11institutetext: Instituto de Astrofísica de Canarias, c/ Vía Láctea s/n,
E-38205 - La Laguna, Tenerife, Spain 11email<EMAIL_ADDRESS>22institutetext: Departamento de Astrofísica, Universidad de La Laguna,
E-38205 - La Laguna, Tenerife, Spain 33institutetext: Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 44institutetext:
Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008
Granada, Spain 55institutetext: Department of Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
66institutetext: Centro de Estudios de Física del Cosmos de Aragón (CEFCA),
Plaza San Juan, 1, E-44001, Teruel, Spain 77institutetext: Department of
Physics and Space Science, Royal Military College of Canada P.O. Box 17000,
Station Forces Kingston, ON K7K 7B4, Canada 88institutetext: Department of
Physics, Engineering Physics and Astronomy, Queens University, Kingston, ON
K7L 3N6, Canada 99institutetext: Centre for Astrophysics and Supercomputing,
Swinburne University of Technology, Hawthorn, VIC 3122, Australia
1010institutetext: The Oskar Klein Centre, Department of Astronomy, Stockholm
University, AlbaNova, SE-10691 Stockholm, Sweden 1111institutetext: Department
of Physics and Astronomy, University of Padova, Vicolo Osservatorio 3, 35122
Padova, Italy 1212institutetext: Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA 1313institutetext: Kapteyn
Astronomical Institute, University of Groningen, Landleven 12, 9747 AD
Groningen, The Netherlands

# An almost dark galaxy with the mass of the Small Magellanic Cloud

Mireia Montes 112233 Ignacio Trujillo 1122 Ananthan Karunakaran 4455 Raúl
Infante-Sainz 66 Kristine Spekkens 7788 Giulia Golini 1122 Michael Beasley 99
Maria Cebrián 1122 Nushkia Chamba 1010 Mauro D’Onofrio 1111 Lee Kelvin 1212
Javier Román 13131122

Almost Dark Galaxies are objects that have eluded detection by traditional
surveys such as the Sloan Digital Sky Survey (SDSS). The low surface
brightness of these galaxies ($\mu_{r}$(0)$>26$ mag/arcsec2), and hence their
low surface stellar mass density (a few solar masses per pc2 or less),
suggests that the energy density released by baryonic feedback mechanisms is
inefficient in modifying the distribution of the dark matter halos they
inhabit. For this reason, almost dark galaxies are particularly promising for
probing the microphysical nature of dark matter. In this paper, we present the
serendipitous discovery of Nube, an almost dark galaxy with $<\mu_{V}>_{e}\sim
26.7$ mag/arcsec2. The galaxy was identified using deep optical imaging from
the IAC Stripe82 Legacy Project. Follow-up observations with the 100m Green
Bank Telescope strongly suggest that the galaxy is at a distance of 107 Mpc.
Ultra-deep multi-band observations with the 10.4m Gran Telescopio Canarias
favour an age of $\sim 10$ Gyr and a metallicity of [Fe/H]$\sim-1.1$. With a
stellar mass of $\sim 4\times 10^{8}$ M⊙ and a half-mass radius of $R_{e}=6.9$
kpc (corresponding to an effective surface density of $<\Sigma>_{e}\sim 0.9$
M⊙/pc2), Nube is the most massive and extended object of its kind discovered
so far. The galaxy is ten times fainter and has an effective radius three
times larger than typical ultra-diffuse galaxies with similar stellar masses.
Galaxies with comparable effective surface brightness within the Local Group
have very low mass (tens of 105 M⊙) and compact structures (effective radius
$R_{e}<1$ kpc). Current cosmological simulations within the cold dark matter
scenario, including baryonic feedback, do not reproduce the structural
properties of Nube. However, its highly extended and flattened structure is
consistent with a scenario where the dark matter particles are ultra-light
axions with a mass of mB=($0.8^{+0.4}_{-0.2}$)$\times 10^{-23}$ eV.

###### Key Words.:

Galaxies: dwarf – dark matter – galaxies: photometry – galaxies: structure –
galaxies: formation

##  1 Introduction

Many cosmological observations at large scales suggest that dark matter can be
well described as a cold and collisionless fluid (see e.g., White & Rees,
1978; Blumenthal et al., 1984; Davis et al., 1985; Smoot et al., 1992).
Nonetheless, the predictions of this model at galactic scales have faced an
increasing number of challenges, such as the “cusp-core problem”, the “missing
satellite problem” or the “too-big-to-fail problem” (see e.g., Boylan-Kolchin
et al., 2011; Weinberg et al., 2015; Del Popolo & Le Delliou, 2017). Many of
these problems can be mitigated by the effect of baryon feedback on the dark
matter distribution (see e.g., Davis et al., 1992; Governato et al., 2010; Di
Cintio et al., 2014). However, if the number of stars or their spatial density
is low enough, it would be difficult to argue that stellar feedback could be
responsible for affecting the dark matter distribution, since there would not
be enough energy to change the location of the dark matter (see e.g.,
Peñarrubia et al., 2012; Oñorbe et al., 2015). In parallel, as long as the
direct detection of dark matter particles remains out of reach, other
alternatives to the cold dark matter model have gained traction to solve the
small scale challenges. These include the warm dark matter scenario (see e.g.,
Sommer-Larsen & Dolgov, 2001; Bode et al., 2001), self-interacting dark matter
(Spergel & Steinhardt, 2000) or fuzzy dark matter (composed of ultra-light
axions with masses in the 10-23-10-21 eV range; see e.g., Sin, 1994; Hu et
al., 2000; Matos & Arturo Ureña-López, 2001). For these reasons, the search
for objects with extremely low stellar surface densities (where the effect of
baryonic feedback is not expected to be relevant) promises to probe the
microphysical nature of dark matter, i.e., the properties of the dark matter
particle.

In recent years, our ability to detect more and more diffuse galaxies with
broadband imaging has increased considerably (see e.g., Sandage & Binggeli,
1984; Conselice et al., 2003; van Dokkum et al., 2015; Román & Trujillo, 2017;
Lim et al., 2020; Tanoglidis et al., 2021; Trujillo et al., 2021; Marleau et
al., 2021; La Marca et al., 2022; Zaritsky et al., 2023), and it is expected
to continue to increase with the arrival of very deep optical surveys (see
e.g., Ivezić et al., 2019). Within this population of very faint galaxies, the
so-called “almost dark” galaxies are of particular interest. These faint
galaxies are missed in the optical catalogues of wide field surveys such as
the Sloan Digital Sky Survey (SDSS, Eisenstein et al., 2011). Although there
is no definition of the surface brightness of an almost dark galaxy, given the
SDSS surface brightness limit (i.e., $\mu_{r}\sim 26.5-27$ mag/arcsec2;
3$\sigma$ in 10″$\times$10″ boxes), galaxies with central surface brightness
fainter than $\mu_{r}(0)\sim 26$ mag/arcsec2 are very difficult to detect in
SDSS catalogues. Therefore, we can use such a value as a rough definition of
what an almost dark galaxy should be. These galaxies represent less than 1% of
the galaxies found in blind HI surveys such as Arecibo Legacy Fast Arecibo
L-band Feed Array (ALFALFA, Giovanelli et al., 2005), and have HI masses
between 107 and 109 M⊙. Since the definition of an almost dark galaxy depends
on whether it is typically detected in the SDSS, its maximum stellar surface
mass density is a function of its stellar population properties (age and
metallicity). In a scenario where the age of the stellar population is old
($\sim 10$ Gyr) and metal-poor ([Fe/H]$\sim-1$), a surface brightness of
$\mu_{r}(0)\sim 26$ mag/arcsec2 corresponds to a few M⊙/pc2. This is very
close to the expected stellar surface density resulting from the gas density
threshold for star formation (Schaye, 2004) and in good agreement with the
values found at the edges of galaxies where star formation suddenly drops off
(Trujillo et al., 2020; Chamba et al., 2022). Consequently, almost dark
galaxies may also be an interesting place to study how galaxy formation occurs
at low densities.

