The Erosita Final Equatorial Depth Survey (Efeds): the X-Ray Catalog

Astronomy & Astrophysics manuscript no. eFEDScat ©ESO 2021 June 29, 2021

The eROSITA Final Equatorial Depth Survey (eFEDS): The X-ray catalog

H. Brunner1, T. Liu1, G. Lamer2, A. Georgakakis3, A. Merloni1, M. Brusa4, 5, E. Bulbul1, K. Dennerl1, S. Friedrich1, A. Liu1, C. Maitra1, K. Nandra1, M. E. Ramos-Ceja1, J. S. Sanders1, I. M. Stewart1, T. Boller1, J. Buchner1, N. Clerc6, J. Comparat1, T. Dwelly1, D. Eckert7, 1, A. Finoguenov8, M. Freyberg1, V. Ghirardini1, A. Gueguen1, F. Haberl1, I. Kreykenbohm9, M. Krumpe2, S. Osterhage1, F. Pacaud10, P. Predehl1, T. H. Reiprich10, J. Robrade11, M. Salvato1, A. Santangelo12, T. Schrabback10, A. Schwope2, and J. Wilms9

1 Max Planck Institute for Extraterrestrial Physics, Gießenbachstraße 1, 85748 Garching, Germany 2 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany 3 Institute for Astronomy and Astrophysics, National Observatory of Athens, V. Paulou and I. Metaxa, 11532, Greece 4 Dipartimento di Fisica e Astronomia "Augusto Righi", Alma Mater Studiorum Università di Bologna, via Gobetti 93/2, 40129 Bologna, Italy 5 INAF-Osservatorio di Astroﬁsica e Scienza dello Spazio di Bologna, via Gobetti 93/3, 40129 Bologna, Italy 6 IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France 7 Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland 8 Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2a, FI-00014 Helsinki, Finland 9 Dr. Karl Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, Sternwartstraße 7, 96049 Bamberg, Germany 10 Argelander-Institut für Astronomie (AIfA), Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany 11 Universität Hamburg, Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany 12 Institut für Astronomie und Astrophysik, Universität Tübingen, Sand 1, D 72076 Tübingen, Germany

Received May 7, 2021; accepted June 30, 2021

ABSTRACT

Context. The eROSITA X-ray telescope onboard the Spectrum-Roentgen-Gamma (SRG) observatory combines a large field of view and a large collecting area in the energy range between ∼0.2 and ∼8.0 keV with the capability to perform uniform scanning observations of large sky areas. Aims. SRG/eROSITA performed scanning observations of the ∼140 square degrees eROSITA Final Equatorial Depth Survey field (the eFEDS field) as part of its performance verification phase ahead of the planned four years of all-sky scanning operations. The observing time of eFEDS was chosen to slightly exceed the depth expected in an equatorial field after the completion of the all-sky survey. While verifying the capability of eROSITA to perform large area uniform surveys and serving as a test and training dataset to establish calibration and data analysis procedures, the eFEDS survey also constitutes the largest contiguous soft X-ray survey at this depth to date, supporting a range of early eROSITA survey science areas. Here we i) present a catalog of detected X-ray sources in the eFEDS field providing source positions and extent information, as well as fluxes in multiple energy bands and ii) document the suite of tools and procedures developed for eROSITA data processing and analysis, which were validated and optimized by the eFEDS work. Methods. The data were fed through a standard data processing pipeline, which applies X-ray event calibration and provides a set of standard calibrated data products. A multi-stage source detection procedure, building in part on experience from XMM-Newton, was optimized and calibrated by performing realistic simulations of the eROSITA eFEDS observations. Source fluxes are computed in multiple standard energy bands, both by forced PSF-fitting and aperture photometry. We cross-matched the eROSITA eFEDS source catalog with previous XMM-ATLAS observations, confirming excellent agreement of the eROSITA and XMM-ATLAS source fluxes. Astrometric corrections were performed by cross-matching the eROSITA source positions with an optical reference catalog of quasars. Results. We present a primary catalog of 27910 X-ray sources (including 542 with significant spatial extent) detected in the 0.2–2.3 keV energy range with detection likelihoods ≥ 6, corresponding to a (point source) flux limit of ≈ 7 × 10−15 erg/cm2/s in the 0.5–2.0 arXiv:2106.14517v1 [astro-ph.HE] 28 Jun 2021 keV energy band. A supplementary catalog contains 4774 low-significance source candidates with detection likelihoods between 5 and 6. In addition, a hard band sample of 246 sources detected in the energy range 2.3–5.0 keV above a detection likelihood of 10 is provided. Finally, we provide in appendix a description of the dedicated data analysis software package, of the eROSITA calibration database and of the standard calibrated data products. Key words. catalogs – surveys – X-ray: general

1. Introduction on the Spektrum-Roentgen-Gamma (SRG) orbital observatory (Sunyaev et al. 2021). It was designed and built, over a period eROSITA (extended ROentgen Survey with an Imaging Tele- of about 12 years, with the goal of realizing a sensitive, wide scope Array; Predehl et al. 2021) is the primary instrument

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field-of-view X-ray telescope with a significantly larger Grasp1 is expected for eRASS at the Ecliptic equator (i.e. over most of at 1 keV than that of either XMM-Newton (by about a factor of the sky) at the end of the 4 years all-sky survey program, while 4) and Chandra (by about a factor of 60), the two most sensitive at the same time covering a sufficiently wide area to provide focusing X-ray telescopes currently in operation. In addition, a large statistical samples of different source classes; in particular, mission plan was devised that included a long (4 year), unin- enough clusters to calibrate the mass-observable relation using terrupted all-sky survey program (the eROSITA All-Sky Survey: weak lensing maps provided by the exquisite optical imaging of eRASS; Predehl et al. 2021) in order to guarantee a large volume the HSC survey. of accessible discovery space. SRG is operated by the Space Re- In a series of accompanying papers, we will present the iden- search Institute of the Russian Academy of Sciences (IKI). tification of the multi-wavelength counterparts of both point-like The scientific motivation for the eROSITA design was the (Salvato et al., Schneider et al., submitted) and extended (Klein desire to detect and spatially resolve a large number (of order et al., submitted) X-ray sources; the resulting clean catalogs of 105) of clusters of galaxies over a wide redshift range (up to clusters of galaxies (Liu A. et al., Bulbul et al., submitted), ac- at least z ∼ 1) in order to constrain cosmological parameters tive galactic nuclei (Liu T. et al., Nandra et al., in prep.) and stars (see e.g. Allen et al. 2011; Pillepich et al. 2018) at the level of (Schneider et al., submitted); the X-ray variability properties of a Stage-IV Dark Energy experiment (Albrecht et al. 2006), via the detected sources (Boller et al., Buchner et al., submitted); the characterization of the growth of structure. X-ray spectral analysis of the point-sources (Liu T. et al., submit- Following the successful launch in July 2019, and before the ted); the X-ray morphological analysis of the clusters (Ghirardini start of the all-sky survey, a number of Performance Verification et al., in prep.); the optical/lensing analysis of the X-ray clusters (PV) observations were carried out during the early phases of the (Ota et al., Ramos et al., Chiu et al., Bahar et al., in prep.); the SRG mission, aimed at verifying all different aspects of the in- properties of non-active galaxies detected by eROSITA (Vulic et struments’ capabilities. These first post-commissioning phases al., submitted), and the discovery of some extreme AGN (Toba of science operations have clearly demonstrated that eROSITA et al., Brusa et al., submitted). Earlier works based on the eFEDS is capable of delivering the design performance in terms of sen- data have been published and include the discovery of a super- sitivity, image quality and spectroscopic capabilities (see e.g. cluster (Ghirardini et al. 2021) and a very high redshift quasar Merloni et al. 2020; Predehl et al. 2021). Nevertheless, the am- (Wolf et al. 2021). bitious scientific goals of eROSITA, and in particular its cos- In this paper, we describe in detail the X-ray observations, mological objectives, require accurate control over a number of the data analysis and calibration procedures, the algorithms used elements, including the modelling of the instrumental and astro- to detect and characterize X-ray sources, and their validation via physical backgrounds, the reconstruction of the selection func- extensive simulation analysis. We also release here the resulting tion for both point-like and extended X-ray sources over very catalogs of X-ray sources, and present in a series of appendices large sky areas, the identification of reliable counterparts of the the description of the dedicated software system (the eROSITA X-ray sources at longer wavelengths, the measurement of their Science Analysis Software System; eSASS), which is also made distances (redshifts), the calibration of the empirical (or phys- public concurrently with this paper. The interested reader will ical) relationships between X-ray observables (such as cluster find there a basic description of the operating principles and al- luminosities, temperatures, density profiles), etc. and cosmolog- gorithms of the data analysis pipeline. A full description of the ically meaningful parameters, particulary cluster masses. eSASS software is also available online3. The eROSITA Final Equatorial Depth Survey (eFEDS) was the largest investment of observing time during the PV phase (about 360ks, or 100 hours, in total), and was designed to test 2. Observations the key elements of the science work flow from X-ray photon de- The SRG mission supports three principal observing modes tection to astrophysics/cosmology. The eFEDS field, an area of (Predehl et al. 2021; Sunyaev et al. 2021). As its main objective, approximately 140 deg2 composed of four individual rectangu- SRG is in the process of performing a four-year survey of the lar raster-scan fields of ∼35 deg2 each, was chosen as it features full sky in continuous scanning mode, in which the spacecraft amongst the richest multi-wavelength coverage for an extrgalac- pointing direction traces great circles in the sky with a rotation tic field of this size, and was visible by eROSITA in the limited speed of 90 degrees per hour (or ∼ 9000/s). In addition, SRG is time period allocated to PV observations. The field co-incides capable of making pointed observations of individual targets, as with an area enriched by deep optical/NIR imaging thanks to well as extended rectangular fields in so-called "field scanning" the HSC Wide area Survey (Aihara et al. 2018), KIDS-VIKING mode. The pattern of the field scanning mode consists of parallel (Kuijken et al. 2019), DESI Legacy Imaging Survey (Dey et al. scans in alternating directions, offset by 6’. Given the eROSITA 2019), and, among others, GAMA (Driver et al. 2009), WIG- field of view (≈ 1 degree in diameter), each sky position is thus GLEz (Drinkwater et al. 2018), LAMOST2 and SDSS (Blan- observed in ten consecutive scans. The maximum supported size ton et al. 2017) spectroscopic coverage; a full description of of the scanned rectangles is 12.5◦ × 12.5◦. In the interest of op- the multiwavelength data available is presented in Salvato et erational simplicity, the orientation of the rectangles is aligned al. (submitted). The field also contains a medium-wide XMM- with the ecliptic coordinate system. For mission planning pur- Newton survey field (the XMM-ATLAS, Ranalli et al. 2015), poses, individual field scan observations are scheduled to be not which provides a useful dataset for comparison and validation of significantly longer than one day, thus fitting between consecu- the eROSITA X-ray analysis pipeline. tive ground contacts with the SRG spacecraft. These constraints The eFEDS observational strategy was designed so as to pro- necessitate splitting the observations of the eFEDS field into four vide uniform exposure over the field about 50% deeper than what sub-fields of size 4.2◦ × 7.0◦ (this is the area with nominal exposure depth; the area is larger by ∼ 0.5◦ on each side, but with 1 In X-ray astronomy, Grasp is a primary survey metric, being the reduced exposure). A scanning speed of 1300.15/s results in a product of the field-of-view average effective area times the field of view uniform exposure depth of ∼ 2.2 ks (∼ 1.2 ks after correcting of the telescope. 2 http://dr5.lamost.org/doc/release-note-v3 3 https://erosita.mpe.mpg.de/edr/DataAnalysis/

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KIDS/VIKING GAMA09 2000

1500 Declination

1000

SDSS BOSS imaging footprint 500

146.000 144.000 142.000 140.000 138.000 136.000 134.000 132.000 130.000 128.000 126.000

Right ascension 0

0.0899 6.0005.0004.0003.0002.0001.0000.000-1.000-2.000-3.000 0.0526

0.0338

0.0244

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0.0173 Declination

0.0161

0.0155

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0.0151 146.000 144.000 142.000 140.000 138.000 136.000 134.000 132.000 130.000 128.000 126.000

