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7. Sources of error

7.1. The photometry (general)

The issue of saturation effects due to limitations in the dynamic range of the COSMOS measuring machine has already been dealt with at length in Sect. 3.5 (click here). The other most common causes of systematic errors in photographic photometry include: differential de-sensitisation of photographic emulsions due to exposure to atmospheric oxygen and water-vapour, vignetting, uneven and/or inadequate hypersensitisation (these effects can prevent the sky density reaching the threshold necessary for a linear response on those areas of the emulsion affected) plate defects (such as scratches or spurious "images'' that are wholly artefact) and inadequacies in background-fitting, sky-subtraction and calibration procedures (which also depend on the accuracy of the reference measurements e.g. photoelectric aperture- [or simulated-aperture-] photometry measurements).

As can be seen from Fig. 13 (click here) and SFig. 14 (click here), for Fields A and B the mean zero-point offset between the isophotal magnitudes generated from the different tex2html_wrap_inline3309 plates is small: tex2html_wrap_inline3945, whilst for Fields C and D it is quite substantial: tex2html_wrap_inline3947. Significant de-sensitisation of Plate J4882 over most of Fields C and D was found to be the cause of this disparity. J4882 was the inferior plate of the two, almost certainly because it was taken before an important modification was made to the UKST plate-holder in December 1982. This modification enabled the plate holder to be flushed with dry nitrogen (which is inert as far as the emulsions are concerned) during exposures, thus preventing de-sensitisation. Note that as J4882 is quite a dark plate (i.e. emulsion densities due to the sky are quite high) the problem in this case was not that the differential de-sensitisation depressed the sky brightness below the threshold for a linear response on the part of the emulsion, but rather that the relative density-to-intensity calibration was based largely on that part of the emulsion's characteristic-response curve between the linear portion and the saturated portion. As the sky was very dense throughout Fields A and B, this calibration was quite adequate for these fields. However, over large areas of Fields C and D, the sky density was depressed onto the central part of the characteristic curve's linear portion for which the adopted relative-calibration polynomial was poorly determined.

As the tex2html_wrap_inline3309 magnitudes were based on both plates in the cases of Fields A and B, but by necessity just on Plate J9229 in the cases of Fields C and Dgif, the errors are tex2html_wrap_inline3955 higher for the latter fields. Mean standard errors on those mean magnitudes that were derived from two plates are tabulated in Table 6 (click here), and were multiplied by tex2html_wrap_inline3955 in order to obtain values applicable to magnitudes derived from one plate. Corresponding errors on the reduced tex2html_wrap_inline3959 tex2html_wrap_inline3441 isophotal radii are shown in Table 7 (click here)gif.

 

magnitude range two plates one plate
tex2html_wrap_inline3967 0.06 0.08
tex2html_wrap_inline3969 0.08 0.11
tex2html_wrap_inline3971 0.10 0.14

Table 6: Mean standard errors on the tex2html_wrap_inline3571 magnitudes quoted in the VPC as a function of the number of plates on which the measurements were based, and as a function of mean apparent tex2html_wrap_inline3571

 

 

magnitude range two plates one plate
tex2html_wrap_inline3967 4.9% 6.9%
tex2html_wrap_inline3969 4.5% 6.4%
tex2html_wrap_inline3971 4.0% 5.7%

Table 7: Mean standard errors on the reduced tex2html_wrap_inline3959 tex2html_wrap_inline3441 isophotal radii in the VPC, expressed as percentages of the corresponding radii measurements, and shown as functions of both the number of plates on which the measurements were based and apparent tex2html_wrap_inline3571

 

Vignetting arises as a consequence of geometric shadowing effects inherent to many telescope designs including that of the UKST. The net effect is that off-axis light is not transmitted as efficiently to the image plane as is on-axis light, with the fractional reduction in efficiency increasing with off-axis distance. In the case of the UKST, the fractional reduction in efficiency is tex2html_wrap_inline3985 within tex2html_wrap_inline3987 of the axis. As the survey area is tex2html_wrap_inline3397 across and more or less centred on the plate centre, only four small areas near to the corners of the survey area could possibly be affected, if the sky density failed to reach the threshold for a linear response (on the part of the photographic emulsion) within these regions. In Sect. 3.3 (click here), it was mentioned that the skies were established to be flat. In order to test for the significance of any apparent slope in the estimated sky as a function of radial distance from a plate's centre, the sky values estimated for the positions of those galaxies with published aperture photometry measurements were plotted as a function of radial distance.

