# A Closer Look at the Extended Edge-on Low-surface Brightness Galaxies

Anna S. Saburova¹, Damir Gasymov¹, Evgenii V. Rubtsov¹, Igor V. Chilingarian¹,², Sviatoslav Borisov³, Ivan Gerasimov¹, Fedor Kolganov⁴, Anastasia V. Kasparova¹, Roman I. Uklein⁵, Michal Biflek⁶,⁷,⁸, Kirill A. Grishin¹,⁹, Anatoly Zasov¹,¹⁰, Mariia Demianenko¹¹, Ivan Yu. Katkov¹,¹²,¹³, Ana Lalović¹⁴, and Srdjan Samurović¹⁴

¹ Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij pr., 13, Moscow, 119234, Russia

² Center for Astrophysics—Harvard and Smithsonian, 60 Garden Street MS09, Cambridge, MA 02138, USA

³ Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland

⁴ Faculty of Physics and Earth System Sciences, Leipzig University, Linnestraße 5, 04103 Leipzig, Germany

⁵ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhniy Arkhyz, Karachai-Cherkessian Republic 357147, Russia

⁶ Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France

⁷ LERMA, Observatoire de Paris, CNRS, PSL Univ., Sorbonne Univ., 75014 Paris, France

⁸ FZU—Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, Prague 182 21, Czech Republic

⁹ Université Paris Cité, CNRS(/IN2P3), Astroparticule et Cosmologie, F-75013 Paris, France

¹⁰ Faculty of Physics, Moscow M.V. Lomonosov State University, Leninskie gory 1, Moscow 119991, Russia

¹¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

¹² New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, UAE

¹³ Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates
¹⁴ Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia

Received 2024 June 14; revised 2024 July 15; accepted 2024 July 22; published 2024 September 30

## Abstract

To understand the origin of extended disks of low-surface brightness (LSB) galaxies, we studied in detail four 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 m telescope and the 10 m Keck II telescope and estimated stellar population properties in the high-surface brightness and LSB 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.

*Unified Astronomy Thesaurus concepts: Galaxy evolution (594); Galaxy rotation (618); Galaxy formation (595); Galaxy physics (612)*

## 1. Introduction

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 (HSB) systems. Freeman’s seminal paper in Freeman (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 arcsec⁻² 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 low-surface brightness galaxies (LSBGs).

Among LSBGs, 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 ($M_b \approx 10^{11} M_\odot$) with substantial angular momentum. Their dynamical masses reach up to $10^{12} M_\odot$ 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 ΛCDM 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 1 order of magnitude short of the typical mass of a gLSB disk. Thus, the question of the formation of

<figure><img src="image_1.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
gLSBGs 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 multicolor 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 LSBGs 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 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 Galaxy Evolution Explorer 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” LSBGs.

The distinction between gLSBGs and intermediate-size
LSBGs is rather arbitrary. We adopt a threshold of four disk
radial scale lengths (4 h) 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 μ<sub>B</sub>(0) + 5log (h) > 27.0 where
μ<sub>B</sub>(0) is the disk B-band central surface brightness, and Zhu
et al. (2023) relied on the H I 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 dis-
tribution 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 LSBGs 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 an HSB 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.

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 LSBGs.

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,<fnref n="15" /> redshifts obtained in
the current paper and the corresponding distances, and the g-
band absolute magnitudes calculated from DESI Legacy Sur-
vey data (a combination of Dark Energy Camera Legacy Sur-
vey, hereafter DECaLS, DR9; and Beijing–Arizona Sky
Survey, hereafter 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 arcseconds and kiloparsecs. This isophote
level is chosen the same as in Saburova et al. (2023) to facil-
itate the comparison. The photometric systems of DECaLS,
BASS, SDSS, and HSC-SSP are different at a few percent 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 Section 2, we give the details of the spectroscopic and photometric observations and the data reduction and analysis. In particular, in Section 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. Section 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 Section 4, we explore the potential formation scenarios for these galaxies. Additionally, we examine their positions on the Tully–Fisher (TF; Tully & Fisher 1977) 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 multimode focal reducer SCORPIO-2 (Afa-
nasiev & Moiseev 2011) mounted in the primary focus of the
6 m telescope Big Telescope Alt-azimuth of SAO RAS (pro-
posals 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 ~5.2 Å spectral resolution (FWHM) and
the 0.′′36 pixel⁻¹ scale. The slit width was 1″ for all cases except
LEDA 1044131, for which we used a narrower 0.′′69 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 long slit and
the 900ZD grating. The spectrum covers the 5000–8400 Å
wavelength range with the spectral resolving power R ~ 3600
(1.5–2.4 Å FWHM) and a pixel scale of 0.′′12 pix⁻¹. The data
reduction was performed using a dedicated IDL data reduction
pipeline for DEIMOS built upon a generic long-slit/multislit data