In this paper, we describe the structural properties of a very extended almost
dark galaxy serendipitously discovered in the IAC Stripe82 Legacy Project
(Fliri & Trujillo, 2016; Román & Trujillo, 2018). This object (which we have
named Nube111$\backslash$noo-beh$\backslash$. Cloud in Spanish.) was found
during a visual inspection of one of the survey fields. The object is not
visible in SDSS and appears quite noisy even in deeper images such as those
produced by the Stripe82 data (see Fig. 1). Dedicated observations with the
Gran Telescopio Canarias and the Green Bank Telescope have allowed to
characterise its nature in detail. This paper presents a comprehensive
analysis of the stellar populations and structural properties of this object.
We also consider the properties of this very faint galaxy within the cold dark
matter and fuzzy dark matter scenarios.

Throughout this work we adopt a standard cosmological model with the following
parameters: $H_{0}=70$ km s-1 Mpc-1, $\Omega_{m}=0.3$ and
$\Omega_{\Lambda}=0.7$. Based on the probable redshift of this galaxy, the
assumed distance is $107$ Mpc, corresponding to a spatial scale of $0.5039$
kpc/arcsec. All magnitudes in this paper are in the AB magnitude system.

##  2 Data

The data used in this paper come from two different facilities: the 10.4m Gran
Telescopio Canarias (GTC) and the 100m Robert C. Byrd Green Bank Telescope
(GBT). The details of each observation are described below.

###  2.1 GTC HiPERCAM images

Deep optical multi-band imaging of Nube was performed using HiPERCAM. HiPERCAM
(Dhillon et al., 2018) is a quintuple-beam, high-speed astronomical imager
capable of simultaneously imaging celestial objects in five different Sloan
filters ($u$, $g$, $r$, $i$, $z$). The image area of each of the five CCDs is
$2048\times 1024$ pixels ($2.7\arcmin\times 1.4\arcmin$; 1
pixel$=0\aas@@fstack{\prime\prime}08$) divided into four channels of
$1024\times 512$ pixels each. Nube was observed on 9 and 10 January 2019. We
followed the dithering strategy described in Trujillo & Fliri (2016) to reduce
as much as possible the scattered light from the telescope structure.

The data reduction of the Nube images follows the steps detailed in Montes et
al. (2020) and briefly described here. The entire reduction process was
carried out in a controlled and enclosed environment as described in Akhlaghi
et al. (2021). After the standard calibration per CCD channel (bias and flat
field), each set of four channels was assembled into a single image. The
different exposures that went into the final images were visually inspected,
and those with low quality (too noisy and/or very bright background) or strong
gradients were discarded. Photometric calibration of these images was
performed using SDSS DR12 (Alam et al., 2015). The size of Nube on the sky
(effective diameter of $\sim$27$\arcsec$; see Fig. 1) is significantly smaller
than the FOV of the camera ($162\arcsec\times 84\arcsec$), allowing reliable
background subtraction and study of the galaxy using these images. The
background subtraction was performed by subtracting a calculated constant
value from the masked image. In addition to masking the foreground and
background sources, we masked a circular region with a radius of $40\arcsec$
centred on Nube (that is $\sim 3$Re of this galaxy, see Sec. 3.1) to avoid
over-subtracting the light associated with the outer parts of the galaxy.

The final exposure time on-source is 1 hour and 8 minutes for each band. The
limiting surface brightness depths of the final images measured in
$10\arcsec\times 10\arcsec$ boxes are 30.5, 31, 30.5, 30 and 29.2 mag/arcsec2
for $u$, $g$, $r$, $i$ and $z$ ($3\sigma$ above the background) respectively,
measured using the method described in Appendix A of Román et al. (2020). The
limiting magnitudes for point-like sources are: 26.2, 26.7, 26.2, 25.8 and 25
mag from u to z (5$\sigma$ within an aperture of 2″).

Figure 1: SDSS RGB image of the 20′$\times$20′ region around Nube. The insets
show a zoom in on the galaxy, showing how it appears on images with different
limiting surface brightness in the r-band (26.7, 28.6 and 30.5 mag/arcsec2;
3$\sigma$ on 10″$\times$10″boxes). Previously known galaxies in the field of
view are labelled.

###  2.2 GBT HI data

We performed $\sim$12 hours of observations with the Green Bank Telescope
(GBT)222The Green Bank Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. along the line of sight (LOS) to Nube between January 2019 and July 2019
(programmes GBT18B-356 and GBT19A-485). Our observational configuration is
identical to that of Karunakaran et al. (2020b), where we used the L-band
receiver and the VErsatile GBT Astronomical Spectrometer (VEGAS) in Mode 7
(spectral resolution = 3 kHz $\sim 0.7$ km/s, bandpass = 100 MHz). The use of
such a wide bandpass, sensitive out to recession velocities of $\sim 14000$
km/s, is essential in the blind search for HI in such a faint object, which
can be at any distance along the LOS.

These data were reduced using the standard GBTIDL333http://gbtidl.nrao.edu/
procedure getps. We removed both narrowband and broadband Radio Frequency
Interference (RFI) before searching for potential HI signals. We note that
broadband RFI (i.e. GPS L3, $\mu 1.381$ GHz) was particularly prominent,
resulting in almost a third of the data being flagged. The effective
integration time of the final calibrated spectrum is therefore $\sim$8.5
hours. We also note that the fluxes are scaled up by a factor of 20% due to
the systematic offset in the GBT noise diode calibration values (Goddy et al.,
2020). We smoothed the resulting RFI-free spectrum at various spectral
resolutions to search for possible HI emission. Fig. 2 shows a faint HI
detection at VHelio = $7480\pm 8$ km/s (red line) with a signal-to-noise ratio
of 6.1, along with the statistically independent XX and YY polarizations (blue
and green lines, respectively) that were co-added to produce the total
spectrum. Although faint, the line is detected in both XX and YY, and it is
also consistently detected in jackknifes about other observables such as
observing date and time. For a number of reasons, which we explain below, we
believe that this detection is most likely associated with Nube.

We estimate the systemic heliocentric velocity ($V_{Helio}$) and velocity
width ($W_{50}$) of the HI detection using the methods described in
Karunakaran et al. (2020a, b), which are based on those of Springob et al.
(2005). Briefly, we fit first order polynomials to each edge of the HI profile
between 15% and 85% of the peak flux and find the velocities corresponding to
the 50% flux value. The mean and difference of these velocities give
$V_{Helio}$ and $W_{50}$ respectively. We correct $W_{50}$ for instrumental
and cosmological redshift broadening according to Springob et al. (2005) and
for ISM turbulence according to Verheijen & Sancisi (2001) (see their section
4; see also Karunakaran et al. 2020b).

We convert $V_{Helio}$ to a kinematic distance ($D$) using the Hubble-Lemaître
law and assuming an uncertainty of 5 Mpc due to peculiar velocities. The
derived distance is $107\pm 5$ Mpc. We measure the HI flux ($S_{HI}$) by
integrating over the line profile whose uncertainties are dominated by the
noise and the 2% diode uncertainty (van Zee et al., 1997). The flux value is
$S_{HI}=0.083\pm 0.02$ Jy km/s. We use the kinematic distance together with
the integrated flux in the standard equation for an optically thin gas (Haynes
& Giovanelli, 1984) to calculate the HI mass:

$\mathrm{M}_{HI}=2.356\times 10^{5}D^{2}S_{HI}\,[M_{\odot}]$ (1)

resulting in $\mathrm{M}_{HI}=2.2^{+0.7}_{-0.5}\times 10^{8}M_{\odot}$. All
derived properties from the HI spectrum are at a spectral resolution of $25$
km/s and are listed in Table 1.

Figure 2: HI detection along the line of sight to Nube. We also show different
polarisations of the data, XX and YY, to better identify which other HI
emission peaks in the spectrum are potentially spurious. The black tick
indicates the location of the peak with the strongest signal in our data. Note
that other distinct peaks are not always present in the two different
polarisations, thus reducing their relevance as real signals.

###  2.3 Possible sources of contamination in HI

Although it is tempting to associate the HI detection with the Nube galaxy, it
could be that the measurement corresponds to another galaxy in the line of
sight. For this reason, a detailed analysis of the velocity distributions of
the galaxies in the Nube region is needed to see if the HI detection is
compatible with any of them.

