GALAXY EVOLUTION THROUGH

THE COSMIC TIME

THAIS IDIART

IAG/ São Paulo University

JOSEPH SILK

Dept. of Astrophysics, Oxford University

JOSÉ A. DE FREITAS PACHECO

Observatoire de la Côte d’Azur

1. SOME CHARACTERISTICS OF ELLIPTICAL GALAXIES, INCLUDING THEORIESOF FORMATION AND HOW TO OBTAIN INFORMATION ABOUT THEIRSTELLAR POPULATIONS

2. THE EVOLUTIONARY MODEL FOR ANALYSIS OF STELLAR POPULATIONS3. MAIN RESULTS ABOUT ELLIPTICALS FORMATION AND EVOLUTION

ELLIPTICAL GALAXIES

ELLIPTICAL GALAXIES CAN BE USED AS STANDARD CANDLES?

It is usually thought Ellipticals were formed in high redshifts, in ashort time range and are quite quiescent until today. So, simplemodels should be enough to estimate their sizes and luminosities.

GALAXY FORMATION THEORIES

MONOLITHIC COLLAPSE (Eggen et al. 1962; Larson 1974)

Gaseous material is assembled in the form of a unique cloudinside dark matter halos

The bulk of stars are formed at high redshifts (z ~ 8-10) in ashort time scale, so E galaxies present old mean stellar populations

HIERARCHICAL SCENARIO (Toomre 1977; White & Rees 1978)

galaxies form from successive non-dissipative mergers of smallerhalos of dark and baryonic matter

galaxies of smaller masses are formed first and can merge toform the most massive and luminous galaxies

massive E galaxies are assembled at low redshifts (~ z=1.5) andpresent younger mean stellar populations

KEY QUESTIONS:

1) WHEN THE BULK OF STARS WAS FORMED ?

2) ELLIPTICALS EVOLVED PASSIVELY OR WERE MODIFIED BY INTERACTIONS WITH ENVIRONMENT (MERGING) ?

AGE DISTRIBUTION OF STELLAR POPULATIONS IN E GALAXIES IS

ESSENCIAL TO UNDERSTAND THEIR ORIGIN AND EVOLUTION.

OBSERVATIONAL TOOLS:

INTEGRATED COLORS INTEGRATED METALLICITY INDICES

INTERPRETATION OF DATA REQUIRES THE USE OF MODELS

THE EVOLUTIONARY MODEL

Galaxy formation and chemical evolution is a function of successive generations of stars

Age and abundance distribution

Successive formation of star clusters of a given age and abundance (metallicity)

Distribution of single stellar populations (SSPs)

Build a library of colors and spectral indices for

SSPs with different ages, chemical abundances

(Z) and initial mass functions (IMF).

FIRST STEP

Evolutionary synthesis of

integrated colors and spectral indices.

Integrated colors for a SSP

Luminosity or absolute magnitude in a given spectral band filter of a star of mass m and evolutive stage i

IMF

Supposing an IMF as a power law of exponent (mass distribution of stars)

Evolutionary synthesis of integrated

colors and spectral indices

(1)

We used the absolute magnitude for stars in Johnson and Cousins

filters U,B,V,Rc,Ic,J,H,K from theoretical isochronal tracks (Girardi et al.

and Salasnich et al. (2000) ) to obtain SSP integrated colors.

sup

inf

( , , ) ( )

m

i

filter filter

m

L age Z m L dm

sup

inf

( , log ,[ / ])( ,[ / ], ) ( )eff

m i

filter i

filterm

T g Fe HL

I age Fe H m I dmL

Spectral indices for a SSP

Spectral index of a star of mass m, evolutive stage iweighted by a luminosity fraction in a given spectral band

(2)

Evolutionary synthesis of integrated

colors and spectral indices

To obtain the stellar contribution for a given spectral index, weselected from the literature a sample of stars from a homogeneous setof stellar atmospheric parameters and chemical abundances of variousnuclear species (Thévenin 1998).

