GC richness, and presence of any nuclei. Based on the histograms of the scores
and a final inspection of the images of each object, we determined the
threshold above which the candidate falls into one of the categories. There
were generally few cases with scores between 2/7 and 5/7, as most of the
histograms were distributed either towards low or high scores or were bimodal
around 0 and 1. We set a threshold of 2 votes out of 7 (${\rm score}=0.286$)
to consider the dwarf candidate as a dE, and the same threshold was used to
classify it as ‘disturbed’, GC-rich, and nucleated (i.e. presence of one or
more nucleus). This threshold was chosen to include as many galaxies with
nuclei, GCs, and signs of tidal disturbances as possible, while still being
confirmed by at least two of the seven contributors.

Figure 5 presents the classification break down of the 1100 dwarf candidates
in our catalogue. A total of 1061 (96%) are classified as dE (dI: 39 or 4%),
581 (53%) are nucleated, 282 (26%) are GC-rich, and 64 (6%) have a disturbed
morphology. Examples of these galaxies are displayed in in Fig. 6, where we
show cutouts of select dwarfs classified as: dE, dI, disturbed morphologies,
nucleated, GC-rich, or a combination of these features.

Table 1: Previous surveys of the Perseus cluster that extend into the dwarf
regime. The second and third columns give the number of catalogue entries that
fall within the Euclid FoV and the number matched sources within $None$,
respectively. Columns (4) – (7) list properties of the surveys: the spatial
coverage, the limiting surface brightness, the primary telescope used for the
survey, and the filters used. The Meusinger et al. (2020) and Wittmann et al.
(2019) samples are further separated into dwarf and non-dwarf members (see
text) for a better comparison.

Reference | $N_{\rm FoV}$ | $N_{\rm matched}$ | Coverage | $\mu_{\rm lim}$ | Telescope | Bands
---|---|---|---|---|---|---
|  |  | [deg2] | [mag arcsec-2] |  |
Meusinger et al. (2020) | 211 | 60 | 10 | … | Alfred-Jenschaa$a$Meusinger et al. (2020) also utilize several auxiliary data sources, including: spectra and $u$, $g$, $r$, $i$, and $z$ imaging from SDSS; $B$,$V$, and $R$ imaging and optical spectra from the CAHA telescope at Calar Alto; NED; WISE; and H$\alpha$ data from the literature.  |  $BR$ 6670aa$a$Meusinger et al. (2020) also utilize several auxiliary data sources, including: spectra and $u$, $g$, $r$, $i$, and $z$ imaging from SDSS; $B$,$V$, and $R$ imaging and optical spectra from the CAHA telescope at Calar Alto; NED; WISE; and H$\alpha$ data from the literature.
dwarf members | 56 | 32 |  |  |  |
Wittmann et al. (2019) | 5339 | 426 | 0.27 | 27 | WHTbb$b$In addition to the WHT imaging, Wittmann et al. (2019) used archival Subaru HSC data in $g$, $r$, and $z$ bands as auxiliary data sets to obtain colours and the $None$ seeing conditions for the morphological classifications. The HSC $g$ band reached a limiting surface brightness of 28.8 mag arcsec-2. | $V$
cluster members | 484 | 389 |  |  |  |
$M_{\rm V}\leq-18$ | 20 | 1 |  |  |  |
$M_{\rm V}>-18$ | 464 | 388 |  |  |  |
non-cluster members | 4855 | 37 |  |  |  |
Wittmann et al. (2017) | 85 | 72 | 0.27 | 27 | WHT | $V$
Conselice et al. (2003) | 53 | 25 | 173 arcmin2 | 24 | WIYN |  $BRU$ cc$c$Only partial $U$ band coverage is available.
Brunzendorf & Meusinger (1999) | 128 | 4 | 10 | 27 | Alfred-Jensch | $B$

222

Figure 7: Map of the colour excess $E(B-V)$ for the dwarf galaxy sample (top)
and the bright galaxy sample (bottom) presented in Cuillandre et al. (2024b).
Figure 8: PSF models with the native pixel scale of $I_{\scriptscriptstyle\rm
E}$, $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$ in the centre of the ERO Perseus images. The
displayed PSF models have a sidelength of $None$ for $I_{\scriptscriptstyle\rm
E}$ and $None$ for $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm
E}$, and $H_{\scriptscriptstyle\rm E}$. The models are displayed on a
logarithmic scale.

##  4  Comparison with previous dwarf catalogues

A number of studies in the literature have attempted to identify membership in
the Perseus cluster, with several studies extending into the dwarf regime
(e.g., Brunzendorf & Meusinger 1999; Conselice et al. 2003; Penny et al. 2011,
2014a; Wittmann et al. 2017, 2019; Meusinger et al. 2020; Gannon et al. 2022).
The methods to determine cluster membership differ; some galaxies in these
catalogues have been confirmed as members with measured distances, while
others are identified as likely members through their morphology and colour.

We first confirmed which galaxies from each source fall within the Euclid ERO
image using Multi-Order Coverage (MOC) maps and the Aladin (Bonnarel et al.
2000) ‘filtering by MOC’ feature. MOC maps provide an International Virtual
Observatory Alliance (IVOA) standard file format to define arbitrary sky
regions (e.g., a FoV) in spherical geometry, using the HEALPix (Górski et al.
2005) tessellation technique; this format allows for the rapid and accurate
comparison of two such regions, or regions and catalogs. The filtered
catalogues were then cross-matched against our dwarf candidate list, using a
$None$ search radius, roughly the average effective radius of our dwarf sample
(see Sect. 5). It should be noted that the vast majority of our matches have
much smaller separations. We summarise the matches between our catalogue and
previous surveys in Table 1. Finally, we also cross-matched the literature
catalogues against each other to create a master list of unique members.

Figure 9: Photometric and structural parameters derived from the surface
profile fitting of the 1100 dwarf galaxy candidates and the bright galaxy
sample from Cuillandre et al. (2024b) in the ERO Perseus field shown in
violet-blue and light-grey colours, respectively. All magnitudes and surface
brightness values were corrected for extinction, as described in Sect. 5.1.

Two prior surveys attempted to separate cluster members from background
objects (Meusinger et al. 2020; Wittmann et al. 2019). This is particularly
important because the Perseus cluster, a member of the Perseus-Pisces
supercluster, is not truly isolated. Additionally, structures have been
identified behind the cluster at $z\approx 0.03$ and $z\simeq 0.06$ (see Fig.
8 in Meusinger et al. 2020, and Aguerri et al. 2020) that could be a source of
confusion.

Wittmann et al. (2019) present a catalogue of 5437 galaxies in the direction
of the Perseus cluster core, nearly all of which fall within the Euclid ERO
FoV. They use morphologies and colour to separate cluster members from
background galaxies, and classify each galaxy into one of eight categories:
dE/ETG cluster members, candidate cluster members, background ETGs, LTGs,
edge-on disk galaxies, galaxies with weak substructure, merging background
galaxies, and excluded sources (e.g., image artefacts or Galactic cirrus). For
this comparison, we adopt the Wittmann et al. nomenclature, where the first
two categories are considered candidate cluster members. They did not attempt
to separate cluster and background LTGs, disk galaxies, or galaxies with weak
substructure; for simplicity, we have merged these with the remaining
categories – aside from the excluded sources – and collectively refer to them
as non-cluster members. After matching the catalogues, we find 349 cluster
members in common between our samples (348 ‘dE/ETG cluster candidates’ and 41
‘candidate cluster members’). In Table 1, we break down the number of proposed
cluster members in two magnitude bins using the $M_{V}$ magnitudes from
Wittmann et al. (2019): massive galaxies with $M_{V}\leq-18$ and a dwarf
sample ($M_{V}>-18$). Only one of our dwarf candidates falls in the massive
galaxy bin, and it has $M_{V}=-18.1$, placing it right on the cusp of the
separation. Among the dwarf candidates, our agreement is $\gtrsim$ 80%.
Interestingly, this is also the typical level of agreement between the seven
classifiers in this work with each other (80% – 90%), and may reflect inherent
biases in the selection of dwarf galaxies that translate into differences
between catalogs.

Only 36 of our proposed dwarf members were labelled as non-cluster objects (18
background ETGs, 7 LTGs, 7 edge-on disk galaxies, and 5 galaxies with weak
substructures) in the Wittmann et al. (2019) sample; none of our galaxies
matched with objects identified as cirrus or image artefacts in their sample.
However, Wittmann et al. note a few caveats in the classifications: small
sources that could not be readily classified given the resolution of the WHT
were classified as background ETGs, some of the LTGs may be legitimate cluster
members, and the classification of galaxies with weak substructures is
ambiguous. Thus, it is entirely possible that our matched objects are
legitimate cluster members, although distance estimates will be required to
prove or disprove their membership. In the region of overlap between the two
surveys, we identify an additional 143 dwarf candidates with no matching
sources within $None$.

Figure 10: Euclid VIS-NISP colours as a function of $I_{\scriptscriptstyle\rm
E}$ measured using aperture photometry within 1 $R_{\rm e}$ of the 1100 dwarf
galaxy candidates and the bright galaxy sample in the ERO Perseus field from
Cuillandre et al. (2024b) shown in violet-blue and light-grey colours,
respectively. The magnitudes were corrected for extinction before the colours
were computed, as described in Sect. 5.1.

The Meusinger et al. (2020) sample includes 1294 galaxies in a 10 ${\rm
deg}^{2}$ field. Only 212 of these galaxies fall within the Euclid ERO FoV,
however, of which 56 are classified as dwarfs according to their absolute
magnitudes. We have a much poorer agreement with their catalogue, matching
just under 50% of their dwarfs, and it is not immediately clear why. However,
their sample was selected through a combination of a visual examination of
Alfred-Jensch Telescope images and visually cleaning an automated catalog
generated from SExtractor. It is entirely possible that the software, being
able to quantify properties of the detections, allowed the authors to select
dwarf candidates that would not have been identified in a visual inspection,
for example: brighter or more disturbed dwarfs. It is also worth noting that
the identification of dwarf galaxies in their sample is somewhat dependent on
which parameter (e.g., absolute magnitude or stellar mass) that is applied, so
these numbers should not be taken as absolutes.

Three of the samples contain distance measurements that can be used to
robustly test cluster membership (Penny et al. 2014a; Meusinger et al. 2020;
Gannon et al. 2022). Penny et al. have Keck-ESI spectra of six dEs in the
cluster core. Meusinger et al. (2020) take spectroscopic redshifts from
various sources (SDSS, TLS Tautenburg telescope, CAHA telescope at Calar Alto
Observatory, NED, and H$\alpha$ data from Sakai et al. 2012 and Moss & Whittle
2000, 2005), while Gannon et al. (2022) obtained integral field spectroscopy
with the Keck Cosmic Web Imager (KCWI; Morrissey et al. 2018). A total of 125
of these confirmed cluster members lie within the Euclid ERO image (all 6 from
Penny et al. 2014a, 3 from Gannon et al. 2022, 116 from Meusinger et al.
2020). Four of the galaxies from Penny et al. (2014a) are in our sample; the
other two are badly contaminated by intracluster light in the core, and were
not flagged during our initial inspection of the images. In the case of Gannon
et al. (2022), we identified all three of their dwarfs that fall within our
FoV. As discussed above, the Meusinger et al. (2020) sample includes massive
and dwarf galaxies; only 9 dwarfs – identified by their absolute $r$
magnitudes – are confirmed cluster members. Of these, four are part of our
sample.

