The emergence of galactic thin and thick discs across cosmic history

MNRAS 540, 3493–3522 (2025) https://doi.org/10.1093/mnras/staf604
Advance Access publication 2025 June 26
The emergence of galactic thin and thick discs across cosmic history
Takafumi Tsukui ,1,2‹
Emily Wisnioski ,1,2
Joss Bland-Hawthorn 2,3
and Ken Freeman 1,2
1Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston Creek, ACT 2611, Australia
2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), ACT 2611, Australia
3Sydney Institute for Astronomy, School of Physics, A28, The University of Sydney, NSW 2006, Australia
Accepted 2025 April 7. Received 2025 April 6; in original form 2024 September 24
ABSTRACT
Present-day disc galaxies often exhibit distinct thin and thick discs. The formation mechanisms of the two discs and the timing
of their onset remain open questions. To address these questions, we select edge-on galaxies from flagship JWST programmes
and investigate their disc structures in rest-frame, near-infrared bands. For the first time, we identify thick and thin discs at
cosmological distances, dating back over 10 Gyr, and investigate their decomposed structural properties. We classify galaxies
into those that require two (i.e. thin and thick) discs and those well fitted by a single disc. Disc radial sizes and vertical
heights correlate strongly with the total galaxy mass and/or disc mass, independent of cosmic time. The structure of the thick
disc resembles discs found in single-disc galaxies, suggesting that galaxies form a thick disc first, followed by the subsequent
formation of an embedded thin disc. The transition from single to double discs occurred around 8 Gyr ago in high-mass galaxies
(109.75
–1011
M), earlier than the transition which occurred 4 Gyr ago in low-mass galaxies (109.0
− 109.75
M), indicating
sequential formation proceeds in a ‘downsizing’ manner. Toomre Q-regulated disc formation explains the delayed thin disc
formation in low-mass galaxies, leading to the observed anticorrelation between the thick-to-thin disc mass ratio and the total
galaxy mass. Despite the dominant sequential formation, observations suggest that thick discs may continue to build up mass
alongside their thin-disc counterparts.
Key words: galaxies: evolution – galaxies: high-redshift – galaxies: kinematics and dynamics – galaxies: structure.
1 INTRODUCTION
In the present universe, disc galaxies, including our Milky Way,
commonly exhibit bimodal disc structures, i.e. geometrically thin
and thick discs (Burstein 1979; Yoshii 1982; Gilmore Reid 1983;
Dalcanton Bernstein 2002; Yoachim Dalcanton 2008; Comerón
et al. 2011, 2014). These disc systems have vertical density profiles
that are better described by two exponential (or sech2
) functions
rather than one. The stars in each disc are usually separable in
some combination of stellar age, metal abundance properties, radial
extent, and/or stellar kinematics (Hayden et al. 2015). Thick discs
predominantly consist of old, metal-poor stars with enhanced [α/Fe]
abundance ratios, suggesting a rapid formation phase at early times.
In contrast, thin discs mainly contain young, metal-rich stars with
lower [α/Fe] ratios, indicating later formation through prolonged
star formation and effective metal accumulation in the interstellar
medium (ISM). Furthermore, in line with the geometrical structure,
the thick disc is kinematically hotter and exhibits lower mean rotation
than the thin disc due to asymmetric drift (Lee et al. 2011).
Several mechanisms have been proposed to explain the disc
dichotomy:
(i) The ‘born hot’ scenario (e.g. Burkert, Truran Hensler 1992;
Brook et al. 2004; Bournaud, Elmegreen Martig 2009; Bird et al.
2013; Leaman et al. 2017; Grand et al. 2020; Bird et al. 2021; Yu
E-mail: tsukuitk23@gmail.com
et al. 2021, 2023) proposes that the thick disc forms first via intense
star formation in a turbulent gas disc, followed by thin disc formation
in a quiet gas disc. Observations show higher ionized gas turbulence
in higher redshift galaxies (Förster Schreiber et al. 2009; Genzel
et al. 2011; Wisnioski et al. 2015; Übler et al. 2019; Wisnioski
et al. 2019), presumably driven by higher gas accretion, gas fraction
and star formation compared to today. A higher gas fraction in
higher-redshift or lower-mass galaxies (e.g. McGaugh Blok 1997;
Tacconi et al. 2013; Tacconi, Genzel Sternberg 2020; Saintonge
Catinella 2022) can drive turbulence and inhibit thin disc formation
(Elmegreen Hunter 2015; van Donkelaar, Agertz Renaud 2022).
In the turbulent phase of galaxy formation with high gas fractions
(fgas 50 per cent), typical in the high redshift universe (Carilli
Walter 2013; Tacconi et al. 2013, 2020), intense star formation expels
gas from the disc and weakens the disc gravitational potential so that
the stellar disc puffs up. This process is not fully reversed when
some of the gas falls back to the disc (Bland-Hawthorn et al. 2024,
Bland-Hawthorn et al. 2025).
(ii) The ‘progressive thickening’ scenario suggests that stars form
near the disc mid-plane and get heated up to form the thick disc by
various density fluctuations or external perturbation (giant molecular
clouds: GMCs, spiral arms, giant clumps, galaxy interaction, e.g.