sup

inf

sup

inf

*

*

( ) ( )( ) [ , ]

( )

t

filter

ttot tot

filter t

t

age agedf

t L I dtdt

L or Idf

t dtdt

Integrated colors and spectral indices

of galaxies (composite spectra)

Star formation rate at a given time t

Luminosity or spectral index of SSPs born in time t (obtained by (1) and (2)),

in a galaxy of age Tfor: age=Tfor- t

* ( )df

tdt

A complex problem arises:

there is not a fundamental theory of star formation

STAR FORMATION RATE IS A FUNCTION OF GAS

MASS IN A GALAXY

HAVE TO FOLLOW THE EVOLUTION OF

INTERSTELLAR MASS

THE EVOLUTION OF THE INTERSTELLAR MASS IN E GALAXIES

One zone model (cannot predict spatial variations, the galaxy is analyzed as a whole)

Galaxy formed by accretion of gas: continuum infall or by mergers in different epochs

Supernova (SN) feedback:a) creates a two phase interstellar medium (IM) hot

and cold, whose stars are formed only in cold gas regions

b) generates galactic winds (mass loss by the galaxy)

Main assumptions:

SECOND STEP

EQUATIONS OF MASS CONSERVATION

gdf

dt infall

df

dt

df

dt ej

df

dt inw d

df

dt

( )GAL

massf

total mass M gas stars

g hot coldf f f

Evolution of the Total Gas Mass

infall/infall tdf

C edt

infall = time scale of galaxy formation

EQUATIONS OF MASS CONSERVATION

ACCRETED GAS

Evolution of the Total Gas Mass

C = normalization constant

cold

dfk f

dt

k = star formation efficiency (Gyrs-1)

EQUATIONS OF MASS CONSERVATION

STAR FORMATION RATE

Evolution of the Total Gas Mass

sup

( )

( ) ( ) ( )

m

ej

r m

m t

df dfm m m t dm

dt dt

( )cold mk f t = Am-(1+) is a IMFmr = mass of remnant star

the star formation rate is calculed at the retarded time (t − m), where m is the lifetime of a star of mass m.

EQUATIONS OF MASS CONSERVATION

EJECTED GAS BY STARS EVOLUTION

Evolution of the Total Gas Mass

wind hot

W

df f

dt

W= wind time scale : estimated by hydrodynamical models considering galaxy mass and mechanical energy released by supernova per time unit.

The rate at which the hot gas of the galaxy is removed by the galactic wind

EQUATIONS OF MASS CONSERVATION

WIND RATE

Evolution of the Total Gas Mass

• Nions = ions per time unit• Nq= ionization rate = ions created by time

• Nions Ne = ions that recombine with electrons (gas cooled)• = recombination coefficient (cm3/s)

In a cloud of H we assume : Nions=Ne

2

ion ionq

gas

dN NN

dt V

EQUATIONS OF MASS CONSERVATION

HOT GAS FRACTION

Evolution of the Hot Gas

Gas fraction cooled by recombination

Number of ionizing fotons emitted by SN

EQUATIONS OF MASS CONSERVATION

Evolution of the Hot Gas

Hot gas fraction returned by stars to the IM

2

(1/ )ejecthot hot

ph SN H

gas

dMdN NN m

dt dt V

Ions (hot gas) generated per time unit:• Supernova explosions• Ejected gas by stars at the end of their evolution

2

( )

( ( ) ( ))

( )

(1/ ( ))

( ) ( )

( )( )

( )

hot

H SNII SNII SNIa SNIa

GAL g

eject

g

GALg hot

H gas

ghot

g

hot

W

dx t

dt

m E t E t

M f t h

dff t

dt

Mf t x t

m V

df tx t

f t dt

x

production of hot gas by SN

Rate of hot gas returned by stars to the IM

Rate of gas cooled by recombination

Background variation

wind

EQUATIONS OF MASS CONSERVATION

Evolution of the Hot Gas

2

( ) ( ( ) ( ))

