1. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations THE STELLAR CONTENT OF GALAXIES: RESOLVED STELLAR POPULATIONS I. Theoretical foundations Laura Greggio - OAPd Ciclo di Lezioni focalizzato sul problema della ricostruzione della Storia di Formazione Stellare dall’analisi dellla distribuzione delle stelle sul diagramma Colore-Magnitudine

2. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Carina: Dwarf Spheroidal Monelli et al. 2004

3. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Large Magellanic Cloud Smecker-Hane et al. 2002 DISK FIELDBAR FIELD Recent enhancement (from 0.1 Gyr ago) Old SF (from 10-3.0 Gyr ago) Enhancement at 3.5 Gyr ago

4. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations NGC 1705 – A Dwarf Blue Galaxy observations interpretation Annibali et al. 2003

5. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Simulations: Color Coding Reflects AGE(Myr ): <10Myr 10↔60 60↔1000 > 1000 SFR constant from 10 Myr to 2 Gyr ago SFR constant from now to 1 Gyr ago

6. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Outline of the Course: Summary of Stellar Evolution Review of general properties of stellar tracks, which determine the appearance of the HRD and its systematics. Bolometric Corrections and Colors How we transform from the theoretical (Log L, Log Teff) plane to the observational (Mag,Color) Basic Relations between Stellar Counts in Selected Regions of the CMD and the SF History Illustrate potentials and limitations of the synthetic CMD method The Simulator and Some Examples Various technicalities, including the treatment of photometric errors

7. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Evolutionary Tracks Padova 94 set Z=Z o Y=0.28 1MO1MO 2.5 M O 5 M O 20 M O 1 M O 100 M O PAGB 0.6 M O 2.5 M O 5 M O To WD ZAHB ZAMS RGB PN

8. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations RGB evolution RGB Bump 0.8 M o 2 M o 100Ro 10 Ro Back to HRD

9. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations RGB : bump and LF Back to HRD 1.2 Mo 1 Mo

10. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Flash and After M tr RGB tip RGB base RGB tip 10 Ro1 Ro P-EAGB 100 Ro 0.03 0.07 0.12 Back to HRD

11. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Clump and Loops Back to HRD TRGB ZAHB 2.2 Mo 9 Mo 4 7 6 5 3 15 10 Ro Age indicator Distance ind Lmax,He Lmin,He

12. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations AGB Bump 2.2 Mo 5 Mo 4 Mo 3 Mo 1 Mo with cost=-1 1.5 Mo with cost=-0.5 BUMP RGB

13. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations PMS LF RGB HB AGB Bump Clump Bump Clump

14. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations First Pulse and TAGB TAGB Ist Pulse TRGB

15. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Massive Stars Chiosi and Maeder 1986 Evolution affected by MASS LOSS OVERSHOOTING

16. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Where the Stars are WR C stars Miras Clump Ceph HB RRLyr WD BSG RSG Back to HRD Dots are equally spaced in There are 1000 dots along each track

17. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Dependence on Metallicity 30 Mo 15 Mo 5 Mo 3 Mo 0.9 Mo Clumps 0.5 Mo 0.55 Mo 0.6 Mo AGB Manque’ Post E-AGB Clumps

18. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Evolutionary Lifetimes tot MS overshooting RGB phase transition rgb He burning

19. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations RGB Luminosities Base TIP

20. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Helium Burning and beyond Ist Pulse He burn L-band RGB trans

21. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Isochrones Girardi et al. 2002 As Z increases: isochrones get fainter and redder loops get shorter WR stars are more easily produced

22. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations Uncertainties and wish list Core Convection: affects star’s luminosity H and He lifetimes shape of tracks around M hook first H shell burning and runway for intermediate mass stars MS width location of RGB bump values of M tr and M up ratios N(HB)/N(AGB) loops extension Mass Loss: on the RGB affects Temperature extension of HB on the AGB affects value of M up and TAGB for massive stars affects surface abundances, upper limit of Red SGs, productions of WR.. Mixing Length, rotation, diffusion, meridional circulation, nuclear reactions… Separate dependence on Y and Z is important Opacity: affects MS width occurrence and extension of loops Blue to Red ratio

