Ciclo di Lezioni focalizzato sul problema della ricostruzione della Storia di Formazione Stellare dall analisi dellla distribuzione delle stelle sul diagramma Colore-Magnitudine
Carina: Dwarf Spheroidal Monelli et al. 2004
Large Magellanic Cloud DISK FIELD BAR FIELD Recent enhancement (from 0.1 Gyr ago) Enhancement at 3.5 Gyr ago Old SF (from 10-3.0 Gyr ago) Smecker-Hane et al. 2002
NGC 1705 A Dwarf Blue Galaxy observations interpretation Annibali et al. 2003
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
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
Evolutionary Tracks Padova 94 set 100 M O Z=Z o Y=0.28 ZAMS PAGB 0.6 M O 2.520 MM O O PN 5 M O To WD 2.5 2.5 M O O ZAHB RGB 1 M O 1M O
Back to HRD RGB evolution 100Ro 2 Mo 0.8 Mo RGB Bump 10 Ro
Back to HRD RGB : bump and LF 1.2 Mo 1 Mo
Back to HRD Flash and After RGB tip RGB tip 1 Ro 10 Ro 100 Ro P-EAGB RGB base 0.03 0.07 0.12 M tr
Back to HRD Clump and Loops 15 TRGB 9 Mo 7 6 5 Distance ind Age indicator Lmax,He Lmin,He 4 3 2.2 Mo ZAHB 10 Ro
AGB Bump 5 Mo BUMP 4 Mo RGB 3 Mo 2.2 Mo 1.5 Mo with cost=-0.5 BUMP 1 Mo with cost=-1 RGB
PMS LF Bump Clump Clump RGB Bump Bump HB AGB
First Pulse and TAGB TAGB Ist Pulse TRGB
Massive Stars Evolution affected by MASS LOSS OVERSHOOTING Chiosi and Maeder 1986
Back to HRD Where the Stars are Dots are equally spaced in BSG WR RSG There are 1000 dots along each track Ceph C stars Miras Clump WD HB RRLyr
Dependence on Metallicity 30 Mo 15 Mo 5 Mo 3 Mo Clumps AGB Manque Post E-AGB Clumps 0.9 Mo 0.5 Mo 0.55 Mo 0.6 Mo
Evolutionary Lifetimes RGB phase transition overshooting tot He burning MS rgb
RGB Luminosities TIP Base
Helium Burning and beyond Ist Pulse He burn L-band RGB trans
Isochrones Girardi et al. 2002 As Z increases: isochrones get fainter and redder loops get shorter WR stars are more easily produced
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.. Opacity: affects MS width occurrence and extension of loops Blue to Red ratio Mixing Length, rotation, diffusion, meridional circulation, nuclear reactions Separate dependence on Y and Z is important
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
Bolometric Corrections and Colors system throughput depends on Teff, gravity and Z
Average of Observed Stellar Spectra: Dwarfs SpT T(K) F c.g.s. O 50000 3.5e+14 A 10000 5.7e+11 G 6000 7.3e+10 M 3500 8.5e+09
Dwarfs SED & Filters BC strongly depends on SpT Cool stars detected in Red Hot stars detected in Blue B V I U COLORS: are Temperature Indicators Cool stars are Red Hot stars are Blue
Effect of gravity B5 B0 M5 Gravity effects are very Important for very hot And very cool stars M2 A0 K5
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
Bolometric Corrections: Empirical Hottest and Coolest stars are 3-4 mags fainter in V than in Bolometric Gravity dependence can amount to 0.5mags
Models Model Atmospheres: Kurucz Grid revised by Castelli Empirical
Model Atmospheres: dependence on gravity Models Empirical
Model Atmospheres: dependence on Metallicity Molecules Blanketing
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 calibration Produce Tables of BC, Col function of (Teff,Log g, [M/H])
Balmer Jump Go Back
Colors from Model Atmospheres Origlia and Leitherer 1998: Bessel, Castelli and Pletz models through Ground Based Filters
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:
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)
Go back M&M: attach empirical calibrations Montegriffo et al. (1998) traslated
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. 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
The models are shown as curves The data are shown as points The ptype encodes the literature source Hot Dwarfs A-K Dwarfs GKM Giants
Dwarfs NM K Giants
Dwarfs Giants Dwarfs
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
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 Lejeune Models: Z dependence Check with Globulars Ridge Lines 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
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
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
Martins et al. 2005 Check versus STELIB stars Check versus INDO-US stars 30000 4.5 0.02 30262 4.18 0.02 3500 1.0 0.01 3700 1.3 0.01 14000 4.5 0.02 13622 3.80 0.05 4000 1.0 0.02 3910 1.6 0.01 7000 4.0 0.02 7031 4.04 0.01 3500 0.0 0.02 3540 0 0.02 4540 0.88 0.02 4500 0.0 0.01
Other Models: 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 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 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
Converted Tracks: B and V
Converted Tracks: V and I
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.