Using NED444The NASA/IPAC Extragalactic Database (NED) is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration we have created a catalogue
of all objects in this database with spectroscopic redshifts in a region
centred around Nube of $100\arcmin\times 100\arcmin$. The total number of
galaxies found is 711. All galaxies with recession velocities in the range
5480$<$$V_{helio}$$<$9480 km/s, 42 galaxies, are plotted in Fig. 3. The
galaxies are colour coded according to the relative velocity of the HI
detection. In this region, there are many galaxies with relative velocities
$\Delta V$$<$-600 km/s from the HI detection (red symbols in the figure).
There is also a smaller group with velocities about 500 km/s greater than the
HI detection (purple symbols close to the centre). Interestingly, there is no
galaxy with known spectroscopic redshift within a radius of 10′ centred on
Nube that has a $|\Delta V|<500$ km/s. This is important because this is the
region where potential contamination from a gas-rich source could mimic the
signal we identify as possibly coming from Nube. To better illustrate this
point, in Fig. 3 we also show the 2D GBT beam response using the well-
characterised pattern at 1.4 GHz from Spekkens et al. (2013). The contours
(from blue to black) indicate where the beam efficiency drops by the factor
indicated on the label.

The closest galaxy in terms of velocity ($\Delta V=-17.8$ km/s) would be the
spiral galaxy to the north: UGC929, in yellow in Fig. 3. This galaxy is 14.7
arcmin or 435 kpc away at the distance corresponding to the HI detection
(i.e., 107 Mpc). This object is close to the first minimum of the beam
response, shown by the grey-scale background image in Fig. 3, which means that
the HI emission, if coming, from UGC929 would be suppressed by a factor of
$\sim$$10^{4}$. If the source of the HI emission is UGC929, this implies that
the HI mass of this galaxy should be $\sim$$10^{12}$ M⊙. Using scaling
relations between stellar mass and HI mass, a galaxy with the stellar mass of
UGC 929 ($M_{*}=2.4\times 10^{10}M_{\odot}$, see Appendix A) is expected to
have a mass in HI of $\sim 2\times 10^{9}M_{\odot}$ and no more than $\sim
2\times 10^{10}M_{\odot}$ (Feldmann, 2020). This is at least 100 times less
gas than what it is needed to reproduce the observations. It is, therefore,
very unlikely that the emission we see at the location of Nube is caused by
the contamination from UGC929. To the northwest in Fig. 3, there is another
galaxy at a similar velocity ($\Delta V=-27.8$ km/s) at 14′ away. This galaxy
appears to be a low-mass galaxy, probably a satellite of UGC929. Given it is
also located in the first minimum of the beam response and its low mass, it is
also very unlikely that it is the source of the HI emission.

None of the galaxies with a confirmed spectroscopic redshift appear to be
responsible for the detection of HI in the Nube region. However, it is
possible that the HI emission is coming from a low-mass galaxy in the region
which, due to its faintness, has no spectroscopic redshift. To investigate
this, we have made a catalogue of all sources with a photometric redshift
within a radius of 10′ around Nube. This radius corresponds to the area where
the response efficiency of the GBT beam is greater than 5% (see Fig. 3). We
used one of the value added catalogues from the DR9 DECaLS survey, which
provides photometric redshifts of sources down to a $5\sigma$ depth of $m_{r}$
= 24 mag (Zhou et al., 2021). The list of objects with a photometric redshift
compatible with the HI emission (i.e., z=0.02502) is given in Table 3. The
vast majority of objects with a photometric redshift compatible with the HI
detection reported in this work are either a star or a point-like source. This
is somewhat to be expected, since at a given magnitude photometric catalogues
are biased towards objects with higher signal-to-noise, and therefore extended
objects are less represented or missing.

Finally, to account for the possibility that some faint and diffuse galaxies
might not have a photometric redshift measured, we visually inspected the
inner 10′ around Nube using the Dark Energy Camera Legacy Survey (DECaLS, Dey
et al., 2019) DR10 images to find extended faint sources that could
potentially be emitting in HI. We found only two very faint galaxies, which
are listed in Table 4. These two galaxies are visually smaller than Nube and
therefore potentially less massive at the same distance. Furthermore, these
objects are found at a radial distance of $\gtrsim$ 4.5′ from the central
direction of the HI beam. While we cannot completely rule out the possibility
that one of these galaxies is responsible for the HI detection, their off-
centre location would imply that they are less likely to be associated with
the HI detection than Nube.

The analysis in this section reinforces the idea that the detection of an
emission peak in HI could be related to the optical detection of Nube.
Moreover, the fact that the HI emission observed coincides with the velocity
of UGC929 (even if it is extremely unlikely to be caused by it) is a further
argument in favour of the HI detection being genuine and not a fluctuation.
Having ruled out contamination of nearby HI sources, there is still the
possibility that the optical and HI detections are unrelated, and therefore
the distance assumed for the optical counterpart of the galaxy may be
incorrect. However, this possibility does come with its own problems. For a
detailed discussion of the implications of the distance for Nube, see the
Appendix B. The scenario that follows from the analysis in this section is
that Nube could be a satellite of UGC929, at a distance of 107 Mpc.

Figure 3: Galaxies found in NED with known spectroscopic redshifts in a range
of $100\arcmin\times 100\arcmin$ around Nube and a recession velocity within
2000 km/s of that of the HI detection (i.e. $V_{helio}=7480$ km/s). The
galaxies are colour-coded according to their relative velocity with respect to
the potential velocity of Nube. The grey-scale background image is the GBT
beam response from Spekkens et al. (2013). The contours indicate where the
efficiency drops by the factor indicated on the label, from 0.05% (black) to
50% (light blue). The top horizontal axis indicates the equivalent size in Mpc
at a distance of 107 Mpc.

##  3 Analysis and results

###  3.1 Radial profiles of Nube

The aim of this paper is to study the properties of Nube in detail in order to
determine its origin. A fundamental way to characterise the shape of a galaxy
is through its radial surface brightness profiles. In addition, multi-
wavelength information provides valuable constraints on galaxy formation
processes. We have, therefore, derived the surface brightness radial profiles
of this galaxy using the optical, multi-wavelength, HiPERCAM data.

To measure the photometry of this galaxy, we first masked out all foreground
and background sources in the image. As can be seen in the insets in Fig. 1,
the galaxy is very faint and almost transparent. Since we cannot determine
whether the clumps on top of the galaxy are part of the galaxy or are objects
in the line of sight of the galaxy, we masked them all, leaving only the
diffuse component for photometry. We used a combination of NoiseChisel
(Akhlaghi & Ichikawa, 2015; Akhlaghi, 2019) and manual masking after visual
inspection. This is a very conservative approach as we are only analysing the
diffuse light of the galaxy. Appendix D shows the mask used in this work.

Once we had masked out all the sources of contamination, we derived the radial
surface brightness profiles of the galaxy. Given the nearly circular shape of
the object, we decided to extract the radial profiles using circular annuli at
different radial distances, up to 30″ from the centre of the galaxy. To derive
the profiles, we use a custom python code. For each radial bin, the surface
brightness was obtained as the $3\sigma$-clipped median of the pixel values.
Fig. 4 shows the surface brightness profiles of Nube for the 5 bands imaged
with HiPERCAM. Some of the profiles are shifted by a constant value, given in
the legend, for ease of viewing. The errors are calculated as a combination of
the Poisson noise in each annulus and the error in the sky given by the
distribution of background pixels in each image. These surface brightness
profiles are corrected for the absorption of our Galaxy (E(B$-$V) = 0.34,
Schlafly & Finkbeiner, 2011).

Figure 4: Radial surface brightness profiles of Nube in the Sloan u, g, r, i
and z bands. The profiles in the i and z bands have been shifted vertically
for ease of visualization.  Figure 5: Upper panel: the HiPERCAM $g-r$ colour
profile of Nube. Bottom panel: Stellar surface mass density profile of Nube.
The upper horizontal axis indicates the equivalent size in kpc at a distance
of 107 Mpc.

We can now study the radial variations of the galaxy’s stellar populations.
The surface brightness profiles are used to determine the radial $g-r$ profile
of the galaxy. The top panel in Figure 5 shows the $g-r$ colour profile of
Nube. The colour profile appears flat at all radii, with an average colour of
$\sim$0.6. This almost flat colour profile could be compatible with a similar
age and metallicity at all radii, up to $10\arcsec$ ($15$ kpc).