<footnote n="15">¹⁵ https://ned.ipac.caltech.edu/</footnote>
<table><caption>**Table 1**
Observed Properties of Galaxies Sample</caption><thead><tr><th>Name (ID)</th><th>UGC 8197 (i)</th><th>LEDA 1044131 (ii)</th><th>FGC 150 (iii)</th><th>2MASX J02300754-0240451 (iv)</th></tr></thead><tbody><tr><td>R.A. (J2000)</td><td>13:05:58.07</td><td>02:23:07.58</td><td>01:20:00.70</td><td>02:30:07.54</td></tr><tr><td>Decl. (J2000)</td><td>58:48:39.3</td><td>-05:29:03.6</td><td>13:03:12.0</td><td>-02:40:45.1</td></tr><tr><td>z (Helio)</td><td>0.028203</td><td>0.069335</td><td>0.043041</td><td>0.058675</td></tr><tr><td>Distance (Mpc)</td><td>125</td><td>306</td><td>190</td><td>259</td></tr><tr><td>M<sub>g</sub></td><td>-19.3</td><td>-20.0</td><td>-19.1<sup>†</sup></td><td>-18.9</td></tr><tr><td>R<sub>27.7,z<sub>0</sub>/h</sub> (arcsec)</td><td>32.5</td><td>18.2</td><td>25.5</td><td>21.5</td></tr><tr><td>R<sub>27.7,z<sub>0</sub>/h</sub> (kpc)</td><td>18.5</td><td>24.4</td><td>21.9</td><td>24.8</td></tr><tr><td>V<sub>rot</sub>, (km s<sup>-1</sup>)</td><td>149</td><td>195</td><td>211</td><td>178</td></tr><tr><td>M<sub>dyn</sub>, 10<sup>11</sup>M<sub>☉</sub></td><td>0.94 ± 0.03</td><td>1.92 ± 0.04</td><td>5.49 ± 0.40</td><td>2.08 ± 0.07</td></tr><tr><td>M<sub>*</sub>, 10<sup>11</sup>M<sub>☉</sub></td><td>0.46 ± 0.11</td><td>0.87 ± 0.2</td><td>0.04 ± 0.01</td><td>0.12 ± 0.03</td></tr><tr><td>M<sub>sph</sub>, 10<sup>11</sup>M<sub>☉</sub></td><td>0.33 ± 0.01</td><td>...</td><td>4.05 ± 0.31</td><td>1.36 ± 0.05</td></tr><tr><td>12 + log(O/H)</td><td>8.621 ± 0.016</td><td>8.626 ± 0.074</td><td>8.444 ± 0.054</td><td>8.507 ± 0.077</td></tr><tr><td>O/H grad. (dex kpc<sup>-1</sup>)</td><td>-0.020 ± 0.003</td><td>-0.011 ± 0.008</td><td>-0.001 ± 0.004</td><td>-0.011 ± 0.006</td></tr><tr><td>Data source</td><td>DECAM-z</td><td>HSC-i (unw.)</td><td>Serb.-L(g)</td><td>HSC-i</td></tr><tr><td>R<sub>knee</sub> (arcsec)</td><td>30</td><td>16</td><td>22</td><td>18</td></tr><tr><td>h (arcsec)</td><td>8.0 ± 0.2</td><td>4.1 ± 0.1/8.6 ± 0.6<sup>†</sup></td><td>15.4 ± 1.1</td><td>6.1 ± 0.2</td></tr><tr><td>z<sub>0</sub> (arcsec)</td><td>1.76 ± 0.03</td><td>...</td><td>1.51 ± 0.02</td><td>0.78 ± 0.01</td></tr><tr><td>h (kpc)</td><td>4.5 ± 0.1</td><td>5.5 ± 0.1/11.5 ± 0.8<sup>†</sup></td><td>13.2 ± 1.0</td><td>7.0 ± 0.2</td></tr><tr><td>z<sub>0</sub> (kpc)</td><td>1.00 ± 0.02</td><td>...</td><td>1.30 ± 0.02</td><td>0.89 ± 0.01</td></tr><tr><td>μ<sub>0</sub></td><td>20.3 ± 0.2</td><td>20.3 ± 0.3</td><td>23.3 ± 0.0</td><td>20.8 ± 0.0</td></tr><tr><td>μ<sub>0,z<sub>0</sub>/h</sub></td><td>22.0 ± 0.1</td><td>...</td><td>25.8 ± 0.2</td><td>23.0 ± 0.1</td></tr><tr><td>(M/L)<sub>bulge</sub></td><td>2.73</td><td>2.61</td><td>0.75</td><td>1.33</td></tr><tr><td>(M/L)<sub>disk</sub></td><td>1.30</td><td>0.51</td><td>0.42</td><td>0.39</td></tr><tr><td>χ<sup>2</sup><sub>W1</sub></td><td>64.72 ± 16.09</td><td>15.14 ± 5.29</td><td>4.09 ± 1.19</td><td>474.11 ± 38.08</td></tr><tr><td>p-value<sub>W1</sub></td><td>0.0</td><td>0.0</td><td>5.10<sup>-9</sup></td><td>0.0</td></tr><tr><td>χ<sup>2</sup><sub>W2</sub></td><td>8.47 ± 2.37</td><td>2.05 ± 0.62</td><td>1.34 ± 0.43</td><td>30.5 ± 5.25</td></tr><tr><td>p-value<sub>W2</sub></td><td>0.0</td><td>0.002</td><td>0.088</td><td>0.0</td></tr></tbody></table>