Wielen 1977; Lacey 1984; Villumsen 1985; Quinn, Hernquist
Fullagar 1993; Di Matteo et al. 2011; Inoue Saitoh 2014). However,
scattering from GMCs alone is shown to be insufficient to produce
thick discs (Robin et al. 2014; Aumer, Binney Schönrich 2016;
Leaman et al. 2017), and is only effective for the thin-disc population
© 2025 The Author(s).
Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative
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provided the original work is properly cited.
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3494 T. Tsukui et al.
MNRAS 540, 3493–3522 (2025)
near the disc mid-plane (Martig, Minchev Flynn 2014; Mackereth
et al. 2019). The internal kinetic energy of star clusters may also
contribute to the heating of these systems when they become unbound
due to gas expulsion (Kroupa 2002). Minor mergers can thicken discs
and also induce disc flaring (Bournaud et al. 2009; Comerón et al.
2011).
(iii) The ex situ scenario requires mergers or satellite accretion to
form a thick disc (Abadi et al. 2003; Yoachim Dalcanton 2006) or
contribute to its growth (Pinna et al. 2019a, b; Martig et al. 2021). In
this scenario, retrograde satellites produce counter-rotating stars in
the thick disc; however, the current observed fraction of thick discs
with counter-rotating stars is smaller than expected (Comerón et al.
2015, 2019).
All mechanisms can explain observed qualitative signatures of
the Milky Way’s two discs, and they are not necessarily mutually
exclusive (Pinna et al. 2024). A key challenge is to quantify their
relative importance (Martig et al. 2014; Agertz et al. 2021; Yu
et al. 2021; McCluskey et al. 2024) as a function of lookback
time and galaxy properties (e.g. mass, environment, and merger
history), and addressing it requires measuring the properties of
two discs for a large sample of galaxies spanning a wide range
of lookback times and galaxy masses. Such measurements offer
a time-machine perspective, as each galaxy has presumably been
influenced by these processes to varying degrees. However, most
insights so far come from studies at z ∼ 0, where thin and thick
discs have been systematically decomposed using high-resolution
images. Leveraging JWST’s imaging capability, this paper aims to
systematically investigate thin and thick discs at higher redshifts,
thereby exploring a much broader cosmic window.
Edge-on galaxies uniquely allow for direct study of their disc
vertical structure and the decomposition of the thin and thick disc
components (e.g. van der Kruit Searle 1981; Yoachim Dalcanton
2006; Comerón et al. 2011, 2012, 2014). Recently, the vertical height
of high-redshift (z ∼ 0.5–5) disc galaxies has been studied using
1D profile fitting to the disc vertical profile. Using Hubble Space
Telescope images at observed V BI bands, Elmegreen et al. (2017)
inferred the presence of thick and thin discs from an anticorrelation
between height and disc intensity of the fitted profiles. Hamilton-
Campos et al. (2023) measured disc heights at rest-frame 0.46–
0.66μm, suggesting that the population median height is similar to
that of Milky Way’s thick disc and does not evolve significantly
over the explored epoch. In contrast, Lian Luo (2024) used
JWST short bands (observing ∼ 1/(1 + z)μm), showing a strong
decreasing trend in disc height towards the present.
The limitation of previous investigations for high-redshift discs,
which did not require two disc components, is the use of a relatively
short rest-frame waveband that can be affected by the presence
of star formation at the observed epoch. JWST observations, with
long filter bands (F277W, F356W, F444W), provide the rest-frame
Ks and H bands for a wide cosmic epoch (z 2, ∼ 10 Gyr ago)
with unprecedented sensitivity and resolution. These passbands are
optimal tracers for stellar mass distribution, much less sensitive to
stellar age and minimally affected by dust extinction and emission.
This offers the best contrast between thin and thick discs and a
comprehensive picture of the stellar mass assembly of the two discs.
In this paper, we construct an edge-on galaxy sample with a
careful visual inspection using ever-increasing JWST public images
and investigate the thin and thick disc structures for the first time
at cosmological redshifts up to redshift z = 2, roughly 10 Gyr
ago, leveraging the rest-frame, near-infrared bands with significantly
improved imaging capability. The paper is organized as follows. In
Section 2, we introduce the sample and parameter measurements.
In Section 3, we show the resulting disc parameters including scale
height and scale lengths with galaxy parameters (e.g. stellar mass
and redshift). In Section 4, we discuss the results with respect to the
literature on disc formation. We summarize our results in Section 5.
In this paper, we adopt a Chabrier initial mass function (Chabrier
2003) and flat -cold dark matter (CDM) dominated cosmology
with a present-day Hubble constant of H0 = 70 km s−1
Mpc−1
, and
a density parameter of pressureless matter M = 0.3.
2 METHODS
2.1 Data and sample selection
We use the publicly released mosaic images from the DAWN JWST
Archive (DJA) which have been homogeneously reduced using the
GRIZLI pipeline (Brammer 2023). The data used primarily comes
from flagship JWST observational programmes including JADES
(Rieke et al. 2023), FRESCO (Oesch et al. 2023), CEERS (Bagley
et al. 2023), COSMOS-Web (Casey et al. 2023), PRIMER (Dunlop
et al. 2021), and NGDEEP (Bagley et al. 2024). A summary of
the mosaic fields, associated JWST programmes, PI names, and the
version of DJA reduction used in the paper is given in Table A1.
