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;