  Here we address the hot Jupiter (hJ) pile-up at 0.05 AU around young
solar-type stars observed in stellar radial velocity surveys, the hJ longterm
orbital stability in the presence of stellar tides, and the hJ occurrence rate
of 1.2 (+-0.38)% in one framework. We calculate the combined torques on the
planet from the stellar dynamical tide and from the protoplanetary disk in the
type II migration regime. We model a 2D nonisothermal viscous disk
parameterized to reproduce the minimum-mass solar nebula and simulate an inner
disk cavity at various radial positions near the star. We choose stellar
rotation periods according to observations of young star clusters. The planet
is on a circular orbit in the disk midplane and in the star's equatorial plane.
We show that the torques can add up to zero beyond the corotation radius around
young stars and stop inward migration. Monte Carlo simulations predict hot
Jupiter survival rates between ~3% (alpha disk viscosity of 1e-1) and 15%
(alpha = 1e-3). Once the protoplanetary disk has been fully accreted, the
surviving hJs are pushed outward from their tidal migration barrier and pile up
near 0.05 AU, as we demonstrate using a numerical implementation of a stellar
dynamical tide model. Orbital decay is negligible on a one-billion-year
timescale due to the contraction of the highly dissipative convective envelopes
in young Sun-like stars. We find that the higher pile-up efficiency around
metal-rich stars can at least partly explain the observed positive correlation
between stellar metallicity and hJ occurrence. Combined with the observed hJ
occurrence rate, our results for the survival rate imply that <8 % (alpha =
1e-3) to <43 % (alpha = 1e-1) of sun-like stars initially encounter an inward
migrating hJ. This reconciles models and observations of young spinning stars
with the observed hJ pile up and hJ occurrence rates.
