  It is assumed that heavy dark matter particles (HDMs) with a mass of O(TeV)
are captured by the Sun. HDMs can decay to relativistic light dark matter
particles (LDMs), which could be measured by km$^3$ neutrino telescopes (like
the IceCube detector). The numbers and fluxes of expected LDMs and neutrinos
were evaluated at IceCube with the $Z^{\prime}$ portal dark matter model. Based
on the assumption that no events are observed at IceCube in 6 years, the
corresponding upper limits on LDM fluxes were calculated at 90\% C. L.. These
results indicated that LDMs could be directly detected in the O(1TeV)-O(10TeV)
energy range at IceCube with 100 GeV $\lesssim m_{Z^{\prime}} \lesssim$ 350 GeV
and $\tau_{\phi} \lesssim 5\times10^{22}$ s.
