Lectures on Stellar Populations Spectral Indices Broad Band Colors are affected by the AGE-METALLICITY DEGENERACY Spectral indices have been introduced

Lectures on Stellar Populations

Spectral IndicesBroad Band Colors are affected by the AGE-METALLICITY DEGENERACYSpectral indices have been introduced to overcome this problem


Lick Indices

C

l

F

FLogMg 5.22

Definition:Worthey, Faber, Gonzales, Burstein 1994

Measurement:Kuntschner and Davies 1997

)1(52c

l

F

FFeEW, e.g.:

MAG, e.g.:


Lick Indices: measurementNOT TRIVIAL

2

1

1

dFFP

dF

FEW

c

l

2

1

1

Trager’s Thesis

dF

FLogMag

c

l2

1

15.2

1. Define Pseudocontinuum Flux in the two side bands

2. Fc(λ) is the straight line through the 2 adjacent FP

Then index is:


Stellar Population Indices are Synthetizednot analyzed

iCi

i

iC

iCi

SSP fIF

FII , : EW

iMg

iiCfLogMg ,24.0*

,2 105.2 : Mag

C

l

F

FI 1 : EW

C

l

F

FLogMg 5.2 :MAG 2

INDICES FOR SSPs:

Start from simplyfied definitions:

with some algebra you get:

In the SSP, each star contributes its index weighted by the star’s contributionto the total continuum flux


SSP Indices: first derive the SED, then ‘measure’ the index

Vazdekis 1999500 stars (Jones, 97) withspectral resolution of 2 A:

Only in the range3820 – 4500 A4780 – 5460 A

Kurucz models have a resolution of 20 ALick indices resolution is 8-10 ANeed a high resolution stellar SED

AND Basically all stars at solar Z


Lick Indices from SEDBertone, Buzzoni et al 2004Models of atmospheres


Alternatively: Fitting Functions

Gorgas et al. 1993


Lick Indices

),,(

*

ZgTf

yccI

eff

ii

Worthey et al.1994


SSP Lick Indices:an example

Metallic line strenghts increase withboth AGE and Metallicity

Hβ gets weaker as age increases and as Metallicity increases

Use combination of metallic andBalmer line strenghts to solve theAGE-METALLICITY degeneracy


First, but very interesting, results:alpha elements overabundance in Es

Worthey, Faber & Gonzales 1992:

At given Fe index, the data Mg indexis stronger than the model predictions

Interpreted as a supersolar Mg/Fe ratio

Among various possibilities: Short Formation timescales for Es

Notice that: ZFe,o=1.3e-03 ZO,o = 5.8e-03Αlpha overabundance is more anFe underabundance


First, but very interesting, results:Age spread among Es

Gonzales et al. 1992:

E galaxies span a small range in metallicity and a wide range in ageThe most metal rich are also the OLDESTThe alpha overabundance syndrome is also evident

2.5

1.6

1.3


Indices: which diagnostic power?

iCi

iSSP fII ,

For magnitues consider 10-0.4(INDEX)

Most of the Index growth occurs in the(upper) MS and in the (lower) RGB

No wander: these are the phases whichMost contribute to the continuum fluxIn the optical

The various fitting functions appear to agree in the relevant evolutionary phases: the final values of the indices happen to agree (at least for this isochrone)


Model Lick Indices compared with GCs data

Puzia et al. (2002) measure Lick Indices for 12 MW GCs, 9 in the BulgeMaraston et al. (2002) derive metallicity by comparing with 12 Gyr old SSP modelsSpectroscopic/Photometric metallicity is available for these clusters: COMPARE THE TWO:

The metallicity derived from the Mg index is approx. OKThe metallicity derived from the Fe index is systematically lowAgain: effect of alpha overabundance (Fe depletion)


Indices with alpha enhancement


Tripicco and Bell (1995):

Stellar sample with solar Z

TB compute high resolution stellarspectra using model atmospheresfor (g,Te) combinations along the M67 isochrone.

Model Indices are computed for solarMixture and for other mixtures in whichEach element abundance is doubledSo as to measure the partial derivative.

Find that some indices trace abundanceSome do not: Fe4668 is very sensitive toC abundance

Compare model indices to a) Stellar valuesb) Worthey fitting functions


DWARFS

GIANTS

TB95

W ff


Effect of elemental variation

Tripicco and Bell 1995: compute variation of Index in response to doubling the abundance of one element, which leaves (almost) constant the total metallicity

Computed for Dwarf Turn-Off star Red Giant


Indices: Correction for alpha overabundancefollowing Thomas, Maraston & Bender (2003)

][][

0

i

Zi

XX

II

3.0

][3.0

][

lnlnln

0

i

i ioldnew

X

X

III

GC

TOC

DC

GC

Gn

TOC

TOn

DC

DnSSP

new FFF

FIFIFII

Tripicco and Bell 95 give : for D, TO and G

For each class compute thecorrected index with:

