OGLE Study of the Sagittarius Dwarf Spheroidal Galaxy and its M54
  Globular Cluster
  We use the fundamental-mode RR Lyr-type variable stars (RRab) from OGLE-IV
survey to draw a 3D picture of the central part of the tidally disrupted
Sagittarius Dwarf Spheroidal (Sgr dSph) galaxy. We estimate the line-of-sight
thickness of the Sgr dSph stream to be FWHM_cen=2.42 kpc. Based on OGLE-IV
observations collected in seasons 2011-2014 we conduct a comprehensive study of
stellar variability in the field of the globular cluster M54 (NGC 6715)
residing in the core of this dwarf galaxy. Among the total number of 268
detected variable stars we report the identification of 174 RR Lyr stars, four
Type II Cepheids, 51 semi-regular variable red giants, three SX Phe-type stars,
18 eclipsing binary systems. Eighty-three variable stars are new discoveries.
The distance to the cluster determined from RRab stars is d_M54 = 26.7
+/-0.03(stat) +/-1.3(sys) kpc. From the location of RRab stars in the
period-amplitude (Bailey) diagram we confirm the presence of two old
populations, both in the cluster and the Sgr dSph stream.
