details. The green points show the observational constraints of the present-day Sun (see Table \ref{['tab:targets']}). The green shades show the meteoritic constraints Lodders21 arbitrarily extending from 1 to 10 Myr. The crosses and small circles in panel b show the observed $A(^7\mathrm{Li})$ values of clusters Dumont+21 and individual stars Carlos+19, respectively, younger than the Sun.
• Figure 3:
• Figure 4: Solar neutrino fluxes. The star and circle symbols show the models with variable and steady $Z_{\mathrm{accretion}}$, respectively. The orange and brown colors illustrate the models with and without turbulent mixing, respectively. The blue color shows the models from Kunitomo+22 (with Asplund+09 abundances without turbulent mixing). The points with error bars are the observational constraints (Table \ref{['tab:targets']}). The dotted, cyan error bar shows an old constraint by Borexino-Collaboration20.
• Figure 5: Evolution of $Y_{\mathrm{surf}}$ of model K2-MZvar-TM (red solid line) and a non-accreting model from Kunitomo+Guillot21 with standard atomic diffusion (i.e., no overshooting and turbulent mixing; gray dashed) starting with a high $Y_{\mathrm{proto}}$ value within the range suggested by Serenelli+Basu10. Turbulent mixing suppresses gravitational settling and thus leads to a reduced $Y_{\mathrm{proto}}$ value.