11institutetext:  Institut für Astronomie & Astrophysik, Eberhard-Karls-
Universität Tübingen, Sand 1, 72076 Tübingen, Germany
11email: B. Stelzer<EMAIL_ADDRESS>22institutetext: INAF -
Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, 90134 Palermo,
Italy 33institutetext: Max-Planck Institut für extraterrestrische Physik,
Giessenbachstrasse, 85748 Garching, Germany

# A first eROSITA view of ultracool dwarfs††thanks: The full versions of
Tables 1 and 2 are only available in electronic format at the CDS via
anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/

B. Stelzer 1122 A. Klutsch 11 M. Coffaro 11 E. Magaudda 11 M. Salvato 33

(Received $<$01-May-2021$>$ / Accepted $<$02-June-2021$>$)

We present the first X-ray detections of ultracool dwarfs (UCDs) from the
first all-sky survey of the extended ROentgen Survey with an Imaging Telescope
Array (eROSITA) onboard the Russian Spektrum-Roentgen-Gamma (SRG) mission. We
use three publicly available input catalogs of spectroscopically confirmed
UCDs and Gaia-selected UCD candidates that together comprise nearly $20000$
objects. In a careful source identification procedure we first extracted all
X-ray sources from the catalog of the first survey, eRASS1, that have a UCD or
candidate within three times their positional uncertainty. Then we examined
all Gaia objects in the vicinity of these $96$ X-ray sources and we associated
them to the most plausible counterpart on the basis of their spatial
separation to the X-ray position and their multiwavelength properties. This
way we find $40$ UCDs that have a secure identification with an X-ray source
(that is bonafide UCD X-ray emitters) and $18$ plausible UCD X-ray emitters
for which we consider it likely that the X-ray source has its origin in the
UCD. Twenty-one of the bonafide and plausible X-ray emitting UCDs have a
spectroscopic confirmation, while the others have been selected based on Gaia
photometry and we computed spectral types from the $G$-$J$ color. The spectral
types of the X-ray emitting UCDs and candidates range between M5 and M9. The
distances of the eRASS1 UCDs range from $3.5$ to $190$ pc. The
spectroscopically confirmed UCDs at the high end of the distance distribution
are known to be members of nearby star forming regions. The majority of the
UCDs from the eRASS1 sample show a ratio of X-ray to bolometric luminosity
well above the canonical saturation limit of $\log{(L_{\rm x}/L_{\rm
bol})}\approx-3$. For the two most extreme outliers, we verified the
hypothesis that these high values are due to flaring activity through an
analysis of the eRASS1 light curve. X-ray spectra could be analyzed for the
two brightest objects in terms of count rate, both showing an emission-measure
weighted plasma temperature of $\langle kT\rangle=0.75$ keV. These
observations demonstrate the potential of eROSITA for advancing our knowledge
on the faint coronal X-ray emission from UCDs by building statistical samples
for which the average X-ray brightness, flares, and coronal temperatures can
be derived.

###### Key Words.:

X-rays: stars, stars: activity, stars: coronae, stars: flare, brown dwarfs

††offprints: B. Stelzer

##  1 Introduction

Ultracool dwarfs (UCDs) are defined as objects with spectral type (SpT) M7 and
later. This group spans the hydrogen-burning mass limit (at $M\sim 0.075\,{\rm
M_{\odot}}$; Baraffe et al., 2002) and it comprises both very low-mass stars
and brown dwarfs. By coincidence, for late-M SpTs ($T_{\rm eff}\sim 2500$ K),
the photospheres become effectively neutral, which leads to high electrical
resistivity, that is reduced coupling between the magnetic field and matter
(Mohanty et al., 2002). This is expected to drastically decrease magnetic
activity which is the result of magnetic stress that built up in photospheric
fields through their interaction with convective motions. The most widely used
observational diagnostics of magnetic activity for M dwarfs is H$\alpha$
emission from a chromosphere. In fact, a strong drop of H$\alpha$ emission is
observed at late-M and early-L SpTs (e.g., Gizis et al., 2000; Mohanty &
Basri, 2003; West et al., 2006). On the other hand, numerous studies have
detected H$\alpha$ emission on UCDs, especially during flares (e.g., Liebert
et al., 1999; Schmidt et al., 2007). Various possibilities on how late-M and
L-type objects may maintain such chromospheric activity have been discussed by
Schmidt et al. (2015). With the advent of the Kepler mission white-light
flares have been observed on some L dwarfs (Gizis et al., 2013; Paudel et al.,
2020), further demonstrating that the magnetic activity in such
photospherically cool objects shares many similarities with the phenomena
observed on higher-mass late-type stars. Further clues as to the nature of
magnetic activity of UCDs can be obtained from a study of their outermost
atmospheric layer, the corona, which in active stars is heated to temperatures
of several $10^{6}$ K leading to radiation in the X-ray band.

Stelzer et al. (2013) show that for M dwarfs, coronal X-ray emission is a more
sensitive activity diagnostics than H$\alpha$ emission: Many early- to mid-M
dwarfs with undetectable H$\alpha$ emission have been detected with ROSAT in
soft X-rays. However, even for the optimistic estimate that the X-ray to
bolometric luminosity ($L_{\rm x}/L_{\rm bol}$) remains constant throughout
the M and L spectral classes, UCDs are faint X-ray emitters as a result of
their low bolometric luminosity. As a consequence, so far only few UCDs have
deep enough X-ray observations to constrain their coronal emission (Stelzer et
al., 2006a). In fact, X-ray detections of UCDs have remained rare, with only
two detections of L dwarfs (Audard et al., 2007; De Luca et al., 2020). On the
other hand, the abovementioned higher sensitivity to coronal, rather than
chromospheric emission of the currently available instrumentation, might at
least partially make up for the weakening of activity signatures at the cool
end of the main-sequence. Therefore, the sparse sample of X-ray detected UCDs
is likely also related to the lack of a deep wide-area X-ray survey.

Studying the emission level and variability in the X-ray band is essential for
understanding the nature of the outer atmospheres of the objects at the bottom
of the main-sequence. This is particularly relevant in view of the peculiar
behavior of UCDs in the radio band where a violation of the Güdel-Benz
relation, an empirical correlation between radio and X-ray luminosities that
holds for all other coronal sources (Güdel et al., 1993), is observed (Berger
et al., 2005). Another peculiarity of the radio properties of UCDs is that for
some of them a highly circularly polarized pulsed emission component is
overlaid on their quiescent, nonvariable gyro-synchrotron emission (Burgasser
& Putman, 2005; Hallinan et al., 2006, 2008).

Despite two decades of observational efforts samples of UCDs with data in all
relevant wavebands are still sparse. Stelzer et al. (2012) have provided
evidence for a distinction of two groups in the heterogeneous observational
picture of UCD activity: A group of objects with X-ray flares and persistent
X-ray emission but no detected radio emission resembles ‘typical’ active
stars, and a second group of objects with radio bursts, mostly also with
detected quiescent radio emission, but no or very weak X-ray emission that
dramatically deviates from this ‘canonical’ behavior. Williams et al. (2014)
argue that the origin of the observed division be the magnetic field strength
and morphology rather than rotation. The puzzling multiwavelength picture that
has emerged for this object class has recently been reviewed by Pineda et al.
(2017).

Many observations of magnetic activity on UCDs have occurred serendipitously,
and the most interesting objects were subsequently observed at other wavebands
to search for connections between the different magnetically induced
emissions. As a result, the sample of UCDs with sensitive multiwavelength data
may not be representative of the UCDs as a class. With the recent launch of
the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) onboard
the Spektrum-Röntgen-Gamma mission (Predehl et al., 2021) we have entered a
new era for the study of X-ray activity on UCDs: While the higher sensitivity
of observatories like XMM-Newton and Chandra is required to detect the
quiescent X-ray emission of all but the most nearby UCDs, the enormous
statistical samples to be observed with eROSITA (many thousand objects) can be
expected to boost the number of detections among UCDs and provide an
unprecedented wealth of information on their flaring activity. In this article
we carry out the first exploration for UCD X-ray emission based on the first
eROSITA All-Sky Survey (eRASS1) which was completed in summer 2020.

We introduce our input sample of UCDs and UCD candidates in Sect. 2. Then we
proceed to the source identification where we match the eRASS1 catalog with
our input samples and subsequently inspect for all matches the plausibility
that the UCD rather than another known Gaia source is the X-ray emitter (Sect.
3). In Sect. 4 the multiwavelength properties of those UCDs to which we have
assigned an X-ray source are presented, and in Sect. 5 we describe the
analysis of X-ray light curves and spectra for the two UCDs with the largest
number of counts in eRASS1. Section 6 comprises our results and a discussion
thereof. Finally, in Sect. 7 we summarize the findings and draw the
conclusions. Appendices are presented for different subsamples of objects that
are in the vicinity of the UCDs and that we assign as the more likely
counterpart of the X-ray source (App. A, and C), and App. B holds a short
discussion on the distinction of stellar and extragalactic objects in
multiwavelength diagrams based on eROSITA data from an observation obtained
during the CalPV phase.

##  2 Sample

We have compiled a list of UCDs to be matched against the eRASS1 source
catalog. Our input list comprises both spectroscopically confirmed UCDs and
new candidate UCDs identified with Gaia. The known UCDs are drawn from the
“list of M6-M9 dwarfs” maintained by J.
Gagné111https://jgagneastro.wordpress.com/list-of-m6-m9-dwarfs/. henceforth
referred to as GagnéM, and the gucds catalog from Smart et al. (2019) which
comprises mostly L and T dwarfs. The new Gaia discovered UCD candidates are
from Reylé (2018). For the sake of homogeneity we limit the sample of known
UCDs to the objects with full photometry and astrometry in Gaia DR2, using the
selection criteria of Reylé (2018) from her definition of the new candidate
UCD sample.

Figure 1: Gaia color-magnitude diagram ($M_{\rm G}$ vs $G-G_{\rm RP}$) for the
lists of UCDs defined in Sect. 2. In each panel all three master tables are
shown but one of them is high-lighted in red: left \- known late-M dwarfs from
J.Gagneś M6…M9 dwarf archive, middle \- known MLTY dwarfs with Gaia-DR2 data
from the gucds sample (Smart et al., 2019), right \- new Gaia-discovered UCD
candidates (Reylé, 2018).

To perform this selection on the GagnéM catalog, we first matched it
separately against catalogs available from the advanced ADQL (Astronomical
Data Query Language) interface of the Gaia archive
222https://gea.esac.esa.int/archive/. in the following way. We used the 2MASS
designation given in GagnéM for the match with the Gaia-DR1 2MASS original
valid catalog. This step provides the parameter tmass_oid which is the 2MASS
identifier in the Gaia catalogs. To map the 2MASS identifier to the Gaia
source number (col. source_id) we matched this output with the Gaia DR2 2 MASS
best neighbor catalog. Subsequently, we extracted all relevant Gaia DR2
information by matching the output of the last step using col. source_id with
the full Gaia DR2 catalog. As of June 2020 the GagnéM catalog contains $8683$
late-M dwarfs of which with the above procedure $8301$ are matched with Gaia
DR2.

For consistency with the Reylé (2018) catalog we required that the objects
from GagnéM that we keep in the list have full photometry (fluxG, fluxBP,
fluxRP $>0$) and astrometry (pmRA, pmDEC, parallax measured), and that the
uncertainty of the parallax $\sigma_{\rm\varpi}<10$ %. This reduces the GagnéM
sample to $4326$ objects, mainly due to the criterion on the error of the
parallax.

The inspection of the multiband photometry in GagnéM showed that further
cleaning of this catalog was necessary: a number of objects present SDSS
magnitudes much too high for the $J$ band magnitude. These mismatches in
GagnéM could be removed with the exclusion criteria $z_{\rm
SDSS}>18.0\leavevmode\nobreak\ \&\&\leavevmode\nobreak\ J<15.5$ and $z_{\rm
SDSS}>18.5\leavevmode\nobreak\ \&\&\leavevmode\nobreak\ J<16.5$. Another $130$
objects were disregarded this way. An additional $2$ objects were removed
because they are outliers in the $M_{\rm G}$ vs $G-G_{\rm BP}$ diagram and
with difference between the position in the 2MASS catalog and the position in
GagnéM larger than $10^{\prime\prime}$ although their proper motion is
relatively small. We have also visually inspected these objects in
ESASky333ESA-Sky is an application to visualize and download archived
astronomical data that is developed at ESAC, Madrid, Spain, by the ESAC
Science Data Centre (ESDC). It is available at https:/sky.esa.int confirming
the wrong match. The final number of objects we consider from GagnéM is,
therefore, $4194$.