Although, in the case of the U9362 (see Fig. 17 (click here)) there does at first sight appear to be a slight fall off in estimated sky brightness as a function of off-axis distance, the size of the slope was found to be tex2html_wrap_inline3991. In other words, the uncertainty on the slope is very much larger than the best estimate of the slope. In the case of J9229, there is even less evidence for any radial variation as this slope was found to be tex2html_wrap_inline3993. These slopes were computed by means of bootstrap resampling with 10 000 realisations in each case, and using as many data points for each galaxy as there were individual aperture measurements for that galaxy; even though only one data point (the mean sky estimate) is shown in Fig. 17 (click here) for each galaxy's position. In summary then, whilst more calibrating galaxies beyond the tex2html_wrap_inline3995 limit would really be required to establish conclusively that vignetting had been properly accounted for, no evidence has been found for significant radial variation in the skies of Plates J9229 and U9362. This does not of course rule out the possibility that there is significant radial variation, but it does establish that the random disagreements between other observers' aperture photometry measurements constitute a much larger effect.

The 1tex2html_wrap_inline3411 ranges of sky density values for Plate J9229 in Fields A, B, C and D were 635-679, 660-690, 540-700 and 545-690 density units respectively. Ignoring localised regions affected by prominent objects, the sky density was subject to variation of the order of 10% (625-690 units) over 95.8% of the scanned area of Plate J9229. The remaining 4.2% corresponded to the corners of the combined area of the four fields, where vignetting reduced the densities. The vignetting was most severe in the outer corners of Fields C and D, where the densities were reduced to about 550 units. Apart from the issue of how well vignetting has been compensated for (which has already been dealt with) the accuracy to which the sky could be determined depended on the noise associated with the background measurements and any bias there may have been in the determination of the mode sky density values to which the background fits were applied.

The bias in the estimation of mode densities was found to be of the order of tex2html_wrap_inline4009 of a sky unit, in the sense that the sky brightness was slightly overestimated. This figure of 0.06% was arrived at by comparing the adopted estimate of the mode for each bin (containing 7225 pixels) with that mode value obtained by interpolating a histogram of density values for that bin. As described in Sect. 3.2 (click here), there were typically 2000+ bins not significantly affected by extended objects. The interpolation process involved fitting a Gaussian curve to the central portion of each histogram's modal peak, using Starlink's ESP package.

The sample standard deviation in the sky values with respect to the background fits was less than 0.25% in sky units (0.20%, 0.22%, 0.23% and 0.25% for Fields A, B, C and D respectively). This is considerably larger than the bias effect which will henceforth be neglected. The VPC's limiting tex2html_wrap_inline3309-isophote of tex2html_wrap_inline4015, was 5.6% of Plate J9229's sky intensity. The random component of the uncertainty on the limiting isophote due to background fitting errors is therefore at most tex2html_wrap_inline4017 for Plate J9229.

  figure882
Figure 17: The estimated surface brightness of the sky on Plate U9362 for the positions of galaxies with published U-band aperture photometry, as a function of radial distance from the plate centre. Note that the points plotted are means for each galaxy, and that some points are very much more significant than others due to either (1) being based on more aperture photometry measurements and/or (2) because they are based on more independent observers' measurements

One of the advantages of having a slight displacement between the different J9229 and J4882 fields was that if an image happened to be truncated by the edge of a field in one coordinate system, it was unlikely to be truncated in the other system. It was therefore possible to base the tex2html_wrap_inline3309 magnitudes of such galaxy images on the most suitable plate. As a result, edge-of-field effects have been minimised, though Fig. 18 (click here) was plotted in order to provide a check on the effectiveness of the background-fitting procedure at the extremities of a field where interpolation was not possible. As can be seen from this figure, the magnitude measurements do tend to be noisier at the field edges than at the field centres, but the increase in noise with distance from the field centres does appear to be quite gradual and without any very steep increase near the edges.

  figure890
Figure 18: Individual standard errors on those mean tex2html_wrap_inline3309 magnitudes that were derived from both tex2html_wrap_inline3309 plates (overlapping images excluded) as a function of distance from the nearest field edge measured in 2.1 pixels

Overlaps between adjacent images could not always be resolved satisfactorily during the image segmentation. Magnitudes and indeed other photometric parameters are therefore less reliable for images with overlapping isophotes, and particularly so in cases where the brightest overlapping isophote approaches the mean (or even the peak) surface brightness quoted for the galaxy.

As the measured mean and peak surface-brightness parameters (as opposed to the extrapolated ones) quoted in the VPC have not been corrected for effects that degrade image resolution; namely diffraction, atmospheric seeing, sampling due to the pixel size of the plate scans and the smoothing of the scans prior to image segmentation; they tend to be slight over-estimates of the true values as measured in tex2html_wrap_inline3441. Unsaturated composite-stellar-profiles (as described in Sect. 3.5 (click here)) were measured in order to estimate the degree to which the resolution of each image had been degraded by smearing effects, particularly the smoothing of the plate-scan data. The FWHM of the unsaturated composite stellar profiles were found to be tex2html_wrap_inline4029 in the case of U9362, tex2html_wrap_inline4031 in the cases of the two tex2html_wrap_inline3309 plates and tex2html_wrap_inline4035 in the case of R2936.

