2 Observations and data analysis

2.1 Observations

Our wide-field, medium deep surveys carried out with the 3.5-m telescope on Calar Alto, Spain in two observing runs from July 21-25, 1993 and August 6-8, 1994. During both campaigns the telescope was equipped with a TEK CCD (CA #7) in the prime focus. The CCD has $1024\times 1024$ pixels with an image scale of $0.403''/{\rm pixel}$. The coordinates of the NEP and other field parameters important for survey work are given in Table 1. To cover the central square degree around the NEP with the field of view (FOV) of $6.9\times 6.9~{\rm arcmin}^2$, an equally spaced grid of $9\times 9$ and $10\times 10$ exposures was taken in B_j and R, respectively. The exposure times of the individual frames are $10~{\rm min}$ in B_j and $6~{\rm min}$ in R. In order to obtain homogeneous photometry over the whole field we carried out a snapshot survey in both bands with short exposure times and a large field of view in photometric conditions. For this purpose we used the 2.2-m telescope on Calar Alto with the focal reducer CAFOS (Meisenheimer 1996). Together with the SITe CCD (CA #1) CAFOS has a circular FOV with $13~{\rm arcmin}$ diameter and $0.531''/{\rm pixel}$. In each band the snapshot survey was performed on a grid of $4\times 4$ exposures with integration times in B_j and R of $3~{\rm min}$ and $2~{\rm min}$, respectively. Although the snapshot survey does not cover the complete field of the deep exposures, there is sufficient overlap with every frame of the deep survey to define a common photometric zeropoint.

All data were obtained using the so-called Röser-BV and Röser-R2 filters. The Röser-BV filter ( $\lambda_{{\rm center}}=497.7~{\rm nm}$ and $\Delta \lambda = 155.9~{\rm nm}$) is similar to the B_j filter (see Gullixson et al. 1995). The Röser-R2 (see Röser & Meisenheimer 1991) avoids the strong OH emission lines at $\lambda > 760~{\rm nm}$, which contaminate the standard Rfilters, with a sharp cutoff at $740~{\rm nm}$.

In both surveys the median value of the full width at half maximum (FWHM) of the point spread function (PSF) is 1.5''.

2.2 Standard reduction

The single raw frames were de-biased and flat-fielded. For every observing run a bias frame was constructed using frames with an integration time of 0 s, taken with closed CCD-shutter.

A "super-flat-field'' in each band was obtained by using all exposures taken in that filter. The de-biased exposures were normalized and the super-flat-field was computed from the median of the data values in every pixel.

Dark-subtraction could be neglected since none of the CCDs displayed significant dark-currents.

2.3 Photometric calibration

Photometric calibration was obtained by observing several standard fields from Christian et al. (1985) and Odewahn et al. (1992). The B-magnitudes of the stars listed there were transformed to B_j using the equations given by Gullixson et al. (1995).

We observed standard fields at different airmasses in all nights when the snapshot survey was carried out. Instead of computing a zeropoint for every exposure of the snapshot survey from the extinction curve individually, we used the large overlap between adjacent frames to enhance the homogeneity of the photometry. In every overlap region bright, unsaturated stars were identified in each pair of neighboring exposures to determine the differential zeropoint between the two exposures. Following the method developed by Glazebrook et al. (1994) this system of differential zeropoints for every overlap was then transformed to a single differential zeropoint for each exposure. In photometric conditions those differential zeropoints of the exposures originate from different extinction, hence extinction correction is done explicitly. We computed the absolute zeropoint of every exposure by adding a constant value, which was determined from $\chi ^2$-minimization of the differences between the zeropoints computed differentially and the zeropoints derived from the extinction curve.

The zeropoints from the snapshot survey were then transferred to each field of the deep survey individually, using several stars in each case.

While we did not find a significant colour term for the Röser-R2 filter, the transformation

 

B_j = b+0.23*(B_j-R) (1)

was applied to convert the instrumental magnitude b to B_j.

