TIDAL ENERGY EFFECTS OF DARK MATTER HALOS ON EARLY-TYPE GALAXIES - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 327

Figure 8. Same as Fig.6 but assuming Υ ∗ = 12 .

R (GG) F (GG) ( = Β ) (42)

where integrations must be performed numerically. Approximate threshold values, ( R) ,

defining MVPE configurations, are listed in Tab. 2 for different GG models. If two-
component virialized density profiles yielded by computer simulations can be fitted by
model parameters, ( Γ ∗ , Γ h , R) , then the pair, (

Β,

Β, R) , defining the related MVPE config-

urations, can be determined.
Values of parameters related to two-component, collisionless, virialized systems at the
end of computer runs performed in a recent investigation (Nipoti et al., 2006), are listed in
Tab.3. Cases (i)-(iv) and (vii) therein appear to be largely aspherical, as shown by the ratio
of the principal axes of inertia, A, B, C, of the stellar subsystem.
In the special case of homeoidally striated ellipsoids (Roberts, 1962) where the bound-
aries are also similar and similarly placed (Caimmi, 1993; Caimmi & Marmo, 2003), the
asphericity effect is expressed by a single shape factor which, for the larger elongation
among cases of Tab.3, C/A = B/A = 0 . 3 , equals about 1.6 instead of 2 related to spheri-
cal shapes (e.g. Caimmi, 1991). Accordingly, values of parameters listed in Tab.3 hold, to
an acceptable extent, also for spherical configurations. The general situation could yield a
larger discrepancy, but the shape of the DM halo at the end of computer runs has not been
mentioned in the parent paper (Nipoti et al., 2006), even if small asphericities are expected
for sufficiently high DM to stellar mass ratios, R > ∼2 . With this caveat in mind, the effect
of oblateness or elongation shall be neglected in the following.