The gucds catalog was extracted by Smart et al. (2019) primarily from an
earlier list of $1885$ UCDs compiled by the same authors (Smart et al., 2017)
that is based on the “list of ultracool dwarfs” by J.
Gagné444https://jgagneastro.com/list-of-ultracool-dwarfs/., a catalog that
complements GagnéM for cooler spectral types. Smart et al. (2019) also added
late-M, L and T dwarfs from some other catalogs and defined the gucds sample
as those objects from their list that have a match in Gaia-DR2 with accurate
Gaia coordinates and astrometry. This list comprises $695$ objects with
spectral types M8 to T6. Applying the criteria on Gaia DR2 photometry and
astrometry from Reylé (2018) as described above for GagnéM reduces this
catalog to $610$ objects. By way of construction of this catalog there is some
overlap with GagnéM. We, therefore, removed all objects that are in both
catalogs from gucds matching the two lists for their Gaia-DR2 source names.
This way our final list from Smart et al. (2019) has $560$ entries.

To summarize, our input catalogs of UCDs to be matched with the eROSITA source
list consist of $4194$ objects extracted from the original GagnéM catalog,
$560$ from Smart et al. (2019) and the full list of $14914$ Gaia-UCD
candidates from Reylé (2018). These lists are henceforth referred to as our
‘cleaned’ samples. Figure 1 shows the $M_{\rm G}$ vs $G-G_{\rm BP}$ diagram
for this cleaned lists of UCDs. The GagnéM and Reylé (2018) catalogs define a
similar area in the Gaia color-magnitude diagram because the latter one was
constructed on the basis of the Gaia properties of the former one (see Reylé,
2018). However, GagnéM starts at SpT M5 while Reylé (2018) includes only
objects with photometric spectral types (SpTs) of M7 or later. This explains
the extension of GagnéM at the upper left end of the distribution in Fig. 1.
We also note that the GagnéM catalog comprises a number of late-M dwarfs that
are members or candidate members of young moving groups. These stand out above
the main-sequence in color-magnitude diagrams. While the focus of this work is
to find X-ray emitting field dwarfs, we keep these young objects in the
catalog as no systematic search for their X-ray emission has been performed
yet.

The class of UCDs is defined through the spectral type. As described in the
previous paragraphs our samples cover different SpT ranges, and the GagnéM
sample comprises also objects that have slightly earlier SpTs than the
canonical boundary for UCDs, M7. Moreover, for the new UCD candidates from
Reylé (2018) only photometric SpTs are available. Since these have been
derived on the basis of Gaia properties of the known confirmed UCDs, a good
agreement between spectroscopic and photometric SpTs is expected. We have
checked this by computing the photometric SpTs for the cleaned GagnéM and
gucds samples using the polynomial relation with $M_{\rm G}$ given by Reylé
(2018). The comparison of the resulting values with the optical spectroscopic
values for the SpT are shown in Fig. 2. While the overall agreement is good
the scatter in the relation together with the inclusion of objects with SpT M5
and M6 in GagnéM implies that not all objects in our lists are genuine UCDs.
Given that based on Fig. 2 the uncertainties, especially of the photometric
SpTs, amount to a few spectral subclasses we prefer to keep all objects in our
sample even if their spectroscopic SpTs are earlier than M7.

Figure 2: Comparison of spectroscopic and photometric spectral types for the
‘cleaned’ GagnéM and gucds samples. The spectroscopic SpTs are obtained from
the original catalogs, the Gagné dwarf archive and Smart et al. (2019), while
the photometric SpTs have been computed using the polynomial relation with
$M_{\rm G}$ from Reylé (2018). Objects with a flag indicating youth or
uncertain spectroscopic SpT in the two catalogs have been omitted, as the
$M_{\rm G}-$SpT relation fron Reylé (2018) is valid for the main-sequence.

##  3 Identification of UCDs among eRASS1 sources

The SRG/eROSITA data on which we base this work are the results of the first
All-Sky Survey, eRASS1. The eRASS1 source catalog is produced at Max Planck
Institut für extraterrestrische Physik (MPE) in Garching with the eROSITA
software eSASS; see Brunner et al. (2021) for a description of the eSASS
software. We use the catalog version 201008 generated with the data processing
version c946555The final eRASS1 catalog will be released in 2022 and presented
in a forthcoming publication., and we henceforth call this catalog eRASS1cat.
This catalog comprises all eRASS1 sources in the western half of the sky in
terms of Galactic coordinates, that is $l\geq 180^{\circ}$. The eRASS data
from the other half of the sky is the property of the Russian eROSITA
consortium and is not available to us.

We cross-matched each of the three cleaned input catalogs of UCDs and UCD
candidates described in Sect. 2 separately with eRASS1cat. For this task we
first corrected the Gaia DR2 positions (J2015.5) to the expected position at
the mean eRASS1 observing date (mid-March 2020) using the Gaia DR2 proper
motions (PM) from our cleaned input catalogs. Then we matched these PM-
corrected coordinates with the eRASS1 boresight-corrected X-ray positions
(cols. ra_corr, dec_corr) in a radius of $30^{\prime\prime}$. Subsequently, we
removed all matches for which the separation between the PM corrected
positions and the eRASS1 positions (henceforth termed ${\rm sep_{ox}}$)
deviate by $>3\times$ the uncertainty in the X-ray position (col. radec_err in
eRASS1cat). This way we obtained $24$ matches in eRASS1cat for our cleaned
GagnéM sample with the widest separation being $24^{\prime\prime}$, and $73$
matches for the sample from Reylé (2018) where the largest value of ${\rm
sep_{ox}}$ is $20^{\prime\prime}$. The latter output catalog comprises one
object with joint Russian-German ownership which was removed from the sample
to adhere to the consortium policies. No matches with our cleaned gucds
sample, derived from the catalog of Smart et al. (2019), fulfilled the
separation criterion, that is no objects from this sample are associated with
an eRASS1 X-ray source.

The corresponding tables of associations between our input catalogs GagnéM and
Reylé (2018) are henceforth referred to as fullmatch-eRASS1-GagneM and
fullmatch-eRASS1-Reyle , respectively. We present the most relevant parameters
of these catalogs in Table 1. Next to the Gaia source_id (col. 1) we provide
the boresight corrected eRASS1 positions (cols. 2 and 3), the error on the
eRASS1 positions (col. 4), and the separation between the proper motion
corrected optical positions and the X-ray positions (${\rm sep_{ox}}$ in col.
5). The broad band ($0.2-5.0$ keV) source count rates and the associated
errors are given in col. 6. In col. 7 we provide the maximum likelihood for
the X-ray detection in the broad band. In col. 8 we list flags for UCDs that
are unique Gaia counterparts to the eRASS1 source (‘U’), objects with archival
X-ray detections (‘X’), and common proper motion pairs involving a UCD or UCD
candidate (‘C’). In col. 9 we mark all UCDs that after our analysis are
considered ‘bonafide’ or ‘plausible’ counterparts to the eRASS1 sources. For
the objects not marked in col. 9 we discard the UCD as being responsible for
the X-ray emission. The flags in the last two columns are based on the
detailed examination of alternative possible counterparts as described in the
remainder of this section.

Table 1: Basic X-ray parameters from eRASS1cat for the UCDs from GagnéM and UCD candidates from Reylé (2018) that are within $3\times$ the uncertainty of the X-ray position. Gaia DR2 | ra_corr | dec_corr | delta_radec | sep_ox | Count rate | DETML | flags | UCD
---|---|---|---|---|---|---|---|---
designation | [deg] | [deg] | [′′] | [′′] | [cts/s] |  |  |
GagnéM
4963614887043956096 | 34.842070 |  $-$39.423258 | 4.63 | 2.32 | 0.064 $\pm$ 0.024 | 12.1 |  | P
5084713036143375744 | 54.130367 |  $-$26.333831 | 2.61 | 5.16 | 0.164 $\pm$ 0.031 | 80.1 | U | B
4869246209213679872 | 65.587646 |  $-$36.102014 | 2.56 | 1.84 | 0.12 $\pm$ 0.023 | 67.6 | U | B
3200303384927512960 | 70.097406 |  $-$5.501610 | 4.0 | 5.28 | 0.109 $\pm$ 0.032 | 24.7 | UX | B
3181197137010596608 | 71.715048 |  $-$11.280513 | 0.96 | 1.09 | 1.683 $\pm$ 0.128 | 1051.0 | C | B
3164100487113671552 | 114.932856 | 13.080929 | 5.63 | 12.48 | 0.081 $\pm$ 0.038 | 10.2 | C |
666988221840703232 | 118.101611 | 16.201617 | 2.9 | 3.54 | 0.395 $\pm$ 0.081 | 63.7 | UX | B
(a) result from counterpart selection: $U$ … UCD is uniq Gaia counterpart, $C$
… common proper motion pair, $X$ … archival
X-ray detection
(b) final counterpart status for the UCD: $B$ … bona-fide, $P$ … plausible
The full table is available in electronic format on the CDS via anonymous ftp
to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/

Given the relatively large eROSITA positional error in the survey mode, the
UCDs associated with a source from eRASS1cat according to the cross-match
described above are not necessarily the correct counterparts of the X-ray
source. We searched for alternative optical/IR counterparts to the eRASS1
detections identified in the first step with a UCD by reversing the search,
that is we matched each of our two fullmatch-eRASS1 samples again with Gaia
DR2 centering the search on the X-ray coordinates (ra_corr, dec_corr) and
using a match radius of $24^{\prime\prime}$, the maximum value with a reliable
UCD-eRASS1 association in the first step. Then we removed all matches with
${\rm sep_{ox}}>3$ radec_err. Since the ‘reverse match’ involved no PM
correction, in this step the previously found UCD candidates could be removed
if they do not fulfill the separation criterion. This is, in fact, the case
for one object from fullmatch-eRASS1-GagneM, and we added this object again to
the list. The resulting list of potential Gaia DR2 counterparts comprises now
$50$ objects for fullmatch-eRASS1-GagneM and $233$ for fullmatch-eRASS1-Reyle.
The task is now to determine for each of the $96$ X-ray sources whether the
UCD or UCD candidate is the most likely Gaia counterpart.

###  3.1 Bonafide eRASS 1 counterparts

We found that $12$ X-ray sources in fullmatch-eRASS1-GagneM and $24$ in
fullmatch-eRASS1-Reyle have a single Gaia counterpart, namely the UCD or UCD
candidate. In the following for simplicity we occasionally omit the
distinction between UCD and UCD candidate, but the reader should keep in mind
that the objects from GagnéM are spectroscopically confirmed while those from
Reylé (2018) are not. In the abovementioned $36$ cases the UCD can safely be
considered to be the cause for the X-ray emission as there is no other Gaia
source within $3\times$ the error of the X-ray position.

To establish the correct counterpart in the remaining cases we took into
account several criteria. First, we carried out a visual inspection of all
cases with multiple Gaia DR2 counterparts in ESASky. This way we found that
among our eRASS1 detections $2$ from fullmatch-eRASS1-GagneM and $12$ from
fullmatch-eRASS1-Reyle have a common proper motion (CPM) companion; one of
them is a triple system. In all but one cases the comoving companion is the
more likely X-ray emitter because it is brighter and closer to the eRASS1
position than the UCD666The CPM companion is not in all cases the Gaia source
that is closest to the eRASS1cat position but it is by far the brightest; see
Appendix A.. We, therefore, remove these $13$ objects from the sample. The one
exception is the UCD Gaia DR2 3181197137010596608 from our GagnéM catalog that
shares a similar proper motion with the source Gaia DR2 3181197137010596480.
These two objects have similar Gaia magnitudes and are a pair of UCDs. Since
this pair is very tight (separation of $1.6^{\prime\prime}$) we can not infer
which of the two is the X-ray source. We provide more information on this and
all other CPM pairs involving UCDs in Appendix A.

Another criterion that was useful to assign the X-ray source to the correct
Gaia source are the X-ray positions in observations with the higher spatial
resolution instruments XMM-Newton and Chandra. Such detections are available
for $7$ of the $24$ objects in fullmatch-eRASS1-GagneM. In all these cases the
archival X-ray source is spatially associated with the UCD according to our
visual inspection. This relatively high fraction of objects with archival
X-ray data is a result of dedicated studies of UCD X-ray emission in the past.
Two of the corresponding eRASS1 sources have multiple potential Gaia
counterparts, and we could assign the UCD as the X-ray emitter thanks to the
archival X-ray detection. In fullmatch-eRASS1-Reyle only $4$ objects are near
an archived XMM-Newton or Chandra source. One of these archival X-ray sources
is closer to the brighter comoving companion of a UCD candidate, and this
object (Gaia DR2 5762038930728469888) has been disregarded as an X-ray emitter
in our previous selection step. In another case both the UCD candidate (Gaia
DR2 3777108250009273856) and its CPM companion are detected with Chandra. The
eRASS1 source is closer to the CPM companion, and this object has also been
removed from the list of UCD candidates in the previous selection step. For
the third one, the UCD candidate Gaia DR2 3902395843353397248, both a Chandra
and an XMM-Newton source are closer to another object, Gaia DR2
3902395813288871936, which has similar optical brightness as the UCD
candidate. This object is a known quasar (see Appendix C). The last one, Gaia
DR2 3754497583659096320, has an XMM-Newton source clearly identified with the
UCD candidate and there is no other Gaia object in the vicinity that is nearly
as bright and close to the eRASS1 X-ray position as the UCD candidate. The
XMM-Newton detection of this UCD was discovered and discussed by Stelzer et
al. (2020). To summarize, with help of the archival X-ray data we eliminated
one additional UCD candidate from the eRASS1 source list fullmatch-
eRASS1-Reyle because the X-ray source is identified as an extragalactic
object.

