# A closer look at the extended edge-on low-surface brightness galaxies

Anna S. Saburova Sternberg Astronomical Institute, Moscow M.V. Lomonosov State
University, Universitetskij pr., 13, Moscow, 119234, Russia  Damir Gasymov
Sternberg Astronomical Institute, Moscow M.V. Lomonosov State University,
Universitetskij pr., 13, Moscow, 119234, Russia  Evgenii V. Rubtsov Sternberg
Astronomical Institute, Moscow M.V. Lomonosov State University,
Universitetskij pr., 13, Moscow, 119234, Russia  Igor V. Chilingarian Center
for Astrophysics — Harvard and Smithsonian, 60 Garden Street MS09, Cambridge,
MA 02138, USA  Sternberg Astronomical Institute, Moscow M.V. Lomonosov State
University, Universitetskij pr., 13, Moscow, 119234, Russia  Sviatoslav
Borisov Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290
Versoix, Switzerland  Ivan Gerasimov Sternberg Astronomical Institute, Moscow
M.V. Lomonosov State University, Universitetskij pr., 13, Moscow, 119234,
Russia  Fedor Kolganov Faculty of Physics and Earth System Sciences, Leipzig
University, Linnestraße 5, 04103 Leipzig, Germany  Anastasia V. Kasparova
Sternberg Astronomical Institute, Moscow M.V. Lomonosov State University,
Universitetskij pr., 13, Moscow, 119234, Russia  Roman I. Uklein Special
Astrophysical Observatory, Russian Academy of Sciences, Nizhniy Arkhyz,
Karachai-Cherkessian Republic 357147, Russia  Michal Bílek Collège de France,
11 place Marcelin Berthelot, 75005 Paris, France  LERMA, Observatoire de
Paris, CNRS, PSL Univ., Sorbonne Univ., 75014 Paris, France  FZU – Institute
of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, Prague 182
21, Czech Republic  Kirill A. Grishin Sternberg Astronomical Institute, Moscow
M.V. Lomonosov State University, Universitetskij pr., 13, Moscow, 119234,
Russia  Université Paris Cité, CNRS(/IN2P3), Astroparticule et Cosmologie,
F-75013 Paris, France  Anatoly Zasov Sternberg Astronomical Institute, Moscow
M.V. Lomonosov State University, Universitetskij pr., 13, Moscow, 119234,
Russia  Faculty of Physics, Moscow M.V. Lomonosov State University, Leninskie
gory 1, Moscow, 119991, Russia  Mariia Demianenko Max-Planck-Institut für
Astronomie, Königstuhl 17, 69117 Heidelberg, Germany  Ivan Yu. Katkov New York
University Abu Dhabi, P.O. Box 129188, Abu Dhabi, UAE  Center for Astrophysics
and Space Science (CASS) New York University Abu Dhabi
PO Box 129188, Abu Dhabi United Arab Emirates  Sternberg Astronomical
Institute, Moscow M.V. Lomonosov State University, Universitetskij pr., 13,
Moscow, 119234, Russia  Ana Lalović  Astronomical Observatory, Volgina 7,
11060 Belgrade, Serbia  Srdjan Samurović  Astronomical Observatory, Volgina 7,
11060 Belgrade, Serbia

###### Abstract

To understand the origin of extended disks of low-surface brightness (LSB)
galaxies, we studied in detail 4 such systems with large disks seen edge-on.
Two of them are edge-on giant LSB galaxies (gLSBGs) recently identified by our
team. The edge-on orientation of these systems boosts their surface
brightnesses that provided an opportunity to characterize stellar populations
spectroscopically and yielded the first such measurements for edge-on gLSBGs.
We collected deep images of one galaxy using the 1.4-m Milanković Telescope
which we combined with the archival Subaru Hyper Suprime-Cam and DESI Legacy
Surveys data available for the three other systems, and measured the
structural parameters of the disks. We acquired deep long-slit spectra with
the Russian 6-meter telescope and the 10-m Keck II telescope and estimated
stellar population properties in the high- and low-surface brightness regions
as well as the gas-phase metallicity distribution. The gas metallicity
gradients are shallow to flat in the range between $0$ and $-0.03$ dex per
exponential disk scale length, which is consistent with the extrapolation of
the gradient – scale length relation for smaller disk galaxies. Our estimates
of stellar velocity dispersion in the LSB disks as well as the relative
thickness of the disks indicate the dynamical overheating. Our observations
favor mergers as the essential stage in the formation scenario for massive LSB
galaxies.

##  1 Introduction

Table 1: Observed properties of galaxies sample. Index $\mathrm{z_{0}/h}$ means correction of magnitude from edge-on orientation to face-on. The first part of the table shows the general properties of the sample. $\mathrm{M_{g}}$ is absolute magnitude in DECaLS g-band ($\dagger$ marks magnitude in SDSS g-band). The second part shows dynamical properties of galaxies, $\mathrm{V_{rot}}$ was obtained from SCORPIO-2 spectra and used in Sec. 2.1.1, dynamical mass $\mathrm{M_{dyn}}$ was calculated within $4h$ distance, $\mathrm{M_{sph}}$ is an estimation of spheroid mass based on the disk relative thickness according to (Khoperskov et al., 2010) and stellar mass estimate $\mathrm{M_{\star}}$ was described in Sec. 4.1. The third part is described in Sec. 2.1.2 and in Fig. 3. The fourth part is devoted to the surface photometry of the galaxies, all parameters are described in Sec. 2.2.2. Mass-to-light ratio (M/L) is given in $(\mathrm{M_{\odot}/L_{\odot}})$ terms for parameters of stellar populations presented in the Fig. 1 for disk and bulge regions. Last part shows $\chi^{2}$ and p-value for W1 and W2 bands (see Sec. 3.5).  Name (ID) | UGC 8197 (i) | LEDA 1044131 (ii) | FGC 150 (iii) | 2MASX J02300754-0240451 (iv)
---|---|---|---|---
RA (J2000) | 13:05:58.07 | 02:23:07.58 | 01:20:00.70 | 02:30:07.54
DEC (J2000) | 58:48:39.3 | -05:29:03.6 | 13:03:12.0 | -02:40:45.1
z (Helio) | 0.028203 | 0.069335 | 0.043041 | 0.058675
Distance, Mpc | 125 | 306 | 190 | 259
$\mathrm{M_{g}}$ | $-19.3$ | $-20.0$ | $-19.1^{\dagger}$ | $-18.9$
$\mathrm{R_{27.7,z_{0}/h}}$, arcsec | 32.5 | 18.2 | 25.5 | 21.5
$\mathrm{R_{27.7,z_{0}/h}}$, kpc | 18.5 | 24.4 | 21.9 | 24.8
$\mathrm{V_{rot}},~{}$km s-1 | 149 | 195 | 211 | 178
$\mathrm{M_{dyn}},~{}10^{11}\mathrm{M}_{\odot}$ | 0.94 $\pm$ 0.03 | 1.92 $\pm$ 0.04 | 5.49 $\pm$ 0.40 | 2.08 $\pm$ 0.07
$\mathrm{M_{\star}},~{}10^{11}\mathrm{M}_{\odot}$ | 0.46 $\pm$ 0.11 | 0.87 $\pm$ 0.2 | 0.04 $\pm$ 0.01 | 0.12 $\pm$ 0.03
$\mathrm{M_{sph}},~{}10^{11}\mathrm{M}_{\odot}$ | 0.33 $\pm$ 0.01 | — | 4.05 $\pm$ 0.31 | 1.36 $\pm$ 0.05
$\rm 12+\log(O/H)$ | $8.621\pm 0.016$ | $8.626\pm 0.074$ | $8.444\pm 0.054$ | $8.507\pm 0.077$
O/H grad., $\rm dex\ kpc^{-1}$ | $-0.020\pm 0.003$ | $-0.011\pm 0.008$ | $-0.001\pm 0.004$ | $-0.011\pm 0.006$
Data source | DECAM-$z$ | HSC-$i$ (unw.) | Serb.-L(g) | HSC-$i$
$\mathrm{R_{knee}}$, arcsec | 30 | 16 | 22 | 18
$h$, arcsec | 8.0 $\pm$ 0.2 | 4.1 $\pm$ 0.1 / $8.6\pm 0.6^{\dagger}$ | 15.4 $\pm$ 1.1 | 6.1 $\pm$ 0.2
$\mathrm{z_{0}}$, arcsec | 1.76 $\pm$ 0.03 | — | 1.51 $\pm$ 0.02 | 0.78 $\pm$ 0.01
$h$, kpc | 4.5 $\pm$ 0.1 | 5.5 $\pm$ 0.1 / $11.5\pm 0.8^{\dagger}$ | 13.2 $\pm$ 1.0 | 7.0 $\pm$ 0.2
$\mathrm{z_{0}}$, kpc | 1.00 $\pm$ 0.02 | — | 1.30 $\pm$ 0.02 | 0.89 $\pm$ 0.01
$\mathrm{\mu_{0}}$ | 20.3 $\pm$ 0.2 | 20.3 $\pm$ 0.3 | 23.3 $\pm$ 0.0 | 20.8 $\pm$ 0.0
$\mathrm{\mu_{0,z_{0}/h}}$ | 22.0 $\pm$ 0.1 | — | 25.8 $\pm$ 0.2 | 23.0 $\pm$ 0.1
$(M/L)_{\textrm{bulge}}$ | 2.73 | 2.61 | 0.75 | 1.33
$(M/L)_{\textrm{disk}}$ | 1.30 | 0.51 | 0.42 | 0.39
$\chi^{2}_{W1}$ | 64.72 $\pm$ 16.09 | 15.14 $\pm$ 5.29 | 4.09 $\pm$ 1.19 | 474.11 $\pm$ 38.08
p-valueW1 | 0.0 | 0.0 | $5\cdot 10^{-9}$ | 0.0
$\chi^{2}_{W2}$ | 8.47 $\pm$ 2.37 | 2.05 $\pm$ 0.62 | 1.34 $\pm$ 0.43 | 30.5 $\pm$ 5.25
p-valueW2 | 0.0 | 0.002 | 0.088 | 0.0

To understand the evolution and formation of disk galaxies, it is essential to
study all their subclasses, including those with extreme properties. The
general principles governing “normal” systems should also apply to these
extreme cases. That is why our picture of the evolution of galaxies will not
be complete without understanding the extreme cases. Historically, research on
disk galaxies was primarily focused on high-surface brightness systems.
Freeman’s seminal paper in 1970 postulated a universal central surface
brightness for galactic thin disks. Almost two decades later, Bothun et al.
(1987) discovered galaxies with much dimmer central surface brightnesses
(fainter than 22 mag./arcsec2 in the B-band), primarily in sparse
environments. As instrumentation and detectors evolved over the years, it
became evident that the number of low-surface brightness (LSB) disks was
significantly underestimated, revealing the diversity of LSB galaxies.

Among LSB galaxies, those with giant disks (gLSBGs) deserve special attention.
These galaxies have extremely extended LSB disks with radii up to 130 kpc
(Boissier et al., 2016). They have the largest disks in the Universe, and they
are the largest concentrations of baryons (M${}_{\textrm{b}}\approx 10^{11}$
M⊙ ) with substantial angular momentum. Their dynamical masses reach up to
$10^{12}$ M⊙ within the disk radius (Saburova et al., 2021). The assembly of
very massive pressure-supported galaxies (giant ellipticals, cluster
dominants) is explained by multiple major and minor mergers. However, the same
scenario cannot be directly applied to gLSBGs, because to preserve the angular
momentum in the end-product, the majority of infalling galaxies must have
their orbital spins aligned, which is hard to reproduce in the $\Lambda$CDM
cosmology (Pawlowski et al., 2024). Rings or disks of satellites were indeed
found around M31 (Ibata et al., 2013), CenA (Müller et al., 2018), and NGC
4490 (Karachentsev & Kroupa, 2024), but even if one takes the combined
baryonic mass in all satellites in the ‘plane’ of these systems, it will fall
order of magnitude short of the typical mass of a gLSB disk. Thus the question
of the formation of giant low surface brightness galaxies is still actively
debated (Kasparova et al., 2014; Galaz et al., 2015; Hagen et al., 2016;
Boissier et al., 2016; Saburova et al., 2018, 2019, 2021).

