3 Photographic photometry

 

3.1 Transformation to the standard photometric system

  Photographic photometry was obtained from several modern epoch (filtered) plates by calibrating the photographic flux using the BVR - CCD observations from Paper I as reference. A catalogue of more than 400 photometric secondary standards was prepared following these criteria:

1.

The photometric standards should be well isolated, in order to avoid the risk of misidentification when targeting MAMA in pavé mode;

2.

The photometric standards should be well distributed along the whole magnitude interval covered by the deep plates, avoiding an excessive presence of faint stars.

Standard magnitudes from Paper I and logarithm of photographic flux were related by fitting a polynomial with a linear colour term. Since our deepest plates are in R and B bands, we used the colour index B-R for the transformation equations:  

$$B = b_0 (B-R) + \sum^{k}_{i=1} b_i {(\log_{10} \phi_{_B})}^{i-1};$$ (1)

 

$$V = v_0 (B-R) + \sum^{m}_{i=1} v_i {(\log_{10} \phi_{_V})}^{i-1};$$ (2)

 

$$R = r_0 (B-R) + \sum^{n}_{i=1} r_i {(\log_{10} \phi_{_R})}^{i-1};$$ (3)

where $\phi_{_X}$ represents the stellar flux measured at one threshold in a X-band plate; B, V and R are the standard Johnson-Cousins magnitudes; b_i, v_i and r_i are the transformation coefficients, and k -1, m -1 and n-1 are the polynomial degrees. Each filtered plate was calibrated in the band closest to that defined by its filter/emulsion combination (Table 1). The coefficients in Eqs. (1) to (3) were obtained by a least squares method for each plate and threshold. The polynomial degree, from 3rd to 5th, was selected depending on the plate response curve, and was the same for every threshold on each plate. Table 3 displays some data about the standard photometric fits: polynomial degree, number of thresholds ($N_{\rm thr}$) and standard deviation of the residuals of the fits, averaged among all thresholds ($<\!\sigma\!\gt$). Regarding the goodness of the fits and the magnitude intervals covered, we decided to use, for the final photographic photometry, the following plates: A 550 for B magnitude; A 575 for V magnitude; OCA 3305 and OCA 3314 for R magnitude. As an example, Fig. 1 shows the relations among standard magnitude and logarithm of flux for one threshold of each selected photometric plate.

  

Figure 1: Relation among logarithm of flux and standard magnitude for the third threshold of each plate selected for deriving photographic photometry

  

Table 3: Photographic photometry: standard deviation of the residuals of the standard stars ($<\sigma\gt$)averaged for all the thresholds on each filtered plate. $N_{\rm thr}$ gives the number of thresholds and "Degree'' is the polynomial degree of the fit

In order to apply the above transformations to non-standard stars, a cross-identification among the different photometric plates is needed. The standard magnitudes are calculated, for a given star, following these steps:

First, as can be easily deduced from Eqs. (1) and (3), the standard R magnitude can be computed from the expression

$$R{=}\frac{r_0 \sum^{k}_{i=1}\! b_i {(\log_{10} \phi_{_B})}^{... ...um^{n}_{i=1}\! r_i {(\log_{10} \phi_{_R})}^{i-1}} {1-b_0+r_0}.$$

For one star detected at a threshold on an R photometric plate, we have a definite value of its flux $\phi_{_R}$. But for obtaining its standard R magnitude we need not only the coefficients $\{r_i; i=0,\cdots,n\}$ for this specific threshold, but also one blue flux $\phi_{_B}$ from one threshold on the B plate, with the corresponding coefficients $\{b_i; i=0,\cdots,k\}$. Our photometric procedure computes different R values using all the $\phi_{_B}$ fluxes (all thresholds) available from the B plate (A 550) for this star, and averages the results using the standard deviation of the residuals of the standard stars in the individual blue fittings as a weight. The process is repeated for all the R thresholds available for this star on this R plate, and the different resulting R values are averaged using the standard deviation of the residuals of the individual R fittings as a weight. The standard deviation of this average is stored. This yields an R standard magnitude for this star on this R plate. The same procedure is followed on the other photometric R plate, yielding another R value with its standard deviation. The two resulting R values are averaged using their standard deviations as weights.

The second step, the determination of standard B magnitudes, is somewhat simpler, because only one photometric plate is used, and because the standard R value has been already computed and can be used in the calculation. From Eqs. (1) and (3) we see that B is obtained as:

$$B = \frac{-b_0 R + \sum^{k}_{i=1} b_i {(\log_{10} \phi_{_B})}^{i-1}}{1-b_0}.$$

For each star detected on the B photometric plate (A 550), one B magnitude is computed from each threshold, and the resulting values are averaged using the standard deviation of the residuals of the standard stars at each threshold as a weight. In a third step, a similar process is applied for the calculation of V from the V photometric plate (A 575), using Eq. (2).

