FORMATION OF ELLIPTICALS:

merging with or without star formation?

Luca CiottiDept. of AstronomyUniversity 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)

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M*(i +1) = 2M*(i)

We start with a population of identical “seed” galaxies

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M*0

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MBH 0 = μM*0&

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μ ≈10−3(Magorrian)

Stellar mass evolution

BH mass evolution (VERY unclear. Classical? Tcoal<Tmerg?)

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MBH (i +1) = 2MBH (i)

i

i+1

Previous equations can be solved as

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M*(i) = 2iM*0

Thus, Magorrian relation is CONSISTENT with DRY galaxy merging PROVIDED

1) BH merging is classical 3) BH coalescence is “fast”

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MBH (i) = 2iMBH 0 = μM*(i)

However, serious problems arise with the other scaling laws…

Energy conservation (+ parabolic orbits)

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2T*(i) = −U*(i)⇒ E(i) = −T*(i) =U*(i) /2(VT)

and so after remnant virialization

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T*(i +1) = 2T*(i)

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*2(i +1) ≡

2T*(i +1)

M*(i +1)=σ *

2(i) =σ *02

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E(i +1) = 2E(i)

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E(i) = T*(i) +U*(i)

A similar analysis with potential energy shows that

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rV *(i) = 2i rV *0

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.

where rV is the “virial radius”

(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 OKAccretions KO

Induced structural non-homology:

Major mergers: m M: OKAccretions: 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)

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Mg0 =α 0M*0

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MBH 0 = μM*0

Gas evolution

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Mg (i +1) = 2Mg (i) − 2ηMg (i) − 2ημMg (i)

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0 ≤ η ≤1

1+ μ(dissipation parameter)

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Mg (i) = 2iqiMg0€

0 ≤ q ≡1−η (1+ μ) ≤1

Stellar mass evolution

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M*(i +1) = 2M*(i) + 2ηMg (i)

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M*(i) = 2i 1+α 0η1−qi

1−q

⎛

⎝ ⎜

⎞

⎠ ⎟M*0

BH mass evolution

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MBH (i +1) = 2MBH (i) + 2ημMg (i)

and so

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MBH (i) = μM*(i)

i.e. Magorrian rel. can be preserved also with gas dissipation

It follows that

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α(i) ≡Mg (i)

M*(i)=

α 0qi

1+α 0η1−qi

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

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E = T* + Tg +1

2(ρ* + ρ g )(φ* + φg )dV∫

For simplicity let assume

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ρg =αρ* ⇒ φg =αφ*

From hydrostatic equilibrium & Jeans equations

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∂P∂r

=α∂ρ*σ

2

∂r⇒ Tg =αT* so that

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E = (1+α )T* + (1+α )2U*

From the 2-component VT

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2T* = −U* −W*g

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W*g = − ρ* < x,∇φg > dV∫ =αU*

so that

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2T* = −(1+α )U*

and for a two-component virialized galaxy

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E = −(1+α )T* =(1+α )2

2U*

In a parabolic merging with gas dissipation

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E(i +1) = 2E(i) − 2η (1+ μ)Tg (i)

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T*(i +1) = 21+α (i)[1+η (1+ μ)]

1+α (i +1)T*(i)

that can be recast as

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*2(i +1) = 1+

η (1+ 2μ)α (i)

1+ (1−ημ)α (i)

⎛

⎝ ⎜

⎞

⎠ ⎟σ *

2(i)

which is a non-decreasing quantity in case of dissipation

and from VT

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.