Test of Clausius' Virial Dynamical Theory of Fundamental Plane By Homogeneous + γ-Free Two Component Galaxy Model

Introduction: the theory of the Fundamental Plane (FP) proposed by Secco (2000, 2001,2005) is based on the existence of a maximum in the Clausius' Virial potential energy (CV) of a stellar component when it is completely embedded inside a dark matter (DM) halo. At the first order approximation the theory was developed by modeling the two-components with two power-law density profiles and two homogeneous cores. In order to test the extension of the theory to an higher order we explore the effect on an homogeneous stellar component due to a DM halo with a density profile characterized by a inner slope γfree and an outer slope -3, according to high resolution rotation curves of Sps (Garrido et al. 2004). The aim is to investigate the role of the dark to bright mass ratio m and of the halo concentration C[D] in order to produce the maximum of CV. Particular attention is devoted to the slope of the density halo profile at the maximum location, to its height in comparison with the CV value when the two component coincide, V[n.] For all the models we choose γ=0. Method: we follow the general method proposed by Caimmi (1993) for two striated ellipsoidals with Zhao-density profiles. Virial equilibrium is described by tensor virial equations extended to two subcomponents (Caimmi & Secco,1992). The interaction terms are numerically performed for different values of m and C [D] and sequences of CV as function of the ratio baryonic to halo virial semi-axis are taken into account. Results: the special configuration at the CV maximum with all the properties discovered with the theory of first order appears if m is greater than a given threshold.The corresponding slope (in absolute value) on the halo DM profile decreases either as m increases at fixed C[D] or as C[D] decreases at fixed m. The same conspiracy between m and C[D] appears in order to obtain the highest values of V[n]. Discussion: the test is relevant in order to confirm the main results of the first order approach and then to move the description of the main features of galaxy FP toward more realistic models.