FIR is problematic in IC 10 because of its proximity, and thus low recession
velocity, relative to the MW. IC 10 has a recession velocity of $-348$
$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, so is somewhat more blue-shifted than
the highest H i velocities ($-150$ $\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$)
considered as belonging to the MW in Planck Collaboration et al. (2011). Those
authors also found that the emissivity of Galactic dust in these high-velocity
clouds is low, so that relatively little dust emission would be expected from
such clouds (see also Bianchi et al. 2017, who analyzed the Virgo cluster).
The H i gas around IC 10 toward the northwest extension is found at about
$-400$ $\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ (e.g., Nidever et al. 2013), a
higher velocity than expected for gas belonging to the MW, and consistent with
being intrinsic to IC 10. It is thus likely that the filamentary dust traced
by the FIR in IC 10 belongs indeed to IC 10. Galactic cirrus tends to have
blue optical colors (Román et al. 2020), but the severe foreground extinction
of $A_{V}$$\ga 4$ toward IC 10, and its possible spatial variation, makes an
accurate color determination difficult, as well as the separation of the
$I_{\scriptscriptstyle\rm E}$ stellar emission from potential cirrus, either
belonging to the MW or IC 10.

In contrast, the case of IC 342 is unambiguous. Dust emission toward IC 342
follows the $I_{\scriptscriptstyle\rm E}$ emission in the spur feature, but
the H i at the recession velocity of IC 342 does not. The conclusion is that
in IC 342, the $I_{\scriptscriptstyle\rm E}$ emission in the spur is due to
foreground cirrus, rather than a stellar stream. Its morphology is mirrored
exactly by the FIR 250 $\mathrm{\SIUnitSymbolMicro m}$-emission, but not in H
i. Consequently, in addition to tracing stars, sensitive Euclid
$I_{\scriptscriptstyle\rm E}$ images, compared with other wavelengths, will be
a powerful diagnostic for the Galactic ISM, in particular for assessing the
importance of the diffuse cirrus component.

###  4.4 Surface brightness profiles

Figure 6: Top: Surface brightness profiles extracted by AutoProf as described
in the text for IC 342 (left panel) and NGC 6822 (right). The four bands are
given by purple, blue, green, and red curves for $I_{\scriptscriptstyle\rm
E}$, $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$, respectively. The $1\sigma$ SB limits from
AutoProf (not rescaled to 100 arcsec2 regions) in units of mag arcsec-2 are
shown as dashed horizontal lines, with colors corresponding to the Euclid
bands. The fluxes have been corrected for foreground extinction (Sect. 4.1;
the uncorrected $I_{\scriptscriptstyle\rm E}$ profile is shown as a dotted
(purple) curve in the top panel. Middle and bottom: $I_{\scriptscriptstyle\rm
E}$ $-$$H_{\scriptscriptstyle\rm E}$ and $Y_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ radial color profiles. The top axis
corresponds to galactocentric radii in units of arcsec, and the bottom in
units of kpc. The mean $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ color over typically a factor of $100$ in
radius is shown as a horizontal dashed line in the middle panel; the light
gray rectangular regions illustrate the full spread in model colors (see Fig.
7) and the dark gray one the standard deviation about the mean of the models.
The mean galaxy $I_{\scriptscriptstyle\rm E}$ $-$$H_{\scriptscriptstyle\rm E}$
with its standard deviation is also shown as a gray rectangular region in Fig.
7.

We have generated surface brightness (SB) profiles for the Showcase galaxies
using AutoProf. AutoProf is a Python-based pipeline for non-parametric profile
extraction, that includes masking, sky determination, centroiding, and
isophotal fitting (Stone et al. 2021). For this paper, we use AutoProf in the
default mode but with $5\sigma$ clipping. Because centers are difficult to
determine, particularly in nearby dwarf galaxies with resolved stars, we have
fixed the profile centers to the NED coordinates for the galaxy. Results are
shown in Fig. 6 for IC 342 and NGC 6822; the profiles of the remaining
galaxies appear in Appendix C (Fig. 26). The sky values determined from
Approach (2), as given in Table 3 and shown in Fig. 22, are consistent to
within a few percent with the sky levels from AutoProf.

In Fig. 6 (and Fig. 26), the surface brightness profiles corrected for
foreground extinction are shown as solid lines, while for
$I_{\scriptscriptstyle\rm E}$ the uncorrected profile is shown as a dotted
line. Because of their low Galactic latitude (see Table 1), for IC 10, IC 342,
and NGC 6822, these corrections can be significant, up to $3$
$I_{\scriptscriptstyle\rm E}$ mag in the case of IC 10. The top horizontal
axis reports the angular galactocentric distance, while the bottom gives the
physical radii in kpc. Figures 6 and 26 show that Euclid is able to trace
galaxy emission out to 20$-$30 kpc in radius in a single ROS.

Figure 7: Synthetic $I_{\scriptscriptstyle\rm E}$ $-$$H_{\scriptscriptstyle\rm
E}$ from the Bruzual & Charlot (2003) models with exponentially declining SFH
(left panel); the same Bruzual & Charlot (2003) models but SSPs (middle); and
PEGASE SSP models from Fioc & Rocca-Volmerange (1997, right) and Le Borgne et
al. (2004). Also shown as gray regions are the mean $I_{\scriptscriptstyle\rm
E}$ $-$$H_{\scriptscriptstyle\rm E}$ colors and their standard deviations, as
reported in the middle panel of Figs. 6 and 26, evaluated over a factor of 100
in galactocentric radius. As discussed in Sect. 4.1, these colors have been
corrected for foreground extinction from our Galaxy. The different behavior of
the models is due to the smoothed-out SFH in the left panel, and the different
treatment of red supergiants (RSGs) that begin to dominate around $10$ Myr,
and the most massive AGB stars around $100$ Myr.

Figures 6 and 26 illustrate the difficulty of determining the sky value when
the galaxy fills the image. IC 342’s profile extends smoothly out to the
limits of the Euclid FoV (1600″ on the diagonal), but does not quite achieve
the SB limits expected from Sect. 3.1. The implication is that the galaxy
emission could have been measured at even larger radii, were it not limited by
the (already large) FoV. On the other hand, the profile of NGC 6822, an
apparently smaller galaxy, approximates the SB limits in the very outer
regions. The problem of large galaxies will be mitigated in the EWS, because
of more continuous coverage.

###  4.5 The diagnostic power of Euclid colors

The radial trends of selected Euclid colors, $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ and $Y_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ are also shown in Figs. 6 and 26. As an
initial evaluation of the photometric calibration (see also Sect. 5), we
compare the colors of the Showcase galaxies with those obtained using
synthetic templates. In particular, we use Bruzual & Charlot (2003) synthetic
models, and calculate the magnitudes using the SED-fitting code lephare
(Arnouts et al. 1999; Ilbert et al. 2006). We assume an exponentially
declining SFH, with an SFR duration $\tau$ in the range $0.1$–$30$ Gyr, ages
up to 14 Gyr, metallicity from sub-Solar to Solar ($0.2\,$$Z_{\odot}$,
$0.4\,$$Z_{\odot}$, and $Z_{\odot}$), and vary the internal extinction with
$E(B-V)$ = $0,0.1,0.2$, and $0.3$ using the attenuation curve of Calzetti et
al. (1994). From the combination of these parameters, we generate a library of
2300 synthetic magnitude sets at $z\,=\,0$. Given the wide range of parameters
explored, most of the galaxies in the local Universe would be expected to
possess colors within the model predictions.

From the distribution of the Euclid colors in the library, we determine the
median and the 16$-$84th quantile of the distributions, and find the following
color ranges: $I_{\scriptscriptstyle\rm E}$ $-$$Y_{\scriptscriptstyle\rm E}$ =
$0.45\,\pm\,0.24$; $Y_{\scriptscriptstyle\rm E}$ $-$$J_{\scriptscriptstyle\rm
E}$ = $0.10\,\pm\,0.08$; and $J_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ = $0.09\,\pm\,0.09$. In Figs. 6 and 26, these
are shown as dark gray rectangular regions. The full color ranges spanned by
the models are illustrated as light gray regions.

Virtually all of the colors shown in Figs. 6 and 26 fall within the ranges
predicted by these models. In the spirals, IC 342, NGC 2403, and NGC 6744,
there is a trend for the outer regions to be bluer than the bulk of the inner
disk, possibly implying an inside-out disk formation scenario (e.g., Williams
et al. 2009b; Gogarten et al. 2010; Wang et al. 2011), consistent with radial
metallicity gradients in nearby spirals (e.g., Sánchez et al. 2014)
Conversely, the central regions of IC 342 and IC 10 are extremely blue,
challenging the spread of allowable colors predicted by the models. However,
as shown in Figs. 2 and 23, the centers of both galaxies are unusual. IC 342
has an extremely young star luminous cluster complex in its nucleus (Böker et
al. 1999; Carson et al. 2015; Balser et al. 2017), the brightest of those
examined by Carson et al. (2015). Figure 2 and HST colors show that it is
extremely blue, associated with a massive H ii region and an X-ray source (Mak
et al. 2008). In IC 10, the NED center position corresponds to a complex of H
ii regions (e.g., Hodge & Lee 1990; Polles et al. 2019), and there are several
more located near the nucleus (e.g., Vacca et al. 2007). Thus, extremely blue
nuclear colors are expected for both IC 342 and IC 10.

We explore this further in Fig. 7, where $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ is plotted as a function of age, and color
coded by metallicity $Z$. We compare the predictions of the Bruzual & Charlot
(2003) models described above and shown in the left panel, with those of
Bruzual & Charlot (2003) for single stellar population (SSP) models and with
PEGASE SSPs by Fioc & Rocca-Volmerange (1997) and Le Borgne et al. (2004).
Also shown as gray regions are the mean $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ color ranges of the Showcase galaxies that
are reported as horizontal dashed lines in Figs. 6 and 26. The models in the
left panel of Fig. 7 were generated with a limited range of metallicities and
ages, as can be seen from the comparison with the SSPs in the right two
panels. In addition to the different parameter ranges, the BC03 models behave
differently due to the smoothed-out SFH in the left panel, compared to the SSP
in the middle one. The BC03 and PEGASE SSP models also differ in their
treatment of red supergiants (RSGs) that begin to dominate at $\sim 10$ Myr,
and the most massive asymptotic giant branch (AGB) stars at $\sim 100$ Myr.

