Transcript Mapping the Dark Matter

Advanced Stellar Populations
Raul Jimenez
www.physics.upenn.edu/~raulj
Outline
• Physics of stellar structure and evolution
• Synthetic stellar populations
• MOPED and VESPA
Light from galaxies
• Is made of a
•
collection of stars at
different evolutionary
stages
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
Both interior and
photosphere
Basics of stellar evolution
Time scales
Dynamical
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 different
Luminosities and Temperatures
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Evolution of stars
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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
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(If you know the sfh of the galaxy you know its metallicity history)
Building an isochrone (not!
trivial)
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Isochrones (continued)
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Horizontal branch
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Isochrones, do they resemble
reality?
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How do the models compare
among themselves?
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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
Broad spectral shape
also contains
information
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
11 x 2 + 1 dust parameter =
23 parameters – significant
technical challenge
To analyse the SDSS data
would take ~200 years
Needs some way to speed this
up by a large factor
Lossless linear compression
Assume:
1
 1
T
1




L
exp

x


C
x




|| C ||1/ 2
2


x = data
= probability of
parameters given
the data, if priors
are uniform
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
Fisher Matrix
 2 ln L
F  
  
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 problem
Large-scale
structure
CMB Map
Galaxy spectrum
CMB Power
Spectrum
Data x
Fourier
coefficients
T/T
Spectrum f
Estimates of Cl
Mean 
0
0
Spectrum (SFR,
metallicity, dust)
Cl
(cosmological
parameters)
Correlation
function +
detector
noise
Instrument,
background,
source photon
noise
Cosmic
variance +
noise,
foregrounds
Covariance C Power
spectrum +
shot noise
e.g. fλ
Linear compression methods
  
  
  
 y  
  
  
  
  
B
 
 
 
  x
 
 
 
 
  
  
 y 
  
  
B
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.
 
 
 
 
 x
 

 
 
C known: MOPED* algorithm
• Consider y1 = b1.x for some
MOPED (weight) vector b1
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
* Multiple Optimised Parameter Estimation and
Datacompression Heavens, Jimenez & Lahav, 1999, MNRAS, 317, 965
b1  C-1 
1
Multiple parameters:
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
Massive compression (→ one
datum per parameter).
Completely lossless if C
independent of 
MOPED vectors
Analytic fits for SSPs
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The mass function of SDSS galaxies over 5 orders of magnitude
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SDSS
Panter et al. (2004) MNRAS 355, 764
Comparison to the Millenium Run
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SFR in galaxies of diff. stellar masses
Heavens et al. Nature 2004
• Split by mass
Stellar masses:
Curves offset
Vertically for
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>1012 M๏ … <
1010 M๏
Galaxies with
more stellar mass
now formed their
stars earlier
(Curves offset
vertically for clarity)
The mass-metallicity relation
Metallicity [Z/Zo]
0.0
-0.5
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-1.0
8
9
10
11
Present stellar mass [Mo]
12
More tests. This time systematics of SDSS and
theoretical models have been included
Models do matter
IMF does not matter
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are need ed to s ee thi s pictu re.
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 use Mark
Correlations (Connecting Stellar Populations and Correlations)
• Treat galaxies not like points, but use
attributes (e.g. luminosity)
• Measure the spatial correlations of the
attributes themselves
• A mark is simply a weight associated with
a point process (e.g. a galaxy catalogue)
Sheth, RJ, Panter, Heavens, ApJL, astro-ph/0604581
For example, use luminosity of galaxies
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SF as a function of environment (Mark Correlations)
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
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MCMC errors
How many bins do I need?
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