   
2.4 Object detection and photometry

Object detection, photometry and morphological classification was carried out with FOCAS (Valdes 1994; Jarvis & Tyson 1981). The reliability of the detection process was extensively tested on simulated images generated with the iraf-package noao.artdata. As in Paper I, the threshold parameters were chosen such that only <1% of the objects found in the artificial images were not real objects, resulting in a reliability of >99% for the detected objects. This was achieved by setting the FOCAS parameters such that after a convolution with the FOCAS built-in digital filter, at least nine connected pixels are required to have intensities $\ge$2.8$\sigma$ to be recorded as an object.

Similar to Paper I we used the FOCAS-total flux $L_{{\rm total}}$ and the flux measured in an aperture $L_{{\rm lfca}}$ for bright and faint sources, respectively (see Paper I for a detailed discussion). The transition from $L_{{\rm total}}$ to $L_{{\rm lfca}}$ was chosen at an object size $\le$28  ${\rm arcsec}^2$. For those objects the flux $L_{{\rm lfca}}$ was measured in the corresponding aperture of 6'' diameter.

   
2.5 Morphological classification

The morphological classification into point-like and extended sources was done in both the B_j- and the R survey. It is based on the FOCAS-resolution classifier (Valdes 1982). This classifier fits a series of templates, which are basically derived by scaling the width of the image PSF to each object. The scale of the best fitting template is then a measure of the resolution of the object and the classification is made from this scale value.

Like every classifier based on the object shape, the FOCAS-resolution classifier does not give reliable results for sources near the completeness limit. Towards lower signal-to-noise ratios the extended parts of galaxies progressively vanish in the background noise. This leads to a misclassification of extended sources as point-like objects. This misclassification affects sources closer than $1.5~{\rm mag}$ to the completeness limit.

Point-like sources are stars, distant quasars, and nuclei of galaxies at low and intermediate redshift which have steep luminosity profiles such that the width of the nuclear profiles down to the level of sky noise is significantly smaller than the PSF. Down to our levels of completeness, the surface density of quasars is about $85~{\rm deg}^{-2}$, which is more than an order of magnitude lower than the density of stars according to the Bahcall-Soneira (Bahcall & Soneira 1980; Bahcall 1986; Mamon & Soneira 1982) model of the Galaxy. Nucleated dwarf galaxies, such as M 32, would be included in our survey out to distances of $200~{\rm Mpc}$. The scale length of the nucleus would be 0.2'', and the surface brightness of the extended emission would be lost in the sky noise. Such nucleated dwarf galaxies would be classified as point-like sources for 90% of the volume sampled. It is still unlikely, that dwarf galaxies present a significant contribution to the point-like sources, since our survey only includes one major galaxy out to the distance of 200 Mpc. The majority of point-like objects that are not stars are distant galaxies with small angular size. In the Hubble deep fields (HDF, HDFS) 12% of all extended objects down to $R=23~{\rm mag}$ have scale-length that would render them unresolved at our resolution. At brighter magnitudes this ratio cannot be determined reliably due to small number statistics.

To derive the number counts of extended objects we used a statistical source-classification in the range of unreliable FOCAS-classification. We extrapolate the number-counts of bright point-like sources by assuming ${\rm d}\log N/{\rm d}m=const$ and compute the number of extended objects by subtracting the expected number of point-like sources from the total number of objects. To test the assumption for the statistical classification we computed the number of stars expected according to the Bahcall-Soneira model in B_j and R. Figures 1 and 2 display the number counts of point-like sources in B_j and R as open circles. Shown as a solid line are the counts expected for the Bahcall-Soneira model. There is a good agreement between the theoretically expected number of stars and the detected number of point-like sources in the range of reliable classification. We actually detect more point-like sources than expected, confirming a contribution of up to ten percent of unresolved galaxies to the list of point-like objects. For the stars no significant change in ${\rm d}\log N/{\rm d}m$down to $B_j=24.25~{\rm mag}$ and $R=23.0~{\rm mag}$ is expected in the model. This confirms the validity of the assumption in the range of unreliable FOCAS-classification and justifies our statistical classification. In the following we will treat point-sources as stars, despite the above mentioned contamination.

