The Stellar Populations,The Stellar Populations,Mass-to-Light Ratios Mass-to-Light Ratios

andandDark MatterDark Matter

in Spiral Galaxiesin Spiral GalaxiesRoelof S. de JongRoelof S. de Jong Steward Steward ObservatoryObservatoryEric BellEric BellRob KennicuttRob KennicuttRob SwatersRob SwatersRob OllingRob OllingDon McCarthyDon McCarthyCedric LaceyCedric Lacey

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OverviewOverview

• IntroductionIntroduction

• Ages and metallicities of stellar populationsAges and metallicities of stellar populations– description of methoddescription of method

– scaling laws with structural parametersscaling laws with structural parameters

• Galaxy evolution modelingGalaxy evolution modeling

• Mass-to-light ratios of stellar populationsMass-to-light ratios of stellar populations– correlation with population colorscorrelation with population colors

– constraints from rotation curvesconstraints from rotation curves

– application to Tully-Fisher relationapplication to Tully-Fisher relation

• Future workFuture work

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Galaxy Formation and EvolutionGalaxy Formation and Evolution

• Huge progress, both observational and theoretical:Huge progress, both observational and theoretical:

– observational: e.g. the star formation history of the observational: e.g. the star formation history of the Universe and of local group galaxiesUniverse and of local group galaxies

– theoretical: hierarchical galaxy formation models in theoretical: hierarchical galaxy formation models in CDM-like universesCDM-like universes

• Something is missing:Something is missing:

We do not not where, when and especially why We do not not where, when and especially why stars are forming in particular galaxiesstars are forming in particular galaxies

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Galaxy Evolution and Structural Galaxy Evolution and Structural ParametersParameters

• What drives the Star Formation History and the What drives the Star Formation History and the Chemical Evolution within disk galaxies?Chemical Evolution within disk galaxies?

– current star formation in disks semi-regular, related to current star formation in disks semi-regular, related to morphology and structural parametersmorphology and structural parameters

– are spirals determined by initial conditions or are infall are spirals determined by initial conditions or are infall and outflow important?and outflow important?

– how is galaxy evolution related to the luminous and how is galaxy evolution related to the luminous and dark matter distribution and galaxy dynamics?dark matter distribution and galaxy dynamics?

• What is the distribution of dark and luminous matter?What is the distribution of dark and luminous matter?

– can we explain the Tully-Fisher relation?can we explain the Tully-Fisher relation?

– does dark matter really follow NFW profile distributions?does dark matter really follow NFW profile distributions?

– do we need alternative gravity (e.g. MOND)?do we need alternative gravity (e.g. MOND)?

Structural parameters:Structural parameters: luminosity, scale size, luminosity, scale size, surface brightness, mass, velocity surface brightness, mass, velocity

distributiondistribution

Statistical studies:Statistical studies: scaling relations scaling relations

Structural parameters:Structural parameters: luminosity, scale size, luminosity, scale size, surface brightness, mass, velocity surface brightness, mass, velocity

distributiondistribution

Statistical studies:Statistical studies: scaling relations scaling relations

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Stellar populations Color-Color Stellar populations Color-Color diagramsdiagrams

Gyr Gyr

Bruzual & Charlot modelsBruzual & Charlot models

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Data & SamplesData & Samples

• Face-on disk galaxies withFace-on disk galaxies with

– data in at least 3 passbands (of which one IR)data in at least 3 passbands (of which one IR)

– good colors over at least 2 disk scale lengthsgood colors over at least 2 disk scale lengths

– de Jong & van der Kruit 1994de Jong & van der Kruit 1994◊ BVRIHK of 64 face-on field spiralsBVRIHK of 64 face-on field spirals

– Verheijen et al. 1998Verheijen et al. 1998◊ BVRK of 34 Ursa Major Cluster spiralsBVRK of 34 Ursa Major Cluster spirals

– Bell et al. 1999Bell et al. 1999◊ BVRIK of 23 Low Surface Brightness galaxiesBVRIK of 23 Low Surface Brightness galaxies

• Samples:Samples:

