Lectures on Early-type galaxies PART II (M. Bernardi)

Plan for today: Galaxy formation models Stellar Populations  Age/Metallicity/  -enhancement Lick Indices and Colors  Correlations with L,  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

Gastrophysics of galaxy formation

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

The optical portion of the galaxy spectrum is due to the light of stellar photospheres K giant star Typical elliptical galaxy

Linear combination of models  galaxy properties (fluxes, colors, and spectra of galaxies) 1)Stellar library (observables) 2)Stellar evolution codes (age/metal) + 1)Star Formation Rate 2)Metal enrichment law 3)Initial Mass Function INGREDIENTS FOR STELLAR POPULATION MODELS  MODEL

Stellar libraries account for stellar evolution (change luminosity, color, spectral features)

1)Star Formation Rate  (t) Instantaneous burst:  (t) ~  (t) (usually called “single stellar population” model SSP) Exponential declining:  (t) ~  -1 exp(-t/  ) Single burst of length  :  (t) ~  -1 for t ≤  t  for  t   Constant:  (t) = const  where  is the e-folding timescale INGREDIENTS FOR STELLAR POPULATION MODELS (Isochrone Synthesis) Spectral energy distribution at time t:

1)Star Formation Rate  (t) 2)Metal enrichment law  t  S [t’,  (t-t’)] is the power radiated per unit wavelength per unit initial mass by a “single stellar population” (SSP) of age t’ and metallicity  (t-t’) S [t’,  (t-t’)] is the sum of the spectra of stars defining the isochrone of a SSP of age t’ and metallicity  (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:

1)Star Formation Rate  (t) 2)Metal enrichment law  t  3) Initial Mass Function  (m) defined such that  (m)dm is the number of stars born with masses between m and m+dm INGREDIENTS FOR STELLAR POPULATION MODELS (Isochrone Synthesis) Spectral energy distribution at time t: m c = 0.08 M   = 0.69

Age (Gyrs) Evolution of the spectrum of a “single stellar population” (SSP) model

For “single stellar populations” (SSP) the evolution is well understood  e.g. basis for understanding globular clusters Early-type galaxy properties dominated by the light of RGB Importance of various parts of stars evolution to a SSP’s total luminosity

Colors and M/L vs Age for a solar metallicity model

Comparison model/data --- model spectrum --- observed spectrum

 metallicity changes increase of heavy elements due to SN explosions 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

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) H  Mg b Fe Average pseudo-continuum flux level: F p =  F d /( 1 – 2 ) EW =  1  F I  F C  d where F C represents the straight line connecting the midpoints of the blue and red pseudo-continuum levels 1  1 

Lick Indices

The central velocity dispersion  appears to play a stronger role in determining the stellar population

Correlation Mg-  tight over large range in galaxy size and all types of hot stellar systems ■ Giant ellipticals (GE) (M < mag) ▲Ellipticals of intermediate L (IE) (-20.5 < M < mag) ● Compact galaxies (CE) ♦ Bright dwarf galaxies (BDW) (M > mag) ▪ Faint dwarf galaxies (FDW) x Bulges of S0/Sa (B) ■▲♦●▪ galaxies with anisotropic kinematics □∆◊○ galaxies rotationally flattened

Bender et al SDSS  Galaxies with larger  are older and/or more metal rich  Stellar population evolves < z < < z < < z < < z < < z < 0.20

Vice-versa  galaxies with larger  have weaker Balmer absorption lines  Strong evolution hi –z (younger population) low –z (older population)

 No correlation between Fe and L --- only with  èDifferential evolution? more massive galaxies evolve differently (slower?) than less massive ones?

