3 Data reduction

3.1 Dark

The masterdark is the median of a stack of 25 individual darks. The rms noise of an individual dark is about 16 to 23 ADU, depending on the NICMOS-3 quadrant. In the masterdark, pixels whose intensity differs by more than 70 ADU from the surrounding ones (they are $\sim1$% of the total number of pixels) were replaced by the local average. These pixels were found to show a different behavior from their neighbors at a low illuminating flux, and a normal behaviour at high illuminating flux (i.e. in calibration and science images).

The gain of the camera was found to be 10 e^-/ADU.

3.2 Flatfielding

This is a challenging task with near-infrared images, and therefore a detailed description of the way we flatfielded our images is necessary. In the near-infrared, observers are faced with rapid changes of the intensity and spectrum of the sky. In the H band, the measured contribution of the telescope and warm-optics background is 80 ADU during the day (in 30 s, shutter closed), and probably less during the night; this is negligible with respect to the sky level and total background emissivity (shutter open), which is usually $\sim$ 3000 ADU in 30 s. We can therefore apply an "optical reduction" to our H-band data.

Our images are quite empty: the majority of the pixels see to the sky most of the times, and the shift between successive exposures is larger than the typical size of objects. Therefore, we decided not to take offset images, and to use the images themselves for flatfielding, thus doubling the time allocated to science frames. The procedure to flatfield our near-infrared images is basically the same as that used for super-flats in the case of optical images.

final = (raw - masterdark)/(superflat - masterdark).

For each image, the superflat is computed as follows:

a) we consider only images taken not longer before or after the exposure to be flat-fielded;

b) the median of each image is computed;

c) we retain only those having a median which differs by less than 5% from that of the image to be flatfielded, with a maximum of 25 images. More liberal limits do not increase the quality of the flatfielding as judged by the flatness of the flattened image. We verified that this choice gives better flatfielded images than taking the temporally nearest 25 (or any number between 9 and 25) images for the creation of the superflat. We interpret the above result as evidence that the spectrum and the intensity of the sky in the near-infrared are correlated. For more than 2/3 of the images, 25 images whose intensities differ by at most 3% were used;

d) the images are divided by their median;

e) the superflat is a median, over the stack, of the median normalized images.

3.3 Check of the photometric accuracy of the flatfielding

We checked the correctness of the flatfielding by comparing the apparent flux of photometric standards (and of other observed objects) imaged in the four quadrants (and at different locations in each quadrant). 0.01 mag is the present upper limit of the error determination of any trend between location in the field of view and flux. The global photometric quality of the data is discussed in Sect. 3.7.

3.4 List of bad pixels

We manually created the bad-pixel list. In general, Moïcam has an excellent cosmetics, and only a few regions required to be masked: two small ($\sim10$-pixel wide) clusters and half a row between two quadrants.

Figure 5: Magnitude error as a function of the 10 $^{\prime \prime }$ aperture magnitude for patch1 (triangles), 0404 (circles) and 0504 (crosses). The two outliers are in a noisier than average region, on the border of the region considered for the final catalogue

3.5 Sky subtraction

From each flatfielded image we subtracted a constant, the sigma clipped mean computed over the whole image.

In passing, we note that the average H-band sky brightness during our 5 nights was 14.2 mag arcsec^-2, more than one magnitude fainter than the values typically encountered at other European northern observatories, such as the William Herschel Telescope at La Palma, or at TIRGO on Gornergrat. It is only 0.1 mag brighter than the mean value observed on Mauna Kea.

3.6 Spatial offset

Most images contain at least one bright object which is common to other neighboring images. The angular shifts between the 675 pointings have been computed manually for several reasons. There was no information written on the image-file headers about the position of the telescope when the images were acquired. Besides, when no bright objects are present, allowing one to produce an accurate position of the centroids automatically and blindly, the image have to be recentered manually. This is also the only way to correct for the presence of ghosts and remnant images (arising from extremely bright sources). Fortunately, these events were rare and they were perfectly corrected after the processing.

