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If massive neutrinos are Dirac particles, the proposed PTOLEMY experimentwill 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-handedcomponents of Dirac neutrinos could also be copiously produced in the earlyUniverse and become an extra thermal or nonthermal ingredient of cosmic relicneutrinos, enhancing the capture rate to $\Gamma^{}_{\rm D} \approx 5.1~{\rmyr}^{-1}$ or $\Gamma^{}_{\rm D} \approx 6.1~{\rm yr}^{-1}$. In this work, weinvestigate the possibility to distinguish between thermal and nonthermalspectra of cosmic relic neutrinos by measuring the annual modulation of thecapture rate. For neutrino masses of $0.1~{\rm eV}$, we have found theamplitude of annual modulation in the standard case is ${\cal M} \approx0.05\%$, which will be increased to $0.1\%$ and $0.15\%$ in the presence ofadditional thermal and nonthermal right-handed neutrinos, respectively. Thefuture detection of such a modulation will be helpful in understanding theMajorana or Dirac nature of massive neutrinos.

Discriminating between Thermal and Nonthermal Cosmic Relic Neutrinos through Annual Modulation at PTOLEMY