A parent sample is selected based on the SEXTRACTOR (Bertin
Arnouts 1996) source catalogues for the JWST mosaic images and
then matched with the 3D HST catalogue (Brammer et al. 2012;
Momcheva et al. 2016). The JWST source catalogues are publicly
available through DJA, compiled by running SEXTRACTOR on the
JWST detection image, which is produced by combining available
long-wavelength filters (F277W+F356W + F444W; Valentino et al.
2023). We extract galaxy parameters from the 3D HST catalogue
including redshift, stellar mass, and star formation rate, while
parameters from the DJA catalogues include the apparent axial ratio
of the galaxy q. Galaxies are selected to be edge-on with an axis ratio
q = a/b 0.3, a stellar mass M∗ 108.5
M, and well separated
from nearby sources by more than 1.5
. This results in 213 possible
sources.
Matching sources against the existing 3D HST catalogue effec-
tively removes erroneous sources from the SEXTRACTOR catalogue,
including the point spread function (PSF) wing of bright stars
and parts of nearby spiral galaxies. Moreover, we visually inspect
all galaxies, removing cases where galaxies show spiral features
(indication of the disc being slightly face-on), significant curvature,
and lopsidedness–potentially due to tidal tails and warping. We use
multiwavelength bands (F090W, F115W, F150W, F200W, F277W,
F356W, F444W) for visual inspection. For some galaxies, the shortest
band (F090W; 0.9 μm) reveals a straight-line dust attenuated feature
for edge-on galaxies and spiral features for slightly face-on galaxies,
helping us to identify edge-on galaxies and non-edge-on galaxies.
After visual inspection, the sample includes 132 galaxies.
For the disc structural analysis, we employ NIRCAM F277W:
2.7 μm, F356W: 3.6 μm, F444W: 4.4μm filter images for galaxies
with redshift z 0.46, 0.46 z 0.82, 0.46 z 1.45, respec-
tively, to maximize overlap with the rest-frame Ks band. For galaxies
at 1.45 z 2.24 and 2.24 z 3, we use the F444W band,
which corresponds to the rest-frame H and J bands, respectively.
Those near-infrared bands are minimally affected by dust extinction
and trace the stellar mass distribution of galaxies as the mass-to-
light ratio is insensitive to the stellar populations (Gavazzi, Pierini
Boselli 1996; Bell de Jong 2001; Courteau et al. 2014). The
systematic differences in the disc height measurements at those dif-
ferent near-infrared bands are small for nearby galaxies (Bizyaev
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Figure 1. NIRCam F227W, F356W, F444W colour composite images of a quarter of our sample sorted by increasing redshift. The remainder of the sample is
shown Figs B1–B3 in Appendix B. The white text on each image indicates the redshift and stellar mass from the 3D HST catalogue as well as the unique ID
from this analysis in Table D1. 1’ scale is denoted by a white bar in the lower right corner of each cut-out.
Mitronova 2009, 8 per cent bigger for H band and 16 per cent bigger
for J band compared to Ks band). This is further expected to be
small for our galaxies which have limited stellar populations born
in the relatively narrow range of the age of the universe ∼ 2.2 Gyr
(for the galaxies at 1.45 z 3, corresponding 9.1 − 11.4 Gyr in
lookback time).
In these long wavelength bands, we do not see any notable dust lane
signatures commonly seen in shorter bands. We further removed 21
galaxies from the sample due to the unavailability of an appropriate
waveband as described above, leaving 111 galaxies in the final
sample. A total of 12, 46, and 53 galaxies have spectroscopic, grism,
and photometric redshifts from the 3D HST catalogue, respectively.
Although we did not impose any redshift cut, the sample only extends
to a redshift of 3, with a visually well-defined disc.
Fig. 1 shows colour composite NIRCam images (F115W, F277W,
F444W) for a quarter of our sample of the galaxies, where the rest
of the galaxies are shown in Figs B1–B3 (Appendix B).
Fig. 2 summarizes our galaxy sample distribution in stellar mass
and redshift and morphological parameters. The stellar mass and
redshift are extracted from the 3D HST catalogue while the apparent
axial ratio q = a/b, semimajor axis a, semiminor axis b is based
on second-order moment measurements of light distribution by
SEXTRACTOR on the JWST detection images. The sample spans a
redshift range of 0.1 to 3.0, corresponding to the lookback time
of about 1.6–11.4 Gyr, ∼ 70 per cent of the age of the universe,
sampling a wide range of stellar masses at all redshifts.
2.2 Inclination deviation from the edge-on orientation
One can easily increase the sample size by allowing a higher axial
ratio (e.g. q 0.4: Hamilton-Campos et al. 2023; Lian Luo 2024)
than our study (q 0.3 also adopted by Elmegreen et al. 2017).
However, relaxing this limit may include many galaxies with large
deviations from the perfectly edge-on case. To test this, we fit a
probability distribution of the apparent axis ratios expected from the
projection of a triaxial spheroid with principal axial length A B
C adopting random viewing angles (Binney 1985).1
We assume the
galaxy’s intrinsic axial ratio, γ = C/A, of the galaxy population
follows a Gaussian distribution and = B/A follows a lognormal
distribution (Ryden 2004). Variables γ and are separable for spiral
galaxies: where γ decides the shape of the distribution at small axial
ratios q and decides the shape at large axial ratios q. Our sample,
with q 0.3, is only sensitive to γ . Therefore, we fix = 0 assuming
the disc is circular (axis-symmetric) and obtain γ = 0.25 ± 0.04
(mean and standard deviation), which is consistent with the result
obtained from the nearby disc galaxies (Ryden 2004). Conversely,
adopting typical lognormal distribution of disc galaxies (Ryden
2004) does not change the γ value we obtained.