Matching our catalogue against others specifically targeting UDGs is also
useful to test our completeness at the faint end. The Wittmann et al. (2017)
catalogue contains 89 UDG candidates; 85 are in the Euclid FoV and we match 72
candidates with our catalogue. A number of other papers (e.g., Li et al. 2022;
Gannon et al. 2022) have built upon the Wittmann et al. (2017) sample and
furthered the study of select UDG candidates. Li et al. (2022) identified 11
UDG candidates based on over-densities of intergalactic GC populations,
detected in the HST PIPER survey, of which nine are in our sample. We also
examined their galaxy CDG-1, a potential galaxy with an over-density of GCs
but no detected diffuse stellar content. All GCs are found in our GC catalogue
(see Sect. 6.5) but we do not find any diffuse emission associated with these
GCs. The most likely scenario is that these are a random grouping of objects
that are not associated with a galaxy. Gannon et al. (2022) obtained follow-up
Subaru/Hyper Suprime-Cam imaging of five UDGs in the Wittmann et al. (2017)
sample; all three of these galaxies that fall within the Euclid ERO FoV are in
our sample. Thus, we appear to be fairly complete at the faint end.

At another extreme, Penny et al. (2012) identified 84 ultra compact dwarf
(UCD) candidates in the Perseus cluster core, and Penny et al. (2014b)
spectroscopically confirmed 14 as members of the cluster. None of these
galaxies – neither the confirmed UCD cluster members nor the UCD candidates –
are in our sample. This is unsurprising, however, as their small sizes and
relatively high surface brightnesses would have precluded their selection
during the visual examination of the images.

In total, 462 of the dwarfs in our sample have already been identified in
previous studies. The remaining 638 galaxies appear to be new detections.

Figure 11: Cutouts of the VIS image for the 93 UDGs in the ERO Perseus field,
comprising 8% of the dwarf sample. The UDGs were selected to have an effective
radius $R_{\rm e}\geq 1.5$ kpc and a central surface brightness in the $g$
band $\mu_{g,0}\geq 24$ mag arcsec-2. The size of the cutouts are proportional
to twice the area determined from the annotation of classifiers, with north up
and east to the left. The UDGs are ordered by decreasing surface brightness
$\langle\mu_{I_{\scriptscriptstyle\rm E},\rm e}\rangle$.

Figure 12: Comparison between $M_{\rm V}$, $R_{\rm e}$, and $\mu_{\rm{V,e}}$
scaling relations of the ERO Perseus dwarf sample (violet-blue), including
UDGs (orange) from this work, and bright galaxies (black) from Cuillandre et
al. (2024b). The basis for this plot is Figure 37 in Kormendy et al. (2009)
with updates from Kormendy & Bender (2012), Bender et al. (2015), Kluge et al.
(2020), Marleau et al. (2021) and Zöller et al. (2024), including brightest
cluster galaxies (BCGs), ellipticals, and classical bulges (dark grey), as
well as dwarf galaxies including UDGs (light grey). For the sake of clarity,
we do not show errorbars. The uncertainties vary significant between the
different galaxies.

Figure 13: Scaling relations of $I_{\scriptscriptstyle\rm E}$ as a function of
the $R_{\rm e}$ (_top_), Sérsic index $n$ (_middle_), and axis ratio
(_bottom_) of the nucleated (_pink_) and non-nucleated (_peach_) dEs in the
ERO Perseus field. We display the distribution of magnitude for the whole
samples, as well as of the $R_{\rm e}$, $n$, and the axis ratio within the
same magnitude range $17.3\leq I_{\scriptscriptstyle\rm E}<23.6$.

##  5  Photometry and structural parameters

###  5.1 Extinction correction

To derive the correct values of the attenuation due to the Milky Way (MW) dust
the following ingredients are needed: the map of the Galactic dust
distribution; an extinction law; the spectral energy distribution (SED) of the
extragalactic source; and the transmission functions of the relevant filters.

The sky region of the Perseus cluster is significantly affected by extinction
from MW dust, as can be seen in Fig. 7. To correct for it, we adopted the
HEALPix (Górski et al. 2005) dust opacity map with $N_{\rm side}=2048$
released by the Planck Collaboration in 2013 (Planck Collaboration et al.
2014).333{https://irsa.ipac.caltech.edu/data/Planck/release_1/all-sky-maps/}
This map provides information on the colour excess $E(B-V)$ – obtained with
data from which point sources were removed –, the optical depth at 353 GHz
$\tau$, and its uncertainty ${\rm d}\tau$. Each galaxy was associated with the
HEALPix pixel containing its coordinates, from which we derived the values of
$E(B-V)$ and its uncertainty ${\rm d}E(B-V)=E(B-V)\,{\rm d}\tau/\tau$.

To derive the attenuation at different wavelengths we used the extinction
curve $k(\lambda)=R_{V}\times A(\lambda)/A_{V}$, where $A(\lambda)$ and
$A_{V}$ are the magnitudes attenuated at the wavelength $\lambda$ and in the
$V$ filter, from Gordon et al. (2023), with $R_{V}=3.1$ implemented through
the dust-extinction package.444https://dust-extinction.readthedocs.io/

The correct derivation of the attenuation in each observed bandpass depends on
the SED of each object (e.g. Galametz et al. 2017). However, since the SED of
each galaxy is unknown, a general approach is to assume a test case SED, e.g.,
a flat spectrum in frequency or a stellar SED. We employed the flux $F$ from a
$5700\,\mathrm{K}$ blackbody, to represent a G7V star, which resembles a
typical galaxy continuum, as a proxy.

Finally, the exact attenuation in each band, especially in the broad bands
that we are considering in the present work, depends also on the shape of the
throughput, including filter, optics, mirror, and detector. We used the
official bandpasses $R(\lambda)$ for NISP (Euclid Collaboration: Schirmer et
al. 2022)555https://euclid.esac.esa.int/msp/refdata/nisp/NISP-PHOTO-
PASSBANDS-V1 and VIS (Cropper et al. 2016; Euclid Collaboration: Scaramella et
al. 2022).

With the above ingredients, for each filter $x$ we derive the quantity $c_{x}$
as

$c_{x}=2.5\operatorname{log_{10}}\frac{\int
R_{x}(\lambda)\,\lambda\,F(\lambda)\,10^{0.4\,k(\lambda)}\,{\rm
d}\lambda}{\int R_{x}(\lambda)\,\lambda\,F(\lambda)\,{\rm d}\lambda}\,,$ (1)

which can be used to obtain the intrinsic magnitudes as $m_{\rm
obs}-c_{x}E(B-V)$. With this approach, we obtained $c_{x}=2.122$, $1.066$,
$0.726$, and $0.470$ in the $I_{\scriptscriptstyle\rm E}$,
$Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$ bands, respectively.

###  5.2 Cutouts

The cutouts for the photometric and structural parameter analysis were
generated with sizes of 9 $R_{\rm e}$ (Poulain et al. 2021), where the
preliminary estimate of $R_{\rm e}$ was determined by using the area in ${\rm
deg}^{2}$ defined by the users with the annotation tool and assuming a visual
extent of the galaxy corresponding to approximately 2 $R_{\rm e}$.

Of the 1100 dwarf cutouts, 16 had to be recut to a smaller than 9 $R_{\rm e}$
size as they fall near the edge of the image, which caused issues with the
fitting algorithms. For these galaxies, we created smaller cutouts while
making sure to have sufficient remaining sky level pixels in the image.
Because a number of galaxies (24) fall outside the FoV of the ERO Perseus
observations in one or more Euclid NIR filters, the measurements for those
galaxies were not possible and therefore the tables of photometric parameters
show no entries for that particular galaxy and filter.

The cutouts were created with the same angular size for all
$I_{\scriptscriptstyle\rm E}$ as well as $Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ images. The
range of cutout regions provided from the annotation tool corresponds to
$None$–$None$ (or $5$ kpc – $60$ kpc).

Figure 14: Examples of dwarfs that stand out due to their number of nuclei
candidates. Figure 15: Examples of dwarfs that stand out due to the presence
of a complex nucleus.

###  5.3 Masking

The masking of contaminating sources in the cutouts is done via two main
steps. The first step is to run MTObjects (Teeninga et al. 2015) that produces
the MTO segmentation image. The advantage of using MTObjects is that it is
capable of locating the faint outskirts of objects. The code is run for all
the $I_{\scriptscriptstyle\rm E}$ and $Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ image cutouts
independently. In order to avoid including the dwarf galaxy in the mask, the
parameter move_factor is optimally selected for the ERO Perseus images and
furthermore, a region of size 1 $R_{\rm e}$, centred on the dwarf galaxy, is
unmasked after this step is completed. The masks are also visually inspected.
The second step involves running SExtractor (Bertin & Arnouts 1996), which is
good at detecting point sources – including within the galaxy of interest – on
all of the $I_{\scriptscriptstyle\rm E}$ and $Y_{\scriptscriptstyle\rm E}$,
$J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ image
cutouts. We run SExtractor three times with different regions of the image
centred on the dwarf masked, as well as different detection and analysis
thresholds, minimum and maximum areas, background mesh sizes and deblending
contrasts.

The MTO and SExtractor masks are then combined to create a final mask. To
ensure that the nucleus of the dwarf has been masked by the SExtractor runs,
the nucleus of each of the nucleated dwarfs identified by our visual
inspection is masked in a final step. The exact position of the nucleus is
determined by finding the maximum pixel value within a region of 15 pixels
around the galaxy coordinates and a region of 4(2) pixels in radius in the
$I_{\scriptscriptstyle\rm E}$ ($Y_{\scriptscriptstyle\rm
E}$,$J_{\scriptscriptstyle\rm E}$,$H_{\scriptscriptstyle\rm E}$) images is
masked in order to make sure that the nucleus does not affect the fit of the
diffuse component of the dwarf galaxy.

Figure 16: Structural, photometric, and positional properties of galaxies in
our sample, with visually selected GC-rich targets identified. The full sample
of dwarf galaxies is shown with violet-blue dots. Gray filled circles
represent galaxies brighter than $I_{\scriptscriptstyle\rm E}=16$, with the
symbol size indicating the galaxy effective radius (upper left panel).
Visually identified GC-rich candidates are denoted by filled orange or empty
orange circles (the latter is used for dwarfs near bright galaxies). The grey
shaded area in the upper right panel represents the expected locus for UDGs,
as defined by van Dokkum et al. (2015) and in Sect. 6.

###  5.4 Photometric and structural parameters

The galaxy modelling was first performed on the $I_{\scriptscriptstyle\rm E}$
images due to the better spatial sampling and spatial resolution. We first
applied a non-parametric galaxy image analysis method to obtain an initial
guess of the structural parameters of each dwarf galaxy using AutoProf (Stone
et al. 2021). The masks were used, but since complete isophotes cannot be
masked using AutoProf (it ignores the mask in this case), the nuclei were not
masked in this first step. A total of 872 sources finished with convergence
and 228 did not converge. The following photometric and structural parameters
were calculated from the AutoProf output: total magnitude
($I_{\scriptscriptstyle\rm E}$); effective radius ($R_{\rm e}$); surface
brightness (central: $\mu_{I_{\scriptscriptstyle\rm E},\rm 0}$, at $R_{\rm
e}$: $\mu_{I_{\scriptscriptstyle\rm E},\rm e}$, and within $R_{\rm e}$:
$\langle\mu_{I_{\scriptscriptstyle\rm E},\rm e}\rangle$); Sérsic index ($n$);
position angle (PA); and axis ratio (AR). For the galaxies with no
convergence, we used the median value of the results from the fits that
finished with convergence for the next step (see below).

These initial estimates of the structural parameters were then used as inputs
to both Galfit (Peng et al. 2010) and AstroPhot (Stone et al. 2023). The model
used for both consists of a two-dimensional (2D) Sérsic function (Sérsic 1963)
combined with a PSF.