We consider the objects identified above and flagged in col. 8 of Table 1
‘bonafide’ counterparts to eRASS1cat X-ray sources. To summarize, we have
identified the optical counterpart to $16$ eRASS1 sources from fullmatch-
eRASS1-GagneM and $38$ from fullmatch-eRASS1-Reyle. Among those $54$
‘bonafide’ eRASS1 counterparts there are $40$ UCDs (flagged in col. 9 of Table
1 with ‘B’), $13$ earlier-type CPM companions to UCDs, and $1$ quasar. In this
way we are more than doubling the number of existing X-ray detections from
UCDs. We caution, however, that $25$ of them, the ones from fullmatch-
eRASS1-Reyle, are UCD candidates that still require spectroscopic
confirmation.

On the left side of Fig. 3 we show various parameter combinations for the
‘bonafide’ counterparts to eRASS1cat X-ray sources. In particular, we display
a Gaia color-color diagram (CCD) and a diagram involving the ratio of X-ray
and optical flux, $f_{\rm x}/f_{\rm G}$. For this latter diagram the X-ray
flux is taken from eRASS1cat column ml_flux_2, the eRASS1 energy band ‘2’. It
represents the $0.6-2.3$ keV band and is the energy band in eRASS1cat that
comes closest to the $0.5-2.0$ keV band typically used for studies of X-ray
populations. The optical flux in our X-ray/optical ratio refers to the Gaia
$G$ band777The $G$ band flux was calculated from the magnitude using the
zeropoints, effective wavelength and bandwidth provided by the Spanish Virtual
Observatory (SVO) filter service at http://svo2.cab.inta-csic.es/theory/fps/.
The curved path that forms the lower envelope in the $G-G_{\rm RP}$ versus
$G_{BP}-G$ diagram outlines the stellar main-sequence as demonstrated by the
black line which represents the Gaia colors from the table A Modern Mean Dwarf
Stellar Color and Effective Temperature Sequence maintained by E. Mamajek888
This table is available at http://www.pas.rochester.edu/$\sim$emamajek. All
UCDs show values for the X-ray flux above the canonical saturation limit of
$\log{(f_{\rm x}/f_{\rm G})}\approx-3$. We discuss this result in Sect. 6.
Here we only note that in Appendix B we argue based on the properties of the
more than $20000$ X-ray sources from the eROSITA Final Equatorial-Depth Survey
(eFEDS)999eFEDS is a $\sim 140$ sq.deg large area in the southern sky that was
observed with eROSITA in scanning mode during its Calibration & Performance
Verification phase with a typical on-source exposure time of $1$ ksec (Brunner
et al., 2021). This is significantly larger than the average exposure during
eRASS1, and the official source catalog comprises $27910$ X-ray detections.
that the part of the Gaia CCD occupied by the UCDs and UCD candidates is not
populated by any other abundant population of X-ray emitters, such as
extragalactic objects or stars. Specifically, while a small number of eFEDS
objects classified ‘galactic’ are located in the same region as the UCDs the
distribution of the ‘extragalactic’ sources are clearly separated from them
(see Fig. 12). In Appendix B we also examine the other diagrams shown in Fig.
3, and specifically the one of $W1$ magnitude versus the abovementioned Band 2
X-ray flux (bottom panel in Fig. 3). In that diagram the black line denotes
the empirical separatrix between ‘extragalactic’ (above) and ‘stellar’ (below)
X-ray emitters that was defined by Salvato et al. (2018) from two X-ray
samples that bracket the eRASS1 survey in terms of X-ray fluxes: the 2 RXS
(Boller et al., 2016) and XMMSL2 (XMM-SSC, 2018) on the low-sensitivity end
and the Chandra COSMOS Legacy Survey (Marchesi et al., 2016) on the high-
sensitivity end. Some contamination between the ‘extragalactic’ and ‘stellar’
groups was seen in Salvato et al. (2018), and might be present in our sample
as well. In particular, from Fig. 3 it can be seen that in our sample of
‘bonafide’ eRASS1 sources no confirmed UCDs but some of the UCD candidates are
located in the ‘nonstellar’ part of this diagram.

Figure 3: Gaia color-color diagram (top), X-ray to $G$ band flux ratio
(middle) and $W1$ magnitude vs X-ray flux (bottom) for subsamples illustrating
the process for the selection of the Gaia counterpart to the eRASS1cat source.
The left panels show the eRASS1cat sources to which a ‘bonafide’ counterpart
has been assigned and the right panels show the possible counterparts for the
remaining sources from eRASS1cat. Small circles represent UCD candidates from
Reylé (2018) and large circles spectroscopically confirmed UCDs from GagnéM.
UCDs from the input master lists are shown in red, their CPM companions in
yellow, and counterparts assigned based on archival X-ray detections in blue.
All other Gaia sources within the search box around the eRASS1cat X-ray
positions are marked in gray. In the right panel the brightest Gaia source and
the one closest to the X-ray position is indicated for each eRASS1cat source.
The black line in the bottom panels is an empirical separator between
extragalactic candidates (above) and stellar candidate (below) introduced by
Salvato et al. (2018).

###  3.2 Plausible eRASS 1 counterparts

Putting aside the $54$ identified ‘bonafide’ eRASS1 objects, there are still
$42$ eRASS1cat sources to which we must assign the optical counterpart. Each
of these X-ray sources has at least two Gaia objects in the search radius. In
the right panels of Fig. 3 the full sample of possible counterparts to the
$42$ still unassigned X-ray sources from fullmatch-eRASS1-GagneM and
fullmatch-eRASS1-Reyle is shown. Since these eRASS1cat sources have several
Gaia counterparts in the search radius they appear more than once in those
panels of the figure that involve Gaia data. Some of the non-UCD Gaia sources
are missing because they have incomplete photometry, while the UCDs and UCD
candidates by definition of our input samples (Sect. 2) are fully
characterized with Gaia.

The same features described above for the ‘bonafide’ counterparts are seen,
such as the main-sequence path in the CCD and high values of $f_{\rm x}/f_{\rm
G}$ for the UCDs. In addition a strongly populated area in the upper left of
both diagrams (defined by relatively blue optical color and high $f_{\rm
x}/f_{\rm G}$ ratio) is evident. Only one of the bonafide eRASS1 counterparts
is located in that region, the quasar 2XMM J123337.5+073133 (see left side of
Fig. 3). That region is, therefore, likely dominated by extragalactic sources.
For the position of different astrophysical populations in the eRASS1 and Gaia
parameter space we refer, again, to Appendix B. Here we define our criteria
for selecting the counterpart to each X-ray source from its pool of Gaia
objects.

To this end, we compare the separations between the positions of the Gaia DR2
and the eRASS1 sources, ${\rm sep_{ox}}$, and the $G$ magnitudes of all
possible Gaia counterparts uncovered in our ‘reversed search’ for these $42$
eRASS1 sources. The Gaia source with the smallest ${\rm sep_{ox}}$ value for
each eRASS1 source is highlighted in the viewgraphs on the right side of Fig.
3 with an annulus. For six out of the eight still unassigned X-ray sources
from fullmatch-eRASS1-GagneM, the UCD is the closest counterpart to the X-ray
position, and for the fullmatch-eRASS1-Reyle sample in $19$ of $34$ cases the
UCD candidate has the smallest ${\rm sep_{ox}}$ value of all Gaia
counterparts. The remaining $17$ have a non-UCD as their closest counterpart.

As a baseline we define as the correct Gaia counterpart for the eRASS1 X-ray
source the one with the smallest $sep_{\rm ox}$ value. $25$ UCDs and UCD
candidates fulfill this criterion. However, in this work we pursue a
conservative approach in which we keep UCDs as counterparts to X-ray sources
only if there is no other obviously more plausible optical counterpart.
Therefore, we examined all other potential Gaia counterparts for these $25$
cases. This way we identified $7$ cases where an object with a brighter $G$
magnitude is in the $3\times$ radec_err match radius. Their optical/IR
properties are presented in Appendix C. Following the conservative approach
described above, we consider these brighter Gaia sources as likely counterpart
to the X-ray emitter, and we remove the corresponding UCDs from the X-ray
sample. The other $18$ UCDs (that are both the closest and the brightest Gaia
counterpart to the X-ray source) are added to the sample investigated in this
article. We henceforth term these UCD X-ray assignments as ‘plausible’,
because due to the presence of other Gaia sources in the match radius they are
somewhat less certain associations than the ‘bonafide’ objects from Sect. 3.1.
These UCDs are marked with ‘P’ in col. 9 of Table 1.

The $17$ non-UCD counterparts with the smallest $sep_{\rm ox}$ among all Gaia
counterparts are not of interest to our study. However, for completeness and
future reference we provide optical/IR parameters of these other astrophysical
X-ray emitters in Appendix C. From a comparison of Fig. 3 and Fig.12 we can
infer that those of them that are located in the upper left in the $G-G_{\rm
RP}$ vs $G_{\rm BP}-G$ diagram are likely extragalactic, while for those that
are located close to the stellar main-sequence the nature can not be
established based on the Gaia color-color diagram. Note that for Table 7 when
$G$ and $J$ magnitudes are available we have computed the corresponding main-
sequence spectral type, but this parameter may be meaningless if the object is
extragalactic.

###  3.3 Reliability of the X-ray sources

The detection threshold for the source detection applied to generate eRASS1cat
was det_like_0 $=6$. At this threshold about $\sim 6.9$ % of sources are
expected to be spurious (Brunner et al., 2021). Among the $58$ eRASS1 detected
UCDs $4$ have det_like_0 $\leq 6.5$, that is statistically none of them is
expected to be a spurious detection.

##  4 Multiwavelength properties of eRASS1-detected UCDs

As we anticipated in Sect. 3 all UCDs that we have identified as X-ray
emitters are marked in the last column of Table 1. To summarize, we have
associated $21$ spectroscopically confirmed UCDs from GagnéM to an X-ray
source from eRASS1cat, of which $15$ as bonafide and $6$ as plausible
counterparts. Among the UCD candidates from Reylé (2018) $37$ have been
assigned as eRASS1 X-ray emitter, $25$ as bonafide and $12$ as plausible
counterparts.

While the multiwavelength properties of the non-UCD X-ray emitters are
presented in the appendices of this work as described above, here we summarize
relevant parameters for the X-ray emitting UCDs and UCD candidates. Table 2
lists the photometry used in this article, that is the Gaia $G$ band, 2MASS
$J$ band and AllWISE $W1$ band (cols. 2-4). For the objects from GagnéM we
provide the SpT from optical spectroscopy (col. 5). In order to have a common
SpT scale for the GagnéM and the Reylé (2018) sample we have computed spectral
types from the $G-J$ color using the table maintained by E.Mamajek8 for all
bonafide and plausible UCDs and UCD candidates (col. 6). This scale has the
advantage that it is valid for the full SpT sequence, while the SpT - $M_{\rm
G}$ relation used in Reylé (2018) has been calibrated only for SpT M7 and
later. In fact, we find that the few M5 objects in GagnéM would all have an
early- to mid-M SpT assigned when using the SpT - $M_{\rm G}$ calibration from
Reylé (2018), at odds with their spectroscopic values.

Since the distance is crucial for the determination of luminosities we have
checked the reliability of the values obtained from inverting the parallaxes.
To this end we have matched all bonafide and plausible X-ray emitting UCDs
with the catalog of Bailer-Jones et al. (2018) in which a probabilistic
approach was used to infer distances from Gaia parallaxes and its standard
deviation and a model for Gaia’s length scale in the Galaxy. The values
$d=1/\varpi$, where $\varpi$ is the Gaia DR2 parallax, are for all targets in
excellent agreement with the distances obtained by Bailer-Jones et al. (2018).
This is not unexpected since our sample by construction comprises only objects
with well-constrained parallax (see Sect. 2). We conclude that all bonafide
and plausible eRASS1 detections among the UCDs and UCD candidates have a
reliable distance value. In col. 7 of Table 2 we provide the Gaia distance
extracted from the catalog of Bailer-Jones et al. (2018).

