  Studies of internal structure of gas giant planets suggest that their
envelopes are enriched with heavier elements than hydrogen and helium relative
to their central stars. Such enrichment likely occurred by solid accretion
during late formation stages of gas giant planets in which gas accretion
dominates protoplanetary growth. Some previous studies performed orbital
integration of planetesimals around a growing protoplanet with the assumption
of an uniform circumstellar disc to investigate how efficiently the protoplanet
captures planetesimals. However, not only planetesimals but also disc gas are
gravitationally perturbed by the protoplanet in its late formation stages,
resulting in gap opening in the circumstellar disc. In this study, we
investigate the effects of such gap formation on the capture of planetesimals
by performing dynamical simulations of planetesimals around a growing proto-gas
giant planet. Gap formation reduces the surface density of disc gas, makes a
steep pressure gradient and limits the growth rate of the protoplanet. We find
that the first effect enhances the capture of planetesimals, while the others
reduce it. Consequently the amount of planetesimals captured during the gas
accretion is estimated to be at most ~3 Mearth. We conclude that the in-situ
capture of planetesimals needs the initial solid surface density more than five
times higher than that of the minimum mass solar nebula for explaining the
inferred large amount of heavy element in Jupiter. For highly dense warm
Jupiters, we would need additional processes enhancing the capture and/or
supply of planetesimals.