The bottom panel of Fig. 5 shows the surface stellar mass density profile for
this galaxy. To derive it, we follow the procedure given in Bakos et al.
(2008) to link the observed surface brightness in the g-band to the radial
variation of the stellar mass to light (M/L) ratio. The M/L ratio was obtained
from the prescriptions given in Roediger & Courteau (2015) assuming a Chabrier
(2003) IMF, using the $g-r$ colour profile. As with the colour profile, the
stellar mass density profile of Nube is also relatively flat compared to the
stellar mass density profiles of galaxies with similar stellar masses (e.g.,
Montes et al., 2021). We expand on this result later in the text.

We have used this stellar mass density profile to measure the radius that
encloses half the mass of the galaxy, or the half-mass radius
($R_{\mathrm{e}}$). This radius is $R_{\mathrm{e}}=13.7\pm 1.7$ arcsec
($6.9\pm 0.8$ kpc at a distance of 107 Mpc). The effective surface stellar
mass density of Nube is $<\Sigma>_{\mathrm{e}}=0.9\pm 0.1$ M⊙ pc-2. The total
stellar mass of the galaxy derived from the surface mass density profile,
assuming circular symmetry, is M${}_{*}=3.9\pm 1.0\times 10^{8}$ M⊙. The
effective surface brightness is $<\mu_{V}>_{e}=26.75\pm 0.02$ mag/arcsec2.
These values, along with other global properties of Nube, are listed in the
Table 1.

To assess the validity of our results, we also fitted Sérsic (1968) models
(using the code GALFIT Peng et al., 2002) to the galaxy in all the different
HiPERCAM bands, independently. The values of the half-light effective radius,
$r_{e}$, and the Sérsic index for each band are given in Table 2. The values
of $r_{e}$ from the GALFIT fits are consistent with those derived using the
surface brightness profiles.

###  3.2 Stellar populations of Nube

Given the very low surface brightness of this galaxy ($\mu_{V}(0)$$\sim$26.2
mag/arcsec2), the use of deep multi-wavelength observations is the best, if
not the only, way to constrain its stellar populations, namely the age,
metallicity and stellar mass-to-light ratio (M/L). To estimate these
quantities, we first constructed the spectral energy distribution (SED) of the
galaxy (see Fig. 6). The photometry at each band was derived measuring the
total flux within a circular aperture with radius equal to the half-mass
radius $R_{e}$ (13.7″) of the galaxy. The purpose of using this aperture
(instead of the total galaxy) is to ensure enough signal to reliably
characterise the SED of Nube. The errors of the photometry of each individual
band that compose the SED are a combination of the photometric errors and the
zero point uncertainties.

To characterise the stellar population properties of the galaxy, we fitted
Bruzual & Charlot (2003) single stellar population (SSP, instantaneous burst)
models to the SED of the galaxy. This is a reasonable assumption given the
homogeneous colour distribution of this galaxy (Fig. 5). The parameters to be
fitted are three: age, metallicity and luminosity, and we assumed a Chabrier
Initial Mass Function (IMF, Chabrier, 2003) for the models. Since the SED is
derived from broadband imaging, it is a good approach to assume an SSP to
describe the stellar populations of this galaxy, since the information we have
is limited. This assumption will give us the average properties of this
galaxy. For the fit, we use the $\chi^{2}$ minimisation approach described in
Montes et al. (2014). We derive a most likely age of $10.2^{+2.0}_{-2.5}$ Gyr
and a metallicity [Fe/H] of $-1.09^{+0.09}_{-0.13}$, values in agreement with
those of old diffuse low-mass galaxies (see e.g., Ruiz-Lara et al., 2018;
Heesters et al., 2023; Iodice et al., 2023). Uncertainties in the parameters
have been estimated by marginalising the 1D probability distribution functions
obtained during the fitting. Since the colour profile of this galaxy is flat
at all radii (see Fig. 5), we assume that the stellar populations obtained for
the inner $R_{e}$ are representative for the whole galaxy.

Figure 6: Spectral energy distribution (SED, filled circles) of Nube derived
from HiPERCAM photometry within the half-mass radius. The best-fit single
stellar population model is shown as the blue line and the best-fit magnitudes
(model convolved with the filter response) are the open circles. The age,
metallicity and mass-to-light ratio corresponding to the best fit model are
given in the figure.

Using the M/L derived from the SED fit
($(\mathrm{M/L})_{\mathrm{V}}=1.8^{+0.3}_{-0.5}$)555This M/L value is
consistent with the M/L ratios derived at each radial distance using the $g-r$
colour profile in Sec. 3.1; a median of $1.7$., the total stellar mass of Nube
is M${}_{*}=4.4\pm 0.8\times 10^{8}$ M⊙, in agreement with the stellar mass
estimate derived in Sec. 3.1. As this stellar mass is derived with the
properties inside $R_{e}$, we prefer to use the previous estimate (Sec. 3.1)
as it is more representative of the whole galaxy.

RA | DEC | z | Distance | log(MHI/M⊙) | log(M∗/M⊙) | $R_{\mathrm{e}}$ | $\mu_{V}(0)$
---|---|---|---|---|---|---|---
|  |  | (Mpc) |  |  | (arcsec) | (mag/arcsec2)
01h23m27.37s | -00d37$\arcmin$27.83$\arcsec$ | 0.02502$\pm 0.00003$ | $107\pm 5$ | $8.35\pm 0.12$ | $8.6\pm 0.1$ | $13.7\pm 1.7$ | $26.23\pm 0.07$
$W_{50}$ | $<\mu_{V}>_{e}$ | $<\Sigma>_{e}$ | Age | [Fe/H] | $b/a$ | $R_{e}$ |
km/s | (mag/arcsec2) | (M⊙pc-2) | (Gyr) |  |  | (kpc) |
$34\pm 11$ | $26.75\pm 0.02$ | $0.9\pm 0.1$ | $10.2^{+2.0}_{-2.5}$ | $-1.09^{+0.09}_{-0.13}$ | 0.97$\pm$0.01 | $6.9\pm 0.8$ |
Table 1: Global properties of Nube. The distance-dependent parameters have
been calculated assuming that the object is at a distance of 107 Mpc.

###  3.3 Dynamical mass of Nube

A rough estimate of the dynamical mass of this galaxy666This calculation
assumes that Nube is in dynamical equilibrium. This is a reasonable assumption
given the large distance to its potential progenitor UGC929. can be obtained
using the following equation from Spekkens & Karunakaran (2018):

$M^{3R_{e}}_{dyn}=6.96\times 10^{5}R_{e}\left(\frac{W_{50}}{2\times
sin(i)}\right)^{2}\,[M_{\odot}]$ (2)

with Re the half-mass radius in kpc, $i$ the inclination of the HI disc in
degrees, and W50 the turbulence-corrected velocity width of the HI line. We
calculate the inclination of the HI disc as follows:

$\cos(i)=(b/a)$ (3)

In Table 1, we provide the axis ratio, $b/a$, of Nube obtained from GALFIT
Sérsic fits to the object (see sec. 3.1). The resulting value (0.97$\pm$0.01)
is the average from the axis ratio measured in the $g$, $r$, and $i$ bands.
That results in an inclination value of 13$\pm$3 deg. It is worth emphasizing
that using the axis ratio of the stellar distribution to characterise the
inclination of the HI disc is a rough approximation. The dynamical mass we
derive for Nube is $2.6\pm 1.7\times 10^{10}$ M⊙ within $3R_{e}=20.7$ kpc.

###  3.4 A search for Globular Clusters

Globular clusters (GCs) provide a complementary way to estimate the distance
to an extragalactic object based on the universality of their luminosity
function. The peak of the GC distribution lies at M${}_{V}=-7.6$ mag for
different galaxies (see e.g., Rejkuba, 2012), making it a secondary distance
indicator. Therefore, the detection of GCs in Nube would help us to validate
the distance obtained with the HI detection. Note that the peak of the GC
luminosity at the distance of 107 Mpc (i.e., a distance modulus of 35.15 mag)
is expected at m${}_{g}\simeq 27.5$ mag, fainter than our point-like 5$\sigma$
limiting magnitudes meaning that it would be difficult to detect GCs, if any,
in our images (see section 2.1). We expect that an ultra-diffuse galaxy of
similar stellar mass than Nube would have around $\sim$10 GCs, although the
range varies from 0 to 30 GCs. However, only the brightest GCs of the system
are expected to be detectable.

