$\Lambda$CDM Predictions for the Satellite Population of M33
  Triangulum (M33) is the most massive satellite galaxy of Andromeda (M31),
with a stellar mass of about $3\times10^9\; M_{\odot}$. Based on abundance
matching techniques, M33's total mass at infall is estimated to be of order
$10^{11}\; M_{\odot}$. $\Lambda$CDM simulations predict that M33-mass halos
host several of their own low mass satellite companions, yet only one candidate
M33 satellite has been detected in deep photometric surveys to date. This
`satellites of satellites' hierarchy has recently been explored in the context
of the dwarf galaxies discovered around the Milky Way's Magellanic Clouds in
the Dark Energy Survey. Here we discuss the number of satellite galaxies
predicted to reside within the virial radius ($\sim$160 kpc) of M33 based on
$\Lambda$CDM simulations. We also calculate the expected number of satellite
detections in N fields of data using various ground--based imagers. Finally, we
discuss how these satellite population predictions change as a function of
M33's past orbital history. If M33 is on its first infall into M31's halo, its
proposed satellites are expected to remain bound to M33 today. However, if M33
experienced a recent tidal interaction with M31, the number of surviving
satellites depends strongly on the distance achieved at pericenter due to the
effects of tidal stripping. We conclude that a survey extending to $\sim$100
kpc around M33 would be sufficient to constrain its orbital history and a
majority of its satellite population. In the era of WFIRST, surveys of this
size will be considered small observing programs.
