# The XMM Cluster Survey: An independent demonstration of the fidelity of the
eFEDS galaxy cluster data products and implications for future studies

D. J. Turner1 ID , P. A. Giles1 ID , A. K. Romer1 ID , R. Wilkinson1 ID , E.
W. Upsdell1 ID , M. Klein2, P. T. P. Viana3,4 ID , M. Hilton5,6 ID , S.
Bhargava7, C. A. Collins8, R. G. Mann9 ID , M. Sahlén19 ID , J. P. Stott11 ID
1Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH,
UK
2Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679,
Munich, Germany
3Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP,
Rua das Estrelas, 4150-762 Porto, Portugal
4Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do
Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
5Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4041, SA
6School of Mathematics, Statistics, and Computer Science, University of
KwaZulu-Natal, Westville Campus, Durban 4041, SA
7Département d’Astrophysique, CEA Paris-Saclay, 91190 Gif-sur-Yvette, France
8Astrophysics Research Institute, Liverpool John Moores University, Liverpool
Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
9Institute for Astronomy, University of Edinburgh, Royal Observatory,
Blackford Hill, Edinburgh EH9 3HJ, UK
10Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala
University, Box 516, SE- 751 20 Uppsala, Sweden
11Department of Physics, Lancaster University, Lancaster LA1 4YB, UK E-mail:
<EMAIL_ADDRESS>(DJT)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the first comparison between properties of clusters of galaxies
detected by the eROSITA Final Equatorial-Depth Survey (eFEDS) and the XMM
Cluster Survey (XCS). We have compared, in an ensemble fashion, properties
from the eFEDS X-ray cluster catalogue with those from the Ultimate XMM
eXtragaLactic (XXL) survey project (XXL-100-GC). We find the distributions of
redshift and X-ray temperature ($T_{\rm X}$) to be broadly similar between the
two surveys, with a larger proportion of clusters above 4 keV in the
XXL-100-GC sample. We find 62 eFEDS cluster candidates with XMM data (eFEDS-
XMM sample); 10 do not have good enough XMM data to confirm or deny, 11 are
classed as sample contaminants, and 4 have their X-ray flux contaminated by
another source. The majority of eFEDS-XMM sources have a longer exposure in
XMM than eFEDS, and the majority of eFEDS positions are within 100 kpc of XCS
positions. Our eFEDS-XCS sample of 37 clusters is used to calculate minimum
sample contamination fractions of ${\sim}$18% and ${\sim}$9% in the eFEDS
X-ray and optically confirmed samples respectively, in general agreement with
eFEDS findings. We compare 29 X-ray luminosities ($L_{\rm X}$) measured by
eFEDS and XCS, which are in excellent agreement. Eight clusters have a $T_{\rm
X}$ measured by XMM and eROSITA, and we find that XMM temperatures are
25$\pm$9% larger than their eROSITA counterparts. Finally, we construct
$L_{\rm X}$ \- $T_{\rm X}$ scaling relations based on eFEDS and XCS
measurements, which are in tension; the tension is decreased when we measure a
third scaling relation with calibrated XCS temperatures.

###### keywords:

X-rays: galaxies: clusters – galaxies: clusters: intracluster medium –
techniques: spectroscopic – instrumentation: miscellaneous

††pubyear: 2021††pagerange: The XMM Cluster Survey: An independent
demonstration of the fidelity of the eFEDS galaxy cluster data products and
implications for future studies–C

##  1 Introduction

X-ray observations of clusters of galaxies provide insights into various
aspects of astrophysics (e.g., Hitomi Collaboration et al., 2016; Bhargava et
al., 2020; Sanders et al., 2021a) and cosmology (e.g., Vikhlinin et al., 2009;
Schellenberger & Reiprich, 2017). Clusters are among the largest
gravitationally bound structures in the Universe and consist of a dark matter
halo, the intra-cluster medium (ICM), and the component galaxies. The ICM is a
high-temperature, low-density plasma that emits strongly in the X-ray band,
with both continuum and emission line components.

The eROSITA instrument mounted on the joint Russian-German Spectrum-Roentgen-
Gamma (SRG, Predehl et al., 2021) mission will contribute significantly to
X-ray cluster astrophysics and cosmology. Its large field of view (${\sim}$1
deg), sensitivity, and energy resolution combine to make it a revolutionary
new instrument. The final eROSITA All-Sky Survey (eRASS) is predicted to
detect approximately 100,000 galaxy clusters above a mass of $5\times
10^{13}$h-1M⊙ (Pillepich et al., 2012). The data sharing agreement between the
German and Russian consortiums that funded eROSITA involves sharing the sky
equally. Most of these clusters will be accompanied by an X-ray luminosity
($L_{\rm X}$) measurement, and roughly 20% (Liu et al., 2021a) of the
observations will yield an X-ray temperature ($T_{\rm X}$) measurement.
However, apart from a handful of the highest flux clusters, it will not be
possible to measure masses via the hydrostatic technique directly from eRASS
data. Therefore, until the all sky survey is complete, it will be necessary to
supplement the eRASS cluster catalogue with mass measurements from the current
generation of X-ray telescopes (i.e. XMM, Chandra) in order to maximise the
scientific yield. After the all sky survey is complete, eROSITA pointed
observations of clusters, will produce some hydrostatic mass estimates, as
demonstrated Sanders et al. (2021b).

The aim of this paper is to explore potential synergies between eRASS cluster
catalogues and the data in the XMM-Newton public archive, and to probe
calibration considerations required for such analyses. The eROSITA and XMM
telescopes have different characteristics that allow them to complement one
another, some of which (such as the effective area at different energies, and
the background level) were explored by Predehl et al. (2021). Comparisons
between the on-axis effective areas of the combined XMM cameras (PN, MOS1, and
MOS2) and the combined eROSITA telescope modules show that the effective areas
are effectively equal between ${\sim}$0.5-2.0 keV, though outside this range
XMM has an advantage. Here XMM complements eROSITA in that it will observe
more source emission at higher energies, which could improve constraints on
spectroscopic X-ray measurements of temperature and luminosity. The larger
field of view of eROSITA ensures that its grasp (the product of effective area
and observing area) is significantly greater than XMM’s below ${\sim}3.5$ keV,
though above that energy XMM’s grasp is greater. Comparisons between the
background levels of a subset of eROSITA’s telescope modules and the XMM-
Newton cameras using a simultaneous observation of NLS1 1H0707-495 (Boller et
al., 2021) revealed that, although the eROSITA background is higher than pre-
launch predictions, it is generally lower than XMM and more temporally stable.
Soft-proton flaring does not significantly impact eROSITA, giving it an
advantage over XMM in this regard, and possibly allowing it to locate more
low-flux sources (such as low surface-brightness galaxy clusters).

In this work we will make use of the recent release of the eROSITA Final
Equatorial-Depth Survey (eFEDS, Brunner et al., 2021). The eFEDS field covers
approximately 140 square degrees of the equatorial
($-2.5^{\circ}<\delta<6.0^{\circ}$) sky. It intersects with several
optical/near-IR photometric and/or spectroscopic surveys, including the Hyper
Suprime-Cam Subaru Strategic Program (HSC SSP, Aihara et al., 2018), the
Galaxy and Mass Assembly survey (GAMA, Driver et al., 2011), and the Sloan
Digital Sky Survey (SDSS, Blanton et al., 2017). We make an indirect
comparison to a similar X-ray survey using the XXL-100-GC catalogue (Pacaud et
al., 2016), then make direct comparisons to XCS measurements.

We wish to ascertain the level of sample contamination in the eFEDS cluster
catalogue, compare the central coordinates of the detected clusters to those
measured by the XMM Cluster Survey (XCS, Romer et al., 1999), and verify the
accuracy of $L_{\rm{X}}$ and $T_{\rm{X}}$ measurements. As eFEDS is the same
depth as the final eRASS, the accuracy of these measurements have implications
for cosmological studies based on eRASS cluster detection (using weak lensing
masses and X-ray luminosities for the mass observable relation). They will
also impact studies based on optical or near-infrared detection (as
luminosities can be used to explore scatter in the mass observable relations),
and astrophysical studies of cluster luminosity-temperature relations to study
the evolution of the intra-cluster medium.

There is a known difference between the galaxy cluster temperatures measured
by XMM and Chandra. This difference has been quantified with functions to
calibrate the temperatures of one telescope to another; Schellenberger et al.
(2015) showed that the difference increases with temperature, with XMM EPIC
temperatures being on average 7% and 23% lower than Chandra ACIS temperatures
for 2 keV and 10 keV clusters respectively. Any analysis which uses both XMM
and Chandra temperatures typically accounts for this (e.g., Farahi et al.,
2019; Migkas et al., 2020). An understanding of whether there is a similar
difference in eROSITA and XMM temperatures will be necessary before any joint
analyses with data from the two telescopes are undertaken, and before scaling
relations from one telescope can be safely used by another.

In §2 we explore the general properties of the eFEDS cluster catalogue and
provide comparisons to a catalogue with similar properties. In §3 we construct
a cluster sample from the eFEDS catalogue with corresponding XMM observations,
which includes a visual inspection of the X-ray data and SDSS/HSC images. We
also compare eFEDS and XCS exposure times and central positions. In §4 we
compare luminosities and temperatures measured by eFEDS and XCS. Finally, in
§5 we generate luminosity-temperature relations, discuss implications of our
findings and how they can be improved. Then in §6 we provide a final summary.
The analysis code and samples are available in a GitHub repository111Analysis
code and samples.

Throughout this work we use a concordance $\Lambda$CDM cosmology where
$\Omega_{\rm{M}}$=0.3, $\Omega_{\Lambda}$=0.7, and $\rm{H}_{0}$=70 km s-1
Mpc-1, consistent with the original eFEDS cluster analysis (and other XCS
works).

##  2 Comparison of the eFEDS Optically Confirmed and XXL-100-GC catalogues

Figure 1: Redshift, temperature, and fractional temperature error
distributions of the eFEDS and XXL-100-GC samples. Redshifts from both samples
come from a variety of sources, and temperatures are measured within 300 kpc
apertures centered on clusters. There are no clusters in common between the
two samples.

