3 Photographic photometry

  With the available plate material we decided to carry out a photographic photometry in addition to the main aim of the project which was the proper motion study.

The instrumental magnitudes of all measured objects obtained by a two-dimensional Gaussian fitting procedure (MRSP programme "profil'', Horstmann et al. 1989) were transformed to the standard system. This was done separately for each plate by using the CCD UBVRI standards of Trullols & Jordi (1997). The standards cover only the central region of the one square degree field around IC348 (see Fig. 1).

  

Figure 1: The one square degree field around IC348 selected for this study. Dots show all objects with Gaussian image profile on at least three plates for which proper motions have been determined. Small circles show the location of the 38 bright stars in the proper motion study of Fredrick (1956). The small dashed rectangle shows the region in which Trullols & Jordi (1997) obtained UBVRI photometry, the region shown by long dashed lines was covered by NIR photometry (Lada & Lada 1995) and the dashed circle shows the main field of ROSAT observations (PSPC) used by Preibisch et al. (1996)

The transformation of the instrumental system to the standard system was done by linear and quadratic polynomial fits using up to 60 standard stars. Unfortunately, we were not able to determine a proper colour equation for this transformation. An attempt to determine the colour term after first fitting the instrumental magnitudes on plate sj01520 with the B standard magnitudes and then investigating the residual magnitude differences as a function of the B-V colours given by Trullols & Jordi (1997) did not yield satisfactory results. The colour equation  

$$B_j= B - 0.28 \cdot (B-V) \qquad -0.1\le (B-V) \le 1.6,$$ (1)

given by Blair & Gilmore (1982) could not be used, since only 12 bright stars out of the 43 standard stars have colours in the range $(B-V) \le 1.6$.

The photographic photometry on the Schmidt plates was a priori expected to be difficult since the central region of IC 348, where the standard stars are located (Fig. 1), is strongly affected by image crowding from bright stars and nebulosities. Moreover, as is obvious from the inspection of Fig. 1, there is strong extinction which is irregularly distributed over the field. Thus, the adopted transformation between the instrumental system to the standard system is only of moderate accuracy. In Table 2, the dispersions of the differences between standard magnitudes and fitted magnitudes of all stars used in the fitting procedure are listed. The Tautenburg plates provide a somewhat higher accuracy due to their better scale but have a brighter limiting magnitude (the blue Palomar plate goes about 2.0 magnitudes fainter compared to the two blue Tautenburg plates).

  

Table 2: Photometric calibration

• [$^{\mathrm{a}}$] 1 = linear, 2 = quadratic polynomial fit.
• [$^{\mathrm{b}}$] Dispersion of magnitude differences (standard - fitted).
• [$^{\mathrm{c}}$] Fit consisted of two straight lines for R < 16 and R > 16.

Comparing the B magnitudes obtained from the Tautenburg plates 9168 and 9177 with the B_j magnitudes obtained from the Palomar plate sj01520, we found large systematic differences (see Figs. 2a and 2b), especially for the bright stars (B < 17). At least a part of these differences is expected to arise from the moderate accuracy of the calibration procedure described above, especially from the omission of the colour term. As a test, we applied the colour equation from Eq. (1) but could not remove the systematic difference between the Palomar and Tautenburg B magnitudes.

A further source of the differences may be the smaller number of bright (B < 16.5) standards used in the calibration of the blue Palomar plate (5 stars) compared to the blue Tautenburg plates (9 stars) and the relatively large error of the magnitude calibration for plate sj01520 (see Table 2). The systematic deviation of the Palomar B_j from the Tautenburg B magnitudes is very similar for both Tautenburg plates. Therefore, we have obtained a simple transformation of the Palomar B_j magnitudes into the system of the mean B magnitudes of the Tautenburg plates  

$$B_{\rm jc,sj01520} = 0.9 \cdot B_{\rm j,sj01520} + 1.8 \qquad B_{\rm j,sj01520} < 17$$ (2)

from a linear polynomial fit using the stars with $B_{\rm j,sj01520} < 17$measured as well on both Tautenburg B plates. For the faint stars ($B_{\rm j,sj01520} \ge 17$) we have not applied any correction, since the Tautenburg B magnitudes become unreliable at $B \sim 19$ (only one standard star with B > 19 was used in the calibration), whereas there were still about 20 standard stars with 19 < B < 21.5 used in the calibration of the blue Palomar plate.

