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Astron. Astrophys. 333, 882-892 (1998)

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2. Systematic detection of parallax star candidates with Schmidt plates

2.1. Selection of the observed zone

Considering a sphere around the Sun of 100 pc diameter, there is no clear objective reason to look for nearby stars in a privileged direction. Therefore mainly observational criterion oriented the choice of our field. Nevertheless the Galactic plane was avoided because of the measuring problems that could arise from too crowded fields. Since we primarily decided to use the CERGA Schmidt Telescope for our observations we selected a region with a declination close to CERGA latitude: this allows observations nearly at the zenith. In such a work it is important to minimize the effects of differential refraction which causes relative displacements of images of stars at different places on the plates (i.e. different hour angle). The right ascension has been chosen so that several optical quasars (13) (Crampton et al. 1988, Véron-Cetty & Véron 1996) are present in the field. These quasars will be lately used as extragalactic references to calibrate the proper motions derived from the observations. The selected field is [FORMULA] centered at [FORMULA], [FORMULA] (PPM star 55623).

2.2. Plate material

In order to carry out this program of systematic detection of nearby stars in a wide field we decided to use Schmidt plates, which offer the advantages to cover wide fields and to reach faint magnitudes. For the astrometric purpose we used 29 plates taken at the CERGA Schmidt telescope (from 1991 to 1994) and 20 plates taken at the Schmidt telescope of Tautenburg (from 1992 to 1994). 24 photometric plates were taken at the Calar-Alto Schmidt Telescope. Their reduction is underway. All the plates were taken through a red filter because the possible nearby stars will have a good probability to be red dwarfs. The use of a filter restricts the effects of differential color refraction (the relative displacements due to refraction of stars of different effective wavelengths) which can introduce spurious parallaxes and which are the major limitation to parallaxes accuracy. Also for this reason exposures were always taken at hour angles smaller than two hours from the meridian to reduce problems due to atmospheric refraction (Murray 1979). Table 1 lists the plates obtained for this project with the date of exposure, the exposure time, the filter and the telescope. In most cases the plates were taken at the maximum of the parallactic ellipse of the studied field .


[TABLE]

Table 1. List of Schmidt plates


2.3. Measurements at MAMA measuring machine and cross-identification

All plates have been digitized at the MAMA measuring machine which provides at the present time the most accurate measurements (repetability of [FORMULA]) which is, indeed, what is required in this parallax work. For each plate, a catalog of (x, y), flux and area has been produced for about 100 000 objects detected, on each plate.

Each plate has been astrometricaly reduced from (xy) to ([FORMULA][FORMULA]) with reference stars from the PPM catalogue (Roeser 1989, Bastian 1991) using a ([FORMULA]) constants plate model. The ([FORMULA][FORMULA]) positions obtained were used to cross-identify stars on the different plates to an arbitrary selected master plate. This master plate has been selected because of the quality of the images and also because of its large number of detected objects. We wrote a routine of cross-identification that considers all objects of a master frame catalogue and searches within a given radius on all the other plate catalogues. Great care was taken to consider a radius large enough to be able to locate on different plates large proper motion stars. The time baseline of our data set being only 4 years we used a radius of [FORMULA]. When multiple cross-identification were possible, we used a criterion of magnitude to discriminate objects. Finally we obtained a catalogue of 52 523 objects with their measurements on each of the 49 plates (when existing, depending on the center and on the limiting magnitudes of the individual plates). Objects with too poor number of correspondences were eliminated from the resulting catalogue. As a consequence the probability that an object in the final catalogue be a spurious object is considerably small.

2.4. The problem of Schmidt plates modeling

There are several ways to handle such an astrometric problem of parallaxes measurement. The simplest way is to write for each detected object, equations linking its ([FORMULA], [FORMULA]) observed positions on the 49 different plates and its stellar parameter (proper motion and parallax). But when we compare the ([FORMULA], [FORMULA]) positions derived from plates taken at several days interval we already notice that the differences obtained are large (with a mean over the field of [FORMULA] and reaching [FORMULA]) and are organized in small trends, generally on the borders of the plates.

In Fig. 1 we present these offsets for two plates taken at two days interval. The individuals differences in right ascension and declination have been averaged over small squares of [FORMULA]. In this plot absurd observations (larger than three times the dispersion about the mean of the residuals) have been eliminated (typically 4 per square).

