FORMATION%20OF%20ELLIPTICALS:

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FORMATION OF ELLIPTICALS

• merging with or without star formation?

Luca Ciotti Dept. of Astronomy University of
Bologna
Ringberg Castle, July 4-8, 2005
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Simple approach based on Scaling Laws
1. The relevance of FP tilt thinnes to obtain
a physical picture of Es structure and formation
was emphasized in Renzini Ciotti (1993, ApJL).
2. This approach was also used in Ciotti van
Albada (2001, ApJL) where, by using elementary
arguments and considering the additional
constraints imposed by the MBH-? relation,
we concluded that gas dissipation is needed.
3. These predictions were confirmed by
high-resolution N-body simulations (Nipoti,
Londrillo Ciotti 2003, MNRAS), showing that
dissipationless (DRY) mergings do not preserve
the Es scaling relations.
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For simplicity Ill review here the EXPECTED
evolution of the galaxy stellar velocity
dispersion and effective radius under multiple
merging events, in the cases of
? DRY (i.e. dissipationless) merging

• Dissipative (i.e., gas rich, star forming) merging

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DRY MERGING (no gas)
We start with a population of identical seed
galaxies

i
?
?
(Magorrian)
i1
Stellar mass evolution
BH mass evolution (VERY unclear. Classical?
TcoalltTmerg?)
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Previous equations can be solved as

• Thus, Magorrian relation is CONSISTENT with DRY
  galaxy merging PROVIDED
• 1) BH merging is classical
• 3) BH coalescence is fast

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However, serious problems arise with the other
scaling laws
Energy conservation ( parabolic orbits)
(VT)
and so after remnant virialization
?
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A similar analysis with potential energy shows
that
where rV is the virial radius
In DRY mergings the velocity dispersion stays
constant while the virial radius doubles in each
merging. This ELEMENTARY prediction is ACCURATELY
CONFIRMED by N-body simulations.
? In the simulations we look at central,
projected velocity dispersion and effective
radius, thus non-homology has only a weak effect
for the considerations above.
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(Nipoti, Londrillo Ciotti 2003) virial
quantities
Solid dots major mergers. The end-product of a
merging is duplicated and merged with its copy.
Empty symbols accretions. The end-product of a
merging is merged with a copy of the t0 seed
galaxy.
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Projected quantities
Central vel. disp. (Faber-Jackson)
Effective radius (Kormendy)
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?
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Fundamental Plane
Major mergers OK Accretions KO
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Induced structural non-homology
Major mergers m ? M OK Accretions m ? M KO
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Thus we have seen that dry merging is unable to
reproduce the mass-velocity dispersion observed
in real galaxies.
It is of particular interest the fact that we can
include gas dissipation in the simple scheme
just described.
The effect of gas dissipation is an increase of
the velocity dispersion.
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GAS DISSIPATION
Self-gravitating systems have negative specific
heat ? cooling?virialization ? heating (i.e.
vel. disp. increases)
Gas evolution
(dissipation parameter)
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Stellar mass evolution
BH mass evolution
and so
i.e. Magorrian rel. can be preserved also with
gas dissipation
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It follows that
i.e. the relative gas amount in the remnant is a
steadily decreasing function along the merging
hierarchy
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Energy equation
For a virialized 2-component galaxy
For simplicity let assume
From hydrostatic equilibrium Jeans equations
so that
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From the 2-component VT
so that
and for a two-component virialized galaxy
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In a parabolic merging with gas dissipation
and from VT
that can be recast as
which is a non-decreasing quantity in case of
dissipation
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CONCLUSIONS

1. Simple dynamical arguments based on Es scaling
   laws do require gas dissipation as a key
   ingredient if merging is the standard way to form
   Es. Low-redshift dry mergings can be considered
   only as rare events.
2. If gas dissipation is important, then the mean
   age of stars in Es is a strong constraint on the
   epoch of substantial merging.
3. From the Magorrian rel. major mergers must be
   followed by QSO activity (however, QSOs may exist
   without merging!)
4. All the scaling relations must be explained by a
   consistent formation scenario. Focussing on a
   subset of scaling relations may easily lead to
   wrong conclusions, such as that dissipationless
   merging is a possible way to form Es.