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XMM-Newton 13H Deep ?eld - I. X-ray sources
N. S. Loaring1 ? , T. Dwelly1 , M. J. Page1 , K. Mason1, I. McHardy2 , K. Gunn2, D. Moss2, N. Seymour3, A. M. Newsam4 , T. Takata5 , K. Sekguchi5 , T. Sasseen6, 7 F. Cordova 1
MSSL, University College London, Dorking, Surrey, RH5 6NT, UK of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK 3 Institut d’Astrophysique de Paris, 98bis, Boulevard Arago, 75014 Paris, France 4 Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf, Birkenhead, CH41 1LD, UK 5 National Astronomical Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96729, USA 6 Department of Physics, University of California, Santa Barbara, CA 93106, USA 7 University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA
arXiv:astro-ph/0507408v1 18 Jul 2005
5 February 2008
We present the results of a deep X-ray survey conducted with XMM-Newton, centred on the UK ROSAT 13H deep ?eld area. This region covers 0.18 deg2 and is the ?rst of two areas covered with XMM-Newton as part of an extensive multi-wavelength survey designed to study the nature and evolution of the faint X-ray source population. We have produced detailed MonteCarlo simulations to obtain a quantitative characterisation of the source detection procedure and to assess the reliability of the resultant sourcelist. We use the simulations to establish a likelihood threshold above which we expect less than 7 (3%) of our sources to be spurious. We present the ?nal catalogue of 225 sources. Within the central 9′ , 68 per cent of source positions are accurate to 2′′ making optical follow-up relatively straightforward. We construct the N (> S ) relation in four energy bands: 0.2-0.5 keV, 0.5-2 keV, 2-5 keV and 5-10 keV. In all but our highest energy band we ?nd that the source counts can be represented by a double powerlaw with a bright end slope consistent with the Euclidean case and a break around 10?14 erg cm?2 s?1. Below this ?ux the counts exhibit a ?attening. Our source counts reach densities of 700, 1300, 900 and 300 deg?2 at ?uxes of 4.1 × 10?16, 4.5 × 10?16, 1.1 × 10?15 and 5.3 × 10?15 erg cm?2 s?1 in the 0.2-0.5, 0.5-2, 2-5 and 5-10 keV energy bands respectively. We have compared our source counts with those in the two Chandra deep ?elds and Lockman hole and ?nd our source counts to be amongst the highest of these ?elds in all energy bands. We resolve > 51% (> 50%) of the X-ray background emission in the 1-2 keV (2-5 keV) energy bands. Key words: surveys - X-ray: selection - background - AGN - cosmology
1 INTRODUCTION It is widely accepted that the majority of the Cosmic X-ray Background (XRB) arises from the integrated emission of discrete extragalactic sources (Schwartz et al. 1976; Giacconi & Zamorani 1987; Maccacaro et al. 1991). The energy density of the XRB peaks at ?30 keV, but the ?rst imaging surveys were carried out at much lower energies: <3.5 keV with Einstein and <2 keV with ROSAT . By the late 1990s ROSAT surveys had resolved 70-80% of the soft XRB, (Shanks et al. 1991; Hasinger et al. 1993, 1998; McHardy et al. 1998). Subsequently, deep XMMNewton and Chandra surveys have essentially resolved the soft XRB into discrete sources (Mushotzky et al. 2000; Hasinger et al.
