2 Observations and data reductions

The data for M 71 and 47 Tuc were collected at the 2.56 m Nordic Optical Telescope (NOT) on La Palma and the Danish 1.54 m telescope at the European Southern Observatory (ESO) on La Silla, respectively. The data for M 71 were collected between June 26 and July 02, 1995. For 47 Tuc the data were gathered over 10 nights in October 1997. The CCD characteristics for both instruments are listed in Table 1.

For both clusters and standard stars the observations during the two observing runs followed the same strategy. At both observatories the instruments are mounted on field rotators, allowing the CCD to be oriented differently (relative to the telescope) from one exposure to the next. After each uvby exposure sequence we thus rotated the CCD camera by 90 degrees to reduce the effects of inaccurate flatfielding due to scattered light in the optical system (Grundahl & Sørensen 1996). Flat fields were obtained during evening and morning twilight on every clear observing night. As for the cluster frames the CCD camera was also rotated 90 degrees between flat fields. In order to estimate the errors in the flat fielding we derived the quotients between the flux weighted mean flat field and each individual flat field image. For the NOT observations we found only very small differences in the quotient images - always less than 1% In the case of the DFOSC these were slightly larger, typically 1-2%, with the u flat fields having the largest variations.

In M 71 we observed a field 2$^\prime$  north of the center. For 47 Tuc we observed a field covering F1 and some of F2 from Hesser et al. (1987) and one more overlapping field towards the cluster center in order to increase the sample of HB and RGB stars. The F1, F2 field has more observations than the inner one resulting in longer total exposure times.

 

 

Table 1: Characteristics for CCDs used.

	NOT	DFOSC
CCD type	SITe	Loral
Size	10242	20482
RON (e-)	13.0	7.7
Gain e-/ADU	8.7	1.8
Pixel size $^{\prime\prime}$/pix	0.175	0.39
Field size	3$^\prime$$\times$3$^\prime$	R= $5\farcm5$
Typical FWHM ( $^{\prime\prime}$)	0.75	1.6

The filters at the 1.54 m telescope were of inadequate size, which caused some vignetting of the CCD corners; these regions were therefore excluded from further analysis. In Table 2 below we summarize the number of uvby observations for each cluster, given as the maximum number of observations and the number of observations on photometric nights for each filter. There is a higher number of y and b observations than v and u for 47 Tuc; this is because the y and b filters were used for aquiring the field resulting in a higher number of short exposure frames. The exposure times for both clusters were typically 300, 600, 900 and 2000 seconds, respectively for the y, b, v, and u filters.

 

 

Table 2: Number of observations.

	M 71	47 Tuc
Ny(max.)	15	20
Nb(max.)	15	17
Nv(max.)	16	17
Nu(max.)	14	14
Ny(photom.)	4	7-13
Nb(photom.)	4	7-11
Nv(photom.)	4	7
Nu(photom.)	4	7

Finally, of relevance for this investigation we also observed the southern open cluster IC 4651 in order to check the photometric calibrations, as it has previously been observed in uvby by Nissen (1988). This comparison will be carried out below.

2.1 Standard star observations and photometry

During both observing runs we adopted stars from the lists of Schuster & Nissen (1988, SN88) and Olsen (1983, 1984) as our standard stars because the observations by these authors were very carefully transformed to the standard uvby system. (The true fundamental uvby standards are too bright (V $\la$ 6) to observe easily with a CCD and 2m class telescopes. Furthermore, they are isolated field stars, so that only one can be placed on the CCD at a time.) Since many of the Schuster & Nissen and Olsen stars are brighter than V $\simeq$ 9.5 - and some are significantly brighter - we chose to defocus the telescopes such that we would not need exposure times shorter than 5 s in the y filter. To shorten readout time, only frames of 300$\times$300 pixels (NOT) and 500$\times$500 pixels (DK1.54 m) were read out. We shall in the following refer to these stars as standard stars, although in a strict sense they are only secondary or even tertiary standards. The stardards were observed over a range of 1-2.5 airmasses, for deriving the extinction coefficients.

The photometry for these frames was done using simple aperture photometry and the magnitude at which the growth curves converged was adopted as the total magnitude. Due to the brightness of the stars the photon noise was negligible in most exposures (0.002 mag or less). Several experiments to determine the sky level were done, and it was found that a 3-sigma clipped mean produced the best results.