3.7 Photometric calibration

Standard stars from the UKIRT faint standard list (Casali & Hawarden 1992) were observed once or twice per night. Each standard star was usually exposed four times or more, at least once per detector quadrant. Figure 3 shows the zero points (solid dots). We supplementary these a few measurements by using as standards the Coma galaxies whose magnitudes are listed in Recillas-Cruz et al. (1990). The latter magnitudes are taken with an InSb photometer within a 14.8 arcsec diaphragm and have an average error of 0.02 mag. Of course, in our comparison with Recillas-Cruz et al. (1990) we use 14.8 arcsec aperture magnitude. These zero-point are shows in Fig. 3 as crosses. When stars and galaxies zero-points are available, the agreement is good, as also shows in Table 1.

 

 

Table 1: Photometric zero point, outside atmosphere, for a 1-s exposure time. The number of objects is given in brackets

Night	Standard	Standard	Adopted
	stars	galaxies	zero point
4/3	20.76 (1)	20.69 (3)	20.76
9/3		20.76 (2)	20.76
3/4		20.76 (2)	20.76
4/4	20.71 (2)	20.71 (9)	20.71
5/4	20.67 (2)		20.67

The field imaged on April 3rd largely overlaps with the field imaged on March 4th and 9th. The magnitudes of the 9 bright objects in the overlapping region are in good agreement, with a typical scatter of 0.03 mag and an average difference of only 0.02 mag, which confirms that these nights were photometric. The fields observed the other nights have too small overlaps to allow a useful comparison in the same way. Nevertheless, all along the recentering procedure, we have checked the consistency of the photometry between different neighboring images of the same bright sources.

Coma was observed through airmasses which differ at most by 0.1 mag. Assuming an atmospheric extinction of 0.059 mag/airmass, the zero-point variation due to airmass variations is at most 0.0059 mag. We neglected this variation (and we assumed an airmass of 1.1 for all observations).

Overall, the agreement between zero points computed from different standard objects (UKIRT stars and Recillas-Cruz et al. (1990) galaxies), the agreement on the magnitude of the same object observed in different nights and the consistency of the photometry of the same object in the various individual 30 s exposures, all these facts suggest us that the zero point error in our photometry is very unlikely to be systematically worse or variable more than 0.02 mag.

Figure 6: A zoom on a few objects. Faint galaxies in the lower panels have $H\sim 17$

3.8 Mosaicking

The images were mosaicked using the task imcombine under IRAF. Files containing the flux scaling, the background value, and the relative offsets were given in input. The task gives in output the composite image, the image of the measured dispersion among the input images, the number of pixels used (i.e. the exposure map in units of 30 s). The expected variance of the composite image has been computed from these quantities, assuming standard laws for the propagation of errors.

The task imcombine has a number of tunable parameters whose setting affects the results. Since we split the desired exposure time into shorter exposures, we composited the images by averaging the fluxes measured in the different images, as we would have done if ideal conditions (low sky flux, perfect NICMOS-3 cosmetics, good telescope tracking) were met. We allowed the exclusion of up to 2 values for each sky direction in order to remove cosmic rays and transient hot pixels. We verified that other schemes (such as taking a median, or a sigma clipped average possibly centered on the median, etc.) do not conserve the flux of the objects within our images (many objects are sufficiently exposed, even when for only 30 s, for accurately measuring their magnitudes and comparing them with those measured on mosaicked images). The reason is that the average of a distribution has the useful characteristic, by definition, to be equal to the integral of the distribution divided by the number of data points. The median, or any other elaborate means of computing the central location of a distribution (in particular when it is formed by a small number of points, as our one) does not have such property and therefore does not conserve the integral of the distribution (the total flux), which is the scientific interesting quantity.

In the mosaicking, we started by compositing the images on a night by night basis. We checked the relative photometry and astrometry first between the composite image and the parent single 30-s images, then among nights when possible. This careful check allowed us to detect mistakes and systematic errors: displacement errors appear in regions of particularly high sigma, when the error is small, or as regions of under-average exposure time with respect to those of the same RA, when errors are large. Photometric errors (due for example to an incorrect setting of the imcombine task), appear quite clearly, for example as a good agreement between fluxes of the same object imaged in different 30-s exposures, but as a discrepant flux in the composite image (or in the image of another night).

In the final image, the seeing is $\sim 1.7$ arcsec FWHM, of which we estimate that $\sim 0.5$ arcsec have been added during the data reduction, and with variations (0.5 arcsec) from region to region.