The last two columns of Table 2 hold the X-ray luminosity ($L_{\rm x}$) and
the fractional X-ray luminosity ($L_{\rm x}/L_{\rm bol}$) in logarithmic
scale. The bolometric luminosity required for the $L_{\rm x}/L_{\rm bol}$
ratio has been calculated with the polynomial fit with SpT from Filippazzo et
al. (2015), and the spectral types used were those derived from the $G-J$
color. The X-ray flux that together with the distance defines $L_{\rm x}$ was
derived from the $0.2-2.3$ keV count rates in eRASS1cat by summing the values
in cols. ml_rate_1 and ml_rate_2 and applying the rate-to-flux conversion
factor $CF_{\rm M,12}=(7.37\pm 0.55)\cdot 10^{-13}\,{\rm erg/cts/cm^{2}}$.
This value was derived from fits of a thermal model (apec) to eFEDS spectra of
early-M dwarfs studied by Magaudda et al. (2021). Note that in Magaudda et al.
(2021) a slightly higher value is reported which refers to a broader eROSITA
energy band ($0.2-5.0$ keV), but the same approach and the same sample of M
dwarf eROSITA spectra was used to derive the value for the $0.2-2.3$ keV band
(that is the sum of eRASS1 energy bands ‘1’ and ‘2’) cited above specifically
for our work.

We recall that in the multiwavelength diagrams that supported the source
identification (Fig. 3) we have made use of the X-ray fluxes tabulated in
eRASS1cat. These fluxes have been calculated for an absorbed power-law (with
$N_{\rm H}=10^{20}\,{\rm cm^{-2}}$ and $\Gamma=1.7$) which is an incorrect
assumption for coronal X-ray emitters. The use of these fluxes for our source
identification procedure is justified by the fact that many of the potential
Gaia counterparts to the X-ray sources are nonstellar. To get an idea on the
effect of the inappropriate use of eRASS1cat fluxes on our sample of UCDs we
have computed the $CF$ for the power-law model given above as the mean of the
ratio between the $0.2-2.3$ keV count rates and the fluxes in the same band
given in eRASS1cat. We find for our sample of $58$ UCDs and UCD candidates a
mean and standard deviation of $CF_{\rm PL}=(9.75\pm 0.21)\cdot 10^{-13}\,{\rm
erg/cts/cm^{2}}$, that is a $30$ % higher $CF$ than the value obtained from
the M dwarf spectra.

Table 2: Multi-wavelength properties of the UCDs and UCD candidates identified as bonafide or plausible counterparts to an eRASS1 X-ray source. Gaia DR2 designation | $G$ | $J$ | $W1$ | ${\rm SpT_{spec}}$ | ${\rm SpT_{G-J}}$ | d | $\log{L_{\rm x}}$ | $\log{(L_{\rm x}/L_{\rm bol})}$ | Young | Young | Binary | Binary
---|---|---|---|---|---|---|---|---|---|---|---|---
of UCD | [mag] | [mag] | [mag] |  |  | [pc] | [erg/s] |  | flag | ref | flag | ref
GagnéM
659464504288593536 | 15.02 | 11.05 | 9.80 | M6 | M6-M6.5V | $13.552_{-0.025}^{+0.026}$ | 27.21 |  $-$3.33 | … | … | … | …
666988221840703232 | 14.77 | 10.88 | 9.61 | M7 | M6-M6.5V | $18.883_{-0.036}^{+0.037}$ | 28.07 |  $-$2.51 | Y | 5,6 | … | …
703790044252850688 | 12.19 | 8.24 | 6.95 | M6.5 | M6-M6.5V | $3.580_{-0.002}^{+0.002}$ | 26.83 |  $-$3.72 | … | … | … | …
908963788782045568 | 19.23 | 15.57 | 14.27 | M6 | M5.5-M6V | $115.884_{-5.625}^{+6.218}$ | 28.94 |  $-$1.78 | … | … | … | …
3181197137010596608 | 12.22 | 8.14 | 7.11 | M5 + M6 | M7V | $18.968_{-0.024}^{+0.024}$ | 28.73 |  $-$1.71 | Y | 5,6 | Y | 1,13
3200303384927512960 | 14.93 | 10.66 | 9.36 | M6.5 | M7-M7.5V | $9.757_{-0.010}^{+0.010}$ | 26.96 |  $-$3.41 | Y | 5,6 | … | …
3830128624846458752 | 16.55 | 12.33 | 11.04 | M7 | M7-M7.5V | $20.123_{-0.099}^{+0.100}$ | 27.52 |  $-$2.87 | … | … | … | …
References: (1) Mason et al. (2001), (5) Shkolnik et al. (2009), (6) Shkolnik
et al. (2012), (13) Winters et al. (2019).
The full table is available in electronic format on the CDS via anonymous ftp
to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

##  5 eRASS1 light curves and spectra

As a result of a combination of the weak activity levels of UCDs and the
limited sensitivity of eRASS1 most X-ray detections of UCDs have a small
number of counts. Although, as we argued in Sect. 3.3, statistically no
spurious detections are expected in our UCD X-ray emitter sample, $25$ % of
them have a detection likelihood det_like_0 $\leq 8$. For these weak sources
on average only $7$ source counts were collected during eRASS1.

Two sources stick out with a count rate ($>1$ cts/s) much above the average.
These are also the only two UCDs for which more than $100$ counts have been
collected during eRASS1, and thus a meaningful spectral and timing analysis is
feasible. We study the eRASS1 spectra and light curves of these two UCDs for
which $227$ counts and $292$ counts are listed for the $0.2-5.0$ keV band in
eRASS1cat, respectively. These values are clear outliers from the trend of low
count numbers in our sample and lead one to suspect flaring activity. One of
the two is the binary UCD Gaia DR2 3181197137010596608 and Gaia DR2
3181197137010596480 (Sect. 3.1), also known as WDS J04469-1117A and B and
listed with SpT M5 + M6 in GagnéM (based on measurements presented by Shkolnik
et al., 2009). The other one is Gaia DR2 5355751581627180288, alias TWA 22 AB,
which is – contrary to its historical assignment to the TW Hya association – a
member of the $\beta$ Pic moving group (Malo et al., 2013) and an astrometric
binary (Bonnefoy et al., 2009) with two components of SpT M6. Both objects for
which we are performing eRASS1 timing and spectral analysis are, thus, not
genuine UCDs. Nevertheless, since the X-ray properties for mid- to late-M
stars are not well known, their X-ray variability and plasma temperature are
of high interest.

Our analysis of the light curves and spectra of WDS J04469-1117AB and TWA 22AB
is based on the merged events files of all seven telescopes for the
corresponding sky tiles that comprise our targets. We extracted the $0.2-5.0$
keV band light curves and spectra, and all required complementary files with
the srctool task of the eROSITA Science Analysis System (eSASS), version
eSASSuser_201009. To this end, we have defined a $40^{\prime\prime}$-radius
circular region centered on the boresight corrected position of the X-ray
source associated with the UCD. For the background region we chose an annular
region with the same center and an inner and outer radius of
$90^{\prime\prime}$ and $180^{\prime\prime}$, respectively.

We used the srctool command with the regular- option which produces a light
curve with regularly spaced bins in which time intervals without data are
automatically discarded. As a result of the sparse sampling in the survey mode
the light curves are dominated by such data gaps. During its All-Sky Survey
eROSITA visits a given sky position several times with a typical time lapse
between one and the next visit of $\sim 4$ h (corresponding to one full
rotation of the spacecraft and called the ‘scan rate’). Each such visit is
called an eRODay. The average number of eRODays for a source is six, and it is
determined by the combination of the scan rate, the orbital speed of eROSITA
($\sim 1^{\circ}{\rm/d}$) and the field-of-view of the instrument (diameter
$1^{\circ}$). However, the number of eRODays and the total on-source exposure
time depend also on the sky position, with more visits taking place for
objects near the ecliptic poles where the great circles traced by the
telescope intersect each other for longer than the abovementioned average.
Moreover, the exposure time per eRODay varies between one scan and the next
one since in subsequent scans the source crosses the circular field-of-view at
different positions.

The regular- option of srctool produces a light curve with bins of user-
defined length irrespective of the temporal sequence of the data-taking which
is different for each source. Since the time interval from the first to the
last eRODay is dominated by data gaps, an arbitrary choice of bin size is
likely to lead to a light curve which comprises bins with extremely low
exposure time, such as when a bin just scratches the beginning or end of an
eRODay. For faint sources this results in bins with very large uncertainties
on the count rate. To take account of these peculiarities related to the
survey mode, we have used a trial-and-error approach to adjust the bin size
and the start time of the binning such as to obtain one single bin per visit
of the source.

The eRASS1 spectra of WDS J04469-1117AB and TWA 22AB, the spectra of their
associated background regions, and the response matrix and ancilliary response
files were extracted with srctool. The spectra were then binned to a minimum
of $10$ counts per bin, and subsequently fitted in the XSPEC environment v
12.11.1 (Arnaud, 1996).

Details of the spectral fitting and the results from the spectral and temporal
analysis for these two objects are presented in Sect. 6.2.

##  6 Results on UCDs detected in eRASS1

###  6.1 Overall properties of the population

Figure 4: Gaia color-magnitude diagram ($M_{\rm G}$ vs $G-G_{\rm RP}$) for the
two input lists of UCDs (GagnéM) and UCD candidates (Reylé, 2018) described in
Sect. 2. The subsamples that our source identification from Sect. 3 ascribes
as bonafide or plausible counterpart to an eRASS1 X-ray source are highlighted
with larger circles and colors, red for the known UCDs and blue for the UCD
candidates.

Figure 5: Distribution of spectral types, distances and X-ray luminosities for
the ‘bonafide’ and ‘plausible’ X-ray emitting UCDs and UCD candidates detected
in eRASS1. SpTs from the GagnéM sample of known UCDs are from optical
spectroscopy, while those from the Gaia UCD candidates from Reylé (2018) are
photometric estimates based on $G-J$ color.

Figure 4 shows the X-ray emitting bonafide and plausible UCDs and UCD
candidates together with the full cleaned input samples GagnéM and Reylé
(2018) in the Gaia color-magnitude diagram. Throughout the remainder of this
paper, the spectroscopically confirmed X-ray emitting UCDs (from GagnéM) are
shown in red and the X-ray emitting UCD candidates (from Reylé, 2018) in blue.

A number of the spectroscopically confirmed UCDs detected in eRASS1 belong to
the group of objects above the main-sequence (flagged ‘Young’ in Table 2).
These are late-M stars in young nearby moving groups. The strong X-ray
emission associated with the youth ($\sim 10...100$ Myr) of stars has played a
major role in the discovery of such co-moving stellar associations based on
ROSAT data (e.g., Kastner et al., 1997, 2003). It is, therefore, not
surprising that an disproportionate fraction of these young objects is
detected in eRASS1. In fact, the young objects are among the strongest X-ray
emitters in the sample of eRASS1 UCD detections (as we show at the end of this
Section). There are only two young objects in the Reylé (2018) sample of X-ray
emitting UCD candidates because that sample was selected from Gaia data on the
basis of the field dwarfs from J.Gagné’s dwarf archive.

In the leftmost panel of Fig. 5 we show the SpT distribution for the combined
sample of bonafide and plausible UCDs detected in eRASS1. Recall that while
the GagnéM catalog comprises spectroscopic spectral types, the new UCD
candidates from Reylé (2018) have only photometric estimates for the SpT. In
Sect. 2 we have demonstrated that there is overall good agreement between
spectroscopic and photometric SpTs derived from the absolute Gaia magnitude,
$M_{\rm G}$, but in Sect. 4 we have argued in favor of a calibration with
$G-J$ color which covers the full range of SpTs present in our sample. In any
case, we caution that in absence of a spectroscopic confirmation the values
provided in Reylé (2018) must be considered tentative. Keeping this in mind,
we see in Fig. 5 that the distributions of the number of X-ray detections for
both the known UCDs and the UCD candidates are peaked at SpT M6…M7. Note that
one UCD, Gaia DR2 4963614887043956096, has an L4-type companion (Artigau et
al., 2015). However, since the higher-mass component is the more likely X-ray
emitter we have assigned a SpT of M6 (the value for the primary) to this
object. The latest SpT with an eRASS1 detection is M9. This is Gaia DR2
5761985432616501376 (2MASS J08533434-0329432) with spectroscopic SpT M9 (in
the optical) and M8.5 (in the NIR) according to GagnéM. No UCDs from the gucds
sample are detected in eRASS1. Therefore, no X-ray detection from any
confirmed L dwarf can be reported from our work.

The distance distribution of the eRASS1-detected UCDs is displayed in the
middle panel of Fig. 5. It shows a peak at $\sim 30$ pc and comprises values
from $3.5$ to $190$ pc. This sample is clearly drawn among the more nearby
objects from the input catalogs, GagnéM and Reylé (2018), which is not
surprising given the fact that eRASS is a flux-limited survey. The UCD with
the largest distance among the eRASS1 detections is CHSM 17173, a member of
the Cha I cloud and likely the youngest in this sample.