The eFEDS cluster catalogue (Liu et al., 2021a) contains 542 candidates, 477
of which are considered to be optically confirmed (Klein et al., 2021) when
assessed using the Multi-component Matched Filter Cluster Confirmation Tool
(MCMF, Klein et al., 2018). All 542 X-ray candidates are accompanied by
redshift ($z$) values. Soft-band (0.5-2.0 keV in the source frame) $L_{\rm X}$
values have been measured for 91% of the X-ray cluster candidate sample. A
smaller percentage, 21%, of $T_{\rm X}$ values were obtained using spectra
extracted from circular apertures centered on the eFEDS coordinates; 69 within
300 kpc, and 95 within 500 kpc (102 candidates have at least one temperature
measurement).

The XXL survey (Pierre et al., 2016) covers ${\sim}50$ deg2 of the sky (over
two separate regions), making it the largest contiguous area survey in the XMM
archive. It consists of 542 separate XMM observations with on-axis exposure
times ranging from 10-20 ks. The contiguous nature of XXL makes it ideal to
compare to eFEDS. As eFEDS and the XXL survey were taken in different parts of
the sky there are no clusters in common. Although we note that the X-CLASS
analysis of the XMM archive (up to August 2015) that made use of the XXL
pipelines does contain some eFEDS candidates (Koulouridis et al., 2021).
Comparisons are limited to ensemble distributions of the cluster samples. We
made use of the XXL-100-GC sample (Pacaud et al., 2016), containing the 100
brightest galaxy clusters observed in XXL, and the sample of 477 optically
confirmed eFEDS candidates. The flux limits of the eFEDS and XXL-100-GC
cluster samples are similar;
${\sim}10^{-14}\>\rm{erg}\>\rm{s}^{-1}\>\rm{cm}^{-2}$.

Figure 1a shows the redshift distributions of the clusters in the two samples
(eFEDS and XXL-100-GC distributions are shown in red and cyan respectively) to
be very similar overall, but that XXL-100-GC detects a higher proportion of
clusters at low redshifts. Next, we compare the respective temperature
distributions. Temperatures for the XXL-100-GC clusters were measured within a
300 kpc aperture (Giles et al., 2016), as were temperatures for eFEDS
clusters, making a direct comparison of the distributions valid. Figure 1b
plots the temperature distributions of the two samples, with the XXL-100-GC
temperature distribution containing a significantly higher proportion of
temperatures above ${\sim}3.5\>\rm{keV}$. Liu et al. (2021a) note that
eROSITA’s ability to measure temperatures for hot clusters at $\gtrsim$5 keV
is limited due to the reduced sensitivity of eROSITA at energies $>$3 keV.
This is a plausible reason for the increased number of higher temperature
clusters in XXL-100-GC compared to eFEDS. The effective area of eROSITA is
${\sim}$150 $\rm{cm}^{2}$ at 5 keV, compared to ${\sim}$900 $\rm{cm}^{2}$ for
EPIC-PN, see Figure 9 in Predehl et al. (2021) for a detailed comparison.
Previous work by Lloyd-Davies et al. (2011) has also shown that more counts
are required to constrain temperatures to the same level for hotter galaxy
clusters. Furthermore, the temperature distribution could also be influenced
by the selection functions of the two surveys, differing measurement
methodology, or a systematic difference in temperatures measured by the
eROSITA and XMM telescopes (we explore this in Section 4.4).

Figure 2: Footprint of eFEDS, given by the black solid line. Cluster candidates present in the eFEDS X-ray catalogue are highlighted by red diamonds. The grey circles highlight XMM observations, with a radius of 15′(the approximate radius of the XMM FoV). Table 1: Summary of the samples defined in this work. Ncl is the number of clusters, N${}_{T_{\rm{eFEDS,500kpc}}}$ the number with eFEDS $T_{\rm{500kpc}}$ values, and N${}_{T_{\rm{XCS,500kpc}}}$ the number with XCS $T_{\rm{500kpc}}$ values. Sample Name | Description | Ncl | N${}_{T_{\rm{eFEDS,500kpc}}}$ | N${}_{T_{\rm{XCS,500kpc}}}$
---|---|---|---|---
eFEDS | The full eFEDS cluster candidates catalogue | 542 | 95 | -
eFEDS-XMM | eFEDS cluster candidates that fall on an XMM observation | 62 | 11 | -
eFEDS-XCS | eFEDS-XMM candidates available for analysis after inspection | 37 | 8 | 28

Finally we compare how well temperatures from the two samples are constrained,
by comparing temperature uncertainties as a fraction of the absolute
temperature value ($\Delta T_{\rm{X}}/T_{\rm{X}}$). Figure 1c shows that, on
average, XXL achieves better temperature constraints than eFEDS, with the mean
percentage uncertainties for XXL and eFEDS being 14% and 25% respectively.
This is consistent with the findings of Lloyd-Davies et al. (2011), who showed
that ${\sim}1000$ background-subtracted soft-band (0.5-2.0 keV) counts are
required to achieve a fractional temperature uncertainty of ${\sim}0.1$ for a
3 keV cluster. In this regard the longer exposures of XXL compared to eFEDS
would give an advantage (especially in the deeper XMM-LSS fields, covering
${\sim}$11 deg2 in the XXL-N field).

##  3 Understanding the eFEDS catalogue contamination fraction

In this section, we make use of archival XMM data that overlaps with the eFEDS
footprint to assemble samples for analysis, and make an estimate of the
contamination fraction in the eFEDS cluster candidate list. For this, we have
used data products (images and source lists) generated by the XMM Cluster
Survey (XCS, Romer et al., 1999). The XCS source lists are constructed by the
XCS Automated Pipeline Algorithm (XAPA) source finder, and a full explanation
of our procedures can be found in Lloyd-Davies et al. (2011). We first
determine which eFEDS X-ray cluster candidates fall within the active area of
an XMM observation (Section 3.1). For these, we generate eROSITA cut-out
images. We then compare, by eye, to the corresponding XMM cut-outs (Section
3.2). We also compare to optical SDSS DR16 (Ahumada et al., 2020) images
obtained from the SDSS cutout server222SDSS Image Cutout Server. As
${\sim}$70% of the eFEDS-XMM sample are at redshifts $z$<0.5 it is generally
appropriate to search for a red sequence using SDSS imagery, however for any
candidate that we could not confirm with SDSS, we then examined images taken
from the second data release of the Hyper Suprime-Cam Subaru Strategic Program
(HSC-SSP PDR2, Aihara et al., 2019)333HSC-SSP PDR2 Image Cutout Server. The
deeper data of HSC-SSP PDR2 ($i$-band limiting magnitude of 26.2 in the wide
field, where the SDSS DR16 $i$-band limiting magnitude is 22.2) allow for
detection of cluster galaxies at much higher redshifts. Our visual inspection
allows us to categorise contaminating objects (Section 3.3) and to estimate
the overall contamination fraction in the eFEDS sample (Section 3.5).

Figure 3: Distribution of exposure times for eFEDS-XMM cluster candidates,
measured at the eFEDS coordinates. Exposures taken from 0.5-2.0 keV exposure
maps, corrected for flaring and vignetting. Dashed line indicates the average
vignetting corrected exposure of the eFEDS field reported by Liu et al.
(2021a).

###  3.1 eFEDS Cluster Candidates in the XMM Footprint

Figure 4: Comparison of eFEDS and XAPA central coordinates, for the subset of
the eFEDS-XCS sample that have been detected by XAPA. Figure 5: eFEDS-XMM
cluster candidate (eFEDS ID 1644) identified as a pair interacting galaxies
with ongoing AGN activity (see Section 3.3.1). The cross-hair indicates the
eFEDS position. Left hand side is a combined PN+MOS1+MOS2 XMM image (ObsID
0822470101), centre is eROSITA, right hand side is HSC. Both XMM and eROSITA
images are cutouts within a radius of 750 kpc, HSC image has a half-side-
length of 750 kpc (at the redshift provided by eFEDS). Figure 6: eFEDS-XMM
cluster candidate (eFEDS ID 3334) without an obvious corresponding source of
emission (see Section 3.3.2). The cross-hair indicates the eFEDS position.
Left hand side is a combined PN+MOS1+MOS2 XMM image (ObsID 0822470101), centre
is eROSITA, right hand side is HSC. Both XMM and eROSITA images are cutouts
within a radius of 500 kpc, HSC image has a smaller half-side-length of 250
kpc (at the redshift provided by eFEDS). Figure 7: Two eFEDS-XMM cluster
candidates in the outskirts of a low redshift foreground AGN. A spurious
eFEDS-XMM cluster candidate (eFEDS ID 8922) is indicated by the cross-hair
(see Section 3.3.2). An eFEDS-XMM cluster candidate (eFEDS ID 16370) is
indicated by the dashed circle. Left hand side is a combined PN+MOS1+MOS2 XMM
image (ObsID 0655340133), centre is eROSITA, right hand side is HSC. Both XMM
and eROSITA images are cutouts within a radius of 1000 kpc, HSC image has a
half-side-length of 1000 kpc (at the redshift for eFEDS ID 8922 provided by
eFEDS). Figure 8: eFEDS galaxy cluster split into two candidates by the source
finder (see Section 3.3.3). Cross-hairs indicate one candidate (eFEDS ID
8602), and the white diamond indicates the other (eFEDS ID 1023). Left hand
side is a combined PN+MOS1+MOS2 XMM image (ObsID 0761730501), centre is
eROSITA, right hand side is HSC. Both XMM and eROSITA images are cutouts
within a radius of 800 kpc, HSC image has a half-side-length of 800 kpc (at
the redshift provided by eFEDS, which is the same for 8602 and 1023). Figure
9: A low redshift eFEDS-XMM cluster candidate (eFEDS ID 150) whose X-ray
emission is dominated by an X-ray bright elliptical galaxy (see Section 3.4).
Left hand side is a combined PN+MOS1+MOS2 XMM image (ObsID 0673180201), centre
is eROSITA, right hand side is HSC. Both XMM and eROSITA images are cutouts
within a radius of 100 kpc, HSC image has a half-side-length of 100 kpc (at
the redshift provided by eFEDS).

