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Lectures on Early-type galaxies PART II (M. Bernardi). Plan for today:. Galaxy formation models Stellar Populations Age/Metallicity/ a -enhancement Lick Indices and Colors Correlations with L, s and environment Comparison between Models and Observations
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Lectures on Early-type galaxies PART II(M. Bernardi)
Plan for today: • Galaxy formation models • Stellar Populations • Age/Metallicity/a-enhancement • Lick Indices and Colors • Correlations with L, s and environment • Comparison between Models and Observations • Environment and Evolution in the SDSS • Constraints on galaxy formation models
Initial fluctuations are seeds of structure Growth is hierarchical; smaller dark matter ‘halos’ merge to form larger ones Gas cools within ‘halos’ Galaxies
Hierarchical models predict the spatial distribution of galaxies (successfully) • Also describe galaxy formation and evolution
CDM: hierarchical gravitational clustering: The most massive galaxies are the last to be assembled, though their stars may be oldest
Age of stellar population may be different from that of host dark matter halo • Measure ages of stellar populations to constrain galaxy formation models
Theoptical portion of the galaxy spectrum is due to the light of stellar photospheres K giant star Typical elliptical galaxy
INGREDIENTS FOR STELLAR POPULATION MODELS • Stellar library (observables) • Stellar evolution codes (age/metal) • + • Star Formation Rate • Metal enrichment law • Initial Mass Function MODEL Linear combination of models galaxy properties (fluxes, colors, and spectra of galaxies)
INGREDIENTS FOR STELLAR POPULATION MODELS (Isochrone Synthesis) Spectral energy distribution at time t: • Star Formation Rate y(t) • Instantaneous burst: y(t) ~ d(t) • (usually called “single stellar population” model SSP) • Exponential declining: y(t) ~ t-1 exp(-t/t) • Single burst of length t: y(t) ~ t-1 for t ≤t; y(t) = 0 fort > t • Constant: y(t) = const • where t is the e-folding timescale
INGREDIENTS FOR STELLAR POPULATION MODELS (Isochrone Synthesis) Spectral energy distribution at time t: • Star Formation Rate y(t) • Metal enrichment law z(t) • Sl[t’,z(t-t’)] is the power radiated per unit wavelength per unit initial mass by a “single stellar population” (SSP) of age t’ and metallicity z(t-t’) • Sl[t’,z(t-t’)] is the sum of the spectra of stars defining the isochrone of a SSP of age t’ and metallicity z(t-t’) • It is computed by interpolating the isochrone at age t’ from the tracks in the HR diagram
INGREDIENTS FOR STELLAR POPULATION MODELS (Isochrone Synthesis) Spectral energy distribution at time t: • Star Formation Rate y(t) • Metal enrichment law z(t) • 3) Initial Mass Function f(m) defined such that f(m)dm is the number of stars born with masses between m and m+dm mc = 0.08 M s = 0.69
Evolution of the spectrum of a “single stellar population” (SSP) model Age (Gyrs)
Colors and M/L vs Age for a solar metallicity model
Comparison model/data --- model spectrum --- observed spectrum
Problem: Age-Metallicity degeneracy Stars weak in heavy elements are bluer than metal-rich stars (line blanketing effects and higher opacities) Galaxy models must account for metallicity changes increase of heavy elements due to SN explosions
Different Age – Same Metallicity Easy to separate young and old populations of the same metallicity
Same Age – Different Metallicity Easy to separate coeval populations of different metallicity
Age – Metallicity degeneracy Hard to separate populations which have a combination of age and metallicity Degeneracy: (∂ lnt/∂ lnZ) ~ -3/2
BUT… Although the continuum spectrum is similar, the absorption lines are stronger for higher metallicity SO…