 

 

Table 2: The source counts in B_j

Filter	mag	$N_{{\rm gal}}$	$\sigma_{N_{\rm gal}}$	$N_{{\rm star}}$	area
Bj	14.625	1.00	1.00		1.0
	15.125	1.00	1.00		1.0
	15.625	1.00	1.00		1.0
	16.125	0.00	0.00		1.0
	16.625	5.02	2.25		1.0
	17.125	8.03	2.83		1.0
	17.625	15.07	3.89		1.0
	18.125	32.15	5.67		1.0
	18.625	34.16	5.84	342.58	1.0
	19.125	59.27	7.70	389.80	1.0
	19.625	93.43	9.66	453.09	1.0
	20.125	161.74	12.72	551.54	1.0
	20.625	262.21	16.19	583.69	1.0
	21.125	404.87	20.12	693.20	1.0
	21.625	727.36	26.97	879.05	1.0
	22.125	1273.87	35.70	970.48	1.0
	22.625	2250.38	47.44	1075.96	1.0
	23.125	3885.19	62.33		1.0
	23.625	7286.75	85.36		1.0
	24.000	10775.98	146.80		0.8
	24.250	15936.32	178.52		0.3

 

 

Table 3: The source counts in R

Filter	mag	$N_{{\rm gal}}$	$\sigma_{N_{\rm gal}}$	$N_{{\rm star}}$	area
R	12.875	0.97	0.97		1.0
	13.375	0.00	0.00		1.0
	13.875	0.97	0.97		1.0
	14.375	0.00	0.00		1.0
	14.875	1.94	1.37		1.0
	15.375	3.88	1.94		1.0
	15.875	11.65	3.37		1.0
	16.375	22.33	4.66	288.70	1.0
	16.875	37.88	6.06	362.09	1.0
	17.375	45.64	6.66	393.30	1.0
	17.875	62.15	7.77	490.41	1.0
	18.375	132.07	13.03	551.59	1.0
	18.875	239.86	15.26	624.42	1.0
	19.375	390.39	19.46	757.47	1.0
	19.875	652.59	25.16	911.88	1.0
	20.375	1028.41	31.60	960.43	1.0
	20.875	1691.10	40.52	1199.05	1.0
	21.375	2460.88	48.88	1386.00	1.0
	21.875	3420.84	57.63		1.0
	22.375	5406.16	72.45		1.0
	22.875	9252.67	94.78		0.6

 

 

Table 4: The source counts in K

Filter	mag	$N_{{\rm gal}}$	$\sigma_{N_{\rm gal}}$	$N_{{\rm star}}$	area
K	7.25			1.93	0.9
	7.75			1.93	0.9
	8.25			5.78	0.9
	8.75			5.78	0.9
	9.25			6.74	0.9
	9.75			10.59	0.9
	10.25			17.34	0.9
	10.75	0.92	1.02	23.12	0.9
	11.25	0.00	0.00	46.23	0.9
	11.75	1.93	1.44	52.01	0.9
	12.25	2.89	1.76	86.68	0.9
	12.75	2.89	1.76	118.47	0.9
	13.25	15.41	4.07	182.03	0.9
	13.75	20.23	4.66	275.45	0.9
	14.25	34.67	6.11	341.91	0.9
	14.75	86.68	9.65	450.74	0.9
	15.25	112.69	11.01	549.95	0.9
	15.75	265.82	16.91	723.31	0.9
	16.25	488.31	22.91	889.93	0.9
	16.75	911.44	31.65	1093.54	0.9
	17.25	1462.21	48.96	1214.90	0.6

   
2.6 Completeness

The completeness function f is derived as described in Paper I. We fit

$$% f(mag) = \left[ \exp \left( \frac{mag-mag_{{\rm 50}}}{b}\right) +1 \right]^{-1}$$ (2)

to the normalized number counts $N(m)/\tilde{N}(m)$ to determine $mag_{{\rm 50}}$, where the number of detected object is half the expected one (as inferred from the normalization). The parameter b was found to be independent within the range of image quality experienced in our survey at b=0.26, while $mag_{{\rm 50}}$ varied in both data sets (B_j and R), reflecting the different image quality for the individual frames. We established the relationship between $mag_{{\rm 50}}$ and the basic parameters of image quality, i.e. background and FWHM of the PSF for the B_j- and the R-data independently, and used this relationship and the corresponding zeropoint to calculate $mag_{{\rm 50}}$ for every survey image. Finally the completeness limit for each image is set at $mag_{{\rm\rm compl}} = mag_{{\rm 50}}-0.6$. At this level the completeness function is $f(mag_{{\rm\rm compl}})>0.9$, and the slope-normalized number counts are indistinguishable from 1.0.