Based on the best-fit population model, Fig. 3 shows the prob-
ability distribution of deviation from the perfect edge-on (i) for
galaxies with apparent axial ratios of q 0.3 and 0.3 q 0.4.
Approximately, 64 per cent of galaxies with q 0.3 have an inclina-
tion deviation of i 7 deg from the perfect edge-on orientation. In
contrast, galaxies with 0.3 q 0.4 have a median inclination devi-
ation of i ∼ 13 deg. Additionally, galaxies with 0.3 q 0.4 can
outnumber those with 0.3 q, comprising 70 per cent of total galax-
ies with q 0.4 in the model. This contamination of galaxies with
1The random viewing angles correspond to uniformly sampling cos(θ) over
[−1, 1] and φ over [0, 2π), where θ is the polar angle and φ is the azimuthal
angle.
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Figure 2. Summary of our 111 edge-on galaxies in redshift z, stellar mass M∗, apparent axial ratio q = b/a, and semimajor axis a. The scatter plots illustrate
the relationships between each pair of parameters, while the histograms on the diagonal represent the number distribution of each parameter in our sample. The
overlaid model line for the axial ratio b/a is the best fit from our population model (Section 2.2).
larger deviations from edge-on poses significant challenges when
measuring their structural parameters, such as vertical height, as these
measurements become biased (see Section 2.4 and Appendix C2). To
minimize potential biases in our structural measurements, we adopt
a stricter axial ratio limit of q 0.3.
However, this choice may preferentially exclude bulge-dominated
galaxies and the thickest disc populations. Future work will address
these population by incorporating higher order information to better
constrain inclination such as dust lanes, and radial changes in q,
mitigating the bulge’s effect on the global q used in this study.
2.3 Point spread function
An accurate PSF is essential for studying the intrinsic light dis-
tribution of galaxies, particularly for identifying the faint, thick
disc component, superimposed by the brighter thin disc component
(Comerón et al. 2018). We measured the effective PSF (ePSF) from
each mosaic image, following star selection methods (Faisst et al.
2022, see also Ito et al. 2024 and Zhuang Shen 2024).2
For
2We used the JWST PSF Pipeline and its forked version https://github.com/
takafumi291/JPP.
each field, we run SEXTRACTOR to identify candidate stars with
source properties class star 0.8 and elongation 1.5. We
select bright, unsaturated stars that lay on a horizontal locus in the
magnitude-size plane, with a minimum signal-to-noise ratio (SNR)
20.3
and no brighter sources within 2 arcsec. We then stacked
the image cut-outs of these selected stars using the PYTHON package
PHOTUTILS (Anderson King 2000; Anderson 2016; Bradley et al.
2024), maintaining the identical pixel sampling of the images to
include the exact pixelization effect.
The measured ePSF per mosaic captures the point source response
influenced by telescope jittering (Morishita et al. 2024), the image
drizzling process, and pixelization. This ePSF is expected to be
broader than the simulated PSF by WebbPSF (Perrin et al. 2014),
which represents the intrinsic PSF properties without these effects.
By fitting a Gaussian function to the ePSF, we measured the
ePSF FWHM of 0.131
, 0.146
, and 0.166
for F277W, F356W,
and F444W, respectively. The measured values do not change
significantly across observations. Because the ePSF is only roughly
3This corresponds to AB magnitudes brighter than 22.5–23.5 depending on
the filter and field.
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Figure 3. The probability distribution of inclination deviation i from a
perfect edge-on configuration (i = 90◦) conditioned with the apparent axial
ratio of the galaxies q 0.3 (blue; adopted in our sample), and 0.3 q 0.4
(black; contribution if relaxing the axial ratio cut q 0.4, which outnumber
galaxies with q 0.3). The distribution is based on the best-fitting population
model to the axial ratio q = b/a number histogram in Fig. 2.
approximated by a Gaussian, the measured ePSF widths depend on
the pixel sampling; here, we used a pixel sampling size of 0.40 arcsec.
In physical scales, these FWHM corresponds to 0.3–1.4 kpc with a
median of 1.1 kpc in our galaxy sample, given the galaxy distance
and band used. The limitation on the smallest measurable structural
scale from the finite PSF width is evaluated in Section 2.4 and in
Appendix C.
2.4 3D fitting and model selection
To measure the disc properties (thickness, size, etc.) of our edge-on
galaxy sample, we use a 3D disc model where the disc luminos-
ity density, ν(R, z), follows an exponential profile radially and a
sech2
profile vertically. In cylindrical coordinates (R, z), ν(R, z) is
expressed as
ν(R, z) = ν0 exp(−R/hR) sech2
(z/(2z0)), (1)
where ν0 is the central luminosity density, and hR and z0 represent
the disc scale length and height, respectively. The sech2
profile,
a solution for the self-gravitating isothermal sheet (Spitzer 1942),
has been widely used to effectively describe and approximate the
vertical thickness of galactic discs (van der Kruit 1988; Yoachim
Dalcanton 2008). The generalized function, sech2/N
, proposed by
van der Kruit Searle (1982) describes non-isothermal disc profiles.