The bluest colors are found at young ages, $\la 10$ Myr, consistent with the
properties of IC 10 and IC 342 in their central regions. Moreover, sub-Solar
metallicity makes these colors even bluer, so appropriate for IC 10 at about
0.3 $Z_{\odot}$ ($\log_{10}(Z/Z_{\odot})\,=\,-0.55$ for the color coding). At
a slightly super-Solar metallicity, the age of the IC 342 nuclear star cluster
is estimated to be $\sim\,$5 Myr (e.g., Carson et al. 2015), so the limits of
the SSP PEGASE models constrain well the observed colors at this young age.

In summary, Euclid colors are diagnostic of the age and metallicity of the
stellar populations in galaxies, and will provide an important tool for the
exploration of broader galaxy populations. At Euclid’s resolution, in the
centers of these nearby galaxies, we are essentially just probing the
brightness of small star clusters or even bright stars. At the same time,
Euclid’s sensitive SB limits allow the examination of galaxy disks to depths
that can reveal disk breaks and faint external features of galaxies that could
be signatures of interaction (e.g., Peters et al. 2017; Sánchez-Alarcón et al.
2023). Details of the SB profiles and color gradients, and the disk properties
of the Showcase galaxies, will be discussed in a future paper.

##  5 Resolved stellar photometry and star counts

Going beyond the integrated light described in Sect. 4, photometry of resolved
stars in nearby galaxies is a powerful tool, not only for understanding
stellar content and galaxy formation scenarios, but also for probing the outer
regions of galaxy disks and disk formation (e.g., Barker et al. 2012;
Crnojević et al. 2016; Hillis et al. 2016; Jang et al. 2020a). The surface
brightness of resolved stellar populations, once corrected for completeness
and projection effects, can reach fainter SB limits than integrated light
alone (e.g., Barker et al. 2012). Thus, through stellar photometry in nearby
galaxies, Euclid opens a new perspective also on resolved stellar populations
and their diagnostic capabilities. Here we present a first look at resolved
stellar photometry in the Showcase galaxies.

###  5.1 Stellar photometry

For all galaxies, point-source photometry was performed with SourceExtractor
(Bertin & Arnouts 1996). Detections were considered inependently in the four
Euclid bands, adopting a mexhat (wavelet) filter before detection, and then
considering as valid detections all sources having even a single pixel
1.5$\sigma$ above the background. The filtering step performed by
SourceExtractor prior to source identification has the effect of “smoothing”
the images, thus minimizing spurious detections despite the low 1.5$\sigma$
detection threshold. The photometric analysis of the identified sources is
performed on the original images. For the photometry, we adopted a 5-pixel
diameter aperture, corresponding to 0$\aas@@fstack{\prime\prime}$5 and
1$\aas@@fstack{\prime\prime}$5 in the VIS and NISP images, respectively. This
aperture, which totals approximately 3 times the PSF FWHM in all Euclid bands,
is sufficiently small to guarantee accurate photometry in moderately crowded
regions of the galaxies. Aperture corrections from 5-pixel to large apertures
of 6″ for VIS and 18″ for the NISP images, totaling about 40 times the FWHM of
the PSFs, were computed from the most isolated, bright, unsaturated stars. The
corrections amount to $-0.27$, $-0.11$, $-0.12$, and $-0.15$ mag in
$I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$,
respectively. Finally, magnitudes were calibrated applying the zero points of
ZP${}_{I_{\scriptscriptstyle\rm E}}$ = 30.13, and ZPNIR = 30.0, as discussed
in Sect. 3. PSF-fitting photometry aimed at characterizing the resolved
stellar content of the innermost star-forming regions will be presented in
subsequent papers.

The photometric catalogs in the VIS and NISP bands were cross-matched by
assigning a 1″ maximum tolerance in separation between sources. For every
galaxy except IC 342 and NGC 6744, we were able to produce a final master
catalog containing only sources with photometric detections in all four bands.
For IC 342 and NGC 6744, in order to achieve sufficient statistics, we adopted
a less conservative approach, and cross-matched the $I_{\scriptscriptstyle\rm
E}$ VIS band with only the $J_{\scriptscriptstyle\rm E}$ and
$H_{\scriptscriptstyle\rm E}$ NISP bands. In any case, the cross-match removes
the majority of spurious detections, such as cosmic rays, emission peaks on
bright star spikes, or residual artefacts from the image reduction pipeline
described in Sect. 3.

Figure 8: SourceExtractor output parameters for NGC 6822, intended to
illustrate the typical selection cuts applied to our photometric catalogs.
Purple points are the sources matched in all four Euclid bands, while yellow
points correspond to our selections. In the top panel, we retain all sources
with a measured FWHM in VIS between 1.2 and 2.5 pixels, while in the bottom
panel, we show our adopted selection in the plane defined by central surface
brightness versus aperture magnitude. Sources with a FWHM smaller than 1.2
pixels (namely smaller than the PSF) are likely artefacts, while sources with
large FWHM values and/or large values of $\mu_{\mathrm{max}}$ compared to
aperture photometry are either saturated stars or extended objects (background
galaxies or resolved star clusters).

Additional selection cuts based on some of the SourceExtractor output
parameters are then applied to remove saturated stars and extended background
galaxies. More specifically, we retain sources that: (i) have a measured FWHM
in VIS between 1.2 and 2.5 pixels; and (ii) lie within the locus populated by
compact sources in the plane defined by central surface brightness
($\mu_{\mathrm{max}}$) versus aperture magnitude, as illustrated in Fig. 8.
Objects with a FWHM smaller than 1.2 pixels (namely smaller than the PSF) are
likely artefacts, while values of the FWHM larger than 2.5 pixels have a high
probability of being associated with extended objects. Indeed, extended
systems (such as background galaxies or resolved star clusters), as well as
saturated stars, tend to have fainter central surface brightnesses compared to
point sources with the same aperture flux. Nevertheless, such selection
criteria are not always effective in removing very compact background galaxies
from the final catalog. With these cuts, we are left with: 332 900, 323 260,
116 551 and 30 755 sources in the $I_{\scriptscriptstyle\rm
E}$–$Y_{\scriptscriptstyle\rm E}$–$J_{\scriptscriptstyle\rm
E}$–$H_{\scriptscriptstyle\rm E}$ matched catalogs of NGC 6822, IC 10, NGC
2403, and Holmberg II, respectively; and 318 366 and 162 286 sources,
respectively, in the $I_{\scriptscriptstyle\rm E}$–$J_{\scriptscriptstyle\rm
E}$–$H_{\scriptscriptstyle\rm E}$ matched catalogs of IC 342 and NGC 6744.

###  5.2 Reddening correction

Individual source magnitudes were corrected for spatially variable foreground
reddening, as described in Sect. 4.1 but for each source position, rather than
assuming a single value for the entire galaxy. Also, rather than using a flat
spectrum as for the integrated light, here we assume a 5700 K blackbody to
approximate a G2V stellar spectrum in order to better emulate the emission
from individual stars. This assumption provides relative ratios of
Aλ/AV=0.726, 0.375, 0.266, and 0.173 for $I_{\scriptscriptstyle\rm E}$,
$Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$, respectively. The correction is modest in the
case of Holmberg II, NGC 2403, and NGC 6744, while it has a major impact on
the CMDs of IC 10, IC 342, and NGC 6822 which suffer the strongest
extinctions. Indeed, the reddening-corrected CMDs of these galaxies exhibit,
besides a global shift toward brighter magnitudes and bluer colors, narrower
and cleaner stellar evolutionary sequences compared to the non-corrected CMDs.

Figure 9: $I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}$-$H_{\scriptscriptstyle\rm E}$ color-magnitude diagram of all sources
within the FoV of NGC 6822, after applying the selection cuts described in
Sect. 5.1 and illustrated in Fig. 8, and after correction for foreground
extinction (Sect. 5.2). Yellow points indicate bright MW and background galaxy
contaminants, namely sources cross-matched with the Gaia DR3 catalog that have
a measured proper motion PM larger than $3\sigma_{\mathrm{PM}}$. The vertical
feature at $I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}\simeq
1.3$, $I_{\scriptscriptstyle\rm E}\gtrsim 21$ is due to the MW M dwarf
population.

Figure 10: Distribution in the $Y_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ plane of sources in the NGC 6822 photometric
catalog, after removal of bright $I_{\scriptscriptstyle\rm E}$ $\lesssim\,20$
MW disk stars in Gaia DR3. In the top panel, the PARSEC stellar isochrones
(Bressan et al. 2012; Marigo et al. 2017) in the Euclid bands are superimposed
in red for different ages (from 10 Myr to 10 Gyr) and metallicities of
$Z\lesssim\,0.006$ (about one third Solar); in blue is the TRILEGAL Galaxy
model. Giant and dwarf stars in NGC 6822 and in the MW overlap at
$I_{\scriptscriptstyle\rm E}$ $-$$H_{\scriptscriptstyle\rm E}$ $\lesssim\,1$,
while the two populations diverge at redder colors. In the bottom panel, we
denote the location of Galactic M dwarf stars, AGB stars in NGC 6822,
background compact red galaxies, and residual spurious detections. The dashed
orange polygon outlines our final selection, which provides a reasonable
compromise between the need of retaining the largest possible number of stars
belonging to NGC 6822, while removing Galactic M dwarfs, compact red galaxies,
and residual spurious detections (see text for details).

###  5.3 Foreground star removal

Figure 11: Left: Final calibrated, reddening-corrected,
$I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ CMD of NGC 6822 after removal of extended
background galaxies, bright MW contaminants and faint Galactic M dwarf stars.
Indicated are the main stellar evolutionary sequences: the blue plume (BP),
populated by massive MS and post-MS stars in the hot core helium-burning phase
(ages $\lesssim\,100$ Myr); red supergiants (RSG), with ages from about 20 Myr
to 50 Myr; bright and red AGB stars with ages from $0.1$ to $2$ Gyr; red giant
branch (RGB) stars, with ages older than 1$-$2 Gyr; the red clump (RC) of low-
mass stars in the core-helium burning phase; and the AGB bump (AGBb). The
blue, green, and red polygons, driven by the comparison with stellar
evolutionary models, indicate the selection regions used to create the star
count maps in Sect. 5.5. as indicated in the legend. Middle:
$I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ CMD (same as left panel) with superimposed
PARSEC stellar isochrones for different ages (10 Myr to 10 Gyr) and for two
metallciity values, $Z=0.006$ and $0.001$ (40% and 6% solar, respectively.).
Right: $J_{\scriptscriptstyle\rm E}$ versus $Y_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ CMD. In this diagram, the oxygen-rich and the
carbon-rich AGB stars (O-AGB and C-AGB) appear well separated and define
vertical and horizontal sequences, respectively.

