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Figure 7. Same as Fig.6 but assuming Υ = 8 .
of the stellar subsystem induced by gravitational action only. If MVPE configurations are
preferred final states of gravitationally bound two-component systems, they must be at-
tained regardless of the formation process, in particular through a monolithic gravitational
collapse of star particles in the potential well of a massive DM halo. In the following, the
monolithic gravitational collapse shall be considered due to its intrinsic simplicity, but the
basic ideas and the results hold true also for more complex galaxy formation processes.
4.2.1.
The VPE for a Two-Component Γ -model
For the sake of exploring numerical simulations performed in a recent investigation
(Nipoti et al., 2006), an additional model must be considered, where each density pro-
file (for fixed mass and scaling radius) depends on a single parameter, Γ, for that reason
called the Γ-model (see, e.g., Dehnen, 1993; Tremaine et al., 1994). Two-component Γ
models shall be hereafter quoted as GG models. In the special case, Γ = 1 , Γ density
profiles reduce to Hernquist density profiles, and GG models coincide with HH models.
Different values of Γ parameter permit the exploration of different inner slopes for the two
components. Following a similar procedure with respect to HH and HP models, within
the energy-conservation paradigm , the counterpart of Eqs. (16)-(17) and (20)-(21) for GG
models reads:
V (GG)
E F (GG)
=
[R (vir) , Β (vir) ]
(41)
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