Download Formation of ellipticals: Merging with or without star formation?

FORMATION OF
ELLIPTICALS:
merging with or without star
formation?
Luca Ciotti
Dept. of Astronomy
University of Bologna
Ringberg Castle, July 4-8, 2005
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.
For simplicity I’ll 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
“DRY” MERGING
(no gas )
We start with a population of identical “seed” galaxies
M*0
MBH0  M*0
&


  103
(Magorrian)
Stellar mass evolution


M* (i 1)  2M* (i)
BH mass evolution (VERY unclear. Classical? Tcoal<Tmerg?)
MBH (i 1)  2MBH (i)
i
i+1
Previous equations can be solved as
M* (i)  2 M*0
i
M BH (i)  2 M BH 0  M* (i)
i

Thus, Magorrian relation is CONSISTENT with DRY galaxy
merging PROVIDED
1) BH merging is classical
3) BH coalescence is “fast”
However, serious problems arise with the other scaling laws…
Energy conservation (+ parabolic orbits)
E(i 1)  2E(i)
E(i)  T* (i)  U* (i)
2T* (i)  U* (i)  E(i)  T* (i) U* (i)/2
(VT)
and so after remnant virialization
 
T (i 1)  2T
*

*
(i)

2T* (i 1)
2
2
 * (i 1) 
  * (i)   *0
M* (i 1)

2

A similar analysis with potential energy shows that
rV * (i)  2 rV *0
i
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.
(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
t=0 seed galaxy.
Projected quantities
Central vel. disp.
(Faber-Jackson)
Effective radius
(Kormendy)

Fundamental Plane
Major mergers OK
Accretions KO
Induced structural non-homology:
Major mergers: m  M: OK
Accretions: m  M: KO
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.
GAS DISSIPATION
Self-gravitating systems have negative specific heat 
”cooling”virialization  ”heating” (i.e. vel. disp. increases)
MBH0  M*0
M g 0   0 M*0
Gas evolution
M g (i  1)  2M g (i)  2M g (i)  2M g (i)
1
0 
(dissipation parameter)
1 

0  q  1 (1 )  1


M g (i)  2 q M g 0
i
i
Stellar mass evolution
M* (i  1)  2M* (i)  2M g (i)
i 

1 q
i
M*(i)  2 1  0
M*0
1 q 

BH mass evolution
and so

M BH (i  1)  2M BH (i)  2M g (i)
MBH (i)  M* (i)
i.e. Magorrian rel. can be preserved also with gas dissipation
It follows that
 (i) 
M g (i)
M* (i)

 0q
i
i
1 q
1  0
1 q
i.e. the relative gas amount in the remnant is a steadily
decreasing function along the merging hierarchy
Energy equation
For a virialized 2-component galaxy
1
E  T*  Tg 
2
For simplicity let assume
 (
*
 g )(*  g )dV
g  *   g  *
hydrostatic equilibrium & Jeans equations
From
2
P



  *  Tg  T*
r
r
so that
E  (1  )T*  (1  ) U*
2

From the 2-component VT
2T*  U*  W*g
W*g    *  x,g  dV  U*
so that

2T*  (1 )U*

and for a two-component virialized galaxy
(1  )
U*
 E  (1  )T* 
2
2
In a parabolic merging with gas dissipation
E(i  1)  2E(i)  2(1 )Tg (i)
and from VT
1  (i)[1 (1 )]
T* (i  1)  2
T* (i)
1  (i  1)

that can be recast as

 (1 2) (i)  2
 * (i  1)  1
 * (i)
 1 (1 ) (i) 
2
which is a non-decreasing quantity in case of dissipation
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.