= 0.3

Get SSP corrected Index as:


Thomas, Maraston and Bender 2003

12 Gyr old, Solar Metallicity SSP Models:

At constant Z, when [α/Fe] increase:

Mg indices get strongerFe indices get weaker[MgFe] stays constant


Thomas, Maraston and Bender 2003comparison to GC data:

Data: Puzia et al GCs

From model Mgb and Fe52get Fe and αs abundance Total Z

Brodie and Huchra 1990: metallicityCalibration of MW and M31 GCs


What have we learnt

• In an SSP each stellar index is weighted with the contribution of the Star to the Total Continuum Flux of the SSPCool Dwarfs have a high Mg index, but cannot be efficiently used to enhance

theSSP Mg index• Metallic Line Strenghts are stronger in older and more metal rich stellar

populations• Balmer Line Strenghts are stronger in younger and more metal poor stellar

populations• Index – Index Diagrams offer a diagnostic for age AND metallicity• Element Abundance Ratios affect the indices in different ways

The Optimist’s View: One Balmer IndexOne Mg IndexOne Fe Index

AGEMETALLICITYα/Fe RATIO


But: Tantalo and Chiosi (2004) SSP Models with α enhancement

Based on Salasnich et al.α enhanced models+ TB 95 response functions

Ages depend on abundance patternAs a consequence, Z also does

Based on patching literatureisochrones+ TB 95 response functions

Based on isochrones + FCT+ TB 95 response functions


Seek better diagnostic for AGE: other Balmer Indices (Hγ , Hδ) unaffected by gas emission

Worthey and Ottaviani 1997

For each index 2 definitions: F for wide (40 A), A for narrow (20 A)central bandapasses

Models: high sensitivity to AGE(but Hβ is still the more sensitive)

Jump from [Fe/H]=-1 to -0.5 due toVariation of HB morphology


New Generation of Models:Thomas,Maraston and Korn 2004

Korn et al. (2005) compute response functions of atmospheres with various (g,Teff) fora wide range of metallicities (1/200 to 3.5 solar). Based on these, TMK re-computeIndices with variable [alpha/Fe] ratios.

Contrary to Hβ (?!)higher order BalmerIndices are sensitive to[α/Fe] ratio (at high Z)

The pseudocontinuacontain Fe lines


Effect on Galaxies AGE Dating

When [α/Fe]=0.2 is used theAges indicated by Hβ and HγF become consistent

When using solar ratio models high order Balmer lines lead to underestimate the age


New Response Functions:Korn,Maraston,Thomas 2005

Model atmospheres with high resolutionfor typical MS,TO and RG stars onIsochrones with Z=-2.25 …+0.67

Determine the response function of21 Lick indices


Korn,Maraston,Thomas 2005

Solid: new response functionsDotted : old response functionsBlack Dots: GCs dataOpen Square: Bulge fieldGrey dots: Es

The new models are almost the sameAs the old.We have much more confidence on themetallicity dependence of the correctionfor non solar [α/Fe] ratioStill not explored the behaviour along theIsochrone


Puzia et al. 2006: AGES, METALLICITIES and ABUNDANCE RATIOsof a sample of extragalactic GCs

Use:[MgFe]’ as total Z indicatorWeighted ave of Balmer Lines as AGE indicator<Fe> and <Mg2> to measure [α/Fe]

Quality of the index as age indicatordepends on:Mean error of the dataTransformation accuracy to the Lick systemError on the original Lick spectraAccuracy of the Lick FFDynamic range of the indexDegeneracy parameter

Notice that many GCs fall out of theGrid. This should be further investigated


CAVEATS: BALMER LINE STRENGTHSdepend on HB morphology

Hβ depends on HB morphology:Models have 10 and 15 GyrSolid: no mass loss

Maraston 2003


CAVEATS: BALMER LINE STRENGTHSdepend on HB morphology

from Puzia et al 2006:OBSERVED BALMER INDICESOFMW GCs (squares)M31 GCs (inv. Triangles)LMC GCs (triangles)

STAR: high Z GCs with blue HB

HBR=(B-R)/(B+V+R)


CAVEATS: SPURIOUS CORRELATIONS

From Thomas et al. 2005:(SFH of Ellipticals)Monte carlo Simulation:

- take indices of one SSP witht=10.7, [Z/H]=0.26,[α/Fe]=0.25- apply observed errors (gaussian) on the diagnostic indices- derive (t,Z,α/Fe)

Error of the procedure can beQuantified into0.1 dex for metallicity0.03 for abundance ratio1.5 Gyr of age

ERRORS ON Hβ INDUCEA SPURIOUS ANTICORRELATION OFAGE AND METALLICITY

Documents

Lectures on Stellar Populations Spectral Indices Broad Band Colors are affected by the AGE-METALLICITY DEGENERACY Spectral indices have been introduced