Genetic Selection of Neutron Star Structure Matching the X-Ray Observations Speaker: Petr Cermak The Institute of Computer Science Silesian University in Opava, Czech Republic

Figs on this page: nasa.gov Zdeněk STUCHLÍK, Petr ČERMÁK, 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

Presentation Topics 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

Neutron star structure atmosphere inner core outer core core surface inner crust outer crust

Model of neutron star - assumptions 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

Model of NS – Structure equations (perturbative scheme) Schwarzschild metric: TOV eq. general relativistic equation of hydrostatic equilibrium where m(r) is mass inside the sphere of radius r

Model of NS – EOS

neutron star acrretion disc gigant star “JET” Figs: nasa.gov Binary systems & neutron stars

Simulation of binary system behavior Figs, Videos: nasa.gov radio “X-ray” and visible OK, let’s take starship Enterprise move with Warp 9 near to binary system

X-ray observation t I Power Frequency Light curve: Power density spectra (PDS): Figs on this page: nasa.gov

hi-frequency QPOs or kHz QPOs low-frequency QPOs frequency power Power density spectra & QPOs

Observed frequency relations

Figs on this page: nasa.gov General belief dominating in the astrophysical community links the kHz QPOs to the orbital motion near the inner edge of an accretion disc.

Orbital motion in strong gravidity Perturbation

Testing frequency relations – 3 models 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 ) Introduced in Stuchlik et al. 2007, STB, Identify the lower QPO frequency with the total precession frequency Notice that in the limit of Swarzschild spacetime all the three relation coincide. The three investigated models relate the observed frequencies to

Therefore comparison of our models with the observed frequency relations which are directly connected to the neutron star structure Neutron star structure modeling using X-Ray observations - relations The fundamental frequencies itself depend on the parameters (M,j,q) of the central neutron star, Outer description Inner description Matching

Neutron star structure modeling using X-Ray observations

Optimization - GA

Features of GA 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

Genetic Selection of Neutron Star Structure

Genetic algorithm – Mutation & Crossover

Genetic algorithm – Sexual reproduction & Death

Genetic algorithm – Shade zone Gen type 3/3/5

Genetic algorithm – Note to Fitness If parameters exceed intervals by given min & max values  Fitness = 1e200

Population diversity x Rate of convergence x …

Parallelization of GA using MPI

Specific for this experiment Parameters of GA  nEOS(4 bits),  c(12 bits),  (14 bits)  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

dependency of on number of members in generation

Fitness function and corresponding parameters with preseted EOS for source 4U

Fitness function and corresponding parameters for all tested EOS for source 4U

Computing times

Future 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.