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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
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Evolution of starsEvolution of stars
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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
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(If you know the sfh of the galaxy you know its metallicity history)
Building an isochrone Building an isochrone (not! trivial)(not! trivial)
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Isochrones (continued)Isochrones (continued)
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Horizontal branch
Isochrones, do they Isochrones, do they resemble reality?resemble reality?
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How do the models How do the models compare among compare among themselves?themselves?
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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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⎞
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=
⎟⎟⎟⎟⎟⎟
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⎛
xy B
⎟⎟⎟⎟⎟⎟
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⎜⎜⎜⎜⎜⎜
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⎛=
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⎛xy B
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
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The mass function of SDSS galaxies over 5 orders of magnitude
Panter et al. (2004) MNRAS 355, 764
SDSS
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Comparison to the Millenium Run
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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
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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
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How well are we fitting?
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Where are the galaxies today that were red and blue in the past?
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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
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SF as a function of environment (Mark Correlations)
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Sheth, RJ, Panter, Heavens, ApJL, astro-ph/0604581
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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?
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