Figure 2 shows the outline of the eFEDS footprint with eFEDS X-ray cluster
candidates (Liu et al., 2021a) indicated by red diamonds. XMM observations
taken within the eFEDS footprint are indicated by grey shaded circles, with a
radius of 15′ (the approximate radius of the XMM field-of-view). There are a
total of 143 XMM observations, covering ${\sim}$15 deg2 (11%) of the sky
within the eFEDS footprint, accounting for overlapping XMM observations.

We used XMM: Generate and Analyse (XGA444XMM: Generate and Analyse GitHub
Turner et al., prepa); a new, open-source, X-ray astronomy analysis module
developed by XCS, to determine which of the 542 eFEDS cluster candidates
listed in Liu et al. (2021a) have also been observed by XMM. An initial search
finds eFEDS candidates with central coordinates within 30′of an XMM
observation aimpoint (this is larger than the XMM field of view to account for
any cases of low-$z$ clusters with centroid offsets). We then refined the
match so that at least 70% of a 300 kpc aperture (centred on the eFEDS
coordinate and assuming the eFEDS redshift) coincides with an XMM observation.
Sixty-two eFEDS candidates met these criteria, and this sub-set is denoted the
eFEDS-XMM sample (see Table 1). Fifty-three of the eFEDS-XMM candidates appear
in the eFEDS optically confirmed sample (Klein et al., 2021).

The distribution of XMM exposure times for the eFEDS-XMM sample is shown in
Figure 3. The light-blue distribution uses the best individual observation
exposure time for each eFEDS-XMM candidate; the grey distribution is the total
exposure time for each candidate. These are vignetting-corrected exposure
times at the eFEDS coordinate (rather than at the respective observation aim-
point). The typical eFEDS vignetting-corrected exposure (1.2 ks) is shown by
the dashed red line for comparison. The majority of exposure times (individual
or total) are longer for XMM than eFEDS.

###  3.2 Constructing the eFEDS-XCS Sample

To judge the quality of the eFEDS candidates in the eFEDS-XMM sample, circular
cut-out images, of radius 500 kpc, were generated from the eROSITA eFEDS data
and XCS processed XMM data. We select the XMM observation with the highest
signal-to-noise within a 300 kpc aperture centered on the eFEDS candidate
coordinate, and use its XCS generated PN+MOS1+MOS2 image (Giles et al., prep).
For the eROSITA cut-outs, the eSASS555Introduction to eSASS evtool software
was used.

Both sets of images used a pixel size of 4.35″, but different energy ranges
were used; 0.5-2.0 keV for XMM and 0.2-2.3 keV for eROSITA. These ranges
reflect those used by the respective XCS and eFEDS source detection routines.

As shown in Predehl et al. (2021), the energy dependent effective area of XMM
(assuming all three cameras are operating) is the same, or greater, than that
of eROSITA. Therefore, we can expect most of the XMM cut-outs to have higher
signal to noise than their eFEDS counterparts, even after accounting for the
fact that the XMM background level is slightly higher than eROSITA’s. In 10
cases, however, we judged the XMM data to be inadequate for further analysis.
This was either because the eFEDS candidate fell on the edge of the field of
view and/or because the signal-to-noise was too low (see Table 4 for details).
These 10 were excluded from further analysis, although it is noteworthy that
in 5 cases, an obvious (by eye) extended source was visible in the
corresponding eROSITA cut-out.

The remaining 52 eFEDS-XMM sources were then visually inspected side-by-side
to judge the quality of the eFEDS candidates. Thirty-seven eFEDS-XMM
candidates were confirmed as clusters suitable for X-ray analysis by this
visual inspection, henceforth called the eFEDS-XCS sample. Generally speaking
the XCS and eFEDS defined centroid positions were in good agreement (with an
offset of less than 100 kpc), but several outliers are present (see Figure 4).
The outliers were due to either low signal to noise eFEDS data, or to eFEDS
point source contamination. Similar examples were noted in Klein et al.
(2021).

The other eFEDS cluster candidates were classified as sample contaminants (11,
Table 5), or as having their X-ray flux contaminated by other sources (4,
Table 6). There are three broad categories of sample contamination, as
described below (Section 3.3).

###  3.3 Categories of contaminating objects in the eFEDS X-ray cluster
candidate catalogue

Here we discuss categories for the different types of contaminating object
that we discovered in the eFEDS X-ray cluster candidate catalogue. The figures
that we use to illustrate these examples are not necessarily on the same
scale, or centered on the same position, as those we used for visual
inspection, and all figures use HSC imagery for clarity. The optical images we
used for general inspection were SDSS, with HSC photometry used in cases were
we needed to clarify our classification.

####  3.3.1 Blended sources

An example of this is eFEDS ID 1644, which is shown in Figure 5; the two
sources at the centre of the XMM image (Figure 5 left; detected as separate
point sources by XCS) in the XMM cut-out appear as a single object in the
eROSITA image. The dominant X-ray source is discussed in Pfeifle et al.
(2019). It is the result of AGN activity in a pair of interacting galaxies.
The two galaxies can be seen in the corresponding HSC image in Figure 5
(right). The blending is likely a result of eROSITA’s 26″ FOV average PSF
half-energy width (HEW), which is larger than the XMM PN camera’s 16.5″ PSF
HEW (at 1.5 keV), in combination with the short eFEDS exposure time. This
source was assigned a class of B2 during the MCMF classification process,
which indicates point source contamination, but it is still retained in the
optically confirmed catalogue.

####  3.3.2 Spurious sources

An example of this is shown in Figure 6. There does not appear to be a source
at the eFEDS candidate centroid position (extended or otherwise) in either the
XMM or eROSITA image (Figure 6, left and middle respectively). We note that
the redshift provided by the eFEDS cluster catalogue for this candidate (eFEDS
ID 3334) is very low ($z{=}0.087$) and so any X-ray cluster emission should be
obvious, unless it is very low surface brightness and/or very extended.
Nonetheless, we do not see evidence of a coincident population of galaxies in
the HSC imagery (Figure 6, right).

Another example is eFEDS ID 8922, which is shown in Figure 7; this cutout is
not centered on the spurious eFEDS cluster candidate, but on the bright source
that causes it. The eFEDS candidate location (at the cross hairs) is in the
outskirts of a bright source (eFEDS ID 3, not present in the cluster candidate
catalogue), and not coincident with any distinct source in either the XMM or
eROSITA image (Figure 7, left and middle respectively). There also does not
appear to be an association of galaxies in HSC imagery (Figure 7, right). The
dominant X-ray source is identified as an AGN in the Million Quasar catalogue
(Flesch, 2021) located in a spiral galaxy visible in the corresponding optical
image. It is also present in the eFEDS AGN catalogue (Liu et al., 2021b).

####  3.3.3 Fragmented sources

An example of this is shown in Figure 8. The white cross-hair indicating the
position of one eFEDS candidate (eFEDS ID 8602), and the white diamond another
(eFEDS ID 1023). The two candidates have almost identical redshifts
($z{=}0.196$ and $z{=}0.197$ respectively). Luminosity measurements for both,
and a temperature estimate for eFEDS ID 1023, are given in Liu et al. (2021a).
We discuss this system further in Appendix B. We note that it is not used
during our luminosity (Section 4.2) and temperature comparisons (Section 4.3
and Section 4.4), or in our luminosity-temperature relation analysis (Section
3).

###  3.4 Clusters with contaminated X-ray emission

In these cases there is evidence, from the SDSS and/or HSC data, for a
physical association of galaxies – which could in turn be responsible for an
extended X-ray source due to emission from a hot ICM – however, we contend
that any ICM emission present is significantly contaminated by other X-ray
sources. One example (eFEDS ID 150) is shown in Figure 9, where the emission
detected by eROSITA appears to originate primarily from the central galaxy
(alternative, but less likely explanations are that this is a fossil group or
a system with a strong cool core). We note that similar examples were
identified in eFEDS, candidates with IDs 3133 and 3008 (see Table 6). An
example of a different type of contaminated emission is presented in Figure 7
(eFEDS ID 16370). The eFEDS candidate is highlighted by the white dashed
circle. There is tentative evidence of X-ray emission in the XMM observation
(especially when smoothing is applied), and the coordinates coincide with a
collection of red galaxies in SDSS and HSC at an SDSS photo-$z$ of $z{=}0.44$
(matching the eFEDS catalogue’s $z$). However, due to the proximity of the
eFEDS candidate to the bright AGN (as discussed in Section 3.3.2), the X-ray
flux in this region will be contaminated by non ICM emission, so we exclude
this cluster from the following analyses.

In this paper we focus on the comparison of the X-ray properties measured by
eROSITA and XMM, so we do not include these four eFEDS candidates in the
analyses presented Section 4. However, it would inappropriate to remove them
from some other types of analyses – such as cluster number count cosmology
based on optical/near-IR selection Klein et al. (2021) – because they are
still associated with galaxy over-densities. All of the sources in Table 6
appear in the eFEDS optically confirmed sample.

###  3.5 The eFEDS contamination fraction

As discussed in Section 3.2 (and collated in Appendix A), 11 of the 62
candidates (18%, Table 5) in the eFEDS-XMM sample were not included in the
eFEDS-XCS sample because they were classified as being in one of the three
sample contaminant types described in Section 3.3. This should be viewed as a
lower limit because, in 10 (of 62) cases (Table 4), it was not possible for us
to confirm the validity of the eFEDS candidate using archival XMM data.

The eFEDS-XCS sample of eFEDS cluster candidates is an order of magnitude
smaller than the full eFEDS X-ray cluster candidate catalogue. Moreover,
several of the eFEDS-XCS clusters were the target of their respective XMM
observations, and that has been shown to introduce selection bias (Giles et
al., prep); this could influence XMM detections and thus the construction of
our eFEDS-XCS sample. Even so, our result is consistent with simulations
performed by the eRASS team that predicted a contamination level of $\sim$20%
(Comparat et al., 2020). It is also consistent with the eFEDS optical
counterparts study (Klein et al., 2021), which measured a contamination
fraction of 17$\pm 3$%.