To obtain the PSF models, we first used SExtractor to detect high SNR sources
(DETECT_MINAREA $=5$; DETECT_THRESH $=100$ for $I_{\scriptscriptstyle\rm E}$
and DETECT_THRESH $=40$ for NISP). Then, point sources were selected and PSF
models were created with PSFEx (Bertin 2011) using the pixel basis,
PSFVAR_DEGREES $=2$, and without over- nor under-sampling. The PSF models at
the centres of the images were reconstructed from the PSFEx output as a linear
combination of the PSF vectors. The PSF models for $I_{\scriptscriptstyle\rm
E}$, $J_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$ are shown in Fig. 8.

The Galfit and AstroPhot codes were run in parametric mode using the above
model and masks. In addition, two runs of AstroPhot were performed using
different sky models, a flat and a plane sky model. The plane sky model was
run in order to improve the fitting outcome of the dwarfs embedded in strong
sky gradients due to a nearby massive (bright) galaxy. All models and
residuals produced by both codes were visually inspected and the output
parameters of the best fits were retained for the final catalogue.

From these runs, a total of 854 dwarf galaxies returned a good fit and
therefore robust structural parameters. The remaining 246 galaxies required
manual intervention. For 123 dwarfs, it was necessary to manually edit the
masks due to bright stars or other sources of contamination that fell within
the central 1 $R_{\rm e}$ of the dwarf, a region that was previously unmasked
in MTO in order to avoid removing the dwarf itself. For the remaining 123
galaxies, patching of the image was needed because adjusting the masks was not
enough. These cases were extreme and showed very strong contamination from
stellar spikes, stars, bright nearby galaxies, or a combination of features.
Of these, the smaller (and faint) dwarfs were the most affected and difficult
to fit. These 89 dwarf galaxies have a Sérsic index of 0.36 or below. For
$n<0.36$ the meaning of $R_{\rm e}$ and $I_{\scriptscriptstyle\rm E}$ changes
(Sérsic 1963); they are no longer at the half light radius. AstroPhot uses the
fourth-order expansion of $b_{n}$ (Sérsic 1963) to get down to $n=0.36$, but
higher orders are needed to go further. Therefore, for the dwarfs with $n\leq
0.36$, the extracted parameters should be treated with caution and with this
limit in mind. Note that some of those galaxies actually have a good fit from
Galfit, so this caution does not apply to all 89 dwarfs.

Histograms of the extracted parameters are shown in Fig. 9 and the values for
each dwarf candidates are given in Table 4. The absolute magnitudes and
effective radii (in kpc) were computed using the distance of 72 Mpc.

###  5.5 Colours

Once the photometry and structural parameters of the dwarfs were obtained,
aperture photometry was performed on all VIS+NIR images to obtain colour
information on the dwarfs. The aperture photometry was done using the python
package photutils and using a circular aperture of 1 $R_{\rm e}$, with the
effective radius taken from the best fit to the dwarf in the
$I_{\scriptscriptstyle\rm E}$ image. The aperture photometry was performed
without using a mask and hence includes any nucleus or contaminating source.
The aperture magnitudes were then corrected for extinction using the method
described in Sect. 5.1 and applied at each dwarf position independently and
for each Euclid passband.

The aperture photometry magnitudes and the extinction correction (EC) at each
galaxy position and Euclid passband are given in Table 5. The distribution of
VIS-NISP aperture colours of the Perseus dwarfs are shown in Fig. 10. We
compare these colours with those of the two dwarf irregular galaxies IC 10 and
Holmberg II presented in (Hunt et al. 2024). We find that their reported
$I_{\scriptscriptstyle\rm E}$ $-$ $H_{\scriptscriptstyle\rm E}$ colours of
$-0.419\pm 0.105$ and $0.029\pm 0.090$, respectively, fall well within the
colour distribution shown in Fig. 10 for the ERO Perseus dwarfs. The NISP-NISP
aperture colours were also computed and can be found in Fig. 33.

##  6  Results

###  6.1 Luminosity and stellar mass function

The luminosity and stellar mass function (LF and SMF, respectively) of the ERO
Perseus galaxy population, consisting mostly of the dwarf galaxy sample
presented here, is discussed in a separate paper (Cuillandre et al. 2024b).
The faint end slope of the LF, $\alpha_{\rm S}$, is found to have a value of
$\alpha_{\rm S}=-1.2$ to $-1.3$. The criteria used to identify all cluster
members, maximize completeness and minimise the contamination of foreground
and background sources, along with the interpretation of the results in terms
of models, can be found in Cuillandre et al. (2024b).

###  6.2 Scaling relations

Galaxy populations can be characterised in structural parameter spaces (see,
e.g., Kormendy 1985; Bender et al. 1992; Binggeli 1994; Kormendy et al. 2009).
In order to compare the structural parameters of our dwarf galaxy sample to
scaling relations in the literature, we have to convert the
$I_{\scriptscriptstyle\rm E}$ magnitudes and surface brightnesses to the $V$
band. To select the UDGs in our sample, we have to convert them to the $g$
band.

The magnitude transformation from $I_{\scriptscriptstyle\rm E}$ to $V$ band is
derived using synthetic photometry of SEDs of old stellar populations with
subsolar metallicities, about ${\rm[Fe/H]}=-0.5$ (Saifollahi et al. 2024),
similar to quiescent dwarf galaxies in cluster environments: $V=$
$I_{\scriptscriptstyle\rm E}$ $\,+\,0.5$. The transformation from the $V$ band
to the SDSS $g$ band is taken from Lupton
(2005):666https://classic.sdss.org/dr4/algorithms/sdssUBVRITransform.php#Lupton2005
$g=V+0.31$.

We select UDGs based on the definition of van Dokkum et al. (2015), i.e.
$\mu_{\rm{g,0}}\geq 24$ mag arcsec-2 and $R_{\rm e}\geq 1.5$ kpc. This
selection cut yields 93 UDGs for our 1100 sample of dwarf galaxies with
structural parameters. This corresponds to $8.5\%$ of our total dwarf sample,
compared to a smaller fraction of $2.7\%$ in the Mass Assembly of early Type
gaLAxies with their fine Structures (MATLAS) survey (Marleau et al. 2021) and
$5.4\%$ reported by Zöller et al. (2024) for A262 and A1656. The VIS cutouts
of the Perseus UDGs are shown in Fig. 11.

The higher fraction of UDGs in our sample is likely due to the greater surface
brightness depth of the ERO data (by $0.5$–$1$ mag when comparing to the
MATLAS survey) and the high angular resolution of the Euclid data that enables
one to clearly distinguish faint dwarfs/UDGs from background sources. The four
UDGs in our sample with the lowest central surface brightness are EDwC-0035,
EDwC-0424, EDwC-0926, and EDwC-0932 ($\mu_{I_{\scriptscriptstyle\rm
E},\rm{e}}=26.5$–$27.3$ mag arcsec-2). Note that other dwarf candidates that
are not classified as UDGs have even fainter surface brightness, with the
faintest, as measured at $R_{\rm e}$, being the dwarf candidate EDwC-0239 with
$\mu_{I_{\scriptscriptstyle\rm E},\rm{e}}=28.7$ mag arcsec-2 (not extinction
corrected).

We investigate which regions the dwarf galaxies in our sample populate in the
$M_{\rm V}$–$R_{\rm e}$, $M_{\rm V}$–$\mu_{\rm{V,e}}$, and
$\mu_{\rm{V,e}}$–$R_{\rm e}$ parameter spaces and compare them to scaling
relations from the literature in Fig. 12. The structural parameters of
ellipticals are taken from Bender et al. (1992) and Kormendy et al. (2009),
while those of classical bulges are from Fisher & Drory (2008), Kormendy et
al. (2009), and Kormendy & Bender (2012). The structural parameters of BCGs
are from Kluge et al. (2020). The literature data points of dwarf galaxies
contain Local Group dwarf spheroidals from Mateo (1998) and McConnachie &
Irwin (2006), Virgo dwarf spheroidals from Ferrarese et al. (2006), Gavazzi et
al. (2005), and Kormendy et al. (2009), dwarf galaxies (including UDGs) from
the MATLAS survey (Poulain et al. 2021; Marleau et al. 2021), and dwarf
spheroidals (including UDGs) in A262 and A1656 (Coma cluster) from Zöller et
al. (2024). Within the data set from the literature, BCGs, ellipticals, and
classical bulges are represented in dark grey, and dwarf galaxies (including
UDGs) are represented in light grey. Bright galaxies from the ERO Perseus
luminosity function project Cuillandre et al. (2024b) are depicted in black.
Our dwarf sample is split up into UDGs (orange) and and non-UDGs (violet-
blue).

The majority of our data points follow the scaling relations of dwarf galaxies
from the literature. In the $M_{\rm V}$–$\mu_{\rm{V,e}}$ and
$\mu_{\rm{V,e}}$–$R_{\rm e}$ parameter spaces, the dwarf distribution is
slightly extended towards fainter $\mu_{\rm{V,e}}$. Furthermore, the diffuse
end of the dwarf parameter relations are more densely populated than in
previous studies. This indicates higher completeness of diffuse galaxies,
presumably due to a combination of the high depth and high spatial resolution
delivered by Euclid that provides a better separation from contaminating
objects. The increased density within the diffuse part of the parameter spaces
is particularly evident in the $M_{\rm V}$–$\mu_{\rm{V,e}}$ relation, which
significantly deviates from the scaling relations reported in Kormendy et al.
(2009). In that paper, a narrow $M_{\rm V}$–$\mu_{\rm{V,e}}$ scaling relation
is reported for the dwarf spheroidals, whereas the distribution of our dwarf
galaxy sample is nearly twice as broad. When comparing with datasets from more
recent dwarf surveys, such as the MATLAS survey (Marleau et al. 2021), the
Next Generation Virgo cluster Survey (NGVS; Ferrarese et al. 2012) and the
Next Generation Fornax Survey (NGFS; Muñoz et al. 2015), we find good
agreement with the spread of the distributions. Examples of galaxies with
structural parameters similar to the most extreme galaxies found in this study
were also reported by Zöller et al. (2024). We also find a few galaxies above
the $M_{\rm V}$–$\mu_{\rm{V,e}}$ and $\mu_{\rm{V,e}}$–$R_{\rm e}$ or below the
$M_{\rm V}$–$R_{\rm e}$ scaling relations of dwarf galaxies; we cannot exclude
the possibility that these could be interloping background galaxies.

Furthermore, we note that while UDGs populate the diffuse extension with
respect to the scaling relations of spheroidals from Kormendy et al. (2009),
there are also some galaxies populating those regions that do not fulfill the
UDG definition. We conclude that the UDG definition does not cover all of the
most extreme diffuse galaxies with respect to these structural parameter
relations, which is in agreement with the findings from Marleau et al. (2021)
and Zöller et al. (2024).

Figure 17: GC selection procedure. Left panel: $I_{\scriptscriptstyle\rm E}$
image of the dwarf EDwC-0791. The green circle shows the 1.5 $R_{\rm e}$
search radius adopted to identify GC candidates around the galaxy. Middle
panel: on-galaxy selection region (large central green circle) and the first
inner background annulus used for background correction (red circles, 5 – 10
$R_{\rm e}$ in size). All sources detected on the galaxy and in the background
region are marked with green (on-galaxy) and red (off-galaxy) empty circles.
The sources that fulfill all selection criteria adopted for identifying GC
candidates are marked with filled red (green) symbols in the outer (inner)
area. The blue symbols in the centre identify GC candidates within $R_{\rm
e}/3$, which are possible nuclear star clusters. Right panel: concentration
index for sources on the galaxy and in the first background annulus. Symbols
and colours are the same as in the middle panel. The dashed orange lines and
the pale orange shaded area mark the ranges adopted for identifying GC
candidates in this plane. The magenta line is the median concentration index
measured on bright stars.