Right ascension 0.015

Fig. 1. The 0.2-2.3 keV exposure map (vignetting corrected, in seconds; upper panel) and background map (in units of counts per pixel; lower panel). The bright circles mark high-exposure regions and are a result of the scanning mode used in the observations. They are created due to the waiting time of the spacecraft before inverting its scanning direction. The darker stripe in the second rectangular chunk on the right is due to the malfunction of 2 of the 7 eROSITA cameras during that period. The upper panel also shows the footprints of a few relevant optical/NIR imaging/spectroscopic surveys. for telescope vignetting) across most of the field. Each source see Predehl et al. 2021). This causes in TM5 and TM7 a spa- is observed continuously for up to 4.7 min in an individual scan tially inhomogeneous raised background at low energies, which when passing through the central part of the field of view and for changes with the orientation of the spacecraft with respect to the shorter time periods in peripheral scans. Sun. While this leads to errors in the energy calibration of the The eFEDS observations were carried out at the beginning of affected areas, the magnitude of this effect for the eFEDS field November 2019 with all 7 eROSITA Telescope Modules (TM1- location is sufficiently small not to negatively affect this work, 7) in operation. However, due to an unrecognized malfunction such that all seven cameras could be used. of the camera electronics, 28% of the TM6 data of eFEDS field Table 1 presents the details of the eFEDS field observations, I and 48% and 43% of the TM5 and TM6 data, respectively, of while the top panel of Figure 1 shows the final exposure map of eFEDS field II could not be used, resulting in a reduced exposure the eFEDS survey in the soft band (0.2–2.3 keV), corrected for depth in the affected areas of up to ∼30% (as visible in Figure 1). vignetting4. Overlaid on that map are the schematic footprints of All eROSITA cameras are protected by light-blocking filters. a few relevant optical/NIR imaging/spectroscopic surveys. For five of the seven cameras, a 200 nm Al layer is deposited Figure 2, instead, shows an RGB exposure corrected image directly on the CCDs, while for the remaining two (TM5 and of the entire field, created using 0.2–0.5 keV (red), 0.5–1 keV TM7) the suppression of optical light is achieved by a 100 nm Al layer on an external filter in the filter wheel. After launch it was found that a small amount of scattered sunlight can reach 4 The corresponding on-axis (un-vignetted) exposures for the 0.2-2.3 the CCDs from the side, bypassing the filter wheel ("light leak"; keV band can be computed by multiplying the exposure by 1.81.

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ObsID Center R.A. Center Dec texp Start time [UTC] ∆α ∆δ [deg] [deg] [s] [arcsec] [arcsec] I 300007 129.55 +1.5 89642 2019-11-03T02:25:50 5.0 -4.2 II 300008 133.86 +1.5 89642 2019-11-04T04:05:52 5.0 -3.2 III 300009 138.14 +1.5 89642 2019-11-05T05:45:54 5.1 -3.5 IV 300010 142.45 +1.5 89642 2019-11-06T07:25:56 4.6 -4.0 Table 1. eROSITA observations of the four sub-ﬁelds of eFEDS. ∆α/∆δ columns: the corrections that have been applied to the raw attitude solutions for each ObsID in order to remove systematic linear oﬀsets of derived X-ray source positions in Right Ascension (RA; α) and declination (DEC; δ), using the Gaia-unWISE AGN candidate catalog of Shu et al. (2019) as an astrometric reference, see section 3.1 for details.

Fig. 2. RGB image of the eFEDS ﬁeld in X-rays, created using 0.2–0.5 (R), 0.5–1 (G), and 1–2 (B) keV bands. Each count-rate image has been smoothed with a Gaussian with σ = 10 pixels (4000). In the upper right corner the inset shows a zoom-in around a newly discovered supercluster (Liu A. et al., submitted).

(green) and 1–2 keV (blue) energy bands, after smoothing each are described in Appendix A.1 and A.2.; calibrated event files count-rate image with a Gaussian with σ = 10 pixels (4000). are described in Appendix C.1. In addition, the standard data processing pipeline provides a range of high level data products such as exposure, background and sensitivity maps, as well 3. Data analysis as X-ray source catalogs and source specific products such as spectra and light curves, described in Appendix C. This work is In this section we describe the details of the data processing with based on the pipeline created calibrated event files while higher the eROSITA Science Analysis Software System (eSASS). The level data products are created by a dedicated pipeline. The data eSASS data analysis package and its tasks are described in detail were processed using pipeline version “c001” released as part in Appendix A. Further documentation including a description the eROSITA Early Data Release5. of all command line parameters is available online3.

3.2. Astrometric corrections and data preparation 3.1. Data reception and standard pipeline processing Some artifacts in the data due to a temporary malfunctioning of eROSITA science and auxiliary telemetry data received during the camera electronics of TM4 are not yet perfectly removed in each daily SRG ground contact are transferred from IKI to the this version of the pipeline. Therefore, in the TM4 data of all the eROSITA Data Center at Max Planck Institute for Extraterres- four observations, we remove two bright pixels (pixel coordinate trial Physics in Garching, Germany, where they undergo vari- RAWX, RAWY: 115, 235 and 178, 225); furthermore, we remove the ous processing steps as part of a standard data analysis pipeline. soft photons with PI (event energy in eV) below 600 and RAWY The data are decommutated, packages, and converted to FITS above 120 in a few columns (RAWX: 121, 125, 127, 259, 262, 380, format (Wells et al. 1981) files in an initial pre-processing step 382). The fraction of removed events is negligible. and subsequently feed through an event processing task chain which creates calibrated X-ray event files suitable for scientific 5 available for download at analysis. The main software tasks of the event processing chain https://erosita.mpe.mpg.de/edr/eROSITAObservations/

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We carry out an initial round of astrometric corrections to the X-ray dataset as follows. We create images and detect sources 0.6 in the 0.2–2.3 keV band separately for each of the four eFEDS ObsIDs (using the methods described below). For each Ob- 0.5 sID, we cross-correlate the detected point sources (EXT=0) with the catalog of Gaia-unWISE AGN candidates from Shu et al. (2019), finding 1600–1900 matches per ObsID. Using an iter- 0.4 ative sigma-clipping algorithm, we then calculate the (RA; α) and declination (DEC; δ) offsets ∆α, ∆δ for each ObsID that re- 0.3 moves the mean linear offsets of the X-ray sources from the Gaia DR2 positions of the reference catalogue. We apply the com- 0.2 puted corrections (see Table 1) to the observation attitude and

then recalculate the event coordinates using the tasks evatt and frequency normalized radec2xy (see Appendix A.2). 0.1 After applying astrometric corrections to each of the four observations separately, we merge them into one, applying filters 0.0 of FLAG=0xc00fff30 (select good events from nominal field 0 1 2 3 4 5 of view, excluding bad pixels) and PATTERN≤ 15 (include sin- Separation/(RADEC_ERR/ 2) gle, double, triple, and quadruple events). On the merged events, we search for background flares by running flaregti (see Ap- Fig. 3. Distributions of the separations between the optical positions and pendix A.5) in the 0.2–5 keV band with source_size=120, the X-ray positions before and after the second-pass corrections. source_like=10, timebin=100, and gridsize=60. There is only one, short (< 1 ks), significant flare detected by flaregti 20 in the entire dataset. By applying the flaregti filter with evtool (see Appendix A.3), the background flare is filtered out. Using evtool, we extract the events in specific energy 10 ranges and create images with a resolution of 400.0 per pixel, a factor 2.4 higher than the size of the physical pixels of the eROSITA 00 cameras (9.6). Both vignetted exposure maps in each band 5 and an unvignetted exposure map are created using expmap.A 4 source detection mask is created with ermask on the basis of the 3 0.2–2.3 keV band vignetted exposure map applying a minimum cut at 1% of the maximum value. 2

3.3. Source detection 1 RADEC_ERR_CORR (arcsec) RADEC_ERR_CORR We create the main eFEDS catalog by running a single-band source detection in the 0.2–2.3 keV band using all TMs. This guarantees the maximal sensitivity, given the shape of the 101 102 103 eROSITA response (Predehl et al. 2021) and as shown by simu- DET_LIKE lation tests (Liu T. et al., submitted). In addition, we also run the same source detection procedure simultaneously in three bands Fig. 4. Positional uncertainty (after astrometric correction, (0.2–0.6, 0.6–2.3, and 2.3–5 keV), in order to select sources with RADEC_ERR_CORR) of all point sources in the main catalog as a particularly hard (or soft) spectra. function of the detection likelihood in the 0.2-2.3 keV energy band. The source detection procedure is as follows. Firstly, an initial catalog is obtained by running erbox in local mode with likemin=6, nruns=2, and boxsize=4. This initial catalog is detection and 58227 sources in the three-bands detection) is only used to create a background map using erbackmap with much larger than the PSF-fitting output catalog. mlmin=6 and snr=40. Having defined a background map, we Finally, we run photon-mode PSF-fitting using now run erbox in global mode with likemin=4, boxsize=4, ermldet, adopting cutrad=15, multrad=15, likemin=5, and nruns=2 to create a further catalog. Using this, we repeat extlikemin=6, extmin=2, extmax=15, nmaxfit=3, the step of creating a background map and running erbox with nmulsou=2. The PSF-fitting is done within a circular re- the same parameters and update the preliminary catalog, so that gion of a radius of cutrad, which is an essential parameter. the preliminary catalog is determined by the parameter settings Through simulation tests, we find that cutrad=15 is a good used in the background map creating and the global erbox de- choice and adjusting it does not make any significant improve- tection, and not affected by the settings in the initial guess. ment on the detection efficiency of point sources. Eventually, Using the preliminary catalog, a final background map is cre- the catalog is formatted using catprep. ated using the same parameters as above. The bottom panel of During the whole procedure of sliding-box detection of Figure 1 shows the resulting background map. the preliminary catalog, background map generating, and PSF- Both the preliminary catalog and the background map are fitting, we use the vignetted exposure map for each band, except then used as input to the point spread function fitting in the next for the 2.3–5 keV hard band. For the hard band, we use the un- step, which selects reliable sources from this catalog. The pre- vignetted exposure map instead, considering that the hard band liminary catalog (containing 84565 sources in the single-band is dominated by particle background.

