The Stellar Assembly History of Galaxies

1
The Stellar Assembly History
of Galaxies

• Decoding the fossil record
• Raul Jimenez
• www.physics.upenn.edu/raulj
• Ravi Sheth
• Licia Verde
• UPenn
• Alan Heavens
• Ben Panter
• Edinburgh

2
Outline

• Data compression
• The fossil record
• Downsizing
• Environment dependence

3
Star Formation History two complementary
approaches

• Two general approaches
• Look for signs of recent SF in galaxies at high z
  (e.g. UV) (e.g. Lilly et al 1996, Madau et al
  1996 Ouchi et al 2003)
• Look at nearby galaxies and date the stars in
  them (fossil record)
• If Copernican Principle holds, they should agree

Ouchi 2003
4
Advantages of fossil approach

• Decouples star formation from mass assembly
• Not so sensitive to uncertain obscuration
• Get SFR for a wide range of cosmic time
• Small statistical errors
• Large galaxy samples
• Faint samples

5
Disadvantages of fossil approach

• Needs a good theoretical spectral synthesis model
• Redshift-time relation is sensitive to cosmology
  (but so are volume elements at high z)
• Poor time- and z- resolution at high z

6
Characterising the SFH

• Current models and data allow the star formation
  rate and metallicity to be determined in around
  8-12 time bins
• 10 x 2 1 dust parameter 21 parameters
  significant technical challenge
• To analyse the SDSS data would take 200 years
• Needs some way to speed this up by a large factor
• We use MOPED

7
What is MOPED?

• Massively Optimized Parameter Estimation and Data
  Compression
• Extracts information from a compressed dataset
• Compression is optimized to contain as much
  information about parameters which define data
• Need to be able to model data to determine
  compression
• Information Compression Technique

8
Lossless linear compression
probability of parameters given the data, if
priors are uniform
Assume
x data ? expected value of data, dependent
on parameters (e.g. age) C covariance matrix
of data y b.x new (compressed) dataset
Lossless? Look at Fisher Matrix
9
Fisher Matrix
Fisher matrix gives best error you can
get Marginal error on parameter v(F-1)
If Fisher Matrix for compressed data is same as
for complete dataset, compression is (locally)
lossless
10
Characterising the problem
11
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.
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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
13
Largest weights given to the x which are most
sensitive to the parameter, and those which are
least noisy. It decides.
b1 ? C-1 ?? ??1
Multiple parameters

• Construct y2b2.x such that y2 is
  uncorrelated with y1
• Maximise F22
• etc

Completely lossless if C independent of ?
Massive compression ( one datum per parameter).

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What does this mean?

• A c2 test requires Nparam calculations, not
  Npixels
• Massive speedup possible
• for Sloan with 2000 flux points, 2000/23
  parameters 100 times
• Allows us to explore any degeneracies on the
  hypersurface Markov Chain Monte Carlo
• No fancy footwork (PCA) Direct link to models
• Need to model the spectrum somehow...

15
Sloan Digital Sky Survey

• 350,000 spectra public in SDSS Data Release 4
  (DR4)
• Final goal 106 galaxy spectra

(Panter, Heavens Jimenez (2003) analysed 37000
SDSS EDR galaxies)
16
Recovering Star Formation History from Sloan
spectra
Markov Chain Monte Carlo method used to find best
solution and marginal errors
17
MCMC errors
18
Sanity Checks

• Stellar Population Models
• Dust model

Stellar masses to SFR Redshift 1/Vmax weight,
determined by selection criteria, with magnitudes
and surface brightness computed from SFH of each
galaxy.
19
MOPED results - Old Populations

• Simple Galaxy
• Oldest component peaked at 9 Gyr
• Burst of Star Formation at 1 Gyr
• MCMC reveals no degenerate solutions

20
MOPED results Young Populations

• More Complex Galaxy
• Oldest component peaked at 9 Gyr, but some
  evidence (real?) of other populations
• Burst of Star Formation at 0.4 Gyr
• Undergoing second burst (obvious from spectrum)
• MCMC reveals no degenerate solutions

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Things dont always go so well...