We follow a similar procedure to detect globular clusters as in Montes et al.
(2020, 2021). In short, we first preselect the GCs based on their morphology
(size and ellipticity), and then we refine the selection based on their
colours. However, in this case we do not have the high spatial resolution of
the _HST_ images to make a preselection based on the morphology of the GCs,
but only the ground-based images. For this reason, we have to impose very
strict shape criteria to minimise contamination in our selection.

We run SExtractor on our images in dual mode, with the $r$-band image as the
detection image. At a distance of 107 Mpc, globular clusters will look like
point sources in the images. Therefore, to pre-select the GC candidates, we
first select stars in our images by imposing that the stellarity parameter in
SExtractor (‘CLASS_STAR’) is greater than 0.98. We do this to estimate the
FWHM of a point-like source in our images, to impose strict conditions on our
detections and to minimise contamination from other objects. We find 6 point-
like objects, 3 of which were detected in Gaia DR3 (Gaia Collaboration et al.,
2023). The FWHM of these point-like objects are between $10$ and $14$ pixels
(0.8″to 1.12″) and their ellipticities are $<0.1$. Therefore, based on these
values, we pre-selected the GC candidates with: ellipticity $<0.1$, $9<$ FWHM
$<15$ pix and $m_{r}<26.2$ mag, in order to minimise false detections.

Figure 7: The $(u-r)-(r-z)$ colour-colour diagram of the initial sample of GC
candidates (blue) of Nube. The green squares are the location of NGC5128
candidates in Taylor et al. (2017) with a probability greater than 95$\%$ of
being true GCs. The black dashed line indicates the convex hull (envelope)
computed as the smallest region containing all the green squares.

After this initial selection, we also applied the $(u-r)-(r-z)$ colour-colour
selection used in Taylor et al. (2017) to narrow down the selection of
GCs777See Muñoz et al. (2014); Lim et al. (2020); Cantiello et al. (2020) for
other examples on using colour-colour diagrams to identify candidate GCs.. To
do this, we defined a colour-colour region based on the position on the
diagram of candidate GCs with a probability of $>$0.95 of being true GCs in
Taylor et al. (2017), the green squares in Fig. 7. To define this region, we
computed the convex hull or convex envelope, i.e., the minimum region
containing all GCs from Taylor et al. (2017) (dashed line in Fig. 7).

Only two sources fall on the area defined by the GCs provided by Taylor et al.
(2017)888Taylor et al. (2017) use the GCs of NGC5128 to generate their
catalogue. NGC5128 is a massive galaxy with intense merger activity.
Therefore, the population of GCs in this massive galaxy includes GCs of a wide
variety of origins, from those formed in-situ in this massive galaxy to those
accreted by mergers with a large number of dwarfs. In this sense, the Taylor
et al. (2017) catalogue is expected to contain a very heterogeneous and
complete sample of GCs.. However, both are very far from Nube ($>$110″or 54
kpc from its centre), so they are unlikely to be associated with the galaxy.
We also checked the three sources near the bottom of the region (u-r$\sim$2,
r-z$\sim$0.25), but they are also not spatially associated with Nube. In
summary, we are unable to detect any GCs associated with Nube, as expected,
considering both our point-like limiting magnitudes and if the distance to the
galaxy is 107 Mpc.

##  4 On the formation mechanism of Nube

###  4.1 Nube in comparison with other Low Surface Brightness galaxies

The galaxy reported in this paper, Nube, has some extreme properties in terms
of size and surface brightness. Fig. 8 shows the structural properties of Nube
compared to other low surface brightness or dwarf galaxies compiled from the
literature. The grey open circles represent low-mass Local Group galaxies from
McConnachie (2012), the green open squares are field dwarfs, while the orange
crosses are satellite dwarfs (orbiting a more massive galaxy) from Carlsten et
al. (2021), pink ‘x’ are UDGs in Coma from van Dokkum et al. (2015), the
golden star is UDG32 from Iodice et al. (2021) and the red diamonds are two of
the LSB galaxies in Virgo from Mihos et al. (2015). Compared to all these
objects, Nube appears quite unique due to its low central surface brightness
and extension for a galaxy of its stellar mass. The closest objects in size,
mass and central surface brightness are the two LSB galaxies in Virgo from
Mihos et al. (2015): VLSB-B and VLSB-C999To derive the mass of VLSB-C, we
assume a B$-$V = 0.7 mag for this galaxy, which is typical for dwarf galaxies
and the M/L colour relation in Bell et al. (2003). and UDG32 in Hydra I
(Iodice et al., 2021). We do not include VLSB-A, as this LSB galaxy is clearly
tidally perturbed, as indicated by its visible tidal tails. VLSB-C appears to
be quite similar in size and brightness to Nube ($R_{e}=5.5$ kpc and
$\mu_{V}(0)=26.7$ mag/arcsec2, Mihos et al., 2015). This galaxy shows no
obvious signs of tidal stripping; possibly it is an LSB galaxy in the cluster
outskirts or falling into the Virgo cluster for the first time.

We also compare Nube with other galaxies that have been described as “almost
dark” in previous works. One example is AGC229385 (also known as Coma P.;
Janowiecki et al., 2015; Brunker et al., 2019). Unlike Nube, this galaxy
appears elongated. It also has an extreme ratio of HI to stellar mass
($M_{HI}/M_{*}$=81; Brunker et al., 2019) compared to Nube ($M_{HI}/M_{*}\sim
1$). This is also the case of AGC229101 (Leisman et al., 2021). This galaxy is
an HI source ($M_{HI}/M_{*}$=98) with a very dim optical counterpart
($\mu_{g}(0)=26.6$ mag/arcsec2) and $R_{e}=3$ kpc. Other two extended “almost
dark” galaxies are AGC229398 and AGC333576 (Gray et al., 2023). Their
effective radii are large, 9 and 4.4 kpc respectively, and their stellar
masses ($\sim$108 M⊙) are also close to Nube. However, their central surface
brightness are significantly brighter than Nube (23.8 and 24.6 mag/arcsec2).

Figure 8: Comparison of the structural properties of Nube with respect to
other Local Group galaxies from McConnachie (2012, grey open circles), dwarf
galaxies in Carlsten et al. (2021, green open squares and orange crosses),
UDGs in Virgo from Mihos et al. (2015, red diamonds), UDG32 in Hydra I from
Iodice et al. (2021, golden star) and Coma from van Dokkum et al. (2015, pink
x). Although the central surface brightness is typical of other dwarf
galaxies, the stellar mass and half-mass radius make Nube, at a distance of
107 Mpc, an extreme object, even more so than the UDGs in Virgo and Coma.

In addition to comparing the global properties of Nube with other low-mass
galaxies, it is also very instructive to compare its surface mass density
profile with respect to galaxies of similar stellar mass. In Fig. 9, we show
the stellar surface mass density of Nube (blue dots) derived from the $g-r$
colours (Sec. 3.1). For comparison, we plot the profiles of dwarf galaxies of
similar stellar mass (grey lines), in the mass range $1-5\times
10^{8}\,M_{\odot}$ from Chamba et al. (2020). This shows how different Nube is
from typical dwarf galaxies of similar mass. Even ultra-diffuse galaxies with
large effective radius are not comparable to this galaxy. For example, the
iconic ultra-diffuse galaxy Dragonfly 44 (DF44), also shown as the green
squares in Fig. 9, has a $r_{e}=4.3\pm 0.2$ kpc (van Dokkum et al.,
2016)101010Other estimates for $r_{e}$ for DF44 are $r_{e}=3.3\pm 0.3$ kpc
(Chamba et al., 2020) and $3.9\pm 0.7$ kpc (Saifollahi et al., 2021)., and a
central surface brightness of $\mu_{g}(0)=24.5$ mag/arcsec2. This is 1.5 times
smaller and $1.4$ mag/arcsec2 brighter than Nube.

