  Reproducing the large Earth/Mars mass ratio requires a strong mass depletion
in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack
model invokes a specific migration history of the giant planets to remove most
of the mass initially beyond 1 AU and to dynamically excite the asteroid belt.
However, one could also invoke a steep density gradient created by inward drift
and pile-up of small particles induced by gas-drag, as has been proposed to
explain the formation of close-in super Earths. Here we show that the asteroid
belt's orbital excitation provides a crucial constraint against this scenario
for the Solar System. We performed a series of simulations of terrestrial
planet formation and asteroid belt evolution starting from disks of
planetesimals and planetary embryos with various radial density gradients and
including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with
shallow density gradients reproduce the dynamical excitation of the asteroid
belt by gravitational self-stirring but form Mars analogs significantly more
massive than the real planet. In contrast, a disk with a surface density
gradient proportional to $r^{-5.5}$ reproduces the Earth/Mars mass ratio but
leaves the asteroid belt in a dynamical state that is far colder than the real
belt. We conclude that no disk profile can simultaneously explain the structure
of the terrestrial planets and asteroid belt. The asteroid belt must have been
depleted and dynamically excited by a different mechanism such as, for
instance, in the Grand Tack scenario.
