A&A 376, 745-750 (2001)
DOI: 10.1051/0004-6361:20011001

CCD standards for U and I in the open cluster NGC 7790[*],[*],[*]

G. Petrov1 - W. Seggewiss2 - A. Dieball2 - B. Kovachev1


1 - Institute of Astronomy, Bulgarian Academy of Sciences, Sofia, Bulgaria
2 - Universitätssternwarte Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

Received 17 November 2000 / Accepted 12 June 2001

Abstract
Photometric U and I standard sequences in the field of the open cluster NGC 7790 are presented. The intention is to achieve wide ranges in magnitude and colour, making these sequences suitable for calibrating deep CCD photometry. The 84 standard stars extend the BVR sequences of Odewahn et al. (1992) to the near UV and IR, respectively.

Key words: techniques: photometric - astronomical data bases: miscellaneous - open clusters: individual: NGC 7790


   
1 Introduction

   
1.1 Photometric standard sequences for imaging detectors

Photometric calibration of the two-dimensional CCD detectors has to be based on standard sequences which should fulfil a number of fundamental requirements: the standard stars should cover as wide as possible a range in colour and should reach to faint magnitudes. The field of view should have the typical dimensions of a CCD field, approximately $5\hbox{$^\prime$ }\times 5\hbox{$^\prime$ }$, and the crowding of stellar images should be a minimum. Of course, the internal and external errors of magnitudes and colours should approach the limits of feasibility.

Practically all modern calibrations refer ultimately to the homogeneous photoelectrically observed set of standard stars by A.U. Landolt (1983). The underlying photometric system is often called UBVRI system for simplicity. However, it relies on a combination of systems from the northern and southern hemispheres that can be summarized under the names Johnson-Kron-Cousins (for its intricate history, see Landolt 1983).

In 1985, Christian and co-workers published six photoelectric BVRI standard sequences suitable for video camera and CCD calibration. They had selected between 6 and 12 stars in or near 6 clusters (M92, NGC 2264, NGC 2419, NGC 4147, NGC 7006, and NGC 7790). Seven years later, Odewahn et al. (1992, OBH) extended three of the previous sequences (NGC 4147, NGC 7006, and NGC 7790) to fainter limits and to wider ranges in colour by means of CCD observations. However, they restricted the photometric bands to B, V, and R. A suitable U standard sequence as well as a wide standard range in I were, so far, still missing.

   
1.2 Standard stars in the open cluster NGC 7790

In 1995, the project "Structure of the Galaxy: evolution and kinematics of open clusters in the anticentre region'' was started as a common investigation of the Universitätssternwarte Bonn, Germany, and the Institute of Astronomy of the Bulgarian Academy of Sciences, Sofia. (Details and results of the project will be given later.) For calibration purposes we used several well-known standard sequences in star clusters, e.g. in M67 (Montgomery et al. 1993), and in M92 (Majewski et al. 1994), but most of our photometry was calibrated with standard stars in the open cluster NGC 7790.

The coordinates of NGC 7790 are RA = $23^{\rm h}$58 $.\!\!^{\rm m}$4 and Dec = +61$^\circ$13$^\prime$ (2000). Therefore, most of the year it can be observed from northern sky observatories. Being an intermediate-age open cluster (approx. 120 Myr, Gupta et al. 2000), it is suitable for calibration of different types of astronomical objects, like clusters and distant galaxies.

The basic sample of our U and I calibration is a list of 13 stars ("primary standards'') in NGC 7790 with observed magnitudes in the passband U which refer to the fundamental standards of Landolt (1983); see Sect. 3. This list is enlarged to a total of 84 stars which are in common with the improved BVR standards from OBH (1992); see Sect. 5. The ranges in magnitudes and colours are, e.g., 13.15 < V < 18.52, 0.39 < B - V < 1.71, and 0.25 < V - R < 1.28 (always given in mag). The stars are spread over a field of view of $5\hbox{$^\prime$ }\times 3\hbox{$.\mkern-4mu^\prime$ }5$ to the south-east of the cluster's centre.

We note for the sake of completeness only that Schmidt (1981) published Strömgren photometry of stars in NGC 7790. Recently Stetson (2000) published Landolt calibrated BVRI data for about 240 stars in a field of $6 \hbox{$^\prime$ }\times 6 \hbox{$^\prime$ }$ centred on NGC 7790.