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Comparing once again the coordinates of the X-ray cata- Single-band detection [0.2–2.3 keV] logue sources with those from the Gaia-unWISE AGN candidate Catalog DET_LIKE EXT_LIKE Sources catalog (Shu et al. 2019), we make a second-pass astrometric Full >5 >0 32684 correction on the catalog in right ascension (RA; α) and decli- Main >6 >0 27910 nation (DEC; δ), allowing a linear shear term in addition to a Supplementary <6 >0 4774 linear shift. We also compute an empirical correction to the raw Point Sources >6 =0 27369 positional uncertainty estimates ∆θ that brings the distribution Extent-Selected >5 >6 542 of observed X-ray to reference catalogue offsets closer to the ex- Three-bands detection pected Rayleigh distribution. The computed corrections are as Catalog DET_LIKE_3EXT_LIKE Sources follows: Hard [2.3-5 keV] >10 =0 246 αCORR = α − (−0.2158 × δ + 0.4526)/ cos(δ)/3600 Table 2. Sample selection criteria δ = δ − (0.086 × δ + 0.0679)/3600 CORR √ 2 2 ∆θCORR = 1.15 × ∆θ + 0.7 (1) We match the X-ray sources to the Shu et al. (2019) AGN Note that for the two harder bands (2.3–5 and 5–8 keV), we catalog adopting a maximum separation of 3000, and display the use an unvignetted exposure map to generate the background X-ray to optical positional separation in Fig. 3. The second-pass map; but in the forced PSF-fitting, the vignetted exposure map is astrometric correction results in a much better consistency be- used, so that the measured count rate is corrected for vignetting. tween the separation distribution and the Rayleigh distribution. Fluxes in each forced photometry energy band are computed by assuming a power-law spectrum with spectral index Γ = 2.0 and The mean and median positional uncertainty, after this correc- 20 −2 tion, are 400.73 and 400.65, respectively. Figure 4 shows the cor- galactic absorption of NH = 3 × 10 cm . Liu T. et al. (submit- rected positional uncertainty as a function of the sources’ de- ted) performed spectral analysis for all the sources in the main tection likelihood in the 0.2–2.3 keV band. α , δ , and catalog, and found that this choice of (average) spectral index CORR CORR leads to an unbiased flux estimation for the whole sample, al- ∆θCORR are added to the source catalogs as columns RA_CORR, DEC_CORR, and RADEC_ERR_CORR, respectively. though there is a residual uncertainty caused by the variety of All parameter errors in the catalogs correspond to 68% con- spectral shapes. This is consistent with the well known fact that fidence limits as determined by the task ermldet. The task de- the average spectral slope of X-ray sources in a blind survey be- termines error margins by varying each fit parameter (X,Y posi- comes steeper as the flux limit in the 0.5–2 keV energy range tions, extent values, and count rates) from the best fit position in increases (see e.g. Hickox & Markevitch 2006). both directions to find the points where the likelihood function ∆C = C−C reaches the value 1.0 (see section A.5 for details). best 3.5. The catalogs The error values from both directions are averaged and a single error value is written to the output file. In the cases where the In this paper, we publish two distinct X-ray catalogs: the single- algorithm to determine the parameter errors failed to converge, band (0.2–2.3 keV) detected sources, and the hard-band (2.3–5 NULL values were written to the respective catalogue columns. keV) selected sources from the multi-band detection process. For the total band rate ML_RATE_0 and the derived count and flux values the errors of the single band rates are added in quadrature, Adopting a low detection likelihood threshold of 5, the treating them as Gaussian errors. For faint sources with large er- single-band detection results in a large sample of 32684 sources rors the error values and in particular the combined errors have to with a high fraction of spurious sources (see § 4.1 for details). be treated with caution. In cases where the determination of the With such a low threshold, many faint but potentially interest- positional error failed (490 sources in the Main catalog, or 1.8% ing sources can be detected, and potential cases of blended faint of the total), a mean RADEC_ERR_CORR of 400.0 was assumed. sources can be checked by multiple-PSF-fitting (see also the dis- cussion in Liu et al. 2020). Our strategy is to adopt a low threshold in the PSF-fitting and to apply further likelihood filtering on 3.4. Forced photometry the output as needed. In this paper, we select the 27910 sources with detection likelihood ≥ 6 as constituting the eFEDS Main We run forced-PSF-fitting photometry in seven energy bands: catalog. The 4774 sources with detection likelihood < 6 are kept 0.2–0.5, 0.5–1, 1–2, 2–4.5, 0.5–2, 2.3–5, and 5–8 keV (Ta- in a supplementary catalog, which we also publish here. ble D). Firstly, we create a background map for each band using the same method as described above for the source detection Figure 5 shows a healpix (Górski et al. 2005) map of the band. Using the preliminary catalog (before PSF-fitting) gener- eFEDS field, color-coded with the projected sky density of ated in the single-band detection as an initial guess, we run the the eFEDS Main catalog point sources. Considering the well- erbackmap background map creating and the erbox detection exposed part of the field, the catalog provides a quite uniform procedure twice using the same parameters as above. Now, a pre- source density across the entire covered area (with an average 2 liminary catalog is created for each band. Using this catalog, the of about 200 sources per deg ). As a general term of reference, final background map is created for each band. The preliminary this average source density is about 70 times larger than that of catalog of each band is only used for creating the background the ROSAT All-Sky survey (Boller et al. 2016), about 10 times map. We input the full single-band detected (or three-bands de- larger than the eRASS1 one, and about a factor 2.5 smaller than tected) catalog into ermldet PSF-fitting, but with the source po- that of the XMM-XXL survey (Chiappetti et al. 2018). sition and extent fixed. This forced PSF-fitting only provides a Most of the three-bands detected sources are already present count rate measurement for each of the chosen bands. The results in the single-band detected catalog, and we only use the three- of the forced fitting are given for all input sources, however, it bands detection here in order to select hard sources. In this way, should be noted that many of the single band measurements are we define a sample of 246 sources with an extent likelihood of not significant, in particular for the hard bands beyond 2 keV. 0 and a 2.3–5 keV band detection likelihood >10 as the Hard

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Fig. 5. Healpix map (Nside=128) showing the projected sky density of the eFEDS Main catalog point sources in equatorial coordinates. Each pixel has a size of ≈0.2098 deg2. eFEDS catalog. The selection criteria for the sub-catalogs are than the physical radius within which the flux of the extended given in Table 2. source is measured, emission from point source might contam- Both the main- and the hard-band selected catalogs are de- inate the extended source signal. Furthermore, a diligent analy- scribed in detail in Appendix D. Fig. 6 displays the distributions sis of the instrumental background and X-ray foreground has to of fluxes converted from the count rates. The Energy Conver- be performed when calculating the extended source flux as the sion Factor (ECF) between the count rates and fluxes is based on source detection algorithm might overestimate the background if a power-law model with Γ = 2.0 and with Galactic absorption the source is very extended. Therefore, the fluxes and count-rates 20 −2 (NH=3 × 10 cm ). given in the main eFEDS catalog must be treated with extreme Using ersensmap, we calculate the sensitivity for point care. We provide the corrected count-rate, flux, and luminosity sources in the 0.2–2.3 keV band. As a reference, in Fig. 7 we measurements of the full extent-selected sample at two fixed ra- compare the sky coverage of the main sample (detection like- dial distances (300 kpc and 500 kpc) in Liu A. et al. (submitted) and at physical overdensity radius of R in Bahar et al. (submit- lihood >6) and of the full single-band detected sample (detec- 500 ted). The characterization of the extended sources in the sample tion likelihood >5), converted to the 0.5–2 keV band, with that of a few contiguous Chandra and XMM surveys, including the is presented in Ghirardini et al. (submitted), while the optical XMM-XXL North and South surveys (Chiappetti et al. 2018), counterparts are given in Klein et al. (submitted). the Chandra COSMOS Legacy survey (Civano et al. 2016), and the XMM-RM survey (Liu et al. 2020). 4. Characterization of the source detection The extent-selected sample is constructed from the main procedure and catalog properties eFEDS catalog in the 0.2–2.3 keV energy band by adopting detection likelihood ≥5 and extent likelihood ≥6, as shown in Ta- 4.1. Completeness and contamination ble 2. Detection of celestial sources in the low-count regime (as in this In this catalog, we detect 542 candidate extended sources. case, and in most of X-ray astronomy), is a particular realization This number corresponds to a density of ∼4 extended sources of a stochastic process. Each catalog generated by such a source per square degree over the full eFEDS field. The extent and detection procedure is statistical in nature, and is always plagued detection likelihoods of this sample are shown in Fig. 8. The by spurious contaminating sources, as well as by incomplete- emission from the detected extended sources is fit using a beta- ness, or missed sources. A high level of completeness (fraction model with a slope fixed to 2/3 and rcore as extent parameter af- of detected true sources above a give threshold) achieved at a low ter convolution with the PSF. The fluxes and count-rates are then contamination level (fraction of spurious sources in the catalog) calculated from the normalisation of this fit model and hence is the essential figure of merit of any source detection procedure. correspond to the total integral over the beta-model. During this We have measured the completeness and contamination of process, a constant temperature of the intra-cluster medium and the eFEDS catalog through an extensive series of simulations constant value of the Galactic absorption (see above) is assumed. (Liu T. et al., submitted, summarized in Appendix E), and we Our source detection algorithm automatically deconvolves the briefly describe here the main outcome of such an analysis. source flux when there is a nearby point-source within a radius Fig. 9 displays the detected fraction of input point sources marked with “multrad”. If the “multrad” parameter is smaller (AGN and stars) in a differential (top panel) and cumulative (bot-

Article number, page 7 of 22 A&A proofs: manuscript no. eFEDScat

supp, 0.2-2.3 keV

main, 0.2-2.3 keV 103 3 10 hard, 2.3-5 keV

102 Number

1 10 102 DET_LIKE

100 2 1 0 log Count rate

supp, 0.2-2.3 keV 101 main, 0.2-2.3 keV 3 10 hard, 2.3-5 keV 101 102 EXT_LIKE

2 Fig. 8. The detection likelihood as a function of extent likelihood of 542 10 extended source candidates in the eFEDS catalog. Number

101 tom panel) manner. Down to a 0.5–2 keV flux limit of 10−14 erg cm−2 s−1, 96% of the simulated sources are detected. Down to × −15 −1 −2 100 a flux limit of 4 10 erg s cm , the completeness reduces to 65%. Using ersensmap, we can calculate the flux limit cor- 14 13 12 11 responding to the detection likelihood threshold (DET_LIKE= 5) log Flux (erg/cm2/s) and thus the sky coverage area curve as a function of such a flux limit. Normalizing this curve to a total area of 1 (black solid Fig. 6. Count rate and flux distributions of the main (blue solid) and the line in Fig. 9), this function also predicts the detectable fraction. supplementary (blue dashed) catalog in the 0.2–2.3 keV band and of the ersensmap hard catalog (orange) in the 2.3–5 keV band. However, such a fraction only reflects the definition of the detectable flux limit. As displayed in Fig. 9, a source above the detectable flux limit could still be missed because of fluctuation and measurement uncertainty in both source and back- 102 eFEDS main catalog ground or by blending with nearby sources; a source below the eFEDS main+supp limit still has a significant probability of being detected because COSMOS Legacy of fluctuation. XMM-RM Fig. 10 contains the main summary of our simulations-aided

) CDWFS assessment of the eFEDS catalog. It displays the distribution of 2

g 1 XXM-XXL-N all the single-band detected (simulated) sources as a function of e 10 d DET_LIKE

( their detection likelihood, . The sample is divided into

a five classes: sources uniquely matched to input point sources e r (class 1, purple in Fig. 10) or uniquely matched to input ex- A tended source (clusters; class 2, red), other sources matched to input point sources (class 3, green) or input clusters (class 4, or- 100 ange), and spurious sources due to background noise fluctuations (class 5, blue). When one input source results in multiple detected sources, the on-site detection which has the largest num- 10 15 10 14 ber of photons is considered as the unique match (class 1 or 2), and the secondary sources (class 3 or 4) correspond to signal in 0.5-2 keV Flux (cgs) the outer PSF wing of the input point sources or to substructures Fig. 7. eFEDS sky coverage area (red) as a function of 0.5–2 keV flux or fluctuations in an input cluster. According to whether the in- calculated using ersensmap at two detection likelihood threshold 5 (for put source is contaminated by nearby sources, class 1 and 2 are the full single-band sample) and 6 (for the main catalog). The sky cov- further divided into three sub-classes: contaminated by nearby erage of a few previous contiguous X-ray surveys are plotted for com- input point sources (dashed lines in Fig. 10), contaminated by parison. nearby input clusters (dotted lines), and uncontaminated ones (dot-dashed lines).

Article number, page 8 of 22 H. Brunner et al.: The eFEDS X-ray catalog

Single-band, Point sources 1.0 Single-band, all fluctuation 0.8 EXT signal 1000 PNT signal 0.6 800 uniq EXT uniq PNT

0.4 Number 600 + extended + blended 500 0.2 + extended 400 point sources Detected fraction (each bin) 1.0 0.6 fluctuation 0.4 uniq PNT 0.3 0.8 0.2 uniq EXT PNT signal 0.1 0.6 EXT signal 0.05 0.4 + extended + blended 0.02 + extended Fraction (>DET_LIKE_0) Fraction 0.2 point sources 0.01 DET_LIKE_0

