Advanced Stellar Populations Advanced Stellar Populations Raul Jimenez raulj.

Advanced Stellar Advanced Stellar PopulationsPopulations

Raul JimenezRaul Jimenez

www.physics.upenn.edu/www.physics.upenn.edu/~raulj ~raulj

OutlineOutline

•Physics of stellar structure Physics of stellar structure and evolutionand evolution

•Synthetic stellar populationsSynthetic stellar populations

•MOPED and VESPAMOPED and VESPA

Light from galaxiesLight from galaxies

• Is made of a Is made of a collection of collection of stars at stars at different different evolutionary evolutionary stagesstages

• In galaxies we In galaxies we only see the only see the integrated lightintegrated light

Sloan Digital Sky Sloan Digital Sky SurveySurveyLargest data-set of Largest data-set of galaxy spectra (about galaxy spectra (about one million of them)one million of them)

Stellar populations models Stellar populations models predict the integrated predict the integrated light of galaxieslight of galaxies• Needs good Needs good stellar stellar evolution modelsevolution models

• Both interior Both interior and photosphereand photosphere

Basics of stellar evolution

Time scalesDynamical tdyn ~ (G)1/2 ~ 1/2 hour for the Sun

Thermal tth ~ GM2/RL ~ 107 years for the Sun

Nuclear timescale tnuclear ~ 0.007qXMc2/L ~ 1010 years for the Sun

Equations of Stellar Evolution

Hydrostatic Equilibrium

Energy Transport

Energy Generation

Remember that stars are simply balls of gas in (more-or-less) equilibrium

Stars come with Stars come with different Luminosities different Luminosities and Temperaturesand Temperatures

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.



Evolution of starsEvolution of stars







Ingredients of Ingredients of synthetic stellar synthetic stellar populationspopulations

A good set of stellar interior models, in particular isochrones.

A good set of stellar photosphere models

From the above two build an isochrone

A choice for the Initial Mass Function



(If you know the sfh of the galaxy you know its metallicity history)

Building an isochrone Building an isochrone (not! trivial)(not! trivial)



Isochrones (continued)Isochrones (continued)





Horizontal branch

Isochrones, do they Isochrones, do they resemble reality?resemble reality?





How do the models How do the models compare among compare among themselves?themselves?



Fits are getting good Fits are getting good nowadaysnowadays

3AA Examples: Young Galaxy3AA Examples: Young Galaxy

3AA Examples: Old Galaxy3AA Examples: Old Galaxy

Determining Star Formation Determining Star Formation History from Galaxy History from Galaxy SpectraSpectra• Various indicators Various indicators over spectral rangeover spectral range

• Broad spectral Broad spectral shape also contains shape also contains informationinformation

• Compare spectra Compare spectra from synthetic from synthetic stellar population stellar population models with models with observed spectraobserved spectra

Characterising the SFHCharacterising the SFH

• Current models and data Current models and data allow the allow the star formation star formation raterate and and metallicitymetallicity to to be determined in around be determined in around 8-12 time periods 8-12 time periods

• 11 x 2 + 1 11 x 2 + 1 dust parameterdust parameter = 23 parameters – = 23 parameters – significant technical significant technical challengechallenge

• To analyse the SDSS data To analyse the SDSS data would take ~200 yearswould take ~200 years

• Needs some way to speed Needs some way to speed this up by a large factorthis up by a large factor

Lossless linear Lossless linear compressioncompression

( ) ( )⎭⎬⎫

⎩⎨⎧ −−−= − T

CL μμ xCx 1

2/1 2

1exp

||||

1

x = data

μ = expected value of data, dependent on parameters (e.g. age)

C = covariance matrix of data

x → y = new (compressed) dataset

Lossless? Look at Fisher Matrix

Assume:= probability of parameters given the data, if priors are uniform

Fisher MatrixFisher Matrix

βααβ θθ ∂∂

∂−≡

LF

ln2

Fisher matrix gives best error you can get:

Marginal error on parameter θβ: σβ =√(F-1)ββ

If Fisher Matrix for compressed data is same as for complete dataset, compression is (locally) lossless

Characterising the Characterising the problemproblem

Large-Large-scale scale structurestructure

CMB MapCMB Map Galaxy Galaxy spectrumspectrum

CMB Power CMB Power SpectrumSpectrum

Data Data xx Fourier Fourier coefficiecoefficientsnts

T/TT/T Spectrum fSpectrum f Estimates Estimates of Cof Cll

Mean Mean 00 00 Spectrum Spectrum (SFR, (SFR, metallicity, metallicity, dust)dust)

CCll (cosmologic(cosmological al parameters)parameters)

CovariancCovariance e CC

Power Power spectrum spectrum + shot + shot noisenoise

CorrelatiCorrelation on functionfunction + + detector detector noisenoise

Instrument, Instrument, background, background, source source photon noisephoton noise

Cosmic Cosmic variancevariance + + noise, noise, foregroundsforegrounds

Linear compression Linear compression methodsmethods

Solve certain eigenvalue problem to make y uncorrelated, and B is chosen to tell you as much as possible about what you want to know.

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e.g. fλ

C known: MOPED* C known: MOPED* algorithmalgorithm

* Multiple Optimised Parameter Estimation and Datacompression Heavens, Jimenez & Lahav, 1999, MNRAS, 317, 965

Choose MOPED vector so that Fisher matrix element F11 is maximised (i.e. y1 “captures as much information as possible about parameter 1”)

Solve generalised eigenvector problem Mb=Cb, where

M=/1 (/1)T

• Consider y1 = b1.x for some MOPED (weight) vector b1

b1 C-1 1

Largest weights given to the x which are most sensitive to the parameter, and those which are least noisy. It decides. Construct y2=b2.x such

that y2 is uncorrelated with y1

Maximise F22

etc

Completely lossless if C independent of

Multiple parameters:

Massive compression (→ one datum per parameter).

MOPED vectorsMOPED vectors

Analytic fits for SSPsAnalytic fits for SSPs



The mass function of SDSS galaxies over 5 orders of magnitude

Panter et al. (2004) MNRAS 355, 764

SDSS



Comparison to the Millenium Run



SFR in galaxies of diff. SFR in galaxies of diff. stellar massesstellar masses

• Split by massSplit by mass

Stellar masses:

>1012 M๏ … < 1010 M๏

Galaxies with more stellar mass now formed their stars earlier(Curves offset vertically for clarity)

Heavens et al. Nature 2004

Curves offsetVertically forclarity





The mass-metallicity relation

Present stellar mass [Mo]

Metallicity [Z/Zo] 0.0

-1.0

128 9 10 11

-0.5

More tests. This time systematics of SDSS and theoretical models have been included

IMF does not matter

Models do matterQuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

How well are we fitting?



Where are the galaxies today that were red and blue in the past?



To study environment To study environment use Mark Correlationsuse Mark Correlations•Treat galaxies not like points, Treat galaxies not like points, but use attributes (e.g. but use attributes (e.g. luminosity)luminosity)

•Measure the spatial correlations Measure the spatial correlations of the attributes themselvesof the attributes themselves

•A mark is simply a weight A mark is simply a weight associated with a point process associated with a point process (e.g. a galaxy catalogue)(e.g. a galaxy catalogue)Sheth, RJ, Panter, Heavens, ApJL, astro-ph/0604581

(Connecting Stellar Populations and Correlations)

For example, use luminosity of galaxies



SF as a function of environment (Mark Correlations)



Sheth, RJ, Panter, Heavens, ApJL, astro-ph/0604581



Metallicity as a function of environment (Mark Correlations)

Sheth, RJ, Panter, Heavens, ApJL, astro-ph/0604581

MCMC MCMC errorserrors

How many bins do I need?



Advanced Stellar Populations Advanced Stellar Populations Raul Jimenez raulj.

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