We also investigated whether any of the 11 cluster candidates that we classed
as sample contaminants (Table 5) are present in the sample of 477 candidates
that Klein et al. (2021) consider to be optically confirmed. We find that 5 of
the 11 are present therein. This compares to 53 in the overall eFEDS-XMM
sample, indicating a minimum contamination fraction of ${\sim}9\%$ in the
Klein et al. (2021) sample. This is slightly high compared to the value of
$6\pm 3$% reported by Klein et al. (2021). However, if we discount eFEDS ID
8602 and 3334 from consideration as sample contaminants (to be more consistent
with approach taken in Klein et al., 2021), the contamination level drops to
${\sim}$6%.

We note that one cluster of the eFEDS-XCS sample (eFEDS ID 5170) does not
appear in the Klein et al. (2021) sample. This candidate was included in our
sample because of its X-ray emission (in XMM and eROSITA images) and evidence
of an over density of red galaxies in the SDSS and HSC photometry.

Figure 10: Comparison of unabsorbed cluster luminosities within a 500 kpc
aperture, in the 0.5-2.0 keV energy band, centered on eFEDS coordinates. Pale
blue line indicates best fit power-law, with 68% confidence levels given by
shaded region. Grey line indicates a power-law fit with slope set to 1 (with
68% confidence levels given by grey shaded region). Cyan diamond is for the
split cluster discussed in Appendix B.

##  4 Comparisons of cluster properties measured by eFEDS and XCS

We use the XGA (Turner et al., prepa) XSPEC (Arnaud, 1996) interface to
measure spectroscopic properties of those clusters that have high enough
quality XMM data, and compare values to those presented in the eFEDS data
release. Note that we do not re-analyse the eFEDS data, but compare to the
measurements given by Liu et al. (2021a). We use XGA v0.2.1, SAS v17.0.0, and
XSPEC v12.10.1.

Figure 11: Temperature and fractional temperature error distributions of the
eFEDS (red) and eFEDS-XCS (pale blue) samples, for measurements made within
500 kpc apertures, centered on eFEDS coordinates.

###  4.1 Fitting Procedure

Cluster spectra are extracted within a 500 kpc fixed aperture (as the eFEDS
catalogue contains a greater number of 500 kpc temperatures than 300 kpc) and
centered on the eFEDS position. Corresponding backgrounds are extracted within
1000-1500 kpc annuli. Non-cluster sources in both the 500 kpc apertures and
background regions are identified using the XCS region files, and their
corresponding events are removed during spectrum generation. We fit absorbed
(with tbabs, Wilms et al., 2000) plasma emission models (APEC, Smith et al.,
2001) to the spectra; these models are standard for XCS analyses, but are also
the same as those used in the eFEDS spectroscopic analysis. To maximise the
similarity of our analysis to eFEDS we opt to use the abundance tables
published by Asplund et al. (2009) when performing our spectral fits. The
abundance parameter of the APEC model in all cases is frozen at 0.3 Z⊙, the nH
parameter of the tbabs model is set from the full-sky HI survey by the HI4PI
Collaboration et al. (2016) using the HEASoft nh tool and frozen. The redshift
parameter is set to the eFEDS catalogue value and frozen. The temperature is
initially set to 3 keV and the normalisation is initially set to 1 cm-5, then
both are allowed to vary.

Each spectrum is first fit independently, and if the measured temperature is
outside of the range $0.01~{}{\rm keV}<T_{\rm{X}}<$20 keV, or either
temperature uncertainty is $>$ 15 keV, then the spectrum will not be included
in the final fit. A simultaneous fit is then performed using only the spectra
that fulfil the requirements outlined above. Temperatures and unabsorbed
luminosities are then determined from this joint fit. We used a given
temperature measurement in further analyses (Sections 4.3, 4.4, and 3) if, a)
the best fit value is less than 25 keV, b) the upper and lower uncertainties
are both positive, and c) the larger uncertainty is less than three times the
smaller. Likewise, fitted luminosities are used in our analyses (Sections 4.2
and 3), if both the upper and lower uncertainties are not greater than the
best fit value, and if the upper and lower uncertainties are both positive.

For a more complete explanation of the spectral fitting process and
comparisons of results with other XMM analyses that confirm the veracity of
measurements produced by this procedure, see Turner et al. (prepb). All
measurements for the eFEDS-XCS sample can be found in Table 9, along with
eFEDS ID, position, and redshift.

###  4.2 Luminosity Comparison

We compare luminosities measured with both XMM and eROSITA, since one of the
main products of eRASS will be large catalogues of X-ray cluster luminosities.
These will be used as the basis of various eROSITA science applications; for
example, a mass-luminosity scaling relation (such as the one recently produced
by Chiu et al., 2021) provides a way to estimate masses and overdensity radii
of a given cluster, enabling X-ray cluster cosmology. Therefore, it is
important to test the fidelity of eFEDS luminosities with XMM data.

The eFEDS analysis presents cluster luminosities measured via a forward-
fitting analysis of 2D count-rate maps, including considerations of the
morphology of the cluster, rather than by the fitting of emission models to
spectroscopic data. In the context of eFEDS, this allows for the measurement
of accurate luminosities for clusters that do not have high enough quality
data to perform spectral fitting. We can directly compare XMM and eROSITA
luminosities for 29 (${\sim}$80%) of the eFEDS-XCS sample. We use a spectral
fitting process to measure unabsorbed (corrected for hydrogen column
absorption) luminosities in the soft (0.5-2.0keV) energy band for those
clusters with a successful XMM temperature measurement.

We fit a power-law with the slope fixed at unity and another power-law with
the slope left to vary to the luminosity comparison, finding the results of
both to be entirely consistent with a one-to-one relation. The fits were
performed in log space using the R package LInear Regression in
Astronomy(lira666LInear Regression in Astronomy, Sereno, 2016a), fully
described in Sereno (2016b). Figure 10 demonstrates an excellent soft-band
luminosity agreement (including the two models) between eFEDS and XCS,
especially considering the differing measurement methods. We also include the
data point for the cluster eFEDS ID 1023 (discussed further in Appendix B),
but do not include it in our comparison fit. Luminosities measured by eFEDS
and XCS are similarly well constrained, though the XCS uncertainties tend to
be slightly smaller.

###  4.3 Temperature Comparison

We have been able to measure temperatures within a 500 kpc aperture for
${\sim}$80% of the eFEDS-XCS sample, though only ${\sim}$30% of those also
have an eFEDS temperature available (see Table 1 for a summary). We first
compare the overall temperature, and fractional temperature uncertainty,
distributions, as we did in Section 2 with the XXL-100-GC sample.

Figure 11a, which shows the overall temperature distributions of the eFEDS and
eFEDS-XCS samples, demonstrates that a larger proportion of XMM temperatures
than eROSITA temperatures are above ${\sim}$4 keV, similar to the behaviour in
Figure 1b with the XXL-100-GC sample. It is likely that this is due to the
difference in telescope sensitivity at high energies, as well as other
selection effects resulting from targeted XMM exposures.

Figure 11b demonstrates that a larger proportion of the eFEDS-XCS clusters
(compared to eFEDS measurements) have a fractional temperature uncertainty of
less than 20%, and as such the XMM temperature measurements are generally
better constrained. However we also note that the temperature fractional error
distribution of the eFEDS-XCS sample extends to larger values than eFEDS.

In summary, archival XMM observations can provide temperatures which are, on
average, better constrained than eFEDS for those clusters that have been
observed by XMM, and can also deliver more temperatures for hotter systems due
to XMM’s greater sensitivity at high energies. As such, the XMM archive will
be a very useful complement to the eRASS.

Figure 12: Comparison of eFEDS and XCS cluster temperatures within 500 kpc, centered on eFEDS coordinates. Pale blue line indicates best fit power-law (slope free to vary), with 68% confidence levels given by shaded region. Grey line indicates a power-law fit with fixed slope of unity (with 68% confidence levels given by the grey shaded region). Cyan diamond is for the split cluster discussed in Appendix B. Table 2: The normalisation, slope, and intrinsic scatter values of the fitted temperature calibration models for 500 kpc apertures. $A_{TT}$ is normalisation, $B_{TT}$ is slope, and $\sigma_{T_{\rm{eROSITA}}|T_{\rm{XMM}}}$ the intrinsic scatter. Calibration Name | $A_{TT}$ | $B_{TT}$ | $\sigma_{T_{\rm{eROSITA}}|T_{\rm{XMM}}}$
---|---|---|---
Power Law | $0.88^{+0.37}_{-0.29}$ | $0.89^{+0.25}_{-0.24}$ | $0.04^{+0.06}_{-0.03}$
Power Law Fixed Slope | $0.75^{+0.10}_{-0.08}$ | 1 | $0.04^{+0.05}_{-0.02}$

###  4.4 Temperature Calibration

Motivated by the known temperature offset between XMM and Chandra
(Schellenberger et al., 2015), we test for a difference in temperatures
measured by XMM and eROSITA. We make a comparison between temperatures
presented in the eFEDS cluster catalogue and XMM temperatures that we have
measured for the same clusters.

The comparison of 8 clusters with measured XMM and eROSITA (eFEDS)
temperatures is given in Figure 12, and shows a systematic offset between the
two telescopes. We also plot the data point for the cluster with eFEDS ID 1023
(discussed further in Appendix B), but do not include it in our comparison
fit. All but one of the clusters are below the one-to-one line, indicating
that the eROSITA temperatures are systematically lower than their XMM
counterparts. To model this, we fit a power law of the form

$\displaystyle{\rm log}\left(T^{\>\rm{eROSITA}}_{\rm{x,500kpc}}\right)$
$\displaystyle={\rm log}(A_{TT})+B_{TT}{\rm
log}\left(T^{\>\rm{XMM}}_{\rm{x,500kpc}}\right)\pm\sigma_{T_{\rm{eROSITA}}|T_{\rm{XMM}}},$
(1)

where $A_{TT}$ is the normalisation, $B_{TT}$ the slope and
$\sigma_{T_{\rm{eROSITA}}|T_{\rm{XMM}}}$ the intrinsic scatter. The fits were
performed in the same way as those in Section 4.2. The best fit parameters are
given in Table 2.