How to disentangle age from metallicity? • Absorption lines (e.g. Lick indices) Average pseudo-continuum flux level: Fp = Fl dl/(l1 –l2) EW = (1-FIl/FCl) dl where FCl represents the straight line connecting the midpoints of the blue and red pseudo-continuum levels Hb Mgb Fe l2 l1 l2 l1
The central velocity dispersion s appears to play a stronger role in determining the stellar population
Correlation Mg-s tight over large range in galaxy size and all types of hot stellar systems ■▲♦●▪ galaxies with anisotropic kinematics □∆◊○ galaxies rotationally flattened ■ Giant ellipticals (GE) (M < -20.5 mag) ▲Ellipticals of intermediate L (IE) (-20.5 < M < -18.5 mag) ● Compact galaxies (CE) ♦ Bright dwarf galaxies (BDW) (M > -18.5 mag) ▪ Faint dwarf galaxies (FDW) x Bulges of S0/Sa (B)
Galaxies with larger s are older and/or more metal rich Stellar population evolves SDSS Bender et al. 1996 --- 0.05 < z < 0.07 ---0.07 < z < 0.09 --- 0.09 < z < 0.12 ---0.12 < z < 0.15 --- 0.15 < z < 0.20
Vice-versa galaxies with larger s have weaker Balmer absorption lines Strong evolution hi –z (younger population) low –z (older population)
No correlation between Fe and L --- only with s • Differential evolution? more massive galaxies evolve differently (slower?) than less massive ones?
Stellar population models How to disentangleagefrommetallicity? Lick Indices vs Age • Absorption lines (e.g. Lick indices)
Stellar population models How to disentangle age from metallicity? • Absorption lines (e.g. Lick indices) metallicity age Additional complication [a/Fe] enhancement
The [a/Fe] enhancement problem SN, which produce most of the metals, are of two types:
Additional complication [a/Fe] enhancement • -elements: Ne, Mg, Si, S, A, Ca (so-named because formed by adding 2,3,…a-particles, i.e. 4He nuclei, to 16O) Large s are a-enhanced --- z < 0.07 ---0.07 < z < 0.09 --- 0.09 < z < 0.12 ---0.12 < z < 0.15
Formation time and timescale • SNae Type II from massive stars/short lives • Top-heavy IMF or short formation timescales at high redshift
Stellar Population Synthesis Models Some recent models Age Metallicity Corrected for a-enhancement ☺ [a/Fe] > [a/Fe] But …… do not match well all the observed parameters !! !!
Problems?? D Hd ~ 1.5Ǻ
Big correction in D4000! D D4000 ~ 0.3!
Problems with models Can we learn something just from the observed absorption lines?
Testing predictions of galaxy formation models … • Early-type galaxies in the field should be younger than those in clusters • Metallicity should not depend on environment • The stars in more massive galaxies are coeval or younger than those in less massive galaxies
Environment …. From ~ 25,000 early-types at z < 0.14 4500 in low density regions 3500 in high density regions L > 3L* SDSS C4 Cluster Catalog (Miller et al. 2005) Lcl > 1.75 x 1011 h-2 L ~ 10L*
The Fundamental Plane The virial theorem: • Three observables + M/L • M/L ~ L0.14 • FP is combination with minimum scatter young old Cluster galaxies 0.1 mag fainter than field galaxies Cluster galaxies older than field by ~ 1Gyr? BCGs more homogeneous --- Cluster --- Field --- BCG
Bernardi et al. 1998 No differences in the Mg2-s relation If Mg2 is a indicator of the age of the stellar population Stars in field and cluster early-type galaxies formed mostly at high redshift
Mg2-s shows no differences because: Galaxies in the field • are younger • but have higher metallicity Kuntschner et al. 2002
….. Evolution Z ~ 0.05 Dt ~ 1.3Gyr D4000 increases with time; Hd, Hg decreases Z~ 0.17
Evolution as a clock Over small lookback times, metallicity cannot have changed significantly; hence observed evolution is due entirely to age differences, not metallicity!
Comparison of environmental differences with evolution measurement allows one to quantify effect of age difference between environments; so calibrate mean metallicity difference too!