In order to derive the transformation from the instrumental system to the standard system we adopted the following equations (after experimenting with different terms and cross terms):

$$y_{{\rm obs}} V_{{\rm std}} + \alpha_y (v-y)+\beta_y (X-1) +\gamma_y T +\delta_y$$

$$b_{{\rm obs}} b_{{\rm std}} + \alpha_b (v-y)+\beta_b (X-1) +\gamma_b T +\delta_b$$

$$v_{{\rm obs}} v_{{\rm std}} + \alpha_v (v-y)+\beta_v (X-1) +\gamma_v T +\delta_v$$

$$u_{{\rm obs}} u_{{\rm std}} + \alpha_u (v-y)+\beta_u (X-1) +\gamma_u T +\delta_u$$

where X and T denote the the airmass and time of that CCD exposure, and (v-y) is the colour on the standard system. On several of the nights the time terms were found to be insignificant. The values for $\alpha$ and $\beta$ were averaged over each observing run, and good consistency was found from night to night. At NOT the transformations are based on observations of 52 different standard stars on two photometric nights. Several of the stars have multiple measurements in order to serve as extinction checks. At the 1.54 m telescope 130 different standard stars were observed in 7 photometric nights. We chose to adopt transformation equations of this form as this has several advantages over transforming the indices: Firstly, the above formulation does not require that stars be observed in all four filters each night, so that it is possible to observe, say, only the u filter for an entire night. Secondly, these equations are more appropriate to the aquisition method of CCD photometry, since the data for the different filters are not obtained simultaneously, unlike the case for the photoelectric photometry of Olsen (1983, 1984) and SN88. Thirdly, the equations are easily modified to accomodate data from non-photometric nights, by eliminating the airmass and time terms and introducing a new zeropoint for each frame obtained under non-photometric conditions. See also Stetson (2000) for a relevant discussion.

Figure 1: The residuals in the transformation to the standard values for the uvby filters as a function of (v-y). Note that there are no trends with colour for the vby filters. The u filter has somewhat enhanced scatter, especially at the reddest colours.

The scatter in the residuals ( $m_{{\rm std.}} - m_{{\rm transf.}})$ is given in Table 3. For the chosen stardards, the highest emphasis was put on stars near the old metal-poor turnoff, but also red stars, including both MS and RGB stars as well as very blue (mainly O and B type) stars were included. We note, however, that there could be enhanced scatter as well as systematic errors in the v and u filters since they contain bands of CN and NH molecules. The 4215 Å CN feature, in particular, is close to the red edge of the v filter, making the transformation of both u and v "risky'' for cluster giants.

In Fig. 1 we have plotted the offsets between the standard magnitudes and our transformed values vs. (v-y) for the Olsen and Schuster & Nissen stars. It is evident from the figure that there are no trends of the residuals with colour, except that for stars redder than (v-y) = 1.1 the scatter appears higher than for the bluer stars. We speculate that this is due to the enhanced importance of CN bands in the cooler stars. Certainly, in the case of the u band there seems to be rather large scatter for the reddest stars, indicating that the transformed values are subject to an extra parameter which is not included in our transformation equations. We note that for the purposes of this paper this enhanced scatter is not a problem. For the NOT observations the scatter in a similar figure does not show trends with colour either, the main difference being a slightly smaller scatter for the u filter. This is mainly due to the fact that only two standard stars with (v-y) > 1.5 were observed at the NOT.

2.2 Cluster photometry

For the cluster photometry we used the DAOPHOT, ALLSTAR and ALLFRAME programs (Stetson 1987, 1994). In order to derive the point spread function (PSF) for each image we made several passes through DAOPHOT/ALLSTAR, and before the final ALLSTAR run each image was examined visually for neighbours close to the PSF candidate stars. Depending on the exact field either the neighbours were added to the star list or the PSF candidate was eliminated from the PSF construction.

 

 

Table 3: Scatter in residuals for std. star transformation.

Filter	NOT	DFOSC
y	0.006	0.007
b	0.006	0.008
v	0.008	0.010
u	0.011	0.013

The total number of PSF stars for each image varied between 30 and 80. We used a spatially constant PSF for all images, as we found that there was no strong spatial variation of the PSF. This may seem surprising in the case of the observations of 47 Tuc obtained with DFOSC, which is a focal-reducer type instrument. However, as previously mentioned, the vignetting of the field by the undersize filters caused the regions of worst PSF variation (CCD corners) to be excluded from our analysis.

After generating the PSFs we derived positional transformations between a master image and all other images of a given field (DAOMATCH), and subsequently a master list of stellar objects was derived using DAOMASTER. This was then fed to ALLFRAME (Stetson 1994) for the derivation of the final profile fitting photometry.

Due to variations in seeing and focus it is necessary to correct the profile fitting photometry to an "absolute'' system (Stetson 1990) such that the photometry for the cluster and standard stars have the same photometric zeropoint. To achieve this, we selected the 40 brightest unsaturated stars in each frame and subtracted all other measured stars from that frame. Following this we derived concentric aperture photometry to large radii and used DAOGROW (Stetson 1990) to derive aperture growth curves and arrive at "total'' magnitudes for the 40 stars. The difference between the profile fitting photometry and the DAOGROW "total'' magnitude for these was then adopted as the "aperture correction.'' Typical errors (standard error of mean) for an image are 0.001-0.003 mag.

In Figs. 2 and 3 we show the estimated photometric standard errors for the two clusters as a function of V magnitude for each of the uvby bands. It is obvious from these plots that the M 71 data have a higher internal precision and reach fainter apparent magnitudes than the 47 Tuc data. This is because of the larger telescope used and the significantly (factor $\sim$2) better seeing for this cluster.