With the advent of the deep wide-field photometric surveys such as Hyper
Suprime-Cam (HSC, Miyazaki et al., 2018) Subaru Strategic Program (Aihara et
al., 2019) and the Dark Energy Spectroscopic Instrument (DESI) Legacy Surveys
(Dey et al., 2019), our team conducted a search for gLSBGs by visual
inspection of multi-color images (Saburova et al., 2023). This was necessary
because the training set for an automated search, e.g. using machine learning
had been too small. Our efforts resulted in a large sample of gLSBGs and
smaller LSB galaxies with similar morphology. Notably, we discovered the first
edge-on gLSBGs, which became the subjects of this work. In this study, we
focus on four edge-on galaxies characterized by extended LSB disks, with their
central regions dominated by high surface brightness (HSB) disks. Among these,
FGC 150 is a _bona fide_ gLSBG, while LEDA 1044131, also identified as a gLSBG
by Saburova et al. (2023), presents a more complex case because of the disk
asymmetry or lopsidedness which however shows regular rotation with the
velocity amplitude of 150 km s-1 and can be traced in the GALEX UV image up to
the radius of 60 kpc. The remaining two galaxies have large disks and may
represent intermediate cases between gLSBGs and smaller ‘classical’ LSB
galaxies.

The distinction between gLSBGs and intermediate-size LSB galaxies is rather
arbitrary. We adopt a threshold of four disk radial scale lengths ($4h$) of at
least 50 kpc as the criterion (see Saburova et al. 2021). At the same time, Du
et al. (2023) used the ‘diffuseness index’ criterion $\mu_{B}$(0) + 5log (h)
$>$ 27.0 where $\mu_{B}$(0) is the disk B-band central surface brightness, Zhu
et al. (2023) relied on the Hi disk size radius. Observations demonstrate that
gLSBGs do not form a distinct population but rather occupy the high-mass and
large-size end of the distribution functions for disk systems (Saburova et
al., 2023). They also do not deviate by their position on the angular momentum
versus baryonic mass relation (Mancera Piña et al., 2021). A key question is
whether gLSBGs are a particular instance of extended ultraviolet (XUV) disks
found in normal spiral galaxies (Gil de Paz et al., 2005; Thilker et al.,
2005). At least two gLSBGs, Malin 1 and UGC 1382 were classified as XUV disks
in the past (Hagen et al., 2016; Boissier et al., 2016). Dwarf LSB galaxies
might also exhibit properties similar to gLSBGs. For example, the low-mass LSB
galaxy Ark 18, located in the Eridanus void (Egorova et al., 2021), has an
extended blue disk surrounding a high surface brightness component, similar to
some gLSBGs. This suggests that gLSBGs might be extreme cases of a more common
phenomenon occurring in normal galaxies. That is why here we study smaller but
still extended disk sizes in addition to gLSBGs.

Table 2: Observing log. All cases except the one marked by ∗ (DEIMOS) correspond to SCORPIO-2.  Galaxy ID | Slit PA | Date | Exp.time | Seeing
---|---|---|---|---
| (deg) |  | (s) | (arcsec)
(i) | 67 | 08.06.2021 | 10801 | 2.5
(ii) | 105 | 30.11.2022 | 3600 | 2.1
(ii)∗ | 91.2 | 25.10.2022 | 4800 | 0.7
(iii) | 159 | 17.08.2020 | 8400 | 3.0
(iv) | 336 | 07.11.2021 | 9900 | 1.5

The edge-on orientation of these systems is beneficial because it enhances
their surface brightness making possible the assessment of stellar population
properties of LSB disks using optical spectroscopy not only in emission but
also in absorption lines. The goal of this paper is to determine the
conditions for LSB disk formation and select the most likely evolutionary
scenario. To shed light on the origin of LSB disks and help to locate missing
reservoirs of accreted gas, we focused on the stellar population properties,
internal dynamics, and gas metallicity of four of these edge-on LSB galaxies.

The main properties of these galaxies are summarized in the first block of
Table 1, which includes the coordinates listed in NASA/IPAC Extragalactic
Database (NED)111https://ned.ipac.caltech.edu/, redshifts obtained in the
current paper and the corresponding distances, and the g-band absolute
magnitudes calculated from DESI Legacy Survey data (a combination of Dark
Energy Camera Legacy Survey, DECaLS DR9 and Beijing–Arizona Sky Survey, BASS,
Zou et al., 2017) for all galaxies except FGC 150, for which we used Sloan
Digital Sky Survey (SDSS) DR8 (Aihara et al., 2011) measurements. The last two
lines of the block give the radius of the deprojected g-band isophote 27.7 mag
arcsec-2 in arcsec and kpc. This isophote level is chosen the same as in
(Saburova et al., 2023) to facilitate the comparison. The photometric systems
of DECaLS, BASS, SDSS, and HSC-SSP are different at a few per cent level
(Toptun et al., 2023), however, the dominating sources of uncertainties of
integrated and surface photometry at such low surface brightnesses are the
systematics of the background subtraction, and they significantly exceed the
differences of photometric systems.

The paper is organized as follows. In Sect. 2 we give the details of the
spectroscopic and photometric observations and the data reduction and
analysis. Particularly in Sect. 2.2.3 we discuss the effect of the deviation
from the edge-on position and the dust on the estimate of the photometric
parameters. Sect. 3 is devoted to the discussion of the main results of the
analysis – the surface photometry, the properties of the stellar population,
the kinematics profiles, and the oxygen abundance of gas and emission line
excitation mechanisms. In Sect. 4 we explore the potential formation scenarios
for these galaxies. Additionally, we examine their positions on the Tully-
Fisher relation, the relationship between radial metallicity gradients and
disk size, and the correlation between stellar mass and gas metallicity.

##  2 observations and data reduction

###  2.1 Long-slit spectral observations

We performed long-slit spectral observations of all four galaxies with the
multi-mode focal reducer SCORPIO-2 (Afanasiev & Moiseev, 2011) mounted in the
primary focus of the 6-m telescope BTA of SAO RAS (proposals 2020-2-456,
2021-1–527, 2021-2-595, P.I.: A. Saburova). We used the VPHG1200@540 grism
covering the 3600–7070 Å wavelength range with $\sim 5.2$ Å spectral
resolution (FWHM) and the 0.36 arcsec pixel-1 scale. The slit width was 1
arcsec for all cases except LEDA 1044131, for which we used a narrower 0.69
arcsec-wide slit oriented along the principal plane of the HSB edge-on disk.
The data were processed using the idl pipeline. The data reduction has been
described in detail, e.g. in Zasov et al. (2015), and includes bias
subtraction, flat correction, wavelength calibration, and sky subtraction,
which was performed using a technique, described in Katkov & Chilingarian
(2011).

HSB and LSB disks in LEDA 1044131 are misaligned and we observed this galaxy
along the LSB disk using DEIMOS (Faber et al., 2003) operated on the Keck-II
10 m telescope (proposal 2022B-N149, P.I.: I. Chilingarian). We used a 0.7
arcsec long slit and the 900ZD grating. The spectrum covers the 5000-8400 Å
wavelength range with the spectral resolving power $\text{R}\sim 3600$
(1.5–2.4 Å FWHM) and a pixel scale of 0.12 arcsec pix-1. The data reduction
was performed using a dedicated idl data reduction pipeline for DEIMOS built
upon a generic long-slit/multi-slit data reduction toolkit originally
developed for the TDS double-beam spectrograph operated at the 2.5 m telescope
of the Moscow State University (Potanin et al., 2020). The substantial
difference with the SCORPIO-2 data reduction was the use of atmospheric
airglow lines for wavelength calibration instead of an internal arc lamp.
Unlike SCORPIO-2 the DEIMOS’s instrumental line spread function does not vary
along the slit. Therefore the sky background subtraction was performed by
averaging out the outer parts of the slit, which do not contain flux from the
galaxy, and then subtracting the sky vector from each row of the frame.

We provide the observing log in Table 2. For both DEIMOS and SCORPIO-2
observations, except the case of 2MASX J02300754-0240451, the instrumental
line-spread function (LSF) was determined from fitting the twilight sky
spectra observed with the same setup fitted against a high-resolution solar
template spectrum from (Kurucz et al., 1984). For the observations of 2MASX
J02300754-0240451, the LSF was determined by fitting emission lines in the arc
spectrum with Gauss-Hermite profiles, due to the lack of twilight observations
for that night. All spectra were corrected for atmospheric absorption using a
technique described in detail in Borisov et al. (2023).

####  2.1.1 Analysis of spectral data

Primary reduction yielded spatially resolved spectra and LSF estimates.
Further analysis of each spectrum involved several sequential steps. In these
steps we used the idl software package nbursts full spectrum fitting technique
(Chilingarian et al., 2007a, b) with XSL simple stellar population models
(Verro et al., 2022), simple stellar population models based on the empirical
X-Shooter Spectral Library ($3500-24800$ Å, R $\sim 10000$) with the Kroupa
(2001) initial mass function and PARSEC/COLIBRI isochrones (Bressan et al.,
2012; Marigo et al., 2013). The nbursts also fits emission line profiles with
Gaussian-Hermite functions concurrently with stellar populations, using a
bounded linear inversion to constrain emission line ratios (e.g. for [Nii] and
[Oiii] doublets). Line fluxes, their uncertainties, and kinematics for
absorption and one or several sets of emission lines are determined in the
same minimization loop.

One of the primary objectives of this paper was to estimate the properties of
the stellar population within the LSB disk region. To fit the absorption lines
in this low-brightness area, we employed extensive binning along the slit to
achieve reasonable signal-to-noise ratios. To obtain unbiased values for
velocity dispersion and stellar population parameters, we corrected the data
for galaxy rotation. Below we provide detailed information on the binning
process and the correction for the rotation.

In the first step, we applied one-dimensional adaptive binning to the spectrum
along the slit within a narrow wavelength range (accounting for the spread due
to the galaxy’s rotation) near H$\mathrm{\alpha}$. This allowed us to
determine radial velocities from bright emission lines at various distances
from the galaxy’s center. The derived rotation curve $v(R)$ was approximated
by the function:

$v(R)=2v_{\textrm{rot}}\tanh((R-R_{c})/h)+v_{\textrm{sys}}$ (1)

where $R_{c}$ is the center position; $h$ is the disk scale length; $v_{sys}$
is the systematic velocity; $v_{rot}$ is the maximum rotation velocity. Then
the entire spectrum was corrected pixel-by-pixel for the rotation of the
galaxy (Fig. 1 top panels). Further steps were performed on the corrected
spectra.

Figure 1: Results of the analysis of SCORPIO-2 long-slit spectra for each
galaxy. Top to bottom panels show the image with slit location (red line),
line-of-sight velocities, velocity dispersions, SSP-equivalent ages, and
metallicities with relative gas-phase metallicities (corrected to
$12+\log$(O/H)${}_{\odot}=8.69$). Blue symbols correspond to ionized gas and
red to stellar parameters. For LEDA 1044131 we also show the results of the
analysis of a DEIMOS long-slit spectrum (green slit on the image). The grey
area is defined by photometric analysis (Fig. 5) and corresponds to the
parameters of bulges or bars because they dominate in the integrated light.
LSB disk spectra corrected for disk kinematics were integrated in large bins;
colored lines show the results of the analysis in these bins.

In the second step, adaptive binning was again applied at the continuum level
near H$\mathrm{\beta}$. This enabled us to get optimal signal-to-noise ratio
(SNR) in the stellar continuum for a more reliable determination of the
properties of stellar populations (SSP age T (Gyr) and metallicity [Fe/H]
(dex)), but in a smaller number of bins than in the first step (Fig. 1 bottom
panels).

In the third step, adaptive binning was once again applied in the close
vicinity of H$\mathrm{\alpha}$ to obtain a larger number of bins with optimal
SNR in the strong emission lines to refine the velocity dispersions from the
first step with the stellar populations determined in the second step (Fig. 1
middle panels).

