Orbiting globular clusters formed in dark matter mini-halos.

We seek to differentiate dynamical and morphological attributes between globular clusters that were formed inside their own dark matter mini-halo, and those who were not. For that, we employ high resolution $N$-body simulations of globular clusters with (and without) an enveloping dark matter mini-halo, orbiting a host galaxy. We set the same prescriptions of the Fornax dwarf spheroidal galaxy and its main five globular clusters, and use $N$-body particles for all components (i.e., stars and dark matter, for both Fornax and its clusters). For clusters embedded in dark matter, we observe that the increment of mass from the extra dark component triggers a tidal radius growth that allows the mini-halo to work as a protective shield against tidal stripping, being itself stripped beforehand the stars. Consequently, tidal effects such as inflation of the stellar velocity dispersion, development of prominent tidal tails, ellipticity increase and diffusion of the stellar distribution profile are generally much milder in clusters originally embedded in dark matter. However, this shielding effect becomes negligible after an important amount of dark matter has been stripped, which happens faster for clusters having simultaneously short orbital periods, low typical orbital radii and relatively high eccentricities. Finally, we notice that even for clusters that retain a large amount of dark matter at redshift zero, their inner regions are still predominantly composed of stars, with the typical density ratio of dark matter to cluster stars being of the order of $1\%$ up to roughly $10~$pc away from the clusters' centre.