Profile Fitting with Genetic Algorithms

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Profile Fitting with Genetic Algorithms

• Barry Fitzgerald

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Plan!

• Genetic Algorithms - an explanation

• Applications to Astrophysics

• P cygni profiles

• Results of fitting

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Backround

• In the early 1960s computer scientists tried to
  find new ways of tackling optimization problems.

• Many looked to nature for ways of solving problems

• Obvious example was Darwins survival of the
  fittest

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Genetic Algorithms - Theory

• Create a population of possible solutions.
• Allow the solutions breed (mix) and mutate.
• Apply a selection criteria which gives better
  solutions greater chance of surviving.
• Repeat until adequate solution is reached

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GAs a general plan
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Recombination
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GAs - Advantages

• Completely general problem solving method
• Gives multiple solutions
• Needs little information about the problem

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GAs Disadvantages

• Hard to tailor to specific problems
• Needs to maintain a population of solutions can
  be slow
• Non-deterministic run it twice and get two
  different answers

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Application to Astrophysics

• Common problem for fitting spectra is trying to
  fit theory to reality.
• This can be transformed into an optmization
  problem by plotting the theoretical spectrum
  against the observed one and then calculating a
  numerical value of goodness of fit.

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Least square fitting
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P-cygni profiles

• Many stars emit not just radiation but also
  matter. Often in the form of stellar winds.
• A sensitive indicator of stellar winds are P
  Cygni profiles.
• These are resonance lines usually seen in the UV
  range with a distinctive shape.

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Typical P Cygni profile

• P Cygni emission line profile of triply ionized
  carbon at 1548.2 Å in the central star of the
  cats eye planetary nebula, NGC 6543.

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Theory
Expanding envelope surrounding stellar surface.
Observer views system from bottom of figure.
Color ranges from blue for largest blueshift to
white for zero Doppler shift to red for largest
redshift. (constantly accelerating radial wind
case)
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Explanation
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Fitting P cygni profiles

• To fit these profiles a program that reads in 16
  parameters about a stellar wind and outputs a
  theoretical profile was used.
• Using a GA this process was run in reverse a
  profile was read in to the computer then the set
  of parameters that best fit that profile was
  searched for.

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Sample run theoretical data
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Real Observed Data
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Conclusions

• Genetic algorithms provide a effective means of
  fitting profiles

In theory!

• However as they are a blind method unphysical
  solutions are often found.

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Further Work

• Apply program to fit doublets may remove some
  amibugities.
• Try to solve the program in stages first fitting
  one part of spectrum then next.
• Add restrictions to stop non physical solutions.