The most important parameters to be delivered from this study are the X-ray
luminosities and the $L_{\rm x}/L_{\rm bol}$ values. In Sect. 4 we have
explained how we have computed the $L_{\rm x}$ values from the tabulated count
rates in eRASS1cat and a rate-to-flux conversion factor derived from eROSITA
observations of early M dwarfs. The distribution of the X-ray luminosities
computed with this $CF$ and the distances from Bailer-Jones et al. (2018) are
visualized in the right panel of Fig. 5. The $L_{\rm x}$ values are remarkably
high, similar to those of mid-M dwarfs. This is seen in the top panel of Fig.
6 where we show the new eRASS1 X-ray detected UCDs and UCD candidates together
with a compilation of X-ray emission from mid-M stars to L-type UCDs from the
literature. The literature data for UCDs (black symbols with SpT M6 and later
in Fig. 6) are from Stelzer et al. (2012), Cook et al. (2014), Williams et al.
(2014) and De Luca et al. (2020). The earlier-type stars shown as black
triangles are from Magaudda et al. (2020) and Magaudda et al. (2021). While
these mid-M dwarfs show X-ray to bolometric luminosity ratios at or below the
canonical saturation limit of $\log{(L_{\rm x}/L_{\rm bol})}\approx-3$, for
most of the UCDs the X-ray to bolometric luminosity ratio is much higher, and
about half of them have $\log{(L_{\rm x}/L_{\rm bol})}$ values above the upper
envelope observed in mid-M dwarfs. As the literature data on UCDs shows,
values as high as $\log{(L_{\rm x}/L_{\rm bol})}\approx-1$ have occasionally
been observed before on UCDs but only during flares (asterisks in Fig. 6).

Figure 6: X-ray luminosity and its ratio with bolometric luminosity for UCDs
and UCD candidates detected in eRASS1 compared to literature samples described
in the text of Sect. 6.1.

Since we have seen that the distances are reliable and the probability even
for the faintest objects to be spurious is small, the only remaining possible
error source in the calculation of the X-ray luminosity is the $CF$. However,
we have shown that even a clearly wrong spectral model leads to a difference
in the $CF$ on the $30$ % level only. We may caution that many of the UCDs
detected in eRASS1 might have been in a high-activity flaring state during the
eROSITA measurement, and therefore the plasma temperatures could be higher
than those of the M dwarfs studied in Magaudda et al. (2021). In fact, the two
UCDs with the highest number of collected counts for which we analyzed the
eRASS1 light curves both show evidence for flares (see Sect. 6.2). From their
X-ray spectra we derive a mean $CF_{\rm UCD,f}=9.27\cdot 10^{-13}\,{\rm
erg/cts/cm^{2}}$. This is about $25$ % higher than the value we used and
would, therefore, lead to even higher $L_{\rm x}$ values. On the other hand,
there is virtually no observational basis for our assumption that the X-ray
temperatures of UCDs are similar to those of early-M dwarfs. It is, actually,
not implausible to speculate that the coronae of UCDs are somewhat cooler than
those of objects with earlier M spectral type given the typical correlation
between X-ray luminosity and temperature observed in GKM stars (Johnstone &
Güdel, 2015). The consequence would be a lower $CF$. However, considering that
all these uncertainties are on the percent level, the $CF$ can not be
responsible for the very high $\log{(L_{\rm x}/L_{\rm bol})}$ level of the
eRASS1 UCD detections. The final possibility for the apparent high
$\log{(L_{\rm x}/L_{\rm bol})}$ values we observe is a wrong identification of
the UCDs and UCD candidates as an X-ray emitter. However, we recall that more
than half of the UCDs that we assigned to an X-ray source have no other known
Gaia object within $3\times$ the uncertainty of the X-ray position; the $36$
objects with flag ‘U’ in Table 1.

To summarize, there is no obvious reason to question the observed values of
$L_{\rm x}$ and $\log{(L_{\rm x}/L_{\rm bol})}$ of these X-ray detections.
Therefore, the most viable conclusion is that many of these objects showed
significant flaring activity during the eRASS1 observation. To test this
hypothesis we have extracted the light curves of the two UCD candidates with
the most extreme $\log{(L_{\rm x}/L_{\rm bol})}$ values in Fig. 6 following
the scheme explained in Sect. 5. These objects are weak detections that have
$\sim 10$ times less counts than the two UCDs mentioned in Sect. 5 that we
discuss in detail in Sect. 6.2. Their eRASS1 light curves clearly show that
outside a short time interval the count rate is consistent with zero,
therefore fully confirming the suspicion that the high activity levels in our
sample results from flares. A detailed study of X-ray variability in the full
sample will be performed in another publication. Here, as an illustration for
the morphology of eRASS light curves, the eROSITA spectral response and, thus,
the potential of eROSITA for UCD science we discuss only the two objects with
the largest number of counts in our sample. This analysis is presented in the
next subsection.

###  6.2 Information from X-ray light curves and spectra

As explained in Sect. 5 we have extracted the eRASS1 light curves and spectra
of the two UCDs with the largest number of counts. The eRASS1 light curves of
these two objects, WDS J04469-1117AB and TWA 22, are displayed in Fig. 7. Each
bin seen in the figure represents one visit of the target by eROSITA, an
eRODay.

Figure 7: eRASS1 light curves of the two UCDs with more than $100$ counts in
the eRASS1cat broad band: top \- the UCD binary WDS J04469-1117AB (bin size is
$80$ s), bottom \- TWA 22 (bin size is $50$ s).

Both objects show clear evidence of flaring. The time lapse between two
consecutive eRODays is $14.4$ ksec, corresponding to the $4$ h interval
required for one satellite rotation. Flares with a duration on the order of
$1$ h – as seen before on UCDs (e.g., Stelzer et al., 2006b) – thus show up as
a single upwards outlying bin. This is the case for WDS J04469-1117AB. For TWA
22AB an event with a decay of at least three and maybe five to six eRODays is
seen, that is this flare lasted up to half a day. As mentioned above a more
detailed analysis of UCD X-ray variability is deferred to a later work.

The X-ray spectra are fitted with a thermal apec model. The two targets are
very close (distance $\lesssim 20$ pc each), and for such small distances the
galactic absorption does not play a relevant role. With a one-temperature
model these spectra are poorly fitted (high $\chi^{2}$ values and significant
residuals). We, therefore, adopted two apec components. We performed fits with
different fixed values for the global abundance ranging between $Z=0.3\,{\rm
Z_{\odot}}$ and $Z=1.0\,{\rm Z_{\odot}}$, and we noticed the expected
degeneracy between abundance and emission measure, that is the fits with
higher abundance yielded a lower emission measure. Within the uncertainties,
however, all emission measures found for the abovementioned range of $Z$ are
compatible with each other. We, therefore, adopted the fit with $Z=0.3\,{\rm
Z_{\odot}}$, a typical value used for modelling stellar corona observed with
poor photon statistics, and we provide the results from the spectral analysis
in Table 3. The EM-weighted mean temperatures are $\langle kT\rangle=0.73\pm
0.11$ keV for WDS J04469-1117AB and $\langle kT\rangle=0.76\pm 0.10$ for TWA
22AB. These mean temperatures are higher than the values derived for early-M
dwarfs from eROSITA spectra (Magaudda et al., 2021). While this might be
surprising at first sight, this is likely to be attributed to a combination of
the young age, which is $\sim 10$ Myr for TWA 22AB (Teixeira et al., 2009) and
$60-300$ Myr for WDS J04469-1117AB (Shkolnik et al., 2009), combined with
their evident flaring activity.

Table 3: Results from spectral fitting of the two brightest eRASS1-detected
UCDs. The abundances were frozen to a global value of $0.3\,{\rm Z_{\odot}}$.

Gaia DR2 | $kT_{1}$ | $kT_{2}$ | $\log{EM_{1}}$ | $\log{EM_{2}}$ | $f_{\rm x,0.2-2.3\,keV}$ |  $\chi^{2}_{\rm red}$ (dof)
---|---|---|---|---|---|---
designation | [keV] | [keV] | [${\rm cm^{-3}}$] | [${\rm cm^{-3}}$] | [$10^{-12}\,{\rm erg\ cm^{-2}s^{-1}}$] |
3181197137010596608 | $0.27\pm 0.08$ | $1.18\pm 0.20$ | $51.36\pm 0.41$ | $51.57\pm 0.30$ | $1.42\pm 0.11$ | 0.79 (13)
5355751581627180288 | $0.28\pm 0.08$ | $1.23\pm 0.19$ | $51.20\pm 0.47$ | $51.51\pm 0.27$ | $1.05\pm 0.08$ | 1.32 (14)

Figure 8: eRASS1 spectra of the two UCDs with more than $100$ counts in the
eRASS1cat broad band: top \- the UCD binary WDS J04469-1117AB, bottom \- TWA
22 AB. Both are shown together with their best-fitting $2$-T apec model and
the residuals of the fit.

For the faint sources the only way to study spectral characteristics is the
hardness ratio ($HR$), traditionally defined as $(X_{\rm j}-X_{\rm i})/(X_{\rm
j}+X_{\rm i})$, where $X_{\rm j}$ and $X_{\rm i}$ are the count rates in a
high ($j$) and a low ($i$) energy band, respectively. For convenience we
assign letters $S$ (soft), $M$ (medium) and $H$ (hard) to the standard energy
bands of eRASS1cat, Band 1 ($0.2-0.6$ keV; $S$), Band 2 ($0.6-2.3$ keV, $M$)
and Band 3 ($2.3-5.0$ keV, $H$). We have examined the $HR$ involving $H$ and
$M$ but $50$ % of the eRASS1 detected UCDs and UCD candidates have no counts
in the hard band making this $HR$ of limited use. Fig. 9 displays the $HR$
defined with $M$ and $S$ versus the summed X-ray flux of Band 1 and Band 2
($0.2-2.3$ keV). Side-by-side with the scale of the $HR$ we provide an
estimate of the plasma temperature. The conversion between $kT$ and $HR$ was
calculated by Foster et al. (2021) from simulated 1T-apec models. According to
their analysis, the hardness ratio $(M-S)(M+S)$ saturates that is it loses its
sensitivity to temperature, at $HR\approx 0.75$ and $kT\approx 0.5$ keV. This
is due to the fact that the bulk of a typical coronal spectrum is comprised in
the energy range defined by $M$ while the $S$-band holds only the softest
emission. A boundary between different energy bands at $\sim 1$ keV would be
more appropriate to characterize stellar X-ray sources, but this information
is not present in the current version of eRASS1cat. Figure 9 shows, however,
that the majority of UCDs are captured well by $(M-S)/(M+S)$, that is they are
not saturated.

Figure 9: eRASS hardness ratios versus flux for UCDs and UCD candidates. The
flux refers to the $0.2-2.3$ keV band (the sum of eRASS1 Band 1 and Band 2)
and the hardness ratio is based on the count rates in the $0.6-2.3$ keV band
(eRASS1 Band 2, $M$) and the $0.2-0.6$ keV band (eRASS1 Band 1, $S$); see text
in Sect. 6.2 for more details.

A caveat to this $HR1-kT$ conversion is that eROSITA spectra of UCDs can
probably not be well described by a $1$-T plasma. This is seen from the
spectral analysis we performed for the two UCDs with the largest number of
counts, WDS J04469-1117 AB and TWA22 AB. Both have $HR\sim 0.46$, that is
according to Fig. 9 we would infer $kT<0.35$ keV. This is, however, much lower
than the mean temperature we have computed above from the spectral fits. We
conclude that $HR1$ is a useful parameter to evaluate the relative spectral
hardness in a sample of eROSITA spectra but quantitative inferences on the
plasma temperature must be taken with caution.

###  6.3 Comparison with previous X-ray detections

As described in Sect. 3.1 a total of $9$ UCDs and candidates from fullmatch-
eRASS1-GagneM and fullmatch-eRASS1-Reyle had previous XMM-Newton and/or
Chandra detections. For one of them the bulk of the eRASS1 emission was
attributed to its nearby CPM companion which is a separate Chandra detection,
and this object is not considered in the comparison between eRASS1 and
archival X-ray fluxes that we present in this section.

For the other $8$ objects we extracted the X-ray fluxes measured in the
earlier observations from the 4XMM-DR9 (Webb et al., 2020) and CSC 2.0 (Evans
et al., 2010), catalogs and list them in Table 4 together with the eRASS1
fluxes obtained as explained below. The majority of these archival X-ray
detections have not been discussed in previous publications dedicated to UCDs,
and a detailed investigation of eventual literature results would not provide
much additional information in our context.