The model varies from the standard sech2
profile only near the mid-
plane (Kruit Searle 1982), becoming either peaked or smoothed
as N approaches 1 or ∞, respectively. Despite these differences,
all variants of the model asymptotically converge to the exponential
profile exp(−z/z0) at large distance, z, from the mid-plane. In the
limiting case where N → ∞, the model matches the exponential
profile exp(−z/z0) at all radii.
For this study, we use the sech2
profile for consistency with existing
literature. Detailed modelling of the mid-plane profile is beyond our
scope, largely due to dust absorption and the limited resolution of
JWST. We also assume an inclination of 90◦
. Our population model
predicts that 64 per cent of our galaxies deviate from 90◦
by no more
than 7◦
(see Section 2.2). Such a slight deviation introduces bias in the
structural parameter measurements, which is known to be small (de
Grijs, Peletier van der Kruit 1997). However, the impact depends
on the intrinsic axial ratio of the disc and image quality (e.g. SNR
and instrumental resolution relative to the source extent). Section 2.5
discusses systematic uncertainties from inclination and other factors
for structural measurements.
To model galaxy surface brightness distributions and measure
the structural properties, we use the IMFIT package (Erwin 2015)
throughout the paper. IMFIT projects the 3D luminosity along
the line of sight on to 2D surface brightness in the sky, con-
volves with the user-supplied PSF, and then minimizes χ2
with
the Levenberg–Marquardt algorithm. It takes the image, variance,
and mask (to define the fitting region) as inputs and outputs
the best-fitting parameters and fit metrics such as the best-fitting
χ2
and Bayesian Information Criterion (BIC). Additionally, IMFIT
allows for the superposition of multiple components such as a
second disc or 2D Sérsic profile, which we employed in later
stages.
First, we fit a single 3D disc model to each cut-out JWST
image for the galaxy sample at the selected waveband for maximal
overlap with rest-frame Ks band (e.g. F277W; z 0.46, F356W;
0.46 z 0.82, F444W; 0.82 z). We set the lower boundary for
the disc scale height to 0.2 pixels, based on our recovery experiment
(see Appendix C1). If the parameter reaches this boundary, we
interpret it as a upper limit on the scale height. The best-fitting
single-disc model captures most of the galaxy’s total flux in the
data. However, some galaxies show systematic residual patterns in
a model-subtracted data map. The most notable are disc-like excess
light off the mid-plane and compact bulge components in the centre of
galaxies.
Secondly, to account for these structures and measure their
structural properties, we consider two additional components: (1)
a 2D Sérsic profile to account for the centrally concentrated light and
(2) a second thicker 3D disc component to account for the disc-like
excess light. For the first component, we allow the Sérsic index to
range from 0.5 to 5, accommodating the range from classical bulges
to disc-like bulges (Kormendy Kennicutt 2004).
To find the best structural fit for each galaxy, we fit a series of
increasingly complex models that include the second disc and central
Sérsic component using IMFIT. These include (i) the single disc model
described above; (ii) two disc model (thin + thick); (iii) a disc + bulge
model; and (iv) a two disc (thin + thick) + bulge model. To avoid
local minima in the χ2
landscape for the multiple component fits,
we repeated Levenberg–Marquard optimization 15 times with initial
starting points randomly drawn from a conservative wide range of
parameters based on the single disc fits. To avoid erroneous solutions
for the bulge being fit to the disc structure, and vice versa for the
model including the bulge component, the χ2
minimum solution was
bounded by a constraint: the bulge effective radius is smaller than
both 2 kpc and the disc scale length.
To ensure robust fits with well-behaved components motivated by
data, we use the following procedures. We determine the necessity for
additional components for each galaxy by comparing the BIC across
models. We assigned the galaxies into 4 models, from the simplest to
more complex models as described above. A more complex model
is justified if the BIC improvement exceeds 15. We visually inspect
the fit results using the model-subtracted residuals, checking each
structural component fits the intended structure.
Although the BIC classification is generally robust, we reclassify
6 galaxies from ‘two discs + bulge’ to ‘a disc + bulge’, and 1
from ‘two discs’ to ‘single disc’, based on the visual insignificance
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MNRAS 540, 3493–3522 (2025)
of the thick disc component.4
One galaxy initially categorized as
‘single + bulge’ was adjusted to ‘single disc’, while three others were
reclassified to ‘two discs’ (2) and ‘two discs + bulge’ (1) because
the bulge component fits the visually significant disc feature. These
11 re-classifications are only a minor subset of the 111 galaxies −
eliminating them instead did not alter our conclusions of the paper.
Fig. 4 shows an example galaxy (ID = 1) best fitted with a ‘two
discs + bulge’ model alongside fits with a single disc (top), two
discs (middle), and two discs + a bulge (bottom) models. For this
galaxy, the ‘single disc + bulge’ model provides a similar fit to
two disc models as the bulge becomes the thin disc component.
We omit it here to avoid redundancy. Fitting a single disc model
leaves systematic flux excesses above the disc mid-plane, clearly
seen in both the residual image and vertical profile (Fig. 4a). Adding
a second disc component successfully accounts for this excess light
(Fig. 4b). The convolved profiles reveal diversity amongst the sample.