###  6.3 Nucleated dwarf properties

The morphological classification of the dwarfs led to a sample of 582
nucleated galaxies, comprising 52.9% of the dwarf sample. A thorough analysis
of the effect of the galaxy luminosity and the environment on the nucleated
fraction will be presented elsewhere (Euclid Collaboration: Sánchez-Janssen,
R., et al. 2024, in prep.). We study as a first step the dependence of the
nucleated fraction on the luminosity and morphology of the dwarfs. In Table 2,
we report the nucleated fraction for the whole sample, as well as for the
subpopulations of dEs and dIs. We divide the samples into two bins, namely
faint and bright dwarfs, by cutting at the mean apparent magnitude of the
sample $I_{\scriptscriptstyle\rm E}=20.4$ [corresponding to
$M(I_{\scriptscriptstyle\rm E})=-13.9$]. Studies across a wide range of
environments have reported that nucleated dwarfs tend to be brighter than non-
nucleated dwarfs, regardless of the morphological type, such that brighter
dwarfs have higher nucleated fractions (e.g., Côté et al. 2006; Ordenes-
Briceño et al. 2018; Sánchez-Janssen et al. 2019a; Habas et al. 2020; Hoyer et
al. 2021; Zanatta et al. 2021; Carlsten et al. 2022). In agreement with the
literature, we find a higher nucleated fraction for the bright dwarfs as
compared to the faint ones, with 81.3% (8.3%) of the bright dEs (dIs) being
nucleated, against 32.5% of the faint dEs and none of the faint dIs. We find
overall a larger nucleation fraction for the dEs as compared to the dIs, which
is consistent with the observations of Habas et al. (2020), but different from
the expectations from Neumayer et al. (2020), where the fraction of nucleated
dEs and dIs are similar. The difference between the two fractions can be
explained by the low statistics of the dI sample, with two of the 39 galaxies
being nucleated, but also from the fact that it is more difficult to identify
nuclei in irregular galaxies due to the presence of star-forming regions and
dust obscuration.

Table 2: The fraction of nucleated dwarfs as a function of the magnitude and morphology of the host dwarf. | dE | dI | All
---|---|---|---
Bright ($I_{\scriptscriptstyle\rm E}<20.4$) | 81.3% | 8.3% | 77.8%
Faint ($I_{\scriptscriptstyle\rm E}\geq 20.4$) | 32.5% | 0% | 31.7%
All | 54.6% | 5.1% | 52.9%

Figure 18: Total GC population versus galaxy $I_{\scriptscriptstyle\rm E}$
magnitude for the full sample of galaxies (upper panel, log scale on the
$y$-axis) and for the sample limited to faint $I_{\scriptscriptstyle\rm E}<15$
ones (lower panel, linear $y$-scale). The full sample is represented by gray
filled circles in the upper panel. Dwarf galaxies are symbol and colour-coded
based on their GC richness score, as labelled. In the upper panel, we also
report fits to the data using the sample of galaxies with $10\leq
I_{\scriptscriptstyle\rm E}\leq 21$ and $N_{\rm GC}\geq 5$ (dashed-dotted
line), as well as a broken linear fit (dashed line) obtained adopting a
separation limit at $I_{\scriptscriptstyle\rm E}=17$. The dotted box in the
upper panel shows the position of the box in the lower panel.

Figure 19: Same as in Fig, 16, except that GC-richness is determined through
automatic GC detection. Symbols size scales for bright galaxies (grey symbols
in the upper right panel) and for the dwarf population (orange symbols in all
panels) according to the total population of identified GC candidates, $N_{\rm
GC}$, adopting different scaling factors for bright and dwarf galaxies for
clarity.

As a second step, we investigate possible differences between the structural
properties of the nucleated and non-nucleated dwarfs. Recent results strongly
indicate that nuclear star clusters (NSCs) in low-mass galaxies grow primarily
via dissipationless merging of pre-existing massive star clusters (Sánchez-
Janssen et al. 2019a; Fahrion et al. 2022). In this scenario, it is expected
that the structural parameters of the host galaxy play a relevant role in both
setting the efficiency of dynamical friction and the strength of the cluster
mass loss as it spirals inwards (Leaman & van de Ven 2022). For example, den
Brok et al. (2014) find that Coma dwarfs that are more concentrated and
rounder tend to host more luminous star clusters. In addition, it has been
shown that nucleated cluster dwarfs are intrinsically rounder, at all
luminosities, than their non-nucleated counterparts (Sánchez-Janssen et al.
2019b; Lisker et al. 2007; Venhola et al. 2019).

In Fig. 13, we show the scaling relations between $I_{\scriptscriptstyle\rm
E}$ and the effective radius $R_{\rm e}$, the Sérsic index $n$, and the axis
ratio of the nucleated and non-nucleated dwarfs in Perseus. Given the low
statistics of the dI sample, we focus here on the dEs only. For each relation,
we also include histograms of the property distributions within the same
magnitude range $17.3\leq I_{\scriptscriptstyle\rm E}<23.6$. We limit the
range of Sérsic index values to $n\geq 0.5$ because smaller values indicate a
3D luminosity distribution that is deficient at the centre, which is
unphysical (Trujillo et al. 2001). From the distributions of
$I_{\scriptscriptstyle\rm E}$, we see that the nucleated dwarfs tend to be
brighter than the non-nucleated ones. Looking at the structural properties at
similar magnitudes, we observe similar ranges of properties. However, the
distributions do not peak at the same value, such that the nucleated
distributions are shifted towards larger $R_{\rm e}$, $n$, and axis ratio.
This means that we observe less nuclei in smaller, high ellipticity dwarfs, as
well as in galaxies with flatter surface brightness profiles. These results
are consistent with the observations in other galaxy clusters and lower
density environments (e.g., Sánchez-Janssen et al. 2019a; Neumayer et al.
2020; Poulain et al. 2021).

###  6.4 Dwarf nucleated substructures

During the visual review of the dwarf candidates, the classifiers were allowed
to identify multiple nuclei in the dwarfs. A galaxy is visually defined as
multinucleated when at least two compact sources of similar luminosity are
located close to the photometric centre and are brighter than other
surrounding compact sources. The presence of multiple nuclei can be linked to
dwarf-dwarf mergers (Pak et al. 2016), where the NSCs of both interacting
galaxies are migrating towards the potential well of the newly formed galaxy.
Another possibility is the observation of a nucleus with a stellar disc,
similar to the double nucleus of M31 (Lauer et al. 1993). Given that the dwarf
nuclei can have similar photometric and structural properties to massive GCs
(e.g., Poulain et al. 2021; Hoyer et al. 2023), we can also be observing the
infall of massive GCs towards the galaxy centre due to dynamical friction
(Lotz et al. 2001). Finally, we cannot exclude the possibility that in some
cases, the candidate nucleus or nuclei might be a background galaxy or
foreground star, seen in projection on top of the galaxy. We show in Fig. 14
examples of four multinucleated dwarfs.

Together with multiple nuclei, reviewers also noted the presence of complex
nuclei in a few tens of objects. These NSCs exhibit some tidal features such
as stellar tails, suggesting an ongoing interaction at the centres of the
galaxies. These types of structures can be identified only with the depth and
high spatial resolution of the VIS observations, since such structures are not
resolved in the other bands. Four such nuclei with complex structure are
visible in Fig. 15. Further investigations are needed to assess the nature of
these substructures, which is beyond the scope of this paper.

###  6.5 Globular clusters

To investigate the GC population in galaxies within our field, we adopted two
distinct approaches. First, we examined galaxies visually identified as GC-
rich, comparing their properties (such as position in the cluster, Sérsic
parameters, etc.) with those of GC-poor galaxies in the sample. Then, we
adopted a more quantitative approach to estimate the total GC population in
each galaxy, and inspected the overall characteristics of the GC systems
within these galaxies. Showing the results for both visual and automatic
detection methods for GC-rich dwarfs serves two key purposes: maintaining
coherence with other sections, which rely on visual inspection, and providing
validation for the visual approach.

####  6.5.1 GC richness from visual inspection

As described in Sect. 3.3, during the visual inspection of dwarf galaxies in
the Perseus field, classifiers were asked to verify the presence of GC
candidates hosted within the galaxies. GC candidates were visually identified
as relatively compact and faint sources with a surface distribution centrally
concentrated around the galaxy. In this context, a dwarf galaxy was
categorized as GC-rich if it contained a minimum of two GC candidates. Part of
the reason we chose this low value was to separate the dwarfs with potential
GC candidates from the vast majority of dwarfs with zero ($\pm 1$) GC
candidates.

With this (somewhat arbitrary) definition of GC richness in mind, Fig. 16
compares the spatial, photometric and structural properties of visually GC-
rich galaxies with those of the non-GC-rich elements in the catalogue. For the
sake of clarity, only dwarfs with GC scores $\geq$ 0.85 are indicated,
corresponding to those receiving 6 votes out of 7.

One possible source of confusion in visually inspecting GC richness could
arise from the proximity, at least in projection, of a dwarf candidate to a
bright, massive companion or to regions of high intracluster GC population
density (Kluge et al. 2024). Figure 16 (upper left panel) shows the positions
of dwarf and bright galaxies in the Perseus field. Here, grey filled circles
represent galaxies brighter than ${I_{\scriptscriptstyle\rm E}}=16$ [absolute
$M(I_{\scriptscriptstyle\rm E})=-18.3$], with symbol size scaled with the
galaxy effective radius. The full sample of dwarf galaxies is reported with
violet-blue dots. GC-rich candidates are denoted by filled or empty orange
circles. Filled orange symbols are assigned to dwarfs projected far from any
bright galaxy, while empty orange circles are used for dwarfs within 5
effective radii of a bright companion.

A first observation is the absence of any obvious GC richness enhancement near
the bright/massive galaxies in the field. This suggests a real over-density of
GCs associated with the dwarfs rather than contamination from the intracluster
GCs or the GC system of a nearby massive companion. Furthermore, we do not
observe significant evidence of any other trends apart from the clustering of
dwarfs around the massive galaxies. Indeed, a clear east-west stretch is
evident both for the dwarfs and the giant galaxies.

The remaining panels of Fig. 16 show the properties of the dwarf galaxy
sample, using the same colour and symbol coding as in the upper left panel,
except for the bright galaxies which are not shown. By considering as
‘consensus sample’ the dwarfs with at least 6 out of 7 votes in favour of GC
richness, in Fig. 16 we observe the following.

  * •

No GC-rich and uncontaminated candidate has $R_{\rm
e}<2\aas@@fstack{\prime\prime}0$ ($\sim$800 pc) or is fainter than
$I_{\scriptscriptstyle\rm E}\sim$22 (lower left panel).

  * •

Two GC-rich objects exhibit $I_{\scriptscriptstyle\rm E}\gtrsim$ 21 [fainter
than the absolute magnitude $M(I_{\scriptscriptstyle\rm E})$ $\sim\,-13.3$].
One of them is located near the denser cluster area, close to the cluster
core, suggesting the possibility of intracluster GCs or bright galaxy GC
contamination. The other dwarf (EDwC-0066) appears as a faint diffuse object
with a handful of point-like sources within one effective radius (lower left
panel).

  * •

Within fixed $I_{\scriptscriptstyle\rm E}$ intervals, and for galaxies
brighter than $I_{\scriptscriptstyle\rm E}\sim 20$, the GC-rich candidates
appear to have, on average, slightly smaller $n$ values compared to the GC-
poor sample. This trend appears to be weak but consistent over the range of
$16\leq I_{\scriptscriptstyle\rm E}\leq 20$. For example, in the 18–19
magnitude bin, we find $\langle n\rangle=1.0\pm 0.1$ for the 19 GC-rich
dwarfs, compared to $\langle n\rangle=1.4\pm 0.3$ for the 28 GC-poor dwarfs
(only including those with a score $\leq 1$ out of 7 votes; lower middle
panel).

