Abstract. We present a comprehensive review of keV-scale sterile neutrino Dark Matter, collecting views and insights from all disciplines involved -cosmology, astrophysics, nuclear, and particle physics -in each case viewed from both theoretical and experimental/observational perspectives. After reviewing the role of active neutrinos in particle physics, astrophysics, and cosmology, we focus on sterile neutrinos in the context of the Dark Matter puzzle. Here, we first review the physics motivation for sterile neutrino Dark Matter, based on challenges and tensions in purely cold Dark Matter scenarios. We then round out the discussion by critically summarizing all known constraints on sterile neutrino Dark Matter arising from astrophysical observations, laboratory experiments, and theoretical considerations. In this context, we provide a balanced discourse on the possibly positive signal from X-ray observations. Another focus of the paper concerns the construction of particle physics models, aiming to explain how sterile neutrinos of keV-scale masses could arise in concrete settings beyond the Standard Model of elementary particle physics. The paper ends with an extensive review of current and future astrophysical and laboratory searches, highlighting new ideas and their experimental challenges, as well as future perspectives for the discovery of sterile neutrinos.

We provide a complete picture to the self-gravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite volume limit in the grand canonical (GCE), canonical (CE) and microcanonical (MCE) ensembles when (N, V ) → ∞, keeping N/V 1/3 fixed. We compute the equation of state (we do not assume it as is customary), as well as the energy, free energy, entropy, chemical potential, specific heats, compressibilities and speed of sound; we analyze their properties, signs and singularities. All physical quantities turn out to depend on a single variable η ≡ G m 2 N V 1/3 T that is kept fixed in the N → ∞ and V → ∞ limit. The system is in a gaseous phase for η < η T and collapses into a dense object for η > η T in the CE with the pressure becoming large and negative. At η ≃ η T the isothermal compressibility diverges. This gravitational phase transition is associated to the Jeans' instability. Our Monte Carlo simulations yield η T ≃ 1.515. P V /[N T ] = f (η) and all physical magnitudes exhibit a square root branch point at η = η C > η T . The values of η T and η C change by a few percent with the geometry for large N : for spherical symmetry and N = ∞ (MF), we find η C = 1.561764 . . . while the Monte Carlo simulations for cubic geometry yields η C ≃ 1.540. In mean field and spherical symmetry c V diverges as (η C − η) −1/2 for η ↑ η C while c P and κ T diverge as (η 0 − η) −1 for η ↑ η 0 = 1.51024 . . .. The function f (η) has a second Riemann sheet which is only physically realized in the MCE. In the MCE, the collapse phase transition takes place in this second sheet near η M C = 1.26 and the pressure and 7 Specific Heats, Speed of Sound and Compressibility 42 8 Discussion 47 9 Acknowledgements 48 A Functional integration Measure in the Mean Field Approach 48 B Calculation of the saddle point 49 C Abel's equation of first kind for the equation of state 49 2 η R