Measurement of TeV dark particles due to decay of heavy dark matter in
  the earth core at IceCube
  In the present paper, it is assumed that there exist two species of dark
matter: a heavy dark matter particle (HDM) with the mass of O(TeV) which is
generated in early universe and a lighter dark matter particle (LDM) which is a
relativistic product due to the decay of HDM. HDMs, captured by the earth,
decay to high energy LDMs, and these particles can be measured by km$^3$
neutrino telescopes, like the IceCube detector. A $Z^{\prime}$ portal dark
matter model is taken for LDMs to interact with nuclei via a neutral current
interaction mediated by a heavy gauge boson $Z^{\prime}$. With the different
lifetimes of decay of HDMs and Z$^{\prime}$ masses, the event rates of LDMs,
measured by IceCube, are evaluated in the energy range between 1 TeV and 100
TeV. According to the IceCube data, the upper limit for LDM fluxes is estimated
at 90\% C.L. at IceCube. Finally, it is proved that LDMs could be directly
detected in the energy range betwen O(1TeV) and O(10TeV) at IceCube with
$m_{Z^{\prime}} \lesssim 500 GeV$ and $\tau_{\phi} \lesssim 10^{21}$ s.
