  We have investigated Saturn's core formation at a radial pressure maximum in
a protoplanetary disk, which is created by gap opening by Jupiter. A core
formed via planetesimal accretion induces the fragmentation of surrounding
planetesimals, which generally inhibits further growth of the core by removal
of the resulting fragments due to radial drift caused by gas drag. However, the
emergence of the pressure maximum halts the drift of the fragments, while their
orbital eccentricities and inclinations are efficiently damped by gas drag. As
a result, the core of Saturn rapidly grows via accretion of the fragments near
the pressure maximum. We have found that in the minimum-mass solar nebula,
kilometer sized planetesimals can produce a core exceeding 10 Earth masses
within two million years. Since Jupiter may not have undergone significant type
II inward migration, it is likely that Jupiter's formation was completed when
the local disk mass has already decayed to a value comparable to or less than
Jovian mass. The expected rapid growth of Saturn's core on a timescale
comparable to or shorter than observationally inferred disk lifetime enables
Saturn to acquire the current amount of envelope gas before the disk gas is
completely depleted. The high heat energy release rate onto the core surface
due to the rapid accretion of the fragments delays onset of runaway gas
accretion until the core mass becomes somewhat larger than that of Jupiter,
which is consistent with the estimate based on interior modeling. Therefore,
the rapid formation of Saturn induced by gap opening of Jupiter can account for
the formation of multiple gas giants (Jupiter and Saturn) without significant
inward migration and larger core mass of Saturn than that of Jupiter.
