Implication of dark matter in dwarf spheroidal galaxies

We examine the correlation between physical quantities to explore the existence of dark matter (DM) in the Local Group dwarf spheroidal galaxies (dSphs). In order to clarify whether DM exists in the dSphs we compare two extreme models of their internal kinematics: [1] a tidal model (the mass of a dSph is estimated with the luminous mass, since the observed large velocity dispersions of the dSphs are attributed to the tidal force by the Galaxy), and [2] a DM model (the mass of a dSph is estimated with the virial mass, since the velocity dispersion is considered to reflect the DM potential). In both models, we find that the relation between the surface brightness of the dSphs and the tidal force by the Galaxy is consistently interpreted. This makes a critical remark about the previous studies that concluded that the tidal force is effective for the dSphs based only on model [1]. We also check the correlation between the Galactocentric distance and the tidal force. Consequently, both models are also supported in this test. Thus, we are unable to judge which of the two is more promising for the dSphs in correlation investigations. The physical process of tidal disruption is also considered. Since the timescale for the tidally perturbed stars td escape is much shorter than the orbital periods of the dSphs, it is difficult for the tidally perturbed dSphs to exist as an assembly. Thus, we suggest that the gravitational field of DM is necessary to bind the dSphs with a large velocity dispersion.