2 Observations and data reduction


The basic observational data for NGC 7790 are presented in Table 1. These frames have been taken with the "Photometrics'' CCD camera at the 2m RC telescope of Rozhen observatory. The detector SITE SI003AB has $1024 \times 1024$ px, with a pixel size of $24 \times 24\,\mu^2$. Two regimes of observations are at disposal to the observer: (1) Gain = 4.93, RON = 1.05 ADUs and (2) Gain = 1.21, RON = 2.73 ADUs. The scale is $0\hbox{$.\!\!^{\prime\prime}$ }31$/px without binning and $0\hbox{$.\!\!^{\prime\prime}$ }62$/px with binning. At the RC focus of the 2 m telescope the field of view is $5\hbox{$^\prime$ }\times 5\hbox{$^\prime$ }$. The filter system is close to Johnson's UBV (including a read-leak suppression filter), and Kron/Cousins' RI:
U: 2 mm UG1 + 1 mm BG39;
B: 1 mm BG14 + 1 mm GG1 + 1 mm BG23;
V: 2 mm GG495 + 1 mm GG11;
R: 1 mm OG570 + 1 mm KG3;
I: 3 mm RG9. After standard image reduction with MIDAS, profile fitting photometry was carried out with DAOPHOT II (Stetson 1991) running under MIDAS.  

   
Table 1: Observational data for NGC 7790 from the 2m RC telescope.
date filter No. of frames scale seeing
    per filter [ $\hbox{$^{\prime\prime}$ }\!$/px] [ $\hbox{$^{\prime\prime}$ }$]
1998-02-28 U, B, V, R, I 2 0.62 $\le$2
1998-08-23 U, B, V, R, I 4 0.62 1.5 ... 2
1998-08-23 U, B, V, R, I 2 0.31 1.5 ... 2
1998-09-06 U, B, V, R, I 10 0.62 2.5 ... 3

   
3 Constructing the U and I standard sequences

Unfortunately, there are no suitable standard stars for U in NGC 7790. The only available U data come from
- Sandage (1958): 22 stars, most of them with one single photoelectric observation only;
- Alcalá & Arellano Ferro (1988, AAF): re-observation of 16 stars from Sandage's list with reference to the Landolt standards;
- Pedreros et al. (1984, PMF): photographic observations calibrated by Sandage's U sequence which they had corrected by 0.075mag due to an apparent offset in the U scale (Sandage's observations are too blue).

The stars of these lists are spread over an area of about $10\hbox{$^\prime$ }\times 10\hbox{$^\prime$ }$ around the centre of the cluster. The dynamical interval of these data - in magnitudes and colours - is not large enough for CCD receivers and improved techniques of data reduction.

From these lists we find 4 AAF stars and 9 PMF stars (from the corrected Sandage sequence) which coincide with BVR standard stars from OBH. We chose these 13 stars as primary standards in the passband U. They are listed in Table 2 with their OBH numbers; the first 4 stars are those from AAF, the following 9 from PMF. Note that we did not use star no. OBH-31 (= AAF-36), because this star has an elliptical shape and is always rejected automatically in the reduction process.

   
Table 2: U and I magnitudes of the 13 primary standard stars and comparison with the calibration via the cluster M92. (All values are given in mag.) For details of notation see text.
No. $U_{\rm s}$ $\sigma(U_{\rm s})$ $I_{\rm s}$ $\sigma(I_{\rm s})$   $U_{\rm M\,92}$ d(U) $I_{\rm M\,92}$ d(I)

29		 13.611 0.0110 12.782 0.0042   13.622 -0.011 12.789 -0.007
30 13.838 0.0110 12.929 0.0046   13.868 -0.030 12.935 -0.007
36 15.063 0.0090 13.917 0.0300   15.116 -0.053 13.936 -0.019
37 15.330 0.0152 14.149 0.0060   15.308 +0.021 14.142 +0.007
51 14.903 0.0131 13.865 0.0064   14.882 +0.021 13.840 +0.025
58 16.358 0.0156 14.724 0.0159   16.363 -0.005 14.754 -0.030
59 16.895 0.0150 15.302 0.0104   16.871 +0.025 15.298 +0.003
62 18.277 0.0247 13.500 0.0260   18.318 -0.041 13.488 +0.013
65 17.079 0.0121 15.080 0.0185   17.147 -0.068 15.097 -0.017
72 14.541 0.0170 13.521 0.0064   14.521 +0.020 13.513 +0.008
77 17.020 0.0142 15.074 0.0092   17.025 -0.005 15.043 +0.031
88 17.178 0.0159 14.649 0.0078   17.090 +0.088 14.654 -0.005
97 15.924 0.0406 11.593 0.0131   15.886 +0.038 11.595 -0.002

We used the same 13 stars to construct our primary standard sequence in the passband I. The first 4 stars (see Table 2) have I magnitudes from the CCD work of Romeo et al. (1989). For the remaining stars we can refer to the basic sequence of Christian et al. (1985).

