3.3 The Basic Reductions of the Photometry

The full description of the basic reductions for the direct images is given in Appendix  (p. ). A summary is given below.

Removal of overscan area.

The readout window for the photometry was the full CCD frame of [1:1060,1:1028]. The section [19:1042,3:1026] was extracted to remove the overscan area. The resulting images had dimensions 1024 pixels $\times$ 1024 pixels.

Subtraction of bias.

Cf. Sect.  (p. ). A bias image was constructed from 55 individual bias images. The mean bias level was 124 ADU, with a small (0.5 ADU) gradient in the y-direction. Small night-to-night variations ($\pm 0.5$ ADU) in level and gradient was seen. It was necessary to use an actual bias image (as opposed to a bias constant), since there was low amplitude structure (0.5 ADU) in the bias images which was also present in the uncorrected science images.

Correction for fat zero.

Cf. Sect.  (p. ). 20 of the 1024 CCD columns were affected more or less severely by fat zero, which is a non-linear response in the CCD output signal to the incoming photon flux. The determination of fat zero behavior for the 20 affected columns was done from a large number of dome flats spanning levels all the way from 1 to 58000 ADU. In these images, the levels in the fat zero columns were mapped as function of the levels in the unaffected neighboring columns. The dome flats used were obtained after the CCD temperature change that happened between night 5 and 6, cf. Table  (p. ). To determine the fat zero effect for the nights before the CCD temperature change, an extra correction had to be determined from the galaxy images themselves, since no low-level flats were available from this period. This was of course somewhat complicated due to the large number of objects (galaxies, stars, and cosmic-ray-events) present in these images. The fat zero effect was in all cases below 100 ADU.

To apply the fat zero correction, we need to know the level that would have been in the given pixel had it not been affected by fat zero. This level was taken as the mean level in two unaffected neighboring columns on both sides and within a running box of height 21 pixels. The fat zero correction worked well in most cases.

Subtraction of dark current.

Cf. Sect.  (p. ). Two dark images were constructed, one for each CCD temperature. The dark current was 10.9 e^-/hour and 33.7 e^-/hour, respectively. It was necessary to use an actual image and not a constant since the images contained significant structure. Each final dark image was based on 3 individual dark images of 1 hour exposure time. 16 additional dark images had to be discarded, since it was discovered that there had been a light leak in the camera.

Shutter correction.

Cf. Sect.  (p. ). The time that the CCD is actually exposed to light is not equal to the exposure time that the observer asks the controller to use. The difference $\delta$ between the latter and the former was determined from 48 dome flats. The value $\delta = 0.41 \pm 0.02$ seconds was found. It was also found that $\delta$ was constant across the CCD, so a scalar value could be used instead of an actual image. The shutter correction is applied by multiplying the image levels by $t/(t+\delta)$, where t is the requested exposure time and $(t+\delta)$ is the actual exposure time. See also Stetson (1989).

Flat field correction.

Cf. Sect.  (p. ). Sky flats were obtained in Gunn r on night 1, 2, and 7, and in Johnson B and Johnson U on night 1, 2, 6, and 7. It was found that there was a difference between the night 1 flats on the one hand and the night 2, (6), and 7 flats on the other hand. Therefore, for each passband, two flats were made, one for night 1, and one (supposedly) for night 2-14. The night 2-14 final images were based on about 12 individual images. The night 1 final images would have been based on only 2-3 individual images had they been made in the same way, which would have given insufficient signal-to-noise. Instead, the pixel-to-pixel variations from the night 2-14 final images were used to construct the night 1 final images, taking only the low frequency variations from the combined night 1 images.

In Gunn r and Johnson B an illumination correction was determined. This correction basically makes the background in the science images flat, which the above sky flats themselves fail to do. The reason for this failure is the different color of the night sky (i.e. the background in the galaxy images) and the morning twilight sky (where the flats were taken). The problem might be accentuated by a red leak in the Gunn r filter (cf. Stetson 1989). The illumination correction was determined from science images containing few galaxies. The so-called empty fields that had been observed did not prove useful. No illumination correction for Johnson U could be determined, since the background level in the galaxy images was too low and since all 5 images contained many galaxies.

The relative uncertainties on the final flat field images (based on photon statistics and read-out noise), and limits on possible remaining low spatial-frequency variations are listed in Table .

