We generate new standard solar models using newly analyzed nuclear fusion cross sections and present results for helioseismic quantities and solar neutrino fluxes. We discuss the status of the solar abundance problem and investigate whether nonstandard solar models with accretion from the protoplanetary disk might alleviate the problem. We examine a broad range of possibilities, analyzing both metal-enriched and metal-depleted accretion models and exploring three scenarios for the timing of the accretion. Only partial solutions are found: one can bring either the depth of the convective zone or the surface helium abundance into agreement with helioseismic results, but not both simultaneously. In addition, detailed results for solar neutrino fluxes show that neutrinos are a competitive source of information about the solar core and can help constrain possible accretion histories of the Sun. Finally, we briefly discuss how measurements of solar neutrinos from the CN-cycle could shed light on the interaction between the early Sun and its protoplanetary disk.Comment: 18 pages, 16 figures, submitted to Ap
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