Figure 9: Surface stellar mass density profile of Nube (blue dots) compared
with other galaxies of similar stellar mass. The profiles of dwarf galaxies
from Chamba et al. (2020) in the same mass range (1-5$\times 10^{8}M_{\odot}$)
have been plotted. We also show the profile of DF44 (green squares), as it is
an iconic large ultra-diffuse galaxy. The vertical lines indicate the half-
mass radius ($R_{e}$) for Nube (blue solid line) and DF44 (green dashed line).

###  4.2 On the nature of Nube

Given the extreme properties of Nube, it is interesting to discuss whether
these properties are a result of the original formation of this galaxy, or
whether they are due to a later evolutionary process caused by the environment
in which it is found. In this section, we discuss two possible alternatives.
In the first, we explore whether Nube can be considered a tidal dwarf galaxy.
The second is whether Nube was born with a stellar density typical of dwarf
galaxies of the same stellar mass and has been deformed by the environment
into this peculiar structure. Either of these two possibilities (if correct)
should be able to explain the stellar populations and the present morphology
of Nube.

####  4.2.1 Is Nube a Tidal Dwarf Galaxy (TDG)?

There is a population of galaxies whose formation mechanisms would not be
associated with what is expected to be the main channel of formation of
galaxies, i.e., gravitational collapse of gas within a dark matter halo. These
galaxies are known as Tidal Dwarf Galaxies (TDGs). They form from material
torn away from larger galaxies by tidal interactions or by harassment (e.g.,
Duc & Bournaud, 2008) and, as a result of their formation, they exhibit
characteristics such as significant gas fractions, low dark matter content,
and metallicity higher than expected for dwarf galaxies of similar mass (e.g.,
Duc, 2012).

Around 95% of the known TDG galaxies are located at relatively modest
distances ($\sim$20 kpc) from their potential progenitors (Kaviraj et al.,
2012). However, Nube is very distant (435 kpc) from its likely progenitor
UGC929. This large distance from its possible parent should not be considered
as a factor against Nube being a TDG, since the selection of TDG galaxies
usually requires a visible tidal tail and is therefore biased towards newly
formed objects. Some simulations suggest that if the TDG is massive enough
(M$>10^{8}\,M_{\odot}$) and escapes the parent galaxy with sufficient
velocity, it could become self-gravitating and avoid falling back into its
progenitor system (Bournaud & Duc, 2006). However, it is unclear how long TDGs
formed in this way could survive without the protection of a massive dark
matter halo, as both axisymmetric and non-axisymmetric instabilities would
eventually destroy the system (Sellwood & Sanders, 2022). Assuming that these
galaxies manage to survive, they are expected to remain gas-rich and very
faint. These old galaxies are therefore good candidates to be identified as
“almost dark” galaxies (see e.g., Cannon et al., 2015; Janowiecki et al.,
2015; Leisman et al., 2017; Román et al., 2021).

The metallicity observed in Nube ([Fe/H] = $-1.09^{+0.09}_{-0.13}$) is similar
to that of normal dwarf galaxies (e.g., McConnachie, 2012). However, it is
lower than expected for currently forming TDGs (solar metallicity, e.g., Duc
et al., 2000), i.e., more metallic as it inherits the metallicity of the more
massive parent galaxies. Nonetheless, given the age of the galaxy (9 Gyr), it
could have formed from ancient spirals with less enriched gas than the present
ones (see e.g., Recchi et al., 2015). Therefore, the relatively low
metallicity of Nube should not necessarily be an indication that it did not
form as a TDG.

Another characteristic of TDGs is their low dark matter content. The dynamical
mass of Nube is $2.6\pm 1.7\times 10^{10}$ M⊙ within $3R_{e}=20.7$ kpc (Sec.
3.3), while the stellar mass is M${}_{*}=3.9\pm 1.0\times 10^{8}$ M⊙ (Sec.
3.2). This means that the ratio of dark matter to stellar mass is between
$20-150$. This amount of dark matter is significantly larger than the amount
of dark matter expected if the galaxy had formed as a TDG
(M${}_{dyn}/M_{*}<$2; Gray et al., 2023). In addition, its gas content
relative to the stellar content is not very large compared to those found in
other TDGs (M${}_{HI}/M_{*}\sim$10, Gray et al., 2023). For these reasons, we
conclude that Nube is with high confidence not a TDG.

####  4.2.2 Nube as a result of environmental processes

If Nube is not a TDG, can its structural properties be explained as the result
of interaction with its environment? It is known that dwarf galaxies can be
dynamically heated and “puffed up” by interactions with more massive galaxies
(e.g., Liao et al., 2019; Tremmel et al., 2020). This puffing could explain
why the age and metallicity of Nube are similar to other regular dwarf
galaxies, while its physical properties (effective radius and central surface
brightness) are extreme. However, against this scenario for the origin of Nube
is the fact that the galaxy does not inhabit a particularly dense environment.
In fact, its nearest massive neighbour, UGC 929, is at a distance of 435 kpc
in projection.

Assuming that Nube and UGC 929 have had a close encounter in the past, we can
make a rough estimate of when this occurred. Considering the current projected
distance between the two objects plus a transverse projected velocity of
$\sim$100 km/s (i.e., 100 kpc/Gyr), the close encounter would have occurred 4
to 5 Gyr ago. Given the dynamical time of each galaxy, this is enough time to
have erased any signature of the perturbation in the central regions of both
objects. We do not find the central region of Nube to be obviously perturbed
(see Fig. 10). Regarding UGC929, we have used deep imaging from DECaLS to
study its morphology. Fig. 13 shows the composite DECaLS image of the galaxy.
We can see in the image that the galaxy appears to be very symmetric, with no
sign of perturbations or interactions. Therefore, if Nube and UGC929 had met
in the past, it would have been long enough for the central shape of both
galaxies to have already been restored.

However, in the outermost parts of Nube it would be possible to study the
effects of this gravitational interaction in the form of tidal distortions.
These deformations produce an S-shaped structure (e.g. Johnston et al., 2002;
Moreno et al., 2022). Thanks to the deep imaging provided by HiPERCAM, we can
investigate whether there is any evidence that this could be the case for
Nube. An interaction capable of distorting the galaxy in this way would be
clearly visible in our ultra-deep imaging ($\sim$30.5 mag/arcsec2; see Sec.
2.1) even long after the interaction (Moreno et al., 2022). Fig. 10 shows an
RGB composite of the image of Nube with a black and white background to
highlight the fainter outskirts of this galaxy. A visual inspection of Nube
shows no obvious signatures of deformation in the outer regions. This can be
seen from the lack of an excess in the outer parts of the surface brightness
and stellar density profiles (Fig. 4 and Fig. 5), which is associated with the
presence of tidal tails (Johnston et al., 2002; Montes et al., 2020).

Figure 10: A region of $100\arcsec\times 100\arcsec$ around Nube. The figure
is a composite of an RGB colour image using the $g$, $r$ and $i$ HiPERCAM
bands and a black and white $g+r$ image for the background.

To improve the visualization of the outer parts of Nube, we also modelled Nube
with GALFIT. To obtain additional signal-to-noise, we have performed a model
fit on a $g+r$ image. Fig. 11 shows the original (left), model (middle) and
residual (right) $g+r$ image. No signs of an excess or deformation can be
seen.

Figure 11: GALFIT model of Nube for the HiPERCAM $g+r$-band. The left panel shows the g+r original image, the middle panel the 2-D Sérsic model fit and the right panel the residuals after subtracting the Sérsic model, after smoothing it with a Gaussian kernel to enhance the residuals.  filter | $r_{e}$ | n | $b/a$
---|---|---|---
| (arcsec) |  |
$u$ | $15.6\pm 0.6$ | $0.60\pm 0.03$ | 0.999
$g$ | $15.9\pm 0.1$ | $0.70\pm 0.01$ | 0.986
$r$ | $15.3\pm 0.1$ | $0.65\pm 0.01$ | 0.962
$i$ | $13.9\pm 0.1$ | $0.60\pm 0.01$ | 0.975
$z$ | $16.0\pm 0.3$ | $0.75\pm 0.02$ | 0.971
Table 2: Multi-band effective radii, axis ration and Sérsic indexes of the
GALFIT (Peng et al., 2002) fits to Nube.

