Extracting Parameters for Stellar Populations Synthesis from SDSS Galaxy Spectra Using Evolution Str

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Extracting Parameters for Stellar Populations
Synthesis from SDSS Galaxy Spectra Using
Evolution Strategies
IAU XXVIth General Assembly
Prague, August 18 2006

• Juan Carlos Gomez
• Olac Fuentes
• Computer Science Department, INAOE, Puebla,
  México
• (thanks to Roberto Cid Fernandes)

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Outline

• Introduction
• Problem
• Evolution Strategy
• General Solution Process
• Results
• Conclusions

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Introduction

• There is a huge amount of astronomical
  information produced by surveys that needs to be
  automatically processed and exploited by
  efficient algorithms. For example, SDSS has more
  than 106 spectra for public availability.
• Galaxy spectra allow the determination of
  intrinsic physical parameters such as the age and
  metallicities distributions, the reddening and
  proportions of their stellar populations.
• Such parameters are useful in cosmological
  studies to understand galaxy formation and
  evolution.

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Problem

• Given an observed galaxy spectrum (O?) we would
  like to determine the relative distribution of
  ages, metallicities, their intrinsic reddening
  and contributions of stellar population
• There parameters are obtained by fitting such O?
  with a linear combination of 3 stellar population
  (young, intermediate and old)

(Cid Fernandes et al. 2005)
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Problem
Young
Intermediate
Old
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Problem

• The goal of the fitting (optimization) task is to
  find the best combination for the parameters
  reddening (r1, r2, r3), metallicities (m1, m2,
  m3), ages(a1, a2, a3) and relative contributions
  (c1, c2, c3) to produce a modeled spectrum that
  minimize the fitness function

(Cid Fernandes et al. 2005) Using simulated
annealing plus Metropolis algorithm
?x?1, ?2, ?3, ?4, ?5, ?6, ?7, ?8, ?9, ?10, ?11,
?12
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Evolution Strategy (ES)

• ES is a stochastic algorithm from Machine
  Learning field, based on natural evolution or
  survival of the fittest, used to solve
  optimization problems, where the most of the
  variables are real.
• Candidate solutions to optimization problem play
  the role of individuals in a population and
  fitness function measures how well an
  individual is adapted to the problem.
• This method presents the great advantage of being
  easy codified and easily parallelized.

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Evolution Strategy
Biological evolution seen as an optimization
process

• Genetic
• Programming

Biological
Genetic Algorithms
Codification (binary, decimal, etc)
Evolution Strategies
Evolution
No codification (real-vector coding)
Evolutionary Algorithms
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Evolution Strategies
Initial Population (set of solutions or
individuals) ? population
xi i1,.., ? Generated randomly
Solution Found!
Evaluate solutions (fitness function)
f(x)
Tolerance in function is reached or maximum
number of cycles is done
Cross-Over xj,ixa,i or xb,i Mutation xj
xj N(0,?) j1,..,? i1,...,m
Generate new population from old individuals by
cross-over and mutation (? population)
Select ? best solutions from merged
populations (? ?)
Evaluate new solutions (fitness function)
f(x)
Tolerance is not reached or maximum number of
cycles is not done
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General Solution Process
Stellar Population Synthesis Parameters.
Generated Initially in a Random Way xi i1,..,
?
Generate new parameters by cross-over and mutation
Each vector x is given to a model creator
Success!
Model Creator

• Rest frame
• Reddening
• correction
• Cut
• Re-bin
• Normalization

Some model fits original spectrum
Set of modeled spectra
Each simulated spectrum is compared with the
original spectrum
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Results

• Results were obtained for 50 spectra taken from
  SDSS R2 randomly. In this presentation we only
  show 3 spectra for simplification.
• Spectra were brought to the rest frame (using
  redshifts in the SDSS data base), sampled from
  3800 to 8000 Å in steps of 1 Å, corrected by
  extinction using the maps given by Schlegel,
  Finkbeiner Davis (1998) (http//irsa.ipac.caltec
  h.edu/applications/DUST/docs/background.html) and
  normalized by the median flux in the 4010-4060 Å
  region.
• Each fitting takes approx. 1 min on a 3Ghz
  Windows PC, using MatLab interpreter.

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Results
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Results
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Results
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Conclusions

• Efficient algorithms are necessary to deal with
  the huge amount of information from astronomical
  surveys.
• Fitting of real galaxy spectra using stellar
  population synthesis models is well performed.
• Even with restrictions, ES is a very well suited
  method to find good models that fit real spectra
  from SDSS.
• Other problems in astrophysics can be addressed
  using ES (initial conditions in interacting
  galaxies, parameters for brightness profiles,
  etc.)