Discriminating between Thermal and Nonthermal Cosmic Relic Neutrinos
  through Annual Modulation at PTOLEMY
  If massive neutrinos are Dirac particles, the proposed PTOLEMY experiment
will hopefully be able to discover cosmic neutrino background via $\nu^{}_e +
{^3}{\rm H} \to {^3}{\rm He} + e^-$ with a capture rate of $\Gamma^{}_{\rm D}
\approx 4~{\rm yr}^{-1}$. Recently, it has been pointed out that right-handed
components of Dirac neutrinos could also be copiously produced in the early
Universe and become an extra thermal or nonthermal ingredient of cosmic relic
neutrinos, enhancing the capture rate to $\Gamma^{}_{\rm D} \approx 5.1~{\rm
yr}^{-1}$ or $\Gamma^{}_{\rm D} \approx 6.1~{\rm yr}^{-1}$. In this work, we
investigate the possibility to distinguish between thermal and nonthermal
spectra of cosmic relic neutrinos by measuring the annual modulation of the
capture rate. For neutrino masses of $0.1~{\rm eV}$, we have found the
amplitude of annual modulation in the standard case is ${\cal M} \approx
0.05\%$, which will be increased to $0.1\%$ and $0.15\%$ in the presence of
additional thermal and nonthermal right-handed neutrinos, respectively. The
future detection of such a modulation will be helpful in understanding the
Majorana or Dirac nature of massive neutrinos.