2001; Brandt et al. 2001; Tozzi et al. 2001; Rosati et al. 2002; Alexander et al. 2003). Optical follow up of these sources has revealed a population composed primarily of unobscured broad line active galactic nuclei (AGN), with an increasing fraction of absorbed AGN at fainter ?uxes (McHardy et al. 1998; Schmidt et al. 1998; Zamorani et al. 1999; Lehmann et al. 2001; Szokoly et al. 2003; Barger et al. 2003). In order to investigate further the nature of the obscured population one has to conduct surveys at harder energies (>2 keV), which are less sensitive to absorption. Surveys carried out using ASCA (Georgantopoulos et al. 1997; Cagnoni, Della Ceca & Maccacaro 1998; Ueda et al. 1998, 2001; Ishisaki et al. 2001) and BeppoSAX (Fiore et al. 1999; Giommi et al. 2000; Fiore et al. 2001) resolved 25-35% of the XRB above 2 keV. More recently, the XMM-Newton and Chan-
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Imaging Cameras (EPICs Turner et al. 2001) were operated in standard full-frame mode. The thin ?lter was used for the PN camera, while the thin and medium ?lters were alternated for the MOS1 and MOS2 cameras. Table 1 gives a summary of the observations. The data were processed using the XMM-Newton Standard Analysis System (SAS) version 6.0. Approximately 40% of the total observation time was a?ected by high particle background ?ares, arising from soft protons hitting the detector. The data were therefore temporally ?ltered to remove these high background periods. In practice, times where the 5-10 keV count rates exceeded 2 s?1 in the MOS cameras and 4 s?1 in the PN camera were excluded. Filtering reduced the total useful exposure time from ?200 ks to ?120 ks. The net live times for the individual detectors after the periods of high background were excised are listed in Table 1. A signi?cant component of the EPIC background comes from instrumental emission lines, in particular the Cu Kα line at 8.1 keV in the PN and the Al Kα line at 1.5 keV in both detectors (Lumb et al. 2002). Events with energies close to those of the emission lines were ?ltered out to minimise the instrumental contribution to the background. Events in bad columns, bad pixels and adjacent to chip edges were also excluded. Images and exposure maps were then constructed from each observation for each detector in four energy bands: 0.2-0.5 keV, 0.5-2 keV, 2-5 keV and 5-10 keV. Single-pixel events were used to construct the PN 0.2-0.5 keV image. Single, double and triple events were used to construct the higher energy PN images. For MOS, all valid event patterns were used to construct the images regardless of energy band. In each energy band, the exposure maps were scaled to the PN thin ?lter response. The images and exposure maps from the di?erent detectors and observations were then summed to produce one image and one exposure map per energy band. The response-weighted summation over each observation and telescope gives total on-axis PN-equivalent live exposure times of 152 ks, 161 ks, 179 ks, and 160 ks, in the 0.2-0.5 keV, 0.5-2 keV, 2-5 keV, and 5-10 keV bands respectively. For the EPIC imaging observing modes, photons are not only registered during the actual integration interval but also during the readout of the CCD. These out-of-time events are hence assigned the wrong position in the readout direction. The fraction of outof-time events is highest for the PN full frame mode (6.3 %) and therefore for each PN exposure, an additional synthetic out-of-time events list was produced by randomising the coordinates of the events within each chip in the readout direction. Out-of-time images were constructed in each energy band by ?ltering these event lists in exactly the same way as the real event lists. These out-oftime images were used as inputs to the background model as described in Section 2.2. The astrometry of the individual observations was corrected for small o?sets between the pointings. A sourcelist was constructed for each observation as described in Section 2.2 and crosscorrelated with the optical positions of the 214 sources found in the Chandra catalogue of McHardy et al. (2003) using the SAS task EPOSCOR. The appropriate o?sets in RA and dec were then applied to each of the individual events to tie the XMM-Newton data to the optical/Chandra /radio co-ordinate frame. The images and exposure maps were then reproduced with the correct astrometry. The actual o?sets in RA and Dec di?ered slightly between the three observations. The ?rst observation (revolution 276, 179 XMM-Newton sources) had o?sets of 1.4′′ , -1.3′′ applied, the second (revolution 281, 106 XMM-Newton sources) had o?sets of 0.5′′ , -0.5′′ applied and the third observation (revolution 282, 257 XMM-Newton sources) had o?sets of 0.6′′ , 0.2′′ applied.
