  Number density profiles are computed for the satellites of relatively
isolated host galaxies in the Illustris-1 simulation. The mean total mass
density of the hosts is well-fitted by an NFW profile. The number density
profile for the complete satellite sample is inconsistent with NFW and, on
scales < 0.5 r_200, the satellites do not trace the hosts' mass. This differs
substantially from previous results from semi-analytic galaxy formation models.
The shape of the satellite number density profile depends on the luminosities
of the hosts and the satellites, and on the host virial mass. The number
density profile for the faintest satellites is well-fitted by an NFW profile,
but the concentration is much less than the mean host mass density. The number
density profile for the brightest satellites exhibits a steep increase in slope
for host-satellite distances < 0.1 r_200, in qualitative agreement with recent
observational studies that find a steep increase in the satellite number
density at small host-satellite distances. On scales > 0.1 r_200 the satellites
of the faintest hosts trace the host mass reasonably well. On scales > 0.4
r_200, the satellites of the brightest hosts do not trace the host mass and the
satellite number density increases steeply for host-satellite distances < 0.1
r_200. The discrepancy between the satellite number density profile and the
host mass density is most pronounced for the most massive systems, with the
satellite number density falling far below that of the mass density on scales <
0.5 r_200.