First, we fit the power law with the slope left free to vary, probing whether
the observed offset evolves with temperature (as found in Schellenberger et
al., 2015, comparing between Chandra and XMM). We measure a slope value of
0.89${}^{+0.25}_{-0.24}$, indicating that the calibration evolves with system
temperature. We note however that due to the large errors, the value of
$B_{TT}$ is consistent with 1 (within 1$\sigma$). The measured intrinsic
scatter of both fits is very low (essentially consistent with zero), which is
as expected. Due to the large errors on the measured slope, we re-fit the
power-law with the slope fixed at unity. This allows us to measure a single
overall normalisation that describes the average difference in temperatures
measured by the two telescopes. We measure a normalisation of
0.75${}^{+0.10}_{-0.08}$, meaning that (on average) eROSITA measures a
temperature ${\sim}25\%$ cooler than those measured by XMM for the same
cluster.

As we have not re-analysed eROSITA data and measured our own eROSITA
temperatures for the eFEDS-XCS cluster sample, the observed temperature
calibration offset could be the result of some mismatch in our respective
methodologies. The accuracy of the measured offset is also limited by small
number statistics, as very few clusters have both an eROSITA and an XMM
temperature. However, we have provided evidence of an offset that requires
further investigation.

##  5 Discussion

In this work we have presented a measurement of the temperature offset between
eROSITA and XMM for a sample of galaxy clusters. Here we discuss potential
impacts of this offset on the derived scaling relations and how the
temperature calibration can be improved.

###  5.1 Comparison of eROSITA and XMM X-ray scaling relations

Figure 13: Soft-band (0.5-2.0 keV) luminosity-temperature relations for the eFEDS and eFEDS-XCS samples. Properties measured within a 500 kpc fixed aperture centered on the eFEDS positions. eFEDS data points are green, eFEDS-XCS data points are grey. Figure 14: Corner plot of the 1$\sigma$ and 2$\sigma$ confidence contours of the $L^{500\rm{kpc}}_{\rm{x,0.5-2.0}}$ \- $T^{500\rm{kpc}}$ relation parameters, for the eFEDS (green contours), eFEDS-XCS (grey contours) and eFEDS-XCS calibrated (blue contours) samples. The diagonal shows the posterior densities of each parameter. Figure 15: Soft-band luminosity-temperature relations for eFEDS, eFEDS-XCS, and calibrated eFEDS-XCS. Properties measured within a 500 kpc fixed aperture centered on the eFEDS positions. Table 3: The normalisation, slope, and residual scatter values from the LIRA fits of the different datasets, for the $L^{500\rm{kpc}}_{\rm{X,0.5-2.0}}$ \- $T_{\rm{X}}^{500\rm{kpc}}$ scaling relation. Relation Name | $A_{LT}$ | $B_{LT}$ | $\sigma_{L|T}$
---|---|---|---
eFEDS | $1.03^{+0.09}_{-0.08}$ | $2.31^{+0.13}_{-0.13}$ | $0.19^{+0.03}_{-0.03}$
eFEDS-XCS | $0.78^{+0.12}_{-0.11}$ | $1.58^{+0.22}_{-0.23}$ | $0.23^{+0.05}_{-0.04}$
eFEDS-XCS Calibrated | $1.04^{+0.15}_{-0.14}$ | $1.76^{+0.25}_{-0.26}$ | $0.22^{+0.06}_{-0.04}$

We have explored the impact on X-ray scaling relations in light of the
temperature offset measured in Section 4.4. We focus on the luminosity-
temperature relation derived from eFEDS and XCS data. We use 28 eFEDS-XCS
clusters with a successful 500 kpc temperature ($T^{\rm 500kpc}_{\rm X}$) and
soft-band luminosity ($L^{\rm 500kpc}_{X,0.5-2.0}$) measurement (instead of
limiting the analysis to the 8 clusters used in Section 4.4 for temperature
calibration), and all available eFEDS candidates and compare the relations.

The $L^{500\rm{kpc}}_{\rm{X,0.5-2.0}}$ \- $L_{\rm{X}}^{500\rm{kpc}}$ relations
for eFEDS (grey points) and eFEDS-XCS (green points) are shown in Figure 13;
the eFEDS relation uses data from 94 clusters. We fit both sets of data using
a power law of the form,

$\displaystyle{\rm
log}\left(\frac{L^{500\rm{kpc}}_{\rm{X,0.5-2.0}}}{E(z)L_{0}}\right)$
$\displaystyle={\rm log}(A_{LT})+B_{LT}{\rm
log}\left(\frac{T^{\rm{500kpc}}_{\rm{X}}}{T_{0}}\right)\pm\sigma_{L|T},$ (2)

where $A_{LT}$ denotes the normalisation, $B_{LT}$ the slope, and
$\sigma_{L|T}$ the intrinsic scatter of the relation. We calculate $E(z)$
using the redshift supplied in the eFEDS catalogue and our chosen concordance
cosmology. The fits are performed using the LIRA package. We set normalisation
values for luminosity and temperature to approximate median eFEDS values;
$L_{0}$=3.0$\times$1043 erg s-1 and $T_{0}$=2.3 keV.

Figure 13 shows the best-fit relations using the eFEDS (green line) and eFEDS-
XCS (grey line) samples respectively. The best-fit values are given in Table
3, with their distributions illustrated in Figure 14. While the distributions
highlight that the parameters of the relation are consistent within their
2$\sigma$ contours, the difference in the central value of the slope warrants
further discussion.

Figure 16: Distribution of XMM observations projected over the sky, indicated
by grey points. The eRASS-DE half of the sky is highlighted by the red region.
The background is the Planck-DustPol (Padovani et al., 2012) map, available
for download on NASA’s Lambda service.

We explore whether this difference can be reduced by accounting for the
observed temperature offset found in Section 4.4. We measure a third version
of the scaling relation, designed to test the effect of the temperature
calibration quantified in Section 4.4. We determine a “calibrated” luminosity-
temperature relation by using the power law model (with slope free to vary),
with parameter values provided in Table 2, to convert the eFEDS-XCS XMM
temperature values to predicted eROSITA values.

Figure 15 shows the model fits for all three relations (with data points
omitted for clarity), and shows that the eFEDS-XCS calibrated scaling relation
has a steepened slope and increased normalisation when compared to the
original eFEDS-XCS relation. Figure 14 shows a shift of the contours and
distributions (the eFEDS-XCS calibrated parameters are given by the blue
contours) towards eFEDS (blue contours). The normalisation of the calibrated
eFEDS-XCS relation is fully consistent with the eFEDS relation, with the
tension in the measured slopes reduced.

###  5.2 Future work to improve the calibration of the XMM to eROSITA
temperature offset

The measured temperature discrepancy described in Section 4.4 and shown in
Figure 12 is based on only 8 sets of measurements, of which only 3 are more
than one sigma from the one-to-one relation. Further investigation is required
to quantify the level of a temperature offset between the XMM and eROSITA. For
this, we plan three complementary approaches:

  * •

Re-analyse the eFEDS cluster candidate observations using an identical
spectroscopic methodology to the XMM analysis. This way, we will have control
of all aspects of the analysis, including which regions are used to mask the
observations for spectrum generation (see a related discussion in Appendix B).
This will be done for all 94 clusters in the eFEDS luminosity-temperature
analysis (Figure 13), which includes the eight clusters featured in Figure 12.

  * •

Propose XMM follow-up observations of a representative sample of eFEDS
clusters with robustly (i.e. percentage error less than 25%) measured eROSITA
temperatures. There are 43 such examples in the eFEDS data release that are
not already included in the analysis shown in Figure 12. We will
preferentially select clusters that fill gaps at the high and low temperature
ends, to better constrain a temperature dependent slope in the calibration
relation (if one exists).

  * •

Repeat the analysis herein after the next eROSITA-DE data release (due in Q4
2022777eROSITA-DE Data Release Schedule). This will cover the whole Southern
sky (red area in Figure 16) and thus overlap with many more archival XMM
observations than did eFEDS (grey points and regions in Figure 16). The next
data release will have an exposure time eight times less shorter than eFEDS
(one pass), but, with ${\sim}$150 times the area, we can still expect it to
yield roughly 1000 robust temperature measurements.

##  6 Summary

In this work we have performed the first comparison between cluster properties
measured by the eFEDS survey and those measured by XMM surveys, both directly
and for ensembles of clusters. A comparison of XXL-100-GC and the eFEDS
optically confirmed sample indicated that the two samples have very similar
redshift distributions, that XXL-100-GC contained proportionally more
temperature measurements above 3.5 keV, and that XXL-100-GC temperatures are,
on average, better constrained than eFEDS temperatures (14% vs 25% average
percentage uncertainties respectively).

We have located and analysed eFEDS cluster candidates that have a counterpart
in an XMM observation; as part of this process we visually inspected eFEDS
cluster candidates that are within an XMM observation and rejected any that
had no ICM emission at the eFEDS coordinates, had obviously contaminated ICM
emission, or too low quality XMM data. The eFEDS-XMM sample contains 62 eFEDS
cluster candidates that have been observed by XMM, and the eFEDS-XCS sub-
sample contains the 37 clusters that pass our visual inspection (Table 1).
During visual inspection we found that 10 candidates (Table 4) did not have
sufficient XMM data to confirm or deny a cluster, 4 had X-ray flux
contamination (Section 3.4, Table 6), and 11 were sample contaminants (Section
3.3, Table 5). We found that the majority of eFEDS-XMM candidates had a longer
exposure time (at their eFEDS position) in XMM than in eFEDS. We also found
that the majority of eFEDS centroid positions for the eFEDS-XCS sample are
within 100 kpc (at the eFEDS redshift) of the XCS centroid positions (for
clusters with an XCS match), though some outliers exist due to low signal-to-
noise eFEDS data.

Our visual inspections of the eFEDS cluster candidates that fall on an XMM
field (using eROSITA, XMM, SDSS and HCS images) have shown that there are some
aspects of eROSITA’s source finding and confirmation steps that can introduce
spurious sources into their catalogues, which in turn could impact their
cosmological analyses. Our inspection process finds that the eFEDS-XMM sample
is (at minimum) ${\sim}$18% contaminated, and that optically confirmed sample
is ${\sim}$9% (${\sim}$6% if made more consistent with the eFEDS sample
selection method) contaminated. This is consistent with predictions from
simulations (Comparat et al., 2020) and eFEDS measured values (Klein et al.,
2021).