   
4 Methods of calibration

For the final calibration we used a three-step iteration method for the following reason: (1) The UBVRI data of the 13 primary standards are taken from different sources with different reliability. The aim of the process is to homogenize the mixed sample and to minimize the influence of bright primary stars determined with lower accuracy. (2) The original sequence covers only a narrow interval of colours and the distribution in magnitude is rather nonuniform. The iteration allows us to enlarge the interval of magnitudes and colours of the standards.

Photometric transformation coefficients were determined in three steps using the following transformation relations:

$\displaystyle U_{\rm st}$ = $\displaystyle a_{0U} + a_{1U} \cdot U_{\rm in} + a_{2U} \cdot (U_{\rm in} - B_{\rm in})$ (1)
$\displaystyle I_{\rm st}$ = $\displaystyle a_{0I} + a_{1I} \cdot I_{\rm in} + a_{2I} \cdot (R_{\rm in} - I_{\rm in})$ (2)

where $M_{\rm st}$ are the photometrically calibrated magnitudes and  $M_{\rm in}$ are the instrumental ones. As the standards and the programme stars are located in the same field, no extinction correction is needed (see e.g. Hardie 1962; Strayzis 1977).

$\bullet$ Step (1): Determine the transformation coefficients using the above 13 stars discussed and compute the First Step Standard Magnitudes (FSSM) for all the objects in the field of interest.

$\bullet$ Step (2): Use an enlarged standard sequence of 25 stars - 12 more stars added to the first 13 primaries with the FSSM (step 1) - and recompute the magnitudes of all stars in the field, in this way getting the Second Step Standard Magnitudes (SSSM). We note that the choice of these 12 additional stars is somewhat arbitrary. Attempts with 10 to 15 stars showed us that it should be an appropriate number of faint stars with small photometric errors and spread over the whole field.

$\bullet$ Step (3): Repeat step 2 for all stars with the magnitudes of the 25 "new'' standards from the SSSM and compute the Third Step Standard Magnitudes (TSSM) of all the stars in the field. Now, the relative change of the coefficients in Eqs. (1) and (2) is 0.005 for a2U and less than 0.0005 for all other coefficients. Furthermore, controlling the differences between SSSM and FSSM, and TSSM and SSSM, our results are internally consistent that no further iteration is needed. An additional check of the quality of our calibration was performed by recalibrating our 13 primary stars using the standard sequence in M92 (see the following section).

   
5 Results

The U and I magnitudes of our 13 primary standard stars are given in Table 2 and are denoted $U_{\rm s}$and $I_{\rm s}$. The standard errors $\sigma(U_{\rm s})$ and $\sigma(I_{\rm s})$of the individual magnitudes are also listed. They are the result of the whole process of reduction and calibration. The mean value is $<\sigma> \,= 0.0165$ mag in U and $<\sigma> \,= 0.0122$ mag in I. The larger error in U reflects the fact that the CCD receivers are less sensitive in the ultraviolet, which means a smaller signal-to-noise-ratio for the observed stars; apart from photon statistics, no other source of noise is significant.

As mentioned above, we applied an independent calibration of our 13 primary stars using the standard sequence in the globular cluster M92 established by Majewski et al. (1994): after extinction correction of the instrumental magnitudes, we carried out the photometric calibration in the form