Figure 7: Detected objects brighter than the completeness magnitude. Crosses are stars, ellipses are galaxies. The area of ellipses is twice the 22 mag arcsec-2 isophotal area. The dashed lines delimit the regions covered by the final catalogue. Coordinates are J2000. For simplicity of display, right ascension is given as $\alpha \times 15 \times \cos 28^{\circ}$

Figure 8: Classification parameter as a function of the 10 $^{\prime \prime }$ aperture magnitude for patch1 (triangles), 0404 (circles) and 0504 (crosses)

Figure 9: Isophotal area (in arcsec2) versus isophotal magnitude (corresponding to $\mu =22$ mag arcsec-2) in the whole field studied. Objects identified as stars are shown as black stars, whereas objects identified as galaxies or unclassified objects are displayed as open circles and crosses, respectively

3.9 Astrometry

In order to provide accurate positions for the objects in our three fields, we used the astrometric catalog of the USNO version 1 (Monet et al. 1999). In the three composite near-infrared images there are significant (>2 arcsec) astrometric distortions (i.e. significant deviations from a linear relation between relative positions measured on our composite images and the actual positions on the sky). Therefore, we first established an approximate conversion from the positions of the objects in our three fields to the USNO using the task geomap in IRAF. We projected our field (represented as in Fig. 7), with the appropriate shifts in RA and DEC, on a red image of the field, taken from the Second Digitized Sky Survey (hereafter POSS-II). Then, we associated objects having similar sizes, ellipticities, position angles and sky positions in our Fig. 7 and on the POSS-II. Most near-infrared objects fall within 2 arcsec of their optical counterpart. Finally, we adopted as coordinates for the near-infrared objects the POSS-II coordinates of the corresponding optical objects (which correspond to epoch 1993.4, date of the POSS-II plate) and precessed them to J2000 using the USNO catalog. The final accuracy of the absolute position is 1 arcsec, given by the quadratic sum of the accuracy of the USNO and the scatter observed in the conversion from POSS-II to USNO coordinates.

A few ($\sim10$) objects, out of $\sim300$, are fainter than the limiting magnitude of the POSS-II, and their positions are therefore accurate to a few arcsec.

3.10 Detection & completeness

For the tasks of detection and photometry, we applied Sextractor (version 2) (Bertin & Arnouts 1996) to our images and rms map. To be detected, objects should have 9 pixels brighter than $1\sigma$ on both the filtered (by a Sex standard "all-ground'' convolution mask with FWHM = 2 pixels) and the unfiltered image.

Inside each field, the exposure time and the noise properties do not change enough to affect the probability of detection of the objects considered in this paper, except near the edge of the field, a region which is hereafter excluded from the analysis. The final useful area is 380 arcmin²; the region exluded because on the border is $\sim40$ arcmin².

Figure 10: Residual magnitude vs. magnitude diagrams for patch1 (triangles), 0404 (circles) and 0504 (crosses) for objects brighter than the H10'' completness magnitude. The scatter is due to variety of surface brightness radial profiles of objects in the studied region. Note that Kron and H10'' magnitudes are quite similar at $H_{10''}\sim 14$

The completeness was computed in each field as described in Garilli et al. (1999). In brief, objects are detected when their central surface brightness (not their magnitude) is brighter than the detection threshold. Objects with a given central surface brightness may have different magnitudes. The completeness magnitude at a given central brightness is taken as the brightest magnitude of the objects having such central surface brightness (see Fig. 4).

Detected objects in the last half-magnitude bin have typically $S/N\sim5$ (see Fig. 5). A note of caution: due to the large number of operations performed on the data and the complex way we do it, magnitude errors could be non strictly poissonian (or Gaussian) in nature, and therefore it could happen that the error distribution has broader wings than a Gaussian.

Table 2 shows the completeness magnitudes for several types of magnitudes.

 

 

Table 2: Nominal completness magnitudes

type	patch1	0404	0504
mag $_{{\rm iso}}$	17.2	16.9	17.2
mag $_{{\rm kron}}$	17.2	17.0	17.2
mag5''	17.4	17.2	17.4
mag10''	17.1	17.0	17.2
mag13''	16.9	17.8	17.9
mag14.5''	16.8	16.8	16.8
mag18.5''	16.5	16.5	16.5