##  5 Nube as a test-bed to explore the nature of dark matter

###  5.1 Nube within the cold dark matter scenario

Given the extreme properties of Nube, it is interesting to see whether
traditional models of cold dark matter are able to reproduce galaxies with
these characteristics. In particular, we are interested in knowing if galaxy
formation models can produce objects with stellar masses, surface brightnesses
and effective radii like Nube. To answer this question, it is worth looking at
simulations that have been able to reproduce the properties of the largest
known ultra-diffuse galaxies. These simulations have sufficient spatial
resolution and stellar population feedback recipes to produce low surface
brightness, large effective radius galaxies like DF44.

Using the FIRE-2 simulations (Hopkins et al., 2018), Chan et al. (2018) find
that isolated field dwarfs, where the effect of stellar feedback (i.e.,
stellar winds, supernovae, etc.) is large, produce galaxies with surface
brightness, effective radius, and stellar masses representative of UDGs (after
imposing artificial quenching to simulate the effect of infall into the
cluster environment). Simulated galaxies with stellar masses around 108 M⊙ and
dark matter halos around 1010 M⊙, such as Nube, have effective radii less than
5 kpc, smaller than what we measure for Nube. NIHAO simulations (Wang et al.,
2015) produce galaxies with similar structural properties to UDGs due to
episodes of gas outflows associated with star formation (Di Cintio et al.,
2017). The dark matter halo masses and stellar masses are consistent with what
we find for Nube. However, the effective radii ($\sim$3 kpc) of these
simulated galaxies are again well below the value we measure for Nube.

Other ways that have been proposed to form UDGs are high-z major mergers
(Wright et al., 2021) or that UDGs populate higher spin halos (Amorisco &
Loeb, 2016; Benavides et al., 2023). However, neither of these scenarios can
reproduce the observed characteristics of Nube. In Wright et al. (2021), major
mergers produce galaxies with $r_{e}<4$ kpc. Benavides et al. (2023) explores
UDGs in the TNG50 simulation and finds that for isolated galaxies of the mass
of Nube, the effective radius is $\lesssim$ 5 kpc.

###  5.2 Nube in the fuzzy dark matter framework

As the microphysical nature of the dark matter is still completely unknown, it
is worth exploring whether extreme objects such as Nube can be compatible with
other alternative dark matter models. In particular, models based on
ultralight (axion-like) scalar particles are gaining recently a significant
interest (fuzzy dark matter; Schive et al., 2014; May & Springel, 2021). Due
to the very small mass of these particles ($\sim$10-22 eV), the quantum
effects are expected to appear at the kpc (i.e., galactic) scale. The
ultralight particles generate dark matter models with large cores. In
particular, the dark matter distribution is expected to generate a central
distribution named soliton followed by a NFW profile in the outer parts
(Schive et al., 2014). The soliton density profile can be well approximated
by:

$\rho_{s}(r)=\frac{1.9(m_{B}/10^{-23}eV)^{-2}(r_{c}/kpc)^{-4}}{[1+9.1\times
10^{-2}(r/r_{c})^{2}]^{8}}M{{}_{\odot}}pc^{-3}$ (4)

with mB the mass of the dark matter particle, rc the core radius where the
density has dropped to one-half its peak value. Equation 29 of Bar et al.
(2018) shows that if the core radius and the virial mass of the dark matter
halo Mh is known, the dark matter particle can be estimated through the
following equation:

$\frac{m_{B}}{10^{-22}eV}=160\left(\frac{r_{c}}{pc}\right)^{-1}\left(\frac{M_{h}}{10^{12}M{{}_{\odot}}}\right)^{-1/3}$
(5)

To get a rough estimate of the core radius, we assume the stellar distribution
follows the shape of the dark matter soliton. This is a reasonable assumption,
as the dark matter is the dominant component generating the global
gravitational potential (Sánchez Almeida et al., 2023). Therefore, we project
the soliton density profile obtaining:

$\Sigma_{\star}(R)=\frac{\Sigma_{\star}(0)}{(1+0.091\times(R/r_{c})^{2})^{15/2}}$
(6)

The stellar mass surface density of Nube fits very well with this equation
(see Fig. 12). We obtain a value of $r_{c}$ = 6.6 $\pm$ 0.4 kpc. The mass of
the dark matter particle compatible with this core radius is
mB=($0.8^{+0.4}_{-0.2}$)$\times$10-23 eV.

We also plot a Navarro, Frenk & White profile (dashed black line, Navarro et
al., 1996) to show that this commonly used profile to describe the
distribution of mass in dark matter halos cannot reproduce the characteristics
of Nube especially at small radii. For Fig. 12, we used the projected NFW
profile in equation 11 in Wright & Brainerd (2000), assuming as transition
radius ($r_{s}$) the core radius of the soliton derived above.

It is interesting to compare the mass of the axion-like particle derived in
this analysis with other studies. Using galactic rotation curves, Bernal et
al. (2018) found an average value of mB$\sim$0.5$\times$10-23 eV, while
Bañares-Hernández et al. (2023) derived mB$\sim$2$\times$10-23 eV. These
values are in good agreement with our estimate using only the structural
properties of the galaxy. Analysing the velocity dispersion of the Fornax and
Sculptor dwarfs, González-Morales et al. (2017) find an upper limit of
mB$<$4$\times$10-23 eV. Based on the angular scale of the CMB acoustic peaks
and anisotropies, Hložek et al. (2018) derive a lower limit of
mB$>$0.1$\times$10-23 eV. Analysis of the stellar heating of the Milky Way
disc due to the substructure within a fuzzy dark matter halo suggests an upper
limit of mB$<$4$\times$10-23 eV (Chiang et al., 2023). These results are
consistent with our estimate for the mass of the axion-like particle.

However, the situation is far from clear. Other estimates of the mass of the
particle are inconsistent with the above results. To name a few, Chen et al.
(2017) using Jeans analysis of the Milky Way satellite dSphs find
mB=(17.9$\pm$3.3)$\times$10-23 eV. Dalal & Kravtsov (2022) suggest that the
size and stellar kinematics of ultra-faint dwarfs imply a lower limit of
mB$>$3$\times$10-19 eV. Although fuzzy dark matter could relieve some of the
small scale tensions appearing in the cold dark matter scenario, more work is
needed to assess this model.

Figure 12: Surface stellar mass density profile of Nube (blue dots) fitted
with a projected soliton shape with core radius of $r_{c}$ = $6.6\pm 0.4$ kpc
(see text for details). The soliton best fit and its errors are indicated by
the red line and the red region. The agreement is remarkable taking into
account that the only free parameter is essentially the core radius. The black
dashed line is a projected NFW profile for comparison.

##  6 Conclusions

In the absence of a laboratory detection of the particles that make up dark
matter, the hope for characterising its nature lies in the analysis of
astrophysical objects. In particular, galaxies with very low surface
brightness (also called “almost dark”) offer an interesting possibility to
constrain the microphysical properties of dark matter. In these galaxies,
baryonic feedback effects are expected to be very moderate, leaving the
spatial distribution of their dark matter halo almost intact.

In this paper, we present the serendipitous discovery in the IAC Stripe 82
Legacy Project (Fliri & Trujillo, 2016; Román & Trujillo, 2018) of a galaxy,
Nube, of stellar mass M∗ = $3.9\pm 1.0\times 10^{8}$ M⊙, very extended
($R_{e}=6.9\pm 0.8$ kpc) and very low surface brightness
($<$$\mu_{V}$$>_{e}=26.75\pm 0.02$ mag/arcsec2) located at 107 Mpc. Using the
GBT radio telescope, we inferred a total halo mass of $2.6\pm 1.7\times
10^{10}$ M⊙ for the galaxy. Current simulations of ultra-diffuse galaxy
formation, which take into account baryonic feedback effects and simulate dark
matter particles as WIMPs (i.e., cold dark matter), are unable to reproduce
objects with the properties of Nube. We have investigated the possibility that
the object could be reproduced with the predictions for the fuzzy dark matter
model. To this end, and under the hypothesis that the distribution of stars in
Nube is representative of the distribution of the dark matter halo, we found
that a soliton-shaped profile (typical of fuzzy dark matter) reproduces the
observed distribution of stars very well. The mass of the axion-like particle
inferred from the fit is mB=($0.8^{+0.4}_{-0.2}$)$\times$10-23 eV. This value
is in good agreement with other astrophysical measurements using the dynamical
properties of other low surface brightness galaxies.

