3 Accuracy of transformation to the std. uvby system

Since there have been no large scale CCD or photoelectric observations of these clusters in uvby we cannot do a rigorous check on our photometry for them; below we shall attempt to carry out indirect comparisons to other uvby photometric investigations.

Figure 2: The photometric precision for $\approx$2700 stars in M 71 with absolute values of Sharp $\leq 0.05$. Sharp is a DAOPHOT parameter which measures how well the shape of the model PSF matches the star it is being fit to. A good fit has a low absolute value of Sharp.

Figure 3: Same as previous figure, except for $\approx$3700 stars in 47 Tuc.

3.1 IC 4651

As part of our observing program for 47 Tuc we also observed the open cluster IC 4651, which has previously been observed photoelectrically in uvby by Nissen (1988). This allows a check of our transformation to the standard system. We have 10 stars in common with Nissen's objects, and a comparison is shown in Fig. 4. As can be seen from this figure there are small systematic differences no larger than 0.01 mag for V, (b-y) and m₁ whereas it is of order 0.02 mag in c₁. We note that our observations on photometric nights for this cluster consists of 1, 2, 2 and 3 exposures in the y, b, v and u filters respectively, and are thus subject to uncertainties in the determination of the photometric zeropoints for each frame (aperture corrections). As noted above, 47 Tuc has many more observations on photometric nights. The observations by Nissen (1988) only included stars very near the turnoff of IC 4651, so the span in colour is not large enough to reveal whether the offsets show any trends with the colour of the stars. Given the limited number of observations of this cluster it is not possible to conclude whether the offsets in the various filters are due to systematic errors in the derived photometric transformations or to errors in the aperture corrections. We emphasize that our IC 4651 data have not been included in the derivation of our photometric calibration equations; thus this comparison is completely independent of Nissen's (1988) photometry.

Figure 4: The difference in our uvby photometry and that of Nissen (1988) for IC 4651. One star which was found to have a close neighbour in our images has been flagged with a separate symbol (+) and is not included in the calculation of the mean offsets and standard deviations indicated in the plots.

3.2 47 Tuc

While we are not aware of any previously published uvby photometry for this cluster, one of us (PBS, unpublished) has re-reduced a large body of BVI CCD data for 47 Tuc, including extensive standard star data (Stetson 2000), allowing us to compare our V photometry from transformed y to true broadband V. This comparison is shown in Fig. 5 and includes 1078 stars in common. The mean offset between the two V scales is $V_{{\rm US}} - V_{{\rm PBS}}~=~-0.0079$, which we regard as very satisfactory since the filters, CCDs and standard stars employed are completely different. The magnitude differences show no trends with colour or magnitude.

Figure 5: Histogram of the difference in V between this study and independently reduced broadband photometry (PBS). The centroid of the fitted Gausian is at -0.0079.

In an attempt to further check our 47 Tuc calibration we compiled from the literature (B-V) photometry and reddenings for the subdwarf stars in R98 and those selected for this study. This allows us to compare the (B-V)₀vs. Strömgren colour relation for field and cluster stars. The (B-V)photometry for 47 Tuc is from the unpublished photometry mentioned above. We show the results in Fig. 6. Here the cluster photometry is plotted as small grey points, and the subdwarfs as black ${\bf +}$ (R99) and $\bullet$ signs (this study). We see that the (B-V)₀ vs. (b-y)₀ and (B-V)₀ vs. (v-y)₀ relations for the field and cluster agree very well. For (u-y) there seems to be some systematic deviation for the reddest stars; however, this is of no importance for the results obtained in this paper. Note that the subdwarfs selected for this plot span the range from -1.0 to -0.5 in [Fe/H] in order to be compatible with the cluster photometry.

In summary, our vby photometry for 47 Tuc seems accurately calibrated with likely errors of order 0.01 mag or less. The error in our u photometry is probably of order 0.02 mag.

We cannot perform a similar test of our M 71 photometry since we did not observe clusters with independent uvby data during the run where this cluster was observed. However the indication from our standard stars is that our data should be well calibrated.

Figure 6: Plot of the (B-V)0 vs. Strömgren colour for field and cluster stars. The 47 Tuc photometry is from this study and the independently reduced BV photometry of PBS. E(B-V) = 0.04 has been assumed for 47 Tuc.