2 Data sources and analysis procedures

2.1 The radio data

In anticipation of the deep ROSAT exposure of the NEP, 1.5 GHz continuum observations of a region of 29.3 square degrees centered on the NEP were carried out with the NRAO Very Large Array in 1990 and 1991. One hundred fourteen contiguous fields were observed in the C configuration giving an effective resolution around 12$^{\prime\prime}$. The survey is sensitive to 1-2 mJy, with the value dependent on location with respect to the field centers and field exposure times. A catalog of 2435 sources was generated, with total flux densities ranging from 0.3 to 1000 mJy and positions for most objects accurate to at least 2$^{\prime\prime}$. The catalog and the survey methodology are given by Kollgaard et al.(1994), and the individual fields are displayed by Hertz et al.(1994). This survey was several fold more sensitive, and produced an order of magnitude more sources, than previous radio surveys of the NEP region (e.g. Loiseau et al.1988; Lacy et al.1992; Lacy et al. 1995 and references therein), with sensitivities similar to the recent NVSS (Condon et al.1998) and FIRST (Becker et al. 1995) VLA surveys.

2.2 The optical data

Optical candidates of RASS-VLA sources, their magnitudes and morphological classifications (starlike or galaxy) were selected primarily from a catalog of objects obtained from COSMOS scans of the second Palomar Observatory Sky Survey (POSS-II) plates provided by W.L.W. Sargent (CalTech). The catalog was created through a collaboration between the Naval Research Laboratory (NRL) and the Royal Observatory, Edinburgh (ROE) in support of the ROSAT mission (Yentis et al.1992). Three blue (IIIa-J and GG395 filter) plates (PSIIJ071, PSIIJ102, and PSIIJ103) and two red (IIIa-F and RG610 filter) plates (PSIIF070 and PSIIF103) were available for candidate selection. Since the red plates covered only about two-thirds of the region of the RASS-VLA survey, they were used mainly in cases of ambiguous classification of sources. Typical limiting magnitudes of the POSS-II plates are $B\rm _J = 22.5$ mag and $R\rm _C = 20.8$ mag; the variation from plate to plate is $\pm 0.4$ mag (Reid et al.1991). Standard star calibrations of individual plates yield photometric accuracies of a few tenths to 0.5 mag. However, resolved and/or bright objects pose certain problems and discrepancies with published magnitudes can exceed these values. The star-galaxy separation is expected to be reliable to a limit of $B \sim 21.0-21.5$ (MacGillivray & Stobie 1984), although bright nearby galaxies pose special problems for the recognition of and integration over their full extent. Magnitudes for brighter objects were obtained from the NASA Extragalactic Database (NED) when available. Astrometric calibration of COSMOS-scanned plates is performed with the FK4 catalog; a conservative estimate of the positional accuracy is 1$^{\prime\prime}$ (MacGillivray, private communication).

Additional candidates, magnitudes and classifications were selected from a catalog of objects obtained from POSS-I O and E plates digitized with the Automatic Plate Measuring (APM) machine at 1.0$^{\prime\prime}$ resolution (McMahon 1991). The catalog was provided to us by R.G. McMahon. We initially consulted the APM catalog to fill in a small survey region covered only by a POSS-II red plate. Although the APM catalog is not as deep as the COSMOS catalog, we found the APM catalog to be more consistent with published magnitudes and have used this to calibrate the magnitudes from the COSMOS plates (Sect. 3.2). The photometric accuracy of APM magnitudes is approximately $\pm 0.5$ mag (Laurent-Muehleisen et al.1996; Gregg et al.1996; see also McMahon & Irwin 1992).

2.3 The X-ray data

The ROSAT All-Sky Survey (RASS) was conducted with the Position Sensitive Proportional Counter PSPC-C on board ROSAT continuously between August 1990 and February 1991. The mission and the instrument are described by Trümper (1983), Pfeffermann et al. (1986), and Aschenbach (1988). A preliminary source list (RASS-I processing) has about 60000 sources (Voges 1992). In recent correlations of this list with radio catalogs (Brinkmann et al.1994, Papers I, II) X-ray data were used which were processed in single 2$^\circ$ survey strips. In this paper we utilize data summed up over the whole mission in the NEP region. The accumulated data were organized in nine 3$^\circ \times$ 3$^\circ$ fields centered on the NEP.

