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;