Total sample of 121 galaxiesTotal sample of 121 galaxies

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Radial Color-Color Observations Radial Color-Color Observations

B-R

B-R

R- K

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Maximum Likelihood FittingMaximum Likelihood Fitting

• Make model grid of eMake model grid of e-t/-t/ττ Star Formation History and Star Formation History and metallicitymetallicity

– parameterize SFH by average age <A>parameterize SFH by average age <A>

• Determine minimum ΧDetermine minimum Χ2 2 between models and databetween models and data

– use all available passbandsuse all available passbands

– take calibration, flatfield and sky errors into accounttake calibration, flatfield and sky errors into account

• Repeat for all radiiRepeat for all radii

• Use Monte Carlo simulations to determine Use Monte Carlo simulations to determine uncertaintiesuncertainties

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Local Age & Local Metallicity Local Age & Local Metallicity versusversus

Local Surface BrightnessLocal Surface Brightness

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Age vs Surface Brightness & Age vs Surface Brightness & LuminosityLuminosity

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Metals vs Surface Brightness & Metals vs Surface Brightness & LuminosityLuminosity

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What determines SFH and What determines SFH and Metals?Metals?

Surface BrightnessSurface Brightness or or LuminosityLuminosity??

RememberRememberluminosityluminosityand surfaceand surfacebrightnessbrightnessare correlated!are correlated!

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The Galaxy Space DensityThe Galaxy Space DensitySurface BrightnessSurface Brightness & & MagnitudeMagnitude

Space density ofSpace density ofspiral galaxies spiral galaxies corrected for corrected for selection effectsselection effects

(de Jong & Lacey (de Jong & Lacey 2000)2000)

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Are Ages mainly determined by Are Ages mainly determined by Surface Brightness or Surface Brightness or Luminosity?Luminosity?

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Is metallicity mainly determined Is metallicity mainly determined by Surface Brightness or by Surface Brightness or Luminosity?Luminosity?

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Summary observationsSummary observations

• Ages are mainly determined by surface Ages are mainly determined by surface brightness, suggesting inside-out disk formationbrightness, suggesting inside-out disk formation

• Metallicity is determined by surface brightness Metallicity is determined by surface brightness and total luminosityand total luminosity

• The observed scatter is larger than The observed scatter is larger than observational errorsobservational errors

So what are the caveats?So what are the caveats?– Changes in the IMFChanges in the IMF

– Other Stellar Population Synthesis modelsOther Stellar Population Synthesis models

– The effect of dust reddeningThe effect of dust reddening

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IMF uncertaintyIMF uncertainty

Salpeter IMFSalpeter IMF

Scalo IMFScalo IMF

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Spectral Spectral synthesissynthesis model model uncertaintyuncertainty

Bruzual & CharlotBruzual & Charlot

Kodama & ArimotoKodama & Arimoto

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The effect of Dust ExtinctionThe effect of Dust Extinction

• Extinction will mainly effect metallicity Extinction will mainly effect metallicity

determinationsdeterminations i.e. reddening vector runs parallel to i.e. reddening vector runs parallel to

metallicity color gradientsmetallicity color gradients

• Reddening not the main cause of the observed trends Reddening not the main cause of the observed trends because:because:– we are using face-on galaxieswe are using face-on galaxies

– of the limits set by overlapping and edge-on galaxyof the limits set by overlapping and edge-on galaxy

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The effect of Dust ExtinctionThe effect of Dust Extinction

• Extinction will mainly effect metallicity Extinction will mainly effect metallicity

determinations determinations i.e. reddening vector runs parallel to i.e. reddening vector runs parallel to

metallicity color gradientsmetallicity color gradients

• Reddening not the main cause of the observed trends Reddening not the main cause of the observed trends because:because:– we are using face-on galaxieswe are using face-on galaxies

– of the limits set by overlapping and edge-on galaxyof the limits set by overlapping and edge-on galaxy

– we see no dependence on galaxy inclinationwe see no dependence on galaxy inclination

– colors are mainly determined by least obscured starscolors are mainly determined by least obscured stars

– patchy dust structure reduces reddening effectpatchy dust structure reduces reddening effect