We have presented comparisons between cluster luminosities and temperatures
measured with eROSITA and XMM. Our analysis finds excellent agreement between
soft-band luminosities measured by eFEDS and XCS for the eFEDS-XCS sample
(Section 4.2), which is very encouraging for future eRASS cosmology analyses.
Such analyses will rely almost exclusively on mass-luminosity relations (such
as the recent eFEDS-HSC work, Chiu et al., 2021), as even full depth eRASS
will not be able to measure temperatures for enough galaxy clusters to use
mass-temperature relations for cosmology. An ensemble cluster comparison was
performed (Section 4.3) between the whole eFEDS cluster candidate sample (that
had successful temperature/luminosity measurements), and the eFEDS-XCS sample
(that had successful temperature/luminosity measurements). It showed similar
results to the XXL-100-GC comparison, with a greater fraction of XMM
temperature measurements being above 4 keV than eFEDS temperatures, and better
average temperature constraints for XMM measurements.

A discrepancy between cluster temperatures measured by eFEDS and XCS has been
found and quantified (Section 4.4), with eROSITA temperatures being (on
average) $25{\pm}9$% cooler than those measured by XMM for the same cluster.
This could hint at the need for a calibration function between the eROSITA and
XMM telescopes (as has been necessary between XMM and Chandra). Several
variables need to be better controlled before we can definitively state that
the observed discrepancy is entirely due to a required temperature
calibration, but we consider it to be a likely explanation.

We also fit and compare luminosity-temperature scaling relations using data
from the eFEDS catalogue and XMM data for the eFEDS-XCS sample, using them to
compare scaling relations measured with eROSITA and XMM data. This has
particular relevance for anyone wishing to use an XMM generated scaling
relation in an eROSITA analysis, or vice versa, as we find a distinct tension
between scaling relations from the eFEDS and eFEDS-XCS samples. We also
generate a second, calibrated, eFEDS-XCS scaling relation which is in better
agreement with the eFEDS relation; normalisation becomes entirely consistent,
and the slope measurement tension is reduced. This again may suggest that a
temperature scaling between XMM and eROSITA is necessary. It is likely,
however, that a large part of the observed tension between the scaling
relations is due to selection effects.

Our comparisons have shown that we can expect a great deal of useful data from
the full eRASS catalogues, and that XMM-Newton still has a significant part to
play as followup instrument. Its archive of 20 years worth of observations is
still extremely valuable to the eROSITA team, and the X-ray astronomy
community as a whole, and there will be many excellent opportunities for
synergies between the two telescopes.

## Acknowledgements

This work is based on data from eROSITA, the soft X-ray 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 Zentrum für Luft- und
Raumfahrt (DLR). The SRG spacecraft was built by Lavochkin Association (NPOL)
and its subcontractors, and is operated by NPOL with support from the Max
Planck Institute for Extraterrestrial Physics (MPE). The development and
construction of the eROSITA X-ray instrument was led by MPE, with
contributions from the Dr. Karl Remeis Observatory Bamberg & ECAP (FAU
Erlangen-Nuernberg), the University of Hamburg Observatory, the Leibniz
Institute for Astrophysics Potsdam (AIP), and the Institute for Astronomy and
Astrophysics of the University of Tübingen, with the support of DLR and the
Max Planck Society. The Argelander Institute for Astronomy of the University
of Bonn and the Ludwig Maximilians Universität Munich also participated in the
science preparation for eROSITA.

The eROSITA data shown here were processed using the eSASS software system
developed by the German eROSITA consortium.

We made use of TOPCAT (Taylor, 2005) during the initial exploration of the
eRASS cluster catalogue.

The new X-ray analysis module developed by XCS (XGA) makes significant use of
Astropy (Astropy Collaboration et al., 2013, 2018), NumPy (Harris et al.,
2020), Matplotlib (Hunter, 2007), and pandas (The pandas development team,
2020; Wes McKinney, 2010). XGA also uses GetDist (Lewis, 2019) to produce
corner plots.

DT, KR, and PG acknowledge support from the UK Science and Technology
Facilities Council via grants ST/P006760/1 (DT), ST/P000525/1 and ST/T000473/1
(PG, KR). PTPV was supported by Fundação para a Ciência e a Tecnologia (FCT)
through research grants UIDB/04434/2020 and UIDP/04434/2020.

## Data Availability

The data underlying this article were accessed from the eROSITA Early Data
Release site, and the XMM science archive. The derived data underlying this
article are available in the article and in its online supplementary material.

## References

  * Ahumada et al. (2020) Ahumada R., et al., 2020, ApJS, 249, 3
  * Aihara et al. (2018) Aihara H., et al., 2018, PASJ, 70, S4
  * Aihara et al. (2019) Aihara H., et al., 2019, PASJ, 71, 114
  * Arnaud (1996) Arnaud K. A., 1996, in Jacoby G. H., Barnes J., eds, Astronomical Society of the Pacific Conference Series Vol. 101, Astronomical Data Analysis Software and Systems V. p. 17
  * Asplund et al. (2009) Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, ARA&A, 47, 481
  * Astropy Collaboration et al. (2013) Astropy Collaboration et al., 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration et al., 2018, AJ, 156, 123
  * Bhargava et al. (2020) Bhargava S., et al., 2020, MNRAS, 497, 656
  * Blanton et al. (2017) Blanton M. R., et al., 2017, AJ, 154, 28
  * Boller et al. (2021) Boller T., et al., 2021, A&A, 647, A6
  * Brunner et al. (2021) Brunner H., et al., 2021, arXiv e-prints, p. arXiv:2106.14517
  * Chiu et al. (2021) Chiu I.-N., et al., 2021, arXiv e-prints, p. arXiv:2107.05652
  * Comparat et al. (2020) Comparat J., et al., 2020, The Open Journal of Astrophysics, 3, 13
  * Driver et al. (2011) Driver S. P., et al., 2011, MNRAS, 413, 971
  * Farahi et al. (2019) Farahi A., et al., 2019, Nature Communications, 10, 2504
  * Flesch (2021) Flesch E. W., 2021, arXiv e-prints, p. arXiv:2105.12985
  * Giles et al. (2016) Giles P. A., et al., 2016, A&A, 592, A3
  * Giles et al. (prep) Giles P. A., et al., in prep
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration et al., 2016, A&A, 594, A116
  * Harris et al. (2020) Harris C. R., et al., 2020, Nature, 585, 357
  * Hitomi Collaboration et al. (2016) Hitomi Collaboration et al., 2016, Nature, 535, 117
  * Hunter (2007) Hunter J. D., 2007, Computing in Science & Engineering, 9, 90
  * Klein et al. (2018) Klein M., et al., 2018, MNRAS, 474, 3324
  * Klein et al. (2021) Klein M., et al., 2021, arXiv e-prints, p. arXiv:2106.14519
  * Koulouridis et al. (2021) Koulouridis E., et al., 2021, A&A, 652, A12
  * Lewis (2019) Lewis A., 2019, arXiv e-prints, p. arXiv:1910.13970
  * Liu et al. (2021a) Liu A., et al., 2021a, arXiv e-prints, p. arXiv:2106.14518
  * Liu et al. (2021b) Liu T., et al., 2021b, arXiv e-prints, p. arXiv:2106.14522
  * Lloyd-Davies et al. (2011) Lloyd-Davies E. J., et al., 2011, MNRAS, 418, 14
  * Migkas et al. (2020) Migkas K., Schellenberger G., Reiprich T. H., Pacaud F., Ramos-Ceja M. E., Lovisari L., 2020, A&A, 636, A15
  * Pacaud et al. (2016) Pacaud F., et al., 2016, A&A, 592, A2
  * Padovani et al. (2012) Padovani M., et al., 2012, A&A, 543, A16
  * Pfeifle et al. (2019) Pfeifle R. W., et al., 2019, ApJ, 875, 117
  * Pierre et al. (2016) Pierre M., et al., 2016, A&A, 592, A1
  * Pillepich et al. (2012) Pillepich A., Porciani C., Reiprich T. H., 2012, MNRAS, 422, 44
  * Predehl et al. (2021) Predehl P., et al., 2021, A&A, 647, A1
  * Romer et al. (1999) Romer A. K., Viana P. T. P., Liddle A. R., Mann R. G., 1999, ArXiv Astrophysics e-prints,
  * Sanders et al. (2021a) Sanders J. S., et al., 2021a, arXiv e-prints, p. arXiv:2106.14534
  * Sanders et al. (2021b) Sanders J. S., et al., 2021b, arXiv e-prints, p. arXiv:2106.14534
  * Schellenberger & Reiprich (2017) Schellenberger G., Reiprich T. H., 2017, MNRAS, 471, 1370
  * Schellenberger et al. (2015) Schellenberger G., Reiprich T. H., Lovisari L., Nevalainen J., David L., 2015, A&A, 575, A30
  * Sereno (2016a) Sereno M., 2016a, LIRA: LInear Regression in Astronomy, Astrophysics Source Code Library (ascl:1602.006)
  * Sereno (2016b) Sereno M., 2016b, MNRAS, 455, 2149
  * Smith et al. (2001) Smith R. K., Brickhouse N. S., Liedahl D. A., Raymond J. C., 2001, ApJ, 556, L91
  * Taylor (2005) Taylor M. B., 2005, in Shopbell P., Britton M., Ebert R., eds, Astronomical Society of the Pacific Conference Series Vol. 347, Astronomical Data Analysis Software and Systems XIV. p. 29
  * The pandas development team (2020) The pandas development team 2020, pandas-dev/pandas: Pandas, doi:10.5281/zenodo.3509134, https://doi.org/10.5281/zenodo.3509134
  * Turner et al. (prepb) Turner D. J., et al., in prepb
  * Turner et al. (prepa) Turner D. J., Giles P A., Romer A K., in prepa
  * Vikhlinin et al. (2009) Vikhlinin A., et al., 2009, ApJ, 692, 1060
  * Wes McKinney (2010) Wes McKinney 2010, in Stéfan van der Walt Jarrod Millman eds, Proceedings of the 9th Python in Science Conference. pp 56 – 61, doi:10.25080/Majora-92bf1922-00a
  * Wilms et al. (2000) Wilms J., Allen A., McCray R., 2000, ApJ, 542, 914