 

Table: Summary of Flat Field Accuracy

Passband	Relative uncertainty	Possible low frequency variations
Gunn r	0.35%	$\leq$ 0.2%
Johnson B	0.31%	< 0.1%
Johnson U	0.31%	< 0.1%

 

Removal of signal from remanence and overflow.

Cf. Sect.  (p. ). Overflow is when a very bright and saturated star causes a stripe from the star to the edge of the image in the given image. Remanence is when these signals are seen in subsequent images in the same columns without the presence of a saturated star. The used CCD was severely affected by both phenomena, with remanence being visible in $\sim$ 20-30 exposures after the one that had caused it! The images were quite successfully corrected for both effects using a labor-intensive method.

Removal of signal from the spectroscopy calibration lamp.

Cf. Sect.  (p. ). In a few cases, the spectroscopy calibration lamp was accidentally on when direct images were obtained. The imprint of the lamp was successfully modeled and subtracted.

Stacking of images.

In the cases where a very bright star in the field made it necessary to take several shorter exposures, these were stacked, i.e. offset to match and then added. This concerned field 33, 35, and 535.

In addition, the following was performed.

Linearity test.

Cf. Sect.  (p. ). Using dome flats with levels from 1 to 58000 ADU it was found that the CCD was linear within 0.7%.

Determination of conversion factor and read-out noise.

Cf. Sect.  (p. ). findgain was used to determine the conversion factor (CF) and read-out noise (RON) for all the dome flats used in the linearity test. findgain reported that the CF increased with level. However, since the linearity test showed the CCD to be linear, the CF had to be constant. We concluded that it was the RON that was level-dependent, probably caused by a malfunction in the read-out electronics.

The variation in the CF reported by findgain was mainly at levels below 1000 ADU. For levels above 1000 ADU, the mean of the 15 determinations of the CF was 1.95 e^-/ADU with an rms scatter of 0.04; this value was adopted. The standard deviation in raw bias images was 2.25 ADU, and this (constant) value was adopted as the RON, corresponding to 4.39 e^-. The effect on the error estimates on the flat fields of using a constant RON instead of a level-dependent one is non-significant.

Seeing determination.

By seeing we mean the full width at half maximum (FWHM) of the point spread function (PSF). For all the galaxy images, the seeing was determined using a script written by I. Jørgensen. It works as follows. All objects in the image is found using daofind. A Gaussian of user specified FWHM is fitted to all objects using imexamine. Based on a number of criteria, only bright but not saturated stars are attempted kept. The median FWHM for these objects is taken to be the first guess on the seeing. The above procedure is then repeated, this time using the first guess on the seeing as parameter for the Gaussian. The output median FWHM of the selected objects is taken as the seeing. The seeing determination is semi-automatic only, since the user has to experiment to find appropriate values for the parameters used for the object selection. It was found that different values were needed for different passbands and exposure times. For 8 out of the 123 galaxy images a manual determination of the seeing was done, and it was found that the two methods agreed well.

For the Gunn r and Johnson B images, the automatic seeing determination was based on about 45 stars, whereas for the Johnson U images it was based on about 5 stars only. The seeing values are shown in Table  (p. ). They are in the range 0.77''-1.88''. When given each of the 227 galaxy observations equal weight, the mean seeing values are 1.1'', 1.2'', and 1.2'' for Gunn r, Johnson B, and Johnson U, respectively. At the distance of HydraI, this corresponds to about 0.5 kpc (for $H_0 = 50\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$; cf. Sect. , p. ). The range in seeing values in pixels is 1.52-3.70 pixels. Thus, in the best seeing conditions (seeing < 2 pixels $\approx$ 1''), the resolution is determined by the CCD pixel size, not the seeing. This is not a big problem, since the resolution obtained in any case is good and sufficient, especially since HydraI is such a nearby cluster. The used CCD scale of 0.5073 arcsec/pixel was found by doing astrometry, see Sect.  (p. ).

The ellipticities of the PSF were in the range 0.03-0.13 with a mean value of 0.06. The PSF was thus quite round, which is important, since an elongated PSF can introduce systematic errors in the ellipticities and position angles determined from the surface photometry; see Franx, Illingworth, & Heckman (1989b), and Peletier et al. (1990).