[FIGURE] Fig. 1. differences in ([FORMULA], [FORMULA]) between two consecutive plates. The individuals differences in right ascension and declination have been averaged over small squares of [FORMULA]

We can notice that the trends are located on the borders of the plate area and are mostly visible in the upper and right part of the plate. The origin of these trends is obviously the ([FORMULA]) constants plate model that was used to derive the ([FORMULA], [FORMULA]) positions that is not sufficient to fully model the distortions on the border of the Schmidt plates. Since about 23 % of the surface of the common field is concerned with this problem, we decided not to eliminate this large surface but to try to find another way to model the distortions. The absence of large trends on the other sides of the field is probably due to the way the plates have been scanned.

We therefore divided the Schmidt reference plate into ([FORMULA]) sub-plates which we treated independently one from the other as different fields. The size of these sub-plates have been chosen in order to have enough well measured stars (about 40) to perform the "plate to plate" transformation. Then, considering one sub-zone, we used a ([FORMULA]) constants model to transform the ([FORMULA]) measurements of each of the 49 plates into the system of the reference plate. To divide the field into sub-zones has the consequence that only relative astrometry can be performed (determination of relative projected proper motions and parallaxes). It will no longer be possible to derive [FORMULA] for the objects.

In Fig. 2 we present for the two same consecutive plates the residuals obtained by such a treatment of each sub-zone. The individuals residuals in x and y have been averaged in each sub-zone of ([FORMULA]). As in Fig. 1, abnormal observations (larger than three times the dispersion about the mean of the residuals) have been eliminated (typically 4 per square).

[FIGURE] Fig. 2. differences in (x,y) between two consecutive plates after adjustment in sub-zones with a [FORMULA] constants polynom. The individuals residuals in x and y have been averaged in each sub-zone of ([FORMULA])

We can notice in Fig. 2 that the trends have been nearly completely removed and that no systematic effect is visible. The mean difference in ([FORMULA]) between the two plates is now [FORMULA] with a maximum of [FORMULA]. The large residuals remaining on the border correspond to zones with few stars. The large decrease of the systematic effect implies that the technic that consists in sharing the Schmidt field into sub-plates which are treated independently allows a uniform coverage of the field and therefore allows to perform relative astrometry within the whole Schmidt plate with a sufficiently good accuracy for parallax measurements.

2.5. Astrometric reduction: equations

In the following, we consider a sub-zone ([FORMULA]) of the master Schmidt plate. The astrometric reduction which will link the measurement of each star on each of the plates to the stellar parameters is described by the following equations that we write for each star on each of the sub-frames considered (including the master frame).

[EQUATION]

[EQUATION]

where ([FORMULA], [FORMULA]) are the measured coordinates of the star on the master plate, (xy) its measured coordinates on the plate i to be transformed into the master plate system. [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA] are the unknown stellar parameters: [FORMULA] = the correction of position on the master plate in right ascension [FORMULA], [FORMULA] = the correction of position on the master plate in declinaison, [FORMULA] = the projected proper motions in right ascention [FORMULA], [FORMULA] = the projected proper motions in declination, [FORMULA] = the parallax; [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA] are the unknown sub-plate parameters which describe the transformation from the sub-plate i to the master sub-plate. [FORMULA] are the parallactic factors.

The small size of the considered zones ([FORMULA]) fully allows us to adopt a fitting model with [FORMULA] constants (translation, rotation and scale factor).

So we have to solve a large over-determined system of equations where the unknowns are the stellar parameters of the common stars and the plate-to-plate transformation coefficients of each of the 49 plates considered.

2.6. Iterative resolution of the system

The iterative methods (Gauss Seidel types) find a natural application to such systems. In this treatment the iterative starting value is taken using null values for the stellar parameters. We then derive plate parameters which are injected into the equations. New values for the stellar parameters are then deduced, and the process iterates until convergence. This method is equivalent to the global overlapping methods developed by Eichhorn (1988) and Googe (1970)

Theoretically, the system of equations is singular, and the obtained solution is not unique. The usual technic consists in introducing constraints which the solution must verify (Murray 1979, Eichhorn 1988). Nevertheless, due to the accuracy that one can reach with plate measurements it would be meaningless to refine the reduction adding constraints. We show in the following Sect.  2.8that we see evidences that the system converges toward a solution close to the physical one (mean of parallaxes close to zero) and therefore that the constraints are not necessary here.

We have treated in this way the data present in all our plates sub-zones. We obtained the stellar parameters for 52 523 common objects (common to a minimum of 20 plates).