$\displaystyle U_{\rm M\,92}$ = $\displaystyle c_U + c_U' \cdot U_{\rm ec} + c_U'' \cdot (U_{\rm ec} - B_{\rm ec})$ (3)
$\displaystyle I_{\rm M\,92}$ = $\displaystyle c_I + c_I' \cdot I_{\rm ec} + c_I'' \cdot (R_{\rm ec} - I_{\rm ec})$ (4)

where $M_{\rm M\,92}$ are the standard magnitudes after photometric calibration via M92 and  $M_{\rm ec}$ are the extinction-corrected instrumental magnitudes. The magnitudes  $U_{\rm M\,92}$ and  $I_{\rm M\,92}$ are displayed in Cols. 6 and 8 of Table 2. The quality of our calibration process is immediately apparent: The sums of the differences d(U) and d(I) to our basic calibration (again Table 2, Cols. 7 and 9) are in both cases exactly 0.000 mag. Therefore no shift in magnitude between the different methods of calibrations can be seen. The mean differences (positive or negative) between the magnitudes of the two calibrations are small: 0.033 mag in U and 0.013 mag in I, respectively.

The NGC 7790 field of OBH is not completely identical to our field because they chose the south eastern part of the cluster whereas we centred our frames onto the cluster´s centre. In addition, not all OBH stars have measurable U values due to the lower sensitivity of the CCD in this passband. As a result, in the overlapping section there are 84 stars for which the complete UBVRI data set is now available. The UBVRI magnitudes and their errors for all these stars are listed in Table 4 with their OBH numbers. We have chosen the notation $U_{\rm s}$, $B_{\rm s}$ etc. The photometric errors of the individual stellar magnitudes after DAOPHOT photometry have been added. The last three columns of the table display the differences between the magnitudes BVR from our work and those from the OBH sequence.

   
Table 3: Magnitude intervals and mean errors for the standard sequences in NGC 7790, and summary of the comparison. (All values are given in mag.)
  This paper   Odewahn et al. (1992)   Difference d
Filter range $<\sigma>$   range $<\sigma>$   shift $<\mid \hspace{-0.1cm} d \mid>$
U 13.61 ... 20.01 0.032            
B 13.61 ... 19.54 0.009   13.64 ... 19.67 0.024   -0.002 0.049
V 13.14 ... 18.48 0.009   13.15 ... 18.52 0.014   -0.002 0.047
R 12.35 ... 17.88 0.017   12.37 ... 17.92 0.021   +0.002 0.059
I 11.59 ... 19.67 0.015            


  \begin{figure} \par\includegraphics[width=9cm,clip]{MS10479f1.eps} \end{figure} Figure 1: Errors of the photometric calibration vs. standard star magnitudes.
Open with DEXTER


 

 
Table 4: Magnitudes and errors of all 84 standard stars. The first column refers to the notation of Odewahn et al. (1992). The last three columns give the difference between the listed magnitudes and those from the BVR sequence of Odewahn et al.'s (1992) paper. (All values are given in mag.) The complete table is availabale only in electronic form at the CDS archive, cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/376/745

No.		 $U_{\rm s}$ $\sigma(U_{\rm s})$ $B_{\rm s}$ $\sigma(B_{\rm s})$ $V_{\rm s}$ $\sigma(V_{\rm s})$ $R_{\rm s}$ $\sigma(R_{\rm s})$ $I_{\rm s}$ $\sigma(I_{\rm s})$ d(B) d(V) d(R)

