SPHEROIDAL POPULATED STAR SYSTEMS

Pietro Giannone Dipartimento di Fisica Universita’ “Sapienza” Roma SUMMARY

Globular clusters and star evolution

Elliptical galaxies

Population synthesis

Star population age / metallicity

Open cluster NGC 3293

Globular

Cluster

M 13

Elliptical galaxy NGC 4374

R

MOTIVATIONS for their STUDY

Globular clusters are the oldest objects in the Universe

- probes for cosmological issues (age of the Universe, Big Bang nucleosynthesis) - protogalactic collapse

Elliptical galaxies are the most populated star systems

Both contribute information on:

- Initial mass function (IMF)- Star formation rate (SFR)- Star evolution- Ages- Chemical composition- Stellar populations - Stellar dynamics- Galactic evolution

CMdiagram

M 3

G6a

OBSERVATIONAL DATA

HB

AGB

RGB

SGB

MS

TO

INGREDIENTS FOR A STELLAR POPULATION SYNTHESIS

- Birth rate function b(m,t,r,Z) - Star evolution - Mass loss from stars - Model atmospheres (conversions) - SNe (progenitors, rate, SNRs) - Nucleosynthesis - Dynamics

Most common assumptions

- i.e. IMF SFR

-

-

xmm )( with

with

)()(),( tmtmb

ktgt )()( 21 k

[Salpeter x=2.35]7.21 x

SIMPLE STELLAR POPULATION

System of stars with the same age and the same initial chemical composition

Age 15 Gyr

Pop. II

6-5

1

35.2

4.0

x

x

for

“ 4.0

4.0

M

MWDs

6-7

Simple Star

Population

(SSP)

i.e .

Coeval Stars with the same initial chemical composition

yr

SSP Model for M3

6-8 (A)°

INTEGRATED COLOURS AND SPECTRA OF SPHEROIDAL SYSTEMS

Observational data

- Colour-magnitude relation

- Mean metallicity-magnitude relation Mass “ relation

- in GCs and DSs , in Es

- [O/Fe] and [ /Fe] [Mg/Fe] sovrasolar

- Increasing spread of metallicities with increasing system mass “ complexity of star populations

-

-

0)(/ VBddMV

0/ Vs dMZd

01.010 4 sZ 02.0 suns ZZ

0gM in GCs and DSs , in Es , in gEs

0 GM34 1010

sung ZZ in the intergalactic medium in clusters of galaxies

EVOLUTIONARY DYNAMICAL MODELS (L. Angeletti, R. Capuzzo, P.G.)

Globular cluster multi-mass stellar components with star-mass loss

sunM5105

Main results

- increasing core concentration and envelope diluition

- velocity dispersion is isotropic in the core and anisotropic in the envelope

- differential central segregation of star masses

- differential “evaporation” of stars (up to 45 % of the initial mass and

40% of the initial number)

Evolution of spheroidal star systems from globular clusters to elliptical galaxies

( to solar masses). Galactic wind when residual thermal energy of

SNRs reaches the gravitational binding energy

GALACTIC WINDS

- Continuous star formation and star evolution progressive metal enrichment overproduction of metals (too redward colours) galactic wind

- Intracluster gas contains metals

(L. Angeletti & P.G.)

510 1110)()( wgwth ttE

Results

26.037.0/)(

08.034.0/)(

105555 6

oawg

owg

w

MM

MM

yrs as mass is increased

“ “ “ “

“ “ “ “

In order to determine light and colours at P’(R) we need to know the number of stars along the line of sight within the system and their specific contributions

drRr

rrdxxR

X R

R

0

*

22

)(2)(2)(

Projection

22 Rrx

line of sight

Star system Apparent disk

r = spatial radial distance R = projected radial distance

x

Fig2a

ADDITIONAL OBSERVATIONAL DATA FOR ELLIPTICAL GALAXIES

Radial projected profiles of various Johnson/Cousins colour and Lick spectral

indices across galaxy images, through slit or circular apertures large variations

Projected radial gradients of indices are suggested to stem from spatial

abundance gradients that developed when Es formed through a monolithic

dissipative collapse

a) Dissipative models of galaxy formation can produce metallicity gradients

b) Star formation can proceed near the center for a longer time than farther out

THE R1/4 LAW OF THE PROJECTED SURFACE BRIGHTNESS

82 n

Surface brightness profilen

e

no R

RaR /1)()( mag/arcsec2

Surface intensity profile n

eno RRbIRI /1)/(exp)(

In terms of the luminosity density

drRr

rrRI R

R

*

22

)(2)(

By inversion

)(r

22

*1)(

rR

dR

dR

dIr

R

r

Generalization of R1/4 to R1/n with for the spherical mass-model derived by deprojection from the surface-brightness profile

R = projected radial distance of the slit position Re = effective radius corresponding to half of the total light

