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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
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