4,967 research outputs found
Quasars can be used to verify the parallax zero-point of the Tycho-Gaia Astrometric Solution
Context. The Gaia project will determine positions, proper motions, and
parallaxes for more than one billion stars in our Galaxy. It is known that
Gaia's two telescopes are affected by a small but significant variation of the
basic angle between them. Unless this variation is taken into account during
data processing, e.g. using on-board metrology, it causes systematic errors in
the astrometric parameters, in particular a shift of the parallax zero-point.
Previously, we suggested an early reduction of Gaia data for the subset of
Tycho-2 stars (Tycho-Gaia Astrometric Solution; TGAS).
Aims. We aim to investigate whether quasars can be used to independently
verify the parallax zero-point already in early data reductions. This is not
trivially possible as the observation interval is too short to disentangle
parallax and proper motion for the quasar subset.
Methods. We repeat TGAS simulations but additionally include simulated Gaia
observations of quasars from ground-based surveys. All observations are
simulated with basic angle variations. To obtain a full astrometric solution
for the quasars in TGAS we explore the use of prior information for their
proper motions.
Results. It is possible to determine the parallax zero-point for the quasars
with a few {\mu}as uncertainty, and it agrees to a similar precision with the
zero-point for the Tycho-2 stars. The proposed strategy is robust even for
quasars exhibiting significant fictitious proper motion due to a variable
source structure, or when the quasar subset is contaminated with stars
misidentified as quasars.
Conclusions. Using prior information about quasar proper motions we could
provide an independent verification of the parallax zero-point in early
solutions based on less than one year of Gaia data.Comment: Astronomy & Astrophysics, accepted 25 October 2015, in press. Version
2 contains a few language improvements and a terminology change from
'fictitious proper motions' to 'spurious proper motions
On the structure of the commutator subgroup of certain homeomorphism groups
An important theorem of Ling states that if is any factorizable
non-fixing group of homeomorphisms of a paracompact space then its commutator
subgroup is perfect. This paper is devoted to further studies on the
algebraic structure (e.g. uniform perfectness, uniform simplicity) of
and , where is the universal covering group of
. In particular, we prove that if is bounded factorizable non-fixing
group of homeomorphisms then is uniformly perfect (Corollary 3.4). The
case of open manifolds is also investigated. Examples of homeomorphism groups
illustrating the results are given.Comment: 18 page
Gevrey estimates for certain moment partial differential equations
We consider the Cauchy problem for inhomogeneous linear moment differential
equations with holomorphic time dependent coefficients. Using such tools as the
formal norms, theory of majorants and the properties of the Newton polygon, we
obtain the Gevrey estimate for the formal solution of the equation.Comment: 13 pages, 1 figur
Entropy of foliations with leafwise Finsler structure
We extend the notion of the geometric entropy of foliation to foliated
manifolds equipped with leafwise Finsler structure. We study the relation
between the geometric entropy and the topological entropy of the holonomy
pseudogroup. The case of foliated manifold with leafwise Randers structure. In
this case the estimates for one dimensional foliation defined by a vector field
in term of topological entropy of a flow are presented
The Tycho-Gaia astrometric solution. How to get 2.5 million parallaxes with less than one year of Gaia data
Context. The first release of astrometric data from Gaia will contain the
mean stellar positions and magnitudes from the first year of observations, and
proper motions from the combination of Gaia data with Hipparcos prior
information (HTPM).
Aims. We study the potential of using the positions from the Tycho-2
Catalogue as additional information for a joint solution with early Gaia data.
We call this the Tycho-Gaia astrometric solution (TGAS).
Methods. We adapt Gaia's Astrometric Global Iterative Solution (AGIS) to
incorporate Tycho information, and use simulated Gaia observations to
demonstrate the feasibility of TGAS and to estimate its performance.
Results. Using six to twelve months of Gaia data, TGAS could deliver
positions, parallaxes and annual proper motions for the 2.5 million Tycho-2
stars, with sub-milliarcsecond accuracy. TGAS overcomes some of the limitations
of the HTPM project and allows its execution half a year earlier. Furthermore,
if the parallaxes from Hipparcos are not incorporated in the solution, they can
be used as a consistency check of the TGAS/HTPM solution.Comment: Accepted for publication in A&A, 24 Dec 201
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