  

Figure 1: Average Survey exposure in sec for the central field centered on the NEP as function of the radial distance from the geometrical center of the Survey exposure map

The exposure ranged from $\sim$ 40000 s near the NEP to $\sim$ 5000 s $\sim 4.5^\circ$ off the NEP. In Fig. 1 we show the radially averaged exposure map of the central region around the NEP. The exposure times are corrected for instrumental vignetting and deadtime effects centered $\sim 3.5'$ north of the nominal position of the NEP. Although the exposure is not exactly rotationally symmetric due to missing Survey strips, the curve clearly shows the arcsin (1/cos$\lambda$) behaviour at larger distances from the NEP, modified by the shadowing of the PSPC's support grid and the non-uniform detector sensitivity. The local minimum at the center is caused by the continuous crossing of the central support grid and broadened by the slight offsets of the satellite orbit after scan reversals. This "exposure hole" can be seen in Fig. 2 where we plot a smoothed grey scale image of the central $\sim 3^\circ \times 3^\circ$ region around the NEP. The image demonstrates the high density of X-ray sources in the inner field and shows the slight asymmetry of the exposure.

  

Figure 2: ROSAT broad band photon image of the central $\sim 3^\circ \times 3^\circ$ of the NEP field. Clearly visible is the slightly non-circular structure of the central parts and the "exposure hole" 3.5$^\prime$ north of the NEP

2.3.1 Source detection

A catalog of X-ray positions and count rates was constructed from a source detection procedure built on standard commands available in the EXSAS environment and applied to each of the nine fields (Zimmermann et al. 1994). Two preliminary source detection procedures were used to generate locations of probable sources, which were used as input into a maximum likelihood procedure for the production of final source lists and properties.

1.

A local detection algorithm was applied to the images with a binsize of 24$^{\prime\prime}$ using broad band (0.1-2.4 keV) and hard band (0.5-2.0 keV) photons. This method counts photons in a sliding window adjusted to the size of the point-spread function, with background measured in the neighbouring pixels. The significance of excesses was measured with a likelihood ratio assuming Poisson statistics. A source was accepted for a likelihood ratio greater than 5, which roughly corresponds to a Gaussian sigma of 2.3. See Cruddace et al.(1988) for a fuller description.

2.

A global detection algorithm was developed as follows. Broad and hard band background images were created by cutting out sources found in step 1 with a likelihood ratio greater than 10 ($\sim 4.5~\sigma$) from the images and applying a bi-cubic spline fit to the residuals after dividing by the exposure map to correct for vignetting. The resulting fit, re-multiplied by the exposure image, provides background values for a sliding window source detection algorithm as described above. A source was accepted for a likelihood ratio greater than 5.

Four source lists were made by applying these two methods to the photon event data in the hard and total bands. The source lists were combined by merging sources lying within $3 \sigma$ positional errors and for overlaps in a circle with a diameter equal to the FWHM of the point-spread function (60$^{\prime\prime}$ for the Survey), taking into account the possible extent (see Zimmermann et al.1994, Sect. 5.2 for details). Source fluxes were measured in the two bands within a 5$^\prime$ radius. Comparison of fluxes for sources in overlapping fields indicate that systematic errors of order 10% may be present in stronger sources, and larger errors for weak sources. Source lists and positions may also be incorrect in unusually crowded regions or for complex extended structures.