Of the four plates reduced, R2936 (for which the limiting isophote adopted corresponded to 10.4% of the sky) was the noisiest, followed by J4882 (7.7%), J9229 (5.7%) and the least noisy U9362 (3.1%). It was unfortunate that without such severe smoothing, limiting isophotes tex2html_wrap_inline4037 brighter would probably have to have been adopted as noise peaks in the plate-scan data would have degraded the images around their edges. The smoothing was also very necessary to reduce image fragmentation (the segmentation of individual galaxy images into two or more major components).

In order to investigate the extent to which the VPC's tex2html_wrap_inline3309 isophotal magnitudes have been degraded by atmospheric seeing, sampling and smoothing; model-galaxy profiles were convolved with a tex2html_wrap_inline4041 FWHM Gaussiangif distribution. Only relatively small images were considered, as the significance of the degradation decreases with increasing image size. The results are tabulated in Table 8 (click here), in which the approximate changes in isophotal radius, tex2html_wrap_inline4043, and isophotal magnitude, tex2html_wrap_inline3571, are shown for a variety of different Sérsic profile parameters (intrinsic index, n, and intrinsic central surface brightness, tex2html_wrap_inline4049,) and for a variety of small intrinsic isophotal radii, tex2html_wrap_inline4043. As can be seen from Table 8 (click here), even though the effects on the isophotal radii can be quite significant, the errors introduced to the isophotal magnitudes are typically of the order of several percent (i.e. several hundredths of a magnitude) even for the small images considered, and are in most cases insignificant compared to the other sources of error quantified earlier. Also, note that a coarse resolution function can cause observed isophotal radii to be either larger or smaller than their intrinsic values, in other words the effect is not uni-directional.

 

n tex2html_wrap_inline4063 tex2html_wrap_inline40654tex2html_wrap4169 tex2html_wrap_inline40656tex2html_wrap4169 tex2html_wrap_inline40658tex2html_wrap4169 tex2html_wrap_inline406510tex2html_wrap4169tex2html_wrap_inline4081
0.25 16.5 +13 +0.16 >17.7 +7 +0.06 >17.4 +5 +0.03 >17.2 +3 +0.01 >16.9
0.50 22.0 [+3 +0.06 19.7]tex2html_wrap_inline3457 +3 +0.04 19.0 +3 +0.03 18.4 -1 -0.02 17.9
0.50 23.5 [-1 -0.08 20.3]tex2html_wrap_inline3457 [+1 +0.00 19.4]tex2html_wrap_inline3457 +1 +0.00 18.8 -5 -0.11 18.4
1.00 22.0 [+5 +0.06 19.2]tex2html_wrap_inline3457 +5 +0.04 18.5 +5 +0.03 17.9 +3 +0.01 17.4
1.00 23.5 [-1 -0.07 20.1]tex2html_wrap_inline3457 [+1 +0.00 19.2]tex2html_wrap_inline3457 +1 +0.00 18.6 -3 -0.06 18.2
2.00 22.0 +9 +0.03 18.8 +9 +0.03 17.9 +7 +0.02 17.3 +5 +0.01 16.9
2.00 23.5 [+1 +0.00 19.7]tex2html_wrap_inline3457 +1 +0.00 18.9 +1 +0.00 18.3 +1 +0.00 17.8

Table 8: Quantification of the effect of the 5-arcsec FWHM resolution function on model galaxy profilestex2html_wrap_inline3377 for a variety of Sérsic parameters (n and tex2html_wrap_inline4049) and isophotal radii tex2html_wrap_inline4043

 

7.2. Equal-area colours

The standard error on each mean colour, as quoted in the VPC, is based upon two colour values generated from either of the two following plate combinations:
1) U9362 and J4882, U9362 and J9229
2) R2936 and J4882, R2936 and J9229.
Assuming that U9362 and R2936 are of similar quality to the tex2html_wrap_inline3309 plates, the standard errors quoted in the VPC need to be multiplied by tex2html_wrap_inline3955 in order to obtain meaningful estimates of the standard errors on the quoted colours, as tabulated in Table 9 (click here).

