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Register a new userAlive and well: a short review about standard solar models
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Authors
Aldo Serenelli
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Standard solar models (SSMs) provide a reference framework across a number of research fields: solar and stellar models, solar neutrinos, particle physics the most conspicuous among them. The accuracy of the physical description of the global properties of the Sun that SSMs provide has been challenged in the last decade by a number of developments in stellar spectroscopic techniques. Over the same period of time, solar neutrino experiments, and Borexino in particular, have measured the four solar neutrino fluxes from the pp-chains that are associated with 99% of the nuclear energy generated in the Sun. Borexino has also set the most stringent limit on CNO energy generation, only $sim 40%$ larger than predicted by SSMs. More recently, and for the first time, radiative opacity experiments have been performed at conditions that closely resemble those at the base of the solar convective envelope. In this article, we review these developments and discuss the current status of SSMs, including its intrinsic limitations.
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The fundamental processes by which nuclear energy is generated in the Sun have been known for many years. However, continuous progress in areas such as neutrino experiments, stellar spectroscopy and helioseismic data and techniques requires ever more accurate and precise determination of nuclear reaction cross sections, a fundamental physical input for solar models. In this work, we review the current status of (standard) solar models and present a detailed discussion on the relevance of nuclear reactions for detailed predictions of solar properties. In addition, we also provide an analytical model that helps understanding the relation between nuclear cross sections, neutrino fluxes and the possibility they offer for determining physical characteristics of the solar interior. The latter is of particular relevance in the context of the conundrum posed by the solar composition, the solar abundance problem, and in the light of the first ever direct detection of solar CN neutrinos recently obtained by the Borexino collaboration. Finally, we present a short list of wishes about the precision with which nuclear reaction rates should be determined to allow for further progress in our understanding of the Sun.
Solar neutrino experiments have yet to see directly the transition region between matter-enhanced and vacuum oscillations. The transition region is particularly sensitive to models of non-standard neutrino interactions and propagation. We examine several such non-standard models, which predict a lower-energy transition region and a flatter survival probability for the ^{8}B solar neutrinos than the standard large-mixing angle (LMA) model. We find that while some of the non-standard models provide a better fit to the solar neutrino data set, the large measured value of theta_{13} and the size of the experimental uncertainties lead to a low statistical significance for these fits. We have also examined whether simple changes to the solar density profile can lead to a flatter ^{8}B survival probability than the LMA prediction, but find that this is not the case for reasonable changes. We conclude that the data in this critical region is still too poor to determine whether any of these models, or LMA, is the best description of the data.
After a short survey of the physics of solar neutrinos, giving an overview of hydrogen burning reactions, predictions of standard solar models and results of solar neutrino experiments, we discuss the solar-model-independent indications in favour of non-standard neutrino properties. The experimental results look to be in contradiction with each other, even disregarding some experiment: unless electron neutrinos disappear in their trip from the sun to the earth, the fluxes of intermediate energy neutrinos (those from 7Be electron capture and from the CNO cycle) result to be unphysically negative, or anyway extremely reduced with respect to standard solar model predictions. Next we review extensively non-standard solar models built as attempts to solve the solar neutrino puzzle. The dependence of the central solar temperature on chemical composition, opacity, age and on the values of the astrophysical S-factors for hydrogen-burning reactions is carefully investigated. Also, possible modifications of the branching among the various pp-chains in view of nuclear physics uncertainties are examined. Assuming standard neutrinos, all solar models examined fail in reconciling theory with experiments, even when the physical and chemical inputs are radically changed with respect to present knowledge and even if some of the experimental results are discarded.
We have evolved 10,000 solar models using 21 input parameters that are randomly drawn for each model from separate probability distributions for every parameter. We use the results of these models to determine the theoretical uncertainties in the predicted surface helium abundance, the profile of the sound speed versus radius, the profile of the density versus radius, the depth of the solar convective zone, the eight principal solar neutrino fluxes, and the fractions of nuclear reactions that occur in the CNO cycle or in the three branches of the p-p chains. We also determine the correlation coefficients of the neutrino fluxes for use in analysis of solar neutrino oscillations. Our calculations include the most accurate available input parameters, including radiative opacity, equation of state, and nuclear cross sections. We incorporate both the recently determined heavy element abundances recommended by Asplund, Grevesse & Sauval (2005) and the older (higher) heavy element abundances recommended by Grevesse & Sauval (1998). We present best-estimates of many characteristics of the standard solar model for both sets of recommended heavy element compositions.
Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher $p$-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schrodinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.
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