  

Table 3: Internal photometric accuracy for blue and red plates described by the standard deviation of magnitude differences after the correction of the B_j and E magnitudes (Eq. (2) and (3)) had been applied

• [$^{\mathrm{a}}$] $B_{\rm T} = (B_{9168}+B_{9177})/2$,    $R_{\rm P2} = R_{\rm sf04859}$.
• [$^{\mathrm{b}}$] Number of common stars in given magnitude interval.

  

Figure 2: Plate-to-plate comparison of calibrated photographic magnitudes (the solid lines indicate zero magnitude differences): a) and b) comparison of B magnitudes obtained on the Tautenburg plates with Bj magnitudes obtained on the POSS2 plate, c) comparison of POSS1 E and POSS2 R plates, d) Comparison of two Tautenburg B plates. Figuresa), b) and c) show the original calibrated magnitudes before the corrections (Eqs. (2) and (3)), respectively for the Bj and E magnitudes had been applied

Figures 2a and 2b show the result before the correction of B_j had been applied. In Fig. 2d the B magnitudes obtained from the two Tautenburg B plates are compared. The internal accuracy of the blue magnitudes obtained from two Tautenburg B plates and one Palomar B_j plate can be described by the standard deviation of the magnitude differences (see Table 3). For the two Tautenburg B plates we obtained a mean B magnitude difference (B₉₁₆₈-B₉₁₇₇) of +0.00 with a standard deviation of 0.27mag over the whole magnitude interval. After excluding the obviously bad measured/calibrated faint stars on the Tautenburg B plates (B > 18, as can be seen from Fig. 2d) we obtained a much better accuracy (0.13mag standard deviation). The general trend in Figs. 2a and 2b can be roughly explained as follows: According to Eq. (1), the Tautenburg B is expected to be a few tenth mag fainter than B_j for typical (B-V). The apparent turnoff of the $B({\rm Tautenburg})-B_j$ relation at fainter magnitudes is likely due to a selection effect near the Tautenburg plate limit. Stars scattered, at fixed B_j, below the mean relation, due to the colour equation and/or due to measuring errors, will be measured on both the Tautenburg plate and the Palomar plate. However, stars scattered above the mean relation will be missed, in general, on the Tautenburg plates.

The standard deviation of the differences between the corrected B_j and the mean Tautenburg B magnitudes is still the largest value among all possible plate-to-plate comparisons shown in Table 3. But it is better than one could expect from the accuracies of the external calibrations given in Table 2.

Between the E and R magnitudes obtained, respectively from the red POSS1 and POSS2 plates there are also small systematic deviations. The E magnitudes of the POSS1 plate e1457 can be transformed to the system of the POSS2 R plate by Eq. (3).

 

$$E_{\rm c,e1457}= -2.21 + 1.307 \cdot E_{\rm e1457} -0.0103 \cdot E^2_{\rm e1457}.$$ (3)

Figure 2c shows the comparison between the red magnitudes before the transformation of the POSS1 E magnitudes to the system of the POSS2 R plate given by Eq. (3) had been applied.

After the correction of Eq. (3) we obtained, as an estimate of the internal magnitude accuracy, the mean difference ($E_{\rm c,e1457}-R_{\rm sf04859}$) and its dispersion over the whole magnitude interval (see Table 3). The dispersion decreases not as strong as for the two Tautenburg B plates if only the bright stars (R < 16) are considered.

  

Figure 3: Proper motion errors as a function of magnitude a) for $\sigma_{\mu_x}$ and b) for $\sigma_{\mu_y}$. The dashed lines show the mean errors as obtained from a second order polynomial fit in case of $\sigma_{\mu_x}$ and from a third order polynomial fit in case of $\sigma_{\mu_y}$. The solid lines show the magnitude dependent proper motion dispersions $\sigma^{+1}_{\mu_x}(R)$ and $\sigma^{+1}_{\mu_y}(R)$ (obtained from adding 1mas/yr to the mean errors) which were used in the determination of membership probabilities by Eq. (4)