23. HRD dots He B band He B band Life time RGB Lum June 2005Lectures on Stellar Populations What have we learnt To place on the HRD whatever mass at whatever age we want to pay attention to: M tr M up M hook : lifetimes and tracks discontinuities Place correctly RGB Tip (as distance indicator) Describe accurately the evolution in core He burning close to RGB transition (Lum extension during evolution) Allow spread of envelope masses for HB stars Describe extension of the loops, location of BSG, Back-to-the-Blue evolution of high mass stars …………. AND if we include a metallicity spread Correctly describe all these systematics as a function of Metallicity

24. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Bolometric Corrections and Colors We do not observe Bolometric, we observe through filters: system throughput depends on Teff, gravity and Z depends on.... stellar radius

25. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Average of Observed Stellar Spectra: Dwarfs O 50000 3.5e+14 A 10000 5.7e+11 G 6000 7.3e+10 M 3500 8.5e+09 SpT T(K) F c.g.s.

26. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Dwarfs SED & Filters IVB U Cool stars detected in Red Hot stars detected in Blue BC strongly depends on SpT COLORS: are Temperature Indicators Cool stars are Red Hot stars are Blue

27. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Effect of gravity Gravity effects are very Important for very hot And very cool stars A0 B0 B5 K5 M2 M5

28. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations COLORS: Empirical Johnson 1966 ARAA 4 193 B-V colors are good Teff indicators for late A, F, G and early K stars For Hot stars SpT is preferred

29. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Bolometric Corrections: Empirical Hottest and Coolest stars are 3-4 mags fainter in V than in Bolometric Gravity dependence can amount to 0.5mags

30. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Model Atmospheres: Kurucz Grid revised by Castelli ModelsEmpirical

31. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Model Atmospheres: dependence on gravity ModelsEmpirical

32. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Model Atmospheres: dependence on Metallicity Blanketing Molecules

33. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Model Atmospheres: Calibration The Models do a good job for the SED of Dwarfs, especially for intermediate Spectral Types Not too bad for Giants and Supergiants also Major problems are met al low Temperatures (Opacity, Molecules) Anyway, the use of Model Atmospheres becomes a MUST because: they allow us to compute Colors and BCs for various Metallicities AND for whatever filters combinations To do that we: Take a grid of Models Perform calibrationcalibration Produce Tables of BC, Col function of (Teff,Log g, [M/H])

34. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Balmer Jump Go Back

35. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Colors from Model Atmospheres Origlia and Leitherer 1998: Bessel, Castelli and Pletz models through Ground Based Filters

36. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Bolometric Correction from Model Atmospheres Nice and smooth BUT Probably off for Late K and M stars Have you noticed that lines of different colors Span different Temperature Range? THIS IS NOT A SUPERMONGO FALIURE:

37. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Tracks on the Log Teff – Log g Plane WE LACK LOW GRAVITY MODELS FOR MASSIVE STARS WE LACK LOW TEMPERATURE AND LOW GRAVITY MODELS FOR LOW MASS STARS (AT HIGH METALLICITIES )

38. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations M&M: attach empirical calibrations Montegriffo et al. (1998) traslated Go back

39. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Bessel, Castelli & Pletz (1998, A&A 333, 231) Compare Kurucz’s revised models (ATLAS9)+ Gustafsson et al revised (NMARCS) models for red dwarfs and giants to empirical colors and BCs for stars in the Solar Neighbourhood (i.e. about solar metallicity). They show color-temperature, color-color, and BC-color relations.color-temperaturecolor-colorBC-color relations Conclude that : 1.There is a general good agreement for most of the parameter space 2.B-V predicted too blue for late type stars, likely due to missing atomic and molecular opacity 3.NMARCS to be preferred to ATLAS9 below 4000 K

40. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Hot Dwarfs A-K Dwarfs GKM Giants The models are shown as curves The data are shown as points The ptype encodes the literature source

41. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Dwarfs Giants K NM

42. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Giants Dwarfs

43. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations BaSeL Grid (Lejeune, Cuisinier and Buser 1997 +) Collect Model Atmospheres from Kurucz +Bessel + Fluks (for RGs) + Allard (for M dwarfs) Correct the model spectra so as to match empirical calibration Put the corrected models on the net

44. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Lejeune Models: Z dependence Check with Globulars’ Ridge Lines BaSeL 2.2 : Corrected Models at solar Z & Z theoretical dependence BaSeL 3.1: Corrected models at various Z based on GCs Ridge Lines 5 GGs with [Fe/H]=-2.2 to -0.7 in UBVRIJHKL For each get Te from V-K (using BaSel 2.2)  BCs vs (Te,g) BaSeL 3.1 Padova 2000: Correction at various Z made to match GCs Ridge Lines with Padova 2000 isochrones ”It is virtually impossible to establish a unique calibration In terms of Z which is consistent with both color –temperature Relations AND GCs ridge lines (with existing isochrones)” Westera et al. 2002

45. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Libraries with high Spectral resolution Recently developed for Population Synthesis Studies, Stellar spectroscopy, Automatic Classification of Stellar and Galaxy Spectra … not so important for Broad Band Colors Observational Libraries take a sample of well observed stars with known parameters Log Te, Log g, [Fe/H] and derive their spectra STELIB – Le Borgne et al. 2003 249 spectra between 3200 and 9500 A, sp.res. ~ 3 A INDO-US – Valdes et al. 2004 885 spectra between 3460 and 9464 A + 400 with smaller wavelength range sp. res. ~ 1 A

46. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Libraries with high Spectral resolution THEORETICAL MODELS Usually constructed on top of a model atmosphere (Kurucz) + Code for synthetic spectrum which solves monochromatic radiative transport with a large list of lines not very important for broad band colors, but could suggest diagnostic tools Martins et al. 2005: 1654 spectra between 3000 and 7000 A with sp. res. ~0.3 A Special care to describe non-LTE and sphericity effects

47. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Martins et al. 2005 30262 4.18 0.02 13622 3.80 0.05 7031 4.04 0.01 4540 0.88 0.02 3700 1.3 0.01 3540 0 0.02 Check versus STELIB stars Check versus INDO-US stars 3910 1.6 0.01 30000 4.5 0.02 14000 4.5 0.02 3500 1.0 0.01 4500 0.0 0.01 7000 4.0 0.02 4000 1.0 0.02 3500 0.0 0.02

48. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Other Models: Bertone et al. : 2500 spectra with resolution of ~ 0.3 A UV grid Optical grid between 850 and 4750 A 3500 and 7000 A Te from 3000 to 50000 K 4000 to 50000 K Log g from 1 to 5 0 to 5 [M/H] from -2.5 to +0.5 -3 to +0.3 Munari et al. : 67800 spectra between 2500 and 10500 A with res of ~1 A cover Te from 3500 to 47500 K, Log g from 0 to 5 [M/H] from -2.5 to +0.5 and [A/Fe]=0,+0.4 Coelho et al. : spectra between 3000 and 1800 A with res of ~0.02 A cover Te from 3500 to 7000 K, Log g from 0 to 5 [M/H] from -2.5 to +0.5 and [A/Fe]=0,+0.4

49. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Converted Tracks: B and V

50. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Converted Tracks: V and I

51. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations What have we learnt When passing from the theoretical HRD to the theoretical CMD we should remember that: At Zo the model atmospheres are adequate for most TSp There are substantial problems for cool stars, especially at low gravities The theoretical trend with Z is not well tested The tracks on the CMD reflect these uncertainties The transformed tracks make it difficult to sample well the upper MS (large BC); the intermediate MS merges with the blue part of the loops; the colors (and the luminosities) of the Red giants and Supergiants are particularly uncertain.

52. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Uncertainty of Stellar Models Gallart, Zoccali and Aparicio 2005 compare various sets of models (isochrones) to gauge the theoretical uncertainty when computing simulations with one set.

53. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Age-dating from Turn-off Magnitude In general the turn-off magnitude at given age agrees Teramo models fit the turn off Magnitude with older ages (at intermediate ages) Notice some difference in isochrone shapes, and SGB for old isochrones

54. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Deriving metallicity from RGB The RGBs can be very different especially at high Z The difference is already substantial at M I =1.5 where the BCs can still be trusted (Te ~ 4500) The comparison to Saviane’s lines Seem to favour Teramo at high Z, but the models do not bend enough at the bright end.

55. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Deriving distance from RGB Tip The RGB Tip is an effective distance indicator in the I band and at low Zs The theoretical location depends on the bolometric magnitude and on The BC in the I band. There is a trend of Padova models to yield relatively faint TRGB at all metallicities. Observations are not decisive, But undersampling at TRGB should lead to systematically faint observed TRGB.

56. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Magnitude location of the HB The HB luminosity can be used as distance indicator as well as to derive Ages of GCs, from the difference between the HB and the TO luminosity (dependence on Z is crucial for this). The models show substantial discrepancies, again with Padova models fainter than Teramo. Observations are very discrepant as well; major difficulties stem from the correction for luminosity evolution on the Horizontal Branch; the necessity to trace the ZAHB to the same Teff point in both observations and models.

57. Def Col emp Col emp Calib Tracks BCP June 2005Lectures on Stellar Populations Summary The TO magnitude at given age of the stellar population seems independent of the set of tracks, except for obvious systematics with input physics (but Teramo models need further investigation) this feature can be safely used for age-dating; The TO temperatures, and in general the shape of the isochrones, seems more uncertain, as they differ in different sets; The colors of RGB stars and their dependence on metallicity are very uncertain; the derivation of Z and Z distribution from RGB stars needs a careful evaluation on systematic error; The magnitude level of the ZAHB and its trend with Z show a substantial discrepancy in the various sets of models AND in the various observational data sets. This is a major caveat for the distance and age determinations based on the level of HB stars. A theoretical error of about 0.2 is also to be associated to the distance determination from the TRGB.

58. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Basic Relations between Stellar Counts on the CMD and SFH On the potentials and limitations of the Synthetic CMDs method We will go through: SSPs :isochrones, MS and PMS phases, FCT,Number-Mass connection CSPs: SSPs with an age distribution, to elucidate relations between ΔN and M(CSP) Ultimately:

59. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Isochrones on the HRD 4 Myr 40 Myr 0.2 Gyr 1 Gyr 15 Gyr Theoretical Isochrones With ages from 4 Myr to 15 Gyr

60. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Mass-Luminosity relation along isochrones RGB mass loss 10 Myr 100 Myr 500 Myr In the j-th luminosity bin each i-th isochrone contributes: Lower and upper integration limits depend on the isochrone, i.e. on age (and Z). A i describes the size of the Stellar Population on the isochrone (SSP)

61. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations LF on the MS Consider a continuous Star Formation Rate ψ(t): the contribution to Δn j from the ages between τ and τ+dτ is proportional to ψ(τ)dτ, and Summing up all the relevant contributions we get: The mass and mass range contributing to the counts in the j-th bin depend on the age. If we neglect this dependence (on the MS we may): The LF on the MS is proportional to the IMF through the M-L relation AND to the SFR over the relevant age range. maximum age contributing to j-th bin IMFM-L

62. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Color Function on the MS The CF on the MS is a better tracer of the SFH Young populations have more blue stars Typical color on the MS depends on age Gallart, Zoccali and Aparicio 2005

63. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Post MS phases approximations: valid for PMS phases is the Stellar Evolutionary Flux: # of leaving the MS per unit time m TO m2m2 m1m1 is the considered PMS evolutionary phase Consider an SSP:

64. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Fuel Consumption Theorem ( Renzini 1981) Is the fuel burnt in the j-th PMS phase if F,L in solar units and b in #/yr The Specific Evolutionary Flux depends weakly on the age of the SSP and on the IMF This can be used for: Planning observations Evaluate crowding effects Tests of Evolution theory

65. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Test of FCT on M3 (Renzini and Fusi Pecci, 1988, ARAA 26, 199)

66. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Application to the SFH problem Start from: Characterize SSP by its Mass in m>0.6: Get: Where:is the Specific Evolutionary Flux # of stars leaving the MS per unit time,per unit MASS of the SSP function of IMF, Age, Metallicity is the Specific Production of j type Stars # of j stars from SSP with unitary Mass function of IMF, Age, Metallicity

67. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Synthetic Tracks interpolated within Padova 94-Z=0.004 generated a fine grid of synthetic tracks with masses of specific in order to finely investigate on the behaviour of at fixed Z=0.004

68. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations The Specific Production of Post-MS Stars of SSPs Number of Stars produced by a 1000 Mo SSP of age τ

69. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations TauMag of SSPs Magnitude Location of Red stars in different phases as the SSP ages : Core Helium Burners First RG ascent Second RG ascent (up to Ist pulse) RGB phase transition

70. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Composite Stellar Populations: YOUNG In general for a CSP, the number of stars in the j-th magnitude bin is: where the integration spans the ages contributing to the j-th bin If the bin intercepts stars from a small age range: where This is the case for Young CSPs (≤ 100 Myrs) for which: The number of stars in the j-th mag bin speaks for the power of the SF episode at a specific age The LF reflects the SFR as a function of age

71. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Young CSP: an example

72. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Blue Helium Burners SFH at Young ages is best Sampled by the Blue Helium Burners. Get detailed SFH up to 0.3 Gyr ago

73. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Composite Stellar Populations : OLD A given Mag bin now spans a wide age range: We get integrated information Consider: The Specific Production of j-type stars from the CSP what we count tool what we get Look at the Specific Production of CSPs under different SFH In specific magnitude bins

74. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Specific Production of CSP: bright AGB stars number of bright AGB stars from a 1000 Mo CSP

75. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Specific Production of CSP: Carbon stars Marigo, Girardi, Chiosi 2003 2MASS data of LMC C stars Marigo and Girardi 2001: Opacity independent of C abundance in the envelope Marigo 2002: Opacity increases with increasing C abundance in the envelope

76. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Specific Production of CSP: AGB stars Marigo, Girardi, Chiosi 2003 selected from 2MASS data of LMC Simulation: foreground contamination before Ist pulse and massive He burners TPAGB: Oxygen rich Carbon rich

77. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Mixture of Pulsators: fundamental & first over-tone

78. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Specific Production of CSP on bright RGB number of stars in the 2 upper I-mags of the RGB from a 1000 Mo CSP

79. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations Specific Production of CSP of He burning Stars at Clump Mags number of Stars at Clump Magnitudes from a 1000 Mo CSP

80. Isocs FCT Eqs Dnj,3 Eqs Dnj,3 plots CSPs Lectures on Stellar Populations What have we learnt When running the simulations we should remember the following rules and check if the output numbers verify the fundamental relations between stellar counts and extracted Total Mass of the CSP The MS LF is sensitive to both the SFR and IMF For the PMS phases there exists a simple and direct relation between the stellar counts in specific regions of the CMD and the Mass of the Stellar Population that produced them The bright portion of the LF of PMS stars allows to recover the SFH with a fair degree of detail, up to 300 Myr (both blue and red) For older ages, it is possible to derive with some confidence the total mass of the underlying CSP On the average there is about 1 bright E-AGB star every 20000 Mo of CSP 1 upper RGB star every 2000 Mo of CSP 1 He burning star every 200 Mo of CSP The determination of the SFR is prone to the non-easy gauge of the age range of the counted stars

81. Lectures on Stellar Populations June 2005 The Simulator Random Extraction of Mass-Age pair (AT FIXED METALLICITY) Place Synthetic Star on HRD Convert (L,Teff) into (Mag,Col) Apply Photometric Error Test to STOP r random in 0↔1 EXIT YESNO Notify: Astrated Mass, # of WDs,BHs,TPAGB..

82. Lectures on Stellar Populations June 2005 Interpolation between tracks: lifetimes

83. Lectures on Stellar Populations June 2005 Interpolation between Tracks: L and Teff of low mass stars

84. Lectures on Stellar Populations June 2005 Interpolation between Tracks: L and Teff of intermediate mass stars

85. Lectures on Stellar Populations June 2005 Photometric Error: Completeness NGC 1705 (Tosi et al. 2001) Completeness levels: 0.95 % thick 0.75 % thin 0.50 % thick 0.25% thin

86. Lectures on Stellar Populations June 2005 Photometric errors: σ DAO and Δm

87. Lectures on Stellar Populations June 2005 Crowding # of stars j in one resolution element (r.e.) where S j is the srf density of j stars and σ r.e. is the area intercepted Probability of j+j blend is Degree of Crowding in the frame With N r.e resolution elements is depends on SFH: In VII Zw 403 (BCD) we detect with HST 55 RSG, 140 bright AGB and 530 RGT(1) stars/Kpc 2 Observed with OmegaCAM we get crow=0.1 at 17,10 and 5.6 Mpc for the 3 kinds resp. In Phoenix (DSp) we detect >4200 RC stars/Kpc 2 : with OmegaCAM crow is 0.1 already at 2 Mpc