( )

(1/ ( )) ( ) ( )

( )( )

( )

hot H SNII SNII SNIa SNIa

GAL g

eject GALg g hot

H gas

ghot hot

g W

dx t m E t E t

dt M f t h

df Mf t f t x t

dt m V

df tx t x

f t dt

SYSTEM OF TWO INTEGRO-DIFFERENTIAL EQUATIONS:

TWO VARIABLES TO DETERMINATE : xhot e fg

inf

sup

( )

( / )

( )( )

(1 ) ( ) ( ) [ (1 )]m

all

m

g

g hot R g hot

m t

hot gt

W

tdf t

k f x m M m k f x dmdt

x fCe

EQUATIONS OF MASS CONSERVATION

Evolution of the Hot Gas Mass

Evolution of Total Gas Mass

inf/

inf[ ( )] 'all

i

eject tii cold all

hoti

W

dfdfX kf t X C e

dt dt

fX

EQUATIONS OF CHEMICAL EVOLUTION

Mass abundance of a given chemical element i

Xi=fi/fg

Mass abundance of accreted gas

THIRD STEP

sup

( )

( )( ) ( ) ( )

i m

eject

i m R cold m

m t

dfSNII SNIa X t m M m kf t dm

dt

sup

min

( ) ( )

m

i cold m

f

SNII m m kf t dm

( )i Ia IaSNIa m t

SUPERNOVA TERMS:

EQUATIONS OF CHEMICAL EVOLUTION

ELEMENT i PRODUCED AND EJECTED BY SN AND STARS

mi = yields for a range of

SNII progenitor mass

mi = mean yield for a SNIa event

OBSERVED PROPERTIES PREDICTED BY

THIS EVOLUTIONARY MODEL

- Integrated absolute magnitudes and colors- Integrated stellar spectra

STELLAR POPULATION :

GAS PROPERTIES:

- Amount of gas (hot and cold) in the galaxy- Amount of gas in the intergalactic medium (wind)

OUTPUT OF THE MODEL

MEAN AGE AND ABUNDANCE OF THE DOMINANT STELLAR POPULATION

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

-23

-22

-21

-20

-19

-18

MB

(U-V)o

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

0.20

0.24

0.28

0.32

0.36

0.40

Mg

2

0.20 0.25 0.30 0.35 0.40

1.2

1.4

1.6

1.8

2.0

2.2

2.4

H

Mg2

BEST FITTINGS OF INTEGRATED PROPERTIES

Free parameters:k = star formation efficiencyγ = IMF exponentτinfall = time scale of galaxy formationMGAL = total mass of the galaxy

(stars+gas)Tfor = time to start star formation

SOME RESULTS FOR THE BEST FITTINGS

Model M

(1010

M)

z80 K

(Gyrs-1)

IMF fg

(10-3)

1 2.2 0.73 0.73 2.43 5.9

2 4.0 0.89 0.77 2.39 6.2

3 6.6 0.90 0.93 2.30 6.7

4 13 1.07 1.00 2.30 6.3

5 25 1.38 1.33 2.26 5.6

6 45 1.82 1.67 2.23 6.1

7 85 2.52 2.00 2.20 7.3

8 160 3.87 2.33 2.17 8.9

Downsizing effect

0 20 40 60 80 100 120 140 160

z80

k

IMF

Mass of Galaxy (1010 M)

Massive Es are formed earlierMassive Es have bigger star formation efficiency The star formation rate is relatively highMassive Es have IMF that favours massive stars formation (flatter IMF)

z80 = redshift at which 80%

of the mass was assembled

CONCLUSIONS

On the average, massive E galaxies form earlier than

Es of smaller masses.

Stellar populations of E galaxies of bigger masses are

older than the smaller ones.

These two results seem to be against the

hierarchical model that predicts smaller structures

forming first in a cold dark mater scenario.

Stellar formation efficiency k increases with galaxy

mass.