Some galaxies are dominated by either thin or thick discs, while
others transition between thin/thick dominance at a certain height.
However, it is difficult to assess the relative dominance of the thin
and thick discs in the PSF-convolved vertical profiles shown in
Fig. 4. PSF wings can cause the thin disc light to extend to large
heights. Characterizing the PSF-deconvolved vertical profile of each
component will be left for future work, which will require verifying
the deconvolved profiles and assessing the uncertainties propagated
from both the assumed model and statistical noise.
2.5 Uncertainties for structural measurements
JWST data allows us to measure the disc structural properties
with high precision. We estimated statistical uncertainties using
Levenberg–Marquardt optimization in IMFIT and verified them by
bootstrap resampling, refitting the resampled data 500 times. We
present our results with these statistical uncertainties throughout the
paper. We also separately estimate systematic uncertainty arising
from our assumptions and simplifications, as detailed in Appendix C,
to help readers interpret our measurements and their limitations.
As the model is not always perfect, higher order structures remain
unmodelled, such as the outer truncation of the disc, and disc
substructure (bar end or clump, see Fig. 4 for residual at −10
kpc). Although dust extinction is not evident in our chosen bands,
it may also bias our results. Such challenges are noted in previous
works for nearby galaxies (Yoachim Dalcanton 2006). To test
the robustness of our results, we have run additional tests that
includes masking different regions of the galaxies (e.g. disc mid-
plane, centre, outside typical truncation radius) and systematic effect
(e.g. inclination, potential dust extinction). In summary, systematic
uncertainty, mainly arising from deviations in the inclination from
90◦
, results in median underestimation of 0.1 per cent, 12 per cent,
1 per cent for scale radii and median overestimations of 17 per cent,
27 per cent, 9 per cent for the scale heights for single, thin, thick
disc, respectively. Experiments masking the bulge region rather than
modelling it confirm that the bulge structure does not influence the
measured properties of the discs. The systematic effects are not
significant compared to the reported trends in Section 3 and as such
do not affect our conclusions.
4In all 6 cases where classification changed based on visual inspection, the
adopted classification corresponds to the second-best model when evaluating
the BIC. Additionally, these 6 galaxies had some of the smallest differences
in BIC between the best and second-best models among the full sample of
galaxies.
3 RESULTS AND ANALYSIS
Of the 111 galaxies in our sample, we find that 28 galaxies are well
fit by a single disc component, 39 are best fit by a single disc + bulge,
19 are best fit by two disc components, and 25 are best fit with two
disc components + bulge. For the remainder of this work, we only
focus on the disc components. We include galaxies that are well fitted
by a single disc, with or without a bulge model, in our ‘single disc’
category (67), which spans a redshift range z = [0.2, 3]. Similarly,
we include galaxies with two discs, with or without a bulge, in our
‘two discs’ category (44), which spans a redshift range z = [0.1, 2].
For galaxies with best fits including two disc components, we refer to
the disc with the shorter scale height as a ‘thin disc’ and the disc with
the larger scale height as a ‘thick disc’. We summarize structural
parameters derived in Table D1 and show corner plots of all the
measured parameters in Figs D1 and D2.
When deriving the mass of individual disc components, we assume
the same mass-to-light ratio (M/L) at rest-frame Ks/H bands for all
subcomponents in the best-fitting model including bulge, single disc,
thin disc, and thick disc. With this assumption, each component’s
mass is derived using the luminosity ratio and the total stellar mass
estimated in the 3D HST catalogue (Momcheva et al. 2016). The
bulge component is not dominant in our galaxies, contributing only
2 per cent of the total luminosity in the median. Therefore, the bulge’s
contribution is almost negligible but is accounted for as described
above to derive the individual disc mass.
This implies the relative mass-to-light ratio of thin and thin discs
in the bands we used, ϒthin/ϒthick, is equal to 1. This allows for
easy adjustments to the mass ratio in future studies when updated
colour or spectroscopic information constraining stellar population
becomes available. However, in Section 3.4, we assume a value of 1.2
for comparison with previous studies, as suggested by the realistic
star formation history (SFH) of the Milky Way’s thin and thick discs
(see Appendix E). This slight adjustment does not affect the overall
discussion.
3.1 Scaling relations for disc scale length and scale height
In this subsection, we investigate the dependence of the disc structural
parameters (radial length, scale height, and the ratio of the two) on
the total mass or the individual disc mass.
3.1.1 Existence of radial/vertical size–mass correlation
Fig. 5 shows the geometrical properties of discs, i.e. disc scale length
(hR), scale height (z0), and the ratio (hR/z0) plotted against the total
stellar mass of the galaxies (M∗). There is a positive correlation
in the M∗ − hR (left) and M∗ − z0 (middle) planes for all disc
categories, suggesting, as expected, more massive galaxies have
larger and thicker discs. However, there is no evident correlation
in the M∗ − hR/z0 plane (right), where thin discs are separated from
both single and thick discs to higher hR/z0.
When hR and z0 are plotted against individual disc mass, Mdisc,
as shown in Fig. 6, rather than the galaxy’s total mass, M∗, the dis-
tributions of single, thin, and thick discs overlap more significantly,
suggesting that the disc mass rather than the total galaxy mass is
more fundamental to characterize the disc properties.