In the final step, we determined the properties of stellar populations and
emission lines in LSB disks as a single bin (the resulting spectra are shown
in Fig. 12 for red and yellow regions in Fig.1). In Fig. 1 we also show the
colour-composite images of the galaxies (top panel) with the overplotted
position of the slit (horizontal line) and the results of gas-phase
metallicity estimates described below (bottom panel).

####  2.1.2 Gas-phase metallicity measurements

As a result of the simultaneous spectral fitting described above, we obtained
emission line fluxes, which were used in the subsequent analysis of ionization
mechanisms and ionized gas metallicities. Baldwin et al. (1981) first
empirically demonstrated that ionization can be distinguished by several
mechanisms using a few easily measured line ratios. Veilleux & Osterbrock
(1987) refined this method to use line ratios that minimize the impact of dust
reddening correction. In Fig. 2 we present BPT diagrams for each galaxy in our
sample with demarcation curves from Kewley et al. (2001) and Kauffmann et al.
(2003). We excluded regions with line flux ratios indicating composite or
shock gas excitation from the gas metallicity analysis. Finally, we checked
other spectra for poor flux measurements and removed them from further
analysis.

Figure 2: Resolved BPT diagrams along slits. Symbols are color-coded
corresponding to their galactocentric distance. The blue dashed line in the
BPT-BPT-NII plot represents the demarcation line introduced by Kauffmann et
al. (2003), which distinguishes between the star-forming and the so-called
composite regions. The additional demarcation lines are taken from Kewley et
al. (2001). They separate composite and AGN regions on the BPT-NII diagram and
categorize star-forming, Seyfert/LINER regions in the BPT-OI and BPT-SII
diagrams. Density plots of emission line measurements from the RCSED database
(http://rcsed.sai.msu.ru, Chilingarian et al., 2017) are shown in grey.

To measure gas metallicity, we first corrected emission line fluxes for dust
attenuation in star-forming regions. We used Fitzpatrick (1999) extinction
curve with $R_{V}=3.1$ accessible via PyNeb package (Luridiana et al., 2015)
with $\rm H\alpha/\rm H\beta$ line ratio and their theoretical ratio 2.86 for
case-B recombination and temperature $10~{}000$ K (Osterbrock & Ferland,
2006). For our sample, we derived gas metallicity with the S2 method from
Pilyugin & Grebel (2016). The radial distribution of metallicity is shown in
Fig. 3 for each galaxy. We present metallicity gradients in Table 1 (the third
block) in the units of $\mathrm{dex\ kpc^{-1}}$. Below, we compare these
measurements with disk scale lengths in Sect. 4.1.

Figure 3:  The radial oxygen abundance 12 + log(O/H) profiles for each galaxy
determined with the S-calibration (Pilyugin & Grebel, 2016). In dark blue,
red, green, and violet colors, we plot individual metallicity measurements at
particular radial distances (symbols) and their linear best-fit approximation
in different lines for UGC 8197 (dash dotted), LEDA 1044131 (solid), FGC 150
(dotted) and 2MASX J02300754-0240451 (dashed) respectively. The blue dotted
line reflects solar metallicity.

###  2.2 Surface photometry

####  2.2.1 Observations with the Milanković telescope

We performed deep photometric observations of FGC 150 with 1.4-m Milanković
telescope equipped with Andor iKon-L 936 CCD camera in the optical unfiltered
‘white’ band (L-band) with a field of view of 13.3 $\times$ 13.3 arcmin, which
proved to be useful for photometric studies of LSB features (Vudragović et
al., 2021). The observations were performed on 01.10.2021 and 18.10.2022. In
total, we acquired 105 images with a duration of 200 sec each, which
corresponds to the total integration time of 5.83 hours. To avoid large-scale
background variations in the resulting co-add, the larger dithering strategy
is necessary (e.g., Duc et al., 2015). Following it, we used the random
offsets of up to 3.6 arcmin, centered on the galaxy.

The data reduction pipeline will be described in detail in Bílek et al., in
prep. In brief, following the basic photometric and astrometric calibration,
we carefully model and subtract the background. It is a two-iteration process
based on the original Milanković Telescope deep-imaging pipeline by Müller et
al. (2019). The first iteration consists of the following steps:

  1. 1.

A mask is created for each image from the objects detected by the sep source
extractor.

  2. 2.

The unmasked regions of each image are robustly fitted by a first degree
polynomial and the image is divided by the polynomial.

  3. 3.

The unmasked parts of all normalized images are robustly averaged into a
master sky-flat.

  4. 4.

For each frame, the master sky-flat is multiplied by the respective polynomial
and subtracted from the frame.

  5. 5.

All background-subtracted images are co-added.

The resulting image already shows most of the final LSB features. Iteration
two is the same as the first with three differences:

  1. 1.

A master mask is generated from the output of the first iteration to hide
virtually all objects, including the faint diffuse emission. It is created in
part by sep again and in part by manual drawing. In the algorithm for the
first iteration the mask from its Step 1. is unified with the master mask.

  2. 2.

The same as in the Step 2. of the first iteration, but now a third-order
polynomial is used.

  3. 3.

When making the final co-add frame, image weights deduced from the images
themselves are applied.

The resulting deep image is shown in the third panel of Fig. 4.

Figure 4: Deep images of the galaxies, a ‘white light’ $L$-band image for FGC
150 obtained with Milanković telescope, and co-added $g+r$ images from HSC SSP
for LEDA 1044131 and 2MASX J02300754-0240451, and from BASS for UGC 8197.

####  2.2.2 Analysis of photometric observations

To proceed with surface photometry we combined the data from Milanković
telescope with the publicly available archival images from DESI Legacy Surveys
(UGC 8197) and HSC SSP DR2 (for LEDA 1044131 and 2MASX J02300754-0240451). To
estimate structural parameters of our edge-on galaxies we performed the
analysis described in detail in Katkov et al. (2019).

LEDA 1044131 has a prominent warp. We proceeded with the analysis by unwarping
the galaxy’s image as follows: First, we adopted the positional angle from the
literature to define the main disk plane. Next, we identified the location of
the warped disk on the image by measuring the maximum intensity across the
disk. We then fitted the position of the warped part of the galaxy disk, as
defined by these measurements, with a 2- or 3-degree polynomial to mitigate
the impact of noise on the measurements of the disk’s maximum intensity. This
polynomial was unique for each side of the galaxy. Finally, we projected these
warps onto the main plane, using the determined polynomials as references for
the observed disk of the galaxy.

After the unwrapping, all the images were processed using the approach
described in Katkov et al. (2019). From the images (see the data sources in
Table 1), we calculated radial profiles parallel to the central cut of the
galaxy within the range $\Delta z\sim\pm 2$ arcsec, and perpendicular to this
cut (parallel to the minor axis) within the range between $R_{\textrm{bulge}}$
and $R_{\textrm{knee}}$. All radial profiles exhibit a complex “knee”
structure characterized by two distinct exponential segments (see Fig. 5). The
presence of a “knee” or break in the surface brightness profile raises an
intriguing question. Most of the considered galaxies exhibit type II profiles,
where the outer part of the surface brightness profile is steeper than the
inner part. The exception is LEDA 1044131, which shows a more complex,
asymmetric profile. According to Pohlen & Trujillo (2006), type II profiles
are found in 66 per cent of late-type galaxies. These profiles are more common
in disc-dominated galaxies located in the field (Sil’chenko et al., 2018).
However, there are no significant differences in the morphological asymmetries
of galaxies with different profile types, indicating that environmental
disturbances or recent satellite accretion do not significantly impact the
formation of surface brightness profile breaks (Tang et al., 2020). Evidence
suggests that type II breaks occur in regions where the age of stellar
populations transitions from young to old (Yoachim et al., 2012; Pfeffer et
al., 2022). This is supported by the presence of a minimum in the colour and
mass-to-light ratio radial profiles at the break radius, while the mass
profiles do not show a corresponding break (Bakos et al., 2008).

To determine the radial disk scales of all galaxies, only the inner section
from $R_{\textrm{bulge}}$ to $R_{\textrm{knee}}$ was used, as this segment is
dominated by the LSB disk.222LEDA 1044131 shows more complex behaviour of the
surface brightness profile, so for this galaxy we also obtained the scale
length for the outermost region between $R_{\textrm{knee}}$ and R=45 arcsec.
The photometric profiles were described by the following function

$I_{R}(R,z)\propto\dfrac{R}{h(z)}K_{1}\bigg{(}\dfrac{R}{h(z)}\bigg{)},$ (2)

where $h(z)$ is the exponential scale length at a given $z$, and $K_{1}$ is
the modified Bessel function of the second kind and first order. We estimated
the FWHM seeing quality for all images using stars in the field and we used a
model that convolves the profiles (Eq. 3 and Eq. 2) with a Gaussian PSF. The
effect of seeing is minimal for the radial decomposition because the central
zone is masked, but it is significant for determining the accurate value of
the vertical scale $z_{0}$.

Fig. 6 shows that the radial scale $h$ of all galaxies, except FGC 150, varies
slightly within the chosen $z$ limits; thus, the mean value of $h(z)$ is
presented in Tab. 1. The galaxy FGC 150 exhibits a symmetric decrease in
$h(z)$. Both the image and the Balmer decrement H$\alpha$/H$\beta$ indicate
that the absorption in this galaxy is minimal, suggesting that this behavior
of $h(z)$ is not due to the presence of a dust in the disk (see Fig.8).
Therefore, for this galaxy, we used the radial scale from the central cut
($z=0$).

The vertical profiles of the galaxies were analyzed similarly. We estimated
the parameters of the vertical profiles for a given galactocentric distance
$R$ using a multi-component model (Spitzer, 1942):

$I_{z}(R,z)\propto\sum_{i}\mu_{i}(R)\textrm{sech}^{2}{\bigg{(}\dfrac{z}{z_{0i}(R)}\bigg{)}},$
(3)

where $\mu_{i}$ and $z_{0i}$ denote the mid-plane surface brightness and the
scale height of each disk component.

All galaxies are accurately described by a single-component model. Within the
examined range of radial distances from $R_{\textrm{bulge}}$ to
$R_{\textrm{knee}}$, no trends in $z_{0}$(R) are observed. Therefore, the mean
value of $z_{0}$ is provided in Table 1.

Figure 5: The radial and vertical photometric profiles on the right side of
each galaxy (see Fig. 4). The radial profiles was taken at different $z$
distances relative to the main planes of the galaxies (from $-2$ to $2$ arcsec
with a $0.5$ arcsec step). The vertical profiles were taken at $R\sim-15..-16$
arcsec for all galaxies. Solid orange lines are profiles at the center plane
($z=0$), blue lines show profiles at negative $z$, red is for positive $z$,
and black dashed lines show models (Eq. 2 for radial profiles or Eq. 3 for
vertical) with parameters from Table 1. Grey shaded regions are excluded from
analysis, the blue dashed lines indicate $\pm R_{\textrm{knee}}$. All disks
were fitted between the shaded region ($R_{\textrm{bulge}}$) and
$R_{\textrm{knee}}$. For LEDA 1044131 we also obtained the radial scale of the
outer disk by fittting the region between $R_{\textrm{knee}}$ and $R=45$
arcsec. Green dashed lines are $27.7$ isophotes in (SDSS-g)-band, which were
recalculated in images bands (from Tab. 1) and deprojected from edge-on
orientation to face-on. $R_{27.7,z_{0}/h}$ are obtained from intersection
between central profiles and $27.7$ isophotes.  Figure 6: The scale lengths
$h$ and heights $z_{0}$ for LSB disks along vertical distance $z$ and $R$,
respectively. All galaxies (with the exception of $h(z)$ for FGC 150) do not
show trends and we used mean values in Table 1.