**Note.** Index $z_0/h$ means correction of magnitude from edge-on orientation to face on. The first part of the table shows the general properties of the sample. $M_g$ is absolute magnitude in DECaLS g band († marks magnitude in SDSS g band). The second part shows dynamical properties of galaxies $V_{rot}$ was obtained from SCORPIO-2 spectra and used in Section 2.1.1, dynamical mass $M_{dyn}$ was calculated within 4 h distance, $M_{sph}$ is an estimation of spheroid mass based on the disk relative thickness according to Khoperskov et al. (2010), and stellar mass estimate $M_*$ was described in Section 4.1. The third part is described in Section 2.1.2 and in Figure 3. The fourth part is devoted to the surface photometry of the galaxies; all parameters are described in Section 2.2.2. Mass-to-light ratio ($M/L$) is given in $(M_*/L_*)$ terms for parameters of stellar populations presented in the Figure 1 for disk and bulge regions. Last part shows $\chi^2$ and p-value for W1 and W2 bands (see Section 3.5).

reduction toolkit originally developed for the Transient 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 (LSF) 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 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).

<table><caption>**Table 2**
Observing Log</caption><thead><tr><th>Galaxy ID</th><th>Slit PA (deg.)</th><th>Date</th><th>Exp. Time (s)</th><th>Seeing (arcsec)</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th></tr></thead><tbody><tr><td>(i)</td><td>67</td><td>08.06.2021</td><td>10,801</td><td>2.5</td></tr><tr><td>(ii)</td><td>105</td><td>30.11.2022</td><td>3600</td><td>2.1</td></tr><tr><td>(ii)*</td><td>91.2</td><td>25.10.2022</td><td>4800</td><td>0.7</td></tr><tr><td>(iii)</td><td>159</td><td>17.08.2020</td><td>8400</td><td>3.0</td></tr><tr><td>(iv)</td><td>336</td><td>07.11.2021</td><td>9900</td><td>1.5</td></tr></tbody></table>

**Note.** All cases except the one marked by * (DEIMOS) correspond to SCORPIO-2. Position angle of the slit is represented by PA.

