  We study the possibility of tidal dissipation in the solid cores of giant
planets and its implication for the formation of hot Jupiters through
high-eccentricity migration. We present a general framework by which the tidal
evolution of planetary systems can be computed for any form of tidal
dissipation, characterized by the imaginary part of the complex tidal Love
number, ${\rm Im}[{\tilde k}_2(\omega)]$, as a function of the forcing
frequency $\omega$. Using the simplest viscoelastic dissipation model (the
Maxwell model) for the rocky core and including the effect of a nondissipative
fluid envelope, we show that with reasonable (but uncertain) physical
parameters for the core (size, viscosity and shear modulus), tidal dissipation
in the core can accommodate the tidal-Q constraint of the Solar system gas
giants and at the same time allows exoplanetary hot Jupiters to form via tidal
circularization in the high-e migration scenario. By contrast, the often-used
weak friction theory of equilibrium tide would lead to a discrepancy between
the Solar system constraint and the amount of dissipation necessary for high-e
migration. We also show that tidal heating in the rocky core can lead to modest
radius inflation of the planets, particularly when the planets are in the
high-eccentricity phase ($e\sim 0.6$) during their high-e migration. Finally,
as an interesting by-product of our study, we note that for a generic tidal
response function ${\rm Im}[{\tilde k}_2(\omega)]$, it is possible that spin
equilibrium (zero torque) can be achieved for multiple spin frequencies (at a
given $e$), and the actual pseudo-synchronized spin rate depends on the
evolutionary history of the system.