As in Paper I the completeness function f(mag) was not used to correct number counts fainter than $mag_{{\rm\rm compl}}$. However objects down to $mag_{{\rm 50}}$ were taken to match the objects found in different filters and to determine the colours of objects. This is justified since those sources in the range $[mag_{{\rm\rm compl}}-mag_{{\rm 50}}]$ which have actually been found, form a statistically selected subsample of sources detected with the high reliability of $99\%$, even if not the entire population is included. Down to $mag_{{\rm 50}}$ of the individual fields we detect $58\,500$, $53\,900$ and $13\,000$ sources in the B_j-, R- and K-survey, respectively.

Figure 1: The number counts for extended and point-like sources in Bj. The solid line is the expected star counts according to the Bahcall-Soneira model

2.7 Astrometry

To obtain a precise absolute astrometry for the detected objects the Guide Star Catalog 1.2 (GSC) was used (Lasker et al. 1990; Russel et al. 1990; Jenkner et al. 1990). There are 430 GSC-stars in the area covered by our surveys, and the number of GSC-stars per exposures ranges from 1 to 11. All GSC-stars except the brightest one (the planetary nebula NGC 6543, $m_V=9.8~{\rm mag}$) were taken to establish the astrometry. We identified the GSC-stars on the survey images and determined plate constants for every observing run and filter using gnomonic projection (see Eichhorn 1974). Using the plate constants and the position of the GSC-stars we then computed the equatorial position of every image center, and, finally, the equatorial positions of all objects found on the images.

Because of the different spacing of the exposures the position of an object in B_j and R is based on a different set of GSC-stars. The astrometry can therefore considered to be independently derived for the B_j- and the R-survey. We took advantage of this in order to compensate for the variable number of GSC-stars per image and to enhance the overall homogeneity of the astrometry. For every overlap between an individual B_j-frame B_kand an individual R-frame R_l we computed $\Delta \alpha_{kl}$ and $\Delta \delta_{kl}$, the mean offset between the B_j- and R-coordinates of bright stars in right ascension and declination, respectively. Then we derived the corrections $\Delta \alpha _{R_k}=\sum_l \Delta \alpha_{kl}$ and $\Delta \delta _{R_k}=\sum_l \Delta \delta_{kl}$( $\Delta \alpha _{B_l}=\sum_k (-\Delta \alpha_{kl})$ and $\Delta \delta _{B_l}=\sum_k (-\Delta \delta_{kl})$ for B_l) and applied them to all positions in the whole frame. This procedure was iterated once to minimize the contribution of a frame with bad astrometry to its overlaps.

We estimated the accuracy of the astrometry using bright stars in the large ($\sim$1') overlap regions between adjacent fields of the R-survey. The accuracy of the object positions was, even for the faintest sources, determined to be <0.8'' in each coordinate.

Figure 2: The number counts for extended and point-like sources in R. The solid line is the expected star counts according to the Bahcall-Soneira model

2.8 Removal of cosmic ray objects

Since most of the survey area is covered only by one frame, the usual approach to remove cosmics with weighting maps or masks (Nonino et al. 1999; Arnouts et al. 1999) could not be followed. Instead we identified sources caused by cosmic ray events and removed them from the object lists.

The criterion whether an object is real or just a cosmic ray hit is the concentration of the brightness distribution

$$% conc = 2.5*\log((Lc/9.0-ispht)/(ssbr/3.0))+mag.$$ (3)

The PSF sets an upper limit in the brightness concentration for real objects. Cosmic ray hits usually have higher values of conc, since their shape is not determined by the PSF and a cosmic ray event usually affects only a few pixels. Conc is easily derived from the FOCAS-parameters Lc (core luminosity), ispht (isophotal brightness) and ssbr (sky-noise) together with the object brightness mag (the nomenclature of the FOCAS-parameters follows Valdes 1982).

Looking at the conc-mag distribution of all objects from an individual image the locus of cosmic ray objects could be identified easily and the objects could then be removed from the lists.

Figure 3: The galaxy counts in Bj from the NEP compared to counts from various other surveys