Although the selection cuts described in Sect. 5.1 are effective in removing a
substantial fraction of extended background galaxies, our photometric catalogs
still suffer from major contamination due to foreground Galactic stars. This
is evident in Fig. 9 where we show, as an illustrative example, the final
calibrated, reddening-corrected $I_{\scriptscriptstyle\rm E}$ versus
$I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$ CMD of NGC 6822. In
the diagram, the vertical band of sources delineating a sharp edge at
$I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}\simeq-0.4$ and
extending toward the red up to $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\simeq 1.3$ are main sequence stars from the
Galactic disk, with the vertical feature at $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\simeq 1.3$, $I_{\scriptscriptstyle\rm E}\ga 21$
due to the M dwarf population. In order to remove these contaminants, we adopt
two complementary steps using (i) the constraints provided by Gaia proper
motions (PMs), and (ii) the implementation of additional selections based on
color-color diagrams in the Euclid bands.

In step (i), we cross-correlate our photometric catalogs with the Gaia DR3
release (Gaia Collaboration et al. 2021), adopting a 1″ maximum tolerance in
RA, Dec coordinates. Since the ERO Showcase galaxies have PMs compatible with
zero within the errors (e.g., McConnachie et al. 2021; Bennet et al. 2023),
likely MW members are identified, and then removed from our catalogs, as those
having a measured proper motion PM larger than $3\sigma_{\mathrm{PM}}$, where
$\sigma_{\mathrm{PM}}$ is the PM uncertainty. With this approach, we
effectively remove bright foreground stars with $I_{\scriptscriptstyle\rm
E}\la 20$ from our CMD. The removed sources are indicated as yellow points in
the CMD of Fig. 9. Nonetheless, it is evident that the vertical sequence of MW
contaminants at $I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm
E}\sim-0.4$ and $I_{\scriptscriptstyle\rm E}\gtrsim 20$ is still present in
the CMD.

Next, we implement step (ii) to remove some foreground contaminants fainter
than $I_{\scriptscriptstyle\rm E}\sim 20$, which do not have a counterpart in
Gaia. More specifically, we apply a selection in the $Y_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ plane, as shown in Fig. 10 for NGC 6822. As
illustrated in the top panel of the figure, stars in the MW and in NGC 6822
populate the same locus of the diagram at $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\lesssim 1$, because the colors of giant and
dwarf stars are degenerate for early spectral types. Indeed, stellar
isochrones (Bressan et al. 2012; Marigo et al. 2017) displayed for a wide
range of ages (10 Myr to 10 Gyr) and metallicities of $\lesssim 40\%$
Solar,888The PARSEC isochrones in the Euclid bands were downloaded from
http://stev.oapd.inaf.it/cgi-bin/cmd. compatible with NGC 6822’s chemical
abundance estimates (Venn et al. 2001; Lee et al. 2006; Patrick et al. 2015),
completely overlap at blue colors with the TRILEGAL Galaxy model (Girardi et
al. 2005, 2012), so that a separation between the two components is not
possible in this regime. On the other hand, the colors of dwarf and giant
stars start to diverge at $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\gtrsim 1$, and Galactic M dwarfs depart from
giants in NGC 6822, forming a relatively bluer sequence with $-0.15\lesssim
Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}\lesssim 0.3$ (see
e.g., Majewski et al. 2003; Bentley et al. 2019, for similar classifications).
The selection outlined in the bottom panel of Fig.10 therefore provides a
sensible strategy for the removal of a large number of MW M-dwarf
contaminants. M dwarfs belonging to NGC 6822 are not present in our catalog
because, at the galaxy distance of 0.5 Mpc, they are too faint to be detected.

The selection illustrated in Fig. 10 also enables the removal of a few
residual spurious detections (typically located at the edge of detectors) and
the contribution from compact red galaxies that survived the initial cuts
based on the SourceExtractor parameters in Sect. 5.1; these sources have IR
colors typically redder than Galactic M dwarfs (see, e.g., Fig. 2 of Bell et
al. 2019) and form a separate sequence with $Y_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ colors intermediate between those defined by
Galactic M dwarfs and AGB stars in NGC 6822. A visual inspection of these
sources in the VIS image confirms that they are compact background galaxies.

After removal of MW contaminants, we are left with 233 900, 199 260, 65 296,
and 16 928 sources in the $I_{\scriptscriptstyle\rm
E}$–$Y_{\scriptscriptstyle\rm E}$–$J_{\scriptscriptstyle\rm
E}$–$H_{\scriptscriptstyle\rm E}$ matched catalogs of NGC 6822, IC 10, NGC
2403, and Holmberg II, respectively; and with 120 747 and 112 872 sources,
respectively, in the $I_{\scriptscriptstyle\rm E}$–$J_{\scriptscriptstyle\rm
E}$–$H_{\scriptscriptstyle\rm E}$ matched catalogs of IC 342 and NGC 6744. The
surviving stars after removal of these contaminants are typically 56$-$70% of
the original sample. The exception is IC 342, where the fraction drops to 38%
due to the high foreground star contamination for this low-Galactic latitude
galaxy, coupled with its relatively large distance (see Table 1), which
hampers the detection of its resolved stellar population.

###  5.4 Identifying individual stellar populations

As an illustrative example, we show in Fig. 11 the final
$I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ and $J_{\scriptscriptstyle\rm E}$ versus
$Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$ CMDs of NGC 6822.
These diagrams present a dramatic improvement when compared to the CMD of Fig.
9, since the removal of foreground and background contaminants unveils the
presence of well-defined stellar evolutionary sequences within NGC 6822, which
is indicated in the left panel of Fig. 11: a blue plume (BP) at $-2\la
I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}\la-1$, populated by
massive main sequence (MS) stars and post-MS stars in the hot core helium-
burning phase, with ages $\la$100 Myr; a vertical sequence of red supergiants
(RSG) at $I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}\simeq 1$,
$17.5\la I_{\scriptscriptstyle\rm E}\la 19.5$, with ages from about 20 Myr to
50 Myr; bright and red ($1.2\la I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\la 5$) AGB stars with ages from about 0.1 to 2
Gyr; and red giant branch (RGB) stars with $0\la I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\la 1.5$, $I_{\scriptscriptstyle\rm E}\gtrsim
20$ and ages older than 1–2 Gyr (and potentially as old as $\sim 13$ Gyr).
Also visible at $-0.4\la I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm
E}\la 0.6$, $I_{\scriptscriptstyle\rm E}\ga 23.5$, towards our detection
limit, is the red clump (RC) of low-mass stars in the core-helium burning
phase, with ages $>$1–2 Gyr. At $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}\simeq 0.3$, $I_{\scriptscriptstyle\rm E}\simeq
22.7$ we detect the AGB bump (AGBb).

Figure 12: Maps of star counts of two Showcase galaxies divided into
individual stellar populations as described in the text: IC 10 (left panel);
and IC 342 (right). Young stars are shown as blue points, AGB stars as green,
and evolved RGB stars as red. More details are given in the text. The star-
counts maps for Holmberg II, NGC 2403, and NGC 6744 are given in Appendix D,
while those for NGC 6822 are shown in Fig. 13. In IC 10 (left panel), young
stars are clearly more concentrated than the older ones, and in IC 342
(right), the young stars clearly delineate the spiral arms out to large
galactocentric radii.

A direct comparison between the observed CMD and the predictions of stellar
models is presented in the middle panel of Fig. 11, where we overplot the
PARSEC stellar isochrones (Bressan et al. 2012; Marigo et al. 2017) in the
Euclid bands for stellar ages in the range 10 Myr$-$10 Gyr; isochrones younger
than $\sim$1 Gyr are displayed for a $Z=0.006$ metallicity (about 30% Solar),
compatible with estimates from H ii regions or young supergiants in NGC 6822
(Venn et al. 2001; Lee et al. 2006; Patrick et al. 2015), while a lower
metallicity of $Z=0.001$ is adopted for older populations. The models were
shifted by applying a distance modulus of $(m-M)_{0}=23.54$ from Fusco et al.
(2012), corresponding to a distance of 510 kpc. This distance is compatible
with the observed RGB tip (TRGB) at $I_{\scriptscriptstyle\rm E}\simeq 20.2$;
indeed, a recent calibration of the TRGB in the Euclid bands based on Gaia-DR3
synthetic photometry predicts an absolute value of
$M_{I_{\scriptscriptstyle\rm E},\mathrm{TRGB}}=-3.3$ (Bellazzini & Pascale,
A&A submitted) that translates into a distance modulus of $23.5$ in
$I_{\scriptscriptstyle\rm E}$, consistent with the distance from Fusco et al.
(2012), but somewhat larger than the 470-kpc distance found by Weisz et al.
(2014).

The right panel in Fig. 11 presents the $J_{\scriptscriptstyle\rm E}$ versus
$Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$ CMD of NGC 6822. In
this CMD, the same stellar evolutionary sequences described for the
$I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ CMD can be easily identified, with the
exception of the less evident RC and AGBb features. On the other hand, there
is a clearer separation between O-rich versus C-rich AGB stars, with the
former delineating an almost vertical sequence with colors $0.35\la
Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}\la 0.55$, and the
latter forming a horizontal feature at $17.9\la J_{\scriptscriptstyle\rm E}\la
18.5$ (see also Nally et al. 2023, for a similar classification based on JWST
data).

Figure 13: Star-count maps obtained as for Fig. 12, but for the closest
Showcase galaxy, NGC 6822 (left panel), and with H i contours overlaid on the
maps (right). H i data are taken from de Blok & Walter (2000); contours are at
2$\sigma$, 4$\sigma$, 7$\sigma$, 10$\sigma$, and 20$\sigma$. The young stars
in NGC 6822 are clearly aligned with the atomic gas, as discussed in the text.

###  5.5 Star-count maps

The features outlined by the polygons in the left panel of Fig. 11 were used
to select stellar populations for different age intervals in the six Showcase
galaxies. These selections were slightly adapted to account for the different
depths sampled, depending on the galaxies’ distances. The age selection thus
enabled the construction of star count maps in different age intervals.

