Measuring anisotropies in the cosmic neutrino background

Neutrino capture on tritium has emerged as a promising method for detecting the cosmic neutrino background ($\mathrm{C}\nu \mathrm{B}$). We show that relic neutrinos are captured most readily when their spin vectors are antialigned with the polarization axis of the tritium nuclei and when they approach along the direction of polarization. As a result, $\mathrm{C}\nu \mathrm{B}$ observatories may measure anisotropies in the cosmic neutrino velocity and spin distributions by polarizing the tritium targets. A small dipole anisotropy in the $\mathrm{C}\nu \mathrm{B}$ is expected due to the peculiar velocity of the lab frame with respect to the cosmic frame and due to late-time gravitational effects. The PTOLEMY experiment, a tritium observatory currently under construction, should observe a nearly isotropic background. This would serve as a strong test of the cosmological origin of a potential signal. The polarized-target measurements may also constrain nonstandard neutrino interactions that would induce larger anisotropies and help discriminate between Majorana versus Dirac neutrinos.

Figure 1

The velocity distribution $f_{\mathrm{C}\nu \mathrm{B}}(u_{\nu })$ is isotropic in the $\mathrm{C}\nu \mathrm{B}$ frame, with ${\mathbf{u}}_{\nu }$ the neutrino velocity (red, solid line) in that frame. In this illustration, the neutrino is left-handed in the $\mathrm{C}\nu \mathrm{B}$ frame, so its spin (purple, dotted line) is ${\widehat{\mathbf{s}}}_{\nu }^{\mathrm{C}\nu \mathrm{B}}=-{\widehat{\mathbf{u}}}_{\nu }$. The lab frame is boosted with respect to the $\mathrm{C}\nu \mathrm{B}$ frame by ${\mathbf{v}}_{\mathrm{C}\nu \mathrm{B}}$, and so the lab-frame neutrino velocity is ${\mathbf{v}}_{\nu }={\mathbf{u}}_{\nu }-{\mathbf{v}}_{\mathrm{C}\nu \mathrm{B}}$.

Figure 2

The NCB detection rate for the $\mathrm{C}\nu \mathrm{B}$ depends on the direction of the polarization vector ${\widehat{\mathbf{s}}}_{\mathbf{H}}$, shown in the left column in Galactic coordinates (Mollweide projection), with the Galactic center (GC) at the origin. A polarization vector ${\widehat{\mathbf{s}}}_{\mathbf{H}}$ that is fixed on the surface of the Earth sweeps out a circle in the sky during the day and is manifested in terms of a daily modulation as a result of the dipole asymmetry. We illustrate this for a polarization vector aligned perpendicular to the Earth’s rotational axis. The path through the sky is shown by the solid blue curves through the Mollweide maps, and the daily-modulating rates are shown in the right column. In the bound (unbound) map, the direction of minimal rate corresponds to the direction ${\widehat{\mathbf{v}}}_{\mathrm{MW}}$ (${\widehat{\mathbf{v}}}_{\mathrm{CMB}}$).