To enable a comparison with the eRASS1 detections of the same objects we
selected the energy band ‘9’ ($0.5-4.5$ keV) from 4XMM-DR9. The CSC 2.0
catalog presents only the broad band flux in the $0.5-7.0$ keV band. However,
since UCDs are soft X-ray emitters, the extension to higher energies should
not provide much additional flux. This choice of XMM-Newton and Chandra energy
bands allow for the closest match to the energy bands present in eRASS1cat,
for which we can provide the flux in the $0.6-5.0$ keV band summing Band 2 and
Band 3. As a side remark we recall from Sect. 6.2 that for many of the eRASS1
sources associated with UCDs there are no counts in Band 3. While there is
some contribution from Band 1 ($0.2-0.6$ keV) the hardness ratio discussed in
Sect. 6.2 shows that for most of them the largest number of counts are
collected in Band 2. This is a combination of the energy dependence of the
effective area of eROSITA and the peak of the X-ray spectrum of UCDs.

It is important to note that the fluxes in 4XMM-DR9 and CSC 2.0 refer to a
power-law model. In Sect. 4 we have shown for a different energy band that
there is a $30$ % difference between the fluxes obtained from a power-law vs a
thermal model. Therefore, to examine the variability of the sources we refer
to the power-law fluxes provided in eRASS1cat, even if this is not the
appropriate model for our targets.

In Fig. 10 we compare the archival X-ray fluxes to the new measurements
obtained during eRASS1, for which we adopt the summed fluxes ml_flux_2 +
ml_flux_3 listed in eRASS1cat and their uncertainties. For $5$ out of $8$ UCDs
the X-ray fluxes measured with eRASS1 are consistent with the earlier data.
For the remaining three, two from fullmatch-eRASS1-GagneM and one from
fullmatch-eRASS1-Reyle, the eRASS1 flux is significantly higher than the XMM-
Newton and Chandra flux. We caution that one of them has a low eRASS1 broad
band detection likelihood of det_like_0$\lesssim 10$. In Sect. 3.3 we have,
however, explained that likely none of the UCDs and UCD candidates that we
have identified as eRASS1 X-ray emitters are spurious detections. Therefore,
the most probable explanation for the enhanced eRASS1 flux is a flare. In any
case, if these objects had been as faint as during the archival X-ray
observation they would not have been detected during eRASS1.

Table 4: Archival X-ray fluxes of UCDs and UCD candidates extracted from the 4XMM-DR9 and CSC 2.0 catalogs. These fluxes are based on a power-law model (see text in Sect. 6.3) Gaia DR2 | eRASS1 flux | 4XMM | ${\rm flux_{Band\,9}}$ | CSC 2.0 | ${\rm flux_{aper,b}}$
---|---|---|---|---|---
designation | ${\rm[10^{-14}\,erg/cm^{2}/s]}$ | name | ${\rm[10^{-14}\,erg/cm^{2}/s]}$ | name | ${\rm[10^{-14}\,erg/cm^{2}/s]}$
3200303384927512960 | $8.10\pm 2.62$ | J044023.6-053005 | $9.10\pm 0.48$ |  |
666988221840703232 | $45.25\pm 26.27$ | J075224.1+161210 | $19.15\pm 1.18$ |  |
703790044252850688 | $40.88\pm 7.66$ | J082948.1+264624 | $37.42\pm 0.55$ |  |
5761985432616501376 | $14.24\pm 4.41$ |  |  | 2CXO J085335.8-032934 | $1.35\pm 0.15$
3875561544817858816 | $42.95\pm 21.29$ | J102044.0+081422 | $24.10\pm 1.35$ | 2CXO J102043.8+081421 | $57.94\pm 2.29$
5201352936175160448 | $8.20\pm 6.43$ | J111022.1-762513 | $0.83\pm 0.07$ |  |
6224387727748521344 | $3.71\pm 1.40$ |  |  | 2CXO J145637.8-280957 | $3.34\pm 0.21$
3754497583659096320 | $4.71\pm 2.61$ | J103958.3-120357 | $0.43\pm 0.18$ |  |
Figure 10: X-ray flux from the 4XMM-DR9 and CSC 2.0 catalogs compared to the
eRASS1cat flux for the $7$ eRASS1 detected UCDs and the one UCD candidate with
an archival XMM-Newton and/or Chandra detection (one object has both an XMM-
Newton and a Chandra detection and is marked with a cross-symbol); the values
for the archival X-ray fluxes are listed in Table 4. The black line
corresponds to equal flux with the two compared instruments. To enable the
comparison with the archival fluxes, the eROSITA fluxes were calculated with a
power-law model.

##  7 Summary and conclusions

We have presented the first X-ray observations for ultracool dwarfs from the
eROSITA all-sky survey. This sample comprises $21$ spectroscopically confirmed
UCDs from the online catalog of M dwarfs maintained by J.Gagné and $37$ UCD
candidates identified with Gaia data by Reylé (2018). Through a careful
examination of alternative optical counterparts to the eRASS1 X-ray sources
and an estimate of the expected number of spurious detections for weak X-ray
emission we have selected this sample from an initial input catalog of $96$
UCDs and UCD candidates that are located in the vicinity of an eRASS1 X-ray
source.

In the course of this selection procedure we found that $14$ of these objects
are in a comoving binary or triple system. This binary fraction of $\sim 15$ %
is similar to the multiplicity rate of $10.4$ % established by Reylé et al.
(2021) irrespective of X-ray emission for the full sample of Gaia-selected UCD
candidates, which is one of the two parent samples of our study.

Eight of the $58$ eRASS1-detected UCDs and UCD candidates have a previous
X-ray detection with XMM-Newton and/or Chandra. For one of them, the candidate
UCD was identified as an X-ray emitter in our recent study for serendipitous
XMM-Newton detections of Gaia-selected UCD candidates Stelzer et al. (2020).

With the scope to understand the nature of the eRASS1 X-ray emitters for which
the optical counterpart is not obviously assigned to the UCD or a companion
star we have studied three multiwavelength diagrams. To support our source
classification we have compared the location of the UCDs and possible
alternative Gaia counterparts in these diagrams with the source population
from the large data base provided through the eFEDS fields using the
systematic classification scheme from Salvato et al. (2021). As a side remark
we note here that our investigation of this multiwavelength space largely
confirms the distinction between galactic and extragalactic sources provided
for the eFEDS X-ray detections by Salvato et al. (2021), but a small fraction
of contaminants might be present in each of the two groups.

Our new eRASS1-detections more than triple the number of known X-ray
detections in the UCD regime. The ratio between the X-ray and bolometric
luminosities of most of them are much higher than the value of $\log{(L_{\rm
x}/L_{\rm bol})}\sim-3$ which is the empirical upper envelope observed for
higher-mass coronally active stars (see e.g., Magaudda et al. (2021). We have
found strong evidence that this is the result of flaring activity. In fact,
the faint quiescent X-ray emission levels of UCDs are – with the exception of
the most nearby ones – not accessible to eRASS1 because of its shallow flux
limit101010The lowest flux in our sample of eRASS1 detected UCDs and UCD
candidates is $\sim 10^{-14}\,{\rm erg/cm^{2}/s}$ in the $0.2-5.0$ keV band.,
and they are at the limit even for dedicated XMM-Newton and Chandra
observations as previous studies of this subject have shown; see e.g., Stelzer
et al. (2006a). Impressive though the increase in X-ray detections we have
achieved with eRASS1 is, one should be aware that we have revealed less than
$0.5$ % of the targets in our input samples.

We note that a significant fraction of our new UCD X-ray detections do not
belong, strictly speaking, to this object class as they have SpTs of M5/M6
and/or evidence of young age. In fact, $10$ of the $21$ spectroscopically
confirmed UCDs with an eRASS1-detection have been characterized as ‘young’ in
the literature (see Table 2). Our two brightest detections, TWA 22 AB and WDS
J04469-1117 AB, belong to this group. These two objects show both quiescent
and flaring X-ray emission in the eRASS1 light curve, and very similar coronal
temperatures of $kT\sim 0.74$ keV. This is significantly higher than the
temperatures derived from analogous observations with eROSITA for earlier-type
M dwarfs (Magaudda et al., 2021), a result that we ascribe to the youth ($\sim
10$ Myr and $<300$ Myr, respectively) and the variability of these two
objects. Our detailed analysis of the eRASS1 data for TWA 22 AB and WDS
J04469-1117 AB gives a preview on the potential of eROSITA for enhancing our
knowledge of the spectral and timing properties of coronal emission at the
bottom of the stellar main-sequence.

If we speculate that each of the $58$ UCDs we detected has shown one X-ray
flare during eRASS1 we can estimate the typical flare frequency for UCDs from
our overall detection rate. Since the detection sensitivity is a strong
function of distance we limit this calculation to a distance of $50$ pc. About
$10$ % of our full input samples, $1858$ objects, are located in this sky
volume, and $33$ of the $58$ X-ray detections are within the same distance
limit. Therefore, under the above hypothesis $\sim 1.7$ % of all UCDs are
flaring during the typical timespan between the first and last eRODay of a
given sky position. This coarse estimate does not take into account the strong
dependence of eRASS exposure time on the sky position nor the long data gaps
inbetween individual eRODays. This value for the flare duty cycle should be
verified by a systematic analysis of the eROSITA light curves of all detected
UCDs as well as on higher statistics that will be obtained by combining our
results with similar studies for the other seven all-sky surveys.

It is finally worth pointing out that while significant efforts are being
dedicated to measuring the X-ray activity levels of UCDs, and the X-ray
emission is being studied for large samples of early-M dwarfs (e.g., Stelzer
et al., 2013; Magaudda et al., 2020, 2021), the regime of mid-M dwarfs (SpT M5
and M6) seems now the most poorly examined domain. In this vein, the inclusion
of such spectral types in the GagnéM sample is a useful addition. The biases
of most studies toward stars earlier than M5 is mainly because optical surveys
that are used for target selection usually suffer from incompleteness at the
cool end; e.g., the M star studies cited above are based on a proper-motion
survey (Lépine & Gaidos, 2011) and this sample was shown by Stelzer et al.
(2013) to be incomplete for SpT later than M4. Similarly, the earlier ROSAT
study of Schmitt & Liefke (2004) included only about a dozen stars with M5/M6
spectral types. Given the uncertainties in the spectral types determined with
different methods (see e.g., Fig. 2) a more detailed assessment of this
observational gap requires a homogeneous treatment of the input samples used
for the search of X-ray detections. The photometric calibration based on Gaia
colors (see Sect. 3.1) and the increasing number of spectroscopic studies that
have become available for M stars, e.g., through LAMOST (Guo et al., 2015),
enable such studies. In the near future it should, therefore, be possible to
reduce the observational biases and to obtain a picture of M dwarf activity
that is continuous through the whole spectral class.

##  Appendix A X-ray emitting common proper motion pairs involving UCDs

Here we provide information on CPM binaries involving a UCD or UCD candidate
from our samples. Images of these systems in the 2MASS $K_{\rm s}$ band are
shown in Fig. 11. In all cases the CPM companions are found as possible Gaia
counterparts in our ‘reverse’ match and they are within $3\,\times$ radec_err
of the X-ray position. All the comoving companions are also brighter than the
UCD and in all but three cases they are closer to the eRASS1 position than the
UCD. Note that we include here also the UCD pair WDS J04469-1117 AB which is
contrary to the other objects of this appendix not removed from the sample
studied in this work.

Figure 11:  $K_{\rm s}$-band images of UCDs from our input catalogs that are
in a CPM binary or triple system. The images are centered on the eROSITA X-ray
source position, and a $15^{\prime\prime}$ radius around this position is
shown as magenta dashed circle. The Gaia DR2 source from our input UCD
catalogs is represented by a red square, its CPM companion by an orange
triangle and further Gaia DR2 sources in the field by cyan diamonds. The
arrows indicate the PM, and their length and orientation are scaled to the
Gaia DR2 values. Note, that for the actual identification of our UCDs with the
eRASS1 catalog the Gaia DR2 coordinates had been propagated with their proper
motions to the mean eRASS1 observing data (see Sect. 3), while here they have
been projected backwards to the 2MASS epoch.

Relevant parameters for the individual systems are summarized in Table 5. We
provide for each UCD identified to be in a multiple system (col. 1) the Gaia
DR2 identifier of its comoving companion (col. 2) and other names for that
object (col. 3). Column 4 is the separation between the UCD and its companion.
Moreover, we give for the companion its magnitudes in the $G$, $J$ and $W1$
band (cols. 5$-$7), and its spectral type derived from $G-J$ as explained in
Sect. 3.1 (col. 8). In col.9 the eRASS1 X-ray fluxes for the $0.2-2.3$ keV
band are provided. Since the companions are coronal X-ray sources we did not
take the fluxes from eRASS1cat which are based on a power-law model but we
computed them from the count rates tabulated in eRASS1cat and the conversion
factor $CF_{\rm M,12}$ calculated from a thermal model fit to M dwarf spectra
by Magaudda et al. (2021) as described in Sect. 4. Finally, cols. 10$-$13
comprise flags for indications for youth / moving group membership and earlier
reports on binarity together with the respective references.