The final maps were smoothed by convolving with a Gaussian kernel the two-
dimensional histograms. Subtraction, in a statistical sense, of foreground
stars or background objects that do not belong to the galaxies was performed
by removing the density of counts computed in regions at large galactocentric
distance, where it is reasonable to assume a negligible presence of the
intrinsic stellar populations from the galaxy. However, this may lead to an
over subtraction of the background in the case of NGC 6822, for which Zhang et
al. (2021) demonstrated that the stellar component extends at faint levels to
beyond the Euclid FoV. The star counts within these regions were calculated,
together with their standard deviation, $\sigma_{\mathrm{bck}}$. The final
maps were constructed by only considering the star counts that exceeded
$\sigma_{\mathrm{bck}}$ by a given signal-to-noise: S/N = 5 for young stars;
and S/N = 3 for RGB and AGB stellar populations, in order to better highlight
low surface brightness structures in the old stellar component.

The stellar populations in the Showcase galaxies will be examined in detail in
future papers, with a careful analysis of completeness limits, local
extinction corrections, and galaxy membership. Here, we present the results of
the preliminary analysis described above. Figure 12 shows smoothed maps of the
star counts for IC 10 and IC 342, while NGC 6822 is presented in Fig. 13. The
remaining maps can be found in Appendix D; we have obtained star counts with
Euclid even for NGC 6744, which has the largest distance in the Showcase
sample (9 Mpc), although there we mostly detect young stars, AGB stars, and
blends of bright RGB stars.

The maps of the giant spirals, IC 342 and NGC 6744, show that young stars
follow closely the spiral structure well into the outer disk, exemplifying the
notion that spiral arms tend to be the sites of recent star formation (e.g.,
Gerola & Seiden 1978; Roberts & Hausman 1984; Wada et al. 2011). Similar
behavior is also seen in M 33, a flocculent spiral (Lazzarini et al. 2022), M
81 (Williams et al. 2009a; Okamoto et al. 2015), and NGC 6946 (Tran et al.
2023). The AGBs in IC 342 also follow the spiral arms, but tend to be more
broadly distributed, possibly implying the lack of a systematic time delay in
the SFH across the arm, similar to the case of M 81 (e.g., Choi et al. 2015).

Conversely, rather than tracing the flocculent spiral structure, the young
stars in NGC 2403 (see Appendix D) are more uniformly distributed across the
disk (see also Barker et al. 2012). This would imply that the young stellar
disk in NGC 2403 has been relatively undisturbed out to a galactocentric
radius $\ga 10$ kpc, similar to its morphological twin, NGC 300 (e.g., Hillis
et al. 2016; Jang et al. 2020b).

Figures 12 and 13 show that in the dwarf galaxies, IC 10 and NGC 6822, the AGB
stars are more centrally concentrated than the RGBs, a common (e.g., Gerbrandt
et al. 2015), but not inevitable (e.g., Bernard et al. 2012), feature in dwarf
irregular galaxies. It is more difficult to characterize the stellar
populations in IC 10 than the other galaxies in the Showcase, because of large
foreground extinction and contamination by foreground stars (e.g., Massey et
al. 2007). We find that the stellar distribution in IC 10 is quite extended in
roughly a circular morphology (see also Fig. 4), consistent with Gerbrandt et
al. (2015). The young-star counts are even more centrally concentrated than
the AGB stars, with the AGB stars possibly showing possibly showing more of a
flattened distribution in the central regions. It is interesting to speculate
that this feature could be a signature of a past star-formation event.
According to Weisz et al. (2014), in IC 10, like other dIrr galaxies, the
majority have stars have formed over the last 2–3 Gyr; some of these are most
likely the progenitors of the AGB population in IC 10 (see also Dell’Agli et
al. 2018). Maps of the atomic gas (see Fig. 4) suggest that IC 10 has
undergone an interaction in the past, or is currently accreting gas (e.g.,
Shostak & Skillman 1989; Nidever et al. 2013; Ashley et al. 2014; Namumba et
al. 2019).

Figure 14: Euclid RGB images of the four previously known dwarf satellites
from Carlsten et al. (2022) that fall in the field of view of the Euclid image
of NGC 6744. Red is given by $H_{\scriptscriptstyle\rm E}$, green by
$Y_{\scriptscriptstyle\rm E}$, and blue by $I_{\scriptscriptstyle\rm E}$. The
sizes of the images are 250″, 150″, 120″, and 120″ on a side, from left to
right; north is up, east to the left. With the exception of NGC 6744A, a well-
known dwarf satellite lying along spiral arms to the northwest of the nucleus,
name designations are from Carlsten et al. (2022). In the cut-out of
dw1906m6357 (third panel from the left), there are also two blue circular
structures that are dichroic ghost artefacts (see also Fig. 1).

The configuration and orientation of the RGB and AGB populations in NGC 6822
shown in Fig. 13 agree with previous maps (e.g., Demers et al. 2006; Sibbons
et al. 2012; Tantalo et al. 2022). In NGC 6822, the young stars are oriented
roughly along the H i emission, as illustrated by the overlay of H i in the
right panel of Fig. 13. Young stars are found where the H i has higher column
density, but are also present in the H i cavities, such as the ‘hole’ toward
the southeast of the nucleus. This orientation of the young population was
also found previously (e.g., Komiyama et al. 2003; de Blok & Walter 2003;
Zhang et al. 2021), implying that high H i column density may foster star
formation. However, NGC 6822 is kinematically complex, with a potentially
counter-rotating component both in the gas and the stars (e.g., de Blok &
Walter 2006; Belland et al. 2020), so the connection of the H i with star
formation may also be influenced by kinematics. Figure 12 shows that the
combined stellar morphology produces an ‘X’-like configuration of the overall
stellar content, with the young stars oriented along a NW-SE direction, like
the H i, and the older RGBs elongated along a NE-SW direction; such a
configuration is consistent with that found in previous studies (e.g.,
Komiyama et al. 2003; de Blok & Walter 2003; Zhang et al. 2021). There is
still debate about whether the unusual properties of NGC 6822 have been caused
by a prior merger or stellar feedback (e.g., de Blok & Walter 2000; Demers et
al. 2006; Cannon et al. 2012; Belland et al. 2020; Zhang et al. 2021), but the
case of NGC 6822 illustrates the potential of Euclid to contribute to this
debate. In summary, Euclid will be a powerful tool for further constraining
the past history of IC 10, NGC 6822, and other dwarf galaxies that will be
observed during its lifetime, as well as assessing the SFH of more massive
disk galaxies and the origin and longevity of spiral arms.

##  6 Dwarf satellites around NGC 6744

The unprecedented combination of low surface brightness sensitivity, high
spatial resolution with a pristine PSF, and wide-area coverage of Euclid
enables the detection and characterization of the low surface brightness dwarf
satellites around their host galaxies, as well as the simultaneous study of
their nuclear star clusters and globular cluster systems. To demonstrate the
capability of Euclid to investigate the satellite systems of nearby galaxies,
we visually identified the dwarf galaxies in the Euclid Showcase fields. Here,
we present some highlights for NGC 6744.

###  6.1 Known dwarf satellites of NGC 6744

It is common to find ensembles of dwarf satellites around nearby galaxies
(e.g., Karachentsev et al. 2014). The dwarf satellite system of the host
galaxy NGC 6744 was explored in the context of the ELVES (Exploration of Local
VolumE Satellites) survey by Carlsten et al. (2022), which confirmed 338
satellites with absolute magnitude $M_{V}<-9$ mag and central surface
brightness $\mu_{0,V}<26.5$ mag arcsec-2 in the vicinity (the majority within
$300$ kpc) of 30 host galaxies in the local volume ($D<12$ Mpc). In
particular, the galaxy NGC 6744 was found to have 15 dwarf satellite
candidates. Of these, five were confirmed via SBF measurements (Carlsten et
al. 2019) or other methods, four were rejected via SBF, and six remained
unconfirmed.

###  6.2 Visual identification of new satellites

In the ERO Showcase field of NGC 6744, we first identified the dwarf
candidates using a combination of the high-resolution VIS image and the lower
resolution (by a factor of 3) VIS+NISP color image. Jafar, an on-line
visualization and annotation tool that makes use of the CDS Aladin lite
facility,999https://aladin.cds.unistra.fr/AladinLite/ was used for identifying
and labelling the dwarfs (see Sola et al. 2022). The use of the color image
was crucial as artefacts of the optical system, the so-called ‘optical
ghosts’, appear as faint small round regions in the VIS image and look very
similar to dwarf galaxies. However, since they are more prominent in the VIS
image than in NISP, they have a very distinctive fuzzy blue color in the
image, unlike the real dwarfs (see Fig. 14).

Of the five confirmed dwarfs of Carlsten et al. (2022), only four fall in the
ERO field of view and thus are also found in our Euclid NGC 6744 dwarf
catalogue, as shown as RGB images in Fig. 14. The second galaxy from the left
is close to the edge of the image, resulting in slightly more artefacts in
NISP.

The capability of Euclid to detect and characterize new populations of dwarf
(satellite) galaxies is highlighted by the detection of a new dwarf satellite
candidate in this ERO field, shown in Fig. 15. The identification of a
previously undiscovered companion was unexpected, since NGC 6744 is a nearby
spiral whose dwarf satellite system has been well studied. The new candidate
galaxy is designated as EDwC1 (Euclid Dwarf galaxy Candidate, number 1), and
located at $\alpha\,=\,$$None$, $\delta\,=\,$$None$ (J2000). EDwC1 is a
nucleated dwarf elliptical with an absolute $I_{\scriptscriptstyle\rm E}$-band
magnitude of $-12.2$, assuming a distance of 8.8 Mpc, with an effective radius
of 0.4 kpc and a surface brightness within one effective radius of 24.1 mag
arcsec-2, placing it clearly within the scaling relations of the classical
dwarf regime. It is located at the end of a spiral arm and therefore has
avoided past detection, most likely because of the high stellar density in
this region. However, the combination of low surface brightness sensitivity
and high spatial resolution of Euclid allows us to easily detect such
galaxies, even in crowded regions.

Figure 15: Newly discovered dwarf satellite of NGC 6744; the image on the left
is 50″$\times$50″. The larger 12′ $\times$ 12′ image on the right shows its
location near a dense stellar region that belongs to one of the spiral arms of
the galaxy. The images are oriented with north up, and east to the left.

###  6.3 Resolved stellar populations of dwarf satellites

Figure 16: Comparison of the zoomed-in images of one of the known satellites
(left panel, dw1906m6357) shown in Fig. 14 and a galaxy (dw1912m6351, right
panel) identified as a background object based on surface brightness
fluctuation measurements by Carlsten et al. (2022). The sharp PSF of Euclid
allows us to clearly see that the stellar population is resolved in the image
on the left (satellite), but not in the image on the right (background
galaxy). The images are 40″ on a side, with north up, and east to the left.