• Broad young and old populations
• But we can still see it!
• MCMC chain reveals degenerate solutions (minimum
  three)
• On AVERAGE the correct SFH is recovered.
  (Panter, 2004)

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3AA Examples Old Galaxy - c22.48
23
3AA Examples Young Galaxy- c21.74
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3AA Examples Old Galaxy 2 - c21.59
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How many bins do I need?
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RESULTS

• Mass function
• Evidence for downsizing
• Mass-metallicity relation
• Assembly of dark matter
• Effects of environment

27
Star Formation History two complementary
approaches

• Two general approaches
• Look for signs of recent SF in galaxies at high z
  (e.g. UV) (e.g. Lilly et al 1996, Madau et al
  1996 Ouchi et al 2003)
• Look at nearby galaxies and date the stars in
  them (fossil record)
• If Copernican Principle holds, they should agree

Ouchi 2003
28
Advantages of fossil approach

• Decouples star formation from mass assembly
• Not so sensitive to uncertain obscuration
• Get SFR for a wide range of cosmic time
• Small statistical errors
• Large galaxy samples
• Faint samples

29
Disadvantages of fossil approach

• Needs a good theoretical spectral synthesis model
• Redshift-time relation is sensitive to cosmology
  (but so are volume elements at high z)
• Poor time- and z- resolution at high z

30
Characterising the SFH

• Current models and data allow the star formation
  rate and metallicity to be determined in around
  8-12 time bins
• 10 x 2 1 dust parameter 21 parameters
  significant technical challenge
• To analyse the SDSS data would take 200 years
• Needs some way to speed this up by a large factor
• We use MOPED

31
The mass function of SDSS galaxies over 5 orders
of magnitude
SDSS
Panter et al. (2004) MNRAS 355, 764
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The NO-evolution of the mass function
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The mass-metallicity relation
0.0
-0.5
Metallicity Z/Zo
-1.0
8
9
10
11
12
Present stellar mass Mo
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SFR in galaxies of different stellar masses

• Split by mass

• Stellar masses
• gt1012 M? lt 1010 M?
• Galaxies with more stellar mass now formed their
  stars earlier

Heavens et al. Nature 2004
Curves offset Vertically for clarity
(Curves offset vertically for clarity)
35
More tests. This time systematics of SDSS and
theoretical models have been included
Resolution does not matter, 20AA is enough.
Models do matter
IMF does not matter
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How well are we fitting?
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Metallicity
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Star formation and dark matter assembly do not
track each other
However, if only 6 of baryons in todays dark
halo are stars, then star formation efficiency
at z2 needs to be only 10 to account for the
observed stellar mass from the fossil record.
Even slow star formation from molecular clouds
can do the job.
Jimenez et al. MNRAS 2005
Dark Matter
Main progenitor
Oldest bin
Oldest bin
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Ratio of the newly-formed stellar mass to the
baryonic mass added to the main progenitor
assuming the nucleosynthesis baryon fraction.
1012
108
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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

• 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
42
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
44
Metallicity as a function of environment (Mark
Correlations)
Sheth, RJ, Panter, Heavens, ApJL, astro-ph/0604581
45
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Conclusions

• SDSS MOPED measure past star formation rate
  from fossil record
• Useful observational data on stellar mass
  function/SFR of different galaxy types
• Most of the stars in massive galaxies (Mgt1011
  M?) already formed at z2
• The main progenitor of todays dark matter halo
  contains enough gas to form the observed stars
• Only 10 of available gas at high-z needs to be
  converted into stars
• Challenge then is to explain why so little gas is
  transformed into stars
• Mark correlations tell us the clustering of
  galaxies

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Results from Sloan Digital Sky Survey SFR of
Universe

• MOPED parallelisation reduces time to about 3
  weeks

Star formation rate
LMC dust model Jimenez stellar models
Gallego et al 95, Tresse Maddox 98, Glazebrook
et al 99, Sullivan et al 00, Lilly et al 96,
Connolly et al 99, Cowie et al 96, Steidel et al
99, Madau et al 96, Ouchi et al 03,Stanway et al
03
See also Baldry et al 2002 Glazebrook et al
2003 Brinchmann et al 2003