Search for RR Lyrae stars in DES ultra-faint systems: Grus I, Kim 2,
  Phoenix II, and Grus II
  This work presents the first search for RR Lyrae stars (RRLs) in four of the
ultra-faint systems imaged by the Dark Energy Survey (DES) using SOAR/Goodman
and Blanco/DECam imagers. We have detected two RRLs in the field of Grus I,
none in Kim 2, one in Phoenix II, and four in Grus II. With the detection of
these stars, we accurately determine the distance moduli for these ultra-faint
dwarf satellite galaxies; $\mu_0$=20.51$\pm$0.10 mag (D$_{\odot}$=127$\pm$6
kpc) for Grus I and $\mu_0$=20.01$\pm$0.10 mag (D$_{\odot}$=100$\pm$5 kpc) for
Phoenix II. These measurements are larger than previous estimations by Koposov
et al. 2015 and Bechtol et al. 2015, implying larger physical sizes; 5\% for
Grus I and 33\% for Phoenix II. For Grus II, out of the four RRLs detected, one
is consistent with being a member of the galactic halo (D$_\odot$=24$\pm$1 kpc,
$\mu_0$=16.86$\pm$0.10 mag), another is at D$_\odot$=55$\pm$2 kpc
($\mu_0$=18.71$\pm$0.10 mag), which we associate with Grus II, and the two
remaining at D$_\odot$=43$\pm$2 kpc ($\mu_0$=18.17$\pm$0.10 mag). Moreover, the
appearance of a subtle red horizontal branch in the color-magnitude diagram of
Grus II at the same brightness level of the latter two RRLs, which are at the
same distance and in the same region, suggests that a more metal-rich system
may be located in front of Grus II. The most plausible scenario is the
association of these stars with the Chenab/Orphan Stream. Finally, we performed
a comprehensive and updated analysis of the number of RRLs in dwarf galaxies.
This allows us to predict that the method of finding new ultra-faint dwarf
galaxies by using two or more clumped RRLs will work only for systems brighter
than M$_V\sim-6$ mag.