####  2.2.3 The impact of the lower inclination and dust on the analysis

It is evident from the images that at least two galaxies, UGC 8197 and LEDA
1044131, are oriented not strictly edge-on and have an inclination angle
slightly less than $i=90^{\mathrm{\circ}}$. Deviation from the edge-on
orientation leads to the overestimation of disk thickness (see Kasparova et
al., 2020). To numerically evaluate this effect, we analysed model images of
dust-free inclined disks with different axial ratios. Following the
prescription for the vertical density profile of an isothermal disk in the
equilibrium state by van der Kruit & Searle (1981), we created the model of an
exponential disk with the 3D luminosity density given by

$I(R,z)=I_{0}e^{-R/h}\mathrm{sech}^{2}\left(\frac{z}{z_{0}}\right),$ (4)

where $I_{0}$ is the central luminosity density, $h$ is the disk scale length,
and $z_{0}$ is its scale height. To simulate 2D images of a galaxy, we
integrated the luminosity density along the line-of-sight in each pixel from
different view points. For each image, we fitted the vertical profile with the
$\mathrm{sech}^{2}$ law to estimate how the thickness estimate is biased.

Fig. 7 shows how deviation from the edge-on orientation affects the computed
thickness. As one can see from the figure, at a given angle, the effect
increases with the major-to-minor axes ratio. For extremely thin galaxies with
an axial ratio of 10, even a slight deviation of 5∘ ($i$=85∘) from the edge-on
orientation can lead to an overestimation of their thickness by nearly a
factor of 2. However, even at this inclination, the vertical profile of a
galaxy is very similar to the $\mathrm{sech}^{2}$-like shape. On top of this,
real-life measurements have some noise that makes it even harder to tell
whether a galaxy is observed strictly edge-on.

Figure 7: Ratio of the best-fit scale height to its real value (when
$i=90^{\mathrm{\circ}}$) as a function of inclination for four different
$h/z_{0}$ ratios.

Three of our galaxies (UGC 8197, LEDA 1044131, and 2MASX J02300754-0240451)
have a prominent dust lane, which usually helps to visually analyse the
inclination of a galaxy with respect to the edge-on position. On the other
hand, this can make it difficult to estimate structural parameters. To
evaluate the influence of dust, we added absorption to the radiative transfer
in our model and simulated images of edge-on galaxies. In our model, the dust
distribution follows the same equation as stars (Fig. 7) but with a smaller
vertical scale $z_{d}$. We then visually determined the mid-plane region to be
masked and fitted the vertical profile with the $\mathrm{sech}^{2}$ law. We
tested this approach with two different values of $z_{d}$: thin dust lane with
$z_{0}$/3 and thick dust lane with $z_{0}$/1.5. For each value of $z_{d}$, we
also made tests with $\tau_{\mathrm{eo}}$=0.5 and $\tau_{\mathrm{eo}}$=5,
where $\tau_{\mathrm{eo}}$ is the total optical depth through the center of
the edge-on disk. Fig. 8 demonstrates the model images for all four cases. Our
modeling has shown that the presence of dust leads to the overestimation of
disk scale length. This effect has earlier been found in (Savchenko et al.,
2023). However, masking the attenuated region around the mid-plane helps to
minimize this effect as well. Also Fig. 8 shows how the determined scale
length depends on the height above/below the mid-plane where the radial
profile is built. In addition, our models allowed us to estimate the
inclinations for these three galaxies as $i\approx 88.5^{\mathrm{\circ}}$ (UGC
8197), $i\approx 85^{\mathrm{\circ}}$ (LEDA 1044131), and $i\approx
89.5^{\mathrm{\circ}}$ (2MASX J02300754-0240451).

Figure 8: Top: Model images of galaxies with different absorption coefficients
$\tau$ and dust disk thicknesses $z_{d}$. Bottom: Disk scale length estimated
from radial profiles at different heights $z$ (in pixels) above/below the mid-
plane for the four models with different $\tau$ and dust disk thicknesses
$z_{d}$ (red curves). The horizontal black curves show the real value of the
scale length. Grey dashed lines correspond to $z_{d}$ of the models. The total
semi-height of each model is 60 pixels.

We conducted a blind test in which our well-experienced team members
responsible for surface photometry did not know the values of the structural
parameters of the models. In all four cases, their approach showed a very good
agreement with the actual values of $z_{0}$ and $h$. We thus conclude that our
approach is robust and might be applied to real observations.

##  3 Properties of individual galaxies

###  3.1 LEDA 1044131

LEDA 1044131 is characterised by the “normally” looking inner part surrounded
by the LSB structures of complex morphology demonstrating a strong warp. Such
structures can be a result of gravitational interaction, e.g. with the in-
falling satellites (see, e.g. Ostriker & Binney, 1989). However alternative
explanations of the warp formation were proposed, e.g. the misalignment
between the stellar and gaseous disks (Roškar et al., 2010) or between the
disk and the halo (Debattista & Sellwood, 1999), bending modes or waves in the
disks (Revaz & Pfenniger, 2004). The closest massive neighbor to LEDA 1044131
with a known redshift, LEDA 1043075, is located in 546 kpc in the projection
of the SW direction (the velocity difference is about 900 km s-1) which could
hardly lead to the formation of warped LSB structures. At the same time, LEDA
1044131 is surrounded by clumpy small objects with unknown redshifts which
could be the satellite candidates or the remnants of the intruder galaxy.

The gaseous kinematics of LEDA 1044131 is quite complex (see Fig. 1). The
emission lines show splitting in the region of the LSB disk where one
component of the line shows slower rotation than another. It is likely related
to the warp, we see the parts of the galaxy with different orientations in the
line-of-sight. The stellar velocity dispersion remains almost constant with
the value of 100 km s-1 , which can indicate the dynamical overheating of the
disk (that means the stellar velocity dispersion is higher than needed for the
disk to be gravitationally stable, see also the discussion). The radial
distribution of the SSP-equivalent stellar age is also surprisingly flat with
the mean value of around 2 Gyr. It can mean that the whole disk is forming
stars at a rate that is independent of radius.The stellar and gaseous
metallicities are solar in the center and become sub-solar in the periphery.
From the BPT diagram it is evident that several disk regions are above the
‘maximum starburst line’ (these regions were excluded from the metallicity
estimation.

###  3.2 FGC 150

FGC 150 was included in the flat galaxies catalogue with a major-to-minor axis
ratio $a/b>7$ (Karachentsev et al., 1993). Our photometric analysis confirms
this conclusion (see Table 1). Even though the inner part of the disk looks
flat, the outermost regions show bending which is well visible in the deep
image (see Fig. 4, third panel). What is also visible from the image are two
clumpy structures, near both sides of the disk which could be possible
satellites that could give rise to the disk warp.

Stars show a flat radial gradient of the velocity in the inner part of the
galaxy and a sharp decrease of the age from 10 Gyr in the center to 2 Gyr in
the LSB disk where the stellar metallicity also decreases abruptly. At the
same time the gaseous metallicity profile is very flat. The inner areas of the
galaxy lie in the LINER region on the BPT diagram indicating possible presence
of AGN.

###  3.3 UGC 8197

UGC 8197 is the least massive and extended galaxy of the sample with a disk
size comparable to that of the Milky Way (see Table 1), however it
demonstrates similar morphology as the more extended systems of our sample. As
it is evident from the HSC image it has a prominent warp which can be a result
of the gravitational interaction. The galaxy LEDA 214068 located North of UGC
8197 is a background galaxy ($\Delta v\sim 30000$ km s-1 ) and could not lead
to the formation of warp. The slit crosses the outer region of the bright
clump seen NE from the galaxy which also appears to be a background source
according to the spectral data. The rotation velocity reaches the plateau at
the distance of 10 arcsec (5.7 kpc) from the center. Ionized gas shows an
almost constant velocity dispersion radial profile. The radial profile of
stellar velocity dispersion rises to the periphery on one side of the disk.
BPT diagram (Fig. 2) shows that most of the regions of the galaxy occupy the
photoionization domain below the ‘maximum starburst line’ which makes possible
the ionised gas metallicity estimates. The central region of UGC 8197
possesses young stars with near-solar metallicity. The gas has the solar value
of metallicity in the inner region. At the same time, the LSB disk is
characterised by a young metal-poor stellar population and a slightly sub-
solar value of gas metallicity. It can indicate the ongoing star formation in
the LSB disk. The presence of enriched gas evidences against the recent
accretion of gas from the cosmic filament to this system.

###  3.4 2MASX J02300754-0240451

2MASX J02300754-0240451 is the galaxy with a very extended ‘regular’ disk (see
Table 1). Its disk also does not show any significant warping at the
periphery. No neighbour massive galaxies are observed within 500 kpc. Both
ionised gas and stars show a steep increase in velocity in the inner region
where the X-shaped bulge which is most likely a bar is situated. The ionised
gas has a change of the velocity gradient and the minimum of the velocity
dispersion which is expected for bar regions (Chung & Bureau, 2004; Saburova
et al., 2017). The bulge of 2MASX J02300754-0240451 has quite low age of
around 5 Gyr which decreases slightly to the periphery. Most of the regions of
2MASX J02300754-0240451 belong to the photoionization domain which allowed us
to estimate the oxygen abundance. The ionised gas metallicity changes from
nearly solar to slightly sub-solar in the outer regions. It argues against the
fresh accretion of metal-poor gas from the filament or a dwarf gas-rich
satellite.

###  3.5 Tentative Active Galactic Nuclei

The BPT diagrams (Fig. 2) demonstrate that the innermost regions of three out
of four galaxies lie in the locus of LINERs, which can be an indication of the
presence of an AGN (Heckman, 1980). The findings of (Ramya et al., 2011;
Subramanian et al., 2016; Saburova et al., 2021) show us that gLSBGs tend to
have too low central black hole masses for their stellar velocity dispersion.
Therefore these AGNs can be powered by black holes in a low-mass SMBH regime.

The recent studies of low-mass AGNs variability (Ward et al., 2022; Cleland &
McGee, 2022) use light curves derived from mid-infrared (MIR) unWISE (Wide-
field Infrared Survey Explorer, WISE + NEOWISE) images (Meisner et al., 2023),
as well as optical Zwicky Transient Facility Forced Photometry (Masci et al.,
2023) light curves of galaxy centers to prove the activity of central black
hole accretion processes. The AGN orientation can be arbitrary relative to its
host galaxy inclination, however, Gkini et al. (2021) found an observational
lack of AGN Type 1 detections in spiral galaxies, because of host galaxy dust
contribution. To check the evidence of AGN activity, we propose to use MIR
variability, because the contribution of the host galaxy on the long
timescales is expected to be constant, and we do not expect to find optical
variability.

We downloaded time-resolved unWISE coadds (unTimely catalog) using the
unTimely Python package (Meisner et al., 2023). Each coadded image includes
more than 12 images taken during each WISE sky-pass, with the standard cadence
of unTimely light curves being 6 months. We chose the aperture photometry
radius as 3 arcseconds for each source because a bigger aperture radius leads
to capturing more than one source for 2MASX J02300754-0240451, FGC 150. We
downloaded ZTF Forced Photometry light curves of these objects and standard
stars for calibration. We note that the ZTF light curves of LEDA 1044131 and
2MASX J02300754-0240451 have huge gaps and poor coverage of dates, hereby they
are out of our consideration. To calibrate ZTF Forced Photometry light curves
we used a post-processing algorithm outlined in Demianenko et al. (2024) and
standard stars correction (Demianenko et al. in prep.).

Because these time-domain surveys were not designed to check the variability
of faint AGN on short time scales and do not have sufficient cadence, we do
not pretend to deliver timescales of the variability ($\tau$) from stochastic
processes (e.g. damped random walk or Gaussian Processes models). We applied
the simplest approach: check forced photometry light curves to test the
presence of variability. We used $\chi^{2}$ statistics, which are widely used
to calculate the $p$-value, and we compared the $p$-value with a certain
significance level to conclude the presence of variability (Sokolovsky et al.,
2017). Our null hypothesis was that all observation points in the light curve
are independent random variables $x~{}\sim\mathcal{N}(\mu,\,\sigma^{2})$,
which form the constant. Then we used the weighted mean as a robust estimator
of the model being a constant source obtained by the method of likelihood
maximization. The number of observations affects the $\chi^{2}$ calculation,
therefore we applied the bootstrap technique to calculate the error
$\sigma_{chi^{2}}$ of $\chi^{2}$ estimation.