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dra deep ?eld surveys have resolved 60-90% of the hard (>2 keV) X-ray background (Hasinger et al. 2001; Giacconi et al. 2001; Tozzi et al. 2001; Cowie et al. 2002; Rosati et al. 2002; Alexander et al. 2003; Manners et al. 2003) probing ?uxes a factor 100× fainter than the ASCA and BeppoSAX surveys. The wide range in resolved fraction arises not only due to the variation in source counts between the surveys, but also due to the uncertainty of the absolute normalisation of the hard XRB, for example the BeppoSAX XRB normalisation from Vecchi et al. (1999) is ?30% higher than the ASCA value from Gendreau et al. (1995). Optical follow up studies of the deepest surveys ?nd a predominance of z < 1 objects which do not show broad emission lines (Barger et al. 2001; Tozzi et al. 2001; Barger et al. 2002; Lamer et al. 2003; Barger et al. 2003). There is an increasing contribution from normal galaxies at the faintest ?uxes, and it appears likely that normal galaxies will outnumber AGN below 0.52 keV ?uxes of 10?17 erg cm?2 s?1 (Bauer et al. 2004). A significant fraction of the hard X-ray sources in these ?elds are optically faint, with R > 24 and are therefore di?cult to identify optically (Alexander et al. 2001; McHardy et al. 2003; Alexander et al. 2003). Despite the great advances made in detecting increasingly fainter X-ray sources, the physical nature and evolution of the faint hard X-ray population remains largely unknown. The redshift distribution and column density distribution of the absorbed AGN are still poorly constrained. Another issue which needs addressing is the relationship between gas and dust absorption in AGN. There have been several cases of a mismatch between optical and X-ray classi?cations, indicating a wide range in dust/gas ratios for obscured sources (Akiyama et al. 2000; Page et al. 2001; Comastri et al. 2001; Maiolino et al. 2001a; Loaring et al. 2003; Carrera et al. 2004). In particular, high quality X-ray spectra are needed to determine the dominant X-ray emission mechanisms and the amount of absorption. We have therefore used XMM-Newton to carry out deep surveys of two widely separated ?elds to probe the X-ray population down to ?uxes ? 10?15 erg cm?2 s?1 in the 0.5-2 and 2-5 keV energy bands. The source counts in these energy bands exhibit a break at ? 10?14 erg cm?2 s?1 (Rosati et al. 2002) around which the maximum contribution to the XRB per logarithmic ?ux interval occurs. This paper presents the X-ray catalogue derived from the ?rst of these two XMM-Newton surveys, carried out in the UK ROSAT deep ?eld area (hereafter the 13H deep ?eld). The ?eld has also been observed with a mosaic of Chandra pointings which cover the whole XMM-Newton ?eld of view and provide accurate source positions. It is complemented with multiwavelength follow up in the UV, optical, near-IR, mid-IR and radio (Seymour et al. 2004). The Chandra catalogue has already been presented elsewhere (McHardy et al. 2003); here we present the XMM-Newton catalogue and observed source counts.
2 OBSERVATIONS AND DATA REDUCTION 2.1 XMM observations The 13H deep ?eld is centred on the sky co-ordinates RA 13h 34m 37.1s, Dec +37? 53′ 02.2′′ (J2000). The XMM-Newton observations were carried out in three separate revolutions during June 2001 for a total exposure time of 200 ks. The European Photon
XMM-Newton Deep Field: X-ray source catalogue
Rev. Date Live Time (ks) MOS1 MOS2 43.1 14.1 59.2 45.8 12.0 60.2 PN 35.5 6.7 47.9 Filter MOS1 MOS2 thin med thin med thin thin
Energy (keV) 0.2–0.5 0.5–2.0 2.0–5.0 5.0–10.0
ECF ( cts per 10?11 erg cm?2 ) 4.7775 4.8905 1.9605 0.5929
276 281 282
12.06.01 22.06.01 23.06.01
Table 1. Summary of 13H deep ?eld XMM-Newton observations showing the date and length of observations and the ?lters used. The live times have had periods of high background excluded.
Table 2. Energy conversion factors (ECF) used to convert between count rate and ?ux.