8

 17.144 0.0130 16.912 0.0040 16.270 0.0035 15.904 0.0056 15.471 0.0070 -0.057 -0.038 -0.010
9 18.170 0.0233 18.045 0.0060 17.073 0.0049 16.497 0.0099 15.887 0.0088 -0.080 -0.047 -0.031
10 18.332 0.0254 18.479 0.0088 17.550 0.0060 16.963 0.0145 16.373 0.0131 -0.026 -0.027 -0.066
11 18.222 0.0360 17.916 0.0060 17.011 0.0060 16.466 0.0090 15.945 0.0050 +0.059 +0.018 +0.012
12 18.761 0.0300 19.010 0.0113 18.045 0.0074 17.458 0.0180 16.899 0.0106 -0.024 -0.024 +0.003
16 16.776 0.0180 16.544 0.0053 15.946 0.0063 15.610 0.0081 15.203 0.0063 +0.012 +0.005 +0.007
17 16.395 0.0102 16.168 0.0031 15.638 0.0042 15.333 0.0056 14.969 0.0061 -0.081 -0.094 -0.110
18 19.074 0.0488 19.119 0.0131 18.151 0.0063 17.545 0.0145 16.928 0.0127 -0.427 -0.181 -0.157
20 16.517 0.0180 16.271 0.0032 15.717 0.0042 15.409 0.0042 15.031 0.0049 +0.027 +0.021 +0.029
21 16.838 0.0344 16.577 0.0035 16.020 0.0033 15.709 0.0040 15.324 0.0056 -0.003 -0.009 -0.031
22 18.335 0.0226 17.204 0.0071 15.767 0.0049 14.916 0.0100 14.029 0.0102 -0.012 +0.000 +0.008
23 17.536 0.0290 16.569 0.0040 14.999 0.0035 14.090 0.0044 13.035 0.0071 +0.003 +0.002 +0.007
24 17.344 0.0170 17.250 0.0053 16.573 0.0049 16.610 0.0057 15.688 0.0053 -0.038 -0.049 +0.365
25 16.996 0.0187 16.781 0.0035 15.838 0.0032 15.282 0.0035 14.696 0.0039 +0.018 +0.047 +0.034
26 17.536 0.0220 17.503 0.0070 16.731 0.0060 16.279 0.0070 15.812 0.0060 -0.017 +0.016 +0.012
27 18.424 0.0265 18.471 0.0081 17.568 0.0057 17.016 0.0177 16.453 0.0141 -0.028 -0.007 -0.036
28 17.840 0.0269 17.587 0.0050 16.817 0.0035 16.370 0.0077 15.892 0.0085 -0.096 -0.102 -0.115
29 13.611 0.0110 13.675 0.0018 13.289 0.0028 13.047 0.0031 12.782 0.0042 -0.021 -0.016 -0.010
30 13.838 0.0110 13.875 0.0021 13.470 0.0039 13.217 0.0039 12.929 0.0046 +0.095 +0.097 +0.094
31 14.064 0.0200 14.094 0.0030 13.685 0.0030 13.419 0.0030 13.122 0.0030 +0.052 +0.088 +0.109
32 16.253 0.0117 15.990 0.0029 15.410 0.0046 15.069 0.0058 14.646 0.0069 -0.006 +0.008 +0.020
34 18.635 0.0320 18.632 0.0095 17.743 0.0088 17.201 0.0205 16.652 0.0152 +0.010 +0.019 +0.031
35 18.996 0.0390 19.490 0.0191 18.315 0.0098 17.610 0.0156 17.007 0.0138 +0.113 -0.076 -0.101
36 15.063 0.0090 15.038 0.0029 14.551 0.0042 14.263 0.0056 13.917 0.0300 +0.027 +0.025 +0.036
37 15.330 0.0152 15.222 0.0035 14.753 0.0064 14.479 0.0040 14.149 0.0060 +0.031 +0.029 +0.037
38 17.077 0.0159 16.816 0.0046 16.186 0.0057 15.790 0.0057 15.348 0.0057 +0.037 +0.054 +0.032
39 18.970 0.0570 18.728 0.0200 17.640 0.0120 16.980 0.0480 16.191 0.0340 -0.063 +0.018 +0.020
40 19.362 0.0760 18.970 0.0260 17.776 0.0100 17.067 0.0420 16.264 0.0630 +0.013 +0.036 +0.053
41 18.772 0.0390 18.643 0.0200 17.737 0.0120 17.193 0.0580 16.593 0.0490 +0.042 +0.028 +0.010
42 19.194 0.0660 18.967 0.0350 17.930 0.0440 17.351 0.0670 16.760 0.0410 +0.249 +0.341 +0.431
43 19.202 0.0371 19.455 0.0159 18.424 0.0120 17.803 0.0237 17.260 0.0279 +0.122 +0.107 +0.089
45 16.646 0.0141 16.365 0.0039 15.809 0.0042 15.490 0.0039 15.119 0.0056 +0.026 +0.031 +0.024
48 16.470 0.0441 16.124 0.0028 15.259 0.0038 14.735 0.0065 14.191 0.0065 +0.006 -0.002 -0.007
49 18.895 0.0500 18.280 0.0220 16.585 0.0120 15.601 0.0130 14.526 0.0110 +0.020 +0.012 +0.036
51 14.903 0.0131 14.854 0.0032 14.421 0.0064 14.163 0.0071 13.865 0.0064 +0.005 -0.009 -0.016
53 17.305 0.0177 16.978 0.0042 16.351 0.0064 16.000 0.0067 15.597 0.0078 +0.029 +0.028 +0.020
54 17.773 0.0210 17.560 0.0057 16.551 0.0078 15.969 0.0134 15.366 0.0177 -0.002 -0.008 +0.022
55 18.653 0.0440 18.987 0.0100 18.021 0.0170 17.471 0.0200 17.030 0.0170 +0.053 +0.072 +0.085


