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Appendix A: Data reduction

Appendix A.1: Overscan correction and master bias

For each exposure, the median value of an overscan region is computed and then subtracted, row by row. Then a masterbias, created as a sigma-clipped (5σ) average of (at least) ten bias frames, is subtracted from all the other scientific and technical exposures for full 2D bias removal.

Appendix A.2: Flat-fielding

The conversion from photons to ADUs, called gain, varies over the whole camera frame, owing to the optical design, pixel response, and electronics behavior. In principle, an exposure of a uniformly illuminated field is sufficient to build a gain-variation map. We use exposures of the sky at twilight. Because of the wide field of the instrument, these twilight flat fields may suffer from illumination variations amounting to some percent units on a degree scale. This undesired effect is mitigated by the illumination-correction procedure described below (Sect. A.5).

A master flat-field is created by averaging a set of twilight flat-fields (typically five); a sigma-clipping rejection procedure helps removing non-stationary features. The method tracks the gain variations at high spatial frequencies well, but sometimes fails at low frequencies. The reason may be the color and flux mismatch between twilight and science exposures. In this case, the twilight flat-fields are combined with some science images taken during the same night with exposure times similar to those of the images under correction. This type of frame combination has been used to process the NGC 4472 exposures. Specifically, we applied the formula (A.1)where(A.2)The superscript indicates the ith CCD, the subscript low is for the low-frequency spatial component obtained by applying a low-pass spatial filter in the Fourier space. The master twilight (TFlat) and master skyflat (SFlat) are produced using a sigma-clipped average of overscan- and bias-corrected twilight frames and sky frames, respectively. The choice of the exposures used to produce the master skyflat requires special care. The dithering pattern of the exposures must be wider than the largest structure in the images (such as galaxies or the halo of bright stars) to avoid fictitious gain variations. Moreover, all the bright features in the science images (galaxies stars, halos, etc.) are accurately masked. In all these formulas, chevron brackets indicate medians done on a 1000 × 2000 pixel central spot in the CCDs.

The terms Gainⁱ × ICⁱ accounts for the average CCD gain and for the illumination correction and is described in Sect. A.5.

	Fig. A.1 Differences of magnitude among observed and SDSS DR8 equatorial stars as a function of x and y pixel coordinates.
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	Fig. A.2 Differences of magnitude among observed and SDSS DR8 equatorial stars as a function of x and y pixel coordinates after applying the surface fit (top). Bottom right panel: contour plot of the IC image. Bottom left panel: IC 3D view.
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Appendix A.3: Defringing

The i-band images need a correction for the fringe pattern caused by thin-film interference of sky emission lines in the detector. This is an additive component and, as such, it must be subtracted. The first step of the defringing is determining the fringing pattern by the formula (A.3)where imsurfit indicates a fifth-order surface Chebyshev polynomial fit.

Once the pattern is found, it must be subtracted from the science image, (A.4)using a scale factor, fr_scale, that is derived as follows. We assume that the fringe-pattern features are quite stable in time. We have then a priori determined the regions in the OmegaCAM frame where they clearly stand out. The best scale factor minimizes within these regions the absolute differences between peak and valley values in the fringe-corrected image.

Appendix A.4: Gain harmonization

The gain harmonization procedure sets the photometric zero point over the whole OmegaCAM mosaic. We derive the relative gain coefficients that minimize the background differences in adjacent CCDs. First we select a set of auxiliary scientific images belonging to the same night and having approximately the same exposure time as the science image to be calibrated.

Each such image is heavily clipped around the median pixel level to flag out all the sources; holes created by the procedure are filled up in a subsequent step. After overscan and bias correction, the auxiliary images are properly scaled and sigma-clipped combined. The scaling factor is calculated as the median over the scientific image divided by the median of the medians. All the holes surviving the stacking procedure are filled by interpolated values. The resulting image, corrected for the master twilight flat-frame, is then fitted with a third-order polynomial surface. This is used to compute 32 median values over subregions of 1000 × 2000 pixels centered on each CCD. These values, normalized to the median of all the CCDs medians, are the relative gain corrections. The gain harmonization correction typically ranges from 0.9 to 1.17.

Appendix A.5: Illumination correction

Another effect to be considered is the scattered light in the telescope and in the camera that is due to insufficient baffling, which produces an uncontrolled redistribution of light. In the presence of this additive contribution to the signal, the flat field is no longer an accurate model of the spatial detector response. Indeed, after flat-fielding, the image background appears perfectly flat, but the photometric response is position dependent (Andersen et al. 1995). This bias in the flat field can be mitigated by applying the illumination correction (IC) map. We determine such a map by comparing our magnitude measurements of stars observed in equatorial fields with the corresponding SDSS DR8 psf magnitudes.