2.2 XMM-Newton Source detection The combined images in each energy band were source-searched simultaneously using the SAS tasks EBOXDETECT and EMLDETECT. EBOXDETECT is a sliding cell detection algorithm which outputs an initial sourcelist. This sourcelist is input for the EMLDETECT task which performs a maximum likelihood PSF ?t to the sources producing re?ned positions and ?uxes for all bands simultaneously. This method results in better source positions than searching in the individual energy bands one at a time because the PSF ?t is based on the maximum number of counts per source. If the best ?t source count rate in any particular energy band is less than zero (i.e. there are fewer counts at the source position in the image than in the background map) the source count rate is set to zero in this energy band. A background map was produced for each combination of observation, detector and energy band (36 background maps in total) using our own software. This software performs a maximum likelihood ?t to the background, assuming a three-component background model: out-of-time events, a ?at unvignetted component, caused primarily by cosmic rays, and a vignetted component representing unresolved faint sources and genuinely di?use emission. For the PN, the out-of-time events contribution to the background was ?xed at 6.3% of the intensity of the synthetic out-of-time images; for the MOS background, we assumed no contribution from out-of-time events. The intensities of the vignetted and unvignetted background components were free parameters in the ?t. To maximise sensitivity an iterative procedure was employed. Initially, sources were detected in each individual image (per detector and per energy band) using a 3-pixel-square sliding cell in EBOXDETECT, with the background computed as the average of the surrounding 7 × 7 pixels. Then, the sources were excised from the individual images and the background ?tted. Each of the background maps from the MOS and PN cameras for a given energy band were then summed to produce one combined background map for each energy band. The resultant background maps were then used for the sliding cell (EBOXDETECT) followed by maximum likelihood (EMLDETECT) source detection on the combined image in each energy band. The sequence of background determination followed by source searching was then repeated several times. We found that the sourcelist and background maps converged after 4 iterations. Likelihood thresholds (DET ML values output from the source detection) of 4 and 5 were chosen for EBOXDETECT and EMLDETECT respectively. These values are related to the probability of a random Poissonian ?uctuation having caused the observed source counts via (Cash 1979): DET ML = ?lnPrandom (1)
ing a power law spectrum with photon index Γ = 1.7. This is a good average within our ?ux range (Page et al. 2003; Mateos et al. 2005); however the sources have a range of photon indices. To assess the impact of such a spread we have calculated the expected conversion factors using photon indices of Γ = 1.4 and Γ = 2.0 respectively. This range represents the expected spread in spectral slope for sources contributing to the XRB. The relatively ?at Γ = 1.4 lower limit corresponds to the XRB slope in the 3-15 keV range, produced by absorbed AGN. The upper limit value is typically found in unabsorbed AGN, and we would therefore expect the bulk of our sources to lie between the two values. The largest e?ect is in the 0.2-0.5 keV and 5-10 keV energy bands where the conversion factors derived are di?erent from those assuming a photon index of Γ = 1.7 by up to 11% and 8% respectively. However, in the 0.5-2 and 2-5 keV bands the photon index chosen only a?ects the conversion factors by 1-2%. The PN response matrices include only single and double pixel events, but for the three highest energy bands our PN images also include triple and quadruple events. In order to take this into account, the count rate to ?ux conversion factors were corrected (by up to 6% in the hardest band) as described in Osborne et al. (2001).
3 MONTE CARLO FIELD SIMULATION We have used an XMM-Newton speci?c extension of the simulation method of Hasinger et al. (1998) to obtain a quantitative characterisation of the source detection procedure and to assess the reliability of the resultant sourcelist. We have used our simulations to ?nd the appropriate detection threshold to be applied to the 13H ?eld. A Monte-Carlo approach is particularly powerful near the survey ?ux limit where a number of di?erent processes contribute to uncertainties in the detected source parameters. Our simulation method consists of several modular steps that are repeated for a large number of synthetic ?elds. Brie?y, an ‘input’ sourcelist was generated independently in each energy band. Each list was then folded through the XMM-Newton imaging characteristics to generate images in each energy band. These images were then source searched to produce ‘output’ sourcelists. A pairing algorithm was used to associate an ‘input’ source with each ‘output’ source. Each of these stages are described in detail in Appendix A. Here we present the results of a comparison between the output and input source properties. These provide an indication of the biases inherent in our survey. One thousand simulated ?elds were used to reduce statistical uncertainties in the analysis.
3.1 Comparison of simulated input and output sources In order to assess the accuracy of source positions and ?uxes, and to estimate the degree to which confusion and Eddington bias a?ects the source counts in our 13H data we have compared the input and
The conversion factors from count rates to ?ux were determined from the EPIC response matrices, over exactly the same energy ranges as those in which the images were constructed, assumc 0000 RAS, MNRAS 000, 000–000
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Figure 1. Greyscale images showing the distribution of positional o?sets between output and input source locations as a function of input ?ux in two energy bands. Those sources within the central 9′ of the XMM-Newton ?eld of view having DET ML 5 are shown. The concentration of positional o?sets as a function of S inp is indicated by the darkness of the greyscale image. The three contours show the distances within which 68, 90, and 95 per of the data lie.