We compare the visual appearance of the images of a known satellite,
dw1906m6357 (see Fig. 14, Carlsten et al. 2022), and one of the galaxies
identified by Carlsten et al. (2022) to be a background contaminant,
dw1912m6351. An example of a zoomed-in image of dw1906m6357 is shown in the
left panel of Fig. 16, compared with dw1912m6351 (right panel), identified as
a background object based on surface brightness fluctuation measurements. The
background object is shown at the same zoomed-in scale, but is characterized
by unresolved stellar light. This illustrates the capability of Euclid to
identify clearly satellites of massive galaxies at the distance of NGC 6744.
As can be seen in Fig. 15, the stellar population of the new dwarf candidate
is also resolved, suggesting that the new dwarf is indeed a satellite of NGC
6744.

##  7 Extragalactic globular cluster candidates in NGC 2403

The investigation of EGCs with Euclid will revolutionize our understanding of
their properties, and the constraints they impose on hierarchical galaxy
formation. Here we present preliminary results for the EGCs around NGC 2403,
while the GC and star-cluster populations of other Showcase galaxies will be
discussed in future papers (Howell et al. 2024, in prep; Larsen et al. 2024 in
prep).

###  7.1 Known clusters and cluster candidates

The first discussion of star clusters in NGC 2403 dates back to Tammann &
Sandage (1968), who presented a list of four candidates that they had
identified on photographic plates from the Hale 200-inch telescope. They noted
that one of their candidates, C4, ‘could well be a globular cluster such as
$\omega$ Cen or 47 Tuc’, while C1–C3 had blue colors resembling those of young
star clusters in the Milky Way. A fifth object, C5, was associated with an H
ii region. The current list of spectroscopically confirmed old ($>$ several
Gyr) GCs in NGC 2403 consists of seven objects: C4, D6, F1, F16, F46, JD1, and
JC15 (Forbes et al. 2022; Larsen et al. 2022). Objects with IDs starting with
a ‘C’ are from the original list by Tammann & Sandage (1968), with a ‘D’
referring to candidates identified by Davidge (2007), and ‘F’ to Battistini et
al. (1984), while clusters JD1 and JC15 were identified by Forbes et al.
(2022).

The top panel in Fig. 17 shows $5\arcsec\times 5\arcsec$ cut-outs from the
Euclid VIS image around the seven confirmed NGC 2403 GCs. The cut-outs show
that all of these clusters are resolved into individual stars in their outer
parts, demonstrating Euclid’s potential for revealing additional candidates.

Known GCs:
Known young clusters / HII regions:
Objects identified as non-clusters:

Figure 17: Euclid VIS images of known GCs in NGC 2403 (top), young clusters
(middle), and non-clusters (bottom). Each image shows a $5\arcsec\times
5\arcsec$ cut-out around each object. North is up, and east to the left in all
images.

A number of other objects have been discussed as potential GCs in the
literature. The middle panel in Fig. 17 shows the four bluer objects from
Tammann & Sandage (1968). The spectra of C1 and C3 exhibit strong Balmer
absorption lines, confirming these objects as young clusters, with ages of a
few hundred Myr (Battistini et al. 1984; Forbes et al. 2022), while Larsen &
Richtler (1998) find an age of about 250 Myr for C2 based on its $UBV$ colors.
By comparing the images of these young clusters with those of the old GCs, it
is evident that morphology alone is not sufficient to identify old GCs as
such. The bottom group of cut-outs in Fig. 17 shows various candidates that
clearly are not stellar clusters. The spectra obtained by Forbes et al. (2022)
already revealed D2 to be a foreground star. The Euclid VIS image shows that
this source (as well as D3) is actually composed of two stars separated by
less than $1\arcsec$, which explains the non-stellar appearance in the ground-
based images from Davidge (2007). The VIS image also shows that D1 is a single
star, while D4 is a background galaxy. None of the additional non-confirmed GC
candidates from Battistini et al. (1984) are stellar clusters. F47 has a non-
zero parallax of $0\aas@@fstack{\prime\prime}88\pm
0\aas@@fstack{\prime\prime}12$ according to Gaia DR3, which demonstrates that
it is a Milky Way foreground star, while the remaining objects are background
galaxies. All coordinates listed in this paper are based on the Euclid VIS
astrometry.101010There are notable discrepancies for many of their candidates
between the coordinates listed by Battistini et al. (1984) and the locations
given on their finding chart.

###  7.2 Searching for new clusters

Having established that the VIS images allow star clusters in NGC 2403 to be
identified based on their resolution into individual stars, we carried out a
search for additional cluster candidates. While we expected clusters to be
identifiable from a careful, visual inspection of the images, the sheer size
of the Euclid VIS image ($36\,000\,\mathrm{pixels}\times 36\,000$
pixels)111111The original VIS detector has $6\times 6$ chips with $4000^{2}$
pixels each, but the ROS dithers and the resulting resampled stacks increase
the size of these images from the original $24\,000\times 24\,000$ pixels.
made it necessary to first apply a preselection to reduce the number of
candidate sources that were then subjected to visual inspection. To this end,
we first generated a source catalogue by running SourceExtractor on the VIS
images with relatively conservative extraction settings: DETECT_MINAREA=6 and
DETECT_THRESH=8, meaning that a source detection requires six connected
pixels, each with a signal of at least 8$\sigma$ above the background noise.
This produced an initial catalogue of 392 099 sources. We also ran
SourceExtractor on the NISP images, using the $Y_{\scriptscriptstyle\rm
E}$-band data for source detection while carrying out photometry on all three
NISP images. The magnitudes were measured within circular apertures with
diameters of 20 pixels on the VIS frame and 6.7 pixels on the NISP frames (in
both cases corresponding to an aperture radius of $1\arcsec$), as well as in
Kron-like (AUTO) apertures.

According to Cuillandre et al. (2024), the encircled energy fractions in the
$I_{\scriptscriptstyle\rm E}$ and $H_{\scriptscriptstyle\rm E}$ filters are
$0.936$ and $0.883$ for a point source measured in a 1″ aperture,
corresponding to a aperture color correction of
$\Delta(I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E})\,=\,0.06$.
While the corrections may differ for more extended sources, we assume that a
similar correction is applicable to the colors of the cluster (candidates) in
NGC 2403. We verified for two clusters, D6 and F1 (which are relatively
isolated), that similar color corrections are indeed obtained. Specifically,
we found a mean correction of 0.05 from 1″ to 8″ for these two clusters,
essentially the same value reported by Cuillandre et al. (2024) for point
sources.

Next, we used the ISHAPE software (Larsen 1999) to measure PSF-corrected sizes
for all sources brighter than $I_{\scriptscriptstyle\rm
E}(\texttt{AUTO})\,=\,22$ mag. ISHAPE requires a PSF subsampled by a factor of
10 with respect to the pixel size of the VIS images, which was produced with
the PSF task in the IRAF version of DAOPHOT (Stetson 1987, 1994) from about
100 stars. ISHAPE then measures the sizes by convolving the PSF with King
(1962) models with a concentration parameter $c=r_{\rm t}/r_{\rm c}=30$ (for
tidal- and core radii $r_{\rm t}$ and $r_{\rm c}$) until the best fit was
obtained for each source. A list of cluster candidates to be inspected
visually was then produced by applying the following selection criteria.

  * •

Magnitude: $17<I_{\scriptscriptstyle\rm E}<21.5$.

  * •

Size: $\mathrm{FWHM}>[0.7-(I_{\scriptscriptstyle\rm E}-17)/10]$ pixels (for
$I_{\scriptscriptstyle\rm E}<19$) and $\mathrm{FWHM}>0.5$ pixels for
$19<I_{\scriptscriptstyle\rm E}<21.5$. Here the FWHM is the intrinsic size of
the object (namely, corrected for the PSF, so that a point source should have
FWHM$\approx$0).

  * •

Color: $I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}<0.9$ (1″), or
equivalently, $I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}<0.96$
(infinite aperture).

At the distance of NGC 2403, the size cut of $\mathrm{FWHM}\,=\,0.5$ VIS
pixels corresponds to a linear $\mathrm{FWHM}\,=\,0.78$ pc or a half-light
radius of $r_{\rm h}\,=\,1.1$ pc for the adopted King models. We found this
cut to effectively eliminate the vast majority of individual stars, while
still comfortably allowing the inclusion of GCs that have typical half-light
radii $\ga 3$ pc (Harris 1996). The magnitude-dependent size cut for
$I_{\scriptscriptstyle\rm E}<19$ accounts for the fact that individual stars
start saturating in the VIS images above this limit, and thus no longer appear
point-like to ISHAPE. The magnitude cuts take into account that the known GCs
are all fainter than $I_{\scriptscriptstyle\rm E}$ = 17, as can be seen in
Fig. 19, and that the ratio of contaminants to GC candidates becomes
unmanageable at $I_{\scriptscriptstyle\rm E}$ $>$ 21.5. The color cut includes
all of the known GCs in NGC 2403, but excludes many background sources with
redder colors.

Figure 18: New GC candidates identified in the Euclid VIS images. Each stamp
image shows a $5\arcsec\times 5\arcsec$ cut-out around each object. North is
up, and east to the left in all images.

The preselection described above left 1227 objects to be visually inspected.
The inspection was done on the Euclid VIS image using the SAOImage DS9 tool
with the preselected sources marked. In this paper we restrict the discussion
to candidates located more than $7\arcmin$ from the center (taken from NED) of
NGC 2403 (about 6.5 kpc in projection), since the higher proportion of younger
objects and increased crowding in the inner regions of the galaxy require a
more comprehensive analysis that is deferred to a follow-up paper. Outside the
$7\arcmin$ radius a total of 866 objects fulfill the selection criteria
outlined above. Based on visual inspection, most of these (781) were found to
be background galaxies, while a smaller number of objects were H ii regions,
individual stars or young clusters in crowded regions of the NGC 2403 outer
disk. Nine objects were identified as probable star-cluster candidates based
on their morphological appearance and are labeled here as ESCC$n$ (Euclid Star
Cluster Candidate $n$). One of these (ESCC9) is fainter than the
$I_{\scriptscriptstyle\rm E}\,=\,21.5$ magnitude cut, but was noticed during
the inspection of the images and added back to the list manually. It is quite
possible that other candidates fainter than $I_{\scriptscriptstyle\rm
E}\,=\,21.5$ are present in the image, but have been missed.