Detected fraction (> Flux) area fraction 0.6 0.0 0.4 14.6 14.2 13.8 13.4 0.3 Input log Flux 0.5-2 keV 0.2 0.1 Fig. 9. The upper and lower panels display the completeness of the eFEDS single-band detected catalog (DET_LIKE≥5) measured from 0.05 simulation in terms of detected fraction in each input-flux bin (upper panel) and detected fraction in a subsample above a given flux limit Fraction (each bin) Fraction 0.02 (lower panel). The blue lines indicate input sources that are uniquely matched to detected point sources with EXT_LIKE<6. In the case of 0.01 the orange lines, the detected sources with EXT_LIKE≥6 are also in- 5 6 7 8 9 101112 14 16 18 20 25 30 cluded. In the case of the green lines, we further include input sources DET_LIKE that are associated with detected sources as secondary input counterparts. For comparison, we also plot the sky coverage area curve mea- Fig. 10. Distributions of all the single-band detected sources as a func- sured by ersensmap adopting DET_LIKE≥5 normalized to a total area tion of detection likelihood. The top panel displays the histogram of the of 1 (black line). detected sources; the bottom panel displays the fraction of each class in each bin (differential distributions); the middle panel displays the fraction of each class above a given detection likelihood (cumulative dis- According to the definition, the logarithmic detection likeli- tributions). The color-code for the various classes considered here is as hood, L corresponds to a probability of exp(−L) of one source follows: blue lines and histograms are for spurious sources (background being spurious. This probability is too low to plot in the bottom fluctuations); purple – unique point sources matched to point sources in panel of Fig. 10; the actual spurious fraction (blue line) is sig- the input simulated catalog; red – unique point sources matched to input clusters; green – other sources matched to input point sources; orange nificantly higher. This is because the likelihood is defined in an – other sources matched to input extended ones. In the lower two pan- ideal situation, considering only Poissonian fluctuations. In real- els, the dashed lines, dotted lines, and dot-dashed lines indicate input ity, additional uncertainties affect the source detection process in sources contaminated by nearby point sources, by nearby clusters, and every step, e.g., background measurement, source de-blending, uncontaminated ones, respectively. etc. That is the reason why the only way to measure the spurious fraction of a catalog reliably is via detailed simulation, as we have done here. 4.2. Aperture photometry and number counts As shown in the middle panel of Fig. 10, above a detection likelihood of 5, the sample include 11.7% spurious sources. This section presents the X-ray point-source number count dis- Adopting a likelihood threshold of 6 or 8, the spurious fraction tribution of the eFEDS survey, which requires a knowledge of reduces to 6.4% or 1.9%, respectively. Thanks to the availability selection function, i.e., the probability of a source with a given of a classifications for all detected sources, the simulation pro- flux to be detected. It has been demonstrated that the selection vides the fraction of any kind of input in any specifically selected function can be estimated on the basis of aperture photometry samples. In the suit of accompanying papers, we have made ex- (Georgakakis et al. 2008; Lehmer et al. 2012). Therefore, we run tensive use of this valuable information in order to estimate, for aperture photometry using apetool (see Appendix A.5). It uses example, the fraction of spurious sources in the hard band se- the aperture source and background counts to calculate a Poisson lected eFEDS point source catalog (Nandra et al., submitted), false rate for each source, i.e., the probability of the source being the fraction of true/spurious clusters in the extended source cata- generated by background fluctuation, which can be expressed log (Liu, A. et al., Klein et al., submitted), etc. (see more detailed in terms of logarithmic likelihood L as − ln(probability). This discussions in Liu, T. et al., submitted). likelihood can be used for sample selection. It can also be con-

Article number, page 9 of 22 A&A proofs: manuscript no. eFEDScat

0.40 Georgakakis+2008 2 10 XMM-RM 0.35 eFEDS

2 CDWFS 0.30

g Cappelluti+2009 e d

) 0.25

S 101 > ( 0.20 N

Relative fraction 0.15

0 10 0.10 10 14 10 13 S (0.5-2 keV) erg cm 2 s 1 0.05

Georgakakis+2008 0.00 10 8 6 4 2 0 2 4 6 8 10 eFEDS (f f )/ f2 + f2 CDWFS XMM eFEDS XMM eFEDS

2 0 Fig. 12. The distribution of the ﬂux diﬀerence of X-ray sources between 10 the XMM-ATLAS and eFEDS observations normalised by the corre- g

e sponding ﬂux uncertainties added in quadrature. The blue line shows a d

) Gaussian distribution with mean of zero and scatter of unity. S > (

N ing an ECF of 5.518 × 1010 cm2/erg, assuming the same spectrum model as used in § 3.4, i.e., a power-law with photon index 2.0. We select point sources with aperture Poissonian likelihood > 12, which results in 13457 sources in the 0.5–2 keV band and 2 3 4 5 6 8×10 13 151 sources in the 2.3–5 keV band. Based on these two sub- S (2-10 keV) erg cm 2 s 1 samples and using the method described in Georgakakis et al. (2008), we calculate the number counts in the 0.5-2 and 2–10 Fig. 11. Point source number counts as a function of fluxes that corrected for Galactic absorption for the 0.5-2 keV (upper panel) and 2-10 keV bands and compare them with those measured in Chandra keV (lowe panel) bands, with the 1-σ uncertainties estimated as the surveys (Georgakakis et al. 2008) and in the XMM-COSMOS square root of source number. In both panels, the eFEDS curves are survey (Cappelluti et al. 2009) in Fig. 11. They show good agree- compared to those of Georgakakis et al. (2008) (compiled from a num- ment. ber of Chandra survey fields) and Masini et al. (2020) (from CDWFS). The apetool-generated catalogues are also used to assess In the soft band we also plot the results from the XMM-COSMOS sur- the photometric calibration of the eFEDS field by comparing the vey (Cappelluti et al. 2009) and from the XMM-RM survey (Liu et al. 2020). In both panels, the dashed and dotted vertical lines indicate the fluxes of the detected sources to external catalogues. The choice flux limits corresponding to 10% and 50% sensitivities. of aperture photometry for this application is because it makes possible the statistically robust estimation of both the random (shot-noise) and systematics uncertainties (e.g. Eddington bias) verted into a sensitivity map containing the minimum required affecting source fluxes (e.g. Laird et al. 2009). This means that number of photons to reach a given likelihood. This map can observational effects can be fully accounted for when comparing be used to correct for the incompleteness of the eFEDS point- fluxes from different experiments to test cross-calibration issues. source catalogue as a function of X-ray flux. During the forced We also choose to use fluxes in the 0.5–2 keV energy interval PSF-fitting photometry for each band, besides calculating the because this is one of the standard bands that many X-ray cata- fluxes, we have also created a background map and a source logues in the literature report fluxes in. In the case of the eFEDS map (source extent model convolved with PSF). Making use of we use the 0.5–2 keV forced-photometry catalogue. them, we run apetool within a radius of 60% encircled energy The external dataset adopted in this work is the XMM- fraction (EEF), adopting an aperture likelihood threshold of 12. ATLAS survey (Ranalli et al. 2015). This is one of the wide-area 2 −14 −1 −2 The aperture size and likelihood threshold are selected accord- (6 deg ) and shallow (F0.5−2keV ≈ 2 × 10 erg s cm ) sur- ing to simulation tests (Liu, T. et al., submitted). In this analysis, veys carried out by the XMM-Newton and also overlaps with the we exclude the border of the field, where the exposure is much eFEDS field. A custom reduction of the XMM-ATLAS survey lower than the typical depth of eFEDS. We adopt the inner re- field is used based on the methods described by Georgakakis & gion where the 0.2–2.3 keV vignetted exposure value is above Nandra (2011). The advantage of using a custom analysis rather 500 s. This region comprises 90% of the total area. than the publicly available XMM-ATLAS catalogue, is control Based on the aperture photometry results, we convert the over systematics. The relevant XMM-Newton observations have 0.5–2 keV count rate to Galactic-absorption-corrected flux us- identification numbers 0725290101, 0725300101, 0725310101. ing an ECF of 1.104 × 1012 cm2/erg, and convert the 2.3–5 keV They are reduced using the XMM-Newton Science Analysis count rate to Galactic-absorption-corrected 2–10 keV flux us- System (SAS) version 18. Sources are detected independently in

Article number, page 10 of 22 H. Brunner et al.: The eFEDS X-ray catalog

3 energy intervals, 0.5–2, 2–8 or 0.5–8 keV to the Poisson false Zentrum für Luft- und Raumfahrt (DLR). The SRG spacecraft was built by Lav- detection threshold of < 4 × 10−6. ochkin Association (NPOL) and its subcontractors, and is operated by NPOL Relevant to this work are the total of 987 sources detected in with support from the Max Planck Institute for Extraterrestrial Physics (MPE). The development and construction of the eROSITA X-ray instrument was led the 0.5–2 keV band to the threshold above. These are compared by MPE, with contributions from the Dr. Karl Remeis Observatory Bamberg against a total of 985 eFEDS sources that lie within the XMM- & ECAP (FAU Erlangen-Nürnberg), the University of Hamburg Observatory, ATLAS footprint and have a detection likelihood in the 0.6– the Leibniz Institute for Astrophysics Potsdam (AIP), and the Institute for As- 2.3 keV band of DET_LIKE>10. This threshold is chosen to min- tronomy and Astrophysics of the University of Tübingen, with the support of DLR and the Max Planck Society. The Argelander Institute for Astronomy of imize spurious detections, while keeping number statistics high. the University of Bonn and the Ludwig Maximilians Universität Munich also The calculation of fluxes for both the eFEDS and XMM-ATLAS participated in the science preparation for eROSITA. The eROSITA data shown fields is based on aperture photometry and uses the Bayesian here were processed using the eSASS software system developed by the Ger- methodology described by Laird et al. (2009) and Georgakakis man eROSITA consortium. We thank Alberto Masini for providing us the data for CDWFS to be included in Fig. 7 and 10. N. Clerc acknowledges support by & Nandra (2011). A description of the basic flux-estimation al- CNES. gorithm is also described in Boller et al. (submitted). The fluxes in both samples are estimated in the 0.5–2 keV spectral band assuming a power-law spectral model with Γ = 1.4 that is absorbed −2 by a Galactic column density of log NH/cm = 20.3. It is em- phasised that this is different from the spectral model adopted for the calculation of fluxes in the main eFEDS catalogue. The reason for this is that the XMM-ATLAS reduction adopts Γ = 1.4 for the determination of fluxes. There are a total of 616 common sources in the eFEDS and XMM-ATLAS samples. These are identified by matching the two catalogues within a radius of 1500. For the sky density of the XMM and ATLAS sources this threshold corresponds to 1 spurious associations. Figure 12 compares the 0.5–2 keV fluxes of the common sources in the two surveys. It plots the histogram of the flux difference between the eFEDS and XMM-ATLAS normalised to the flux errors (68% confidence interval) added in quadrature. This distribution is compared with a Gaussian of unity variance and zero mean. There is no evidence for strong systematic offsets in Figure 12 suggesting an overall good photometric agreement between the XMM-ATLAS and eFEDS data analysis. There are however more sources with large normalised flux differences compared to the normal distribution expectation. We attribute this excess power at the wings of the histogram in Figure 12 to the intrinsic flux variability of AGN. This effect is discussed further in Boller et al. (submitted).

5. Conclusions In this work, by publishing and documenting the full catalog of X-ray sources detected in the eFEDS field, we complete the verification of the eROSITA design performance, and demonstrate the ability of the instrument as a powerful survey machine for the X-ray sky. With the exception of the all-sky surveys, the eFEDS itself represents the largest contiguous X-ray survey in the soft X-rays energy range, as illustrated in Figure 13, where we show the point-sources flux limit (in the 0.5-2 keV energy range) – area scatter plot of X-ray surveys larger than 1 deg2. Also in terms of sheer number of detected sources excluding all-sky surveys, eFEDS stands out as the richest contiguous survey field to date. This paper serves a twofold purpose: it makes public the catalog of X-ray sources detected in the eFEDS field during the SRG/eROSITA PV observations of 2019 for further scientific in- vestigations, and at the same time describes, for the first time in a comprehensive manner, the data processing and analysis of eROSITA field scanning observations, including the relevant dedicated software tools. The interested reader will find those in the Appendix. Acknowledgements. This work is based on data from eROSITA, the primary instrument aboard SRG, a joint Russian-German science mission supported by the Russian Space Agency (Roskosmos), in the interests of the Russian Academy of Sciences represented by its Space Research Institute (IKI), and the Deutsches

Article number, page 11 of 22 A&A proofs: manuscript no. eFEDScat

Fig. 13. Point-sources ﬂux limit (in the 0.5–2 keV energy range) vs. area scatter plot of a few selected X-ray surveys larger than 1 deg2. Existing surveys from Einstein (light green downwards triangle), ROSAT (dark green upwards triangles), XMM-Newton (blue circles) and Chandra (purple squares) are shown for reference. Filled points mark contiguous surveys, empty non-contiguous ones. To allow a fair comparison, we have considered for each survey the total area covered (x-axis) and a ﬂux limit that corresponds roughly to a completeness level of 66%. The dotted lines mark the loci of constant number of sources, based on the number counts in the 0.5–2 keV energy rage of Mateos et al. (2008) (double power-law model). The surveys shown, from left to right are: The Subaru/XMM-Newton Deep Survey (SXDS; Ueda et al. 2008); the XMM-COSMOS survey (Cappelluti et al. 2009); the COSMOS-Legacy survey (Civano et al. 2016); the XMM-Newton Medium Survey (XMS; Barcons et al. 2003); the XMM-Newton Bright Survey (XMM-BCS; Della Ceca et al. 2004); the XMM-RM survey (Liu et al. 2020); the XMM-ATLAS survey (Ranalli et al. 2015); the Chandra Deep Wide Field Survey (CDWFS; Masini et al. 2020); the Chandra Multiwavelength Project (ChamP; Kim et al. 2007); XMM-SERVS (Brandt 2020); the ROSAT International X-ray/Optical Survey (RIXOS; Mason et al. 2000); XMM-XXL N & S (Chiappetti et al. 2018); Stripe82X (LaMassa et al. 2016); NEP (Henry et al. 2006); the second Chandra Serendipitous Sources Catalog (CSC2.0; Civano, priv. comm.); the Einstein Observatory Extended Medium-Sensitivity Survey (EMSS; Gioia et al. 1990); the fourth XMM-Newton serendipitous source catalog (4XMM; Webb et al. 2020), and the second ROSAT all-sky survey catalog (2RXS Boller et al. 2016).