output properties of our simulations. The simulations should mimic any biases found in the real data. We matched each output source found in the simulated images to the closest valid input source. We consider an input source as valid when its ?ux, S inp , contributes a reasonable fraction (>20 per cent) to the total output ?ux, S out . No upper limit was applied to the radius at which input and output sources were matched in order to assess the typical o?sets between input and output positions. Fig. 1 shows the distribution of measured positional o?sets as a function of input ?ux, S inp . The greyscale image shows the relative density of sources at a given S inp . The dark band shows where the majority of sources lie. All sources with DETML values > 5 and o?axis angles < 9′ are shown. The contour lines plotted correspond to the positional o?sets within which 68, 90 and 95 per cent of the data lie. The mean positional o?set decreases with increasing ?ux and is < 10′′ for all but the faintest ?uxes. In the 0.5-2 keV energy band, 95 per cent of sources with S inp > 5 × 10?16 erg cm?2 s?1 and o?axis angles 9′ have positional o?sets < 10′′ . In the 5-10 keV energy band, 95 per cent of sources with S inp > 5 × 10?15 erg cm?2 s?1 and o?axis angles 9′ have positional o?sets < 10′′ . Those with o?axis angles > 9′ have systematically larger positional o?sets (larger by ? 2′′ over the majority of ?ux ranges). Any sources with higher positional o?sets are most likely due to incorrect associations. A discussion of the positional accuracy found in the real 13H data and its comparison with the simulations is deferred to Section 4.3. Subsequently, we matched output sources to input sources within a radius rcut = 5′′ , 8′′ , and 10′′ for o?axis angles of 0 ? 9′ , 9 ? 12′ and > 12′ respectively, re?ecting the degradation of the XMM PSF (Kirch 2004) away from the optical axis. Where more than one candidate input source lay within rcut , the brightest was chosen. The brightest input candidate within rcut must be the ‘correct’ input counterpart in the sense that it is the largest contributor to the output source counts. In practice, when averaged over the
1000 simulations, only 0.6, 1.7, 1.5 and 0.5 output sources per ?eld had more than one valid (5S inp S out ) input candidate within rcut in the 0.2-0.5, 0.5-2.0, 2.0-5.0, and 5.0-10 keV energy bands. The output ?uxes and positions were then compared with the corresponding input values. There are several reasons why we might expect a di?erence between the input and output ?ux distributions and source counts: i) a systematic or statistical ?ux measurement inaccuracy, ii) source confusion, iii) statistical ?uctuations in the background which may be detected as sources, and iv) Eddington bias. All these factors must be considered together when interpreting the 13H ?eld data. The intrinsic accuracy of the source detection photometry is best evaluated at high ?uxes and low o?axis angles, where ii), iii) and iv) are less important. The bright end of Fig. 2 illustrates the high ?delity of the detected ?uxes, S out , to the input ?uxes, S inp . Considering sources with S inp > 5 × 10?14 erg cm?2 s?1 , with o?axis angles < 9′ the average S out /S inp ratio is 1.01±0.03 (1σ) in energy bands 0.2-0.5, 0.5-2 and 2-5 keV. In our highest energy band the average S out /S inp ratio is also 1.01 but the scatter is larger (1σ = 0.06). The distribution of S out /S inp is shown in Fig. 3 for three ?ux intervals in each energy band. At bright ?uxes (S inp = 2 × 10?14 erg cm?2 s?1 ) the distribution is narrow, symmetrical and centred on S out /S inp = 1, because the statistical errors on the ?uxes are small. At intermediate ?uxes (S inp = 6 × 10?15 erg cm?2 s?1 ) the distributions are still relatively symmetrical, but they are slightly broader as the statistical errors on the ?uxes are larger. However, at the faintest ?uxes, the distributions are much broader and signi?cantly skewed towards larger S out /S inp ratios. The increased width is due to the increased statistical errors on the ?uxes. The distributions are shifted towards larger S out /S inp ratios because at such faint ?uxes sources are unlikely to be detected unless they are enhanced by Poisson ?uctuations or by source confusion. Source confusion occurs when two or more nearby input sources fall in a single resolution element of the detector and rec 0000 RAS, MNRAS 000, 000–000
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Sout/Sinp 0.10 1.00 10.00 Sinp (10-14 erg cm-2 s-1) 100.00
1.0 10.0 Sinp (10-14 erg cm-2 s-1)
Figure 2. Scatter plots of input vs output ?ux in two selected energy bands. We only show those detected sources having DET ML 5 and input counterparts within 5′′ , 8′′ , and 10′′ for input o?axis angles of 0 ? 9′ , 9 ? 12′ and > 12′ respectively. Sources with S out /(S inp + 3σout ) > 1.5 are plotted as triangles. The results for 100 simulations are shown for clarity.
