The Caterpillar Project: A Large Suite of Milky Way Sized Halos
  We present the largest number of Milky Way sized dark matter halos simulated
at very high mass ($\sim$$10^4$ M$_\odot$/particle) and temporal resolution
($\sim$5 Myrs/snapshot) done to date, quadrupling what is currently available
in the literature. This initial suite consists of the first 24 halos of the
$Caterpillar$ $Project$ (www.caterpillarproject.org) whose project goal of 60 -
70 halos will be made public when complete. We resolve $\sim$20,000
gravitationally bound subhalos within the virial radius of each host halo. Over
the ranges set by our spatial resolution our convergence is excellent and
improvements were made upon current state-of-the-art halo finders to better
identify substructure at such high resolutions (e.g., on average we recover
$\sim$4 subhalos in each host halo above 10$^8$ M$_\odot$ which would have
otherwise not been found using conventional methods). For our relaxed halos,
the inner profiles are reasonably fit by Einasto profiles ($\alpha$ = 0.169
$\pm$ 0.023) though this depends on the relaxed nature and assembly history of
a given halo. Averaging over all halos, the substructure mass fraction is
$f_{m,subs} = 0.121 \pm 0.041$, and mass function slope is d$N$/d$M\propto
M^{-1.88 \pm 0.10}$ though we find scatter in the normalizations for fixed halo
mass due to more concentrated hosts having less subhalos at fixed subhalo mass.
There are no biases stemming from Lagrangian volume selection as all Lagrangian
volume types are included in our sample. Our detailed contamination study of
264 low resolution halos has resulted in obtaining very large and
unprecedented, high-resolution regions around our host halos for our target
resolution (sphere of radius $\sim$$1.4 \pm 0.4$ Mpc) allowing for accurate
studies of low mass dwarf galaxies at large galactocentric radii and the very
first stellar systems at high redshift ($z \geq$ 10).