We have plotted the errors versus the calibrated magnitudes for all passbands in Fig. 1. The means $<\sigma>$ of the individual errors can be read off Table 3. As expected, the mean error in the U band is fairly large: $<\sigma>$ = 0.032 mag. The individual errors become large above U = 19 mag, but still are quite small for magnitudes below U = 18 mag (see Fig. 1). With only few exceptions, the individual errors in B and V are less than 0.03 mag below 19 mag. For the R band the errors are as usual quite small - less than 0.02 mag for all magnitude intervals - except for a group of 7 stars between 17 to 18 mag which show errors of about 0.05-0.06 mag (outside the frame of Fig. 1). This might be due to the effect of severe crowding because the R fields are quite rich in stars. The errors from the I frames are fully acceptable; they are less than 0.04 mag below I = 16 mag. There are unexpected large photometric errors for stars Nos. 21, 48, and 97 in U (see Fig. 1, upper left panel). Careful inspection of the original frames shows no reason for such errors: the three stars are isolated, comparatively bright, and far from the edges of the frames. Nevertheless, we did not remove the stars from our list so that the larger errors are a warning for possible users.

The errors of the colours have been computed following the rules of error propagation. As expected from Fig. 1, these errors increase with increasing magnitudes. No other tendency is apparent.

Finally, we compare our results with those of OBH. The ranges in the magnitudes BVR and the means of the individual errors are compared in the first two sections of Table 3. The errors of our work are marginally smaller, but, in principle, the results are quite similar. The differences d(B) = $B_{\rm s} - B_{\rm od}$; d(V) = $V_{\rm s} - V_{\rm od}$; and d(R) = $R_{\rm s} - R_{\rm od}$, in the sense "our magnitude minus OBH's magnitude'', are listed in the last columns of Table 4. The differences have been plotted in Fig. 2 vs. the magnitudes from this paper. No systematic difference between the two calibrations can be seen. Indeed, the mean deviations from the zero-axes are only 0.05 mag (see also the last column of Table 3; only star No. 106, which has the extremely large difference of 0.5 mag in all three bands, has been omitted from the calculation).

  \begin{figure} \includegraphics[width=6.8cm,clip]{MS10479f2.eps} \end{figure} Figure 2: Comparison of our calibrated BVR magnitudes with the corresponding magnitudes of Odewahn et al. (1992).
Open with DEXTER

The sum of all differences in each passband gives the shift in magnitude between the two standard sequences. It is apparent from Table 3 (right section) that the shifts are only two thousandths of a magnitude.

We conclude that our calibration of the standard sequence in the NGC 7790 field perfectly agrees with OBH's calibration for the bands B, V, and R, and we, therefore, have an additional strong indication that our calibrations for the bands U and I are in good state, too.

6 Concluding remarks

We have constructed a primary standard sequence of 13 stars in U and I in the field of the open cluster NGC 7790. With these standards we were able to extend the B, V, and R sequences of OBH to the bands Uand I. These new standard sequences contain 84 stars over wide ranges of magnitude and colour.

We emphasize that three factors support the reliability of the new U and I sequences:

$\bullet$ We applied a three-step iteration method which integrates additional stars into the process of calibration. This leads to higher accuracy for a sample of stars covering wider intervals of magnitude and colour.

$\bullet$ We applied an independent calibration to our 13 primary standard stars using the standard sequence in the globular cluster M92 (Majewski et al. 1994). The results of both calibrations agree very well with each other (see Table 2).

$\bullet$ A comparison of our BVR results with those of OBH for the 84 stars in common again gives perfect agreement.

Acknowledgements
We would like to thank L. King for a critical reading of the manuscript. G. P. and B. K. are grateful to the Director of the Institute at Bonn and to the staff of Hoher List Observatory for the kind hospitality. This work was supported by the Deutsche Forschungsgemeinschaft DFG under grant 436BUL113/91, which is a common project between the Universitätssternwarte Bonn and the Institute of Astronomy of the Bulgarian Academy of Sciences. The outstanding financial support is gratefully acknowledged.

References

 

Copyright ESO 2001