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;