In Figs 5 and 6, we show power-law fits for each population,
where the length and height are proportional to the power of stellar
masses, Mβ
∗ . Table 1 summarizes the measured slope β and intercept
α with the Spearman’s rank correlation coefficients and associated
p-values against the null hypothesis that there is no correlation
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Figure 4. An example fit of a galaxy (ID = 1) in our sample, with ‘two discs + bulge’ model being the best model according to our criteria (Section 2.4).
The three groups of panels from top to bottom display the best fit with (a) a single disc, (b) two discs, and (c) two discs + a bulge, respectively. Each group of
panels show from left to right the data, model, and residual in the top row and the vertical surface brightness profiles at different radii in the bottom. All images
and profiles are PSF-convolved. Each profile is extracted at the radius indicated above it. Assuming the twofold symmetry of the disc galaxies, we show the
average profile of four quadrants. The galaxy’s redshift z, χ2
ν of each fit and derived disc parameters are also shown. Notably, there remains significant excess
light above the disc mid-plane for the single disc model, which is eliminated by adding a second disc component. The central excess is accounted for by two
discs + bulge models, but even ignoring it entirely, the derived parameters do not change by more than 20 per cent, consistent with the conservative systematic
error of our sample (Appendix C).
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Figure 5. Disc geometrical parameters hR (left), z0 (middle), and hR/z0 (right) are plotted against galaxy stellar mass M∗. The symbols used are: open black
circles for single discs, open blue triangles for thin discs, and open red squares for thick discs in our galaxy sample, covering redshifts from ∼ 0.1 to 3. Similar
filled symbols represent the thin and thick discs of the Milky Way (Bland-Hawthorn Gerhard 2016) and M31 (Collins et al. 2011). The measurements assuming
a single disc component of M31 by Dalcanton et al. (2023) are also shown.
Figure 6. Same symbols as used in Fig. 5, but plotted against the stellar mass of each component rather than the galaxy’s total stellar mass. In the left panel
showing disc scale length hR, the scaling relation for the z = 0 SDSS sample derived by Gadotti (2009) is shown. We multiply the original relation by 2 to
account for suggested systematics in Boardman et al. (2020) due to the galaxy’s orientation (see the text).
between the parameters. To find the best fits, robust to outliers,
we used LTSLINEFIT (Cappellari et al. 2013), the implementation
of the least trimmed squares approach (Rousseeuw Leroy 1987;
Rousseeuw Driessen 2006). The method effectively finds the
global minima of the χ2
computed for all possible subsets of the data
excluding potential outliers up to half of the sample. This method can
also take into account the uncertainty for all coordinates. We used
the statistical uncertainty for our disc length and height measure-
ments and 0.2 dex uncertainties for stellar masses (Schreiber et al.
2011).
The radial scaling relations, hR − M∗ and hR − Mdisc, show
similar slopes, β, for thick and single discs, while thin discs have
a shallower slope, suggesting a difference in their build-up process
(i.e. a different total angular momentum history, Mo, Mao White
1998). The slopes measured here for all disc and galaxy masses are
similar to what was found in Wel et al. (2014). Fits to the vertical
height scaling relations, z0 − M∗ and z0 − Mdisc, reveal similar
slopes for all disc types suggesting that the disc scale height may
be determined by local vertical equilibrium. In fitting hR/z0 − M∗
and hR/z0 − Mdisc, there is no statistically significant correlation (see
p-values in Table 1) for any disc type, so we do not attempt a fit to the
data.
3.1.2 Galaxies form a thick disc first, then a thin disc
Notably, the thick discs and single discs show significant overlap
in all diagrams (Figs 5 and 6). This similarity implies that single
discs correspond to the thick discs observed in galaxies with two
disc components. This may suggest that most galaxies initially form
a thick disc, which is observed as a single disc, followed by the later
formation of a thin disc. This observational insight of the sequential
formation is further explored by later analyses throughout this paper
(Sections 3.2.2, 3.3, 3.4, and 4).
3.1.3 Comparison with other studies (z∼0, MW, high-z)
The distribution of the thick and single disc populations in the hR −
Mdisc plane are consistent with an extrapolation of measurements
at z ∼ 0 for SDSS disc galaxies (Gadotti 2009) after the following
correction. Radii measured for edge-on galaxies are typically ∼ 2
times larger than those measured for face-on galaxies (Boardman
et al. 2020), presumably due to unaccounted projection effects and
the increased sensitivity of the edge-on configuration. Accordingly,
we multiplied the relation originally derived in Gadotti (2009) for
z ∼ 0 galaxies by 2. Some of the scatter in the hR − M∗ relation may
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Table 1. Best-fitting linear relation to the disc geometrical parameters for a
thick, thin, single disc with galaxy’s total stellar mass M∗ or corresponding
disc stellar mass Mdisc. For a geometrical parameter X and either mass M, the
linear relation log(X/kpc) = α + β(log(M/M) − 9.5) is fitted to find α and
β. We chose the pivot mass of 9.5, close to the median disc mass, which does
not affect the best-fitting values and only weakly influences uncertainty. The
1σ observed scatter around the best-fitting is also shown. Additionally, for
each parameter pair, the Spearman correlation coefficient r is reported along
with the p-value for the null hypothesis in parentheses.