From

L

M

r

r

)(

)(

),,()()( rRnMfrL

Mr e

*

)(4)(

)(

)(4)(0

2

R

r

r

drrrGr

rGMr

drrrrM

gravitational potential

and derivatives2222 /,/,/,/ dddddrddrd

02/)( 2 vrbinding energy

For unit mass at r

rvJrvJ r )(sin0 angular momentum

constant

maximum value

Models with isotropic velocity dispersion: 22

tr vv

d

d

d0

2

2

2 8

1)(

Energy distribution function

For the mass density of stars at r

dJdJJr

JrJd

r

22 )(

)(4),,(

)()1()(

8

1)(

2

2

02

2

2

rr

rr

q

d

d

dq

a

q

qq

Anisotropic models: 22

tr vv

Osipkov-Merritt models 02 2

2

ar

Jq

= anisotropic radius

(for qra i.e. isotropic models)

Distribution function of q’s

where

PROBLEM to derive the metallicity distribution function, through the spatial radial mass-density, from the energy distribution and the angular momenta

ar1

(L. Angeletti & P.G.)

law, ”Simple model” (SM) , “Concentration model” (CM) , and additions

SM : a one-zone and close-box model with instantaneous gas recycling

Gas is well mixed and its uniform metallicity (by mass) is

oM

tGtgg

)()(

)1

ln1(

g

ggpZ s

gpZ g ln (for 1Zp

g gZ 1) , (for )1Z

where

Mean star metallicity p = metal yield

nR /1

= Gas mass

Galaxy mass

Ms(t) = Mo - G(t) = total mass of the stellar component (long-living stars and compact stellar remnants)

0oZ(with )

*

1.0

100

*

100

1.0

)()()(

)()(

m

mf

Z

dmmmmdmmm

dmmmm

p

p will be expressed in units of Zsun= 0.0169

mf(m) = mass of the “final remnant” of a star with mass m

= mass of the new metals ejected by a star with mass mmZ(m)

p = metal yield = fractional mass of the new metals formed in stars and ejected into the ISM with respect to the total mass “locked up” in stars

- At time ta gas contracts within a decreasing mass coordinate Ma= M(ta) and

forms stars with Ap’s within Ma and Z=Za .

The mass of all stars with Ap’s within Ma (and all Z’s ) is (generalized ansatz)

c

aa gMs )(

concentration index

CM : takes into account the gas contraction in the galaxy

In the model M = Lagrangian mass coordinate (in units of Mo)

10 c

From SM + CM : )(lnln aaa Msc

pgpZ

where )( aa tgg and

Two-parameter ( p and c ) family models

),(

),(),(

M

aa ZM

ZMZM

We define

),( aZM

c

MMa MMsgMsZMZM /1)()(),(),(

aZZ = cumulative mass of the stars with Ap’s within and

)(ln Msc

pZZ M

Metallicity distribution function

a

aa Z

ZMZM

),(

),(

for the stars with Ap’s within M

aMM (born until ta )

= cumulative mass

of the stars with Ap’s within andM

The radial profile of index I is

dZZIZM

dJJJr

Jddr

Rr

rR

SSP

JZ

ap

r J

r

R

R

ap

r

)(),(

)(

4)(2)(

),(

0

)(

0

)(

0 22

*

22

'

0

)(2)'(R

dRRRR

Integrated value of index I within a circular concentric aperture with radius (eventually the galaxy radius)

At r, from ),( J 2/1

2

apap rJr apap rMsM

),( ZM ap

'R

c

Tafig2b

Tafig3b

RESULTS

Sample of 11 Es

Ranges of parameters for the best fits:

o

ea

sun

Rr

Zp

c

n

/1

2.2/1.1

95.050.0

84 an increase of n smoothes variations of the radial gradients

between core and envelope

gradient slopes increase with increasing c

increasing p moves index (except ) profiles upwardsH

anisotropy produces shallower profiles in the envelopes

We also considered (for Mg2 )

i) Changes of age from 13 to 17 Gyr

ii) Star formation in an initial main burst lasting 2 Gyr and in a delayed minor episode (1 Gyr long and starting at age 8 Gyr)

iii) A spread of durations for the star formation lasting from 2 to 11 Gyr after the initial burst

iv) A terminal wind at time tw involving the gas mass 0.05 Mo when Mw= 0.18Mo and r(Mw) = 0.4 Re(B)

Results of the additional implementations:

i) An increase of age operates like changes of p

ii) Delayed episodes of star formation flatten the index behaviours in the cores and steepen them in the envelopes

iii) Prolonged phases of star formation emphasize the tendencies mentioned in ii)

iv) A terminal wind flattens the index profiles in the envelopes improving the fit

1. Non-solar partition for metals in SSPs

2. Lack of reliable SSPs for Z > 0.05

3. Opacity and surface convection for star models

4. Model atmospheres for log Teff - colours and BC for cool stars

5. Contributions of BHB and PAGB stars to light and colours

6. Contribution of evolved binaries

7. IMF

8. SFR

9. Degeneracy of relation 10. Non-uniform gas density

11. Instantaneous gas recycling to be replaced by stellar lifetimes

12. Dark matter

PROBLEMS

Z

CONCLUSIONS

1. Stars in each globular cluster are coeval and were formed with the same initial chemical composition owing to a prompt wind from the stellar system SSP

