Associations of dwarf galaxies in a $\Lambda$CDM Universe
  Associations of dwarf galaxies are loose systems composed exclusively of
dwarf galaxies. These systems were identified in the Local Volume for the first
time more than thirty years ago. We study these systems in the cosmological
framework of the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model. We consider
the Small MultiDark Planck simulation and populate its dark matter haloes by
applying the semi-analytic model of galaxy formation SAG. We identify galaxy
systems using a friends of friends algorithm with a linking length equal to
$b=0.4 \,{\rm Mpc}\,h^{-1}$, to reproduce the size of dwarf galaxy associations
detected in the Local Volume. Our samples of dwarf systems are built up
removing those systems that have one (or more) galaxies with stellar mass
larger than a maximum threshold $M_{\rm max}$. We analyse three different
samples defined by ${\rm log}_{10}(M_{\rm max}[{\rm M}_{\odot}\,h^{-1}]) = 8.5,
9.0$ and $9.5$. On average, our systems have typical sizes of $\sim 0.2\,{\rm
Mpc}\,h^{-1}$, velocity dispersion of $\sim 30 {\rm km\,s^{-1}} $ and estimated
total mass of $\sim 10^{11} {\rm M}_{\odot}\,h^{-1}$. Such large typical sizes
suggest that individual members of a given dwarf association reside in
different dark matter haloes and are generally not substructures of any other
halo. Indeed, in more than 90 per cent of our dwarf systems their individual
members inhabit different dark matter haloes, while only in the remaining 10
per cent members do reside in the same halo. Our results indicate that the
$\Lambda$CDM model can naturally reproduce the existence and properties of
dwarf galaxies associations without much difficulty.