  * •

For $I_{\scriptscriptstyle\rm E}\leq 20$, there appears to be a tendency for
the central surface brightness of GC-rich dwarfs to be slightly fainter than
that of the entire sample of dwarfs in the same magnitude range (lower right
panel).

  * •

The Sérsic exponent, $n$, shows a correlation with the host galaxy central
surface brightness. This behaviour has been previously observed (e.g.,
Ferrarese et al. 2006); here, we find that it appears to be independent of the
GC richness (upper middle panel).

  * •

Approximately 40 GC-rich uncontaminated dwarfs (orange filled circles in the
figure) have $R_{\rm e}\geq 1.5$ kpc; among them, about ten have central
surface brightness $\mu_{\rm{I_{\scriptscriptstyle\rm E},0}}\,\gtrsim\,23.2$
mag arcsec-2 (equivalent to $\mu_{\rm{g,0}}\,\gtrsim\,24.0$ mag arcsec-2),
hence are possible GC-rich UDG candidates (upper right panel).

Figure 20: Galaxy positions and GC content. Left panel: The violet-blue
circles indicate the positions of dwarf galaxies, with symbol size scaled to
the specific frequency, $S_{{N}}$. Gray circles mark the brightest galaxies in
the field, with magnitudes $8\leq I_{\scriptscriptstyle\rm E}\leq 13$. Middle
panel: total population of GC candidates in dwarf galaxies, $N_{\rm GC}$ (log
scale), plotted against the cluster-centric distance, $R_{\rm Cl}$, from the
BCG. Symbol sizes correspond to those in the left panel. Right Panel: Specific
frequency versus magnitude plot, colour and symbols are as in left panel,
except that the symbol size is scaled to $N_{\rm GC}$. The red curve shows the
relation from Lim et al. (2020) for UDGs in Virgo, while the orange curve is
for UDGs in Coma (Lim et al. 2018). The horizontal dashed line shows the
$S_{N}=1$ level.

Figure 21: Top left: Projected distribution (white dots) and density map of
the 1100 dwarf candidates within the Euclid ERO FoV of the Perseus cluster.
Top right: The density map (white contours) of the dwarf candidates are
overlaid on the Euclid ERO $I_{\scriptscriptstyle\rm E}$ image of the cluster.
Middle left and right: Same as above but for the ultra diffuse galaxies
identified as cluster members. Bottom left and right: Same as above but for
the bright (non-dwarf) galaxies identified as cluster members. The iso-density
centres of the dwarfs, as well as the iso-density centre of the GCs and the
isophotal centre of the ICL at semimajor-axis radius 320 kpc, are indicated
with the two red, green, and blue crosses, respectively.

####  6.5.2 GC richness from automatic detection

Using the photometric catalogue of Kluge et al. (2024) we conducted a
comprehensive analysis of detected sources to identify and characterise GC
candidates associated with each galaxy in our footprint of the Perseus cluster
(Table 4). To estimate the total GC population, we made several assumptions
and adopted the procedures already used in the literature (e.g. Cantiello et
al. 2020) and outlined below.

At the distance of Perseus, the typical size of a GC, assuming a half-light
radius of 3 pc based on Milky Way GCs (Harris 1996), is about one order of
magnitude smaller than the typical FWHM of the data in question. Therefore,
these sources can be considered point-like in the ERO Perseus dataset.

Initially, we extracted galaxy characteristics (position, effective radius
$R_{\rm e}$, etc.; Table 4) to identify all sources in the photometric
catalogue within 1.5 $R_{\rm e}$ of each galaxy (Lim et al. 2018). We adopted
3.7 $R_{\rm e}$ for bright galaxies (Forbes et al. 2017). Additionally,
sources within 3 background annuli with inner and outer radii equal to 5 and
10 $R_{\rm e}$, 10 and 13.25 $R_{\rm e}$, and 13.25 and 15.9 $R_{\rm e}$, were
identified around each galaxy. We then estimated three over-density values of
sources on-galaxy (one value for each background annulus) by subtracting the
off-galaxy density from the on-galaxy density. The number of extra sources on-
galaxy was then obtained by multiplying the over-density by the effective area
of the galaxy. We chose not to apply a further factor of 2 due to spatial
coverage, based on a series of empirical tests derived from estimates of
$N_{\rm GC}$ within 4 $R_{\rm e}$. By comparing the total GC population
estimated within 1.5 and 4.0 $R_{\rm e}$, we find that not doubling the
population within 1.5 $R_{\rm e}$ provides a better match with the results
within 4 $R_{\rm e}$ (which are spatially more complete). We adopted as
reference the central value of the three estimates derived using all
background annuli. The numbers and their uncertainties are reported in Table
4. Using the same sample of selected GC candidates on-galaxy, we also counted
the number of objects within $R_{\rm e}/3$ of the galaxy photocentre, which
are potentially nuclear star clusters. The number of these candidates, $N_{\rm
NSC}$, is also reported in Table 4.

Subsequently, we refined the analysis to consider only sources that satisfied
certain properties for compactness, such as concentration index, FWHM, and
elongation. To further narrow down the GC candidate list, we restricted the
analysis to compact sources within the expected turnover magnitude (TOM),
$I_{\scriptscriptstyle\rm E}\leq I_{\scriptscriptstyle\rm E}^{\rm TOM}$, at
the distance of Perseus. For $I_{\scriptscriptstyle\rm E}^{\rm TOM}$ we
assumed the distance modulus $m{-}M=34.3$, and derived an absolute TOM of
$M(I_{\scriptscriptstyle\rm E})^{\rm TOM}\approx-8.0$ (see also Saifollahi et
al. 2024). This corresponds to assuming $M_{V}^{\rm TOM}=-7.5$ (Rejkuba 2012,
and references therein) adjusted by a 0.5 offset from the $V$ band to the
$I_{\scriptscriptstyle\rm E}$ band. Consequently, the expected TOM in
$I_{\scriptscriptstyle\rm E}$ is approximately 26.3. For the bright cut-off
for GC candidates, we considered using a magnitude of 22.7, estimated assuming
a 3 $\sigma_{{\rm GCLF}}$ cut brighter than the expected TOM, adopting a GC
luminosity function (GCLF) width of $\sigma_{\rm GCLF}=1.2$. Although
$\sigma_{\rm GCLF}=1.0$ or smaller is more in line with expectations for
dwarfs (Villegas et al. 2010), we opted for a larger value due to the
(fractionally small) depth of the cluster and the wide range of galaxy
magnitudes we consider.

Finally, adopting the procedure described above for assessing the excess of
sources on galaxies, and assuming that the GC candidates sample is basically
complete at the peak of the GCLF (Kluge et al. 2024), we double the number of
selected sources for an estimate of the total population of GC on the galaxy,
$N_{\rm GC}$, under the assumption of Gaussian GCLF. The entire procedure
adopted is depicted in Fig. 17, for the dwarf galaxy EDwC-0791.

As a preliminary test, we compared the GC richness results obtained through
visual inspection with the number of GC candidates, $N_{\rm GC}$, extracted
using the procedure described above. Figure 18 shows $N_{\rm GC}$ versus
$I_{\scriptscriptstyle\rm E}$, colour-coded based on the GC richness score
obtained from our initial visual inspection (as labelled). The upper panel
shows the full sample on a logarithmic scale, while the bottom panel displays
only the sample of dwarf galaxies over a limited range of $N_{\rm GC}$,
adopting a linear scale.

An initial notable finding is that, except for one dwarf (EDwC-0055), all 37
galaxies with a visual GC richness score of 100% are estimated to have a
population of $N_{\rm GC}>$ 0\. The case of EDwC-0055 – shown in the upper
left panel of Fig. 14 – is intriguing: despite not being in proximity to any
apparent source of GC contamination, it exhibits a clear concentration of
point-like sources within $R_{\rm e}/2$ and visually appears GC-rich according
to our adopted definition. We made several tests on the estimated $N_{\rm GC}$
value for this galaxy and found it to be robust against changes in the
background regions used. A key factor influencing the outcome might be the
presence of three point-like sources close in projection in the galaxy core,
which might impact the algorithms for compactness selection. Furthermore,
adopting a fainter magnitude limit for GC selection, the $N_{\rm GC}$ for this
galaxy indeed makes it GC-rich. This may suggest that the galaxy lies in the
background of the cluster or that its GC population is skewed toward fainter
magnitudes due to sample size effects, or a combination of both.

Expanding the comparison to objects with a visual GC score of $\geq$ 0.85
(equivalent to six out of seven total votes in favour of GC richness), out of
70 dwarfs, four exhibit $N_{\rm GC}=1$, while the rest have $N_{\rm GC}>$ 2,
thus effectively meeting our visual definition of GC richness. A final note
regarding the comparison between visual and automated richness assessments is
that, in all cases with a score of $\geq$ 0.85, the two estimates are
consistent within the $N_{\rm GC}$ uncertainties reported in Table 4, which
were estimated from the Poisson scatter of the three background regions.

In Fig. 19, we present the same structural, photometric and positional
properties of the galaxy sample as shown in Fig. 16, in this case using the
estimated $N_{\rm GC}$ values rather than visual classification. To identify
GC-rich dwarfs quantitatively, we first determined the median population of
GCs for dwarf galaxies with $N_{\rm GC}>1$, and found $\langle N_{\rm
GC}\rangle=4$. Then, we further constrained the GC-richness by measuring its
robustness against our estimated uncertainty. Specifically, we required
$\Delta N_{\rm GC}/N_{\rm GC}\leq 0.5$, i.e. imposing that the fractional
error on $N_{\rm GC}$ must be less than or equal to 50%. In the figure we
adopt for bright, dwarf and GC-rich (contaminated and uncontaminated) galaxies
the same symbol and colour coding as Fig. 16. Furthermore, the symbol sizes of
bright (gray dots in the upper left panel) and GC-rich dwarfs (orange circles
in all panels) scale with the total population of GC candidates, adopting
different scaling factors for bright and dwarf galaxies for clarity. The
overall consistency of the results shown in Fig. 16 and Fig. 19 provides
evidence of the validity of the visual inspection approach adopted, with the
additional evidence that brighter galaxies tend to host a larger GC
population.

In the upper panel of Fig. 18, we also present the $N_{\rm GC}$ estimates for
the bright galaxies in the field. The approach adopted here, as described
above, is probably not optimal for these bright galaxies. This is because the
background correction to $N_{\rm GC}$ in the more contaminated inner cluster
regions, when using our criteria, might not be optimal and would need to be
fine-tuned for each single bright/extended galaxy. For the purposes of this
work, however, we maintain the current procedure.

Despite this limitation, the upper panel of Fig. 18 shows the expected
correlation between $N_{\rm GC}$ and $I_{\scriptscriptstyle\rm E}$, i.e.,
between the (mass of the) total GC population and the galaxy mass (Spitler &
Forbes 2009; Burkert & Forbes 2020), spanning approximately 10 magnitudes and
about three orders of magnitude in $N_{\rm GC}$, including the bright and
massive galaxies in our sample. In this panel, we plot the linear fit equation
to $\operatorname{log_{10}}N_{\rm GC}$ versus $I_{\scriptscriptstyle\rm E}$,
adopting different $I_{\scriptscriptstyle\rm E}$ magnitude intervals (see
figure caption) and including all galaxies with $N_{\rm GC}>4$. Although the
scatter is notably large – especially considering that both quantities are on
a log scale – the known correlation is well identified. A linear fit to these
data for the range of $10\leq I_{\scriptscriptstyle\rm E}\leq 21$ appears to
align with the entire data set of magnitudes and
$\operatorname{log_{10}}N_{\rm GC}$ values (Pearson correlation coefficient
$r=-0.8$). However, we find that the slope of the $N_{\rm GC}$-magnitude
relation changes for galaxies fainter than $I_{\scriptscriptstyle\rm E}=17$.
Therefore, our results seem to support similar analyses from the literature
about the flattening of the $N_{\rm GC}$-magnitude relation for faint galaxies
(Harris et al. 2013; Burkert & Forbes 2020; Jones et al. 2023). Further
refinements are in progress, with a more specific selection of GCs around
bright galaxies and possibly involving a colour selection in the GC
identification procedure using the NISP data.

