spectral indices
DESCRIPTION
Spectral Indices. Broad Band Colors are affected by the AGE-METALLICITY DEGENERACY Spectral indices have been introduced to overcome this problem. Lick Indices. Definition: Worthey, Faber, Gonzales, Burstein 1994. EW, e.g.:. MAG, e.g.:. Measurement:. Kuntschner and Davies 1997. - PowerPoint PPT PresentationTRANSCRIPT
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Spectral IndicesBroad Band Colors are affected by the AGE-METALLICITY DEGENERACYSpectral indices have been introduced to overcome this problem
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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.:
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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:
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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
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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
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Lick Indices from SEDBertone, Buzzoni et al 2004Models of atmospheres
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Alternatively: Fitting Functions
Gorgas et al. 1993
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Lick Indices
),,(
*
ZgTf
yccI
eff
ii
Worthey et al.1994
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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
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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
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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
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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)
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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)
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Indices with alpha enhancement
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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
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DWARFS
GIANTS
TB95
W ff
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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
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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:
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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CAVEATS: BALMER LINE STRENGTHSdepend on HB morphology
Hβ depends on HB morphology:Models have 10 and 15 GyrSolid: no mass loss
Maraston 2003
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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)
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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