Cut-outs of the nine new cluster candidates are shown in Fig. 18, and Table 2
lists the coordinates and photometry for all of the sources discussed in this
paper. For $I_{\scriptscriptstyle\rm E}$ we give both the AUTO magnitudes and
the magnitudes within an $r\,=\,1\arcsec$ circular aperture, while only the
$r=1\arcsec$ magnitudes are given for the NISP bands. In most cases, the AUTO
magnitudes capture a larger fraction of the total light, while we use the
fixed-aperture measurements to define colors.

Figure 19: Color-magnitude diagram for known young and old clusters in NGC
2403 and our newly identified cluster candidates.

A CMD of the previously known and new cluster candidates is shown in Fig. 19.
For reference we also include the literature candidates identified as non-
clusters. In this figure, we have corrected the $I_{\scriptscriptstyle\rm
E}-H_{\scriptscriptstyle\rm E}$ colors by 0.06 to account for the aperture
corrections from 1″ to infinity, as described above. We first note that most
of the new cluster candidates have colors similar to the already known GCs,
spanning the range $0<I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm
E}<0.9$, and we tentatively identify them as GC candidates. The younger
clusters (C1, C3, and C5) are generally bluer than the old GCs (C2 was not
detected by SourceExtractor in the NISP images), while the background galaxies
tend to be redder although there is some overlap in color with the GCs. One of
our new candidates, ESCC4, has blue colors similar to those of the known young
clusters, suggesting that this cluster too may be relatively young.

Figure 20: Euclid VIS image of NGC 2403 with previously known GCs (magenta,
see also Fig. 17), new GC candidates (red), and the new young cluster
candidate ESCC4 (blue) marked. The dashed circle indicates the inner
$7\arcmin$ limit of our search, beyond which we focus our discussion in this
paper. North is up, and east to the left.

The turn-over of the GC luminosity function (GCLF) is expected at
$M_{V}\approx-7.5$ (Rejkuba 2012). From simple stellar population models based
on PARSEC isochrones (Marigo et al. 2017), the $V-I_{\scriptscriptstyle\rm E}$
color of an old, moderately metal-poor ($\mathrm{[Fe/H]}\approx-1.5$) GC is
about $V-I_{\scriptscriptstyle\rm E}\approx 0.5$; hence we expect the GCLF
turn-over at $M_{I_{\scriptscriptstyle\rm E}}\approx-8.0$ or
$I_{\scriptscriptstyle\rm E}\approx 19.6$ for the distance and $A_{V}$ value
of NGC 2403. It is evident, then, that the confirmed GC sample from the
literature only probes the brighter part of the GCLF, to about 1 mag brighter
than the GCLF turn-over, and we should expect a number of fainter GCs to be
present in NGC 2403. Our new candidates are all fainter than those in the
existing list, so that it may be assumed that the census of GCs in NGC 2403
was already fairly complete down to the $I_{\scriptscriptstyle\rm E}\approx
18.5$ limit of the previous studies, at least for galactocentric radii
$>7\arcmin$. With Euclid we can now probe GCs that are significantly fainter
than the GCLF turn-over. A detailed discussion of the NGC 2403 GCLF is
complicated by differences in the spatial distributions of the samples from
the literature compared with our new candidates, with four of the known GCs
(C4, F46, JD1, JC15) lying within the $7\arcmin$ limit imposed here.
Nevertheless, defining a combined sample of confirmed GCs located outside
$7\arcmin$ (D6, F1, F16) and our new candidates (excluding ESCC4), the mean
apparent magnitude is $I_{\scriptscriptstyle\rm E}\,=\,19.7\,\pm\,0.3$ with a
dispersion $\sigma_{I_{\scriptscriptstyle\rm E}}\,=\,1.06\pm 0.17$, which is
very close to the expected GCLF turn-over magnitude and dispersion.

The positions of the known and new GC candidates are indicated on the VIS
image of NGC 2403 in Fig. 20. The two outermost new candidates, ESCC1 and
ESCC5, are located at projected galactocentric distances of
$r_{\mathrm{GC}}=15\aas@@fstack{\prime}6$ (14.5 kpc) and
$r_{\mathrm{GC}}=19\aas@@fstack{\prime}7$ (18.3 kpc), respectively, beyond the
most distant cluster previously known (D6 at
$r_{\mathrm{GC}}=14\aas@@fstack{\prime}3$). This illustrates the power of the
combination of a wide field and excellent image quality provided by Euclid.

Table 2: Star cluster candidates in NGC 2403

ID | Note | RA | Dec |  $I_{\scriptscriptstyle\rm E}$(AUTO) |  $I_{\scriptscriptstyle\rm E}$($r=1^{\prime\prime}$) |  $Y_{\scriptscriptstyle\rm E}$($r=1^{\prime\prime}$) |  $J_{\scriptscriptstyle\rm E}$($r=1^{\prime\prime}$) |  $H_{\scriptscriptstyle\rm E}$($r=1^{\prime\prime}$)
---|---|---|---|---|---|---|---|---
C4=D5 | Known GC | $None$ | $None$ | $17.53$ | $17.66$ | $17.28$ | $17.30$ | $17.34$
D6 | Known GC | $None$ | $None$ | $18.56$ | $18.67$ | $18.24$ | $18.23$ | $18.26$
F1 | Known GC | $None$ | $None$ | $18.42$ | $18.63$ | $18.29$ | $18.30$ | $18.36$
F16 | Known GC | $None$ | $None$ | $18.61$ | $18.70$ | $18.25$ | $18.22$ | $18.21$
F46 | Known GC | $None$ | $None$ | $17.56$ | $17.68$ | $17.34$ | $17.39$ | $17.46$
JD1 | Known GC | $None$ | $None$ | $18.36$ | $18.43$ | $18.11$ | $18.14$ | $18.21$
JC15 | Known GC | $None$ | $None$ | $18.63$ | $18.71$ | $18.14$ | $18.09$ | $18.11$
C1 | Young | $None$ | $None$ | $18.67$ | $18.93$ | $18.82$ | $18.94$ | $19.05$
C2 | Young | $None$ | $None$ | $18.12$ | $18.36$ | … | … | …
C3 | Young | $None$ | $None$ | $18.73$ | $19.09$ | $19.12$ | $19.32$ | $19.52$
C5 | Young | $None$ | $None$ | $16.84$ | $17.14$ | $17.31$ | $17.76$ | $18.13$
D1 | Star | $None$ | $None$ | $21.06$ | $20.97$ | $19.68$ | $19.58$ | $19.55$
D2 | Two stars | $None$ | $None$ | $18.34$ | $18.32$ | $17.33$ | $17.42$ | $17.61$
D3 | Two stars | $None$ | $None$ | $19.63$ | $19.57$ | $17.74$ | $17.66$ | $17.68$
D4 | Galaxy | $None$ | $None$ | $19.34$ | $19.87$ | $19.49$ | $19.49$ | $19.41$
F2 | Galaxy | $None$ | $None$ | $17.66$ | $18.65$ | $17.79$ | $17.59$ | $17.38$
F6 | Galaxy | $None$ | $None$ | $17.29$ | $18.17$ | $17.42$ | $17.24$ | $17.02$
F19 | Galaxy | $None$ | $None$ | $19.23$ | $19.63$ | $19.30$ | $19.31$ | $19.22$
F20 | Galaxy | $None$ | $None$ | $17.85$ | $18.62$ | $17.93$ | $17.76$ | $17.58$
F24 | Galaxy | $None$ | $None$ | $18.50$ | $18.94$ | $18.17$ | $18.02$ | $17.84$
F28 | Galaxy | $None$ | $None$ | $17.20$ | $18.00$ | $17.24$ | $17.10$ | $16.92$
F31 | Galaxy | $None$ | $None$ | $17.94$ | $18.64$ | $18.10$ | $17.97$ | $17.80$
F47 | Star | $None$ | $None$ | $18.13$ | $18.10$ | $17.47$ | $17.36$ | $17.28$
ESCC1 | New GC cand. | $None$ | $None$ | $21.06$ | $21.33$ | $20.83$ | $20.83$ | $20.86$
ESCC2 | New GC cand. | $None$ | $None$ | $19.21$ | $19.39$ | $19.02$ | $19.02$ | $19.06$
ESCC3 | New GC cand. | $None$ | $None$ | $20.57$ | $20.76$ | $20.40$ | $20.43$ | $20.52$
ESCC4 | Young cluster cand. | $None$ | $None$ | $21.19$ | $21.18$ | $21.19$ | $21.43$ | $21.62$
ESCC5 | New GC cand. | $None$ | $None$ | $19.70$ | $19.83$ | $19.57$ | $19.65$ | $19.74$
ESCC6 | New GC cand. | $None$ | $None$ | $19.93$ | $19.93$ | $19.53$ | $19.50$ | $19.48$
ESCC7 | New GC cand. | $None$ | $None$ | $19.99$ | $20.29$ | $19.97$ | $20.00$ | $20.08$
ESCC8 | New GC cand. | $None$ | $None$ | $18.93$ | $19.38$ | $19.07$ | $19.09$ | $19.16$
ESCC9 | New GC cand. | $None$ | $None$ | $21.56$ | $21.83$ | $21.05$ | $20.99$ | $21.01$

121212The photometry here has not been corrected for Galactic foreground
extinction. The formal photometric errors are all $\leq 0.01$ mag, but do not
include the uncertainties due to background subtraction, choice of aperture,
and other factors that affect the true uncertainties in the quantities listed.
We estimate total photometric errors of $0.2$–$0.3$ mag once these unknown
contributions to the uncertainties are taken into account.

##  8 Summary and conclusions

We have presented the first-look analysis of Euclid Early Release Observations
with VIS and NISP imaging of the Nearby Galaxy Showcase. Galaxies in the
Showcase range in distance from $0.5$ Mpc (NGC 6822) to 8.8 Mpc (NGC 6744),
and include three dwarf galaxies (Holmberg II, IC 10, and NGC 6822), and three
spirals (IC 342, NGC 2403, and NGC 6744). The galaxies were selected to be
among the apparently largest galaxies on the sky, in order to guarantee their
photogenic nature, but also to enable an in-depth scientific analysis. The
sample is described in Sect. 2.

The surface brightness limits of the VIS and NISP stacked images are
calculated in Appendix A, with a summary given in Sect. 3.1. Confirming
previous estimates based on simulations for VIS, and exceeding previous
expectations for NISP, we find that in 1 ROS, Euclid can probe $1\sigma$
surface brightness depths in 100 arcsec2 regions of $30.5$ AB mag arcsec-2 in
VIS, and $29.2$–$29.4$ AB mag arcsec-2 in NISP.