The left panel of Fig. 20 shows the positions of the dwarfs in the field
(violet-blue circles), with symbol size scaled to the GCs specific frequency
($S_{N}=N_{\rm GC}\times 10^{0.4(M_{V}+15)}$). In the panel, we also show the
positions of galaxies in the five brightest magnitude ranges ($8\leq
I_{\scriptscriptstyle\rm E}\leq 13$), indicated by gray circles. While we find
that galaxies with the largest $N_{\rm GC}$ are scattered around the field,
inspecting $S_{{N}}$ it appears that galaxies located around the east-west
strip, where most of the brightest cluster members are found, tend to exhibit
larger $S_{{N}}$ values on average, especially south of the BCG region.

In the middle panel of Fig. 20, we plot the $N_{\rm GC}$ values versus the
cluster-centric radius, $R_{\rm Cl}$, measured with respect to the BCG. In
general, there seems to be no compelling evidence of a correlation between
$N_{\rm GC}$ or $S_{{N}}$ and $R_{\rm Cl}$.

As a final test for the GC populations in dwarf and bright galaxies in the
field, we compared the $S_{{N}}$ versus $V$ band magnitude relation for our
entire sample with the mean relations derived for UDGs in the Coma cluster
(Lim et al. 2018) and in Virgo (Lim et al. 2020), all shown in the right panel
of Fig. 20. Ignoring the elements with $N_{\rm GC}<4$, where the population is
typically consistent with zero within uncertainties, our $S_{{N}}$ estimates
for dwarfs appear to range between the Virgo and Coma mean relations. Previous
studies have shown that low-mass galaxies in denser environments can have
higher $S_{\rm N}$ (Peng et al. 2008; Mistani et al. 2016; Lim et al. 2018).
Therefore, our results possibly indicate that Perseus is dynamically
intermediate: not evolved and relaxed like Coma, not as active and still in
evolution as Virgo. For the bright galaxy component, i.e., all galaxies with
$I_{\scriptscriptstyle\rm E}<16.3$, we estimate a median $\langle
S_{N}\rangle=0.9$, which appears slightly smaller than the average for
galaxies of this magnitude (Harris et al. 2017). However, the scatter is quite
large, and, as explained above, the procedure adopted here to estimate $N_{\rm
GC}$ for bright targets will probably require further refinements, which will
be subject of a future dedicated paper.

As a final note, we encourage the reader to approach the GC selection
presented in this section with due consideration. It is based on morphometric
and photometric selection from single-band data, along with statistical
background decontamination. However, potential residual contamination on the
galaxy or in the background estimation regions, coupled with spatially
changing background (particularly relevant for brighter galaxies and around
bright companions), represents a significant limitation that may affect our
estimates of $N_{\rm GC}$. To enhance our analysis, future observations with
spatial resolution and depth similar to VIS, especially in the near-IR (e.g.,
from Roman or JWST), are required. These observations will provide the
necessary colour constraints for a more robust cleaning of the sample from
interlopers.

###  6.6 2D spatial distribution

In Fig. 21 we show the projected distribution and the density map and contours
of the Perseus dwarf galaxies and UDGs across the ERO FoV. The projected
density of the bright galaxy sample from Cuillandre et al. (2024b) is also
shown in the same figure.

The dwarf distribution has two main iso-density centres located on each side
of the bright galaxy distribution. The main iso-density centre is located
approximately at RA $=$ $3^{\rm h}\,19^{\rm m}\,12^{\rm s}.0$ and Dec $=\,$$$
and the second one, located to the left of the main iso-density centre, is
centred approximately at RA $=$ $3^{\rm h}\,20^{\rm m}\,8^{\rm s}.4$, Dec
$=\,$$$. The double iso-density centre could be the result of recent merger
activity reported for this cluster. It is worth noting that the bright
galaxies were not removed from the image when the data were visually inspected
for the identification of dwarfs in the field via the annotation tool.
Therefore, we may be missing a handful of dwarfs that are within the halo of
the massive (bright) galaxies.

Figure 21 also shows the iso-density centre of the GCs and the isophotal
centre of the ICL at semimajor-axis radius 320 kpc measured by Kluge et al.
(2024). The ICL isophotal centre is measured at ($3^{\rm h}\,19^{\rm
m}\,22^{\rm s}.253$, $None$) and the GC iso-density centre at ($3^{\rm
h}\,19^{\rm m}\,35^{\rm s}.031$, $None$). The ICL isophotal centre is located
westward of the BCG core by 60 kpc (Kluge et al. 2024). The comparison of the
location of the dwarfs, GCs, and ICL in the ERO field indicates that all three
distributions appear to have a main centre displaced to the west of the galaxy
light distribution, with the dwarf main centre being the most displaced (about
$110$ kpc) from the BCG. This agreement likely indicates that these shifts are
real and not driven by some bias introduced in the data reduction and
analysis. The brightest X-ray emission is centred on the BCG and only on
larger scales is offset to the east, i.e., opposite to the ICL (Kluge et al.
2024).

The 2D projected distribution of UDGs appears strongly asymmetric with respect
to the cluster centre, showing a large offset to the west of the iso-density
centres of the dwarf distribution. An asymmetry of the UDGs with respect to
the cluster centre has also been reported for the Hydra I cluster (La Marca et
al. 2022). For that cluster, roughly half of the UDGs are concentrated close
to the cluster core, in the same direction as the GCs and ICL centres, and
around a subgroup of galaxies to the north, while the other half are found
uniformly distributed at larger clustercentric distances. We also note a
similar split in the distribution for the UDGs in Perseus, with approximately
half concentrated in the west over-density and the remaining half found more
uniformly distributed at larger clustercentric distances. There is a hint that
the spatial distribution of the UDGs may be associated with over-densities of
bright galaxies in the cluster. This would be consistent with the ﬁndings for
other galaxy clusters where over-densities of UDGs are found close to
subgroups of galaxies (Janssens et al. 2019). If the UDGs are associated with
the grouping of bright galaxies, this may suggest that the UDGs joined the
cluster via accretion of subgroups. On the other hand, we cannot rule out that
they could also be native to the cluster (Sales et al. 2020).

##  7  Conclusions

As part of the Euclid ERO series of papers, we have used Euclid imaging of the
Perseus cluster to demonstrate the capabilities of the telescope for dwarf
galaxy science. The depth, spatial resolution, and FoV have allowed us to
detect and characterize 1100 dwarf galaxy candidates in a 0.7 deg2 field,
slightly offset from the BCG, NGC 1275. We visually classified their
morphologies, extracted their photometric and structural properties,
quantified their GC populations, and mapped their spatial distribution across
the cluster. Some of our key findings are highlighted below:

  * •

With 1100 dwarf candidates, this catalogue more than doubles the number of
dwarfs associated with the Perseus cluster in the literature. The detections
appear to be robust, and the dwarfs follow known scaling relations in the
literature, although the diffuse end of the dwarf parameter relations are more
densely populated than in previous studies. Morphologically, the sample can be
separated into: 96% [4%] dEs [dIs]; 53% [47%] nucleated [non-nucleated]; 74%
[26%] GC-poor [GC-rich], and 94% [6%] not morphologically disturbed
[morphologically disturbed]. Furthermore, 8% of the dwarfs can be classified
as UDGs. The UCDs were not considered during the visual examination of the
images due to their small sizes and relatively high surface brightnesses.

  * •

The nucleated dwarfs in the Perseus cluster follow the same trends found in
the literature, with nuclei typically found in brighter, larger, and rounder
dwarfs with flatter surface brightness profiles. In this work, however, we
also illustrate the potential for Euclid to identify complex nuclear
structures; it appears that several nuclei are associated with tidal features,
suggesting that we are witnessing formation or transformation events. With the
large number of dwarfs expected from the EWS, we may be able to place
observational constraints on the frequency of these events.

  * •

The combination of the surface brightness sensitivity, spatial resolution and
wide field of Euclid allowed us to detect and characterise the GC systems of
the dwarf galaxies. We automated the GC detection, and the resulting
correlation between $N_{\rm GC}$ and $I_{\scriptscriptstyle\rm E}$, including
the flattening below $I_{\scriptscriptstyle\rm E}\sim 17$, agrees well with
the literature. In terms of distribution, the dwarfs with the largest GC
counts can be found scattered throughout the cluster, but those with the
largest $S_{N}$ values are typically concentrated south of the BCG,
potentially another indication of a recent merger. Our $S_{N}$ estimates for
the Perseus dwarfs appear to range between the mean relations of those in the
Virgo and Coma clusters, suggesting that Perseus is dynamically intermediate,
neither as active as the Virgo cluster nor as relaxed as the Perseus cluster.

  * •

We compared the 2D projected distribution of the dwarfs in the cluster with
those of both the GCs and ICL distributions (Kluge et al. 2024). The dwarf
distribution is characterized by a double iso-density centre, perhaps due to a
recent merger event. The main iso-density centre of this distribution is
shifted to the west of the BCG, in agreement with the iso-density centre of
the GCs and the isophotal centre of the ICL at semimajor-axis radius 320 kpc.
The UDGs show a more asymmetric distribution than the dwarf population as a
whole; roughly half of the UDGs are located westward of the cluster centre, in
the same direction as the GC iso-density centre and the ICL isophotal centre,
while the other half can be found more uniformly distributed at larger
clustercentric distances. There is a hint that the spatial distribution of the
UDGs may be associated with over-densities of bright galaxies in the cluster,
which could indicate their recent accretion via groups. However, we cannot
rule out that they may also be native to the cluster.

The ERO VIS images of the Perseus cluster have demonstrated the capability of
Euclid to not only detect new LSB galaxies, including those close to bright
stars, but more importantly, to identify them as genuine dwarf galaxies. The
pristine PSF and high spatial resolution of Euclid provide the ability to
distinguish dwarfs from other sources, such as background galaxies, without
the need of follow-up observations. Furthermore, we showed that Euclid offers
the added benefit of being able to also provide a census of the GC systems and
nuclei associated with the dwarfs. In particular, looking for high
concentrations of GCs in the Euclid surveys shows great potential for the
detection of GC-rich dwarfs and UDGs.

The upcoming EWS will have a sky coverage $\sim$ 14 000 deg2. Although it is
expected to be about 0.75 mag arcsec-2 less deep than the data presented in
this work, it will transform our ability to characterise dwarf galaxies across
a range of stellar masses and located in a variety of environments. The
analysis of such a large data set will require the development of automatic
detection methods, which are currently underway. The dwarf catalogue presented
here should prove to be a useful benchmark for testing present and future
machine learning techniques.

###### Acknowledgements.

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). This work has
made use of the Early Release Observation (ERO) data from the Euclid mission
of the European Space Agency (ESA), 2024, https://doi.org/10.57780/esa-
qmocze3. O. Marchal would like to acknowledge Thomas Boch and Matthieu Baumann
at the Observatoire de Strasbourg. M. Poulain and A. Venhola are both
supported by the Academy of Finland grant number 347089. A. Ferré-Mateu
acknowledges support from RYC2021-031099-I and PID2021-123313NA-I00 of
MICIN/AEI/10.13039/501100011033/FEDER,UE,NextGenerationEU/PRT. L. Hunt, R.
Scaramella, M. Cantiello, and R. Habas acknowledge funding from the Italian
INAF Large Grant 12-2022.

