Implication of Dark Matter in Dwarf Spheroidal Galaxies

We examine the correlation between physical quantities to explore theexistence of dark matter (DM) in the Local Group dwarf spheroidal galaxies(dSphs). In order to clarify whether DM exists in the dSphs we compare twoextreme models of their internal kinematics: [1] a tidal model (the mass of adSph is estimated with the luminous mass, since the observed large velocitydispersions 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 thevelocity dispersion is considered to reflect the DM potential). In both models,we find that the relation between the surface brightness of the dSphs and thetidal force by the Galaxy is consistently interpreted. This makes a criticalremark about the previous studies that concluded that the tidal force iseffective for the dSphs based only on model [1]. We also check the correlationbetween the Galactocentric distance and the tidal force. Consequently, bothmodels are also supported in this test. Thus, we are unable to judge which ofthe two is more promising for the dSphs in correlation investigations. Thephysical process of tidal disruption is also considered. Since the timescalefor the tidally perturbed stars to escape is much shorter than the orbitalperiods of the dSphs, it is difficult for the tidally perturbed dSphs to existas an assembly. Thus, we suggest that the gravitational field of DM isnecessary to bind the dSphs with a large velocity dispersion.Comment: 15 pages LaTeX, 4 figures, to appear in PAS