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Among the different strategies aiming to detect WIMP dark matter (DM), a neutrino signal coming from the Sun would be a smoking gun. This possibility relies on the DM capture by the Sun driven by the local DM distribution assumptions: the local mass density and the velocity distribution. In this context, we revisit those astrophysical hypotheses (also relevant for direct detection). We focus especially on the DM velocity distribution considering different possibilities beyond the popular Maxwellian distribution. Namely, some alternatives can be considered through analytical approaches and by looking into cosmological simulations of spiral galaxies. Most of the fitting formulas used to constrain the local velocity distribution function fail to describe the peak and the high velocity tail of the velocity distribution observed in simulations, the latter being improved when adding the local escape velocity of DM into the benchmark fitting models. In addition we test the predictions by the Eddington inversion method and also illustrate the importance of the galactic dynamical history. We estimate the resulting uncertainties on the DM capture rate by the Sun and conclude that different velocity distributions will affect the capture rate of DM by the Sun up to a $15-20\%$. On top of that, the calculation of the intrinsic variance of the capture rate leads to poorly controlled uncertainties especially for high WIMP masses ($>$30 GeV) raising concerns about the capture scenario. 20 pages, 7 figures, JCAP format

The interaction of ultra-high-energy cosmic rays (UHECRs) with pervasive photon fields generates associated cosmogenic fluxes of neutrinos and photons due to photohadronic and photonuclear processes taking place in the intergalactic medium. We perform a fit of the UHECR spectrum and composition measured by the Pierre Auger Observatory for four source emissivity scenarios: power-law redshift dependence with one free parameter, active galactic nuclei, gamma-ray bursts, and star formation history. We show that negative source emissivity evolution is favoured if we treat the source evolution as a free parameter. In all cases, the best fit is obtained for relatively hard spectral indices and low maximal rigidities, for compositions at injection dominated by intermediate nuclei (nitrogen and silicon groups). In light of these results, we calculate the associated fluxes of neutrinos and photons. Finally, we discuss the prospects for the future generation of high-energy neutrino and gamma-ray observatories to constrain the sources of UHECRs. Comment: 30 pages, 11 figures