Genetic Selection of Neutron Star Structure Matching the X-Ray Observations

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Genetic Selectionof Neutron Star Structure
Matching the X-Ray Observations
WMSCI 2007

• Speaker
• Petr Cermak
• The Institute of Computer Science
• Silesian University in Opava,
• Czech Republic

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Zdenek STUCHLÍK, Petr CERMÁK, Gabriel TÖRÖK,
Martin URBANEC, Pavel BAKALA Institute of
Physics, Faculty of Philosophy and
Science, Silesian University in Opava, CZECH
REPUBLIC Institute of Computer Science, Faculty
of Philosophy and Science, Silesian University in
Opava, CZECH REPUBLIC
Figs on this page nasa.gov
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Presentation Topics
WMSCI 2007

• Motivation
• Neutron Star Structure modeling
• Matching X-Ray Observation, QPOs
• Genetic Algorithms
• Advanced Genetic Algorithms
• Parallelization of GA using MPI
• GA Implementation
• Experimental Results
• Conclusion

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Neutron star structure
WMSCI 2007
atmosphere
surface
outer crust
inner crust
core
outer core
inner core
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Model of neutron star - assumptions
WMSCI 2007

• Matter is described as perfect fluid
• Perfect fluid is described by pressure and energy
  density
• Relation between pressure and energy density is
  given by EOS
• Axially symetric and stationary spacetime
• Given by Hartle-Thorne metric

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Model of NS Structure equations(perturbative
scheme)
WMSCI 2007
Schwarzschild metric
TOV eq. general relativistic equation of
hydrostatic equilibrium
where m(r) is mass inside the sphere of radius r
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Model of NS EOS
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Binary systems neutron stars
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JET
gigant star
acrretion disc
neutron star
Figs nasa.gov
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Simulation of binary system behavior
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OK, lets take starship Enterprise move with Warp
9 near to binary system
radio
X-ray
and visible
Figs, Videos nasa.gov
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X-ray observation
WMSCI 2007
Light curve
I
t
Power density spectra (PDS)
Power
Frequency
Figs on this page nasa.gov
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Power density spectra QPOs
WMSCI 2007
power
low-frequency QPOs
hi-frequency QPOs or kHz QPOs
frequency
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Observed frequency relations
WMSCI 2007
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General belief dominating in the astrophysical
community links the kHz QPOs to the orbital
motion near the inner edge of an accretion disc.
WMSCI 2007
Figs on this page nasa.gov
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Orbital motion in strong gravidity
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Testing frequency relations 3 models
WMSCI 2007
The three investigated models relate the observed
frequencies to
1. The precession frequency relation involved in
the relativistic precession model
Related the kHz QPOs to the Keplerian and
periastron precession at an inner-disc orbit.
2.
correspond to the so called vertical precession
resonance ( Bursa 2005 )
3. Identify the lower QPO frequency with the
total precession frequency
Introduced in Stuchlik et al. 2007, STB, 2007
Notice that in the limit of Swarzschild spacetime
all the three relation coincide.
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Neutron star structure modelingusing X-Ray
observations - relations
WMSCI 2007
The fundamental frequencies itself depend on the
parameters (M,j,q) of the central neutron star,
Outer description
which are directly connected to the neutron star
structure
Inner description
Therefore comparison of our models with the
observed frequency relations
Matching
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Neutron star structure modelingusing X-Ray
observations
WMSCI 2007
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Optimization - GA
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Features of GA
WMSCI 2007

• Wide range limits of utilization than classical
  optimization methods.
• Operate with global structure chromosome
• For orientation of optimization process need
  fitness function
• Addition information may decline time markedly
• GA uses statistical trans. rules for control of
  searching procedures

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Genetic Selection of Neutron Star Structure
WMSCI 2007
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Genetic algorithm Mutation Crossover
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Genetic algorithm Sexual reproduction Death
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Genetic algorithm Shade zone
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Gen type 3/3/5
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Genetic algorithm Note to Fitness
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If parameters exceed intervals by given min max
values ? Fitness 1e200
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Population diversity x Rate of convergence x
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Parallelization of GA using MPI
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Specific for this experiment
WMSCI 2007

• Parameters of GA
• nEOS(4 bits), ?c(12 bits), ?(14 bits)
• 301 989 888 combination
• Sexual reproduction
• Life time (Death) parametr set to 5
• uniform crossing
• Gene type 3/3/5, shade zone
• Gray code
• Implementation
• Code writen in c (NET, gcc)
• MPI-2

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dependency of on number of members
ingeneration
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Fitness function and correspondingparameters
with preseted EOS for source 4U1636-53
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Fitness function and correspondingparameters for
all tested EOSfor source 4U1636-53
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Computing times
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Future
WMSCI 2007

• Include q parameters into computation
• Include others parameters describing magnetic
  fields (min additional 3 parameters)
• Portal for astrophysical online computing
• Solving problem with random generator on
  different platform and SW
• Distribution parallel over all available platform.