##  Appendix A Excluded Cluster Candidates

Table 4: eFEDS-XMM galaxy cluster candidates excluded from further analysis
due to one or more XMM-Newton data quality issues.
† indicates that the candidate was present in the optically confirmed sample from Klein et al. (2021). eFEDS ID | RA | Dec | $z$ |  Notes
---|---|---|---|---
8094† | 133.644 | -1.677 | 0.595 |  On the edge of the XMM field of view.
7700 | 133.669 | -2.159 | 0.472 |  On the edge of the XMM field of view.
1797† | 133.876 | -1.11 | 0.754 |  On the edge of the XMM field of view (the eROSITA image confirms presence of an extended source).
11836† | 135.272 | -1.424 | 0.405 |  On the edge of the XMM field of view, and the XMM observation is shallow (1023 s exposure at the eFEDS coordinates). The eROSITA image confirms presence of an extended source.
9877† | 136.04 | 0.642 | 0.311 |  Low signal-to-noise XMM image (7489 s exposure at the eFEDS coordinates) which has been affected by flaring.
2757† | 134.756 | 1.114 | 0.162 |  Low signal-to-noise XMM image (6870 s exposure at the eFEDS coordinates).
5858 | 136.687 | 1.19 | 0.441 |  Low signal-to-noise XMM image (15020 s exposure at the eFEDS coordinates). eROSITA image confirms presence of extended source.
2074† | 136.971 | 1.569 | 0.163 |  Low signal-to-noise XMM image (5331 s exposure at the eFEDS coordinates).
11837† | 138.201 | 0.413 | 0.308 |  Low signal-to-noise XMM image (29479 s exposure at the eFEDS coordinates) which has been affected by flaring. The eROSITA image confirms presence of an extended source.
1376† | 133.23 | -1.627 | 0.343 |  XMM data too shallow for confirmation. The eROSITA and SDSS data indicate a likely cluster, but eFEDS coordinate is offset from the extended emission and SDSS galaxies.

This section details the eFEDS-XMM X-ray cluster candidates that were not
included in eFEDS-XCS sample, as discussed in Section 3. Basic information
about the samples used in this work is available in Table 1. Table 4 contains
candidates that were not included due to the low quality of the XMM data
available, Table 6 contains galaxy clusters whose X-ray emission has been
significantly contaminated by another X-ray source and as such were not
included in the eFEDS-XCS sample. Table 5 contains sample contaminants that
were not included in the eFEDS-XCS sample (see Section 3.2).

Table 5: eFEDS-XMM galaxy cluster candidates classed as contaminants during
our visual inspection of XMM, eROSITA, and SDSS images.
† indicates that the candidate was present in the optically confirmed sample from Klein et al. (2021). eFEDS ID | RA | Dec | $z$ |  Notes
---|---|---|---|---
1644† | 130.396 | 1.031 | 0.507 |  Blend: In XMM image two point sources are detected, due to XMM’s smaller PSF effect. The source is the target of the XMM observation and is associated with an interacting pair of active galaxies. (see Figure 5).
3334† | 130.508 | 0.995 | 0.087 |  Spurious: There is not an X-ray source at this location in either the XMM or eROSITA images, nor do there appear to be any associated galaxies in the SDSS/HSC images.
8602† | 132.593 | 0.269 | 0.196 |  Fragmented: The ICM emission from a single cluster that has been classified as coming from two eFEDS candidates, ID 8602 and 1023.
5909† | 133.83 | -1.721 | 0.365 |  Spurious: There is an X-ray source at the eFEDS candidate location, but it is a defined as point source by XCS in the higher signal to noise XMM data. There are no associated galaxies in the SDSS or HSC images.
8922† | 134.067 | -1.663 | 0.514 |  Spurious: In eFEDS, this is a spurious detection of the outskirts of the emission from an X-ray bright spiral galaxy. In the higher resolution XMM image, there is no source at this location.
9463 | 136.753 | 1.176 | 0.799 |  Blend: In the higher signal to noise (18501 s exposure) XMM image, two point sources are detected.
13484 | 136.766 | 1.132 | 0.307 |  Spurious: There is no obvious extended X-ray emission in either the eROSITA or XMM data. There are no associated galaxies in the SDSS or HSC images.
13299 | 138.691 | 4.439 | 0.348 |  Spurious: In eFEDS, this is a spurious detection of the outskirts of the emission from an X-ray bright star.
11754 | 140.018 | 1.007 | 0.033 |  Spurious: This is a spurious detection in the outskirts of the nearby eFEDS candidate ID 150 ($z$=0.017).
5702 | 130.295 | 0.867 | 0.415 |  Spurious: In the higher signal to noise (130445 s exposure) XMM image, a point source is detected which appears to be associated with a blue (i.e. likely AGN) object in the SDSS and HSC images.
6840 | 135.597 | 1.868 | 0.561 |  Spurious: In the XMM image, XCS detects a point source which appears to be associated with a blue (i.e. likely AGN) object in the SDSS and HSC images.
Table 6: eFEDS-XMM galaxy cluster candidates which appear to be galaxy
clusters whose X-ray emission is significantly contaminated by another source.
† indicates that the candidate was present in the optically confirmed sample from Klein et al. (2021). eFEDS ID | RA | Dec | $z$ |  Notes
---|---|---|---|---
16370† | 134.098 | -1.604 | 0.425 |  eFEDS candidate coincident with a collection of galaxies in SDSS/HSC; however X-ray emission is contaminated by low redshift spiral galaxy.
150† | 140.009 | 1.039 | 0.017 |  SDSS/HSC indicates the presence of a group of galaxies, however, the X-ray emission originates primarily from the central galaxy.
3133† | 140.649 | -0.412 | 0.055 |  SDSS/HSC indicates the presence of a group of galaxies, however, the X-ray emission originates primarily from the central galaxy.
3008† | 130.451 | 0.82 | 0.078 |  SDSS/HSC indicates the presence of a group of galaxies, however, the X-ray emission originates primarily from the central galaxy.

##  Appendix B eFEDS Candidate 1023

This galaxy cluster has been been split into two sources by the eFEDS source
finder; a visual inspection confirmed a single extended X-ray source (in both
eROSITA and XMM images) and a single projected distribution of red galaxies
(Section 3.3.3). XCS also detected this as a single extended source.

One of the two eFEDS catalogue entries that make up this cluster has measured
eROSITA $T_{\rm{X}}$ and $L_{\rm{X}}$ values. These values will be impacted by
the masking of emission from the other component. Therefore it would not be
appropriate to include those values in the comparisons presented in Figures 10
or 12.

However, we have attempted to mimic the eROSITA values using XMM data. This
involves manually adding a region to be excluded when the XMM spectra are
generated. This region is centered on the eFEDS X-ray candidate catalogue
coordinates for eFEDS-8602, and uses the ‘extent’ value for that candidate
published in the optical counterpart catalogue as the radius of the new
exclusion region. Doing this, we find the XMM determined $L_{\rm{X}}$ and
$T_{\rm{X}}$ values are consistent with those presented in Liu et al. (2021a);
see Figures 10 and 12 (cyan diamond).

##  Appendix C eFEDS-XCS Data and Measurements

In Table 7 we present information on the XMM data that were used for each
eFEDS-XCS cluster, including the unique XMM observation identifier and which
instruments had usable data. We also include information on which instruments
of which observations were contributed to the final luminosity and temperature
measurements of each eFEDS-XCS cluster. In Table 9 we present temperature and
luminosity values measured for the clusters in the eFEDS-XCS sample. We use
XGA to generate spectra and run XSPEC fits for these clusters. The fitting
procedure is discussed in more detail in Section 4.1. All measurements are
centered on the eFEDS coordinates from the X-ray cluster candidate catalogue,
with redshift information also taken from that catalogue.

