511 research outputs found
Multidimensional Dynamical Systems Accepting the Normal Shift
The dynamical systems of the form \ddot\bold r=\bold F (\bold r,\dot\bold
r) in accepting the normal shift are considered. The concept of
weak normality for them is introduced. The partial differential equations for
the force field \bold F(\bold r,\dot\bold r) of the dynamical systems with
weak and complete normality are derived.Comment: AMS-TeX, ver. 2.1, IBM AT-386, size 16K (ASCII), short versio
Extensive population synthesis of isolated neutron stars with field decay
We perform population synthesis studies of different types of neutron stars
taking into account the magnetic field decay. For the first time, we confront
our results with observations using {\it simultaneously} the Log N -- Log S
distribution for nearby isolated neutron stars, the Log N -- Log L distribution
for magnetars, and the distribution of radio pulsars in the --
diagram. We find that our theoretical model is consistent with all sets of data
if the initial magnetic field distribution function follows a log-normal law
with and . The
typical scenario includes about 10% of neutron stars born as magnetars,
significant magnetic field decay during the first million years of a NS life.
Evolutionary links between different subclasses may exist, although robust
conclusions are not yet possible.
We apply the obtained field distribution and the model of decay to study
long-term evolution of neuton stars till the stage of accretion from the
interstellar medium. It is shown that though the subsonic propeller stage can
be relatively long, initially highly magnetized neutron stars ( G) reach the accretion regime within the Galactic lifetime if their
kick velocities are not too large. The fact that in previous studies made 10
years ago, such objects were not considered results in a slight increase of the
Accretor fraction in comparison with earlier conclusions. Most of the neutron
stars similar to the Magnificent seven are expected to become accreting from
the interstellar medium after few billion years of their evolution. They are
the main predecestors of accreting isolated neutron stars.Comment: 4 pages, conference "Astrophysics of Neutron Stars - 2010" in honor
of M. Ali Alpar, Izmir, Turke
Population synthesis of DA white dwarfs: constraints on soft X-ray spectra evolution
Extending the population synthesis method to isolated young cooling white
dwarfs we are able to confront our model assumptions with observations made in
ROSAT All-Sky Survey (Fleming et al., 1996). This allows us to check model
parameters such as evolution of spectra and separation of heavy elements in DA
WD envelopes. It seems like X-ray spectrum temperature of these objects is
given by the formula T_{X-ray} = min(T_eff, T_max). We have obtained DA WD's
birth rate and upper limit of the X-ray spectrum temperature: DA birth rate in cubic parsec per year and T_max = 41000 K. These values
are in good correspondence with values obtained by other authors (Liebert et
al., 2004; Wolff et al., 1996). From this fact we also conclude that our
population synthesis method is applicable to the population of close-by
isolated cooling white dwarfs as well as to the population of the isolated
cooling neutron stars.Comment: 4 pages, 3 figures, conference "European White Dwarf Workshop, 2010",
Tubingen, German
Population growth in discrete time: a renewal equation oriented survey
Traditionally, population models distinguish individuals on the basis of
their current state. Given a distribution, a discrete time model then specifies
(precisely in deterministic models, probabilistically in stochastic models) the
population distribution at the next time point. The renewal equation
alternative concentrates on newborn individuals and the model specifies the
production of offspring as a function of age. This has two advantages: (i) as a
rule, there are far fewer birth states than individual states in general, so
the dimension is often low; (ii) it relates seamlessly to the next-generation
matrix and the basic reproduction number. Here we start from the renewal
equation for the births and use results of Feller and Thieme to characterise
the asymptotic large time behaviour. Next we explicitly elaborate the
relationship between the two bookkeeping schemes. This allows us to transfer
the characterisation of the large time behaviour to traditional
structured-population models
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