### 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, 2007b) with X-Shooter Spectral Library (XSL) simple stellar population (SSP) models (Verro et al. 2022), SSP models based on the empirical XSL (3500–24800 Å,
$R \sim 10,000$) 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 [N II] and [O III] 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 (SNRs). 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 1D adaptive binning to the spectrum along the slit within a narrow wavelength range (accounting for the spread due to the galaxy's rotation) near $H\alpha$. 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

$$v(R) = 2v_{\text{rot}} \tanh((R - R_c)/h) + v_{\text{sys}}, \quad (1)$$

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

In the second step, adaptive binning was again applied at the continuum level near $H\beta$. This enabled us to get optimal 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 (Figure 1 bottom panels).

In the third step, adaptive binning was once again applied in the close vicinity of $H\alpha$ 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 (Figure 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 the Appendix). In Figure 1, we also show the color-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 Figure 2, we present Baldwin, Phillips & Terlevich (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.

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 $H\alpha/H\beta$ 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 Figure 3 for each galaxy. We present metallicity gradients in Table 1 (the third block) in the units of dex per kiloparsec. Below, we compare these measurements with disk scale lengths in Section 4.1.

## 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 $13'3 \times 13'3$, 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 s each, which corresponds to the total integration time of 5.83 hr. To avoid large-scale background variations in the resulting coadd, the larger dithering strategy is necessary (e.g., Duc et al. 2015). Following it, we used the random offsets of up to $3'6$, centered on the galaxy.

The data reduction pipeline will be described in detail in M. Bílek et al. (2024, in preparation). 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. A mask is created for each image from the objects detected by the sep source extractor.

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

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

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

5. All background-subtracted images are coadded.

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

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. This is the same as in Step 2 from the algorithm of the first iteration, but now, a third-order polynomial is used.
<figure><img src="image_2.png" /><figcaption>**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 gray area is defined by photometric analysis (Figure 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.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Resolved BPT diagrams along slits. Symbols are color-coded corresponding to their galactocentric distance. The blue dashed line in the BPT-N II 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-N II diagram and categorize star-forming, Seyfert/LINER regions in the BPT-O I and BPT-S II diagrams. Density plots of emission line measurements from the RCSED database (http://rcsed.sai.msu.ru, Chilingarian et al. 2017) are shown in gray.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**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.</figcaption></figure>

3. When making the final coadd frame, image weights deduced from the images themselves are applied.

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

### 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° 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 $Δz \sim \pm 2''$, and perpendicular to this cut (parallel to the minor axis) within the range between $R_{\text{bulge}}$ and $R_{\text{knee}}$. All radial profiles exhibit a complex “knee” structure characterized by two distinct exponential segments (see Figure 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% of late-type galaxies. These profiles are more common in

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Deep images of the galaxies, a “white light” L-band image for FGC 150 obtained with Milanković telescope, and coadded $g + r$ images from HSC SSP for LEDA 1044131 and 2MASX J02300754-0240451, and from BASS for UGC 8197.</figcaption></figure>

disk-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 color 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 $R_{\text{bulge}}$ to $R_{\text{knee}}$ was used, as this segment is dominated by the LSB disk.<fnref n="16" /> The photometric profiles were described by the following function

$$I_R(R, z) \propto \frac{R}{h(z)} K_1\left(\frac{R}{h(z)}\right), \qquad (2)$$

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 (Equations (3) and (2)) with a Gaussian point-spread function. The effect of seeing is minimal for the radial decomposition because the central zone is masked, but it is