###### Acknowledgements.

We thank the referee for their useful comments that helped improve the
original manuscript. We are indebted to Amelia Trujillo González for
suggesting the name of the galaxy explored in this work. The authors want to
thank Scott Carlsten for providing the tables of the structural parameters of
the dwarf galaxies in Carlsten et al. (2021). We also thank Betsy Adams and
Pierre-Alain Duc for useful discussions. This publication is part of the
Project PCI2021-122072-2B, financed by MICIN/AEI/10.13039/501100011033, and
the European Union “NextGenerationEU”/RTRP. I.T. acknowledges support from the
ACIISI, Consejería de Economía, Conocimiento y Empleo del Gobierno de Canarias
and the European Regional Development Fund (ERDF) under grant with reference
PROID2021010044 and from the State Research Agency (AEI-MCINN) of the Spanish
Ministry of Science and Innovation under the grant PID2019-107427GB-C32,
financed by the Ministry of Science and Innovation, through the State Budget
and by the Canary Islands Department of Economy, Knowledge and Employment,
through the Regional Budget of the Autonomous Community. MM and IT acknowledge
support from IAC project P/302302. NC acknowledges support from the research
project grant ‘Understanding the Dynamic Universe’ funded by the Knut and
Alice Wallenberg Foundation under Dnr KAW 2018.0067. Based on observations
made with the GTC telescope, in the Spanish Observatorio del Roque de los
Muchachos of the Instituto de Astrofísica de Canarias, under Director’s
Discretionary Time. This work makes use of the following code: astropy (The
Astropy Collaboration et al., 2018), SExtractor (Bertin & Arnouts, 1996),
SCAMP (Bertin, 2006), SWarp (Bertin, 2010), Gnuastro (Akhlaghi & Ichikawa,
2015), photutils v0.7.2 (Bradley et al., 2019), pillow (van Kemenade et al.,
2020), numpy (Oliphant, 2006), scipy (Virtanen et al., 2020), Astrometry.net
(Lang et al., 2010), GALFIT (Peng et al., 2002).

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##  Appendix A Properties of UGC929

Given the difference in distance between both galaxies, we assumed that Nube
is a satellite of UGC 929. UGC 929 is at a projected distance of 14.7$\arcmin$
(435 kpc at a distance of 107 Mpc) from Nube. To calculate the stellar mass of
UGC929, we use the DECaLS g and r images, obtaining the M/L ratio using the
Roediger & Courteau (2015) prescriptions and assuming a Chabrier (2003). The
stellar mass of the galaxy is $M_{*}=2.4\times 10^{10}M_{\odot}$.

Figure 13:  A region of $250\arcsec\times 250\arcsec$ ($\sim$123 kpc $\times$
123 kpc) around the galaxy UGC929. The figure is a composite of an RGB image
using the $g$, $r$ and $z$ from DECaLS and a black and white $g+r+z$ image for
the background. This galaxy is at the same redshift that Nube, but 14.7′ to
the north-west. The blue arrow indicates the direction of Nube. There is no
evidence of morphological disturbance that could point to gas expulsion as the
origin of Nube.

##  Appendix B Alternative distances to Nube

Some of the most peculiar properties of Nube depend on the assumed distance to
the galaxy. In Section 2.3 we found that it is unlikely that another nearby
galaxy could be responsible for the HI emission we detected. However, we
cannot completely rule out the possibility that the HI detection is not
related to Nube. In that case, the galaxy could be at a different distance
from the one assumed in this work. For this reason, it is worth exploring what
alternative distances are potentially possible.

One possibility is that Nube is a satellite of a galaxy in the field of view
other than UGC929. Exploring the nearby galaxies with spectroscopic redshifts
(Fig. 1), Nube could be associated with UGC928 (8248 km/s). However, if it is
associated with UGC928 (projected separation of $\sim 3.8\arcmin$), Nube will
be even further away and its properties will be even more extreme.
Alternatively, Nube could be closer to us. In Fig. 14 we show the inferred
properties of Nube at different distances, from 2 Mpc (white) to the assumed
distance of 107 Mpc (darker blue). The only galaxy in the field of view with a
spectroscopic redshift that is closer to us is UGC931 (Fig. 1) at $\sim 30$
Mpc (Springob et al. 2009). If Nube it is associated with UGC931, its
properties will also be peculiar. Its stellar mass and $R_{e}$ will be similar
to those of UDGs, but it would have a significantly lower central surface
brightness (3rd to 4th hexagon from the left, upper right panel in Fig. 14).

For Nube to be a more normal galaxy, the distance should be between 2 and 10
Mpc. In this case, Nube will be more like the low-mass Local Group galaxies of
McConnachie (2012), such as Phoenix (M∗ = $0.7\times 10^{6}$ M⊙, $r_{e}$ = 454
pc and $\mu_{V}(0)$ = 25.8 mag/arcsec2) or the dwarfs of Carlsten et al.
(2021). However, there is no nearby massive galaxy to act as a host for Nube
in such case, and therefore it would be a rare example of an isolated very
low-mass galaxy.

Figure 14: Same as Fig. 8 but showing Nube at different distances 2, 10, 25,
50, 75 and 107 Mpc.

##  Appendix C Photometric redshifts and other sources around Nube

Given the spatial resolution of the GBT data, in section 2.3 we discussed the
possibility that the HI detection corresponds to another source and not to
Nube. Table 3 lists all galaxies with photometric redshifts within 10′ of
Nube. Table 4 lists faint sources that have neither spectroscopic nor
photometric redshifts, but could be responsible for the HI emission.

RA | DEC | z | mr | distance
---|---|---|---|---
(deg) | (deg) |  | (AB mag) | (arcmin)
20.7455 | -0.6473 | 0.028$\pm$0.03 | 17.3 | 7.3*
20.8104 | -0.6972 | 0.025$\pm$0.03 | 20.4 | 5.5a
20.8105 | -0.7059 | 0.025$\pm$0.02 | 21.0 | 5.9a
20.8349 | -0.6543 | 0.025$\pm$0.1 | 20.3 | 2.5*
20.7561 | -0.5262 | 0.027$\pm$0.05 | 17.2 | 8.9*
20.7682 | -0.5045 | 0.026$\pm$0.2 | 20.2 | 9.2*
20.7984 | -0.6008 | 0.025$\pm$0.1 | 20.6 | 4.2*
20.8535 | -0.5496 | 0.026$\pm$0.1 | 20.0 | 4.5*
20.8571 | -0.5475 | 0.025$\pm$0.01 | 12.1 | 4.6*
20.9294 | -0.4799 | 0.026$\pm$0.09 | 20.4 | 9.5*
21.0163 | -0.6003 | 0.027$\pm$0.15 | 20.5 | 9.2*
Table 3: List of objects with photometric redshifts compatible with the HI detection reported in this paper. The vast majority of these objects are stars or point-like sources (marked with *), another two sources (marked with a) are part of a known galaxy, UGC931. RA | DEC | Distance to Nube
---|---|---
(deg) | (deg) | (arcmin)
20.9390 | -0.6132 | 4.5
20.9092 | -0.5122 | 7.2
Table 4: List of faint sources around Nube that we cannot exclude as
responsible for the HI emission reported in this work.

##  Appendix D Masks for photometry and surface brightness profiles

Masking is a key component in obtaining reliable photometry and surface
brightness profiles of the galaxy under study. In section 3.1 we describe how
the HiPERCAM mask used to derive the photometry and surface brightness
profiles of Nubewas created. Fig. 15 shows the mask used to derive the
photometry and surface brightness profiles of the galaxy.

Figure 15: Mask (blue regions) applied to a HiPERCAM RGB colour (g+r+i) image
of a region $100\arcsec\times 100\arcsec$ around Nube. The black and white
background is a $g+r$ image. The image shows the need for thorough masking in
these ultra-deep images.