2.7. Separation of stars and diffuse objects

We have separated the stars from extended objects in our final catalog using the method proposed by Moreau et al. (1994). We fitted a [FORMULA] order polynomial to the diagram [FORMULA] given in Fig. 3 with a [FORMULA] iterative point rejection among objects having an area larger than 30 pixels. The convergence is riched at the [FORMULA] iteration. A frontier between starlike and diffuse objects was then plotted at [FORMULA] (of the fit) below the fitted polynomials. A set of 3452 diffuse objects has been obtained in this way. We also rejected [FORMULA] objects with an area below 30 pixels because at this point of the diagram it is not possible to discriminate starlike objects from diffuse objects. Remain [FORMULA] starlike objects in our final catalog.

[FIGURE] Fig. 3. Log(area)/Log(Flux) diagram. Separation of diffuse objects from starlike objects. Selected stars lie on the upper sequence. The line represents the limit between stars and diffuse objects. Diffuse objects are located under the separation line.

2.8. Results and selection of the nearby candidates

We present in Fig. 4 the histogram of the obtained parallaxes for the starlike objects.

[FIGURE] Fig. 4. Frequency of parallaxes

The characteristics of the distribution of proper motions and parallaxes are given in Table 2.


[TABLE]

Table 2. Characteristics of the resulting catalogue


The negative part of the histogram is due to errors of measurement and should not be a priori eliminated. We selected the parallax candidates in the resulting catalogue as follows: we first eliminated from our sample objects whose parallax was far outside the astrometric limits (outside 1 to 100 pc) so we retain: [FORMULA]. We then eliminated from this selection, stars with a relative precision on the parallax greater than 80 %: [FORMULA] and we also eliminated from our sample too poor determinations of the parallax: [FORMULA]. These criterion were not sufficient to isolate a small enough number of objects. We therefore had to constrain the selection with a criterion on a detectable proper motion (which unfortunately is going to slightly bias our selection of candidates). At the end of this treatment we obtained a list of 32 good nearby star candidates for which we needed a confirmation. We therefore had to accurately measure the parallax of these objects with a telescope with a longer focal length.

2.9. Comparison to other proper motion catalogs

We looked into our catalog for objects with know proper motion [NLTT catalog (Luyten 1979a, 1979b, 1979c and 1979d)]. We found 34 common objects. We independently found two Giclas stars (Giclas 1967) present in our catalog and absent from the NLTT catalog. We inserted these objects in our comparison. We present in Table 3 the cross identifications of these 36 objects and the result of the comparison of their proper motions. We give in col. 1 the NLTT or Giclas designation, in col. 2 our number, in col. 3 and 4 the NLTT catalog [FORMULA] and [FORMULA] coordinates, in col. 5 the catalog R magnitude, in col. 6 the catalog proper motion in right ascention, in col. 7 the catalog proper motion in declination, in col. 8 the difference of proper motions between the catalog and our results, and in col. 9 the photographic magnitude (when available). Note that data concerning stars G203-021 and G203-022 come from the Lowell proper motion survey (Giclas 1967).


[TABLE]

Table 3. Comparison of common stars to NLTT and to our catalog.


From the 36 objects of Table 3, five have very large discrepancies between the catalog proper motion value and our result. These objects are +41:2725, LP225-53, G203-021, G203-022 and G203-034. The reasons of these large differences are probably the following: +41:2725 is very bright and has not been well measured on our plates (same effect is visible for star +43:2659); LP225-53 is faint (fainter than 17.5) and has probably been not well measured (same effect is visible for stars LP225-67 and LP225-68). In the case of G203-021, G203-022 and G203-034 the reason is not obvious. For G203-021 we will see later that CCD observations will allow to determine a significant value for the parallax and the proper motion. These proper motions will be in good agreement with the values given in the catalog. This example shows probably the limitation of the method consisting in searching parallax candidates on Schmidt plates.

When we eliminate these 5 abnormal objects we obtain a list of 31 common objects with a mean [FORMULA] [FORMULA] [FORMULA] /yr. We can notice that the comparison of proper motions is in good agreement with the accuracy announced in Table 2 and even much better in declination. This result gives a reasonable confirmation of the uncertainty estimates.

Table 4 in Sect.  3.1gives the coordinates of the nearby candidates that have been observed with CCD. It is interesting to note that in our selection the stars P5, P15 and P18 are objects present in large proper motion surveys. (P5=G203-21, P15=LP226-8, P18=LP226-9).


[TABLE]

Table 4. Coordinates of the new presumed nearby candidates


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© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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