For each photometric bandpass, we calculated the $p$-value of $\chi^{2}$
distribution with the number of degrees of freedom calculated as the number of
observations in a given passband minus one. Since even after all calibration
steps we expect to have systematic errors in light curves, we use reduced
$\chi^{2}+3\sigma_{\chi^{2}}>2$ as additional strict variability criteria.
Therefore, the variability confirmation criterion is given as the following
conditions:

$\text{p-value}<0.05,~{}\chi^{2}+3\sigma_{\chi^{2}}>2.$ (5)

The Table 1 lists reduced $\chi^{2}$ and $p$-value for $W1$ (3.4 $\mu m$) and
$W2$ (4.6 $\mu m$) photometric bands respectively. We found strong variability
in $W1$ passband in all sources, $W2$ variability in UGC 8197 and 2MASX
J02300754-0240451. We did not find optical variability as expected. This is
consistent with AGN behavior in mid-IR (Lyu et al., 2019), where we expect to
see the presence of variability in $W1$, a decrease in the variability
amplitude in $W2$ compared to $W1$, and the RMS of $W1$ $\lesssim$0.1 mag.

We found our galaxies as extended radio sources at 3GHz in the Quick Look
catalog of the Very Large Array Sky Survey (VLASS) (Gordon et al., 2020)
without the signature of point sources at their centers. However, the absence
of strong radio emission does not imply the absence of a low-mass AGN (as does
an X-ray non-detection). We did not find any archival X-ray data deep enough
to validate our AGN candidates. As a summary, we propose centers of these
galaxies as potential AGNs, with deep X-ray follow-up observations required to
confirm their nature.

##  4 Discussion

The primary objective of this paper is to explore the formation mechanisms of
LSB galaxies with extended disks. We do not advocate for a single formation
scenario for all the galaxies studied, particularly considering the range of
scenarios proposed by Saburova et al. (2021) for gLSBGs. However, given the
similar morphology of these systems, it is plausible to hypothesize that they
share a common formation process.

Several formation scenarios could be responsible for a building-up of the
extended disks Saburova et al. (2021), we shortly discuss them below.

Scenario a: major merger with fine-tuned orbital parameters can lead to the
formation of extended disks (Saburova, 2018; Zhu et al., 2018). What is
expected in the scenario?

  * •

Flat or shallow radial gradients of gas metallicity and stellar
age/metallicity.

  * •

The stellar disk should be dynamically overheated having the velocity
dispersion ($\sigma_{*}$) significantly above the critical value needed for
the gravitational stability of the disk.

  * •

The collisional excitation of gas could be seen in the BPT diagnostic
diagrams.

Scenario b: the formation of gLSBG can occur via minor mergers with gas-rich
dwarf galaxies (Peñarrubia et al., 2006). What is expected in the scenario?

  * •

A significant radial gas-phase metallicity gradient should be observed because
the metallicity of dwarf satellites is expected to be low.

  * •

The remnants of disrupted satellites should be seen in the velocity and gas
metallicity profiles.

  * •

Stellar velocity dispersion $\sigma_{*}$ should be close to critical. Thus the
disk should not be significantly dynamically overheated which is observed in
most of the spiral and some of the lenticular galaxies (Zasov et al., 2011).

Scenario c: unusual properties of giant disks could be explained by the
unusually large radial scale of a dark matter (DM) halo, a sparse dark halo
with a shallow potential well Kasparova et al. (2014). What is expected in the
scenario?

  * •

Large dark matter halo radial scale and the low central density as
reconstructed from the rotation curve modeling.

  * •

The stellar velocity dispersion is close to that expected for a marginally
gravitationally stable disk.

  * •

The presence of age and metallicity radial gradients in stellar population
which is indicative of the “standard” inside-out formation.

Scenario d: a giant disk is formed by accretion of metal-poor gas from a
cosmic filament on-to a pre-existing elliptical or spiral HSB galaxy formed in
a “standard way” by accretion and mergers Saburova et al. (2019).

What is expected in the scenario?

  * •

Sharp gas metallicity gradient should be observed because the disk is built-up
from pristine metal-poor material.

  * •

Kinematically decoupling such as counter-rotation should be common ($\sim$50%
of cases).

  * •

Inward non-circular motions should be seen in the gLSB disk.

  * •

The old stellar disks should be gravitationally stable at the same extent as
in the case of the absence of a newly formed gaseous extension.

Let’s examine the proposed scenarios using the data obtained in this study.

###  4.1 Metallicity gradients

The metallicity radial gradients could be used as a clue to a formation
scenario of a galaxy. The considered galaxies have a low slope of the gas
metallicity (see Table 1). The different slopes support distinct scenarios of
disk formation. In this work, we also test the merger scenario. For galaxies
formed in this way, simulations predict a flat abundance gradient caused by
the tidal torques transferring the matter to the centers of galaxies and
mixing the gas in the peripheral areas of the disks (Rupke et al., 2010). On
the other hand, Bresolin & Kennicutt (2015) showed a tight relation between
metallicity gradient and B-band scale length, which they speculated as an
occurrence of local mass surface density — ($\Sigma_{M}-Z$; Rosales-Ortega et
al. 2012) or local stellar surface brightness ($\Sigma_{L}-Z$; Pilyugin et al.
2014b) metallicity relation. Thus to figure out if the obtained radial
gradients of metallicity are indeed low and can speak in favour of the merger
scenario the most informative is not the sole value of the gradient but its
correspondence to the disk size and possible deviation from this relation.

In Fig. 9, we demonstrate the comparison of the radial ionized gas metallicity
gradient with the exponential disk radial scale length. Note that these scale
lengths were not obtained in the B band (here we neglect the difference
between the scale estimates in different bands). The line corresponds to the
relation described by Eq. 1 in Bresolin & Kennicutt (2015). The position of
the late-type LSB galaxies from Bresolin & Kennicutt (2015) is shown by dark
blue squares, while the HSB sample (Pilyugin et al., 2014a, b) is overlaid as
grey squares. The galaxies of our sample are shown by red stars. We
additionally plotted values for 2 gLSBGs from literature: UGC 1922 (Saburova,
2018) and Malin 1 (Junais et al., 2024) as blue pentagon and cyan plus,
respectively. As one can see from Fig. 9 all galaxies of our sample have the
radial gradients of metallicity that agree well with that expected from their
disk sizes according to the data on other LSB and HSB galaxies. It might
testify against significant radial mixing of metals in the galaxies of our
sample which would lead to the deviation of the galaxies towards the top area
of the diagram. We note that observations of oxygen abundance radial profile
flattening is more difficult for galaxies with huge disks.

Figure 9: The relation of metallicity radial gradient and the disk scale
length for different samples. By grey squares, we present the sample of HSB
galaxies (slopes from Pilyugin et al. 2014a, and scale lengths from Pilyugin
et al. 2014b). The Bresolin & Kennicutt (2015)’s LSB sample is plotted as dark
blue circles, while ours is shown in red stars. We additionally overlaid two
galaxies available in the literature: UGC 1922 (Saburova, 2018) and Malin 1
(Junais et al., 2024) as blue pentagon and cyan plus, respectively. Note that
Malin 1 has two disks. The black dashed line is eq. 1 adopted from Bresolin &
Kennicutt (2015). Figure 10: Mass-metallicity relation. The LSB sample
analysed in this work is shown in red squares (data are summarized in Table
1). Malin 1 and UGC 1922 from the literature are superimposed with cyan plus
and blue pentagon, respectively (Junais et al. 2024 provided the
O3N2-calibrated metallicity measurements for Malin 1, while Saburova 2018 is
the reference for the oxygen abundance of UGC 1922. Masses for both galaxies
are taken from Saburova et al. 2021 In addition, we overlay the relation
obtained for local Universe (z = 0) from Duarte Puertas et al. (2022)
(violet), which uses empirical calibrations, that agree well with the MANGA
sample metallicities determined with the S2 calibration Pilyugin & Grebel
(2016) (superimposed background 2D source density distribution and its 2-nd
degree polynomial mean approximation shown by the orange line).

The good agreement of the radial metallicity gradient with that expected for
the observed disk scale lengths for normal spiral galaxies speaks against the
_recent_ major merger scenario. The BPT diagram does not show the collisional
excitation of gas which makes it even less possible.

The gas metallicity data are also useful to consider the possibility of
another scenario – the formation of the extended disks containing the emission
regions from the metal-poor gas of the cosmic filaments. Previously we already
noted that the gas-phase metallicity is only slightly sub-solar in the outer
regions of the considered galaxies which does not get in line with that
scenario.

In Fig. 10, we also compare the central gas metallicities (which are close to
the mean within effective radius due to the relatively low radial gradients)
with the stellar masses. We derived the stellar mass estimates from the DECaLS
and SDSS integrated magnitudes in the bands used for the photometric analysis,
combined with the photometric parameters of the disks and the mass-to-light
ratios of the bulge and disk regions obtained from the spectral fitting (see
Table 1). For the comparison, we also show the relations found by Duarte
Puertas et al. (2022); Cao et al. (2023). As one can see from Fig. 10, the
positions of our galaxies agree well with that found by Duarte Puertas et al.
(2022) for other galaxies, which means that the gaseous metallicities are not
too low for the expected stellar mass which could be expected in the recent
accretion from the cosmic filament scenario. At the same time, the position of
our systems deviates from that of the blue edge-on LSB galaxies that
demonstrate inefficient oxygen abundance enhancement (Cao et al., 2023), which
can indicate the different evolution history of these types of LSB galaxies.

Another argument against the metal-poor gas in-fall is that the metallicity
gradients are not lower than expected from the observed disk sizes.

###  4.2 On the gravitational stability of the disks

As previously noted, the difference between the stellar velocity dispersion
and its threshold value for the gravitational stability of the disk serves as
a crucial diagnostic criterion that can illuminate the formation scenario. A
thin isothermal stellar disk is locally stable when the radial stellar
velocity dispersion, $\sigma_{r}$, exceeds the critical value:

$(\sigma_{r})_{\rm crit}=Q_{T,\rm crit}\cdot 3.36G\Sigma_{d}/\varkappa,$ (6)

where $\varkappa$ is the epicyclic frequency, $\Sigma_{d}$ is the surface
density of the disk, and $Q_{T,\rm crit}$ is the Toomre’s stability parameter
which is equal to unity for small radial perturbations of a thin disk.

In more realistic cases, $Q_{T,\rm crit}$ for a marginally stable disk may
differ from unity due to non-radial perturbations, finite disk thickness, or
the presence of multiple disk components (see discussion in Garg & Banerjee,
2017). Additionally, the Toomre expression is derived under the epicyclic
approximation, which is valid when the radial velocity dispersion is small
compared to the circular rotation velocity. Numerical simulations bypass these
restrictions, demonstrating that for more realistic models, the Toomre
parameter typically ranges between 2 and 3 for stellar or two-component
stellar+gas disks, depending on disk parameters and initial conditions (see,
e.g. Khoperskov et al., 2003; Inoue et al., 2016; Garg & Banerjee, 2017; Zasov
et al., 2017, and references therein). Current estimates of the Toomre
parameter for several stellar-gaseous disks of LSB galaxies almost universally
demonstrate that their disks are gravitationally stable at all radii. The
minimum values of the stability parameter $(Q_{T})_{min}$ are close to 3, with
the minimum $Q_{T}$ reached at some distance from the center, in the region
corresponding to R/h$\sim$2–4 (Garg & Banerjee, 2017; Aditya et al., 2023).
For super-thin LSBs observed edge-on, the data are contradictory. For
instance, for FGC 2366, $(Q_{T})_{min}\sim 3$ (Aditya et al., 2023), while for
UGC 7321, $Q_{T}$ is significantly higher ($Q_{T}>>1$) (Ghosh & Jog, 2014).

For the galaxies considered in this study, only the upper limit $(Q_{T})_{up}$
can be estimated for a given distance from the center, as there is no data on
their gas density, whereas the contribution of Hi to the rotation curves of
gLSB galaxies can be comparable to that of their stellar disks (see f.e.
Pickering et al., 1997).