Article number, page 12 of 22 H. Brunner et al.: The eFEDS X-ray catalog

Appendix A: eSASS Data Analysis Software important role in the whole processing chain, because it affects Package key performance parameters of eROSITA, such as the spectral resolution and sensitivity, and also the spatial resolution. This Appendix describes the software tasks comprising the eROSITA Science Analysis Software System (eSASS). eSASS provides a set of command line tools for pipeline processing the energy. The task energy tries to reconstruct the energy of each eROSITA data and for performing interactive data analysis tasks. detected photon from the charge distributions found in individual The eSASS tasks interact with the eROSITA calibration database pixels and constrains, as a by–product, also its sub-pixel posi- described in Appendix B. Calibrated data products provided by tion. It makes use of the results of the pattern task, which must the data analysis pipeline are described in Appendix C. A full de- thus be executed beforehand. The reconstruction of the energy scription of each eSASS task including usage examples is avail- of an incident photon consists essentially of three steps: First, able online3. a CTI (Charge Transfer Inefficiency) correction: the charge loss caused by shifting the charge from its original location to the readout node must be corrected for. Second, a Gain correction: Appendix A.1: X-ray event processing the eROSITA CCDs are characterized by parallel readout, where evprep. This task generates an event-list file in the format each transfer channel is equipped with an amplifier of its own, agreed for eROSITA from the raw FITS6 files created from and the amplification factors need to be individually determined. telemetry by the archiver software. The evprep task performs Third, a recombination of the reconstructed energies from all the many other corrections, including: pixels of a pattern. In addition to these essential steps for X–ray spectroscopy, it is possible to obtain also an improved location of – Detects a variety of error and out-of-limit conditions and sets the center of the charge cloud from the individual components, corresponding bits of the event FLAG masks. so that the location where the X–ray photon had hit the CCD can – Corrects offsets in the Camera Electronics (CE) time stamps be determined with sub-pixel resolution (Dennerl et al. 2012). energy as specified in the calibration database. The task is crucial for the whole processing chain, because the absolute energy scale and the spectral resolution rely – Converts the times in Good Time Intervals (GTI) and House- on it. keeping (HK) extensions from the low-cadence but reliable ITC time system to the higher-cadence CE time system. – Unpacks the compressed event energy data for observations Appendix A.2: Spacecraft attitude and boresight performed in PMENV2 mode. – Excludes bad time intervals read from the calibration attprep. The task attprep converts the attitude time series database from the sequence of GTIs. from the SRG orientation sensors (SED26/1, SED26/2, BOKZ, – Calculates and stores dead time corrections. or Q-Gyro, see also appendix B.4) into the eSASS intermediate attitude format. The input attitude is provided as a time series of orientation quaternions for the SED26/1, SED26/2, Q-Gyro ftfindhotpix. The task ftfindhotpix is a tool to detect and FITS files and as an orientation matrix for the BOKZ FITS file. save the positions of bad pixels by analyzing the data with sta- The nominal cadence is 1 per second with time tags given in tistical methods. The task can be run in either ‘single‘ or ‘block‘ SRG space craft clock (SCC). The intermediate attitude de- mode where the Poisson mean value of a single pixel (and its im- scribes the orientation of the nominal coordinate system of the mediate neighbours) or a block of pixels is compared to a given central eROSITA camera TM1 as a time series of RA (J2000), threshold which denotes the maximum probability in percent for DEC (J2000), and roll angle, which is defined as the clockwise false positive of a bad pixel. In addition a number of additional angle of camera X-axis with respect to the north direction. The parameters like number of framebunches to consider, minimum rotational transformations between the sensor coordinate sys- number of events in a framebunch, and the minimum fraction of tems and the TM1 camera coordinate system are stored as rota- frames for which is a pixel is considered bad, can be optimised tion quaternions in a calibration file for each sensor. The output to decrease the probability of false positives. At present, the de- FITS file contains the intermediate attitude data set from the pri- tection of bad pixels is turned off and ftfindhotpix only sets mary sensor in the the first FITS extension and all sensor specific bits of the FLAG mask for events which lie on or next to a pixel attitude data sets in additional extensions. The primary sensor is listed in the calibration database as bad (various types are recog- the Q-Gyro, if present, or else the SED26/1, SED26/2, or BOKZ nized thereof), and writes valid entries from the calibration to a in this order. BADPIX extension in the event list file. telatt. The task telatt calculates attitude time series specific pattern. The charge cloud released by the absorption of an X– for one of the telescope modules TM1 .. TM7. The input atti- ray photon may extend over several pixels. The task pattern tude is read from the intermediate attitude file written by task tries to identify these pixels, so that the total released charge attprep. The camera-specific boresight angles are read from can be reconstructed. This, however, is not always possible in calibration files in the form of Euler angles and applied to the a unique way (e.g., when the charge clouds released by two pho- input attitude. The resulting attitude time series is written as Eu- tons overlap). The general driver for the photon reconstruction ler angles RA (J2000), DEC (J2000), and roll angle either to a in pattern is to find the simplest, most likely explanation for separate FITS file or as a FITS extension to the camera-specific the observed charge distribution. If no such explanation can be events file. found, the pattern is marked as invalid. Valid patterns consist of 1 – 4 pixels, with 1 and 2 pixel patterns (‘singles’ and ‘doubles’) being the most important ones. The task pattern performs an evatt. The task evatt is used to project event positions to equatorial sky coordinates. The task reads an event list for a single 6 Wells et al. (1981) telescope module, the corresponding attitude time series (as writ-

Article number, page 13 of 22 A&A proofs: manuscript no. eFEDScat ten by task telatt), and a GTI table. For all events in the inter- are taken into account, the source model is convolved by the PSF vals specifies by the GTI table, the telescope attitude is interpo- to compute how much flux is lost outside the extraction region lated to the arrival time of each event. The event position in the for each time step. The task supports a number of geometric re- detector coordinate system given in the detector pixel columns gions for source extraction, including circles, ellipses and boxes, RAWX, RAWY and sub-pixel information in the SUBX, SUBY in addition to a generic mask image option, all of which can be columns of the event table is projected to equatorial coordinates combined or subtracted. srctool also has the ability to compute by means of a tangential projection with the interpolated attitude extraction regions automatically given a source list. In this mode and using the plate scale from a calibration file. the aim is to increase the source and background extraction circular regions until the signal to noise ratio is maximised, while taking into account excluding neighbouring sources. radec2xy. The task radec2xy computes X and Y sky pixel coordinates (sine projection; pixel size 000.05) corresponding to the right ascension and declination (J2000) event coordinates in the Appendix A.4: Map creation eROSITA event files. The projection centre must be specified on expmap the command line. Sky pixel coordinates are required for image expmap. The task generates FITS-format exposure binning (evtool) and may be used for spectral and light curve maps to match in register with the location and dimensions of extraction (srctool). a supplied template image. The exposure is expressed in units of seconds each sky location was in the field of view. It can optionally be folded with the telescope vignetting function in each Appendix A.3: X-ray event binning energy band. The algorithm samples periods of GTI in the input event list and projects the CCD onto the sky at each sam- evtool. The task evtool provides three capabilities: ple time according to the record of spacecraft attitude contained 1. Merging several event lists. All canonical extensions are in CORRATT extensions. Other inputs to the maps are bad pix- merged. Note that each input event list must cover a differ- els as listed in the BADPIX extensions, dead time as recorded in ent range of telescope modules (TMs) – it is not permitted to the DEADCOR extensions, the detector mask, and the vignetting merge 2 or more event lists that deal with the same TM(s). function. While the vignetting function is energy dependent, we follow the approach of XMM-Newton exposure maps (XMM- 2. Filtering the events on a subset of the columns. Filter modes 7 available are: SAS ) to not weight the vignetting with an assumed spectral – FLAG column (via bit mask, either exclusive or inclusive). model. This results in systematic errors of the vignetted exposure – PAT_TYP column (effectively via bit mask). and derived count rates and fluxes in the energy bands of inter- expmap – TM_NR column (via a list of desired numbers). est in the few percent range. Future versions of the may – PI column (via a list of energy bounds). provide an option to fold the vignetting function with a suitable – TIME column (via a GTI specification). spectral model. Exposure maps for individual telescope modules – RA, DEC columns (via a region specification). and also weighted all-eROSITA ‘merged’ maps are available as outputs. 3. Creation of FITS images. The pixel sizes on the sky, the image dimensions in pixels, and the image centre location, are all specifiable. Some auto-sizing operations are also avail- ermask. The task ermask uses the exposure maps to calculate able. Most of the extensions in the input event list(s) are op- detection masks. The masks are FITS images with the same di- tionally discardable for image output. mensions as the exposure maps. Pixels in image areas useable for source detection are set to 1, all other pixels are set to 0. The area selection is based on two configurable thresholds: srctool. The srctool task is responsible for the generation of standard source products, including spectra, response matrices, – a lower limit for the exposure as a fraction of the maximum background spectra and lightcurves. It takes as input the cali- map value, brated event file, source lists, region files and the calibration data. – an upper limit for the spatial gradient of the exposure map. The task is designed to create products taking into account the scanning of the telescope across the sky. The mechanism it uses erbackmap. The task erbackmap calculates a background map to do this is to take a set of sample points as a function of position based on a photon count image, the corresponding exposure and as a function of energy, given a source model and extraction map, the detection mask, and an initial source list. In a first step region. Both the source regions and background regions are sam- the task calculates a mask to blank out circular regions around pled in this way. These samples are propagated through time to the sources from the input list. The radii of these circles depend take account of the vignetting and bad pixels as a source scans on the source count rate, the PSF, and on source extent param- across the detectors, which is included in the computation of the eters from the input list. A second step smoothes the remain- source-specific effective area curves and in the area calculation ing images and interpolates the map into the masked out regions for light curves. The GTI and exposure for a source are computed around the input sources. For this step two options are available: from when the sample points for a source enter and exit the field of view. Similarly, the area on the sky of the source when used – a 2-dimensional smoothing spline, for background subtraction and the geometric area of the extrac- – an adaptive smoothing algorithm (recommended). tion region are computed as the average values computed from The adaptive smoothing algorithm convolves the input images the sample points during the good time intervals. The accuracy with Gaussian smoothing kernels of different scales and, for each to which the output effective areas and exposure times is calcu- pixel, chooses the smoothed map which reaches the user-defined lated depends on parameters giving the spacing of the sample signal-to-noise ratio. points on the sky and in time. srctool takes account of source morphology by a model chosen by the user (for example a point 7 Users Guide to the XMM-Newton Science Analysis System, Issue source, top hat, beta model or a provided image). If PSF losses 16.0, 2021 (ESA: XMM-Newton SOC)

