**Publication date:** Dec 2007

**Abstract:**

Assuming a resonant origin of the twin peak quasiperiodic oscillations

observed in the X-ray neutron star binary systems, we apply a genetic

algorithm method for selection of neutron star models. It was suggested

that pairs of kilohertz peaks in the X-ray Fourier power density spectra

of some neutron stars reflect a non-linear resonance between two modes

of accretion disk oscillations. We investigate this concept for a

specific neutron star source. Each neutron star model is characterized

by the equation of state (EOS), rotation frequency Ω and central

energy density rho_{c}. These determine the spacetime structure

governing geodesic motion and position dependent radial and vertical

epicyclic oscillations related to the stable circular geodesics.

Particular kinds of resonances (KR) between the oscillations with

epicyclic frequencies, or the frequencies derived from them, can take

place at special positions assigned ambiguously to the spacetime

structure. The pairs of resonant eigenfrequencies relevant to those

positions are therefore fully given by KR, rho_{c}, Ω, EOS and can

be compared to the observationally determined pairs of eigenfrequencies

in order to eliminate the unsatisfactory sets (KR, rho_{c}, Ω,

EOS). For the elimination we use the advanced genetic algorithm. Genetic

algorithm comes out from the method of natural selection when subjects

with the best adaptation to assigned conditions have most chances to

survive. The chosen genetic algorithm with sexual reproduction contains

one chromosome with restricted lifetime, uniform crossing and genes of

type 3/3/5. For encryption of physical description (KR, rho_{c},

Ω, EOS) into the chromosome we use the Gray code. As a fitness

function we use correspondence between the observed and calculated pairs

of eigenfrequencies.

**Authors:**

Urbanec, Martin; Stuchlík, Zdeněk; Török, Gabriel; Bakala, Pavel; Čermák, Petr;