Part II: Low Energy Galactic Neutrinos

Abstract

We study low energy galactic neutrinos in the Milky Way under two fundamentally different descriptions of gravity, showing that neutrinos provide a sensitive probe of gravity underlying nature. If gravity is a quantum interaction, its long range character leads to the formation of an atom like bound neutrino structure. We compute its mass distribution and find that, within a radius 292 kpc, the total mass is only ten to the minus 29 of the galaxy dark matter, ruling it out as a dark matter candidate. Nevertheless, experimental confirmation of this structure would constitute direct evidence for gravity as a quantum force mediated by gravitons. If gravity instead arises from spacetime curvature, neutrinos interact only via the short range weak force and are therefore effectively collisionless. In this regime, neutrinos behave as free classical particles orbiting the galaxy and experience no Fermi pressure. We show that such a population can be sufficiently compact to reproduce the Milky Way rotation curve, making neutrinos viable dark matter candidates. The extremely small neutrino antineutrino annihilation cross section further implies near equilibrium between neutrinos and antineutrinos, potentially addressing the matter antimatter asymmetry.

Figures (7)

• Figure 1: Probability distributions for single particle in n=21. We plot here few probability distributions for principal quantum number n=21 and a sample of angular momenta. We note that all the distributions from (a) to (d) have similar shape and only differ on how stretched they are. We note that all the distributions have 21 peaks. In all cases, the plot range starts at $10R$.
• Figure 2: Probability distributions for many particles at once. We plot few probability distributions for principal quantum number ranging from (a) $n=6$ composed of $N=72$ normalized wavefunctions to (d) $n=21$ composed of $N=882$ normalized wavefunctions. We notice that the triangular shape of the distribution get more accentuated with higher principal number $n$. In all cases, the plot range starts at $10R$.
• Figure 3: Triangular fit. We see that as the number of particles in a distribution that starts at $n=1$ and fills every state to a given $n$ increases, the shape approaches a right triangle. We assume that the triangular shape is maintained as $n$ grows large. The area of the triangle represents the number of particles $A=N=2n^2$. The size of the base, $r$, is 4/3 of location of the peak of the asymptotic wavefunction with largest $n$ and $\kappa=n$. The height, $h$, is defined by $A$ and $r$.
• Figure 4: Mass probability distribution for the neutrino atom. The units are in $10^9\textup{M}_\odot/kpc$. This distribution ranges from nearly the center of the galaxy to nearly the edge at 292 kpc. (a) Assuming that the neutrino atom is dark matter we obtain a mass distribution made of neutrinos. The area under this graph is of order of $10^{-29}$ times smaller that the expected dark matter in the Milky-Way galaxy. (b) The neutrino atom is slightly more massive in the presence of dark matter not made of neutrinos.
• Figure 5: Neutrino density as a function of radial distance. The dashed green line is the density calculated along the galactic disk, the dotted orange line is the density calculated along the axis of symmetry of the galaxy and the solid blue line is the weighted average of the two densities. We note that the non-spherically symmetric galactic disk does not seem to affect significantly the density distribution. According to this plot, the neutrino density at $8.3 kpc$, the location of the solar system, is $0.0136\times10^9\textup{M}_\odot/kpc^3$.