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##  Appendix A Properties of the dwarf galaxy candidates

The dwarf galaxy candidates are classified by visual inspection with the
methodology described in Sect. 3. The final sample contains 1100 dwarf
galaxies of which 96% are classified as dE, and 4% as dI. The dE galaxies are
further classified as nucleated (53%), GC-rich (26%), and with disturbed
morphology (6%).

Table 3 lists the entire sample of dwarf galaxy candidates, ordered by
increasing RA. The columns are as follows: a unique identifier (ID), RA in
degrees, Dec in degrees, morphology (either dE or dI), GC-rich flag (recall
that in the visual classification we defined dwarfs with $N_{\rm GC}>2$ GCs as
GC-rich), a flag for the presence of a nucleus (Nucleated), and a disturbed
morphology flag (Disturbed). Both dE and dI galaxies could be classified as
disturbed.

Table 4 lists the photometric and structural parameters of the dwarf galaxy
candidates (ordered by increasing RA) obtained with the methodology described
in Sect. 5. The column definitions are as follows: a unique identifier (ID),
RA in degrees, Dec in degrees, apparent magnitude in the
$I_{\scriptscriptstyle\rm E}$ filter ($I_{\scriptscriptstyle\rm E}$),
effective radius in arcsec ($R_{\rm e}$), Sérsic index (n), axis ratio (AR),
position angle in radians (PA), central surface brightness
($\mu_{I_{\scriptscriptstyle\rm E},\rm 0}$, mag arcsec-2), surface brightness
at $R_{\rm e}$ ($\mu_{I_{\scriptscriptstyle\rm E},\rm e}$, mag arcsec-2),
surface brightness within $R_{\rm e}$ ($\langle\mu_{I_{\scriptscriptstyle\rm
E},\rm e}\rangle$, mag arcsec-2), the number of associated globular clusters
($N_{\rm GC}$), and the number of nuclear star clusters ($N_{\rm NSC}$).

Table 5 lists the aperture magnitudes and extinction corrections (EC)
described in Sect. 5.5 and 5.1, respectively. The columns are: a unique
identifier (ID), the apparent magnitude in the $I_{\scriptscriptstyle\rm E}$
filter, the extinction correction in $I_{\scriptscriptstyle\rm E}$, the
apparent magnitude in the $Y_{\scriptscriptstyle\rm E}$ filter, the extinction
correction in $Y_{\scriptscriptstyle\rm E}$, apparent magnitude in the
$J_{\scriptscriptstyle\rm E}$ filter, the extinction correction in
$J_{\scriptscriptstyle\rm E}$, the apparent magnitude in the
$H_{\scriptscriptstyle\rm E}$ filter, and the extinction in
$H_{\scriptscriptstyle\rm E}$. The dwarf galaxy candidates are ordered by
increasing RA.

Finally, images of the 1100 dwarf galaxy candidates in the final sample of
this work are shown in Fig. 22. The cutouts were created from the
$I_{\scriptscriptstyle\rm E}$ image. For better visibility, the dimensions of
each cutout have been scaled to twice the area of the original annotations and
an arcsinh stretch has been applied. The dwarf candidates are ordered by
decreasing surface brightness $\langle\mu_{I_{\scriptscriptstyle\rm E},\rm
e}\rangle$.

Table 3: Table of the visual properties of the dwarfs galaxy candidates. The
full table will be available as supplementary material at the Strasbourg
astronomical Data Center (CDS; https://www.aanda.org/for-authors/latex-
issues/tables).

ID | RA | Dec | Morphology |  00GC-rich00 | Nucleated |  00Disturbed
---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  |
EDwC-0001**$*$Denotes dwarf candidates that fall just outside of the Euclid footprint, and that were identified in an earlier data product with a slightly larger FoV. They are included here for completeness. | 48.975450 | 41.692800 | dE | Yes | Yes | Yes
EDwC-0002 | 49.021117 | 41.783423 | dE | No | No | No
EDwC-0003 | 49.033821 | 41.683320 | dE | Yes | Yes | No
EDwC-0004 | 49.047517 | 41.621950 | dE | No | Yes | No
EDwC-0005 | 49.064550 | 41.624950 | dE | No | No | Yes
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
EDwC-1095 | 50.325621 | 41.517185 | dE | No | No | No
EDwC-1096 | 50.329711 | 41.521662 | dE | No | Yes | No
EDwC-1097 | 50.335171 | 41.549552 | dE | Yes | Yes | No
EDwC-1098 | 50.344780 | 41.503080 | dE | No | Yes | No
EDwC-1099 | 50.349776 | 41.570365 | dE | No | No | No
EDwC-1100**$*$Denotes dwarf candidates that fall just outside of the Euclid footprint, and that were identified in an earlier data product with a slightly larger FoV. They are included here for completeness. | 50.360450 | 41.540150 | dE | No | No | No

777

Table 4: Photometric and structural properties of the dwarf galaxy candidates.
The full table will be available as supplementary material at the Strasbourg
astronomical Data Center (CDS) (https://www.aanda.org/for-authors/latex-
issues/tables).

ID | RA | Dec |  $I_{\scriptscriptstyle\rm E}$ |  $R_{\rm e}$ |  $n$ | AR | PA |  $\mu_{I_{\scriptscriptstyle\rm E},\rm{0}}$ |  $\mu_{I_{\scriptscriptstyle\rm E},\rm{e}}$ |  $\langle\mu_{I_{\scriptscriptstyle\rm E},\rm{e}}\rangle$ |  $N_{\rm GC}$ |  $N_{\rm NSC}$
---|---|---|---|---|---|---|---|---|---|---|---|---
| [deg] | [deg] | [mag] | [arcsec] |  |  | [rad] |  [mag arcsec-2] |  [mag arcsec-2] |  [mag arcsec-2] |  |
EDwC-0001**$*$Denotes dwarf candidates that fall just outside of the Euclid footprint, and that were identified in an earlier data product with a slightly larger FoV. They are included here for completeness. | 48.975450 | 41.692800 |  15.64 $\pm$ 0.31 |  15.00 $\pm$ 1.72 |  3.82 $\pm$ 0.17 |  0.89 $\pm$ 0.01 |  1.95 $\pm$ 0.04 |  16.83 $\pm$ 0.01 |  24.76 $\pm$ 0.24 |  19.16 $\pm$ 0.00 |  6.0 $\pm$ 17.0 | 1
EDwC-0002 | 49.021117 | 41.783423 |  22.82 $\pm$ 0.26 |  1.25 $\pm$ 0.07 |  0.50 $\pm$ 0.21 |  0.69 $\pm$ 0.06 |  2.61 $\pm$ 0.12 |  24.54 $\pm$ 0.61 |  25.29 $\pm$ 0.62 |  24.93 $\pm$ 0.36 |  0.0 $\pm$ 0.0 | 0
EDwC-0003 | 49.033821 | 41.683320 |  17.99 $\pm$ 0.00 |  7.57 $\pm$ 0.03 |  0.35 $\pm$ 0.00 |  0.50 $\pm$ 0.00 |  2.76 $\pm$ 0.00 |  23.49 $\pm$ 0.00 |  23.93 $\pm$ 0.01 |  22.15 $\pm$ 0.00 |  5.0 $\pm$ 5.0 | 3
EDwC-0004 | 49.047517 | 41.621950 |  19.08 $\pm$ 0.28 |  3.50 $\pm$ 0.34 |  1.47 $\pm$ 0.17 |  0.41 $\pm$ 0.01 |  1.26 $\pm$ 0.01 |  20.87 $\pm$ 0.05 |  23.71 $\pm$ 0.13 |  21.90 $\pm$ 0.01 |  0.0 $\pm$ 2.0 | 1
EDwC-0005 | 49.064550 | 41.624950 |  19.25 $\pm$ 0.02 |  4.24 $\pm$ 0.09 |  1.65 $\pm$ 0.03 |  0.46 $\pm$ 0.00 |  0.51 $\pm$ 0.01 |  21.25 $\pm$ 0.00 |  24.48 $\pm$ 0.26 |  22.21 $\pm$ 0.00 |  1.0 $\pm$ 3.0 | 1
EDwC-0006 | 49.066602 | 41.735277 |  22.75 $\pm$ 0.25 |  1.70 $\pm$ 0.12 |  1.13 $\pm$ 0.23 |  0.54 $\pm$ 0.04 |  0.12 $\pm$ 0.06 |  23.87 $\pm$ 0.16 |  25.98 $\pm$ 0.04 |  24.92 $\pm$ 0.06 |  $-$1.0 $\pm$ 0.0 | 0
EDwC-0007 | 49.067834 | 41.780197 |  21.94 $\pm$ 0.03 |  2.68 $\pm$ 0.09 |  1.18 $\pm$ 0.04 |  0.45 $\pm$ 0.01 |  1.78 $\pm$ 0.01 |  23.77 $\pm$ 0.01 |  25.98 $\pm$ 0.14 |  24.59 $\pm$ 0.00 |  1.0 $\pm$ 2.0 | 0
EDwC-0008 | 49.069858 | 41.731817 |  20.57 $\pm$ 0.07 |  5.88 $\pm$ 0.37 |  1.40 $\pm$ 0.07 |  0.82 $\pm$ 0.01 |  1.61 $\pm$ 0.06 |  24.37 $\pm$ 0.01 |  27.05 $\pm$ 0.01 |  23.98 $\pm$ 0.00 |  $-$1.0 $\pm$ 4.0 | 2
EDwC-0009 | 49.070800 | 41.719650 |  19.74 $\pm$ 0.00 |  3.15 $\pm$ 0.01 |  0.32 $\pm$ 0.00 |  0.32 $\pm$ 0.00 |  2.02 $\pm$ 0.00 |  22.91 $\pm$ 0.00 |  23.29 $\pm$ 0.06 |  22.97 $\pm$ 0.00 |  5.0 $\pm$ 3.0 | 0
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
EDwC-1095 | 50.325621 | 41.517185 |  22.06 $\pm$ 0.02 |  2.00 $\pm$ 0.06 |  0.68 $\pm$ 0.03 |  0.48 $\pm$ 0.01 |  0.97 $\pm$ 0.02 |  24.16 $\pm$ 0.02 |  25.30 $\pm$ 0.06 |  24.61 $\pm$ 0.02 |  $-$1.0 $\pm$ 0.0 | 0
EDwC-1096 | 50.329711 | 41.521662 |  21.62 $\pm$ 0.23 |  2.30 $\pm$ 0.17 |  1.71 $\pm$ 0.23 |  0.41 $\pm$ 0.02 |  3.04 $\pm$ 0.03 |  22.05 $\pm$ 0.06 |  25.40 $\pm$ 0.13 |  23.89 $\pm$ 0.01 |  $-$1.0 $\pm$ 0.0 | 0
EDwC-1097 | 50.335171 | 41.549552 |  20.38 $\pm$ 0.02 |  3.63 $\pm$ 0.08 |  1.04 $\pm$ 0.02 |  0.68 $\pm$ 0.01 |  1.48 $\pm$ 0.02 |  23.58 $\pm$ 0.01 |  25.48 $\pm$ 0.05 |  23.43 $\pm$ 0.00 |  6.0 $\pm$ 4.0 | 2
EDwC-1098 | 50.344780 | 41.503080 |  17.24 $\pm$ 0.01 |  5.98 $\pm$ 0.04 |  2.01 $\pm$ 0.01 |  0.94 $\pm$ 0.00 |  1.26 $\pm$ 0.02 |  20.09 $\pm$ 0.00 |  24.10 $\pm$ 0.00 |  20.43 $\pm$ 0.02 |  6.0 $\pm$ 5.0 | 0
EDwC-1099 | 50.349776 | 41.570365 |  21.11 $\pm$ 0.02 |  2.88 $\pm$ 0.08 |  0.51 $\pm$ 0.03 |  0.71 $\pm$ 0.01 |  1.60 $\pm$ 0.05 |  24.67 $\pm$ 0.02 |  25.45 $\pm$ 0.06 |  24.13 $\pm$ 0.00 |  1.0 $\pm$ 2.0 | 0
EDwC-1100**$*$Denotes dwarf candidates that fall just outside of the Euclid footprint, and that were identified in an earlier data product with a slightly larger FoV. They are included here for completeness. | 50.360450 | 41.540150 |  19.24 $\pm$ 0.03 |  5.92 $\pm$ 0.05 |  0.36 $\pm$ 0.01 |  0.50 $\pm$ 0.01 |  2.06 $\pm$ 0.01 |  24.17 $\pm$ 0.01 |  24.63 $\pm$ 0.03 |  23.10 $\pm$ 0.00 |  $-$2.0 $\pm$ 3.0 | 0

888

Table 5: Aperture magnitudes and extinction correction (EC) in the Euclid
$Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and
$H_{\scriptscriptstyle\rm E}$ bands for each dwarf galaxy candidate. The full
table will be available as supplementary material at the Strasbourg
astronomical Data Center (CDS) (https://www.aanda.org/for-authors/latex-
issues/tables).

