**Publication date:** Feb 2008

**Abstract:**

Assuming a resonant origin of the 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 kilo-Hertz 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. In several specific models, the two modes

are related to physically plausible combinations of Keplerian, vertical

and radial frequencies of geodesic orbital motion. We investigate this

concept for a specific neutron star source, a fixed pair of modes and

various neutron star equations of state. Each neutron star model is

characterized by the equation of state (EOS), rotation frequency

($Omega$) and central energy density ($rho_mathrm c$). These

determine the spacetime structure governing geodesic motion and position

dependent radial and vertical epicyclic oscillations related to the

stable circular geodesics. When the parameters of neutron star model are

fixed, the two considered modes imply a frequency-frequency relation

which can be compared to the observation in order to eliminate the

unsatisfactory sets (KR,$rho_mathrm c, Omega$, 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 best 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_mathrm c,

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

function we use correspondence between the observed and calculated pairs

of eigenfrequencies.

**Authors:**

Stuchlik, Zdenek; Cermak, Petr; Torok, Gabriel; Urbanec, Martin; Bakala, Pavel;