88. Lectures on Stellar Populations June 2005 Another way to put it: (Renzini 1998) # of blends in my frame is # of j stars in my frame (if SSP) iswhere L is the lum sampled by the r.e. # of blends in my frame becomes # of blends increases with the square of the Luminosity and decreases with the number of resolution elements

89. Lectures on Stellar Populations June 2005 Pixels and Frames: Example (2) (3) (1) (4) (1)A.O.: σ(r.e.) ≈ 0.14x0.14 ….. n RGT ≈ 8 in one r.e. (2) HST: σ(r.e.) ≈ 0.06x0.06…..n RGT xn RGT ≈2e-04 … N(r.e.)≈1e+05 (3)…………………………………………≈ 2e-05….. (4) GB : σ(r.e.)≈0.3 sq.arcsec….n RGT xn RGT ≈0.044…N(r.e.)≈1.3e+04

90. Lectures on Stellar Populations June 2005 How Robust is the Result? The statistical estimator does not account for systematic errors TheoreticalTransformedErrors Applied EACH STEP BRINGS ALONG ITS OWN UNCERTAINTIES THE SYSTEMATIC ERROR IS DIFFUCULT TO GAUGE

91. Lectures on Stellar Populations June 2005 Why and How Well does the Method Work? Think of the composite CMD as a superposition of SSPs, each described by an isochrone The number of stars in is proportional to the Mass that went into stars at τ ≈0.1 Gy This is valid for all the PMS boxes, with different proportionality factors Perform the exercise for all isochrones

92. Lectures on Stellar Populations June 2005 Methods for Solution: Blind Fit used by Hernandez, Gilmore and Valls Gabaud Harris and Zaritsky (STARFISH) Cole; Holtzman; Dolphin Dolphin 2002, MNRAS 332,91: Review of methods and description of Blind fit Generate a grid of partial model CMD with stars in small ranges of ages and metallicities Construct Hess diagram for each partial model CMD Generate a grid of models by combining partial CMDs according to SFR(t) and Z(t) DATA PURE MODEL PARTIAL CMD Ages: 11  12 Gyr [M/H]:-1.75  -1.65

93. Lectures on Stellar Populations June 2005 Use a statistical estimator to judge the fit: m i is the number of synthetic objects in bin i n i is the number of data points in bin i Minimize fit --  get best fit + a quantitative measure of the quality of the fit

94. Lectures on Stellar Populations June 2005 My prejudice: The model CMDs may NOT contain the solution If wrong Z is used, the blind method will give a solution, but not THE SOLUTION The method requires a lot of computing: Does this really improve the solution? (apart from giving a quantitative estimate of the quality of the fit) Dolphin: “ The solution with RGB+HB was extremely successful, measuring …the SFH with nearly the same accuracy as the fit to the entire CMD.”

95. Lectures on Stellar Populations June 2005 Methods for Solution: Tailored Fit Count the stars in the diagnostic boxes: Their number scales with the mass in Stars in the corresponding age range Younger than 10 Myr Between 10 and 50 Myr Between 50 Myr and 1 Gyr Construct partial CMD constrained to reproduce the star’s counts within the boxes. The partial CMDs are coherently populated also with stars outside the boxes

96. Lectures on Stellar Populations June 2005 Compare the total simulation to the data Use your knowledge of Stellar evolution to improve the fit AND decide where you cannot improve, and where you need a perfect match The two methods should be viewed as complementary

97. Lectures on Stellar Populations June 2005 Simulation

98. Lectures on Stellar Populations June 2005 What have we learnt When computing the simulations we should pay attention to The description of the details in the shape of the tracks, and the evolutionary lifetimes (use normalized independent variable) The description of photometric errors, blending and completeness (evaluate crowding conditions: if there is more than 1 star per resolution element the photometry is bad; crowding condition depends on sampled luminosity, size of the resolution element and star’s magnitude) Different methods exist to solve for the SFH: the BLIND FIT is statistically good, but does not account for systematic errors; it seems too complicated on one hand, could miss the real target of measuring the mass in stars on the other; the TAILORED FIT goes straight to the point of measuring the mass in stars of the various components of the stellar population; it’s unfit for automatic use; the solution reflects the prejudice of the modeler; the quality of the fit is judged only in a rough way.