<footnote n="16">¹⁶ LEDA 1044131 shows more complex behavior of the surface brightness profile, so for this galaxy, we also obtained the scale length for the outermost region between $R_{\text{knee}}$ and $R = 45''$.</footnote>
<figure><img src="image_6.png" /><figcaption>Figure 5. The radial and vertical (on the right side) photometric profiles of each galaxy (see Figure 4). The radial profiles were taken at different z-distances relative to the main planes of the galaxies (from −2" to 2" with a 0.5" step). The vertical profiles were taken at R ~ −15" − 16" 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 (Equation (2) for radial profiles, or Equation (3) for vertical) with parameters from Table 1. Gray shaded regions are excluded from analysis; the blue dashed lines indicate ±R<sub>knee</sub>. All disks were fitted between the shaded region (R<sub>bulge</sub>) and R<sub>knee</sub>. For LEDA 1044131, we also obtained the radial scale of the outer disk by fitting the region between R<sub>knee</sub> and R = 45". Green dashed lines are 27.7 isophotes in (SDSS-g) band, which were recalculated in images bands (from Table 1) and deprojected from edge-on orientation to face on. R<sub>27.7,z<sub>0</sub>/h</sub> are obtained from intersection between central profiles and 27.7 isophotes.</figcaption></figure>

significant for determining the accurate value of the vertical scale z₀.

Figure 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 Table 1. The galaxy FGC 150 exhibits a symmetric decrease in *h(z)*. Both the image and the Balmer decrement Hα/Hβ 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 Figure 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 multicomponent model (Spitzer 1942):

$$I_z(R, z) \propto \sum_i \mu_i(R) \mathrm{sech}^2 \left( \frac{z}{z_{0i}(R)} \right), \quad (3)$$

where $\mu_i$ and $z_{0i}$ denote the midplane 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<sub>bulge</sub> to R<sub>knee</sub>, no trends in z₀(R) are observed. Therefore, the mean value of z₀ is provided 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°. Deviation from the edge-on orientation leads to the over-estimation of disk thickness (see Kasparova et al. 2020). To numerically evaluate this effect, we analyzed model images of

<figure><img src="image_7.png" /><figcaption>Figure 6. The scale lengths *h* and heights z₀ 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.</figcaption></figure>

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

$$I(R, z) = I_0 e^{-R/h} \mathrm{sech}^2 \left( \frac{z}{z_0} \right), \quad (4)$$

where $I_0$ is the central luminosity density, *h* is the disk scale length, and z₀ 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 viewpoints. For each image, we fitted the vertical profile with the sech² law to estimate how the thickness estimate is biased.

Figure 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
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Ratio of the best-fit scale height to its real value (when $i = 90^\circ$) as a function of inclination for four different $h/z_0$ ratios.</figcaption></figure>

axes ratio. For extremely thin galaxies with an axial ratio of 10, even a slight deviation of 5° ($i = 85^\circ$) 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 sech²-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.

Three of our galaxies (UGC 8197, LEDA 1044131, and 2MASX J02300754-0240451) have a prominent dust lane, which usually helps to visually analyze 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 (Figure 7) but with a smaller vertical scale $z_d$. We then visually determined the midplane region to be masked and fitted the vertical profile with the sech² 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 $\tau_{eo} = 0.5$ and $\tau_{eo} = 5$, where $\tau_{eo}$ is the total optical depth through the center of the edge-on disk. Figure 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 midplane helps to minimize this effect as well. Also, Figure 8 shows how the determined scale length depends on the height above/below the midplane where the radial profile is built. In addition, our models allowed us to estimate the inclinations for these three galaxies as $i \approx 88^\circ.5$ (UGC 8197), $i \approx 85^\circ$ (LEDA 1044131), and $i \approx 89^\circ.5$ (2MASX J02300754-0240451).

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.

<figure><img src="image_9.png" /><figcaption>**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 midplane 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. Gray dashed lines correspond to $z_d$ of the models. The total semiheight of each model is 60 pixels.</figcaption></figure>