The differences of magnitudes, Δm(x,y), as a function of the position are fitted with a generalized additive model (GAM; Wood 2011) to derive a surface used to correct the science images during the pre-reduction stage. GAM also provides a well-behaved surface when the standard stars do not sample the field of view uniformly, and in general the resulting image has a smoother behavior at the frame edges than do simple polynomial fits. Figures A.1 and A.2 illustrate the position dependency of the zero point before and after the IC application and the IC shape. The statistics on the differences in magnitude between the reference photometric catalog and the magnitude of sources before and after the illumination correction are the following: STD = 0.09 and MAD = 0.084 before and STD 0.05 and MAD 0.026 after the correction. The IC was created using 2189 sources. As shown in Eq. (A.1), the IC is embedded in the master flat field. In this way, the images have a uniform zero point all over the field, but the background does not appear flat. To have a flat background, the properly rescaled IC surface is also subtracted from the images.

Appendix A.6: Photometric and astrometric calibration

In VST-tube, the absolute photometric calibration is performed by observing standard star fields each night and comparing their OmegaCAM magnitudes with SDSS DR8 photometry. For the data analyzed in this work, the absolute photometric calibration was derived using 4392 sources in the g and 4489 in the i band. For each night and band, the zero point (ZP) and color term were obtained using the tool Photcal provided by Mario Radovich (Radovich et al. 2004). The extinction coefficient was derived from the extinction curve M.OMEGACAM.2011-12-01T16:15:04.474 provided by ESO. Table A.1 lists the fitted values for the zero points and color terms obtained for the nights used for the absolute photometric calibration.

Relative photometric correction among the exposures was obtained by minimizing the quadratic sum of magnitude differences between overlapping detections. The tool used for this task was SCAMP (Bertin 2006). The final coadded images were then normalized to an exposure time of one second of time and a ZP of 30 mag.

The absolute and relative astrometric calibrations were performed using SCAMP. For the absolute astrometric calibration we refer to the 2MASS catalog. Compared to this catalog, the rms of the residuals after the astrometric correction has been applied is 0.28′′. The rms on the residuals of the differences between coordinates of overlapping detections, that is, the internal astrometric accuracy, is 0.09′′. The image resampling for the application of the astrometric solution and final image coaddition is made with the program SWARP (Bertin et al. 2002).

Appendix B: Convolution by the scattering profile of the point spread function

To evaluate the contribution of the scattered light, which is indeed a reason of concern for the surface photometry of galaxy outskirts, we first derived an extended stellar point spread function (PSF) by combining the unsaturated azimuthally averaged light profiles of stars of different luminosities, properly shifted in magnitudes. Our interest is not in the seeing profile, that is, in the inner few arcseconds of the PSF, but instead in the wings produced by the scattering in the mirror and in the atmosphere (Capaccioli & de Vaucouleurs 1983).

The measured PSF profiles for the g and i band are shown in Fig. B.1, normalized to unity up to the last observed point. Although the inner PSF has an average behavior that is uncorrelated with the actual seeing of each of the images contributing to the final mosaic, it could not be used for deconvolving the inner regions of the galaxy. Nonetheless, it must be kept just for providing a way to normalize the PSF itself.

To extend the PSF beyond the observational limits, we adopted the polynomial expansion of Capaccioli & de Vaucouleurs (1983), which was used to interpolate the total PSF profile (see Fig. B.1): (B.1)where c₀ = 2.187 × 10^-6 (mag/arcsec²), c₁ = 1.725 × 10^-5, c₂ = −8.559 × 10^-6 and c₃ = 1.570 × 10^-6 for the g band and c₀ = −9.497 × 10^-4 (mag/arcsec²), c₁ = 2.109 × 10^-3, c₂ = 1.157 × 10^-3 and c₃ = 2.134 × 10^-4 for the i band. As expected, the g PSF spans a wider range than in the i band. The total integrated energy included in the inner regions, r^{1 / 4} ≤ 2.3, is 94% of the total flux from the stars for the g band.

	Fig. B.1 Adopted extended PSF for VST.
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The expressions B.1 were used to estimate the effect of the scattered light in the outskirts of the galaxies of this study, which have quite different sizes. It is indeed expected that the effect will be quite different at the same surface brightness level between angularly large and small galaxies.

Two methods were employed. The first method is a plain numerical convolution of each galaxy modeled through azimuthally averaged light profiles under the assumptions that the isophotes are ellipses of average flattening and no twisting. At first order, the difference between the model and its convolution provides an estimate of the excess of light in the observed galaxy caused by the broad smearing of the extended PSF.

Another method consists of a straightforward deconvolution of the noiseless model of the galaxy by the extended PSF. To this end, we used the IRAF task LUCY. The two methods provide very consistent results that will be illustrated in a forthcoming paper (Spavone et al., in prep.).

One additional comment is in order about the effect of the background interpolation on the partial removal of the excess of light that is due to PSF scattering. It is expected and verified numerically that small galaxies will be widely broadened by the PSF wings. If this causes the outer light profile to become much flatter, one may expect that the background interpolation procedure is capable of removing part of it, if not all. This is precisely what our numerical experiments show (Spavone et al., in prep.).

Appendix C: Additional tables

© ESO, 2015