We estimated the disk surface density from the photometric data presented in
Sect. 2.2.2 and the mass-to-light ratios obtained from the spectral fitting
(see Table 1). In this estimation, we took into account the extinction
calculated from the spectra using the Balmer decrement. Formally calculated
$(Q_{T})_{up}$ values for the corresponding R at the radial distances of the
LSB bins (see Fig. 5) are the following: 20 (R=10.2 kpc), 135 (R=12.6 kpc),
9.5 (R=9.2 kpc), 70 (R=16.6 kpc) for LEDA 1044131, FGC 150, UGC 8197 and 2MASX
J02300754-0240451. Despite a rough estimate of the values, they clearly
indicate a strong dynamic overheating of the disks. Note that these estimates
were done under the assumption that the observed stellar rotation velocities
are close to circular ones and that the stellar velocity dispersion is
isotropic in the first approximation. In the stellar disks of galaxies,
$\sigma_{r}>\sigma_{\phi}$ (for galaxies with a flat rotation curve in the
epicyclic approximation $\sigma_{r}/\sigma_{\phi}\approx\sqrt{2}>1$), but this
inequality only strengthens the conclusion about the large reserve of
stability of disks. Even a comparable amount of cool gas with the velocity
dispersion $\approx 10$ km/s would not change this result.

Such overheating of the disks would mean that the observed star formation
there is not related to the large-scale instability. The reason for the high
$Q_{T}$ values is the very low surface density of the stellar disks for their
high angular rotation speed due to a massive dark halo. Only a multiple excess
of a gas surface density over the stellar one could alter this conclusion,
bringing the disk to a marginally stable state with $Q_{T}<3$.

One can formally estimate the scale height of the stellar disk for the
velocity dispersion of stars obtained from our observations. If disk thickness
is determined by its gravity, its half-thickness $z_{0}=\sigma_{z}^{2}/\pi
G\Sigma_{*}$. Assuming that the vertical velocity dispersion $\sigma_{z}$, as
in ”normal” galaxies, does not differ much from the azimuthal one, which for
edge-on galaxies is close to the observed line-of-sight dispersion, it is easy
to see that the resulting scale heights for our galaxies turn out to be
unrealistically large, comparable to the galaxy radius, which is incompatible
with the existence of a disk. However, stellar disks of the considered
galaxies are not too thick: the estimates of $z_{0}$ from photometry give the
values of $z_{0}$ close to 1 kpc (see Table 1). This indicates the presence of
some additional force holding stars near the disk plane, which significantly
exceeds the force of self-gravity.

A massive dark halo can provide an additional force compressing the disk, in
addition to disk self-gravity. The acceleration component perpendicular to the
disk plane associated with halo gravity grows linearly with distance $z\ll R$
from the disk plane (as in the case of a homogeneous disc), and is equal to
$g_{z}(R,z)=M_{h}(R)/(R^{2}+z^{2})\cdot(z/R)$, where $M_{h}(R)=V_{rot}^{2}R/G$
is the halo mass within a sphere of radius $R$. Simple estimates of the
expected scaleheight of low density equilibrium stellar disks of our galaxies
allow us to conclude that the observed values of $z_{0}$ (about 1 kpc) require
the vertical dispersion of stellar velocities to be significantly smaller than
the circular rotation velocity in the dominant field of spherical halo. This
is consistent with very close values of the measured stellar and gas rotation
velocities (see Fig. 1). However, the estimates of stellar velocity dispersion
in the outer disk regions are averaged over a large interval of $R$, and
therefore cannot be used to estimate the vertical scale profile of the disks
directly.

Below we consider if the high values of the stellar velocity dispersion can be
a result of a projection effect. Since our galaxies are edge-on, we see the
regions along a line-of-sight at different radial distances. In the absence of
a significant amount of dust, it can lead to the artificial increase of the
observed stellar velocity dispersion. In order to assess the change of the
LOSVD parameters in comparison to the intrinsic galaxy kinematics we
calculated a series of simple luminosity-weighted LOSVD models for a set of
given radial velocity dispersion and rotational velocities at large distances
from the galaxy centers. For the modeling we used several general assumptions
about the kinematics in the LSB disk: (i) a flat rotation curve in the outer
region of the disk, (ii) a Gaussian distribution of the radial and azimuthal
velocity components at each point of the disk, (iii) a fixed ratio of the
velocity dispersion components $q=\sigma_{r}/\sigma_{\phi}$. The parameters of
the model are: rotational velocity $V_{\text{rot}}$, radial velocity
dispersion $\sigma_{r}$, and $q$, which was assumed to be equal to
$1/\sqrt{2}$ as in the case of the epicyclic approximation for the flat
rotation curve. Finally, the LOSVD is determined as a luminosity-weighted sum
of projected azimuthal and radial velocity distributions onto the line of
sight. The model is essentially a simplified version of one discussed in Zasov
& Khoperskov (2003). We performed the calculations of the LOSVD for the grid
of realistic rotational velocities:
$V_{\text{LOS}}<V_{\text{rot}}<V_{\text{LOS}}+60$ km/s, and radial velocity
dispersions: $50<\sigma_{r}<170$ km/s, where $V_{\text{LOS}}$ is the measured
line-of-sight rotational velocity for each galaxy, taken at the distance of 4
exponential scale lengths from the center. These simulations showed that the
real velocity of rotation is on average about 10% higher than the directly
measured from the line-of-sight data, and $\sigma_{\text{LOS}}$ is
overestimated by 5-10% with respect to the azimuthal velocity dispersion. Thus
the projection effect does not lead to the significant overestimation of the
Toomre parameter.

###  4.3 On the dark matter halos

Another question that needs to be answered is related to the properties of the
dark matter halos in considered galaxies. The edge-on position despite having
its advantage has also a shortcoming that hampers the reliable estimate of the
inner part of the rotation curve from the long-slit spectral data. The
projection effects together with the internal absorption make the line-of-
sight velocity radial profiles of little use to reconstruct the mass
distribution of the edge-on galaxies (Zasov & Khoperskov, 2003). Thus we did
not attempt to get the structural parameters of the dark matter halo, however,
it is still possible to calculate the mass fraction of the dark halo.
According to the photometric mass estimates, the dark matter halo dominates by
mass in four considered galaxies (see Table 1).

Another method for calculating the mass fraction of the dark matter halo
involves using numerical N-body simulations, which reveal a correlation
between the ratio of the disk’s vertical and radial scales and the mass ratio
of the spherical subsystem to the disk. Specifically, as the relative
thickness of the disk decreases, the contribution of the spherical subsystem
to the total mass increases (Khoperskov et al., 2010). The spherical subsystem
encompasses both the bulge and the dark matter halo. In scenarios where disks
are dynamically overheated, as in our case, this approach provides the lowest
estimate for the spheroidal mass. However even for these estimates the masses
of the spheroidal components make a bulk contribution to the total dynamical
masses (see Table 1, second block) which confirms the previous conclusion.

An indirect conclusion on the ratio between baryon and dark mass can be drawn
from the Tully–Fisher 1977 relation, specifically, its baryonic variant that
relates the mass of baryons with the rotation velocity (see, e.g., Ponomareva
et al., 2018; Lelli et al., 2019). However, because the neutral gas mass
measurements normally used to construct the TF relation are not available for
the galaxies considered here, we use the stellar TF relation that relates the
stellar mass with the rotation velocity at the plateau of the rotation curves.
The stellar TF relation is shown in Fig. 11. Pink stars denote the positions
of our four galaxies, filled symbols correspond to the 7 gLSBGs from Saburova
et al. (2021). Open circles correspond to the systems from the Spitzer
photometry and accurate rotation curves database (SPARC) (Lelli et al., 2016),
the line gives the relation found by Reyes et al. (2011). Fig. 11 shows that
three out of four galaxies lie within spread on the top part of the baryonic
TF relation. However, FGC 150 seems to lack stellar mass for its rotation
velocity. It can either indicate the higher dark matter fraction in this
system or a high fraction of neutral gas which would put this galaxy in line
with other disk galaxies on the baryonic TF relation.

Figure 11: The Tully-Fisher relation connecting the stellar mass and rotation
velocity. Coloured symbols correspond to LSB systems. Stars show the position
of edge-on galaxies considered in the current paper, and other coloured
symbols demonstrate gLSBGs from Saburova et al. (2021). The line gives the
relation found by Reyes et al. (2011). Grey open circles correspond to the
systems from SPARC database (Lelli et al., 2016).

##  5 Conclusions

The galaxies studied in this paper represent gLSBGs and an intermediate
“chain” between gLSBGs and moderately-sized low-surface brightness galaxies
(LSBGs). The stellar and dynamical masses of these galaxies are comparable to
those of well-studied gLSBGs (Saburova et al., 2021). They exhibit flat radial
ionized gas metallicity gradients, similar to other gLSBGs (see Fig. 9). The
stellar population of the bulges, however, appears to be younger than that
observed in other gLSBGs. In the sample from Saburova et al. (2023), only 8
per cent exhibit a truncated surface brightness profile (type II), as we see
in the galaxies presented here. However, most galaxies from Saburova et al.
(2023) are not observed edge-on. According to (Saburova et al., 2023),
approximately 13,000 gLSBGs are expected to be found across the entire sky up
to a redshift of $z=0.1$, indicating that these galaxies are relatively rare.
The published gLSBG samples contains only a few dozen of these systems, and
the number varies depending on the criteria used to define gLSBGs.

Based on the observational data collected, we conclude that gLSBGs do not
constitute a unique class of objects but represent the high-mass, low-surface
density, large-disk end of the population of disky galaxies. However, the
question remains as to which circumstances are favorable for the formation of
these giant disks. Thus this paper aims to clarify the evolutionary paths of
low surface brightness (LSB) galaxies with extended disks. Let’s summarize the
arguments supporting the scenarios proposed at the beginning of Section 4.
According to our data, the most promising scenarios involve mergers. However,
the observational data do not distinguish between mergers with different mass
ratios. We observe flat ionized gas metallicity radial profiles in the studied
galaxies. Thus most probably the disks were not formed from the gas-rich
metal-poor dwarf galaxies. At the same time the metallicity gradient values
align with those expected for the disk scale length of normal spiral galaxies,
suggesting that the formation paths of our systems are not particularly
extreme or exotic. Although disk galaxies can form through major mergers, this
is likely not the primary formation channel for these systems, as major
mergers tend to destroy the disk structure (Rodriguez-Gomez et al., 2017;
Kulier et al., 2020). Thus, we give less credibility to the major merger
scenario, though we do not discard it completely. The disks of our systems
look thin and regular (perhaps, except LEDA 1044131), and appear to be
virialized, suggesting that they have completed at least 3–4 full rotation
periods, which exceeds 2 Gyr for all our objects. The stellar velocity
dispersion and relative disk thickness support the presence of dynamically
overheated disks, which is consistent with a merger scenario, as are the flat
metallicity profiles. Additionally, deep images of the galaxies reveal
possible remnants of disrupted satellites in the form of clumps, which,
however, do not have a spectroscopic confirmation.

Because we do not observe extremely low metallicity at the outer regions of
these galaxies and the central value of the gas metallicity agrees with that
expected for a given stellar mass for normal spiral galaxies, we conclude that
the formation of LSB disks via gas accretion from intergalactic filaments is
quite improbable. We cannot rule out the possibility that the dark matter
halos of the observed galaxies possess peculiar properties, such as a high
radial scale and low central density. It is possible that we are observing
end-products of mergers combined with these specific dark matter halo
characteristics. However, the mergers look essential in the formation scenario
of LSB disks.

To advance the study of gLSBGs, we need Hi and optical spectral observations
of a larger sample of these systems. This will allow us to examine their
properties in greater detail, including the parameters of their dark matter
halos, and provide further insights into their nature. Additionally, deep
X-ray observations of the central regions of gLSBGs can be used to assess the
activity of their nuclei.

