Title: Faint stellar system in the outer Milky Way halo

Abstract:
In a luminosity vs half-light radius diagram, globular clusters and dwarf galaxies are separated in 
radius at high luminosities (Mv < -3 mag). At fainter luminosities, however, these two types of 
objects overlap at half-light radii of about 20 to 30 pc.
To study these objects we performed a survey of direct N-body simulations, in a Milky Way-like 
potential, of clusters that dissolve between 8 and 12 Gyr. In these last 4 Gyr, considering all 
observable stars, we found that the size of the cluster changes, due to the orbital motion and 
the surface density background (SDB). 
The tidal modulation, caused by the orbital motion, allows the cluster to look bigger at 
apocentre than pericentre. Besides, simulating the SDB of a Milky Way-like galaxy, we found 
that the size of the same cluster is smaller with a Koposov1-like SDB than with a Willman1-like 
SDB.
It is therefore possible that some of the objects, that were classified as ultra-faint galaxies, 
because of their large sizes, are, in fact, nearly dissolved star cluster in apocentre with a low 
SDB.
Remarkable fluctuations has been seen in the evolution of the velocity dispersion due to a not 
stable size of the cluster. Moreover, we will have an analytic prediction on how many nearly 
dissolved star clusters we should expect in the halo of Milky Way. 
In conclusion, we believe that this study could shed more light on the nature of extended 
objects in the outer Milky Way halo.