  We have investigated how envelope pollution by icy planetesimals affects the
critical core mass for gas giant formation and the gas accretion time-scales.
In the core-accretion model, runaway gas accretion is triggered after a core
reaches a critical core mass. All the previous studies on the core-accretion
model assumed that the envelope has the solar composition uniformly. In fact,
the envelope is likely polluted by evaporated materials of icy planetesimals
because icy planetesimals going through the envelope experience mass loss via
strong ablation and most of their masses are deposited in the deep envelope. In
this paper, we have demonstrated that envelope pollution in general lowers the
critical core masses and hastens gas accretion on to the protoplanet because of
the increase in the molecular weight and reduction of adiabatic temperature
gradient. Widely- and highly-polluted envelopes allow smaller cores to form
massive envelopes before disc dissipation. Our results suggest that envelope
pollution in the course of planetary accretion has the potential to trigger gas
giant formation with small cores. We propose that it is necessary to take into
account envelope pollution by icy planetesimals when we discuss gas giant
formation based on the core-accretion model.