3.2 The photographic photometric catalogue

The final photometric catalogue (Table 6, available only in electronic form) contains a total number of 39762 stars, 38304 having complete BVR photographic photometry, and 1458 only BR photographic photometry. The stars are designated by their identification number on the master plate OCA 3305. Table 4 gives the number of stars by interval of magnitude in each band.

  

Table 4: Photographic photometry: total number of stars (N) in the photographic photometric catalogue and standard deviation ($\sigma$) of the differences with CCD photometry for the stars in common, in magnitude intervals

The absolute accuracy of the photographic photometry is limited by several factors. One of them is the emulsion and developing uniformity. Since our photometric standards are located in the center of the scanned zones, the photometric calibration would be strictly valid only in this area. But we extrapolated the calibrations and applied them to the whole $2.3^{\circ}\times2.3^{\circ}$ region. We have no means of evaluating the possible existence of photometric inhomogeneities on the photometric plates, but visual inspection of them shows an apparent good regularity of emulsions and developing.

Another source of error arises from the quality of the original CCD photometry used for the calibration. We have no reason to suspect systematic effects in the CCD data. We refer to Paper I for a detailed discussion of them.

Further uncertainties may be caused by the transformation from the effective band defined by the emulsion/filter combinations to the standard system. This effect is taken into account to some extent by means of the colour term introduced in the transformation equations. The effect of the colour term coefficients was small in all cases, and introducing further colour terms (quadratic, and so on) in the transformation equations did not improve the goodness of the fits.

The non-linearity of the photographic response is well corrected by using the appropriate polynomial degree in the transformation. The ultimate limit of accuracy lies in the intrinsic precision of the photographic emulsion. For these reasons, it is usually difficult to reach precisions better than 0.1 mag in photographic photometry. The average standard deviations of the residuals of the photometric fits (Table 3) seem to indicate that we have reached, or even improved, this limit.

In order to estimate the quality of our photographic photometry as a function of magnitude, we compared the obtained BVR values with the whole photometric catalogue from Paper I. As explained, a subsample of around 400 of these stars were used as secondary standard for the calibration, but the comparison with the whole set allows a better determination of the photometric uncertainties as a function of magnitude. Figure 2 displays the results of the comparison. Table 4 includes the standard deviations of the differences CCD-photographic in one magnitude bins and applying a 3$\sigma$ clipping to the data in each interval. The differences contain contributions as from photographic and from CCD photometric errors, but the second are small compared to the first ones.

  

Figure 2: Comparison of photographic photometry with the whole CCD photometric sample from Paper I. The panels, from top to bottom, show the differences CCD-photographic in B (1477 stars), V (1498 stars) and R (1536 stars) bands.

3.3 Raw photographic photometry for cross-
identifications

 As explained in Sect. 4.1, the cross-identification step of the plate-to-plate transformation algorithm applies a double position-brightness criterion for matching the stars and, thus, it requires some kind of brightness estimator for every object in each plate, not only in filtered ones.

Just for cross-identification purposes, for every plate and threshold we performed a least squares fit of magnitude as a function of logarithm of flux without colour terms. The fitted model was a polynomial, and the standard stars were those used in Sect. 3.1. These polynomials were applied to all the detected objects and the different magnitudes coming from different thresholds in the same plate were averaged using as weight the object area at each threshold.

The reference bands for these raw magnitude calibrations were selected in accordance with each plate/emulsion characteristics. Johnson's B magnitude was used for non-filtered plates (Tautenburg, Heidelberg) and for B-like filtered plates (A 550, POSS 1461-O). For AC plates, the photographic magnitude values quoted in the original plate measurements were used directly. The instrumental PDS magnitudes from Shanghai plates were transformed into Johnson's B magnitude fitting a 2nd degree polynomial using the B-CCD measurements as reference. Although our master plate (OCA 3305) matches the R band, we performed a raw calibration also into Johnson's B filter, in order to allow the cross-identification with B-like plates.

R-like plates (the master plate OCA 3305, OCA 3314, A 573 and POSS 1461-E) were fitted in a similar way to the standard Cousins' R band. V-like plates (OCA 3308 and A 575) were fitted, for comparison purposes, with Cousins' R band, and this raw R magnitude was used to perform their cross-identification with the master plate. When there was cross-identification of the CCD pseudo-plate with the master plate, the R magnitude from Paper I was compared to the raw R magnitude computed in the master plate.

Several stars were saturated in some or all plates. These objects were maintained in the files, labelled as "bright'', and they received a special treatment in the cross-identification procedures.