Article number, page 14 of 22 H. Brunner et al.: The eFEDS X-ray catalog ersensmap. The task ersensmap uses the eSASS exposure background counts bi in each input image i using the (logarith- maps and background maps to estimate the detection limits in mic) likelihood eROSITA observations. For each map pixel the task calculates the detection limits for aperture methods as employed by the task erbox or for the PSF fitting method as used by task ermldet. In Li = − ln PΓ(ni, bi) (A.1) the aperture case the algorithm iteratively determines the source where P is the regularised incomplete Gamma function flux necessary to reach the given likelihood threshold according Γ to equation A.1. In the PSF fitting case the task calculates the R x flux necessary to reach the likelihood threshold determined by e−tta−1dt 0 the C statistic (equation A.2). In both modes the task can also PΓ(a, x) = R ∞ . e−tta−1dt handle the case where several input images are used for simulta- 0 neous source detection as implemented in erbox and ermldet. In the case of multiple input images (e.g., in different en- For the conversion between fluxes and count rates, energy con- ergy bands), a combined likelihood is computed using Fisher’s version factors have to be given as task parameters. method (Fisher 1932). The probability values Pi from n independent tests of the same null hypothesis can be combined as 0 Pn 2 Appendix A.5: Source detection and photometry L = −2 i=1 ln Pi, which follows a χ distribution with 2n degrees of freedom. The combined detection likelihood of a source flaregti. The task flaregti creates a set of GTIs which op- can therefore be calculated as timise the ability of sources to be detected, or created from a fixed count rate threshold. The first step is to remove bright      Xn  point sources using a simple detection algorithm which identi- L = − ln 1 − P n, L  . fies bright pixels in a binned image, which are later excluded det  Γ  i i=1 from lightcurve production. A lightcurve of the count rate per unit area is then computed from the data in a given energy band, The source list is filtered using a threshold on the combined like- given the input GTIs. A regular grid of points are chosen over the lihood. For the significant sources the following parameters are area of sky contained within the event file. For each of these grid calculated for each input image and for the combined data set: points, lightcurves are constructed, by only taking those time bins where the point in question is within the field of view of – raw box counts, the telescope. Each of these lightcurves is analysed to either, in – PSF-corrected box counts with errors, standard operation choose an optimal threshold for that spatial – PSF-corrected count rates with errors, location, or to apply a fixed threshold. When calculating an op- – source fluxes with errors, timal threshold, the task chooses a threshold which minimizes – background counts, the flux at which a source of a specified size can be detected – detection likelihood values, against the average sky surface brightness. Once it has a set of – source exposure values (for each input image only), thresholds for each grid point, the task then identifies for each – centroid positions in image and equatorial coordinates (com- time bin within the lightcurve which grid point is closest to the bined values only) with errors, centre of the field of view. For each time bin, the threshold of – the image rebinning step in which the source is most signifi- this nearest grid point and the measured rate is used to decide cant, whether a time bin is good or bad and then constructs the GTIs. – hardness ratios of the form HR12 = (cr2 − cr1)/(cr1 + cr2) These flare-based GTIs are merged with the original input GTIs with errors. to make new combined GTIs for each TM. The task then repeats the whole processes back to the source detection stage based on ermldet. The task ermldet applies a PSF fitting algorithm to these new GTIs, for a given number of iterations. flaregti determine source parameters for a list of input positions. It can writes the output FLAREGTI GTI data back into the original also apply multi-PSF fits in order to de-blend neighbouring X- event file as extensions or to a separate GTI file, and optionally ray sources. The source PSF can be generated using the follow- writes lightcurve, point source mask and spatial threshold files. ing methods:

– from 2D PSF images stored in calibration files for a grid of erbox. The task erbox is based on a sliding box algorithm to photon energies and off-axis angles (pointed observations). detect peaks in the input count images. The task can be run in – from 2D images of the PSF averaged over the detector area two modes: and stored for a grid of photon energies. – reconstruction of a source-specific PSF by averaging the – local mode, which estimates the background from a region PSFs of each source photon, the event-specific PSFs are surrounding the source box. stored in calibration files as sets of shapelet coefficients for a – map mode, which uses the background maps generated by grid of energies and detector positions. – calculation of event specific PSFs using the shapelet coeffi- erbackmap at the position of the source. cients stored in calibration files ("photon mode").

The algorithm first smooths the input images with a beta A maximum likelihood fitting procedure is applied to the function type kernel and then searches for peaks in the smoothed sources in the input list, starting with the most significant source images. This peak search can be repeated several times after re- and then working on the sources in the order of descending like- binning the input images by a factor of 2×2, effectively doubling lihood. Neighbouring sources can be combined for simultane- the box size. The peaks are then tested for statistical significance ous fitting, and input positions can also be split up into multiple by comparing the number of box counts ni with the expected sources.

Article number, page 15 of 22 A&A proofs: manuscript no. eFEDScat

The source models are generated using PSFs which are op- Assuming ∆C follows a χ2 distribution, parameter errors cor- tionally folded with an extent model. The extent model is either responding to 68% confidence intervals can be calculated by a Gaussian kernel or a beta model of the form varying the parameter of interest from its best value in both di- !−3β+1/2 rections until C = Cbest + 1.0 is reached. These boundaries are (x − x )2 + (y − y )2 f x, y 0 0 determined by an iterative procedure and the errors for both di- ( ) = 1 + 2 rc rections are averaged and written to the output table. In cases where for one direction the algorithm fails to converge after the with β = 2/3, the core radius rc is a free fit parameter. The mod- given number of iterations, the errors determined for the other els are multiplied with the exposure map to account for instru- direction are adopted. In case no error margin can be determined mental effects and the background is added. The model parame- in either direction, a zero is written to the output table. The po- ters are: sitional errors are given in units of image pixels for both X and – x, y positions in image coordinates for each source, Y positions as well as an error√ radius in units of arc seconds: – source extent radius for each source, ∆(RA, Dec) = pixelsize × ∆X2 + ∆Y2. For derived quantities – source count rate for each source and input image. as the sum of count rates in multi-band fits or the hardness ratios between energy bands the count rate errors are propagated The source parameters are optimized by minimising the C- treating them like Gaussian errors. statistic (Cash 1979): For each source passing the likelihood thresholds the following source parameters are written to the output source list: N X – best fit position with errors in image, equatorial, and galactic C = 2 (e − n ln e ) (A.2) i i i coordinates; i=1 – best fit source extent value with errors; where ei is the expected model value of pixel i, ni is number – best fit counts, count rates, and fluxes with errors; of photon events in pixel i, and N the total number of image – likelihood values for detection and extent; pixels used for the fit. Once the fit has converged at a set of best – exposure and background map values at the source position; fitting parameters, the significance of each source is tested by – hardness ratios of the form HR12 = (cr2 − cr1)/(cr1 + cr2) calculating with errors ; – the radius of the subregion used for fitting, the PSF fraction ∆C = Cnull − Cbest, covered by that region and the fraction of pixels with valid detection mask values. where Cnull is the C-statistic of the null hypothesis (i.e. model with zero net counts) and Cbest is the value for the best fitting The source list contains several rows per source: one per in- model. The fitting algorithm of ermldet can optionally obtain put image, plus summary rows over the energy bands and, where an individual PSF for each photon event depending on its en- applicable, a summary over different instruments. ergy and detector position; where applicable, the event PSF is convolved with the extent model. In this case the C-statistic in equation A.2 is summed over the number of events rather than apetool. The task apetool has three main functionalities: i) over the number of image pixels. produces maps of the size (radius in pixels) of the PSF across According to Cash (1979), ∆C approximately follows under the eROSITA field-of-view (PSF maps), ii) performs aperture certain conditions a χ2 distribution with the number of degrees of photometry at a set of user-defined positions and iii) generates freedom ν equal to the number of free model parameters. Hence sensitivity maps following the methodology described by Geor- the probability P that ∆C results from a chance fluctuation of the gakakis et al. (2008). background can be calculated using the regularised incomplete The PSF of eROSITA is modeled using the shapelet basis functions (Refregier 2003; Refregier & Bacon 2003). The Gamma function PΓ: shapelet coefficients that describe the distribution of photons at ! a certain energy and at a given position on the eROSITA field of ν ∆C P = 1 − P , . view are stored in a calibration file. For the construction of the Γ 2 2 PSF map the apetool first extracts the GTI from the attitude file. For each time interval the shapelet coefficients at the posi- Based on the value of P, a logarithmic detection likelihood tions of a given pixel are retrieved from the calibration file. The average of each shapelet coefficient across all time intervals is L = − ln(P) used to reconstruct a model of the PSF at the position of interest. This is then used to measure the size of the PSF in pixels at is obtained for each source. In case of simultaneous multi-source encircled energy fractions (EEF) between 40-95% in steps of 5 fits, sources falling below the user defined likelihood threshold per cent. The apetool estimates the PSF size in a regular grid are removed and the fitting procedure is iteratively repeated. The of positions on the eROSITA field-of-view. The density of the conditions for ∆C to follow a χ2 distribution are not completely grid is a trade-off between speed, size of the final PSF map, and fulfilled in the low count-rate regime, and thus P does not cor- an adequate description of the variations of the PSF size across respond to the actual false alarm probability. We use extensive the field of view. The default setup is a grid of 21 × 21 positions simulations (Liu et al., submitted) to determine the false detec- along the X and Y direction. tion probabilities at various levels of L. After each source fit, In the case of aperture photometry there are two options, ei- the best fitting model is added to the internal background map ther extract counts at source positions defined in a source cata- used for the model fits of subsequent (fainter) sources. The fi- logue generated by the ermldet task or at arbitrary user-defined nal source model + background maps can be written as FITS positions. The difference between the two options is the for- images. mat of the input and output source lists. In the first case, the

Article number, page 16 of 22 H. Brunner et al.: The eFEDS X-ray catalog ermldet source catalogue is supplemented with aperture pho- HEASARC8 CALDB framework for managing calibration files. tometry products. These include i) the total counts at a given Each of the seven telescope modules of eROSITA has its own position (source and background) extracted within an aperture set of calibration files. The names of the calibration files follow of size defined in units of EEF, ii) the background counts ex- a naming convention that specifies the telescope module, cali- tracted from the source maps generated by the ermldet, iii) the bration type and, if necessary, the type of detector or filter for mean exposure time, iv) the EEF used to define the extraction which this calibration file is intended, as well as the date from radius, v) the size of the extraction radius in pixels and vi) the which this information is valid and the version number of the Poisson probability that the extracted counts (source + back- file. For example tm2_badpix_190712v01.fits contains the ground) are a fluctuation of the background. These quantities can information on the bad pixels of TM2 valid from 12 July 2019 be combined to estimate the source’s flux. The case of aperture (i.e. before launch) in the first version. photometry at arbitrary source positions corresponds to science applications related to e.g. X-ray stacking analysis or searches for faint X-ray emission (i.e. below the formal X-ray detection Appendix B.1: Telescope and point spread function threshold) associated with counterparts selected at other wave- Vignetting. ‘Vignetting’ is defined here as the flux of a point lengths or external (non-eROSITA) X-ray catalogues. The aper- source contained in a circle of 40radius relative to that flux at the tures within which counts are extracted at user-defined positions on–axis position. The vignetting data base contains parameters are expressed in terms of EEF. The quantities as listed above are for computing this value for any given photon energy and off– estimated and stored in an output file. axis angle. Comparisons between the measured values and the The sensitivity map generated by apetool has units of modeled vignetting curves are shown in Fig. 7 of Dennerl et al. counts. They represent the minimum number of photons (source (2020). and background) within the extraction aperture (expressed in EEF units) at a given position on the detector, so that the Pois- son false detection probability is lower than a user-defined value. Point spread function: images. In the ground calibration, im- The Poisson false detection probability is defined as the proba- ages of the Point Spread Function (PSF) were obtained at the bility of the background fluctuating in a random fashion to pro- MPE PANTER facility9 individually for each mirror assembly duce counts within an aperture above a given value. This prob- (MA) at the energies of the C–K, Cu–L, Al–K, Ag–L, Ti–K, ability is given by the survival function of the Poisson proba- Fe–K, and Cu–K emission lines, covering the energy range from bility distribution. The resulting sensitivity maps can be com- 0.3 to 8.0 keV. The MAs were placed 124 m away from an X– bined with the aperture photometry determiend by apetool for ray point source and mounted together with the X–ray camera the ermldet sources to provide an accurate representation of ‘TRoPIC’ on a rigid platform, which could be tilted horizontally the point-source selection function (probability of detecting a and vertically. The TRoPIC X–ray CCD is identical in its pixel source) at a given Poisson false detection threshold (see Geor- size to the eROSITA CCDs, but consists of only 256×256 pixels. gakakis et al. 2008). The combination of the apetool sensitiv- In order to sample the full eROSITA focal plane, TRoPIC was ity maps with the aperture photometry of the ermldet-detected mounted on a manipulator, which shifted it to five different posi- sources (also via apetool) enables, among others, the accurate tions for covering the central and the four outer parts of the FoV. estimation of the X-ray point-source number count distribution The four outer TRoPIC positions sampled the PSF on a rectan- as a function of X-ray flux, i.e. log N − log S (see Section 4.2). gular 60 × 60 grid in 121 images, covering the offset angles from The sensitivity map FITS file includes three image exten- −300 to +300. The central TRoPIC position measured the PSF sions, i) the sensitivity map itself, i.e. the minimum number of in 36 images on a 60 × 60 grid which was shifted by 30 with re- counts as described above as a function of detector position, ii) spect to the outer grid and covered the off-axis angles between the expected background within the extraction radius and iii) −150 and +150. This resulted in 157 images per MA and energy. the corresponding average exposure time (mean of the exposure In order to save measurement time, Cu–L exposures were only map) within the extraction radius. With these three components done for TM1 and TM2, and the outer part of the FoV was only it is possible to estimate the detection probability of a source sampled in the upper right quadrant at Ag–L, Ti–K, Fe–K, and with a given count-rate or flux. The resulting area or sensitivity Cu–K except for TM1, where the full grid was covered in all the curve is stored in the fourth (table) extension of the sensitivity 7 energies. map fits files. It includes count rate and the corresponding area In order to obtain the required large number of PSFs within a in square degrees within which a source of this count-rate can be reasonable time, the measurements were taken at very high pho- detected. This calculation makes no assumptions on the X-ray ton rates, taking extreme pile–up into account and making use spectral shape of the source. of the fact that, if the dominant incident energy is known, the number of photons per pixel can be reconstructed from the total charged released there. In this mode, however, it is not possible catprep. The task catprep re-formats the source lists written to apply the usual technique to identify and suppress the traces by the tasks ermldet and apetool. The output format contains of minimum ionizing particles by selecting only valid pixel pat- only one row per source; the energy band specific values are terns, because photon pile–up may also create ‘invalid’ pixel pat- written as separate columns. The task also assigns a source iden- terns. This problem could be solved by developing specific cri- tification string containing the root name of the input file, the teria for spotting ‘suspicious’ pixel patterns, by removing all the source number from the input list, and the processing version. ‘contaminated’ CCD frames, and by visually checking the remaining frames for each of the 4860 PSF exposures. It turned ∼ Appendix B: eROSITA calibration database out that only 5% of the frames needed to be rejected. In this way, the exposure time per PSF could be reduced from several The eSASS calibration database (CALDB) contains all information that is required for calibrating the data collected with 8 https://heasarc.gsfc.nasa.gov/ the eROSITA telescope modules (TMs). It is based on the 9 https://www.mpe.mpg.de/heg/panter