Table 7: The XMM data used in the analysis of the eFEDS-XCS sample, individual clusters denoted by their unique eFEDS ID. ObsID contains the unique identifier(s) of the XMM observation(s) used. T denotes true, F denotes false, - denotes that either no successful spectral fit was performed, or the data for that cameras was not available. Columns with a subscript A (e.g. $\rm{PN}_{\rm{A}}$) indicate whether that instrument is available for an ObsID. Columns with a subscript radius (e.g. $\rm{PN}_{\rm{500kpc}}$) indicate whether that instrument’s data contributed to the final XSPEC fit from which we extract temperature and luminosity information. eFEDS ID | ObsID | PNA | MOS1A | MOS2A | PN500kpc | MOS1500kpc | MOS2500kpc
---|---|---|---|---|---|---|---
6605 | 0202940101 | T | T | T | F | F | F
0202940201 | T | T | T | T | T | T
144 | 0650381601 | T | T | T | T | T | T
7831 | 0784350101 | T | T | T | T | T | T
1023 | 0761730501 | T | F | T | T | - | T
6125 | 0761730501 | T | F | T | T | - | T
339 | 0655340137 | T | T | T | T | T | T
4810 | 0655340137 | T | T | T | T | F | F
1458 | 0655340135 | T | T | T | T | T | T
2079 | 0651170301 | T | T | T | T | T | T
569 | 0783881001 | T | T | T | T | T | T
1385 | 0783881001 | T | F | T | T | - | T
8857 | 0725290142 | T | T | T | - | - | -
3171 | 0725300134 | T | F | T | F | - | T
0725290144 | T | T | T | T | T | F
0725290145 | T | F | T | T | - | T
8881 | 0725290139 | T | T | T | F | F | F
0725290146 | T | T | T | T | F | T
1104 | 0655340160 | T | T | T | T | F | T
0804410201 | T | T | T | T | T | T
4232 | 0655340160 | T | T | T | F | F | F
0804410201 | T | T | T | T | T | T
5655 | 0725300158 | T | T | T | T | T | F
0725300159 | T | F | T | T | - | T
0725300136 | T | T | F | T | F | -
1712 | 0725300140 | T | T | F | T | T | -
0725300132 | T | T | T | T | F | F
0725300131 | T | T | T | F | F | T
5774 | 0725300157 | T | T | T | - | - | -
0725310131 | T | T | T | - | - | -
3590 | 0725310152 | T | T | T | T | F | F
0725300160 | T | F | T | F | - | F
12660 | 0725290131 | T | T | T | T | T | T
0725290154 | T | T | T | F | T | T
3585 | 0725310149 | T | T | T | T | F | F
0725310150 | T | T | T | T | F | T
0725310131 | T | F | F | T | - | -
5170 | 0725300152 | T | F | T | T | - | F
0725300153 | T | T | T | T | F | F
9359 | 0725300145 | T | F | T | T | - | T
0725300146 | T | T | T | T | F | F
Table 8: continued eFEDS ID | ObsID | PNA | MOS1A | MOS2A | PN500kpc | MOS1500kpc | MOS2500kpc
---|---|---|---|---|---|---|---
3259 | 0725300144 | T | T | T | T | T | T
0725300151 | T | T | T | F | F | T
7086 | 0725310133 | T | F | F | - | - | -
0725310147 | T | F | T | - | - | -
0725310148 | T | T | T | - | - | -
0725310157 | F | F | T | - | - | -
0402780801 | T | T | T | - | - | -
5219 | 0725310158 | T | T | T | T | F | F
0725310147 | T | F | F | T | - | -
0725310159 | T | T | T | T | F | F
7084 | 0725310157 | T | T | T | - | - | -
885 | 0725310142 | T | T | T | T | T | T
0725310141 | T | F | T | T | - | T
2004 | 0800400501 | T | F | T | T | - | T
3523 | 0800400501 | T | T | T | F | T | T
372 | 0602830401 | T | F | F | T | - | -
4253 | 0602830401 | T | F | T | F | - | T
534 | 0804410101 | T | T | T | T | T | T
0650381801 | T | T | T | T | T | T
100 | 0804410501 | T | T | T | T | T | T
857 | 0823710301 | T | T | T | T | T | T
12565 | 0802220601 | T | F | F | - | - | -
Table 9: eFEDS-XCS galaxy cluster XGA measured values, RA, Dec, and redshift are taken from the eFEDS X-ray cluster candidate catalogue. $T^{\rm{XGA}}_{\rm{x},500kpc}$ are temperatures within 500 kpc apertures, given in keV. $L^{\rm{XGA,52}}_{\rm{x,500kpc}}$ and $L^{\rm{XGA,bol}}_{\rm{x,500kpc}}$ are 0.5-2 .0keV and bolometric luminosities within a 500 kpc apertures, in units of 1043erg $\rm{s}^{-1}$. All uncertainties calculated from 68% confidence limits, equivalent to $1\sigma$. eFEDS ID | RA | Dec | z | T${}^{\rm{XGA}}_{\rm{x},500kpc}$ | L${}^{\rm{XGA,52}}_{\rm{x,500kpc}}$ | L${}^{\rm{XGA,bol}}_{\rm{x,500kpc}}$
---|---|---|---|---|---|---
6605 | 130.353 | 0.777 | 0.41 | $1.61^{+0.17}_{-0.13}$ | $2.32^{+0.16}_{-0.17}$ | $4.81^{+0.46}_{-0.41}$
144 | 131.37 | 3.461 | 0.33 | $5.8^{+0.59}_{-0.48}$ | $19.18^{+0.84}_{-0.67}$ | $67.1^{+3.88}_{-3.88}$
7831 | 132.272 | 2.243 | 0.4 | $1.61^{+0.1}_{-0.11}$ | $2.82^{+0.21}_{-0.15}$ | $5.87^{+0.44}_{-0.43}$
1023† | 132.616 | 0.251 | 0.2 | $3.08^{+0.14}_{-0.13}$ | $3.55^{+0.04}_{-0.05}$ | $9.29^{+0.25}_{-0.22}$
6125 | 132.627 | 0.558 | 0.19 | $2.39^{+0.33}_{-0.31}$ | $0.98^{+0.05}_{-0.05}$ | $2.35^{+0.2}_{-0.18}$
339 | 133.071 | -1.025 | 0.46 | $5.57^{+0.81}_{-0.63}$ | $18.3^{+0.71}_{-0.76}$ | $62.82^{+4.09}_{-6.48}$
4810 | 133.13 | -1.208 | 0.55 | $2.06^{+2.12}_{-0.72}$ | $4.56^{+1.06}_{-1.85}$ | $10.14^{+3.84}_{-4.1}$
1458 | 133.554 | -2.357 | 0.38 | $4.47^{+0.78}_{-0.72}$ | $11.59^{+0.53}_{-0.75}$ | $35.63^{+3.34}_{-4.39}$
2079 | 133.696 | -1.359 | 0.35 | $3.27^{+0.56}_{-0.38}$ | $4.59^{+0.23}_{-0.27}$ | $12.23^{+0.86}_{-0.98}$
569 | 134.086 | 1.78 | 0.72 | $4.94^{+0.16}_{-0.16}$ | $29.96^{+0.55}_{-0.44}$ | $96.29^{+2.02}_{-1.94}$
1385 | 134.113 | 1.705 | 0.73 | $6.47^{+1.49}_{-1.11}$ | $7.06^{+0.4}_{-0.37}$ | $26.2^{+2.66}_{-3.5}$
8857 | 134.658 | 1.449 | 0.75 | - | - | -
3171 | 135.269 | 1.279 | 0.25 | $1.7^{+0.24}_{-0.2}$ | $2.64^{+0.26}_{-0.63}$ | $5.69^{+0.76}_{-1.3}$
8881 | 135.314 | 0.844 | 0.31 | $3.27^{+4.56}_{-1.79}$ | $1.13^{+0.34}_{-0.36}$ | $3.02^{+1.2}_{-1.7}$
1104 | 135.372 | -1.648 | 0.31 | $5.96^{+0.32}_{-0.32}$ | $10.94^{+1.11}_{-0.81}$ | $38.75^{+4.67}_{-4.06}$
4232 | 135.443 | -1.632 | 0.29 | $1.95^{+0.53}_{-0.3}$ | $0.99^{+0.1}_{-0.14}$ | $2.19^{+0.36}_{-0.33}$
5655 | 135.735 | 1.774 | 0.12 | $0.97^{+0.11}_{-0.12}$ | $0.02^{+0.11}_{-0.02}$ | $0.04^{+0.19}_{-0.04}$
1712 | 135.74 | 0.805 | 0.52 | $2.08^{+1.74}_{-0.63}$ | $6.12^{+2.32}_{-1.85}$ | $13.68^{+4.61}_{-4.53}$
5774 | 136.036 | 1.432 | 0.84 | - | - | -
3590 | 136.078 | 2.112 | 0.81 | $4.99^{+8.64}_{-2.3}$ | $10.17^{+1.35}_{-3.57}$ | $32.84^{+7.6}_{-13.35}$
12660 | 136.08 | -1.077 | 0.31 | $2.68^{+1.51}_{-0.81}$ | $0.81^{+0.21}_{-0.14}$ | $2.01^{+0.55}_{-0.47}$
3585 | 136.42 | 1.539 | 0.64 | $4.0^{+1.46}_{-0.94}$ | $8.81^{+2.0}_{-1.89}$ | $25.52^{+6.27}_{-6.63}$
5170 | 136.473 | 0.379 | 0.37 | $1.22^{+0.14}_{-0.18}$ | $2.33^{+0.38}_{-0.46}$ | $4.42^{+0.74}_{-0.94}$
9359 | 136.502 | -0.423 | 0.3 | $1.92^{+1.46}_{-0.51}$ | $1.0^{+0.66}_{-0.67}$ | $2.2^{+1.89}_{-1.4}$
3259 | 136.504 | 0.015 | 0.2 | $2.53^{+1.06}_{-0.59}$ | $1.22^{+0.33}_{-0.19}$ | $2.96^{+0.87}_{-0.68}$
7086 | 136.654 | 1.148 | 0.79 | - | - | -
5219 | 136.977 | 0.961 | 0.74 | $4.74^{+2.17}_{-1.44}$ | $9.92^{+1.76}_{-1.6}$ | $31.21^{+5.25}_{-7.57}$
7084 | 137.025 | 1.331 | 0.66 | - | - | -
885 | 137.308 | -0.204 | 0.31 | $2.99^{+0.52}_{-0.37}$ | $5.65^{+0.49}_{-0.44}$ | $14.52^{+1.38}_{-1.55}$
2004 | 137.314 | -1.018 | 0.82 | $5.57^{+4.09}_{-1.96}$ | $6.17^{+2.72}_{-3.36}$ | $21.12^{+10.09}_{-10.65}$
3523 | 137.386 | -0.839 | 1.13 | $5.61^{+2.19}_{-1.11}$ | $26.33^{+2.91}_{-3.09}$ | $93.83^{+11.49}_{-17.28}$
Table 10: continued eFEDS ID | RA | Dec | z | T${}^{\rm{XGA}}_{\rm{x},500kpc}$ | L${}^{\rm{XGA,52}}_{\rm{x,500kpc}}$ | L${}^{\rm{XGA,bol}}_{\rm{x,500kpc}}$
---|---|---|---|---|---|---
372 | 138.723 | 4.27 | 0.14 | $2.46^{+0.84}_{-0.67}$ | $1.8^{+0.11}_{-0.09}$ | $4.35^{+0.5}_{-0.4}$
4253 | 138.801 | 4.585 | 0.36 | $5.18^{+-5.18}_{-3.76}$ | $1.18^{+0.3}_{-1.18}$ | $3.96^{+5.96}_{-1.84}$
534 | 139.042 | -0.397 | 0.32 | $6.04^{+0.35}_{-0.35}$ | $13.86^{+0.32}_{-0.34}$ | $49.42^{+1.96}_{-1.85}$
100 | 140.338 | 3.291 | 0.33 | $7.83^{+0.31}_{-0.31}$ | $19.66^{+0.25}_{-0.23}$ | $79.71^{+0.85}_{-1.93}$
857 | 140.55 | -0.459 | 0.32 | $5.86^{+0.24}_{-0.23}$ | $9.51^{+0.13}_{-0.11}$ | $33.41^{+0.66}_{-0.84}$
12565 | 142.473 | 0.467 | 0.15 | - | - | -