Abstract: We present a full Bayesian analysis of the combination of current neutrino oscillation, neutrinoless double beta decay and Cosmic Microwave Background observations. Our major goal is to carefully investigate the possibility to single out one neutrino mass ordering, namely Normal Ordering or Inverted Ordering, with current data. Two possible parametrizations (three neutrino masses versus the lightest neutrino mass plus the two oscillation mass splittings) and priors (linear versus logarithmic) are exhaustively examined. We find that the preference for NO is only driven by neutrino oscillation data. Moreover, the values of the Bayes factor indicate that the evidence for NO is strong only when the scan is performed over the three neutrino masses with logarithmic priors; for every other combination of parameterization and prior, the preference for NO is only weak. As a by-product of our Bayesian analyses, we are able to (a) compare the Bayesian bounds on the neutrino mixing parameters to those obtained by means of frequentist approaches, finding a very good agreement; (b) determine that the lightest neutrino mass plus the two mass splittings parametrization, motivated by the physical observables, is strongly preferred over the three neutrino mass eigenstates scan and (c) find that logarithmic priors guarantee a weakly-to-moderately more efficient sampling of the parameter space. These results establish the optimal strategy to successfully explore the neutrino parameter space, based on the use of the oscillation mass splittings and a logarithmic prior on the lightest neutrino mass, when combining neutrino oscillation data with cosmology and neutrinoless double beta decay. We also show that the limits on the total neutrino mass Sigma m(nu) can change dramatically when moving from one prior to the other. These results have profound implications for future studies on the neutrino mass ordering, as they crucially state the need for self-consistent analyses which explore the best parametrization and priors, without combining results that involve different assumptions.

Abstract: Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range [10(-)(10) – 10(2)] M-circle dot, for constant scattering cross sections and s-wave annihilations. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, at the local galactic position, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by E-c/T-chi similar to 30, where E-c is the escape energy of DM particles at the core of the object and T-chi is their temperature. In that case, the minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, m(ev)(ap) similar or equal to 0.7 GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor smaller than three within the range 10(-41) cm(2) <= sigma(p) <= 10(-31) cm(2), where sigma(p) is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic, and details on the density and temperature profiles of celestial bodies have also a small impact.