In Sect. 4, we assessed the properties of the integrated light in the Showcase
galaxies, and presented RGB images in Figs. 1, 3 in the main text, and Figs.
23, 2, 24, and 25 in Appendix B. These composite images illustrate Euclid’s
unique capacity to probe a large FoV, but also to provide exquisite detail on
parsec scales in nearby galaxies.

Sections 4.2 and 4.3 compared high-contrast Euclid $I_{\scriptscriptstyle\rm
E}$ images with representative galaxies having H i and FIR data. The
characteristic blue colors of diffuse cirrus emission combined with
multiwavelength FIR data can disentangle foreground cirrus emission
originating in the MW from potential stellar streams. This will be important
not only for the studies of nearby galaxies, but also for probing the ISM of
the Galaxy. Radial surface brightness and color profiles were discussed in
Sects. 4.4 and 4.5, where we also compared the observed Euclid colors
$I_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$ with stellar
population synthesis models as seen in Fig. 7. This comparison is a validation
of measurements and models and shows that Euclid colors provide a powerful
diagnostic of the age and metallicity of galaxies in the local Universe.
Moreover, Euclid colors have identified extremely blue young nuclear star
clusters in IC 342 and IC 10.

Section 5 gave a detailed analysis of resolved stellar photometry, finding
altogether $1.3\times 10^{6}$ stars in the Showcase galaxy images. After
carefully removing as well as possible foreground stars and background compact
galaxies (see Figs. 9, 10), CMDs for NGC 6822 demonstrate the resulting well-
sampled stellar statistics provided by a single Euclid ROS. By selecting young
stars, AGBs, and RGBs from regions defined within the CMDs as in Fig. 11, we
were able to construct star-count maps that probe the spiral structure, and
the age differentiation across dwarf galaxies. In particular, Fig. 12
demonstrates that young stars clearly trace spiral structure in IC 342, and
Fig. 13 shows that in NGC 6822 the distribution of young stars is perfectly
matched by the morphology of the H i emission.

Ensembles of dwarf galaxy satellites around a parent galaxy are common, and we
have investigated the dwarf galaxy system of NGC 6744 in Sect. 6. Although the
satellites of NGC 6744 have been previously studied, not only do we recover
the four known dwarf satellites within the Euclid FoV, we also identify a
previously unknown dwarf satellite candidate, EDwC1, as shown in Fig. 15. This
new discovery sets the stage for the new dwarf satellite demographics that can
be obtained with Euclid.

In Sect. 7, our analysis of the Euclid imaging of NGC 2403 revealed nine new
star cluster candidates as shown in Fig. 18, eight of them almost certainly
evolved clusters, thus true GCs. This new census more than doubles the number
of known GCs around NGC 2403, and extends the galactocentric radius at which
they have been found out to 18.3 kpc, $40$% further away than previously
identified. Euclid is poised to transform the study of extragalactic GCs in
nearby galaxies.

In conclusion, the ERO Nearby Galaxy Showcase demonstrates the power of Euclid
to probe large areas of sky, but at the same time, with exquisite spatial
scales and sensitivity. This unique combination will revolutionize studies of:
resolved stellar populations and star-formation histories; the extent and
origin of galaxy disks, together with their spiral structure; the demographics
of dwarf satellites; star clusters within and around galaxies; and the
measurement of the ISM via dust extinction and cirrus emission on scales of a
few parsecs. Using data from the EWS and EDS, it will be possible to pursue
not only the core cosmological science that was the main aim of the mission,
but also to examine galaxy populations in the nearby Universe with
unprecedented detail.

###### Acknowledgements.

We wish to acknowledge our colleague Mario Nonino, who recently passed away,
for his important contribution to the Euclid mission. Mario was the
coordinator of the OU-MER pipeline, one of the central organizational units of
the Science Ground Segment, and an important member of the Euclid Local
Universe Science Working Group. We are grateful to Fabian Walter, I-Da Chiang,
and Karin Sandstrom for passing on H i moment maps, and are deeply indebted to
Michele Bellazzini for enlightening discussions. LKH, PD, RS, and CT
acknowledge funding from the Italian INAF Large Grant 12-2022. AMNF is
grateful for support from the UK STFC via grant ST/Y001281/1. JHK and JR
acknowledge grant PID2022-136505NB-I00 funded by
MCIN/AEI/10.13039/501100011033 and EU, ERDF; their work is co-funded by the
European Union, however views and opinions expressed are those of the
author(s) only and do not necessarily reflect those of the European Union.
Neither the European Union nor the granting authority can be held responsible
for them. This work was partly carried out using GNU Astronomy Utilities
(Gnuastro, ascl.net/1801.009) version 0.21.43-3101. Work on Gnuastro has been
funded by the Japanese Ministry of Education, Culture, Sports, Science, and
Technology (MEXT) scholarship and its Grant-in-Aid for Scientific Research
(21244012, 24253003), the European Research Council (ERC) advanced grant
339659-MUSICOS, the Spanish Ministry of Economy and Competitiveness (MINECO,
grant number AYA2016-76219-P), and the NextGenerationEU grant through the
Recovery and Resilience Facility project ICTS-MRR-2021-03-CEFCA. This research
has made use of the NASA/IPAC Extragalactic Database (NED), which is funded by
the National Aeronautics and Space Administration and operated by the
California Institute of Technology. This research has also relied on AutoProf,
a package for galaxy image photometry (Stone et al. 2021), and on Astropy
(http://www.astropy.org), a community-developed core Python package and an
ecosystem of tools and resources for astronomy (Astropy Collaboration et al.
2013, 2018, 2022). This work has made use of the Early Release Observations
(ERO) data from the Euclid mission of the European Space Agency (ESA), 2024,
https://doi.org/10.57780/esa-qmocze3. The Euclid Consortium acknowledges the
European Space Agency and a number of agencies and institutes that have
supported the development of Euclid, in particular the Agenzia Spaziale
Italiana, the Austrian Forschungsförderungsgesellschaft, funded through BMK,
the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches
Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in
Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a
Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de
Ciencia, Innovación y Universidades, the National Aeronautics and Space
Administration, the National Astronomical Observatory of Japan, the
Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the
Research Council of Finland, the Romanian Space Agency, the State Secretariat
for Education, Research, and Innovation (SERI) at the Swiss Space Office
(SSO), and the United Kingdom Space Agency. A complete and detailed list is
available on the Euclid web site (http://www.euclid-ec.org).

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##  Appendix A Details on sky level and estimates of limiting surface
brightness

Table 3: Sky levels and SB limiting magnitudes $\mu_{\mathrm{lim}}$ within 100
arcsec2 areas in empty sky regions

Property | Holmberg II | IC 10 | IC 342 | NGC 2403 | NGC 6744 | NGC 6822
---|---|---|---|---|---|---
$\mu_{I_{\scriptscriptstyle\rm E}}$ sky | 22.62 | 22.29 | 22.42 | 22.66 | 22.36 | 21.74
(1) $\mu_{I_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 30.56 | 30.40 | 30.41 | 30.62 | 30.41 | 30.09
(2) $\mu_{I_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 30.67 | 30.69 | 30.59 | 30.76 | 30.57 | 30.19
(3) $\mu_{I_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 30.61 | 30.63 | 30.52 | 30.63 | 30.47 | 30.04
| 30.49 $\pm$ 0.20b
(mag arcsec-2) | 30.3c
$\mu_{Y_{\scriptscriptstyle\rm E}}$ sky | 22.64 | 22.28 | 22.40 | 22.52 | 22.22 | 21.60
(1) $\mu_{Y_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.51 | 29.50 | 29.39 | 29.47 | 29.35 | 28.77
(2) $\mu_{Y_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.37 | 29.21 | 29.22 | 29.35 | 29.25 | 28.77
(3) $\mu_{Y_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.16 | 29.06 | 29.09 | 29.17 | 29.05 | 28.53
| 29.18 $\pm$ 0.26b
(mag arcsec-2) | 28.7c
$\mu_{J_{\scriptscriptstyle\rm E}}$ sky | 22.68 | 22.39 | 22.50 | 22.56 | 22.26 | 21.67
(1) $\mu_{J_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.71 | 29.32 | 29.59 | 29.66 | 29.51 | 28.97
(2) $\mu_{J_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.54 | 29.52 | 29.48 | 29.56 | 29.45 | 29.00
(3) $\mu_{J_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.32 | 29.21 | 29.28 | 29.36 | 29.25 | 28.77
| 29.36 $\pm$ 0.24b
(mag arcsec-2) | 28.9c
$\mu_{H_{\scriptscriptstyle\rm E}}$ sky | 22.80 | 22.53 | 22.66 | 22.68 | 22.39 | 21.83
(1) $\mu_{H_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.72 | 29.30 | 29.42 | 29.68 | 29.57 | 29.02
(2) $\mu_{H_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.57 | 29.19 | 29.51 | 29.60 | 29.48 | 29.08
(3) $\mu_{H_{\scriptscriptstyle\rm E}}$ 1$\sigma$ SB limit | 29.38 | 29.29 | 29.34 | 29.40 | 29.27 | 28.91
| 29.37 $\pm$ 0.22b
(mag arcsec-2) | 28.9c

a In this and subsequent rows, the numbers in parentheses correspond to the
different approaches: (1) the standard deviation among 100 arcsec2 tiles
following gnuastro/noisechisel; (2) Gaussian fits of the masked sky regions
following Román et al. (2020); and (3) noise in the radial brightness profiles
from AutoProf following Stone et al. (2021).

b Mean and standard deviation of 1$\sigma$ AB magnitude limits averaged over
all galaxies and methods.

c 1$\sigma$ AB magnitude limits taken from Euclid Collaboration: Scaramella et
al. (2022), after having removed the asinh offset.

We estimate the limiting surface brightness $\mu_{\mathrm{lim}}$ in an
equivalent 100 arcsec2 region as a function of the signal standard deviation
$\sigma$ using three different approaches.

  1. (1)

gnuastro/noisechisel (Akhlaghi & Ichikawa 2015; Akhlaghi 2019a, b) was run on
each of the images, with a tile size corresponding to 100 arcsec2. noisechisel
employs a noise-based approach to detect highly extended and diffuse objects
that are deeply embedded within a significant background of noise. It
determines the median $\sigma$ over tiles where there are no detections,
rather only empty sky background. We experimented with various options for
noisechisel and found that, although there was some variation ($\pm\,0.1$
mag), on the whole, results were stable. The median $\sigma$ from
gnuastro/mkcatalog was converted to $\mu_{\mathrm{lim}}$ (AB mag arcsec-2, Eq.
1), and reported as ‘(1)’ in Table 3.