0.6 0.5 Fraction 0.4 0.3 0.2 0.1 0.0 0.6 0.5 Fraction 0.4 0.3 0.2 0.1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Sout/Sinp 0.5 1.0 1.5 2.0 2.5 3.0 Sout/Sinp 2.0-5.0 keV
2x10-14 cgs 2x10-15 cgs 2x10-16 cgs
2x10-14 cgs 2x10-15 cgs 2x10-16 cgs
2x10-14 cgs 2x10-15 cgs 2x10-16 cgs
2x10-14 cgs 2x10-15 cgs 2x10-16 cgs
Figure 3. The distribution in output (S out ) ?ux to input ?ux (S inp ) ratio for three illustrative input ?ux ranges. The solid line represents the sources in the ?ux interval centred on S inp = 2 × 10?14 erg cm?2 s?1 (1 × 10?14 ? 4 × 10?14 erg cm?2 s?1 ). The dotted line represents sources in the ?ux interval centred on S inp = 6 × 10?15 erg cm?2 s?1 (3 × 10?15 ? 1.2 × 10?14 erg cm?2 s?1 ) and the dashed line represents sources in the ?ux interval centred on S inp = 4 × 10?16 erg cm?2 s?1 (2 × 10?16 ? 8 × 10?16 ). The ?ux intervals were chosen such that ?logS inp = 0.3.
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Figure 4. a) Fraction of ?ux ampli?ed sources as a function of ?ux. b) Fraction of unmatched sources as a function of ?ux. (0.2-0.5 keV (dotted), 0.5-2 keV (solid), 2-5 keV (dashed), 5-10 keV (dot-dashed)). The fraction of ?ux ampli?ed sources is < 0.4 per cent in all energy bands and is signi?cantly less than the fraction of unmatched sources.
sult in a single output source. This results in a ?ux ampli?cation in the output source and a net loss of fainter sources. The position of the output source will be close to the centroid of the merged input sources. Therefore when two input sources of similar ?ux are confused, the output position does not correspond to either of the input positions. Source confusion can limit the depth of any deep survey depending on the size of the telescope beam, and on the sky-density of objects as a function of ?ux. In practice, we cannot distinguish between a source boosted by photon noise or one confused with another faint source, therefore we consider the two e?ects jointly. We class sources as ‘?ux ampli?ed’ (corresponding to ‘confused’ sources in Hasinger et al. 1998) if S out /(S inp + 3σout ) > 1.5 (where σout is the 1σ error on the output ?ux S out ). Fig. 4a shows the fraction of ?ux ampli?ed sources as a function of input ?ux in our four energy bands. The fraction is less than 0.4 per cent at all ?uxes in all energy bands. This fraction will depend on the exact definition of ?ux ampli?cation. Using a less stringent de?nition of S out /(S inp + 3σout ) > 1.2 still results in a fraction well below 2% in each energy band at all ?uxes. We class an output source as ‘unmatched’ when there are no valid (S out 5S inp ) input sources within rcut (corresponding to ‘spurious’ sources in Hasinger et al. 1998). These are mainly caused by positive ?uctuations in the background. Fig. 4b shows the fraction of unmatched sources as a function of ?ux in each energy band. As expected, the unmatched fraction is highest at very faint ?uxes, where up to 30% of the sources are unmatched. Unmatched sources are many times more numerous than the ?ux ampli?ed sources at any ?ux. In our simulations we curtailed our input sourcelists at ?uxes 5× fainter than those found in the 13H data in each energy band in order to speed up processing time. In order to assess the impact of the simulation ?ux limit on the number of ?ux ampli?ed and spurious sources, we have also produced a smaller number of simulations to a greater depth, reaching ?uxes 10× fainter than those found in the 13H data. The fraction of ?ux ampli?ed sources in
these faint simulations agrees with the fraction found in our original simulations to within 0.02 per cent. Likewise, the fraction of unmatched sources agrees to within 2 per cent. We are therefore satis?ed that our chosen ?ux limits are su?ciently deep. In order to investigate the ?ux limits at which confusion noise dominates over Poisson errors, we have produced and sourcesearched a small number of ultra-deep simulations with no Poisson noise. The results are presented and discussed in Appendix B, and show that the 13H ?ux limits are more than a factor of 4 brighter than the ultimate XMM-Newton confusion limit in any of the 4 energy bands. Eddington