Up: Construction of the Tycho
Subsections
Once the individual positions are brought to the same reference system
(namely, ICRS/Hipparcos), the only step left before the derivation of proper
motions is to collect those that belong to the same star, i.e. to identify
Tycho stars in the Astrographic Catalogue. Prior to describing the actual identification
procedure, we should emphasize the importance of this step for the
construction of a reference catalogue. The overall reliability of the
catalogue contents, and especially of the proper motions, to a great extent
depends on the correctness of this procedure.
The identification of observations is significantly different from the
reference stars identification problem addressed in Sect. 3.3,
the two procedures having different objectives: the former aims to establish
a definite correspondence between individual observations of the same object,
while for the latter such a correspondence is merely an intermediate step
necessary to adjust the coordinate system of the plate measurements to that
of the reference catalogue.
The standard procedure of identification by position, the so-called
window-based approach, defines a window, i.e. a cone of some
predefined size centred on the object to be identified (in our case, the
Tycho star). It then studies the candidates, i.e. observations (in
our case, the images measured on the AC plates) lying within the window. The
most suitable candidate is then used to assign the identification.
Obviously, the absence of robust characteristics, like e.g. the pattern
parameters of the reference stars identification procedure, makes the
window-based approach highly sensitive to errors and peculiarities of the
individual observations. The random and systematic errors of position as well
as duplicity or variability may lead to a misidentification, which in the TRC
case will result in a large error of the derived proper motion.
To lower the number of probable misidentifications and thus to assure
reliability of the TRC contents, the standard window-based approach was
complemented by constraints on Tycho stars and Astrographic Catalogue observations.
- 1.
- Rejection of stars with high Tycho proper motion:
identification of all Tycho stars without limiting the proper motion would
result in the necessity of a large window, which in turn would lead to an
intolerably high number of misidentifications. To avoid this, only Tycho
stars with a modulus of the Tycho proper motion less than 180 mas/yr were
subjected to identification. The threshold value corresponds to the lower
limit of the proper motion modulus of stars included in the NLTT catalogue
(Luyten 1979;
Luyten & Hughes 1980).
As a result, stars with high proper motion are missing in TRC. This may be
a drawback from the point of view of stellar kinematics, but proper motions
of the stars in question are generally available from Hipparcos.
- 2.
- Dynamic window: the window size was adjusted individually for
every AC plate by the limit on the proper motion modulus and the difference
between plate epoch and mean epoch of the Tycho Catalogue, J1991.25.
- 3.
- Isolation of observations subject to identification: an
identification was accepted as such only if both the Tycho star and the
measured image on the particular AC plate were the only representative of
the respective catalogue within the identification window. This constraint
was necessitated by the absence of suitable photometric data in the Astrographic Catalogue,
which prevented isolation of observations on the basis of brightness.
The window-based approach with the constraints outlined above allowed
one-to-one identification for 96% of the Tycho stars satisfying the
selection criteria (cf. Sect. 2.2.2). Reliable
identification for an additional 2% of the Tycho stars was obtained by the
special treatment of the problem cases.
Two types of problem cases were handled:
- "Field star": a Tycho star with two AC candidates within the
identification window, one of them usually being an image of a
fainter, unrelated (field) star. The problem cases of this type were
solved with the use of the brightness estimates in AC: the brightest
of the two candidates was chosen. This approach was applied only if
the Tycho star was brighter than the Tycho completeness limit
(otherwise the identification with the brightest candidate may be
false due to the absence of the true counterpart star in the Tycho
Catalogue),
and if the brightness estimates of the AC images allowed a secure
"bright''
/"faint'' classification.
- "Two-to-two identification'': two close Tycho stars matching two close
AC images. Such cases were handled on the basis of the relative
brightness of the candidates: the brightest of the two Tycho stars
was identified with the brightest of the two AC images, and vice
versa. Cases of this type were solved only if blue magnitudes of the
Tycho stars and brightness estimates of the AC images differed enough
to allow a secure "bright''/"faint'' classification.
On the average, more than 98% of the Tycho stars satisfying the selection
criteria (cf. Sect. 2.2.2) were identified in the AC. The
identification percentage varied from zone to zone, between 96.43%
(Cordoba) and 99.54% (Hyderabad South).
To conclude, we note that the identification of Tycho stars in the Astrographic Catalogue was
based solely on constraining the upper limit of the proper motion modulus and
on photometric data. It thus made no use of any further kinematic assumptions
(e.g., choosing the closest candidate) to avoid kinematic biases in the TRC
proper motions.
Up: Construction of the Tycho
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