2. Intermediate-mass Es experienced an early wind allowing for a moderate inhomogeneity of metallicities among stars

3. Star formation was prolonged in gEs leading to a mixture of star metallicities

4. Es are characterized by different space mass densities

5. Gas distributions (and therefore star formations) differed in Es

6. Mean star metallicities in Es range from solar to sensibly sovrasolar abundances

7. Different metal enrichments in Es evidentiate differences in their evolutions

more stellar populations

Proposed scenarios for the formation of Es

1. All luminous Es are coeval and old systems, that formed through a monolithic

dissipative collapse, occurred early in the evolution of the Universe

2. Es formed through a lengthy hierarchical clustering of small objects into larger

ones with star formation extended over a long time

Inside Ma it is assumed that

i) Newly formed stars are distributed radially like the stars born before ta

ii) Stars that form at ta have Ap’s within Ma

Therefore the mass of the stars with Ap’s within Ma ,

and born until ta is

aZZ

c

aaaaaa MMsgMsZM /1)()(),(

SM and CM provide explicitly a two-parameter ( p and c ) family of

metallicity distribution functions

Information on ages

Age spread of a few Gyr among the central regions of most Fornax and Virgo Es

Age spread of some Gyr among the innermost regions of the field or Es in small

groups

STAR EVOLUTIONSingle stars

Conservation of massHydrostatic equilibriumEnergy balanceRadiative and/or conductive energy transportConvective energy transport

Criterion for the radiative stability

Equation of stateOpacityNuclear energy generation

Quiescent nucleosynthesis

Input data: star mass m and initial chemical composition ( Y , Z )

Mass loss and stellar winds

Eddington luminosity

Reimers formula

with

MLL Ed

4105

(solar units)

M

LR

dt

dM 13104 Msun yr-1

33

1

Cloud fragmentation

Protostar

Mass

? =

Mass loss

Cooling

White Dwarf

Gravitational Contraction

Nebular Remnant +

Neutron star (pulsar)

> 8

Explosive Nuclear Termofusion

Supernova II

Zn.. Ba.. Pb.. U

H, He, C, O …… FeQuiescent Nuclear Termofusion

8 8w

48.0077.0 if MMSemi-empirical estimate for 8iM

Quiescent nucleosynthesis 15 Msun3-2

Cosmic

Abundances

Cosmological Nucleosynthesis

Explosive Nucleosynthesis

Quiescent Nucleosynthesis

J1a

F8b

eff

M 3

G6a

MS H He in the coreSGB +RGB H He in the shellHB He C+O in the core, H He in the shellAGB He C+O in a shell, H He in a shell

Evolutionary tracks [ i.e. loci of constant m with L(t) and Teff(t) ] isochrones [ i.e. loci of constant t with L(m) and Teff(m) ]

HB

AGB

RGB

TOSGB

MS

Luminosity functions i.e. frequencies of stars in the various evolutionary stages

Fig22c

Fig23c

26.023.0 Y

N

NR

RG

HB

)55

186.0(log)33

370.0( RY

ZZZ

YYY p

7.2228.0

),(

YfRG

HB

24.023.0 pY

Globular cluster M13

Isochrones of7 , 9 , 12 , and 15

Gyr

GCs are coevalwith = 13 Gyr TO

Luminosity functions of pre-white-dwarf stars and white-dwarf stars at ages: 9.5 Gyr and 12.3 Gyr. Comparison with data for M3

6-6

6-2a

Radial ratioof projectednumericaldensities ofstars in variousevolutionarystages

i.e. with differentmasses

segregation

R

R

Fig25a/26a

M 15 Radiale profiles in the V and B photometric bands from surface

brightness and star counts (solid curves are seeing profiles)

R R

Fig27a

O x

y

1M2M

2M

Jacobi’sintegral

CUV 22 0V

0V

Hill’scurves

d sd

c W UMa

Roche classification L10a

8.00+5.33 0.67

“ “ “

6.665+6.665 1.00

3.83+9.50 2.48

2.90+10.43 3.60

(solar masses and radii)

21 MM PA

13.0 1.5

“ “

12.0 1.3

17.8 2.4

25.4 4.2

(periods in days)

L9a

L2

L4

L5

L6

L8

MS+MSRapid transferof matter

Mass

inversionSeparation

large

small

Slow transfer of matter

Case C

Termofus.

He in

core/shell

Case B2:

Termofus.

He in core

H in shell

Case B1

Termofus.

H in shell

Case A

Termofus.

H in core

WR stars

Blue Dwarfs

WhiteDwarfs

AlgolSystems

3020

3020

3

3

Conservativeevolution

.

.

21

21

constM

GAMMh

constMMM

.4-1a

4-7a

Losses ofMass andAngular momentum

MS+WDHe

Nucleartermofus.

Stellar wind

Transfer of mass

NovaeLow-massX raysources

Transfer of mass

MS + NS Accretion

Stellar wind

MassiveX raysources

Losses of Mass andAngularmomentum

MS + WDC

Nucleartermofus.

4-8a

WD + WD

GravitationalwavesCoalescence

ChWD MM SN I SNR