Limits on the significant mass-loss scenario based on the globular clusters of the Fornax dwarf spheroidal galaxy

Many of the scenarios proposed to explain the origin of chemically peculiar stars in globular clusters (GCs) require significant mass-loss ($\ge 95\mathrm{\%}$) to explain the observed fraction of such stars. In the GCs of the Fornax dwarf galaxy significant mass-loss could be a problem. Larsen et al. (2012) showed that there is a large ratio of GCs to metal-poor field stars in Fornax and about $20-25\mathrm{\%}$ of all the stars with $[\mathrm{F}\mathrm{e}\mathrm{/}\mathrm{H}]<-2$ belong to the four metal-poor GCs. This imposes an upper limit of $\sim 80\mathrm{\%}$ mass-loss that could have happened in Fornax GCs. In this paper, we propose a solution to this problem by suggesting that stars can leave the Fornax galaxy. We use a series of $N$-body simulations, to determine the limit of mass-loss from Fornax as a function of the initial orbital radii of GCs and the speed with which stars leave Fornax GCs. We consider a set of cored and cuspy density profiles for Fornax. Our results show that with a cuspy model for Fornax, the fraction of stars which leave the galaxy, can be as high as $\sim 90\mathrm{\%}$, when the initial orbital radii of GCs are $R=2-3\mathrm{k}\mathrm{p}\mathrm{c}$ and the initial speed of stars is $v>20\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$. We show that such large velocities can be achieved by gas expulsion induced mass-loss but not stellar evolution induced mass-loss. Our results imply that one cannot interpret the metallicity distribution of Fornax field stars as evidence against significant mass-loss in Fornax GCs, if mass-loss is due to gas expulsion.