4 log(N)-log(S)

As the residual systematic errors after the application of these astrometric corrections are below the width of the point-spread function, we could co-add the images of the different cameras. Combined PN+MOS1+MOS2 images were accumulated in the bands 0.2-0.5 keV, 0.5-2 keV, 2-4.5 keV and 4.5-10 keV, respectively. Figure 2b shows the exposure-corrected image of all cameras combined in an X-ray ``real-colour'' representation. The red, green and blue colours refer to the 0.5-2, 2-4.5 and 4.5-10 keV images, respectively. A population of green and blue objects is showing up in this image, i.e. obscured faint X-ray sources which have been postulated by the X-ray background population synthesis models. There are several diffuse sources with red colours which are X-ray clusters of galaxies already identified from the ROSAT data (Schmidt et al. 1998; Hasinger et al. 1998b; Thompson et al. 2000).

The SAS source detection algorithms have been applied to the data. These are an improved variant of the ROSAT source detection algorithms described in Hasinger et al. (1998a) consisting of simple sliding window box detection algorithms, using either a local background estimate (LDETECT) or a background map derived from the images smoothed by a bi-cubic spline function after bright sources have been removed (MDETECT) as well as a multi-ML source detection and parameter estimation task. The main improvement for the XMM data is, that these algorithms are run simultaneously for several independent energy bands, keeping the source positions and extent fixed for all energy bands, while adding the source existence likelihoods from the individual energy bands together. This improved algorithm is both more sensitive and less subject to source confusion and yields source count rates in all energy bands.

Source detections were accepted with likelihood values above 10 (about 4$\sigma$) and inside an off-axis angle of 10 arcmin. The resulting detection statistics are given in Table 2. The raw source count rates have been converted to X-ray fluxes by applying a correction for vignetting (up to a factor of 2 at an off-axis angle of 10 $\hbox{$^\prime$ }$) and dead time plus out of time events (assumed to be 8% for the combination of all three detectors) as well as the counts-to-flux conversion factor (ECF) according to Table 2. The average energy conversion factors for the whole observation have been computed using the most recent response matrices weighted with the respective exposure times for the three different detectors. The vignetting function has been assumed to depend linearly on off-axis angle, while the azimuthal dependence expected for the MOS cameras has been ignored. Due to the still preliminary status of the current EPIC calibration and the simplifying assumptions made here we have to assume systematic flux errors on the order of 10% in addition to the uncertainty due to the range in possible photon indices (see Table 2).

   

Table 2: Detection results for different energy bands

Banda	$\Gamma$b	ECFc	$S_{\rm lim}$d	$N_{\rm src}$e	N(>S)f
0.2-0.5	$2.0\pm0.5$	$7.16\pm1.01$	0.40	120	1380
0.5-2	$2.0\pm0.5$	$10.20\pm0.04$	0.31	148	1800
2-10	$2.0\pm0.5$	$1.79\pm0.40$	1.4	112	1400
5-10	$1.6\pm0.5$	$1.28\pm0.11$	2.4	61	1060

^a Energy band in keV in which the flux is given (see text).

^b Assumed range in photon index.

^c Energy conversion factor in cts s^-1 per $10^{-11}~{\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$.

^d Minimum detected flux in $10^{-15}~{\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$.

^e Number of sources detected within 10 arcmin radius.

^f Source density in deg^-2.

The corresponding cumulative log(N)-log(S) distributions are shown in Fig. 3. In the soft band (0.5-2 keV) the data reach a flux limit about a factor of three deeper than the ROSAT HRI survey (Hasinger et al. 1998a), and are about 50% less sensitive than the recent Chandra surveys (Mushotzky et al. 2000; Giacconi et al. 2000). In the 2-10 keV band the XMM data are as deep as the published Chandra surveys. In the very hard 5-10 keV band, which has been pioneered by the BeppoSAX observations (Fiore et al. 1999), XMM is entering new territory, reaching more than a magnitude deeper than BeppoSAX. As described above, the flux conversion still has to be regarded as uncertain by at least 10%. Also no corrections for confusion or Eddington biases have been made yet (see e.g. discussion in Hasinger et al. 1998a). Nevertheless, the comparison of the XMM source counts with the Chandra and ROSAT data, in particular in the 0.5-2 keV band, indicates that confusion is not a severe problem for the source counts.

Figure 4: X-ray spectral diagnostic diagrams based on hardness ratios (see text). The symbols refer to different classes of objects detected in the XMM deep survey of the Lockman Hole: filled circles are type-1 AGN spectroscopically identified in the ROSAT ultradeep HRI survey (Lehmann et al. 2001), open circles are type-2 AGN, correspondingly. Open squares are clusters or groups of galaxies and plus signs are spectroscopically not identified ROSAT sources (most likely type 2 AGN, see Lehmann et al. 2000) with photometric redshifts. Open diamonds refer to the newly detected XMM sources. Two representative error bars are shown; for clarity only sources with hardness errors less than 0.1 are plotted. The grid gives the expected hardness ratios for power law models with photon indices $\Gamma =$ 0, 1, 2 and 3 (dashed lines) and neutral hydrogen absorption (in the observed frame) of $\log N_{\rm H}$ between 20 and 23 in steps of 0.5 (solid lines)