– reddening is caused by absorption only, not by scatteringreddening is caused by absorption only, not by scattering

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• Scattering Scattering preferably to face on preferably to face on directiondirection

• Reddening follows Reddening follows absorption curve, absorption curve, not extinction curvenot extinction curve

• For low optical For low optical depth reddening depth reddening insignificantinsignificant

Dust modeling with scatteringDust modeling with scattering

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Conclusion Age & Metallicity Conclusion Age & Metallicity CaveatsCaveats

• Only very unusual IMFs can mimic our resultsOnly very unusual IMFs can mimic our results

• Other Spectral Synthesis Models will only Other Spectral Synthesis Models will only change the absolute age and metallicity values change the absolute age and metallicity values

• Dust will at most effect metallicities a bitDust will at most effect metallicities a bit

The relative rankings of The relative rankings of Ages & MetallicitiesAges & Metallicities

are Robustare Robust

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Simple Galaxy Evolution ModelsSimple Galaxy Evolution Models

• Simple closed box models:Simple closed box models:

– Start with exponential gas diskStart with exponential gas disk

– Form stars according to Schmidt law: (surface density)Form stars according to Schmidt law: (surface density)nn

– Instantaneous recycling of metalsInstantaneous recycling of metals

– Maximum likelihood fitting on resulting integrated colorsMaximum likelihood fitting on resulting integrated colors

• Additional bells and whistles:Additional bells and whistles:

– Mass dependent metal free gas infallMass dependent metal free gas infall

– Mass dependent enriched gas blowoutMass dependent enriched gas blowout

– Mass dependent epoch of formationMass dependent epoch of formation

– Fluctuations due to small starburstsFluctuations due to small starbursts

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Galaxy evolution modelsGalaxy evolution models

Closed box modelClosed box modelMass dependent formation epoch model with star burstMass dependent formation epoch model with star burstMass dependent formation epoch modelMass dependent formation epoch model

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Modeling conclusionsModeling conclusions

• Simple closed box models with a star formation Simple closed box models with a star formation rate dependent on local gas density explains the rate dependent on local gas density explains the basic observed trends between stellar ages & basic observed trends between stellar ages & metallicities and galaxy surface brightness metallicities and galaxy surface brightness parametersparameters

• Enriched gas blowout or mass dependent Enriched gas blowout or mass dependent formation epoch models are needed to explain the formation epoch models are needed to explain the metallicity dependence on total luminosity of the metallicity dependence on total luminosity of the galaxygalaxy

• Small burst of star formation explains the scatter Small burst of star formation explains the scatter on the observed relationson the observed relations

• What about masses instead of luminosities?What about masses instead of luminosities?

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Why stellar M/Ls?Why stellar M/Ls?

• Stellar M/Ls needed to do dynamics in Stellar M/Ls needed to do dynamics in situations where we have more matter than situations where we have more matter than just stars, e.g.just stars, e.g.– (baryonic) Tully-Fisher and other scaling (baryonic) Tully-Fisher and other scaling

relationsrelations– rotation curve decompositionrotation curve decomposition

• Dynamics is needed to model star formation Dynamics is needed to model star formation and galaxy evolutionand galaxy evolution• How? Many approaches possible:How? Many approaches possible:– Milky Way kinematicsMilky Way kinematics– galaxy kinematicsgalaxy kinematics

◊ streaming motions induced by bars or spiral armsstreaming motions induced by bars or spiral arms◊ vertical velocity dispersion in stellar disks vertical velocity dispersion in stellar disks

– stellar population synthesisstellar population synthesis

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Galaxy evolution modelsGalaxy evolution models

Closed box modelClosed box modelMass dependent formation epoch modelMass dependent formation epoch modelMass dependent formation epoch model with star burstsMass dependent formation epoch model with star bursts

Even in K mass-to-light ratio varies by factor of 2Even in K mass-to-light ratio varies by factor of 2The optical color of a stellarThe optical color of a stellarpopulation is a good M/L indicatorpopulation is a good M/L indicator

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Color-ML for hierarchical galaxy Color-ML for hierarchical galaxy modelmodel