# 3. Properties of Individual Galaxies

## 3.1. LEDA 1044131

LEDA 1044131 is characterized 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 infalling 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 Figure 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 subsolar 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 catalog 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 Figure 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 an active galactic nucleus (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 N of UGC 8197 is a background galaxy ($\Delta v \sim 30,000$ 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" (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 (Figure 2) shows that most of the regions of the galaxy occupy the photoionization domain below the “maximum starburst line,” which makes possible the ionized 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 characterized by a young metal-poor stellar population and a slightly subsolar 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 neighbor massive galaxies are observed within 500 kpc. Both ionized 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 ionized 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 ionized gas metallicity changes from nearly solar to slightly subsolar 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 (Figure 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), and 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 (Cleland & McGee 2022; Ward et al. 2022) use light curves derived from mid-infrared (MIR) unWISE (Wide-field Infrared Survey Explorer, hereafter WISE; WISE + NEOWISE) images (Meisner et al. 2023), as well as optical Zwicky Transient Facility (ZTF) 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" 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 postprocessing algorithm outlined in Demianenko et al. (2024) and standard stars correction (M. Demianenko et al. 2024, in preparation).

Because these time-domain surveys were not designed to check the variability of faint AGN on short timescales 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 $x \sim N(\mu, \sigma^2)$, 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 1. 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:

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

The Table 1 lists reduced $\chi^2$ and p-value for W1 (3.4 µm) and W2 (4.6 µm) photometric bands respectively. We found strong variability in W1 passband in all sources, and there is W2 variability in UGC 8197 and 2MASX J02300754-0240451. We did not find optical variability as expected. This is consistent with AGN behavior in MIR (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 3 GHz in the Quick Look catalog of the Very Large Array Sky Survey (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 nondetection). 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 LSBGs 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 briefly discuss them below.

**Scenario a.** 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?

1. There are flat or shallow radial gradients of gas metallicity and stellar age/metallicity.

2. 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.

3. 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?

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

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

3. The 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?

1. There is a large DM halo radial scale and the low central density as reconstructed from the rotation curve modeling.

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

3. There is 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 onto a preexisting elliptical or spiral HSB galaxy formed in a “standard way” by accretion and mergers Saburova et al. (2019). What is expected in the scenario?

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

2. Kinematically decoupling such as counterrotation should be common (~50% of cases).

3. Inward noncircular motions should be seen in the gLSB disk.

4. 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 us 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 favor
<figure><img src="image_10.png" /><figcaption>**Figure 9.** The relation of metallicity radial gradient and the disk scale length for different samples. By gray 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 Equation (1) adopted from Bresolin & Kennicutt (2015).</figcaption></figure>

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 Figure 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 Equation (1) in Bresolin & Kennicutt (2015). The position of the late-type LSBGs from Bresolin & Kennicutt (2015) is shown by dark blue circles, while the HSB sample (Pilyugin et al. 2014a, 2014b) is overlaid as gray squares. The galaxies of our sample are shown by red stars. We additionally plotted values for two 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 Figure 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 toward the top area of the diagram. We note that observations of oxygen abundance radial profile flattening are more difficult for galaxies with huge disks.

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 subsolar in the outer regions of the considered galaxies, which does not get in line with that scenario.

In Figure 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

<figure><img src="image_11.png" /><figcaption>**Figure 10.** Mass-metallicity relation. The LSB sample analyzed 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 from Pilyugin & Grebel (2016; superimposed background 2D source density distribution and its second degree polynomial mean approximation shown by the orange line).</figcaption></figure>

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) and Cao et al. (2023). As one can see from Figure 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 LSBGs that demonstrate inefficient oxygen abundance enhancement (Cao et al. 2023), which can indicate the different evolution history of these types of LSBGs.

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:

$$ (\sigma_r)_{\text{crit}} = Q_{T,\text{crit}} \cdot 3.36G\Sigma_d / \kappa, \qquad (6) $$

where $\kappa$ is the epicyclic frequency, $\Sigma_d$ is the surface density of the disk, and $Q_{T,\text{crit}}$ is the Toomre's stability parameter, which is equal to unity for small radial perturbations of a thin disk.

In more realistic cases, $Q_{T,\text{crit}}$ for a marginally stable disk may differ from unity due to nonradial 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 LSBGs 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 superthin 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 ($Q_T \gg 1$) (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 H I to the rotation curves of gLSBGs can be comparable to that of their stellar disks (see e.g. Pickering et al. 1997).