ID |  $I_{\scriptscriptstyle\rm E}$ | EC ($I_{\scriptscriptstyle\rm E}$) |  $Y_{\scriptscriptstyle\rm E}$ | EC ($Y_{\scriptscriptstyle\rm E}$) |  $J_{\scriptscriptstyle\rm E}$ | EC ($J_{\scriptscriptstyle\rm E}$) |  $H_{\scriptscriptstyle\rm E}$ | EC ($H_{\scriptscriptstyle\rm E}$)
---|---|---|---|---|---|---|---|---
EDwC-0001**$*$Denotes dwarf candidates that fall just outside of the Euclid footprint, and that were identified in an earlier data product with a slightly larger FoV. They are included here for completeness. | 16.63 $\pm$ 0.00 | 0.26 $\pm$ 0.01 | … | 0.13 $\pm$ 0.01 | … | 0.09 $\pm$ 0.00 | … | 0.06 $\pm$ 0.00
EDwC-0002 | 23.72 $\pm$ 0.06 | 0.29 $\pm$ 0.01 | 23.17 $\pm$ 0.05 | 0.15 $\pm$ 0.01 | 23.33 $\pm$ 0.05 | 0.10 $\pm$ 0.00 | 23.50 $\pm$ 0.05 | 0.07 $\pm$ 0.00
EDwC-0003 | 16.80 $\pm$ 0.00 | 0.26 $\pm$ 0.01 | 16.41 $\pm$ 0.00 | 0.13 $\pm$ 0.01 | 16.42 $\pm$ 0.00 | 0.09 $\pm$ 0.00 | 16.48 $\pm$ 0.00 | 0.06 $\pm$ 0.00
EDwC-0004 | 19.54 $\pm$ 0.01 | 0.26 $\pm$ 0.02 | 18.85 $\pm$ 0.01 | 0.13 $\pm$ 0.01 | 18.92 $\pm$ 0.01 | 0.09 $\pm$ 0.01 | 18.47 $\pm$ 0.01 | 0.06 $\pm$ 0.00
EDwC-0005 | 19.83 $\pm$ 0.01 | 0.26 $\pm$ 0.02 | 19.32 $\pm$ 0.01 | 0.13 $\pm$ 0.01 | 19.34 $\pm$ 0.01 | 0.09 $\pm$ 0.01 | 19.23 $\pm$ 0.01 | 0.06 $\pm$ 0.00
EDwC-0006 | 23.63 $\pm$ 0.05 | 0.28 $\pm$ 0.01 | 23.57 $\pm$ 0.06 | 0.14 $\pm$ 0.01 | 23.28 $\pm$ 0.05 | 0.10 $\pm$ 0.00 | 23.23 $\pm$ 0.05 | 0.06 $\pm$ 0.00
EDwC-0007 | 22.52 $\pm$ 0.03 | 0.30 $\pm$ 0.01 | 22.08 $\pm$ 0.03 | 0.15 $\pm$ 0.01 | 22.07 $\pm$ 0.03 | 0.10 $\pm$ 0.00 | 21.97 $\pm$ 0.03 | 0.07 $\pm$ 0.00
EDwC-0008 | 20.86 $\pm$ 0.02 | 0.28 $\pm$ 0.01 | 20.05 $\pm$ 0.01 | 0.14 $\pm$ 0.01 | 19.83 $\pm$ 0.01 | 0.10 $\pm$ 0.00 | 19.56 $\pm$ 0.01 | 0.06 $\pm$ 0.00
EDwC-0009 | 20.11 $\pm$ 0.01 | 0.28 $\pm$ 0.01 | 19.52 $\pm$ 0.01 | 0.14 $\pm$ 0.01 | 19.47 $\pm$ 0.01 | 0.09 $\pm$ 0.00 | 19.39 $\pm$ 0.01 | 0.06 $\pm$ 0.00
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
EDwC-1095 | 22.59 $\pm$ 0.03 | 0.33 $\pm$ 0.02 | 22.21 $\pm$ 0.03 | 0.17 $\pm$ 0.01 | 22.19 $\pm$ 0.03 | 0.11 $\pm$ 0.01 | 22.15 $\pm$ 0.03 | 0.07 $\pm$ 0.00
EDwC-1096 | 22.26 $\pm$ 0.03 | 0.33 $\pm$ 0.02 | 21.95 $\pm$ 0.03 | 0.17 $\pm$ 0.01 | 21.85 $\pm$ 0.03 | 0.11 $\pm$ 0.01 | 21.82 $\pm$ 0.03 | 0.07 $\pm$ 0.00
EDwC-1097 | 21.00 $\pm$ 0.02 | 0.32 $\pm$ 0.02 | 20.70 $\pm$ 0.01 | 0.16 $\pm$ 0.01 | 20.63 $\pm$ 0.01 | 0.11 $\pm$ 0.01 | 20.63 $\pm$ 0.01 | 0.07 $\pm$ 0.00
EDwC-1098 | 18.00 $\pm$ 0.00 | 0.35 $\pm$ 0.02 | 17.42 $\pm$ 0.00 | 0.17 $\pm$ 0.01 | 17.31 $\pm$ 0.00 | 0.12 $\pm$ 0.01 | 17.22 $\pm$ 0.00 | 0.08 $\pm$ 0.00
EDwC-1099 | 21.73 $\pm$ 0.02 | 0.32 $\pm$ 0.02 | 21.25 $\pm$ 0.02 | 0.16 $\pm$ 0.01 | 21.25 $\pm$ 0.02 | 0.11 $\pm$ 0.01 | 21.23 $\pm$ 0.02 | 0.07 $\pm$ 0.00
EDwC-1100**$*$Denotes dwarf candidates that fall just outside of the Euclid footprint, and that were identified in an earlier data product with a slightly larger FoV. They are included here for completeness. | 19.94 $\pm$ 0.01 | 0.34 $\pm$ 0.02 | 19.37 $\pm$ 0.01 | 0.17 $\pm$ 0.01 | 19.29 $\pm$ 0.01 | 0.11 $\pm$ 0.01 | 19.34 $\pm$ 0.01 | 0.07 $\pm$ 0.00

999

Figure 22: Cutouts of the $I_{\scriptscriptstyle\rm E}$ image with arcsinh
stretching of all our dwarf candidates, ordered by decreasing surface
brightness $\langle\mu_{I_{\scriptscriptstyle\rm E},\rm e}\rangle$. The size
of the cutouts are proportional to twice the area determined from the
annotation of the classifiers, with north up and east to the left. The figure
continues on the next pages.

Figure 23: Continued.

Figure 24: Continued.

Figure 25: Continued.

Figure 26: Continued.

Figure 27: Continued.

Figure 28: Continued.

Figure 29: Continued.

Figure 30: Continued.

##  Appendix B Visual properties of the galaxies not included in the final
dwarf catalogue

The final catalogue of dwarf galaxies presented in Appendix A is based on the
voting system presented in Sect. 3. A score of 0.7 (corresponding to the
agreement of 5/7 classifiers) was the threshold we adopted to keep or reject a
galaxy from the final catalogue. Some 160 objects from our initial list of
1260 objects fall below this threshold and were subsequently removed from the
sample. Nevertheless, these are objects that were initially flagged as
potential dwarf candidates by at least two team members, and may include some
legitimate dwarf galaxies; hence, we include their properties here. Table 6
presents the visual properties of the candidates, ordered by increasing RA.
The columns include: a unique identifier (ID), RA in degrees, Dec in degrees,
morphology (either dE or dI), a GC-rich flag (where dwarfs with $N_{\rm GC}>2$
GCs were considered GC-rich), a flag denoting the presence of a nucleus
(Nucleated), and a flag for galaxies with disturbed morphologies (Disturbed).

Images of these rejected candidates are shown in Fig. 31. The cutouts were
created from the $I_{\scriptscriptstyle\rm E}$ image. For better visibility,
the dimensions of each cutout have been scaled to twice the area of the
original annotations and an arcsinh stretch has been applied. The dwarf
candidates are ordered by increasing RA.

Table 6: Visual properties of the dwarf galaxy candidates not included in the final catalogue. The full table will be available as supplementary material at the Strasbourg astronomical Data Center (CDS; https://www.aanda.org/for-authors/latex-issues/tables). ID | RA | Dec | Morphology |  00GC-rich00 | Nucleated |  00Disturbed
---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  |
1101 | 49.003850 | 41.815750 | dE | No | No | No
1102 | 49.025050 | 41.822250 | dE | No | Yes | Yes
1103 | 49.040055 | 41.820055 | dE | No | No | Yes
1104 | 49.055566 | 41.797613 | dE | No | No | No
1105 | 49.071610 | 41.690478 | dE | No | No | No
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
1256 | 50.314450 | 41.437250 | dE | No | No | No
1257 | 50.317150 | 41.477000 | dE | No | No | No
1258 | 50.319350 | 41.467400 | dE | No | No | No
1259 | 50.326200 | 41.478567 | dE | No | No | No
1260 | 50.344600 | 41.583450 | dE | No | No | No

Figure 31: Cutouts of the $I_{\scriptscriptstyle\rm E}$ image with arcsinh
stretching of the 160 objects rejected as dwarf candidates, ordered by
increasing right ascension. The size of the cutouts are proportional to twice
the area determined from the annotation of the classifiers, with north up and
east to the left. The figure continues on the next page.

Figure 32: Continued.

##  Appendix C Euclid NISP-NISP colours as a function of VIS magnitude
$I_{\scriptscriptstyle\rm E}$

Following the discussion of the colours in Sect. 5.1, we also include the
Euclid NISP-NISP colours in Fig. 33.

Figure 33: Euclid NISP-NISP colours as a function of $I_{\scriptscriptstyle\rm
E}$ measured using aperture photometry within 1 $R_{\rm e}$ of the 1100 dwarf
galaxy candidates and the bright galaxy sample in the ERO Perseus field from
Cuillandre et al. (2024b) shown in violet-blue and light-grey colours,
respectively. The magnitudes were corrected for extinction before the colours
were computed, as described in Sect. 5.1.