2. WENSS

2.1. Mosaicing

Interferometry with an east-west array uses the Earth's rotation to sample visibilities over complete elliptical loci in the spatial frequency (u,v) plane. 12 hours are normally required to image a single field. Given the small primary beam ( HPBW at 92 cm) of the WSRT, mapping of large areas of sky in this way is prohibitively time consuming. However, at the price of a decrease in sensitivity, a reasonable synthesized beam can be obtained by observing a single field for considerably less than these 12 hours, provided the visibilities are sampled for several short integrations, regularly spaced throughout a 12 hour observation. By cycling through a regular grid of pointings and observing each field intermittently, a relatively large area of sky can thus be mapped efficiently. This ``mosaicing'' technique was implemented as a standard observing mode at the WSRT in 1990 (Kolkman 1993) and has been used to construct WENSS.

WENSS utilizes mosaicing patterns of approximately 80 fields, covering about 100 square degrees. Using an integration time of 20 seconds and a slew time of 10 seconds this results in 18 ``spokes'' per field, per single 12 hour synthesis. For the 92 cm observations, six different telescope configurations are combined for a total of 108 spokes per field. The configurations are defined by the separation between telescope ``9" and telescope ``A", which are: 36, 48, 60, 72, 84, and 96 m. This results in a radial sampling of 12 m, corresponding to half the antenna diameter. This sampling strategy results in a position for the first grating ring at in right ascension and in declination. Figure 1 (click here) illustrates the u,v-sampling of a single field for an observation in mosaicing mode.

  
Figure 1: u,v coverage for a mosaic observation with 108 spokes, resulting from a combination of 18 spokes from 6 array configurations (12 meter increment). The scale is for a wavelength of 92 cm and for clarity the tracks are shown for an observation at

In order to cover the sky north of declination , the sky was divided into four zones. Three zones are centered on declinations of , , , with a different mosaic pattern used in each zone. The layout of these WENSS mosaics is displayed in Fig. 2 (click here). The polar cap, the fourth zone, will be discussed elsewhere.

  
Figure 2: Layout of the WENSS mosaics currently (March 1996) observed and processed. The five darker shaded mosaics comprise the mini-survey described later in this paper. The symbols mark strong (3C) radio sources. Lines of constant galactic latitude (, , and ) are indicated

An optimal trade-off between uniform sensitivity and efficiency would be obtained with a grid of fields with a regular spacing between fields that is equal to the half-power width of the primary beam (HPBW). Technical considerations require a pattern of fields on a grid with an hour-angle separation in right ascension that is constant. At low declination we therefore use grid patterns for the mosaics that are simple rectangular grids of fields. At a declination of this would lead to a somewhat less efficient pattern since the actual spacing between adjacent points of constant RA decreases rather rapidly. This leads to the more complicated pattern of Fig. 3 (click here). At high declination the grid-separation in right ascension in this pattern is doubled. This is the pattern used by the mosaics that cover the mini-survey. The grid spacings in the three declination zones are listed in Table 2 (click here).

   

Declination zone Grid pattern

6.60 1.33

8.18 1.33

12.74 1.33

  
Figure 3: The field pattern for the mosaics. In this case the pattern for mosaic WN66-255 is shown. The field are numbered according to the sequence of observation. Missing numbers refer to so-called ``moving'' pointings, inserted to bridge large field separations

2.2. Observations

Observations for WENSS were carried out with the WSRT in a standard set-up. The mosaicing mode described previously prescribed the telescope configuration for the WSRT. At 92 cm observations were carried out with the DXB backend, at a frequency of 325.125 MHz, with a total bandwidth of 5 MHz. In the winter of 1991 3 frequency channels were used. This was later changed to 7 frequency channels. The number of frequency channels has no notable influence on the quality of the maps.

2.3. Reduction

Mosaics were calibrated and reduced using the WSRT reduction package NEWSTAR (Netherlands East-West Synthesis Telescope Array Reduction). Initially, each field was calibrated and reduced separately in a way that is comparable to the calibration/reduction of standard 12 hour syntheses. This procedure started with the flagging of bad data and an absolute gain and phase calibration using one or more primary or secondary calibrators (3C 48, 3C 147, 3C 286, and 3C 295). A ``dirty'' map was then made by a Fast Fourier transform (FFT) of the visibility data. The brightest sources from this map were selected and used to construct a first model. For this model the predicted visibilities were determined and subtracted from the visibility data. On the predicted visibilities we performed a phase-only self-calibration, which was then used to correct the residual visibility data. From the residual visibility data a new map was constructed and additional components for the model were extracted. The improved model was again used in a phase only self-calibration. This process was repeated a third and final time. (Wieringa 1991a). This process removes the time-dependent phase errors caused by the ionosphere. These phase errors are the dominant source of error deforming the sources. Only for fields with very strong (more than a few Jy) sources we also did a phase and gain self-calibration. (Wieringa 1991a).