 

magnitude range (tex2html_wrap_inline3607) (tex2html_wrap_inline3609)
2 plates 1 plate 2 plates 1 plate
tex2html_wrap_inline3967 0.18 0.20 0.19 0.22
tex2html_wrap_inline3969 0.17 0.19 0.16 0.18
tex2html_wrap_inline3971 0.16 0.18 0.16 0.18

Table 9: Estimated mean standard errors on colours in the VPC, as a function of the number of plates on which the measurements were based, and as a function of mean apparent tex2html_wrap_inline3571

 

Systematic errors must also be present due to differences between the resolution functions inherent to different plate scans. Systematic differences between the equal-area and total colours were however found to be very small in the case of the tex2html_wrap_inline3609 index, though more noticeable in the case of the tex2html_wrap_inline3607.

7.3. Total magnitudes and colours

The estimated random errors on the total magnitudes quoted in the VPC are listed in Table 10 (click here). They are based on several assumptions and approximations, and are therefore only intended as rough estimates. The mean extrapolation from tex2html_wrap_inline3571 to tex2html_wrap_inline3741 is 0.35 mag, and the estimated standard error on a mean extrapolation was taken to be tex2html_wrap_inline4207 magnitudes. This value was propagated with each of the mean standard errors on tex2html_wrap_inline3571 values listed in Table(s) 6 (and 10) to yield mean standard-error estimates on tex2html_wrap_inline3741 values. From Fig. 8 (click here) it can be seen that the uncertainty on any estimate of (B-V) based on a value of (tex2html_wrap_inline3609) is tex2html_wrap_inline3765 mag. The offset between the B and tex2html_wrap_inline3309 systems is tex2html_wrap_inline4223, whence the mean error in the tex2html_wrap_inline3741-to-tex2html_wrap_inline3745 conversion was taken to be 0.07 magnitudes. This was increased to 0.1 magnitude in order to take into account uncertainties in the colour-coefficient term, and propagated with the mean standard deviation estimates for tex2html_wrap_inline3741 values in order to obtain mean standard deviation estimates on tex2html_wrap_inline3745 values. The mean extrapolations from U25 to tex2html_wrap_inline4235 and from tex2html_wrap_inline3787 to tex2html_wrap_inline3913 were found to be 0.45 and 0.25 mag respectively. Therefore the random errors on the tex2html_wrap_inline4241 colours can be expected to be considerably smaller than those on the tex2html_wrap_inline4243 ones. This was confirmed by intercomparisons between the equal-area and total colours.

 

Magnitude range tex2html_wrap_inline4247 tex2html_wrap_inline4249 tex2html_wrap_inline4251
Two plates:

tex2html_wrap_inline3967

0.06 0.13 0.16
tex2html_wrap_inline3969 0.08 0.14 0.17
tex2html_wrap_inline3971 0.10 0.15 0.18

One plate:

tex2html_wrap_inline3967

0.08 0.14 0.17
tex2html_wrap_inline3969 0.11 0.16 0.19
tex2html_wrap_inline3971 0.14 0.18 0.21

Table 10: Estimated mean standard errors on the isophotal and total magnitudes quoted in the VPC, as a function of the number of plates on which the measurements were based, and as a function of mean apparent tex2html_wrap_inline3571

 

7.4. Galaxy magnitudes from other sources

In the absence of alternative measurements for most of the objects suffering from saturation effects in the VPC, those sources listed in Sect. 5 (click here) have had to suffice. It is hoped that for the bright galaxies concerned, these sources are reasonably reliable.

7.5. Equatorial coordinates

An indication as to the accuracy of the astrometry is given by the residuals between the positions as quoted in the AGK3 catalogue and those calculated according to the plate solution adopted. The root-mean-squared residual was 2.28 (0.87 in right ascension and 2.11 in declination). As the segmentation software did not centroid the galaxy images, but assigned (x,y) coordinates to the brightest pixel within each image, this quantity is, as expected, quite similar to the pixel size of the segmented images: 2.148. The lack of a centroiding algorithm was not a problem for the saturated galaxies however, as RC3 positions were generally adopted for them.

7.6. Radial velocities

These errors were taken from those sources of radial-velocities listed in Sect. 5 (click here) without modification. In the cases of the following VPC (VCC) objects, there are very large mutual disagreements between different sources in the literature, and the true errors may be very much larger than the values quoted: VPC 25, 424, 447, 502, 545, 624 and 810 (which correspond to VCC 325, 815, 870, 945, 1035, 1148 and 1355 respectively).

7.7. Morphological types

Owing to the small plate scale of the UKST plates, and the high degree of saturation exhibited by many of the galaxy images, even approximate typing was not always possible. The majority of those morphological types obtained from the VCC (see Sect. 5 (click here)) were presumed to be correct, but one mis-classification was noticed. Binggeli et al.'s (1985) VCC 500 was classified as an S0, instead of as a ringed-spiral. This has been corrected in the VPC. Note that the re-classifications listed in de Vaucouleurs & Corwin (1986) all concern spiral-galaxy subclasses, and are therefore beyond the scope of the broad classifications provided by the VPC.


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