bias (Eddington 1913) results in a systematic o?set in the number of sources detected at a given ?ux. The magnitude of this e?ect depends on the both the statistical errors on the measured ?ux values and on the intrinsic slope of the N (S ). As there are generally many more faint sources than bright ones, uncertainties on the measured ?ux values will result in more faint sources being up-scattered than bright sources being down-scattered. Therefore we would expect more faint sources to be detected than are actually input, and the output source counts at a given ?ux to be greater than those input. In the case of our simulations the situation is further complicated due to the double powerlaw form of the N (S ) distribution and the fact that the ?ux error distribution is nonuniform and a function of several parameters including ?ux and o?axis angle. The level of Eddington bias expected in the 13H deep ?eld is shown in Fig. 5 where the simulated input and output source counts are compared. Below S knee the ratio rises as the statistical errors on the ?ux measurements increase. At the lowest ?ux interval there is a drop in output source counts. The reason for this is the strong skew in S out /S inp at the faintest ?uxes (see Fig. 3) which boosts the output ?uxes. The output/input source counts ratio is a minimum at S knee where both the statistical errors on the ?ux measurement are low and the source counts become ?at. Above S knee the output/input source count ratio is constant within the errors with a value of ?
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Figure 5. Simulated output (crosses) 0.5-2 keV N (S ) distribution normalised by the input distribution. The error bars represent Poisson errors on the output source counts. The dotted line represents the case where the input and output source counts are equal. The source counts are most disparate at faint ?uxes where the output counts are enhanced by up to 23%.
Figure 6. Plot showing the fraction of ?ux ampli?ed or unmatched sources for a range of lower DET ML limits. Results are shown for each energy band, 0.2-0.5keV (large dash), 0.5-2keV (solid line), 2-5keV (small dash), 5-10keV (dot-dash). The dotted line shows the 5% badness level.
1.05 indicating that Eddington bias a?ects our bright counts at the 5% level. 3.2 Assessing the reliability of the 13H sources In this section we describe how we determined from our simulations the appropriate detection threshold to be applied to the 13H ?eld EMLDETECT sourcelist. Our aim was to produce a sourcelist such that nearly all erroneous detections are removed whilst retaining the maximum number of real sources. For each detected source, EMLDETECT measures the detection maximum likelihood statistic, DET ML, which takes account of source counts, background counts, and the PSF. For the real data, the SAS task EMLDETECT provides both single-band and multiband measurements of DET ML. For the simulated images we are limited to single band measurements as the four bands are simulated independently. To simulate all four bands simultaneously would require a priori knowledge of the sources’ intrinsic X-ray spectra, redshifts and column densities which we do not have. The value of DET ML for any single detection is directly related to the probability of the source being caused by a random Poisson ?uctuation via Eqn. 1. However, it is di?cult to translate a minimum threshold value of DET ML applied to the whole sourcelist into a total number of expected spurious sources in the ?eld as the probability is a function of position within the ?eld, due to the varying PSF and exposure map. This is therefore best explored via a large number of Monte-Carlo simulations. Using the simulated sourcelists in each band, we calculated the fraction of sources which were either ?ux ampli?ed or unmatched as a function of the minimum detection threshold DET MLmin . This is shown in Fig. 6. To restrict the fraction of bad sources in our ?nal 13H sourcelist we use the value of DET MLmin in each band at which only 5 percent of sources are either ?ux amc 0000 RAS, MNRAS 000, 000–000
pli?ed or unmatched in our simulations; these are 5.