Neutrino bound states and bound systems

Abstract

Yukawa interactions of neutrinos with a new light scalar boson φ can lead to formation of stable bound states and bound systems of many neutrinos (ν-clusters). For allowed values of the coupling y and the scalar mass m φ , the bound state of two neutrinos would have the size larger than 10 12 cm. Bound states with sub-cm sizes are possible for keV scale sterile neutrinos with coupling y > 10 −4 . For the ν-clusters we study in detail the properties of final stable configurations. If there is an efficient cooling mechanism, these configurations are in the state of degenerate Fermi gas. We formulate and solve equations to describe the density distributions in ν-clusters for different values of the total number of neutrinos, N . In the non-relativistic case, they are reduced to the Lane-Emden equation. We find that (i) stable configurations exist for any number of neutrinos; (ii) there is a maximal central density ∼ 10 9 cm −3 determined by the neutrino mass; (iii) for a given m φ there is a minimal value of N y 3 for which stable configurations can be formed; (iv) for a given strength of interaction (∝ y/m φ ), the minimal radius of ν-clusters exists. We discuss the formation of the ν-clusters from relic neutrino background in the process of expansion and cooling of the Universe. One possibility is the development of instabilities in the ν-background at T < mν which leads to its fragmentation. Another way is the growth of initial density perturbations in the ν-background and virialiazation in analogy with formation of the Dark Matter halos. For allowed values of y, cooling of ν-clusters due to φ-bremsstrahlung and neutrino annihilation is negligible. ν-clusters can be formed with the sizes ranging from ∼ km to ∼ 10 Mpc.

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