A Gaia DR 2 and VLT/FLAMES search for new satellites of the LMC
  A wealth of tiny galaxies populates the surroundings of the Milky Way. Some
of these objects might have their origin as former satellites of the Large
Magellanic Cloud. Examples of the importance of understanding how many systems
are genuine satellites of the MW or the LMC are the implications that the
number and mass function of satellites have for dark matter theories and the
treatment of baryonic physics in simulations of structure formation. Here we
aim at deriving the bulk motions and estimates of the internal velocity
dispersion and metallicity properties in four recently discovered distant
southern dwarf galaxy candidates, Columba I, Reticulum III, Phoenix II and
Horologium II. We combine Gaia DR2 astrometric measurements, photometry and new
FLAMES spectroscopic data in the region of the CaII triplet lines; such
combination is essential for finding potential member stars in these low
luminosity systems. We find very likely member stars in all four satellites and
are able to determine (or place limits on) the systems bulk motions and average
internal properties. The systems are found to be very metal-poor, in agreement
with dwarf galaxies and dwarf galaxy candidates of similar luminosity. The only
system that we can place firmly in the category of dwarf galaxies is Phx II,
given its resolved large velocity dispersion ($9.5_{-4.4}^{+6.8}$ km/s) and
intrinsic metallicity spread (0.33 dex). Also for Col I we measure a clear
metallicity spread. The orbital pole of Phx II is well constrained and close to
that of the LMC, suggesting a prior association. The uncertainty on the orbital
poles of the other systems are presently very large, so that an association
cannot be excluded, apart from Col I. Using the numbers of potential former
satellites of the LMC identified here and in the literature, we obtain for the
LMC a dark matter mass of M$_{200}=1.9_{-0.9}^{+1.3}\times10^{11}$ M$_\odot$.
