  We study the evolution of debris created in the giant impacts expected during
the final stages of terrestrial planet formation. The starting point is the
debris created in a simulation of the Moon-forming impact. The dynamical
evolution is followed for 10 Myr including the effects of Earth, Venus, Mars
and Jupiter. The spatial distribution evolves from a clump in the first few
months to an asymmetric ring for the first 10 kyr and finally becoming an
axisymmetric ring by about 1 Myr after the impact. By 10 Myr after the impact
20% of the particles have been accreted onto Earth and 17% onto Venus, with 8%
ejected by Jupiter and other bodies playing minor roles. However, the fate of
the debris also depends strongly on how fast it is collisionally depleted,
which depends on the poorly constrained size distribution of the impact debris.
Assuming that the debris is made up of 30% by mass mm-cm-sized vapour
condensates and 70% boulders up to 500 km, we find that the condensates deplete
rapidly on ~1000 yr timescales, whereas the boulders deplete predominantly
dynamically. By considering the luminosity of dust produced in collisions
within the boulder-debris distribution we find that the Moon-forming impact
would have been readily detectable around other stars in Spitzer 24 micron
surveys for around 25 Myr after the impact, with levels of emission comparable
to many known hot dust systems. The vapour condensates meanwhile produce a
short-lived, optically thick, spike of emission. We use these surveys to make
an estimate of the fraction of stars that form terrestrial planets, F_TPF.
Since current terrestrial planet formation models invoke multiple giant
impacts, the low fraction of 10-100 Myr stars found to have warm (~150 K) dust
implies that F_TPF ~<10%.