To summarize, among the $13$ pairs comprised of a UCD and a GKM star that are
detected in eRASS1, $8$ were previously known as binary stars, and $4$ are
members of a young moving group but they were unknown as binaries. As expected
from their brightness in the images the companions are of earlier SpT than the
UCD, with the exception of the abovementioned UCD pair; see also Sect. 3.1. In
most cases the companion is a mid-M dwarf. Since among late-type, magnetically
active stars with earlier SpTs have higher X-ray luminosity (e.g., Schmitt &
Liefke, 2004) and in all cases both components of the CPM system are
reasonably close to the X-ray position, we associate the X-ray source in all
these cases with the stellar companion and not with the UCD. These systems
have, therefore, been removed from our X-ray analysis, again with the
exception of the UCD binary. Note that the basic X-ray parameters from eRASS1
are found in Table 1 for these binary systems.

Table 6 holds the astrometric parameters from Gaia DR2: proper motion in right
ascension and declination for both components in the binaries (cols.2+3 and
cols.5+6) and the distance for the companion inferred by Bailer-Jones et al.
(2018) from Gaia DR2 data (col. 7). Not unexpectedly, considering their high
PM, all these binaries are nearby with distances $\lesssim 150$ pc.

Table 5: Optical/IR parameters of CPM companions to UCDs and UCD candidates that have a proper-motion corrected position at the mean eRASS 1 observing date within $3\,\times$ the positional error of an eRASS1 source. Gaia DR2 designation | Gaia DR2 designation | Other name | ${\rm sep_{UC}}$ | $G$ | $J$ | $W1$ | SpType | $f_{\rm x,Band\,2}$ | Youth | Youth | Binary | Binary
---|---|---|---|---|---|---|---|---|---|---|---|---
of UCD | of companion | of companion | ${\rm[{\prime\prime}]}$ | [mag] | [mag] | [mag] |  | ${\rm[erg/cm^{2}/s]}$ | flag | ref | flag | ref
2999273759851225856 | 2999273759850687360 |  | 5.89 | 16.11 | 12.52 | 11.39 |  M5.5$-$M6V |  (4.46 $\pm$ 2.03)$\cdot 10^{-14}$ | Y | 5 | N | …
3164100487113671552 | 3164100487115775488 | BD+13 1727 | 11.02 | 9.44 | 8.04 | 7.92 |  K2$-$K2.5V |  (5.97 $\pm$ 2.67)$\cdot 10^{-14}$ | N | … | Y | 2
3181197137010596608∗ |  3181197137010596480∗ | WDS J04469-1117 AB | 1.52 | 12.22 | 8.14 | 7.84 | M7V |  (123.36 $\pm$ 13.22)$\cdot 10^{-14}$ | N | … | Y | 3,4
3777108250009273856 | 3777111239307270528 |  BD$-$03 3000 | 20.68 | 9.58 | 8.25 | 7.93 |  K1.5$-$K2V |  (6.07 $\pm$ 2.87)$\cdot 10^{-14}$ | N | … | Y | 1,10
4709450095539630080 | 4709450095539630208 |  | 6.42 | 14.63 | 11.47 | 10.23 |  M4$-$M4.5V |  (4.59 $\pm$ 1.62)$\cdot 10^{-14}$ | N | … | Y | 10,11,12
5013728217560115328 | 5013728221855947264 |  | 9.05 | 14.0 | 11.45 | 10.49 |  M2$-$M2.5V |  (2.73 $\pm$ 1.15)$\cdot 10^{-14}$ | N | … | Y | 11,12
5541067154025506048 | 5541067158327484288 |  CD$-$37 4268 | 19.34 | 9.77 | 8.76 | 8.37 |  G1$-$G2V |  (5.54 $\pm$ 1.94)$\cdot 10^{-14}$ | N | … | N | …
5762038930728469888 | 5762038930729097728 | UCAC4 434-049409 | 8.84 | 10.89 | 8.63 | 7.98 |  M0$-$M0.5V |  (9.21 $\pm$ 2.98)$\cdot 10^{-14}$ | N | … | Y | 10,12
5774202926652248832 | 5774202930948040064 |  | 6.74 | 16.08 | 12.86 | 11.76 |  M4$-$M4.5V |  (2.41 $\pm$ 1.10)$\cdot 10^{-14}$ | Y | 7 | N | …
5810656757928226560 | 5810656753637344384 |  CD$-$68 1857 | 18.18 | 8.58 | 7.62 | 7.89 |  G0$-$G1V |  (3.31 $\pm$ 1.54)$\cdot 10^{-14}$ | N | … | Y | 9,10
6061624891182052224 | 6061625097356185216 |  | 12.72 | 14.49 | 11.41 | 10.41 |  M4$-$M4.5V |  (5.02 $\pm$ 1.45)$\cdot 10^{-14}$ | Y | 6,7 | N | …
6068636442466042240 | 6068636438170702848 | TYC 8662-1667-1 | 13.07 | 11.11 | 9.78 | 9.12 |  K1.5$-$K2V |  (2.71 $\pm$ 1.21)$\cdot 10^{-14}$ | N | … | Y | 12
6078707625378651264 | 6078707621090084736 |  | 5.68 | 15.81 | 12.55 | 11.42 |  M4.5$-$M5V |  (2.91 $\pm$ 1.14)$\cdot 10^{-14}$ | N | … | Y | 10,11
6093120294382123648 | 6093120298678786944 |  | 6.21 | 14.56 | 11.59 | 10.58 |  M3.5$-$M4V |  (10.45 $\pm$ 2.54)$\cdot 10^{-14}$ | Y | 8 | N | …
∗ This pair is a binary UCD that is not resolved with 2 MASS. Spectral types
are M4.9 and M6 and an age range of $60-300$ Myr was estimated (Shkolnik et
al., 2009)
References: (1) Washington Double Star Catalog, (2) Cruz et al. (2007), (3)
Shkolnik et al. (2009), (4) Shkolnik et al. (2012), (5) Zari et al. (2017),
(6) Goldman et al. (2018), (7) Zari et al. (2018),
(8) Damiani et al. (2019), (9) Kervella et al. (2019), (10) Hartman & Lépine
(2020), (11) Sapozhnikov et al. (2020), (12) Tian et al. (2020)

Table 6: Astrometric parameters of the UCD and UCD candidates and their companions for comoving systems from Table 5. Gaia DR2 designation | ${\rm pm\\_ra_{UCD}}$ | ${\rm pm\\_dec_{UCD}}$ | Gaia DR2 designation | ${\rm pm\\_ra_{C}}$ | ${\rm pm\\_dec_{C}}$ | d
---|---|---|---|---|---|---
of UCD | [mas/yr] | [mas/yr] | of companion | [mas/yr] | [mas/yr] | [pc]
2999273759851225856 |  $-$32.31 |  $-$17.91 | 2999273759850687360 |  $-$37.02 |  $-$23.02 | 75.96${}_{-0.92}^{+0.95}$
3164100487113671552 |  $-$77.38 |  $-$158.68 | 3164100487115775488 |  $-$74.63 |  $-$156.23 | 49.58${}_{-0.13}^{+0.13}$
3181197137010596608 |  $-$142.39 |  $-$57.56 | 3181197137010596480 |  $-$141.22 |  $-$42.79 | 18.9${}_{-0.04}^{+0.04}$
3777108250009273856 |  $-$66.82 |  $-$89.92 | 3777111239307270528 |  $-$67.27 |  $-$88.25 | 64.53${}_{-0.18}^{+0.18}$
4709450095539630080 |  $-$26.87 |  $-$32.18 | 4709450095539630208 |  $-$31.13 |  $-$35.96 | 30.19${}_{-0.05}^{+0.05}$
5013728217560115328 | 10.92 | 15.35 | 5013728221855947264 | 11.59 | 13.36 | 81.25${}_{-0.21}^{+0.21}$
5541067154025506048 | 4.91 |  $-$17.43 | 5541067158327484288 | 5.52 |  $-$17.31 | 100.86${}_{-0.27}^{+0.27}$
5762038930728469888 |  $-$181.12 | 7.25 | 5762038930729097728 |  $-$193.47 | 6.27 | 36.11${}_{-0.29}^{+0.29}$
5774202926652248832 | 8.67 |  $-$18.45 | 5774202930948040064 | 7.68 |  $-$17.89 | 159.02${}_{-1.89}^{+1.93}$
5810656757928226560 |  $-$68.17 |  $-$151.42 | 5810656753637344384 |  $-$74.18 |  $-$151.64 | 65.65${}_{-1.36}^{+1.42}$
6061624891182052224 |  $-$33.99 |  $-$15.64 | 6061625097356185216 |  $-$34.29 |  $-$15.95 | 109.93${}_{-0.85}^{+0.86}$
6068636442466042240 |  $-$12.69 |  $-$27.96 | 6068636438170702848 |  $-$15.3 |  $-$28.2 | 116.96${}_{-0.59}^{+0.6}$
6078707625378651264 |  $-$123.32 |  $-$38.38 | 6078707621090084736 |  $-$124.02 |  $-$38.74 | 91.6${}_{-0.66}^{+0.67}$
6093120294382123648 |  $-$23.56 |  $-$20.67 | 6093120298678786944 |  $-$22.8 |  $-$21.33 | 135.55${}_{-1.16}^{+1.18}$

##  Appendix B eROSITA source populations

To understand the properties of objects that are not bonafide counterparts to
an eRASS1 source and that are not UCDs we examine the eROSITA, Gaia and WISE
parameter space.

In Sect. 3.2 we have argued for evidence of distinct populations of different
astrophysical populations in the $G-G_{\rm RP}$ vs $G_{\rm BP}-G$ diagram. To
verify this claim we make use of the main eFEDS point source catalog (Brunner
et al., A&A submitted). We adopt the results from the dedicated source
identification procedure described by Salvato et al. (2021) that classifies
the eFEDS X-ray sources as either galactic or extragalactic. In the
extragalactic category we consider the objects labeled as ‘SECURE
EXTRAGALACTIC’ and those labeled ‘LIKELY EXTRAGALACTIC’, and analogously in
the galactic category where we consider the ‘SECURE GALACTIC’ and ‘LIKELY
GALACTIC’ ones. We limit our study to the objects that have full Gaia
photometry ($G$, $G_{\rm RB}$ and $G_{\rm RP}>0$), valid data in the lowest
WISE band ($W1>0$) and reliable counterpart according to a quality flag
(CTP_quality $>=3$) defined by Salvato et al. (2021).

In Fig.12 we display the two groups of objects in the $G-G_{\rm RP}$ vs
$G_{\rm BP}-G$ diagram. The distribution of the ‘extragalactic’ objects in
Fig. 12 resembles a combination of the ‘quasar’ and ‘galaxy’ CCDs presented by
Bailer-Jones et al. (2019), with a weak extension onto the stellar main-
sequence (drawn as a green line). The ‘galactic’ objects clearly follow that
sequence, but with a signifiant upwards spread, thus also showing some overlap
with the ‘extragalactic’ population. These overlaps might be related to
residual contamination of each group with objects from the other type.

Figure 12: Gaia color-color diagram for the two subsamples of eFEDS sources
identified as extragalactic (gray) and galactic (red) by Salvato et al.
(2021). The stellar main-sequence (green) is obtained from the table
maintained by E.Mamajek8.

In Fig. 13 we examine for the same two groups of objects the $W1$ vs
$\log{f_{\rm x}}$ diagram which was introduced by Salvato et al. (2018) to
tentatively distinguish extragalactic from galactic objects based on an
empirical dividing line shown in blue in Fig. 13. Overall this line
distinguishes well the two populations as already suggested by Salvato et al.
(2018); (see Salvato et al., 2021, for a discussion of this diagram with
relation to the eFEDS population).

Figure 13: WISE $W1$ magnitude versus logarithm of the X-ray flux in $0.6-2.0$
keV for the objects from the main eFEDS catalog distinguishing ‘galactic’ from
‘extragalactic’ sources as described in the text. The line denotes the
empirical separator between stars and other objects as defined by Salvato et
al. (2018) with extragalactic sources being located above the line.

We finally show the X-ray over optical flux ratio versus Gaia color for the
eFEDS sample in Fig. 14 where with few exceptions the ‘galactic’ and
‘extragalactic’ objects are clearly separated. The small group in the right
panel that is above the main locus of the ‘galactic’ sources shows strong
overlap with the galactic objects above the separator in the $W1$ vs $f_{\rm
x}$ diagram, with $155$ of $176$ galactic sources ($\sim\leavevmode\nobreak\
88$ %) that are upwards outliers in terms of $f_{\rm x}/f_{\rm G}$ ratio being
located above the line in the $W1-f_{\rm x}$ diagram. These objects could be
flaring stars or compact objects.

