Advanced Stellar Populations Advanced Stellar Populations Raul Jimenez

Outline Physics of stellar structure and evolution Physics of stellar structure and evolution Synthetic stellar populations Synthetic stellar populations MOPED and VESPA MOPED and VESPA

Light from galaxies Is made of a collection of stars at different evolutionary stages Is made of a collection of stars at different evolutionary stages In galaxies we only see the integrated light In galaxies we only see the integrated light

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

Stellar populations models predict the integrated light of galaxies Needs good stellar evolution models Needs good stellar evolution models Both interior and photosphere Both interior and photosphere

Basics of stellar evolution Time scales Dynamical t dyn ~ (G  ) 1/2 ~ 1/2 hour for the Sun Thermal t th ~ GM 2 /RL ~ 10 7 years for the Sun Nuclear timescale t nuclear ~ 0.007qXMc 2 /L ~ 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 different Luminosities and Temperatures

Evolution of stars

Ingredients of synthetic stellar populations 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 (not! trivial)

Isochrones (continued) Horizontal branch

Isochrones, do they resemble reality?

How do the models compare among themselves?

Fits are getting good nowadays

3AA Examples: Young Galaxy

3AA Examples: Old Galaxy

Determining Star Formation History from Galaxy Spectra Various indicators over spectral range Various indicators over spectral range Broad spectral shape also contains information Broad spectral shape also contains information Compare spectra from synthetic stellar population models with observed spectra Compare spectra from synthetic stellar population models with observed spectra

Characterising the SFH Current models and data allow the star formation rate and metallicity to be determined in around 8-12 time periods Current models and data allow the star formation rate and metallicity to be determined in around 8-12 time periods 11 x dust parameter = 23 parameters – significant technical challenge 11 x dust parameter = 23 parameters – significant technical challenge To analyse the SDSS data would take ~200 years To analyse the SDSS data would take ~200 years Needs some way to speed this up by a large factor Needs some way to speed this up by a large factor

Lossless linear compression 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 Matrix Fisher matrix gives best error you can get: Marginal error on parameter θ β : σ β =√(F -1 ) ββ If Fisher Matrix for compressed data is same as for complete dataset, compression is (locally) lossless

Characterising the problem Large-scale structure CMB Map Galaxy spectrum CMB Power Spectrum Data x Fourier coefficients  T/T Spectrum f Spectrum f Estimates of C l Mean  00 Spectrum (SFR, metallicity, dust) C l (cosmological parameters) Covariance C Power spectrum + shot noise Correlation function + detector noise Instrument, background, source photon noise Cosmic variance + noise, foregrounds

Linear compression methods 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. e.g. f λ

C known: MOPED* algorithm * Multiple Optimised Parameter Estimation and Datacompression Heavens, Jimenez & Lahav, 1999, MNRAS, 317, 965 Choose MOPED vector so that Fisher matrix element F 11 is maximised (i.e. y 1 “captures as much information as possible about parameter  1 ”) Solve generalised eigenvector problem Mb= Cb, where M=  /  1 (  /  1 ) T Consider y 1 = b 1.x for some MOPED (weight) vector b 1

b 1  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 y 2 =b 2.x such that y 2 is uncorrelated with y 1  Maximise F 22  etc Completely lossless if C independent of  Multiple parameters: Massive compression ( → one datum per parameter).

MOPED vectors

Analytic 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. stellar masses Split by mass Split by mass Stellar masses: >10 12 M ๏ … < M ๏ Galaxies with more stellar mass now formed their stars earlier (Curves offset vertically for clarity) Heavens et al. Nature 2004 Curves offset Vertically for clarity

The mass-metallicity relation Present stellar mass [Mo] Metallicity [Z/Zo]

More tests. This time systematics of SDSS and theoretical models have been included IMF does not matter Models do matter

How well are we fitting?

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

To study environment use Mark Correlations Treat galaxies not like points, but use attributes (e.g. luminosity) Treat galaxies not like points, but use attributes (e.g. luminosity) Measure the spatial correlations of the attributes themselves Measure the spatial correlations of the attributes themselves A mark is simply a weight associated with a point process (e.g. a galaxy catalogue) A mark is simply a weight associated with a point process (e.g. a galaxy catalogue) Sheth, RJ, Panter, Heavens, ApJL, astro-ph/ (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/

Metallicity as a function of environment (Mark Correlations) Sheth, RJ, Panter, Heavens, ApJL, astro-ph/

MCMC errors MCMC errors

How many bins do I need?