1,108 research outputs found
Rigorous treatment of barycentric stellar motion: Perspective and light-time effects in astrometric and radial velocity data
High-precision astrometric and radial-velocity observations require accurate
modelling of stellar motions in order to extrapolate measurements over long
time intervals, and to detect deviations from uniform motion caused for example
by unseen companions. We aim to explore the simplest possible kinematic model
of stellar motions, namely that of uniform rectilinear motion relative to the
Solar System Barycentre, in terms of observable quantities including error
propagation. The apparent path equation for uniform rectilinear motion is
solved analytically in a classical (special-relativistic) framework, leading to
rigorous expressions which relate the (apparent) astrometric parameters and
radial velocity to the (true) kinematic parameters of the star in the
barycentric reference system. We present rigorous and explicit formulae for the
transformation of stellar positions, parallaxes, proper motions, and radial
velocities from one epoch to another, assuming uniform rectilinear motion and
taking into account light-time effects. The Jacobian matrix of the
transformation is also given, allowing accurate and reversible propagation of
errors over arbitrary time intervals. The light-time effects are generally very
small but exceeds 0.1 mas or 0.1 m/s over 100 yr for at least 33 stars in the
Hipparcos Catalogue. For high-velocity stars within a few tens of pc from the
Sun light-time effects are generally more important than the effects of the
curvature of their orbits in the Galactic potential.Comment: Accepted for publication in A&
Gaia astrometry for stars with too few observations - a Bayesian approach
Gaia's astrometric solution aims to determine at least five parameters for
each star, together with appropriate estimates of their uncertainties and
correlations. This requires at least five distinct observations per star. In
the early data reductions the number of observations may be insufficient for a
five-parameter solution, and even after the full mission many stars will remain
under-observed, including faint stars at the detection limit and transient
objects. In such cases it is reasonable to determine only the two position
parameters. Their formal uncertainties would however grossly underestimate the
actual errors, due to the neglected parallax and proper motion. We aim to
develop a recipe to calculate sensible formal uncertainties that can be used in
all cases of under-observed stars. Prior information about the typical ranges
of stellar parallaxes and proper motions is incorporated in the astrometric
solution by means of Bayes' rule. Numerical simulations based on the Gaia
Universe Model Snapshot (GUMS) are used to investigate how the prior influences
the actual errors and formal uncertainties when different amounts of Gaia
observations are available. We develop a criterion for the optimum choice of
priors, apply it to a wide range of cases, and derive a global approximation of
the optimum prior as a function of magnitude and galactic coordinates. The
feasibility of the Bayesian approach is demonstrated through global astrometric
solutions of simulated Gaia observations. With an appropriate prior it is
possible to derive sensible positions with realistic error estimates for any
number of available observations. Even though this recipe works also for
well-observed stars it should not be used where a good five-parameter
astrometric solution can be obtained without a prior. Parallaxes and proper
motions from a solution using priors are always biased and should not be used.Comment: Revised version, accepted 21st of August 2015 for publication in A&
Impact of basic angle variations on the parallax zero point for a scanning astrometric satellite
Determination of absolute parallaxes by means of a scanning astrometric
satellite such as Hipparcos or Gaia relies on the short-term stability of the
so-called basic angle between the two viewing directions. Uncalibrated
variations of the basic angle may produce systematic errors in the computed
parallaxes. We examine the coupling between a global parallax shift and
specific variations of the basic angle, namely those related to the satellite
attitude with respect to the Sun. The changes in observables produced by small
perturbations of the basic angle, attitude, and parallaxes are calculated
analytically. We then look for a combination of perturbations that has no net
effect on the observables. In the approximation of infinitely small fields of
view, it is shown that certain perturbations of the basic angle are
observationally indistinguishable from a global shift of the parallaxes. If
such perturbations exist, they cannot be calibrated from the astrometric
observations but will produce a global parallax bias. Numerical simulations of
the astrometric solution, using both direct and iterative methods, confirm this
theoretical result. For a given amplitude of the basic angle perturbation, the
parallax bias is smaller for a larger basic angle and a larger solar aspect
angle. In both these respects Gaia has a more favourable geometry than
Hipparcos. In the case of Gaia, internal metrology is used to monitor basic
angle variations. Additionally, Gaia has the advantage of detecting numerous
quasars, which can be used to verify the parallax zero point.Comment: 8 pages, 2 figures; Accepted for publication in Astronomy &
Astrophysic
Super-critically accreting stellar-mass black holes as ultraluminous X-ray sources
We derive the luminosity-temperature relation for the super-critically
accreting black holes (BHs) and compare it to the data on ultraluminous X-ray
sources (ULXs). At super-Eddington accretion rates, an outflow forms within the
spherization radius. We construct the accretion disc model accounting for the
advection and the outflow, and compute characteristic disc temperatures. The
bolometric luminosity exceeds the Eddington luminosity L_Edd by a logarithmic
factor 1+0.6 ln mdot (where mdot is the accretion rate in Eddington units) and
the wind kinetic luminosity is close to L_Edd. The apparent luminosity for the
face-on observer is 2-7 times higher because of geometrical beaming. Such an
observer has a direct view of the inner hot accretion disc, which has a peak
temperature T_max of a few keV in stellar-mass BHs. The emitted spectrum
extends as a power-law F_E ~ E**{-1} down to the temperature at the
spherization radius T_sp ~ mdot**(-1/2) keV. We associate T_max with a few keV
spectral components and T_sp with the soft, 0.1-0.2 keV components observed in
ULXs. An edge-on observer sees only the soft emission from the extended
envelope, with the photosphere radius exceeding the spherization radius by
orders of magnitude. The dependence of the photosphere temperature on
luminosity is consistent with that observed in the super-Eddington accreting
BHs SS 433 and V4641 Sgr. Strong outflows combined with the large intrinsic
X-ray luminosity of the central BH explain naturally the presence of the
photoionized nebulae around ULXs. An excellent agreement between the model and
the observational data strongly argues in favour of ULXs being super-critically
accreting, stellar-mass BHs similar to SS 433, but viewed close to the symmetry
axis.Comment: 8 pages, 5 figures; heavily revised version; accepted to MNRA
The method of composition and structural analysis in the system of professional training of designer
In the formation of the professional competences of the designer, his compositional and design skills, an effective method is the composition and structural analysis that allows stimulating the creative search of designer in his own conceptual projects. In the article, the professional training of designers is considered within the framework of higher educationВ формировании профессиональных компетенций дизайнера, его композиционных и проектировочных умений, эффективным методом является композиционно-структурный анализ, позволяющий стимулировать творческий поиск дизайнера в собственных концептуальных проектах. В статье профессиональная подготовка дизайнеров рассматривается в рамках вузовского образовани
Charged Current Neutrino Cross Section and Tau Energy Loss at Ultra-High Energies
We evaluate both the tau lepton energy loss produced by photonuclear
interactions and the neutrino charged current cross section at ultra-high
energies, relevant to neutrino bounds with Earth-skimming tau neutrinos, using
different theoretical and phenomenological models for nucleon and nucleus
structure functions. The theoretical uncertainty is estimated by taking
different extrapolations of the structure function F2 to very low values of x,
in the low and moderate Q2 range for the tau lepton interaction and at high Q2
for the neutrino-nucleus inelastic cross section. It is at these extremely low
values of x where nuclear shadowing and parton saturation effects are unknown
and could be stronger than usually considered. For tau and neutrino energies
E=10^9 GeV we find uncertainties of a factor 4 for the tau energy loss and of a
factor 2 for the charged current neutrino-nucleus cross section.Comment: 20 pages and 11 figure
- …