Figure 14: Logarithm of the X-ray over $G$ band flux versus Gaia blue and red
photometer color for the full eFEDS sample. Two panels with the same data are
shown to visualize the overlap of the extragalactic and galactic candidates
selected from Fig. 13. The extragalactic sample is highlighted in red in the
left panel and the galactic sample is red in the right panel.

To summarize, these figures support the classification scheme of Salvato et
al. (this volume) in terms of galactic versus extragalactic sources, but a
small subsample of them is overlapping each other. The extragalactic sample
reaches down to the upper stellar main-sequence. The upwards outliers in the
sample of ‘galactic’ objects (with $\log{(f_{\rm x}/f_{\rm G})}\geq-2$) could
be AGN or flaring stars.

##  Appendix C Non-UCD eRASS1 counterparts

In Table 7 we list the properties of the ‘plausible’ counterparts to eRASS1
X-ray sources that are not UCDs or UCD candidates. Table 7 provides their
photometry ($G$, $J$ and $W1$ in cols. 3-5), spectral type estimated from
$G-J$ assuming a main-sequence star and adopting the same calibration as in
Sect. 3.1 (col. 6). Clearly, the spectral type is meaningful only if the
object is a star. Furthermore, Table 7 holds the Gaia DR2 distance from
Bailer-Jones et al. (2018) (col. 7), X-ray fluxes from eRASS1cat for the
$0.6-2.3$ keV band and the $2.3-5.0$ keV band (cols. 8 and 9). The latter
energy band was included because is relevant for extragalactic objects which
tend to be harder X-ray sources than coronally active stars. Finally, in cols.
10 and 11 the classification from the literature and the corresponding
reference are given.

The objects in Table 7 belong to two groups selected with different criteria
(see Sect. 3.2). The final classification of these objects is not within the
scope of our work. However, here we briefly discuss the two groups and the
possible nature of its members.

The first group comprises eRASS1 sources that have a UCD or UCD candidate as
the Gaia object with the smallest X-ray to optical separation but where
another Gaia source in the match radius is brighter suggesting the association
of the eRASS1 emission with this object rather than the UCD. All but one of
these $7$ objects have been classified as a star in the literature. In
contrast to the objects from Appendix A these stars do not share the proper
motion with the UCD.

The other group are Gaia sources that have the smallest value for the X-ray to
optical separation among all Gaia objects in the match radius of $3\times$ the
radec_err around the eRASS1 position. One of these objects, Gaia DR2
3902395843353397248, was identified as a bonafide eRASS1 X-ray source on the
basis of an archival XMM-Newton observation. This is a known quasar, 2XMM
J123337.5+073133, from the catalog of Miller et al. (2011). The XMM-Newton
data was analyzed by Stelzer et al. (2020) in a study of serendipitous X-ray
detections of UCDs from the XMM-Newton archive. In that work the source was
recognized as an extragalactic object on the basis of its X-ray spectrum which
is consistent with a power-law of typical index ($\Gamma\sim 2$) but not with
thermal emission at temperatures typical for M-type dwarfs.

The position of the other non-UCDs that are closest Gaia counterparts to
eRASS1 sources in the multiwavelength parameter space can be seen in the right
panels of Fig. 3, where they are represented as gray circles surrounded by an
annulus. Note that some sources without blue and red photometer, and WISE data
are missing in these diagrams. From comparison with Fig. 14 these objects are
likely a mixture of extragalactic objects and stars, and this is consistent
with the information compiled from the literature.

Table 7: Multi-wavelength properties of non-UCDs considered to be more plausible counterparts to eRASS1 sources than the UCD in its vicinity. Gaia DR2 designation | Gaia DR2 designation | $G$ | $J$ | $W1$ | SpType | Dist | $f_{x,\leavevmode\nobreak\ band\leavevmode\nobreak\ 2}$ | $f_{x,\leavevmode\nobreak\ band\leavevmode\nobreak\ 3}$ | Object type | Ref.
---|---|---|---|---|---|---|---|---|---|---
of UCD | of alternative counterpart | [mag] | [mag] | [mag] |  | [pc] |  [erg/cm2/s] |  [erg/cm2/s] |  |
bright Gaia source but not closest to X-ray source
4842003953209804672 | 4842003953209804928 | 14.63 | 13.64 | 12.78 | G1–G2V | $1737.61_{-58.92}^{+63.10}$ | $(27.78\pm 10.79)\cdot 10^{-15}$ | … | Star | 4
652944911438186368 | 652944915732919168 | 16.92 | 15.25 | 14.28 | K4–K4.5V | $1095.41_{-140.00}^{+184.69}$ | $(47.52\pm 27.08)\cdot 10^{-15}$ | $(36.46\pm 33.49)\cdot 10^{-14}$ | Star | 2,10
720165105283287808 | 720165105284271744 | 13.02 | 11.05 | 10.21 | K7–K8V | $134.26_{-7.51}^{+8.44}$ | $(109.63\pm 42.96)\cdot 10^{-15}$ | … | Star | 2,10
5411645461381996928 | 5411645465686894208 | 13.76 | 12.10 | 11.48 | K4–K4.5V | $3357.67_{-212.13}^{+241.87}$ | $(84.62\pm 25.74)\cdot 10^{-15}$ | … | Star | 4
5449824525188538112 | 5449824490828691584 | 18.77 | 16.41 | 15.06 | M1V | $1616.61_{-503.95}^{+908.12}$ | … | $(62.07\pm 30.40)\cdot 10^{-14}$ | Star | 4
5854998824943562240 | 5854998820633388544 | 19.75 | … | … | … | $3380.43_{-1639.10}^{+2929.38}$ | $(26.81\pm 8.66)\cdot 10^{-15}$ | $(2.08\pm 4.96)\cdot 10^{-14}$ | Star | 4
5854998824943562240 | 5854998824943561728 | 15.96 | 13.25 | 11.73 | M3–M3.5V | $430.05_{-9.35}^{+9.76}$ | $(26.81\pm 8.66)\cdot 10^{-15}$ | $(2.08\pm 4.96)\cdot 10^{-14}$ | Galaxy | 4
5905136482143969280 | 5905136486450575616 | 13.80 | 12.49 | 11.52 | K1–K1.5V | $903.21_{-23.89}^{+25.20}$ | $(43.00\pm 20.74)\cdot 10^{-15}$ | $(28.82\pm 22.38)\cdot 10^{-14}$ | Star | 4
non-UCD Gaia source closest to X-ray source
5985290231327158144 | 5985290231264640000 | 20.29 | … | … | … | $2136.11_{-1251.67}^{+2527.68}$ | $(34.85\pm 16.38)\cdot 10^{-15}$ | … | … | …
6235533167875990272 | 6235533163576299520 | 18.14 | 16.14 | … | K7–K8V | $2387.40_{-1011.38}^{+2823.78}$ | $(64.78\pm 25.84)\cdot 10^{-15}$ | $(14.81\pm 18.61)\cdot 10^{-14}$ | Galaxy | 4
3426062907707797376 | 3426062912004133632 | 15.74 | 12.69 | 11.72 | M4V | … | $(63.15\pm 30.31)\cdot 10^{-15}$ | … | Star | 6,10
3537678013829356032 | 3537678009534395520 | 20.81 | … | 15.99 | … | $1011.59_{-473.74}^{+928.31}$ | $(47.71\pm 17.37)\cdot 10^{-15}$ | $(6.4\pm 7.67)\cdot 10^{-14}$ | Galaxy | 4
3902395843353397248 |  3902395813288871936∗ | 19.17 | … | 14.10 | … | $2301.06_{-651.12}^{+939.98}$ | $(119.02\pm 34.17)\cdot 10^{-15}$ | $(11.00\pm 12.02)\cdot 10^{-14}$ | QSO | 1
4633181951787913344 | 4633181956082468736 | 20.86 | … | 14.87 | … | … | $(32.75\pm 13.85)\cdot 10^{-15}$ | … | AGN | 5,8
4682521921904033408 | 4682521921904033024 | 19.69 | … | 14.67 | … | $1179.81_{-419.12}^{+754.84}$ | $(29.13\pm 8.86)\cdot 10^{-15}$ | … | AGN | 5,8
4820214342870659968 | 4820214347166884096 | 17.05 | 15.98 | 14.89 | G4–G5V | $3625.70_{-567.14}^{+745.52}$ | $(29.31\pm 11.73)\cdot 10^{-15}$ | … | Star | 4
4907225329405739904 | 4907225329405740672 | 19.79 | … | … | … | $1900.08_{-613.83}^{+953.67}$ | $(28.66\pm 14.92)\cdot 10^{-15}$ | … | Star | 4
4948028068473626368 | 4948028068473523200 | 20.71 | … | 16.02 | … | … | $(29.12\pm 13.13)\cdot 10^{-15}$ | … | Galaxy | 4
5263797568772960256 | 5263797641784398080 | 21.08 | … | … | … | … | $(9.46\pm 3.73)\cdot 10^{-15}$ | $(2.74\pm 2.68)\cdot 10^{-14}$ | Galaxy | 4
5317092619649544960 |  5317092550945911552† | 10.86 | 10.06 | 9.50 | F6–F7V | $370.06_{-3.35}^{+3.41}$ | $(28.11\pm 14.56)\cdot 10^{-15}$ | $(3.85\pm 13.49)\cdot 10^{-14}$ | Star | 7,9
5387954181261184896 | 5387953979397582336 | 20.92 | … | 15.47 | … | … | $(46.72\pm 18.39)\cdot 10^{-15}$ | … | AGN | 5,8
5479448529535828992 | 5479448529538083200 | 20.58 | … | 14.59 | … | $1782.32_{-791.88}^{+1312.52}$ | $(16.46\pm 6.95)\cdot 10^{-15}$ | $(3.76\pm 4.51)\cdot 10^{-14}$ | AGN | 5,8
5790470927042226816 | 5790470927034553984 | 19.83 | … | … | … | $1731.19_{-849.79}^{+1917.51}$ | $(8.32\pm 6.27)\cdot 10^{-15}$ | … | … | …
5800676697044928640 | 5800676697044928000 | 12.58 | 10.47 | 9.84 | K9–M0V | $201.28_{-10.17}^{+11.29}$ | $(14.92\pm 10.04)\cdot 10^{-15}$ | $(6.54\pm 8.89)\cdot 10^{-14}$ | VB | 11
5800676697044928640 | 5800676697042535296 | 12.71 | 10.47 | 9.84 | M0–M0.5V | $206.97_{-8.20}^{+8.89}$ | $(14.92\pm 10.04)\cdot 10^{-15}$ | $(6.54\pm 8.89)\cdot 10^{-14}$ | VB | 11
5878773221280041472 | 5878773216960788096 | 12.14 | 10.92 | 10.39 | G9–K0V | $314.34_{-4.09}^{+4.19}$ | $(72.80\pm 26.28)\cdot 10^{-15}$ | … | Star | 3
5991061121183402880 | 5991061121134832896 | 20.41 | … | … | … | $3448.57_{-1706.88}^{+2794.23}$ | $(96.52\pm 28.33)\cdot 10^{-15}$ | … | … | …
Other name from SIMBAD: ∗ 2XMM J123337.5+073133, † TYC 8573-3247-1
References: (1) Schneider et al. (2007), (2) Vasconcellos et al. (2011), (3)
Saito et al. (2012), (4) McMahon et al. (2013), (5) Secrest et al. (2015), (6)
Cook et al. (2016), (7) Stevens et al. (2017),
(8) Assef et al. (2018) , (9) Cantat-Gaudin et al. (2018), (10) Xiang et al.
(2019), (11) this work.

###### Acknowledgements.

We thank the anonymous referee for careful reading and constructive comments.
AK is supported by the Deutsche Forschungsgemeinschaft (DFG) project number
413113723. MC and EM acknowledge funding by the Bundesministerium für
Wirtschaft und Energie through the Deutsches Zentrum für Luft- und Raumfahrt
e.V. (DLR) under grant numbers FKZ 50 OR 2008 and FKZ 50 OR 1808. 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 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, 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/NRTA software system developed
by the German eROSITA consortium. This publication makes use of data products
from the Two Micron All Sky Survey, which is a joint project of the University
of Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation and of data products from
the Wide-field Infrared Survey Explorer, which is a joint project of the
University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, funded by the National
Aeronautics and Space Administration. We present results from the European
Space Agency (ESA) space mission Gaia. Gaia data are being processed by the
Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is
provided by national institutions, in particular the institutions
participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission
website is https://www.cosmos.esa.int/gaia. We acknowledge ESASky, developed
by the ESAC Science Data Centre (ESDC) team and maintained alongside other ESA
science mission’s archives at ESA’s European Space Astronomy Centre (ESAC,
Madrid, Spain) and the SVO Filter Profile Service (http://svo2.cab.inta-
csic.es/theory/fps/) supported from the Spanish MINECO through grant
AYA2017-84089.

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