Article number, page 17 of 22 A&A proofs: manuscript no. eFEDScat

tions of a circular Gaussian proﬁle. In one dimension these are described by the relation

1 2 1 − x h n i 2 − 2 φν(x; β) = 2 βπ 2 n! Hn(x/β) e 2 β , (B.1)

where n is a non-negative integer, Hn(x) is the Hermite polyno- mial of order n and β is the scale of shapelet function. In the case of 2-dimensional images with coordinates (x, y) the shapelet basis functions are given by the relation

ψν,µ(x, y; β) = φν(x; β) · φµ(y; β). (B.2) In this case the order of the shapelet function is characterised by the two non-negative integers n, m and there is a single scale β for both φν(x), φµ(y). The choice of the scale β depends on the size of the features to be modelled. The motivation for using this set of functions is that they have been used to reconstruct the complex shapes of galaxies in optical surveys for weak lensing applications (Massey et al. 2007). In the case of the eROSITA PSF we use 3 independent sets Fig. B.1. Example of the 1.5 keV TM1 PSF at an off–axis angle of 300 of shapelet functions, ψν,µ(x, y; β), each of which corresponds to in the original resolution (left) and the reconstructed resolution (right), a different scale. They are intended to model the core, the main- × where each original pixel is subdivided into 10 10 subpixels. The body and the wings of the PSF. The scales of each of the three histograms at bottom show the flux distribution in the brightest pixel components are fixed to β = 1, 1.5 and 6 pixels of the ground- row (left) and in the ten corresponding subpixel rows (right). Note how 00 the modified bicubic resampling method enhances fine structures. The calibration images that have a pixel scale of 9.8. The number white circle indicates where the minimum HEW was found. of shapelet orders used is set by the requirement n + m ≤ Nmax, where Nmax = 0, 10 and 8 for each of the three scales β = 1, 1.5 and 6 pixels, respectively. The choice of Nmax = 0 for the smallest scale translates to a single Gaussian function to model hours to ∼ 80 seconds, boosting the efficiency by two orders of the core of the PSF. There are 66 and 45 shapelet coefficients magnitude. for Nmax = 10 (scale β = 1.5 pixels) and Nmax = 8 (scale The further processing of the PSFs required to transform β = 6 pixels). The total number of coefficients (free parame- their location on TRoPIC to that on the eROSITA focal plane. ters) that describe the PSF shapelet model at a given position on This made it necessary to calibrate the geometrical properties of the detector and energy is 112. The choice of the β, Nmax val- the PANTER setup, consisting of several distances and angles, ues is the result of experimentation and represents the minimum in total seven geometrical quantities, which needed to be deter- number of scales and coefficients that provide a reasonable rep- mined. resentation of the PSF at all off-axis angles and energies (see Another challenge was that the PSFs were available only at Figure B.2). Fixing the scale and Nmax of the shapelets enables the native 900.5 resolution provided by the TRoPIC pixel size the coaddition/stacking of PSFs across energies and off-axis an- (subpixel resolution could not be utilized here because of the gles in the shapelet-coefficient space rather than the image-pixel high pile–up). In order to increase the spatial resolution, it was space and significantly accelerates (factors of 10-100) the calcu- tried to find ‘plausible’ flux distributions which agreed with the lation of the model PSFs. measured ones after binning them into 900.5 × 900.5 pixels. This The ground-based calibration of the PSF has been carried was done by developing a modified method of bicubic spline in- out in the MPE PANTER facility. The PSF was measured in 7 terpolation, which was made to be flux conservative (Fig. B.1). energies 0.3, 1.5, 2.0, 4.5, 5.4 and 6.4 keV. For each energy a These images are the basis for modeling the PSF. More details point-source was imaged in a grid of positions between 0 and 0 0 are presented in Dennerl et al. (2020). 30 in the X and Y direction with a step of 5 . Each of the resulting PSF images was fit with the shapelet model described above to determine the maximum-likelihood coefficients (112 for each Point spread function: shapelet model. The eROSITA optics PSF image). Figure B.2 shows an example PSF image taken at and large field of view translate to a complex PSF shape that PANTER for the TM1 module for photons with energy 1.5 keV. depends on both off-axis angle and energy. The regular nearly For comparison the shapelet-model reconstruction of the PSF is Gaussian PSF on-axis is distorted with increasing off-axis angle, also presented in this figure. The shaplet coefficients were then leading to elongated features and asymmetries (see Figure B.2) packed in calibration files that are accessed by the various eSASS that are hard to model using analytic functions. This has moti- tasks. For a given input position on the eROSITA detectors and a vated an approach whereby the PSF at a given position is linearly given energy the shapelet coefficients are estimated using linear decomposed into an appropriately chosen 2-dimensional set of interpolation in three dimensions (2 space and 1 energy dimen- localised basis functions. The PSF can then be represented by sions). the coefficients of the basis function components. The decom- position is using the shapelet functions proposed by Refregier Appendix B.2: Pattern recombination and energy calibration (2003); Refregier & Bacon (2003), which represent a complete and orthonormal set in the 2-dimensional space. The shapelets While no calibration data are needed for the pattern recombina- are weighted Hermite polynomials and correspond to perturba- tion, this is very different for the energy calibration, because each

Article number, page 18 of 22 H. Brunner et al.: The eFEDS X-ray catalog

tain the date and the direction of each such time shift (0 → 1 or 1.5keV Panter PSF Shapelet model 1 → 0).

Detector maps. The detector maps are intended to hold fractional sensitivity values of each detector pixel. While the detector maps are evaluated by eSASS tasks expmap and srctool, it is currently not foreseen to make use of this calibration mechanism and all pixel values are set to 1.0.

FOV maps. The FOV maps define the field of view of each camera. Pixels outside the mask will receive the OUT_OF_FOV flag (set by task evprep), they will not be projected onto the sky, and the corresponding areas will be excluded from the exposure maps.

Fig. B.2. Example of the 1.5 keV TM1 PSF at an off-axis angle of about 2800. The image on the left shows the PANTER calibration image. On Appendix B.4: Boresight the right is the PSF reconstrction using the shaplet model described in the text. Star trackers and gyroscopes. For each of the four attitude sources of the SRG satellite (SED26/1, SED26/2, BOKZ, Q- Gyro) a calibration file is maintained. Each file holds an orien- CCD column is characterized by an individual CTI and gain, and tation quaternion defining the transformation between the coor- these values depend on the energy, the CCD temperature, and dinate system of the respective device and the nominal camera the time of the observation. The initial database, which did not orientation of telecope module TM1. yet consider the last two dependencies, contains already 21 616 parameters. Another database, consisting of a total of 1 799 sub- X-ray telescopes. The geometrical parameters for each tele- pixel maps, is used for a fast reconstruction of the subpixel posi- scope module are stored in respective instrument calibration tion from the distribution of the charge over the pattern (Dennerl files. Each file contains the plate scale and the camera boresight et al. 2012). with respect to the nominal orientation of TM1, the boresight is stored in the form of Euler angles (pointing offsets in X, Y, and Appendix B.3: Detector and camera characterization roll angle). Bad pixels. The bad pixel calibration files characterize individual bad pixels and groups of bad pixels (specified as rectangles) Appendix C: eROSITA Standard Calibrated Data of each camera by type, affected amplitude range and time when Products they were active. The list of bad pixel is updated continuously as the behaviour of the detectors evolves. The eROSITA data analysis pipeline provides a set of calibrated data products described below. All products are FITS files com- plying (where feasible) with established standards such that in Bad times. These calibration files contain the start and end addition to eSASS a range of general purpose astronomical data times of periods when data is either unavailable or scientifi- analysis tools may be used. A full description of the main prod- cally unusable due to a malfunction. In addition, time periods ucts files is available online3. are listed in which a TM is offline due to a camera reset (Predehl et al. 2021) or is switched off e.g. due to an orbit correction. In Cal-PV such time periods were set for TM3 and TM6. Appendix C.1: Calibrated event files eROSITA calibrated event files are containers which provide a Time shifts. Both the Interface and Thermal Controller (ITC) full set of X-ray event and auxiliary data required for most data and the Camera Electronics (CE) store a local copy of the on- analysis tasks in multiple FITS extensions. They consist of one board time source (OTS) counter (Predehl et al. 2021). These EVENTS FITS table extension holding data from one or several local copies are incremented by a 1 Hz pulse signal from space- eROSITA cameras as well as various camera specific extensions. craft. Both ITC and CEs can only be updated with the OTS time word from the spacecraft when they are in a specific mode. For X-ray events. The EVENTS FITS table extension holds informa- the time being this is only the case when a CE is reset or switched tion on each observed event as well as for recombined, calibrated on. On such occasions it can happen that the time counter of the X-ray photons. Event coordinates are provided in units of detec- CE jumps by 1 s. tor and sky pixel coordinates and as right ascension and decli- Time shifts can be detected in survey or in field scan mode nation. Further information includes event arrival times, raw and (if the scan velocity is high enough) because data from CEs calibrated event amplitudes, a variety of event pattern type infor- with incorrect time synchronization will be projected to incorrect mation (see Appendix A.1, pattern), as well as a set of event sky locations. With pointed observations, such shifts can usually flags characterising each event. only be detected when observing a stable clock such as a pulsar. It is known from pulsar observations in the Cal-PV phase that time shifts happened but the first corrected time shift is only Good time intervals. Good Time Intervals (GTI) are provided from 24.11.2019 (for TM2). The timeoff calibration files con- for each camera in the GTIn FITS table extensions, where n is

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TM number. The GTI indicate the time periods when each cam- Sensitivity maps. The sensitivity maps contain limiting ﬂuxes era was operational and collecting event data. Optionally a set for sources detectable in an eROSITA observation. The nominal of FLAREGTIn FITS table extensions is included which specify unit of the pixel values is erg/(s cm2), but depends on the energy low background time periods free of background ﬂares (see Ap- conversion factor provided to the task. pendix A.5, flaregti).

