If massive neutrinos are Dirac particles , the proposed PTOLEMY experiment will hopefully be able to discover cosmic neutrino background via \nu _ { e } + { { } ^ { 3 } } { H } \to { { } ^ { 3 } } { He } + e ^ { - } with a capture rate of \Gamma _ { D } \approx 4 ~ { } { 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 _ { D } \approx 5.1 ~ { } { yr } ^ { -1 } or \Gamma _ { D } \approx 6.1 ~ { } { 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 ~ { } { 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 .