Even a Even a hierarchical hierarchical galaxy formation galaxy formation model shows model shows strong correlation strong correlation between color between color and M/Land M/LK

I

B

Cole et al. (2000) models

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Different population synthesis Different population synthesis modelsmodels

• The slope of the The slope of the color-M/L relation is color-M/L relation is independent of independent of stellar population stellar population synthesis models synthesis models usedused

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Different Initial Mass FunctionsDifferent Initial Mass Functions

• The slope of the The slope of the color-M/L relation color-M/L relation is independent of is independent of models and IMFs models and IMFs usedused

• The normalization of The normalization of the relation depends the relation depends on the IMF used, i.e. on the IMF used, i.e. the amount of low the amount of low mass starsmass stars

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Rotation curve M/L constraintRotation curve M/L constraint

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Maximum disk constraintsMaximum disk constraints

• The color-M/L relation The color-M/L relation must be normalized must be normalized below all maximum below all maximum disk valuesdisk values

Salpeter IMF

Salpeter IMF

• A Salpeter IMF is A Salpeter IMF is too massivetoo massive

data

Verh

eije

n (

19

97

)

bad data point due to beam smearing

• Distribution suggests Distribution suggests IMF similar in most IMF similar in most galaxies and close to galaxies and close to maximum disk for a maximum disk for a fraction of the galaxiesfraction of the galaxies

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• Stellar masses derived Stellar masses derived from different from different passbands using the passbands using the color-M/L relation agree color-M/L relation agree to within 10% rmsto within 10% rms

• The Tully-Fisher The Tully-Fisher relations derived from relations derived from different passbands are different passbands are identical to within the identical to within the errorserrors

• The slope is very steepThe slope is very steepVVrot rot ~ M ~ M**

4.54.5

Stellar Mass Tully-Fisher relationStellar Mass Tully-Fisher relation

• Raw Tully-Fisher relation Raw Tully-Fisher relation has different slopes and has different slopes and offsets in different offsets in different passbandspassbands

• Tully et al. (1998) Tully et al. (1998) extinction corrections extinction corrections makes the slopes makes the slopes steeper, but do not steeper, but do not bring them into bring them into agreementagreement

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Baryonic Tully-Fisher relationBaryonic Tully-Fisher relation

• Add in the HI gas mass Add in the HI gas mass to calculate the baryonic to calculate the baryonic Tully-Fisher relationTully-Fisher relation

• The slope is less steep The slope is less steep than stars only and less than stars only and less than than

VVrot rot ~ M~ Mbarbar3.53.5

• Slope problematic for Slope problematic for MOND, but consistent wit MOND, but consistent wit hierarchical CDM galaxy hierarchical CDM galaxy formation models with formation models with some fine-tuningsome fine-tuning

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Future work: Stellar Velocity Future work: Stellar Velocity DispersionsDispersions

An isothermal disk yields:An isothermal disk yields:

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Future work: Rotation CurvesFuture work: Rotation Curves

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Future work: stellar populationsFuture work: stellar populations

Ages of young star clusters Ages of young star clusters in merging galaxiesin merging galaxies

Ages and metallicities of resolved Ages and metallicities of resolved stellar populations in nearby disk stellar populations in nearby disk galaxiesgalaxies

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ConclusionsConclusions

• Local star formation history in disks mainly set by local Local star formation history in disks mainly set by local surface density, resulting in inside-out disk formationsurface density, resulting in inside-out disk formation

• Metallicity regulated by both surface density and massMetallicity regulated by both surface density and mass

• Realistic galaxy evolution models predict a strong Realistic galaxy evolution models predict a strong correlation between population color and M/Lcorrelation between population color and M/L

• Maximum disk constraints support this observationally Maximum disk constraints support this observationally and suggest that a Salpeter IMF is too massiveand suggest that a Salpeter IMF is too massive

• The stellar mass Tully-Fisher relation is independent of The stellar mass Tully-Fisher relation is independent of originating passbandoriginating passband

• The baryonic Tully-Fisher relation has a maximal slope The baryonic Tully-Fisher relation has a maximal slope of about 3.5 +/- 0.2 of about 3.5 +/- 0.2