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  1. 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

  2. Open cluster NGC 3293

  3. Globular Cluster M 13

  4. Elliptical galaxy NGC 4374

  5. 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

  6. OBSERVATIONAL DATA AGB HB CM diagram M 3 RGB SGB TO MS G6a

  7. 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 - - [Salpeter x=2.35] with with

  8. SIMPLE STELLAR POPULATION System of stars with the same age and the same initial chemical composition Age 15 Gyr Pop. II for “ WDs 6-5

  9. Simple Star Population (SSP) i.e . Coeval Stars with the same initial chemical composition yr 6-7

  10. ° (A) SSP Model for M3 6-8

  11. 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 - - in GCs and DSs , in Es , in gEs in the intergalactic medium in clusters of galaxies

  12. EVOLUTIONARY DYNAMICAL MODELS (L. Angeletti, R. Capuzzo, P.G.) Globular cluster multi-mass stellar components with star-mass loss 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)

  13. 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.) 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 Results yrs as mass is increased “ “ “ “ “ “ “ “

  14. x line of sight Star system Apparent disk r = spatial radial distance R = projected radial distance Projection 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

  15. 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 Fig2a

  16. 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

  17. THE R1/4 LAW OF THE PROJECTED SURFACE BRIGHTNESS 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 totallight mag/arcsec2 Surface brightness profile Surface intensity profile In terms of the luminosity density By inversion

  18. From constant gravitational potential and derivatives For unit mass at r binding energy angular momentum maximum value

  19. Models with isotropic velocity dispersion: Energy distribution function For the mass density of stars at r

  20. Anisotropic models: Osipkov-Merritt models = anisotropic radius (for 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

  21. (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 (with ) (for ) , (for ) Gas mass where = Galaxy mass p = metal yield Mean star metallicity Ms(t) = Mo - G(t) = total mass of the stellar component (long-living stars and compact stellar remnants)

  22. 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 mZ(m) = mass of the new metals ejected by a star with mass m mf(m) =mass ofthe“finalremnant” of a star with mass m p will be expressed in units of Zsun= 0.0169

  23. CM : takes into account the gas contraction in the galaxy In the model M = Lagrangian mass coordinate (in units of Mo) - 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) where concentration index and From SM + CM : Two-parameter ( p and c ) family models

  24. We define = cumulative mass of the stars with Ap’s within and (born until ta ) = cumulative mass of the stars with Ap’s within and Metallicity distribution function for the stars with Ap’s within M

  25. At r, from The radial profile of index I is Integrated value of index I within a circular concentric aperture with radius (eventually the galaxy radius)

  26. c

  27. Tafig2b

  28. Tafig3b

  29. RESULTS Sample of 11 Es Ranges of parameters for the best fits: 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 upwards anisotropy produces shallower profiles in the envelopes

  30. 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)

  31. 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

  32. PROBLEMS 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

  33. 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

  34. 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

  35. 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 SM and CM provide explicitly a two-parameter ( p and c ) family of metallicity distribution functions

  36. 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

  37. STAR EVOLUTION Single stars Conservation of mass Hydrostatic equilibrium Energy balance Radiative and/or conductive energy transport Convective energy transport Criterion for the radiative stability Equation of state Opacity Nuclear energy generation Quiescent nucleosynthesis Input data: star mass m and initial chemical composition ( Y, Z)

  38. Msun yr-1 Mass loss and stellar winds Eddington luminosity Reimers formula with (solar units)

  39. Cloud fragmentation Protostar Gravitational Contraction Quiescent Nuclear Termofusion H, He, C, O …… Fe Explosive Nuclear Termofusion Mass loss Cooling Mass ? Supernova II = > 8 White Dwarf Zn.. Ba.. Pb.. U Nebular Remnant + Neutron star (pulsar) Semi-empirical estimate for LiDeSa

  40. Quiescent nucleosynthesis 15 Msun 3-2

  41. Cosmological Nucleosynthesis Quiescent Nucleosynthesis Explosive Nucleosynthesis Cosmic Abundances J1a

  42. eff F8b

  43. Evolutionary tracks [ i.e. loci of constant m withL(t) and Teff(t) ] isochrones [ i.e. loci of constant t withL(m) and Teff(m) ] AGB RGB HB SGB TO MS M 3 MS H He in the core SGB +RGB H He in the shell HB He C+O in the core, H He in the shell AGB He C+O in a shell, H He in a shell G6a

  44. Luminosity functions i.e. frequencies of stars in the various evolutionary stages Fig22c

  45. h h = - + - Y ( 0 . 370 ) log R ( 0 . 186 ) 33 55 = ¸ Y 0 . 23 0 . 26 N R HB N RG Fig23c

  46. Globular cluster M13 Isochrones of 7 , 9 , 12 , and 15 Gyr GCs are coeval with TO = 13 Gyr

  47. 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

  48. R Radial ratio of projected numerical densities of stars in various evolutionary stages i.e. with different masses segregation R 6-2a

  49. R R M 15 Radiale profiles in the V and B photometric bands from surface brightness and star counts (solid curves are seeing profiles) Fig25a/26a

  50. Fig27a