How to disentangle age from metallicity? Absorption lines (e.g. Lick indices) Stellar population models Lick Indices vs Age

metallicity age Stellar population models How to disentangle age from metallicity? Absorption lines (e.g. Lick indices) Additional complication  [  /Fe] enhancement

The [  /Fe] enhancement problem SN, which produce most of the metals, are of two types:

Large  are  -enhanced --- z < < z < < z < < z < 0.15 Additional complication  [  /Fe] enhancement  -elements: Ne, Mg, Si, S, A, Ca (so-named because formed by adding 2,3,…  -particles, i.e. 4 He nuclei, to 16 O)

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 Corrected for  -enhancement ☺ [  /Fe] > [  /Fe]  Age Metallicity do not match well all the observed parameters !!  !! But ……

Problems??  H  ~ 1.5Ǻ

Big correction in D4000!  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 …. SDSS C4 Cluster Catalog (Miller et al. 2005) L > 3L* L cl > 1.75 x h -2 L  ~ 10L * From ~ 25,000 early-types at z < in low density regions 3500 in high density regions

Cluster galaxies 0.1 mag fainter than field galaxies Cluster galaxies older than field by ~ 1Gyr? BCGs more homogeneous --- Cluster --- Field --- BCG The Fundamental Plane The virial theorem: Three observables + M/L M/L ~ L 0.14 FP is combination with minimum scatter oldyoung

Bernardi et al No differences in the Mg 2 -  relation If Mg 2 is a indicator of the age of the stellar population  Stars in field and cluster early-type galaxies formed mostly at high redshift

Mg 2 -  shows no differences because: Galaxies in the field are younger but have higher metallicity Kuntschner et al. 2002

….. Evolution Z ~ 0.05 Z~ 0.17  t ~ 1.3Gyr D4000 increases with time; H , H  decreases

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!

Some implications: early-type galaxies in the field should be younger than those in clusters Observed differences cluster-field small (~ 1 Gyr)

Color-Magnitude-  relation

Age – Metallicity from Color-Magnitude Models from Bruzual & Charlot (2003) 12 4 Age [Z/H]=0.6 [Z/H]=0 9 1 [Z/H]=0.6 [Z/H]= Age [Z/H]=0 [Z/H]= Age Bernardi et al. (2004b) L ↑ Age↑ [Z/H] ↑ L ↑ Age↑ [Z/H] ↓

Kodama et al. (1998) Slope of C-M independent of redshift out to z~1 C-M due to Mass-[Z/H] not Mass-Age

C-M due to Mass-[Z/H]  residuals from C-M due to Age In contrast to published semi- analytic galaxy formation models Bernardi et al. (2004b) Age  Age of stellar population increases with galaxy mass: Massive galaxies are older

At fixed L/Mass: 1) more massive galaxies are older 2) fainter galaxies are older 3) galaxies with smaller R are older 4) higher  galaxies are older

Color-Magnitude

Color-Magnitude is a consequence of Color-  & L- 

The Most Massive Galaxies: Double Trouble? 105 objects with (  > 350 km/s) Single/Massive?  Galaxy formation models assume  < 250 km/s  BHs (2 x 10 9 M  ) Superposition?  interaction rates  dust content  binary lenses

● Single/Massive ڤ Double ◊ BCG Sheth et al Expect 1/300 objects to be a superposition Bernardi et al. 2005c

‘Double’ from spectrum and image

‘Double’ from spectrum, not image

‘Single’ ?

● Single/Massive ڤ Double ◊ BCG Doubles are outliers BCGs are bluer than main sample at fixed 

Dry Mergers?

HST images: with ACS-HRC SDSS HST  = 407 ± 27 km/s SDSS J ” 1’

SDSS J  = 404 ± 32 km/s HST SDSS 1’ 3’

HST: ACS-HRC 6 single4 multiple  = 369 ± 22  = 383 ± 27  = 385 ± 34  = 385 ± 24  = 395 ± 27  = 402 ± 35  = 404 ± 32  = 407 ± 27  = 408 ± 39  = 413 ± 35 Single galaxies with  ~ 400 km/s  Some semi-analytic models use a cut at V c = 350 km/s (i.e.  = 350/√2 ~ 250 km/s)  Cut should be at higher V c ??

Color Gradients In monolithic collapse models color gradients are caused by winds which create metallicity gradients In hierarchical models, mergers scramble the stellar populations, so gradients are expected to be much shallower