We estimated the disk surface density from the photometric data presented in Section 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 Figure 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$^{-1}$ 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 disk), 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 scale height 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 a spherical halo. This is consistent with very close values of the measured stellar and gas rotation velocities (see Figure 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 $V_{rot}$, 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: $V_{LOS} < V_{rot} < V_{LOS} + 60$ km s$^{-1}$, and radial velocity dispersions, $50 < \sigma_r < 170$ km s$^{-1}$, where $V_{LOS}$ is the measured line-of-sight rotational velocity for each galaxy, taken at the distance of four 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 $\sigma_{LOS}$ 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 DM halos in considered galaxies. The edge-on position despite having its advantage has also a shortcoming
<figure><img src="image_12.png" /><figcaption>**Figure 11.** The Tully–Fisher relation connecting the stellar mass and rotation velocity. Colored symbols correspond to LSB systems. Stars show the position of edge-on galaxies considered in the current paper, and other colored symbols demonstrate gLSBGs from Saburova et al. (2021). The line gives the relation found by Reyes et al. (2011). Gray open circles correspond to the systems from SPARC database (Lelli et al. 2016).</figcaption></figure>

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 DM halo; however, it is still possible to calculate the mass fraction of the dark halo. According to the photometric mass estimates, the DM halo dominates by mass in four considered galaxies (see Table 1).

Another method for calculating the mass fraction of the DM 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 DM 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 TF 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 Figure 11. Pink stars denote the positions of our four galaxies, and filled symbols correspond to the seven gLSBGs from Saburova et al. (2021). Open circles correspond to the systems from the Spitzer photometry and accurate rotation curves

(SPARC) database (Lelli et al. 2016), and the line gives the relation found by Reyes et al. (2011). Figure 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 indicate either the higher DM 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.

## 5. Conclusions

The galaxies studied in this paper represent gLSBGs and an intermediate “chain” between gLSBGs and moderately sized 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 Figure 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% 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 contain 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 LSBGs with extended disks. Let us 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, although 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 three to four 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 DM 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 DM halo characteristics. However, the mergers look essential in the formation scenario of LSB disks.

To advance the study of gLSBGs, we need H I 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 DM 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.

## Acknowledgments

We thank the anonymous referee for valuable comments that helped to improve the paper. A.Z.'s, I.G.'s, D.G.'s, A.K.'s, and E.R.'s research on the analysis and fitting of the long-slit spectra, ionized 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. I.C.'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). M.D. 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 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 Astropy,<fnref n="17" /> 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.

## Appendix

### LSB Disk Spectra

In Figure A1 we demonstrate the results of NBURSTS full spectrum fitting of the spectra of the disks coadded in the large spatial bins.

<footnote n="17">17 http://www.astropy.org</footnote>
<figure><img src="image_13.png" /></figure>

**Figure A1.** 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 Figure 1. Black lines show the observed spectra of the LSB disks (flux density); red, cyan, and dark gray lines show the total best-fitting models, pure emission line components, and fitting residuals respectively; the shaded gray areas denote the masked regions excluded from fitting.

## ORCID iDs

Anna S. Saburova https://orcid.org/0000-0002-4342-9312

Damir Gasymov https://orcid.org/0000-0002-1750-2096

Evgenii V. Rubtsov https://orcid.org/0000-0001-8427-0240

Igor V. Chilingarian https://orcid.org/0000-0002-7924-3253

Sviatoslav Borisov https://orcid.org/0000-0002-2516-9000

Ivan Gerasimov https://orcid.org/0000-0001-7113-8152

Fedor Kolganov https://orcid.org/0000-0002-9609-7980

Anastasia V. Kasparova https://orcid.org/0000-0002-1091-5146

Roman I. Uklein https://orcid.org/0000-0002-1098-6649

Michal Biflek https://orcid.org/0000-0003-3104-3372

Kirill A. Grishin https://orcid.org/0000-0003-3255-7340

Anatoly Zasov https://orcid.org/0000-0001-9914-4466

Mariia Demianenko https://orcid.org/0000-0002-8297-6386

Ivan Yu. Katkov https://orcid.org/0000-0002-6425-6879

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