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.
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
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.
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.
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.
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.
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:
Isochrones on the HRD 4 Myr Theoretical Isochrones With ages from 4 Myr to 15 Gyr 40 Myr 0.2 Gyr 1 Gyr 15 Gyr
Mass-Luminosity relation along isochrones In the j-th luminosity bin each i-th isochrone contributes: 10 Myr Lower and upper integration limits depend on the isochrone, i.e. on age (and Z). 100 Myr 500 Myr A i describes the size of the Stellar Population on the isochrone (SSP) RGB mass loss
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: maximum age contributing to j-th bin 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): IMF M-L The LF on the MS is proportional to the IMF through the M-L relation AND to the SFR over the relevant age range.
Gallart, Zoccali and Aparicio 2005 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
Post MS phases Consider an SSP: approximations: valid for PMS phases m 2 m 1 m TO is the Stellar Evolutionary Flux: # of leaving the MS per unit time is the considered PMS evolutionary phase
Fuel Consumption Theorem (Tinsley 1976; Renzini 1981) if F,L in solar units and b in #/yr Is the fuel burnt in the j-th PMS phase 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
Test of FCT on M3 (Renzini and Fusi Pecci, 1988, ARAA 26, 199)
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
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
The Specific Production of Post-MS Stars of SSPs Number of Stars produced by a 1000 Mo SSP of age
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
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
Young CSP: an example
Blue Helium Burners SFH at Young ages is best Sampled by the Blue Helium Burners. Get detailed SFH up to 0.3 Gyr ago
Composite Stellar Populations : OLD A given Mag bin now spans a wide age range: We get integrated information Consider: what we count The Specific Production of j-type stars from the CSP what we get tool Look at the Specific Production of CSPs under different SFH In specific magnitude bins
Specific Production of CSP: bright AGB stars number of bright AGB stars from a 1000 Mo CSP
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
Specific Production of CSP: AGB stars Simulation: foreground contamination before Ist pulse and massive He burners TPAGB: Oxygen rich Carbon rich selected from 2MASS data of LMC Marigo, Girardi, Chiosi 2003
Mixture of Pulsators: fundamental & first over-tone
Specific Production of CSP on bright RGB number of stars in the 2 upper I-mags of the RGB from a 1000 Mo CSP
Specific Production of CSP of He burning Stars at Clump Mags number of Stars at Clump Magnitudes from a 1000 Mo CSP
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
The Simulator (AT FIXED METALLICITY) Random Extraction of Mass-Age pair Place Synthetic Star on HRD r random in 0 1 Convert (L,Teff) into (Mag,Col) Apply Photometric Error NO Test to STOP YES Notify: Astrated Mass, # of WDs,BHs,TPAGB.. EXIT
Interpolation between tracks: lifetimes
Interpolation between Tracks: L and Teff of low mass stars
Interpolation between Tracks: L and Teff of intermediate mass stars
Photometric Error: Completeness NGC 1705 (Tosi et al. 2001) Completeness levels: 0.95 % thick 0.75 % thin 0.50 % thick 0.25% thin
Photometric errors: σ DAO and Δm
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
Another way to put it: (Renzini 1998) # of blends in my frame is # of j stars in my frame (if SSP) is where 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
Pixels and Frames: Example (1) (2) (3) (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 RGTxn RGT 0.044 N(r.e.) 1.3e+04
How Robust is the Result? The statistical estimator does not account for systematic errors Theoretical Transformed Errors Applied EACH STEP BRINGS ALONG ITS OWN UNCERTAINTIES THE SYSTEMATIC ERROR IS DIFFUCULT TO GAUGE
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
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
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
My prejudice: The model CMDs may NOT contain 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. If wrong Z is used, the blind method will give a solution, but not THE SOLUTION
Count the stars in the diagnostic boxes: Their number scales with the mass in Stars in the corresponding age range Methods for Solution: Tailored Fit (see Bertelli et al 1992, ApJ, ***,***) Between 10 and 50 Myr 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 Younger than 10 Myr Between 50 Myr and 1 Gyr
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
Simulation
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.