### Acknowledgement

We thank the anonymous referee for valuable comments that helped to improve
the paper. AZ, IG, DG, AK, ER research on the analysis and fitting of the
long-slit spectra, ionised gas metallicity estimates, and interpretation of
the kinematic and metallicity profiles and evaluation of the photometric
parameters was supported by The Russian Science Foundation (RSCF) grants No.
23-12-00146. IC’s research is supported by the Telescope Data Center at
Smithsonian Astrophysical Observatory. A. L. and S. S. acknowledge support by
the Astronomical Station Vidojevica and funding from the Ministry of Science,
Technological Development and Innovation of the Republic of Serbia, contract
No. 451-03-66/2024-03/200002, and by the EC through project BELISSIMA (call
FP7-REGPOT-2010-5, No. 256772). MD is grateful to Frank Kiwy for valuable
explanations about the unTimely catalog explorer tool.

Observations with the SAO RAS telescopes are supported by the Ministry of
Science and Higher Education of the Russian Federation. The renovation of
telescope equipment is currently provided within the national project ”Science
and universities.” This work was supported by a NASA Keck PI Data Award
(project 2022B-N149), administered by the NASA Exoplanet Science Institute.
Data presented herein were obtained at the W. M. Keck Observatory from
telescope time allocated to the National Aeronautics and Space Administration
through the agency’s scientific partnership with the California Institute of
Technology and the University of California. The Observatory was made possible
by the generous financial support of the W. M. Keck Foundation. The authors
wish to recognize and acknowledge the very significant cultural role and
reverence that the summit of Maunakea has always had within the indigenous
Hawaiian community. We are most fortunate to have the opportunity to conduct
observations from this mountain.

The Legacy Surveys consist of three individual and complementary projects: the
Dark Energy Camera Legacy Survey (DECaLS; Proposal ID 2014B-0404; PIs: David
Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID
2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy Survey
(MzLS; Prop. ID 2016A-0453; PI: Arjun Dey). DECaLS, BASS and MzLS together
include data obtained, respectively, at the Blanco telescope, Cerro Tololo
Inter-American Observatory, NSF’s NOIRLab; the Bok telescope, Steward
Observatory, University of Arizona; and the Mayall telescope, Kitt Peak
National Observatory, NOIRLab. Pipeline processing and analyses of the data
were supported by NOIRLab and the Lawrence Berkeley National Laboratory
(LBNL). The Legacy Surveys project is honored to be permitted to conduct
astronomical research on Iolkam Du’ag (Kitt Peak), a mountain with particular
significance to the Tohono O’odham Nation.

The Hyper Suprime-Cam (HSC) collaboration includes the astronomical
communities of Japan and Taiwan, and Princeton University. The HSC
instrumentation and software were developed by the National Astronomical
Observatory of Japan (NAOJ), the Kavli Institute for the Physics and
Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High
Energy Accelerator Research Organization (KEK), the Academia Sinica Institute
for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University.
Funding was contributed by the FIRST program from Japanese Cabinet Office, the
Ministry of Education, Culture, Sports, Science and Technology (MEXT), the
Japan Society for the Promotion of Science (JSPS), Japan Science and
Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK,
ASIAA, and Princeton University.

This work made use of Astropy333http://www.astropy.org, a community-developed
core Python package and an ecosystem of tools and resources for astronomy
(Astropy Collaboration et al., 2013, 2018, 2022), particularly Photutils
(Bradley et al., 2023), and in addition Python package SciPy (Virtanen et al.,
2020). This paper makes use of software developed for the Large Synoptic
Survey Telescope. We thank the LSST Project for making their code available as
free software at http://dm.lsst.org

