Environmental Engineering Reference
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spiral galaxies (for an exhaustive review on DM refer to, Freeman and McNamara, 2006).
The current investigation aims to provide further insight on the tidal action induced by mas-
sive halos on hosted galaxies, taking into consideration special sequences of two-component
systems, intended to model early-type galaxies (hereafter quoted as ETGs) and their hosting
halos.
The idea of exploring two-component systems, a stellar spheroid completely embedded
in a DM halo, moves from the fact that the virial potential energy (hereafter quoted as
VPE) of the stellar component, shows a non-monotonic trend as a function of the radius,
as opposed to one-component systems. This behavior is induced by the DM halo tidal
potential, and is more effective for shallower DM halo density profiles. The occurrence
of extremum points in potential energy could be highly rewarding, as in mechanics they
correspond to stationary points and may be special configurations for the system. These
extremum points could be a key to the explanation of the so called “tilt” of the Fundamental
Plane (FP) (see, Bender et al., 1992).
The current investigation is based on two ETGs density profiles of astrophysical interest,
using the formalism of the two-component virial theorem for an explicit expression of the
VPE of the stellar subsystem embedded in the DM halo. The models and related special
sequences of two-component systems, intended to represent ETGs, are defined in Section 2..
An analysis of VPE extremum points, with the further restriction of energy conservation,
is performed and discussed in Section 3.. Comparisons between model predictions and
both data from observations and results from computer simulations, are made in Section 4..
Conclusions are drawn in Section 5..
2.
Models
Hernquist cuspy mass density profiles shall be used for the bright stellar component as
best compromise between a reliable description of ETG luminosity profiles, and the need
of dynamical and photometric analytical quantities when exploring models. The explicit
formulation is:
M
∗
2
Π
R
∗
R
(
R
∗
+
R
)
3
Ρ
N
2
Π
1
S
(1 +
S
)
3
Ρ
∗
(
R
)
=
=
(1)
S
≡
R
R
∗
Ρ
N
≡
M
∗
;
R
∗
3
where M
∗
is the total mass, R
∗
is a scaling radius, and the asterisk denotes the stellar sub-
system. Aiming to explore the effect of either a cored or a cuspy DM density profile on the
VPE, Hernquist stellar profiles shall be coupled to either Hernquist cuspy DM profiles:
M
h
2
Π
R
h
R
(
R
h
+
R
)
3
Ρ
N
2
Π
R
Β
S
(
Β
+
S
)
3
Ρ
h
(
R
)
=
=
(2)
or Plummer cored DM profiles:
R
Β
2
(
Β
2
+
S
2
)
5/2
R
R
h
2
(
R
h
2
+
R
2
)
5/2
3
M
∗
4
Π
3
Ρ
N
4
Π
Ρ
h
(
R
)
=
=
(3)
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