  2. (2)

Following Román et al. (2020), we fit a Gaussian to the distribution of the
masked signal with sky background only; the images were masked with the
noisechisel detection masks computed as above [approach (1)]. The best-fit
Gaussian $\sigma$ for all galaxies are given in Table 3 as ‘(2)’, converted to
limiting AB magnitudes as above. Thse fits themselves are shown in Fig. 21.
The sky levels $\mu_{\mathrm{sky}}$ in Table 3 are calculated from the best-
fit central values from the Gaussian fits for each band.

  3. (3)

AutoProf (Stone et al. 2021) was run on each of the images using 5$\sigma$
clipping to better mask bright sources. In addition to the surface brightness
profiles described in Sect. 4.4, AutoProf of necessity measures the background
signal and its uncertainty $\sigma$. These values are reported in Table 3 as
‘(3)’, and converted to $\mu_{\mathrm{lim}}$ in a 100 arcsec2 region as in Eq.
(1).

Figure 21: Distributions of counts (ADU pixel-1) over the entire masked region
of empty sky for NGC 2403 and and NGC 6822 (top panels); Holmberg II, IC 10
(middle); and IC 342, NGC 6744 (bottom). The data are shown as solid lines,
and the Gaussian best fits as dashed ones. The four bands are given by purple,
blue, green, and red for $I_{\scriptscriptstyle\rm E}$,
$Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$, respectively. The $I_{\scriptscriptstyle\rm E}$
VIS band counts have been multiplied by the ratio of the pixel area ($\times
9$) to be shown together with the NIR bands. In most cases, the data (traced
by a solid curve) are so close to a Gaussian as to be indistinguishable from
the best fit (shown by a dashed curve).

Figure 22: SB limits obtained with the various methodologies plotted against
sky brightness for the four Euclid bands. For the method that does not
directly give sky brightness [Approach (1)], we used the mean of the sky
values from Approaches (2) and (3). There is a correlation of the SB limits
with sky brightness, with brighter sky having brighter limits, and a variation
with methodology, up to $0.3$–$0.4$ mag arcsec-2.

We measure counts $C$ per pixel in images, with intrinsic uncertainty $\sigma$
per pixel, and want to determine the uncertainty of surface brightness
$\mu_{\mathrm{lim}}$ in units of mag arcsec-2 over some spatial scale,
$b^{2}$. The scaling reported in Eq. (1) can be explained as follows,
considering a signal-to-noise of $n$, a linear pixel size $p$ (arcsec pixel-1)
and a region of area $b^{2}$ arcsec2.

  1. (1)

Assuming that the noise $\sigma$ inherent in $C$ is uncorrelated from pixel to
pixel, the noise $\sigma_{b}$ that is obtained in a region of area $b^{2}$
arcsec2 adds in quadrature, resulting in
$\sigma_{b}\,=\,\sigma\,\sqrt{b^{2}/p^{2}}\,=\,\sigma\,b/p$, since
$b^{2}/p^{2}$ is the number of pixels in the region. We then would need to
divide by $b^{2}$ to convert this value into mag arcsec-2, so that

$\displaystyle\mu_{\mathrm{lim}}\,=\,\mu(\sigma_{b})\,=$
$\displaystyle\mathrm{ZP}-2.5\,\log_{10}(n\,\sigma\,b/p)+2.5\,\log_{10}(b^{2})\,$
(2) $\displaystyle\mathrm{mag\,arcsec}^{-2}\ ,$

equivalent to the formulation in Eq. (1). This is also the reasoning followed
in https://www.gnu.org/software/gnuastro/manual/html_node/Surface-brightness-
limit-of-image.html.

  2. (2)

Alternatively, we can first convert the intrinsic per-pixel uncertainty
$\sigma$ to units of mag arcsec-2 considering only the conversion of pixel
size to arcsec2:

$\mu(\sigma)\,=\,\mathrm{ZP}-2.5\,\log_{10}(n\,\sigma)+2.5\,\log_{10}(p^{2})\,\quad\mathrm{mag\,arcsec}^{-2}\
.$ (3)

However, we seek $\sigma_{b}$, the noise that is obtained in a region of area
$b^{2}$ arcsec2, so consider that $\sigma_{b}$ is the error of the mean
$\sigma$ within the region of size $b^{2}$. Thus dividing by the square root
of the number of pixels ($b^{2}/p^{2}$) within the region gives

$\mu_{\mathrm{lim}}\,=\,\mu(\sigma_{b})\,=\,\mu(\sigma)+2.5\,\log_{10}(b/p)\,\quad\mathrm{mag\,arcsec}^{-2}\
,$ (4)

again equivalent to the formulation in Eq. (1).

Results are compared graphically in Fig. 22 where the SB limits
$\mu_{\mathrm{lim}}$ obtained with different methods are plotted against sky
surface brightness. The lack of deviation of the sky value for the individual
galaxies, namely the small horizontal scatter, implies that the overall sky
brightness can be determined quite robustly.

Table 3 and Fig. 22 show that from galaxy to galaxy, there can be up to $0.5$
mag of difference in the derived SB limits, with an excursion that suggests
that the fainter SB limits are associated with fainter sky brightness. A large
portion of the variation in the measured sky brightness is almost certainly
due to the influence of zodiacal light (see e.g., Cuillandre et al. 2024),
since there is no trend with foreground extinction (not shown). For each
Euclid band, we have fit the data in Fig. 22 using a robust-linear method (the
python package statsmodels), shown as a dashed line in each of the panels.
Judging from the fits, over roughly $1$ mag arcsec-2 variation in sky surface
brightness, the noise levels can vary up to $0.5$ mag arcsec-2.

Approach (1) calculates the standard deviation $\sigma$ of the sky within 100
arcsec2 tiles, while in approaches (2) and (3), $\sigma$ is computed across
the entire masked (non-detected) image of the galaxy. Specifically, approach
(3) analyzes the distribution of pixel values in the outer part of the image
surrounding the galaxy. This implies that the first method could measure
small-scale variation, while the last two could essentially capture large-
scale variations across the images. However, this is not completely borne out
by the results in Fig. 22, although in the NISP bands, there is a tendency for
the latter two methods to give brighter limits.

Here and in Sect. 3 we assess the noise level in the stacked data products
used in our analysis, assuming that the pixels are intrinsically uncorrelated
[see Eqs. (1) and (4)]. However, the process of stacking images inherently
creates covariances between pixels; individual pixels in the original frames
are spread out over multiple pixels in the final stacked image. In the
simplest bilinear stacking procedures, each pixel is divided into four pixels
in the final image, although with the more sophisticated stacking in the
$I_{\scriptscriptstyle\rm E}$ data reduction, a Lanczos kernel is used which
spreads the pixel over a 7$\times$7 kernel in the final pixel stack. We can
empirically determine the average noise in pixels by taking the standard
deviation in dark parts of the image; then, we can extract the covariance
between pixels using dark patches of the frame. We find that a typical pixel
in the $I_{\scriptscriptstyle\rm E}$ band has a $10$–$15$% correlation with
its immediate neighboring pixels, and $\la 5$% correlation with pixels two
steps away. For NISP bands ($Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$), combined
with a bi-linear method, the correlation is slightly stronger at $20$–$30$%
for immediate neighbors, and $3$–$8$% correlation for second neighbors. These
correlations are typical of stacked images and simply allow us to better
understand the depth achieved with Euclid. Further description of the
covariance properties in the stacked images can be found in Cuillandre et al.
(2024), which describes the process in more detail.

##  Appendix B Euclid imaging capabilities

The continuation of Figs. 1 and 3 (Sect. 4) is shown here for IC 10, IC 342,
NGC 2403, and NGC 6822.

Figure 23: Same as for Fig. 1, but for IC 10, and, as before, with
$H_{\scriptscriptstyle\rm E}$ green, $Y_{\scriptscriptstyle\rm E}$ red, and
$I_{\scriptscriptstyle\rm E}$ blue. Extinction has been corrected and sky
subtracted as described in the text (Sects. 3.1 and 4.1). In the top left
panel, the full FoV of $0\aas@@fstack{\circ}7\,\times\,0\aas@@fstack{\circ}7$
is shown, while in the bottom one the inner 6′ $\times$ 6 ′ region is
displayed corresponding to the white box in the upper panel. The top right
panel shows the zoomed-in 30″ $\times$ 30″ RGB image of the blue nucleus also
seen in the radial color profiles (Sect. 4.4, App. C, and Fig. 26). The dark
boxes in IC 10 result from an incorrect orientation of the instruments
relative to the roll angle of the satellite during observation (this was the
first galaxy observed within the ERO Showcase).

Figure 24: Same as for Fig. 1, but for NGC 2403.

Figure 25: Same as for Fig. 1, but for NGC 6822.

##  Appendix C Surface brightness profiles of four Showcase galaxies

Here we show surface-brightness profiles of the remaining four galaxies that
are not given in the main text (Sect. 4.4).

Figure 26: Surface brightness profiles extracted by AutoProf, as described in
the text: Holmberg II and IC 10 in the top row; and NGC 2403 and NGC 6744 in
the bottom. The four bands are given by purple, blue, green, and red for
$I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$,
respectively. The $1\sigma$ SB limits from AutoProf in units of mag arcsec-2
are shown as dashed horizontal lines, with colors corresponding to the Euclid
bands. The fluxes have been corrected for foreground extinction (Sect. 4.1) in
order to be consistent with the $I_{\scriptscriptstyle\rm E}$
$-$$H_{\scriptscriptstyle\rm E}$ radial color gradient shown in the middle
panel, and $Y_{\scriptscriptstyle\rm E}$ $-$$H_{\scriptscriptstyle\rm E}$
shown at the bottom. The uncorrected $I_{\scriptscriptstyle\rm E}$ profile is
shown as a dotted (purple) curve in the top panel. The mean
$I_{\scriptscriptstyle\rm E}$ $-$$H_{\scriptscriptstyle\rm E}$ color over
typically a factor of $100$ in radius in the inner galaxy is shown as a
horizontal dashed line in the middle panel.

##  Appendix D Star-count maps of four Showcase galaxies

Here we present the maps of the star counts of the remaining three galaxies
that are not shown in the main text (Sect. 5).

Figure 27: Star-count maps obtained as described in Sect. 5, but for Holmberg
II (top left), NGC 2403 (top right), and the most distant Showcase galaxy, NGC
6744 (bottom).