## References

  * Aditya et al. (2023) Aditya, K., Banerjee, A., Kamphuis, P., et al. 2023, MNRAS, 526, 29, doi: 10.1093/mnras/stad2599
  * Afanasiev & Moiseev (2011) Afanasiev, V. L., & Moiseev, A. V. 2011, Baltic Astronomy, 20, 363.  https://arxiv.org/abs/1106.2020
  * Aihara et al. (2011) Aihara, H., Allende Prieto, C., An, D., et al. 2011, ApJS, 193, 29, doi: 10.1088/0067-0049/193/2/29
  * Aihara et al. (2019) Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, PASJ, 71, 114, doi: 10.1093/pasj/psz103
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167, doi: 10.3847/1538-4357/ac7c74
  * Bakos et al. (2008) Bakos, J., Trujillo, I., & Pohlen, M. 2008, ApJ, 683, L103, doi: 10.1086/591671
  * Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5, doi: 10.1086/130766
  * Boissier et al. (2016) Boissier, S., Boselli, A., Ferrarese, L., et al. 2016, A&A, 593, A126, doi: 10.1051/0004-6361/201629226
  * Borisov et al. (2023) Borisov, S. B., Chilingarian, I. V., Rubtsov, E. V., et al. 2023, ApJS, 266, 11, doi: 10.3847/1538-4365/acc321
  * Bothun et al. (1987) Bothun, G. D., Impey, C. D., Malin, D. F., & Mould, J. R. 1987, AJ, 94, 23, doi: 10.1086/114443
  * Bradley et al. (2023) Bradley, L., Sipőcz, B., Robitaille, T., et al. 2023, astropy/photutils: 1.8.0, 1.8.0, Zenodo, doi: 10.5281/zenodo.7946442
  * Bresolin & Kennicutt (2015) Bresolin, F., & Kennicutt, R. C. 2015, MNRAS, 454, 3664, doi: 10.1093/mnras/stv2245
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x
  * Cao et al. (2023) Cao, T.-w., Wu, H., Galaz, G., et al. 2023, ApJ, 948, 96, doi: 10.3847/1538-4357/acc864
  * Chilingarian et al. (2007a) Chilingarian, I., Prugniel, P., Sil’Chenko, O., & Koleva, M. 2007a, in IAU Symposium, Vol. 241, IAU Symposium, ed. A. Vazdekis & R. Peletier, 175–176, doi: 10.1017/S1743921307007752
  * Chilingarian et al. (2007b) Chilingarian, I. V., Prugniel, P., Sil’Chenko, O. K., & Afanasiev, V. L. 2007b, MNRAS, 376, 1033, doi: 10.1111/j.1365-2966.2007.11549.x
  * Chilingarian et al. (2017) Chilingarian, I. V., Zolotukhin, I. Y., Katkov, I. Y., et al. 2017, ApJS, 228, 14, doi: 10.3847/1538-4365/228/2/14
  * Chung & Bureau (2004) Chung, A., & Bureau, M. 2004, AJ, 127, 3192, doi: 10.1086/420988
  * Cleland & McGee (2022) Cleland, C., & McGee, S. L. 2022, Monthly Notices of the Royal Astronomical Society, 515, 5905–5913, doi: 10.1093/mnras/stac2188
  * Debattista & Sellwood (1999) Debattista, V. P., & Sellwood, J. A. 1999, ApJ, 513, L107, doi: 10.1086/311913
  * Demianenko et al. (2024) Demianenko, M., Grishin, K., Toptun, V., et al. 2024, in Astronomical Society of the Pacific Conference Series, Vol. 535, Astronomical Society of the Pacific Conference Series, ed. B. V. Hugo, R. Van Rooyen, & O. M. Smirnov, 283, doi: 10.48550/arXiv.2201.03712
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168, doi: 10.3847/1538-3881/ab089d
  * Du et al. (2023) Du, W., Cheng, C., Du, P., Du, L., & Wu, H. 2023, ApJ, 959, 105, doi: 10.3847/1538-4357/ad05bd
  * Duarte Puertas et al. (2022) Duarte Puertas, S., Vilchez, J. M., Iglesias-Páramo, J., et al. 2022, A&A, 666, A186, doi: 10.1051/0004-6361/202141571
  * Duc et al. (2015) Duc, P.-A., Cuillandre, J.-C., Karabal, E., et al. 2015, MNRAS, 446, 120, doi: 10.1093/mnras/stu2019
  * Egorova et al. (2021) Egorova, E. S., Egorov, O. V., Moiseev, A. V., et al. 2021, arXiv e-prints, arXiv:2103.00211.  https://arxiv.org/abs/2103.00211
  * Faber et al. (2003) Faber, S. M., Phillips, A. C., Kibrick, R. I., et al. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4841, Instrument Design and Performance for Optical/Infrared Ground-based Telescopes, ed. M. Iye & A. F. M. Moorwood, 1657–1669, doi: 10.1117/12.460346
  * Fitzpatrick (1999) Fitzpatrick, E. L. 1999, PASP, 111, 63, doi: 10.1086/316293
  * Freeman (1970) Freeman, K. C. 1970, ApJ, 160, 811, doi: 10.1086/150474
  * Galaz et al. (2015) Galaz, G., Milovic, C., Suc, V., et al. 2015, ApJ, 815, L29, doi: 10.1088/2041-8205/815/2/L29
  * Garg & Banerjee (2017) Garg, P., & Banerjee, A. 2017, MNRAS, 472, 166, doi: 10.1093/mnras/stx1918
  * Ghosh & Jog (2014) Ghosh, S., & Jog, C. J. 2014, MNRAS, 439, 929, doi: 10.1093/mnras/stu013
  * Gil de Paz et al. (2005) Gil de Paz, A., Madore, B. F., Boissier, S., et al. 2005, ApJ, 627, L29, doi: 10.1086/432054
  * Gkini et al. (2021) Gkini, A., Plionis, M., Chira, M., & Koulouridis, E. 2021, A&A, 650, A75, doi: 10.1051/0004-6361/202140278
  * Gordon et al. (2020) Gordon, Y. A., Boyce, M. M., O’Dea, C. P., et al. 2020, Research Notes of the American Astronomical Society, 4, 175, doi: 10.3847/2515-5172/abbe23
  * Hagen et al. (2016) Hagen, L. M. Z., Seibert, M., Hagen, A., et al. 2016, ApJ, 826, 210, doi: 10.3847/0004-637X/826/2/210
  * Heckman (1980) Heckman, T. M. 1980, A&A, 87, 152
  * Ibata et al. (2013) Ibata, R. A., Lewis, G. F., Conn, A. R., et al. 2013, Nature, 493, 62, doi: 10.1038/nature11717
  * Inoue et al. (2016) Inoue, S., Dekel, A., Mandelker, N., et al. 2016, MNRAS, 456, 2052, doi: 10.1093/mnras/stv2793
  * Junais et al. (2024) Junais, Weilbacher, P. M., Epinat, B., et al. 2024, A&A, 681, A100, doi: 10.1051/0004-6361/202347669
  * Karachentsev et al. (1993) Karachentsev, I. D., Karachentseva, V. E., & Parnovskij, S. L. 1993, Astronomische Nachrichten, 314, 97, doi: 10.1002/asna.2113140302
  * Karachentsev & Kroupa (2024) Karachentsev, I. D., & Kroupa, P. 2024, MNRAS, 528, 2805, doi: 10.1093/mnras/stae184
  * Kasparova et al. (2020) Kasparova, A. V., Katkov, I. Y., & Chilingarian, I. V. 2020, MNRAS, 493, 5464, doi: 10.1093/mnras/staa611
  * Kasparova et al. (2014) Kasparova, A. V., Saburova, A. S., Katkov, I. Y., Chilingarian, I. V., & Bizyaev, D. V. 2014, MNRAS, 437, 3072, doi: 10.1093/mnras/stt1982
  * Katkov & Chilingarian (2011) Katkov, I. Y., & Chilingarian, I. V. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 442, Astronomical Data Analysis Software and Systems XX, ed. I. N. Evans, A. Accomazzi, D. J. Mink, & A. H. Rots, 143, doi: 10.48550/arXiv.1012.4125
  * Katkov et al. (2019) Katkov, I. Y., Kniazev, A. Y., Kasparova, A. V., & Sil’chenko, O. K. 2019, MNRAS, 483, 2413, doi: 10.1093/mnras/sty3268
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055, doi: 10.1111/j.1365-2966.2003.07154.x
  * Kewley et al. (2001) Kewley, L. J., Dopita, M. A., Sutherland, R. S., Heisler, C. A., & Trevena, J. 2001, ApJ, 556, 121, doi: 10.1086/321545
  * Khoperskov et al. (2010) Khoperskov, A., Bizyaev, D., Tiurina, N., & Butenko, M. 2010, Astronomische Nachrichten, 331, 731, doi: 10.1002/asna.200911402
  * Khoperskov et al. (2003) Khoperskov, A. V., Zasov, A. V., & Tyurina, N. V. 2003, Astronomy Reports, 47, 357, doi: 10.1134/1.1575851
  * Kroupa (2001) Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x
  * Kulier et al. (2020) Kulier, A., Galaz, G., Padilla, N. D., & Trayford, J. W. 2020, MNRAS, 496, 3996, doi: 10.1093/mnras/staa1798
  * Kurucz et al. (1984) Kurucz, R. L., Furenlid, I., Brault, J., & Testerman, L. 1984, Solar flux atlas from 296 to 1300 nm
  * Lelli et al. (2016) Lelli, F., McGaugh, S. S., & Schombert, J. M. 2016, AJ, 152, 157, doi: 10.3847/0004-6256/152/6/157
  * Lelli et al. (2019) Lelli, F., McGaugh, S. S., Schombert, J. M., Desmond, H., & Katz, H. 2019, MNRAS, 484, 3267, doi: 10.1093/mnras/stz205
  * Luridiana et al. (2015) Luridiana, V., Morisset, C., & Shaw, R. A. 2015, A&A, 573, A42, doi: 10.1051/0004-6361/201323152
  * Lyu et al. (2019) Lyu, J., Rieke, G. H., & Smith, P. S. 2019, ApJ, 886, 33, doi: 10.3847/1538-4357/ab481d
  * Mancera Piña et al. (2021) Mancera Piña, P. E., Posti, L., Pezzulli, G., et al. 2021, A&A, 651, L15, doi: 10.1051/0004-6361/202141574
  * Marigo et al. (2013) Marigo, P., Bressan, A., Nanni, A., Girardi, L., & Pumo, M. L. 2013, MNRAS, 434, 488, doi: 10.1093/mnras/stt1034
  * Masci et al. (2023) Masci, F. J., Laher, R. R., Rusholme, B., et al. 2023, A New Forced Photometry Service for the Zwicky Transient Facility.  https://arxiv.org/abs/2305.16279
  * Meisner et al. (2023) Meisner, A. M., Caselden, D., Schlafly, E. F., & Kiwy, F. 2023, The Astronomical Journal, 165, 36, doi: 10.3847/1538-3881/aca2ab
  * Miyazaki et al. (2018) Miyazaki, S., Komiyama, Y., Kawanomoto, S., et al. 2018, PASJ, 70, S1, doi: 10.1093/pasj/psx063
  * Müller et al. (2018) Müller, O., Pawlowski, M. S., Jerjen, H., & Lelli, F. 2018, Science, 359, 534, doi: 10.1126/science.aao1858
  * Müller et al. (2019) Müller, O., Vudragović, A., & Bílek, M. 2019, A&A, 632, L13, doi: 10.1051/0004-6361/201937077
  * Osterbrock & Ferland (2006) Osterbrock, D. E., & Ferland, G. J. 2006, Astrophysics of gaseous nebulae and active galactic nuclei, 2nd edn. (University Science Books)
  * Ostriker & Binney (1989) Ostriker, E. C., & Binney, J. J. 1989, MNRAS, 237, 785, doi: 10.1093/mnras/237.3.785
  * Pawlowski et al. (2024) Pawlowski, M. S., Müller, O., Taibi, S., et al. 2024, arXiv e-prints, arXiv:2405.06016, doi: 10.48550/arXiv.2405.06016
  * Peñarrubia et al. (2006) Peñarrubia, J., McConnachie, A., & Babul, A. 2006, ApJ, 650, L33, doi: 10.1086/508656
  * Pfeffer et al. (2022) Pfeffer, J. L., Bekki, K., Forbes, D. A., Couch, W. J., & Koribalski, B. S. 2022, MNRAS, 509, 261, doi: 10.1093/mnras/stab2934
  * Pickering et al. (1997) Pickering, T. E., Impey, C. D., van Gorkom, J. H., & Bothun, G. D. 1997, AJ, 114, 1858, doi: 10.1086/118611
  * Pilyugin & Grebel (2016) Pilyugin, L. S., & Grebel, E. K. 2016, MNRAS, 457, 3678, doi: 10.1093/mnras/stw238
  * Pilyugin et al. (2014a) Pilyugin, L. S., Grebel, E. K., & Kniazev, A. Y. 2014a, AJ, 147, 131, doi: 10.1088/0004-6256/147/6/131
  * Pilyugin et al. (2014b) Pilyugin, L. S., Grebel, E. K., Zinchenko, I. A., & Kniazev, A. Y. 2014b, AJ, 148, 134, doi: 10.1088/0004-6256/148/6/134
  * Pohlen & Trujillo (2006) Pohlen, M., & Trujillo, I. 2006, A&A, 454, 759, doi: 10.1051/0004-6361:20064883
  * Ponomareva et al. (2018) Ponomareva, A. A., Verheijen, M. A. W., Papastergis, E., Bosma, A., & Peletier, R. F. 2018, MNRAS, 474, 4366, doi: 10.1093/mnras/stx3066
  * Potanin et al. (2020) Potanin, S. A., Belinski, A. A., Dodin, A. V., et al. 2020, Astronomy Letters, 46, 836, doi: 10.1134/S1063773720120038
  * Ramya et al. (2011) Ramya, S., Prabhu, T. P., & Das, M. 2011, MNRAS, 418, 789, doi: 10.1111/j.1365-2966.2011.19530.x
  * Revaz & Pfenniger (2004) Revaz, Y., & Pfenniger, D. 2004, A&A, 425, 67, doi: 10.1051/0004-6361:20041386
  * Reyes et al. (2011) Reyes, R., Mandelbaum, R., Gunn, J. E., Pizagno, J., & Lackner, C. N. 2011, MNRAS, 417, 2347, doi: 10.1111/j.1365-2966.2011.19415.x
  * Rodriguez-Gomez et al. (2017) Rodriguez-Gomez, V., Sales, L. V., Genel, S., et al. 2017, MNRAS, 467, 3083, doi: 10.1093/mnras/stx305
  * Rosales-Ortega et al. (2012) Rosales-Ortega, F. F., Sánchez, S. F., Iglesias-Páramo, J., et al. 2012, ApJ, 756, L31, doi: 10.1088/2041-8205/756/2/L31
  * Roškar et al. (2010) Roškar, R., Debattista, V. P., Brooks, A. M., et al. 2010, MNRAS, 408, 783, doi: 10.1111/j.1365-2966.2010.17178.x
  * Rupke et al. (2010) Rupke, D. S. N., Kewley, L. J., & Barnes, J. E. 2010, ApJ, 710, L156, doi: 10.1088/2041-8205/710/2/L156
  * Saburova (2018) Saburova, A. S. 2018, MNRAS, 473, 3796, doi: 10.1093/mnras/stx2583
  * Saburova et al. (2019) Saburova, A. S., Chilingarian, I. V., Kasparova, A. V., et al. 2019, MNRAS, 489, 4669, doi: 10.1093/mnras/stz2434
  * Saburova et al. (2021) —. 2021, MNRAS, 503, 830, doi: 10.1093/mnras/stab374
  * Saburova et al. (2018) Saburova, A. S., Chilingarian, I. V., Katkov, I. Y., et al. 2018, MNRAS, 481, 3534, doi: 10.1093/mnras/sty2519
  * Saburova et al. (2023) Saburova, A. S., Chilingarian, I. V., Kulier, A., et al. 2023, MNRAS, 520, L85, doi: 10.1093/mnrasl/slad005
  * Saburova et al. (2017) Saburova, A. S., Katkov, I. Y., Khoperskov, S. A., Zasov, A. V., & Uklein, R. I. 2017, MNRAS, 470, 20, doi: 10.1093/mnras/stx1200
  * Savchenko et al. (2023) Savchenko, S. S., Poliakov, D. M., Mosenkov, A. V., et al. 2023, MNRAS, 524, 4729, doi: 10.1093/mnras/stad2189
  * Sil’chenko et al. (2018) Sil’chenko, O. K., Kniazev, A. Y., & Chudakova, E. M. 2018, AJ, 156, 118, doi: 10.3847/1538-3881/aad37b
  * Sokolovsky et al. (2017) Sokolovsky, K. V., Gavras, P., Karampelas, A., et al. 2017, MNRAS, 464, 274, doi: 10.1093/mnras/stw2262
  * Spitzer (1942) Spitzer, Lyman, J. 1942, ApJ, 95, 329, doi: 10.1086/144407
  * Subramanian et al. (2016) Subramanian, S., Ramya, S., Das, M., et al. 2016, MNRAS, 455, 3148, doi: 10.1093/mnras/stv2500
  * Tang et al. (2020) Tang, Y., Chen, Q., Zhang, H.-X., et al. 2020, ApJ, 897, 79, doi: 10.3847/1538-4357/ab98fd
  * Thilker et al. (2005) Thilker, D. A., Bianchi, L., Boissier, S., et al. 2005, ApJ, 619, L79, doi: 10.1086/425251
  * Toptun et al. (2023) Toptun, V. A., Chilingarian, I. V., Grishin, K. A., & Katkov, I. Y. 2023, PASP, 135, 084102, doi: 10.1088/1538-3873/aceca0
  * Tully & Fisher (1977) Tully, R. B., & Fisher, J. R. 1977, A&A, 500, 105
  * van der Kruit & Searle (1981) van der Kruit, P. C., & Searle, L. 1981, A&A, 95, 105
  * Veilleux & Osterbrock (1987) Veilleux, S., & Osterbrock, D. E. 1987, ApJS, 63, 295, doi: 10.1086/191166
  * Verro et al. (2022) Verro, K., Trager, S. C., Peletier, R. F., et al. 2022, A&A, 661, A50, doi: 10.1051/0004-6361/202142387
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
  * Vudragović et al. (2021) Vudragović, A., Bilek, M., Muller, O., Samurović, S., & Jovanović, M. 2021, in XIX Serbian Astronomical Conference, Vol. 100, 169–174, doi: 10.48550/arXiv.2103.11721
  * Ward et al. (2022) Ward, C., Gezari, S., Nugent, P., et al. 2022, ApJ, 936, 104, doi: 10.3847/1538-4357/ac8666
  * Yoachim et al. (2012) Yoachim, P., Roškar, R., & Debattista, V. P. 2012, ApJ, 752, 97, doi: 10.1088/0004-637X/752/2/97
  * Zasov et al. (2015) Zasov, A., Saburova, A., Katkov, I., Egorov, O., & Afanasiev, V. 2015, MNRAS, 449, 1605, doi: 10.1093/mnras/stv454
  * Zasov & Khoperskov (2003) Zasov, A. V., & Khoperskov, A. V. 2003, Astronomy Letters, 29, 437, doi: 10.1134/1.1589861
  * Zasov et al. (2011) Zasov, A. V., Khoperskov, A. V., & Saburova, A. S. 2011, Astronomy Letters, 37, 374, doi: 10.1134/S1063773711050069
  * Zasov et al. (2017) Zasov, A. V., Saburova, A. S., Khoperskov, A. V., & Khoperskov, S. A. 2017, Physics Uspekhi, 60, 3, doi: 10.3367/UFNe.2016.03.037751
  * Zhu et al. (2023) Zhu, Q., Pérez-Montaño, L. E., Rodriguez-Gomez, V., et al. 2023, MNRAS, 523, 3991, doi: 10.1093/mnras/stad1655
  * Zhu et al. (2018) Zhu, Q., Xu, D., Gaspari, M., et al. 2018, MNRAS, 480, L18, doi: 10.1093/mnrasl/sly111
  * Zou et al. (2017) Zou, H., Zhou, X., Fan, X., et al. 2017, PASP, 129, 064101, doi: 10.1088/1538-3873/aa65ba

##  Appendix A LSB disk spectra

Figure 12: The results of nbursts full spectrum fitting using XSL SSP models
for the spectra of LSB disks (+HSB disk for LEDA 1044131) coadded in the large
spatial bins shown by red and yellow regions in Fig. 1. Black lines show the
observed spectra of the LSB disks (flux density); red, cyan, and dark grey
lines show the total best-fitting models, pure emission-line components, and
fitting residuals respectively; the shaded grey areas denote the masked
regions excluded from fitting.