Since, at low frequency, the ionosphere introduces substantial absolute phase errors that are not corrected for in the self-calibration, each field can have an absolute position uncertainty of typically 5''. The positions of each field within the mosaic were therefore corrected using a system of secondary position calibrators from the JVAS survey (Patnaik et al. 1992), combined with calibrators whose positions were obtained through pointed 21 cm WSRT observations. These latter calibrators were included to obtain a more uniform distribution of calibrator sources over the sky. Fields that did not contain position calibrators were tied into this system using additional strong sources that were present in adjacent overlapping fields.

In the final step of the reduction process, the individual fields were combined into a single mosaic. To do this the self-calibrated model-subtracted visibility data of all fields in a mosaic were Fourier-transformed onto the same reference grid. The residual maps were cleaned, using the CLEAN algorithm (Högbom 1974) and corrected for selfcal bias (Wieringa 1991a). The model and the clean-components were restored using a Gaussian restoring beam with a full-width at half maximum (FWHM) of (at 92 cm). The maps of the individual fields were then added using a weight that is proportional to the sensitivity of each field at that position in the mosaic (i.e. inversely proportional to the square of the attenuation of the primary beam)

The reduction steps described here apply to the total intensity maps. The polarization maps require additional calibration steps that will be discussed elsewhere.

2.4. Frame production

From the mosaics, we made maps with a uniform sensitivity and a regular size. We call these maps frames. These frames were constructed in the same way as the maps for the mosaics, but can incorporate fields from different mosaics.

The 92 cm frames are degree in size, and positioned on a regular degree grid over the sky. This grid coincides with the position grid of the new Palomar Observatory Sky Survey (POSS) plates. All frames have a standard pixel format, and use the WSRT-specific north-polar cap (NPC) projection. This projection is defined by the following relation between the pixel (x,y) and celestial coordinates ():

with the reference pixel , and the pixel size pix, the same for all 92 cm frames. The reference position is given in B1950 coordinates.

2.5. Source extraction

A procedure to extract a list of discrete radio sources from a frame was written in IDL, the Interactive Data Language.

The procedure starts with obtaining the noise level at each point in the map, by interpolating the rms-noises for a regular grid of fields (size: pixels) within the map. A minimization fit of a Gaussian to the intensity distribution establishes an rms-noise level for each of these fields. We then use the following, recursive, definition of a source, based on the appearance of a distinct ``island'' of detected brightness in the map:

Given a pixel of intensity , the set of all the pixels that are adjacent to either this pixel, or another pixel within this set, constitutes an island. This island we call a source. To obtain a more realistic estimate of the integrated flux, taking account of the noise, all pixels directly adjacent to this set are added to the island.

A local maximum is defined as a pixel whose intensity is larger than all eight surrounding pixels. Based on the number of local maxima within the island, we distinguish: single-component (``S") sources, with 1 local maximum, multiple component (``M") sources, with 2-4 local maxima, and extended (``E") sources, with more than 4 local maxima.

The relevant source parameters are: position (x,y), peak and integrated flux density (S,SI), the size of the major and minor axes (FWHM, ), and the position angle (). For each source, these parameters are first computed from the brightness distribution using weighted moment analysis, with the peak flux , and the integrated flux , with the , and and the FWHM of the major and minor axis of the restoring beam. The remaining parameters are computed from the weighted first and second order moments:

with: , , , and the eccentricity . and are solved from the eccentricity and the ratio .

An attempt is made to fit an ``S" or ``M" source with a model consisting of a number of elliptical Gaussians equal to the number of local maxima. The Gaussians are parameterized by:

   

Mosaic Mosaic center (B1950) Epochs of observation (yymmdd)

Right Ascension Declination 36 m 48 m 60 m 72 m 84 m 96 m

WN66_217 930201 930131 940416 930102 930128 930126

WN66_236 920112 920214 930109 911201 911215 911222

WN66_255 910216 910223 910311 910114 910205 910208

WN66_274 910217 910224 910302 910120 910202 910209

WN66_293 910218 910225 910303 910329 910201 910210

   

Frame Map Center (B1950)

RA Dec WNH60_218 WNH60_228 WNH60_237 WNH60_247 WNH60_256 WNH60_266 WNH60_275 WNH60_285 WNH60_294 WNH65_220 WNH65_231 WNH65_242 WNH65_253 WNH65_264 WNH65_275 WNH65_286 WNH65_297 WNH70_221 WNH70_234 WNH70_247 WNH70_260 WNH70_273 WNH70_286 WNH70_299

The fitting-algorithm is based on the Levenberg-Marquardt algorithm from Numerical Recipes (Press et al. 1992). The parameters from these fits are converted to position, flux densities, major and minor axis and position angle and used to describe the source. If the algorithm fails to properly fit a source are the values from moment analysis used to parameterize the source. The values from moment analysis are also used for ``E" sources. For ``M" sources as a whole the position and morphology are established through moment analysis, while the peak flux density is the maximum of the peak flux densities of the components and the integrated flux density is the sum of the integrated flux densities of the components.

We find that the estimates of the flux densities and the source morphology are affected by biases at low signal-to-noise ratios. We therefore apply empirical corrections to the flux-density estimates. These corrections are discussed in Sect. 3.4 (click here).