Appendix C.3: Source level products Live time. The DEADCORn FITS table extensions provide the fractional live time for each 50 ms time interval of each camera. Source catalogs. Source catalogues are written as FITS tables The DEADORn extention tracks the fraction of the detector area by the tasks ermldet and apetool and then re-formatted by the not available for the detection X-ray events due to MIPs (Mini- task catprep. The final format contains one row per source with mum Ionizing Particles) hitting the detector. Where applicable, a column for each of the source parameters described in section the DEADCORRn extension also records exposure losses when a A.5. fraction of the exposure time is intentionally discarded, for instance to prevent count rates exceeding technical limitations. Spectra. Spectra are produced by the task srctool and are standard OGIP-compliant10 data products. The task writes out- Telescope specific attitude. Right ascension, declination and put spectra for each TM and a combined spectrum. Each spec- roll angles with respect to the camera (RAWX, RAWY) coordinate trum consists of the number of counts in an extraction region system are provided for each camera in the CORRATTn FITS table within each PI channel after filtering has been applied. There are extensions with a time resolution of one second. some subtleties in how srctool defines various output quantities due to the scanning nature of the eROSITA telescope. The ONTIME is the total amount of time the source is within the Bad pixel information. The BADPIXn FITS table extensions list field of view during the input GTIs. The time intervals within and characterise bad pixels of each camera. The information pro- the ONTIME (source specific GTIs) are normally written to the vided includes the affected energies and time intervals as well as srctool output products as GTI extensions. The EXPOSURE is the bad pixel type (bright, deed, masked on-board, etc.). The for- the ONTIME reduced to account for dead time fraction given in mat of the bad pixel event file extensions is closely related to the the input event file. The BACKSCAL is the average area on the sky bad pixel calibration files described in Appendix B.3. of the source or background extraction region during the source- specific GTIs. For background subtraction, it is often useful to know the geometric area on the sky of the extraction region, Housekeeping information. For each camera four FITS table which is written as a srctool-specific keyword called REGAREA. extensions are provided which hold a subset of the eROSITA The geometric area of where the source model is non-zero is housekeeping data required for event calibration and exposure written as RGDMAREA. In addition to the standard COUNTS column calculation, such as for instance the observing mode and filter in the output spectra, srctool also writes columns containing the wheel position of each camera. number of single, double, triple or quad patterns in each channel. The total number of counts of each type is written into keywords as CNTS_S, CNTS_D, CNTS_T and CNTS_Q, and the total as Appendix C.2: Count images and maps CTS. When combining spectra, srctool adds the counts and computes average ONTIME and EXPOSURE values, while BACKSCAL, Images. The eSASS science images are created by task evtool REGAREA and RGDMAREA are exposure-weighted averages. and are stored in the primary extension of a FITS file. The FITS header contains the standard eSASS keywords copied from the original event file, keywords describing the event selection, and Light curves. The output light curve files contain the binned X- a World Coordinate System (WCS) header. By default the FITS ray lightcurve in several bands, following OGIP recommenda- file also contains the EVENTS and auxiliary extensions from the tions for time analysis data files. The columns include the mid- original events file with the same selections applied as used for point of the time bin (TIME), the width of the bin (TIMEDEL; the creation of the image. δT ), the number of counts in each band (COUNTS; c), the number of counts in the background region in each energy band (BACK_COUNTS; cB), the fraction of the nominal on-axis effective Exposure maps. The exposure maps contain the results of the collecting area computed in each band (FRACAREA; fA), the frac- exposure calculation performed by task expmap. The exposure tion of the time bin which overlaps with input GTIs and when maps can either contain the raw exposure times for each map the source was visible in the field of view (FRACTIME; fT ), the pixel (unvignetted exposure) or the exposure multiplied with the product of the fractional collecting area and fractional temporal energy and off-axis angle dependent telescope vignetting func- coverage (FRACEXP; fE = fA fT ), the mean off-axis angle during tion (vignetted exposure). In both cases the unit of the pixel val- the bin, and the ratio by which the background counts need to ues is seconds. The WCS header is identical with that of the input be scaled to give the background contribution in the source aper- template image. ature (BACKRATIO, r). The RATE column is calculated from the other columns in each band as (c − r cB)/( fE δT ). The 1σ uncertainty on the rate is given for each energy band in RATE_ERR, Background maps. The background maps contain the source providing there√ are more than 25 counts in the respective counts free sky + detector background as determined by the task column, using c + r cB/( fE δT ). erbackmap. The values are stored in units of counts/pixel, the image size and WCS coordinate system of a background map is identical with the respective science image. 10 OGIP FITS Working Group, https://heasarc.gsfc.nasa.gov/

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Appendix C.4: Detector response and effective areas number of NULL values in the PSF-fitting error measurement columns, e.g., “ML_RATE_ERR”, “RADEC_ERR_ERR”, and Response matrices. Response matrices (RMFs) generated by “EXT_ERR”, because of failure in the calculation caused by a srctool are OGIP-format response files, containing standard software problem. MATRIX and EBOUNDS extensions. The output depends on the pattern selection chosen by the user. Output response matrices are the sum of the response matrices for the different patterns. Appendix E: eFEDS Simulations Similarly to spectra, srctool writes response matrices for the individual TMs and for the combination. The combined response In order to inspect and optimize the source detection for matrix is the exposure-weighted average of the individual re- eROSITA, we run extended simulations as described in Liu, T. sponse matrices. Currently the different TMs are assumed to et al. submitted. The simulation of eFEDS is briefly summarized here. have the same response, and variation with time is not included 11 in the calibration. We use sixte-2.6.2 to create mock eFEDS event files and implement 18 realizations. To make them as representative as possible to the real data, we input the real eROSITA calibra- Auxiliary response files. The Auxiliary response files (ARFs) tion files and eFEDS attitude file, and AGN, star, and cluster cat- made by srctool are OGIP-compliant. These files include sev- alogs generated from cosmological simulations (Comparat et al. eral different effects which are applied to the on-axis effec- 2020). We measure the mean X-ray and particle background tive area, including vignetting, PSF correction and corrections spectra from the eFEDS data and simulate the source signal, X- for when the source is partially visible. The ARF files con- ray background, and particle background separately to account tain a SPECRESP extension, containing the standard columns for their different vignetting. We run the eFEDS source detec- of ENERGY_LO, ENERGY_HI and SPECRESP giving the effective tion pipeline on the mock data and then associate the detected area curve. In addition, srctool writes for diagnostic purposes sources to the input on the basis of the source-ID flag on each columns which give the corrections applied to the on-axis effec- photon. By checking the number of photons contributed by each tive area due to PSF (as CORRPSF), vignetting (as CORRVIGN) input source in the core region of a detected source, we iden- and both combined (CORRCOMB). tify its primary and secondary (if exists) input counterparts. The point sources (AGN and stars) and extended sources (clusters) Appendix D: Description of Catalog Entries are considered separately. Therefore, we identify not only the cases where one input source is uniquely matched to one detected source which is classified (as point- or extended source) Band energy range ECF correctly or not, but also the cases where one input source is keV cm2/erg detected as multiple sources and the cases where one detected single-band detection source is due to a blending of multiple input sources. 0.2–2.3 1.074×1012 Based on the input-output association, we can measure the three-bands detection completeness (detected fraction) and contamination level (frac- 1 0.2–0.6 1.028×1012 tion of spurious sources), i.e., the source detection efficiency. Ac- 2 0.6–2.3 1.087×1012 cording to the measured effect of any adjustment on the source detection procedure and parameters on the source detection effi- 3 2.3–5 1.147×1011 ciency, we can optimize the source detection pipeline. post-hoc photometry s 0.5–2 1.185×1012 t 2.3–5 1.147×1011 References u 5–8 2.776×1010 11 Aihara, H., Arimoto, N., Armstrong, R., et al. 2018, PASJ, 70, S4 b1 0.2–0.5 9.217×10 Albrecht, A., Bernstein, G., Cahn, R., et al. 2006, arXiv e-prints, astro b2 0.5–1 1.359×1012 Allen, S. W., Evrard, A. E., & Mantz, A. B. 2011, AARA, 49, 409 b3 1–2 1.014×1012 Barcons, X., Carrera, F. J., Ceballos, M. T., et al. 2003, Astronomische 11 Nachrichten, 324, 44 b4 2–4.5 1.742×10 Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017, AJ, 154, 28 Table D.1. eFEDS catalog energy bands Boller, T., Freyberg, M. J., Trümper, J., et al. 2016, A&A, 588, A103 Brandt, W. N. 2020, in American Astronomical Society Meeting Abstracts, Vol. 235, American Astronomical Society Meeting Abstracts #235, 138.01 Cappelluti, N., Brusa, M., Hasinger, G., et al. 2009, A&A, 497, 635 Table D lists the energy bands and corresponding ECF used Cash, W. 1979, ApJ, 228, 939 in this work. The ECF are calculated assuming an absorbed Chiappetti, L., Fotopoulou, S., Lidman, C., et al. 2018, A&A, 620, A12 power-law with a slope of 2.0 and with a Galactic absorbing Civano, F., Marchesi, S., Comastri, A., et al. 2016, ApJ, 819, 62 column density of 3×1020 cm−2. The main and the supplemen- Comparat, J., Eckert, D., Finoguenov, A., et al. 2020, The Open Journal of As- trophysics, 3, 13 tary catalogs from the 0.2–2.3 keV single-band detection share Della Ceca, R., Maccacaro, T., Caccianiga, A., et al. 2004, A&A, 428, 383 the same columns as described in Table D. In the case of the Dennerl, K., Andritschke, R., Bräuninger, H., et al. 2020, in Society of Photo- three-bands detected hard catalog, there are four sets of PSF- Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 11444, So- fitting output columns (as listed in section 2 of Table. D), which ciety of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 114444Q have an energy-band suffix in the column name indicating the Dennerl, K., Burkert, W., Burwitz, V., et al. 2012, in Society of Photo-Optical three source detection bands (1,2,3) or the summary of the three Instrumentation Engineers (SPIE) Conference Series, Vol. 8443, Space Tele- bands (0). The only exception is the “ML_EXP_Band”, which is scopes and Instrumentation 2012: Ultraviolet to Gamma Ray, ed. T. Taka- only for the three individual band (1,2,3) but not for the sum- hashi, S. S. Murray, & J.-W. A. den Herder, 844350 Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168 mary case (0). The hard catalog has an additional column of Drinkwater, M. J., Byrne, Z. J., Blake, C., et al. 2018, MNRAS, 474, 4151 “ID_main”, which stores the source ID in the main catalog for the overlapping sources. All the three catalogs contain a small 11 https://www.sternwarte.uni-erlangen.de/research/sixte/

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Column Format Units Description 1. Source properties form PSF-fitting detection; 21 columns Name 22A .. ID_SRC J .. Source ID RA D deg Right ascension (J2000) DEC D deg Declination (J2000) RADEC_ERR E arcsec Combined positional error RA_CORR D deg Right ascension (J2000), corrected DEC_CORR D deg Declination (J2000), corrected RADEC_ERR_CORR D arcsec Combined positional error, corrected EXT E arcsec Source extent parameter EXT_ERR E arcsec Extent error EXT_LIKE E .. Extent likelihood DET_LIKE E .. Detection likelihood ML_RATE E cts/s Source count rate measured by PSF-fitting ML_RATE_ERR E cts/s 1-σ count rate error ML_CTS E cts Source net counts measured from count rate ML_CTS_ERR E cts 1-σ source counts error ML_FLUX E erg/cm2/s Source flux in the detection band ML_FLUX_ERR E erg/cm2/s 1-σ source flux error ML_EXP E s Vignetted exposure map value at the source position ML_BKG E cts/arcmin2 Background at the source position inArea90 L True if inside the inner region with 0.2-2.3 keV vignetted exposure above 500s, which comprises 90% of the total area 2. Forced PSF-fitting results for seven energy Bands (Table. D.1); 7×9 columns DET_LIKE_Band D .. The same as above in section 1 ML_RATE_Band D cts/s ... ML_RATE_ERR_Band D cts/s ... ML_CTS_Band D cts ... ML_CTS_ERR_Band D cts ... ML_FLUX_Band D erg/cm2/s ... ML_FLUX_ERR_Band D erg/cm2/s ... ML_EXP_Band D s ... ML_BKG_Band D cts/arcmin2 ... 3. Aperture photometry results for seven energy Bands (Table. D.1); 7×5 columns APE_CTS_Band J cts Total counts extracted within the aperture APE_EXP_Band D s Exposure map value at the given position APE_BKG_Band D cts Background counts extracted within the aperture, excluding nearby sources using the source map APE_RADIUS_Band D pixels Extraction radius APE_POIS_Band D .. Poisson probability that the extracted counts (APE_CTS) are a background fluctuation Table D.2. Columns of the main catalog and the supplementary catalog, which are based on the single-band detection. The forced PSF-fitting and aperture photometry results (section 2 and 3) have a suffix in the column name indicating the energy band (Table. D.1). NULL values in the error columns indicate a failure of the error determination algorithm for a small fraction of objects, see Appendix A.5.

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