  Jupiter Trojans are thought to be survivors of a much larger population of
planetesimals that existed in the planetary region when planets formed. They
can provide important constraints on the mass and properties of the
planetesimal disk, and its dispersal during planet migration. Here we tested a
possibility that the Trojans were captured during the early dynamical
instability among the outer planets (aka the Nice model), when the semimajor
axis of Jupiter was changing as a result of scattering encounters with an ice
giant. The capture occurs in this model when Jupiter's orbit and its Lagrange
points become radially displaced in a scattering event and fall into a region
populated by planetesimals (that previously evolved from their natal
transplanetary disk to ~5 AU during the instability). Our numerical simulations
of the new capture model, hereafter jump capture, satisfactorily reproduce the
orbital distribution of the Trojans and their total mass. The jump capture is
potentially capable of explaining the observed asymmetry in the number of
leading and trailing Trojans. We find that the capture probability is
(6-8)x10^-7 for each particle in the original transplanetary disk, implying
that the disk contained (3-4)x10^7 planetesimals with absolute magnitude H<9
(corresponding to diameter D=80 km for a 7% albedo). The disk mass inferred
from this work, M_disk=14-28 M_Earth, is consistent with the mass deduced from
recent dynamical simulations of the planetary instability.