  

Figure 3: Distance in arcsec between the same sources found from the total detector and the inner part only for the central $3^\circ \times 3^\circ$ field

  

Figure 4: Count rates of the same objects as found from the total detector and the inner part only

For most of the RASS it has been shown that the highest signal-to-noise is achieved with the full field of view of the detector for the source detection algorithm, even though the point spread function of the X-ray telescope degrades rapidly in the outer regions of the PSPC detector (Aschenbach, private communication). However, in regions of high source density like the NEP, the degraded point spread function causes an increase of the background flux through source confusion. We therefore repeated the source detection procedure for the deep central 3$^\circ \times$ 3$^\circ$ NEP field using only photons from the inner part ($r_{\rm det} < 20$$^\prime$) of the PSPC where the point spread function is uniform and narrow ( 30$^{\prime\prime}$). Although this reduces the exposure by 2/3 compared to the analysis using the full detector, we found that the number of sources increased from 266 sources to 583 sources when only the inner detector is used. The density of sources at the center of the field reaches $\simeq$100 sources/square degree.

We have compared source properties obtained using the whole PSPC and the inner detector alone. Figure 3 shows that positional offsets are generally less than 10$^{\prime\prime}$; exceptions are due to extended sources. We conclude that the internal accuracy of source positions is about $\sim\!5$$^{\prime\prime}$ for unresolved sources. Even after accounting for systematic errors the accuracy should be better than the $\sim$ 18$^{\prime\prime}$(68% level) found for the whole RASS (Voges et al.1996) due to repeated exposure of the NEP region during the survey. For many sources, the inner detector analysis yielded more source photons, increased likelihood values and higher count rates (Fig. 4). The improvement is most pronounced for weaker sources. Outliers are again due to extended sources, indicating that source properties for these sources are highly dependent on the particular data analysis path chosen.

The result of our analysis, using the inner detector for the central 3$^\circ \times$ 3$^\circ$ field and the full detector in the remainder of the 9$^\circ \times$ 9$^\circ$ region around the NEP, is the detection of more than 1700 sources. Due to the higher exposure, the central field contains 583 of these sources.

2.3.2 Spectra and fluxes

Only 18 sources have sufficient photons to permit direct estimation of the X-ray spectra. These spectra are discussed in Sect. 2.3.3. To estimate source fluxes for the remaining sources, we follow the analyses in Papers I and II and assume a power law spectrum with photon index $\Gamma = 2.1$ and galactic absorption $N\rm _H$ (Dickey & Lockman 1990) in the direction of the source. $N\rm _H$ varies relatively smoothly even on shorter angular scales (Elvis et al.1994). The unabsorbed X-ray fluxes in the ROSAT band $f_{\rm 0.1-2.4\ keV}$ are computed using the source count rates and the energy-to-counts conversion factor for a power law fit (ROSAT AO-2 technical appendix, 1991). The resulting fluxes will be inaccurate for sources with intrinsic absorption, different power law or complex spectra. We report here only errors due to the counting statistics.

Fluxes for sources in the inner field can be compared with those found by Bower et al.(1996) in their pointed observations. They report fluxes assuming a power law index of $\Gamma = 2.0$ and a narrower (0.5 - 2 keV) energy interval, giving a systematic reduction factor of $\sim$ 0.4 compared to our values. Taking this into account, we find excellent agreement between the fluxes in most cases, indicating consistency between the data analyses for pointed observations and the approach followed here.

2.3.3 X-ray bright objects

Eighteen of the RASS sources in Tables 1-3 have >100 photons, allowing simple spatial and spectral fitting of the PSPC data. Note that in some cases the objects are in crowded fields or in regions with strongly changing exposure so that the background subtraction may not be accurate. Table 4 presents the results of spectral fits using a power model with Galactic column densities. The columns give the source name, the number of vignetting- and deadtime-corrected counts, the fitted power law photon index with its 1$\sigma$ error, the reduced $\chi^2$ for the fit, a likelihood parameter ML$_{\rm ext}$ that increases with the probability that the source is spatially extended, and remarks. In most cases the photon index is consistent with the expected $\Gamma = 2.1$(Sect. 2.3.2), albeit with large statistical errors.

 

Table 1: Compact X-ray/radio sources in the NEP

 

Table 2: Extended X-ray/radio sources in the NEP

 

Table 2: continued

 

Table 2: continued

 

Table 3: Possible additional X-ray/radio sources in the NEP

 

Table 4: Power law fits to strong sources