Parameters pair α β Spearman r
Single disc
hR − M∗ 0.50 ± 0.01 0.26 ± 0.03 0.08 0.44 (2 × 10−4)
z0 − M∗ −0.43 ± 0.02 0.17 ± 0.02 0.10 0.53 (4 × 10−6)
hR/z0 − M∗ – – – −0.14 (0.26)
hR − Mdisc 0.51 ± 0.02 0.26 ± 0.03 0.08 0.36 (2 × 10−3)
z0 − Mdisc −0.43 ± 0.02 0.16 ± 0.03 0.10 0.49 (3 × 10−5)
hR/z0 − Mdisc – – – −0.15 (0.23)
Thin disc
hR − M∗ 0.37 ± 0.02 0.20 ± 0.04 0.13 0.44 (3 × 10−3)
z0 − M∗ −0.74 ± 0.02 0.27 ± 0.04 0.14 0.58 (8 × 10−5)
hR/z0 − M∗ – – – −0.20 (0.22)
hR − Mdisc 0.43 ± 0.03 0.18 ± 0.04 0.13 0.44 (3 × 10−3)
z0 − Mdisc −0.65 ± 0.02 0.23 ± 0.03 0.12 0.65 (5 × 10−6)
hR/z0 − Mdisc – – – −0.26 (0.11)
Thick disc
hR − M∗ 0.53 ± 0.02 0.22 ± 0.03 0.10 0.66 (1 × 10−6)
z0 − M∗ −0.33 ± 0.01 0.19 ± 0.03 0.09 0.58 (3 × 10−5)
hR/z0 − M∗ – – – 0.09 (0.58)
hR − Mdisc 0.60 ± 0.02 0.26 ± 0.04 0.11 0.62 (6 × 10−6)
z0 − Mdisc −0.27 ± 0.02 0.22 ± 0.04 0.10 0.49 (7 × 10−4)
hR/z0 − Mdisc – – – 0.17 (0.27)
partly result from the mild size evolution across the large range of
redshifts covered by this sample z∼ 0.1 to 3 (e.g. Wel et al. 2014),
which is discussed in the next section.
The scaling relations z0 − M∗ defined above align well with the
Milky Way’s values (Bland-Hawthorn Gerhard 2016)5
and M31’s
values (Dalcanton et al. 2023), as shown in Fig. 5. However, the scale
length hR of the Milky Way thin and thick discs are comparatively
shorter than in the scaling relation z0 − M∗, confirming the long-
standing notion that the Milky Way’s disc scale-length is shorter
than the typical disc scale length expected for a galaxy of its
stellar mass (Licquia, Newman Bershady 2016; Boardman et al.
2020). However, we note that being inside of the Milky Way makes
radial length measurement uncertain (Bland-Hawthorn Gerhard
2016). Recently, Lian et al. (2024) suggested that the Milky Way’s
disc exhibits a broken-exponential profile which could lead to an
underestimated scale length by the steeply declining outer part,
potentially reconciling the observed discrepancy with other galaxies.
The measured z0 − M∗ for single and thick discs in this sample
are well aligned with the z = 0.5–3.5 results from Elmegreen et al.
(2017) for edge-on galaxies using the HST /F814W filter (0.8μm)
in two Frontier Field Parallels, assuming a single disc fit.6
However,
Lian Luo (2024) reports no significant z0 − M∗ correlation for
5These values enclose the recent determination of thick and thin disc
properties of MW using a rather similar approach in this study: decomposing
the edge-on integrated light of MW (Mosenkov et al. 2021).
6Note the difference of the adopted definition of H in Elmegreen et al. (2017),
their values need to be halved to compare with our data, z0 = H/2 equivalent
to an exponential scale height).
a sample of galaxies at z = 0.2 − 5 using the F115W filter (1.2
μm) of JWST /NIRCAM. Both studies measured disc thickness
assuming a single disc component. The discrepancy may be attributed
to differences in the selection criteria for edge-on galaxies. Our study
and that of Elmegreen et al. (2017) adopt stricter criteria, selecting
galaxies with an axial ratio of 0.3 and visually eliminating those
with warping and tidal tail structures. In contrast, Lian Luo (2024)
uses an axial ratio of 0.4, which may result in a sample dominated
by the galaxies with axial ratio between 0.3 and 0.4 (see Fig. 3 and
associated discussion in Section 2.2 as well as fig. 3 in Hamilton-
Campos et al. 2023) and such measurements may be affected by
warping and tidal structure.
3.2 Evolution of disc scale length and scale height
3.2.1 Single discs
Fig. 7 shows the disc scale length, hR, scale height, z0, and the
ratio hR/z0 as a function of lookback time for single disc galaxies.
This subsample provides a good reference to see how the size and
thickness of single discs evolve and to be compared with the literature
fitting single components, without potential systematics from the
thin/thick disc decomposition. We include individual measurements
(black circles) as well as the median in each lookback time bin of
2 Gyr widths (black diamonds). The median of each bin, along with
1σ statistical uncertainties,7
is overlaid in Fig. 7. We also include for
comparison in each panel a z = 0 reference sample from Yoachim
Dalcanton (2006).
To account for the different numbers of galaxies with a range of
masses in each bin, we correct the size and thickness dependency
on the galaxy’s stellar mass, as seen in Fig. 5. For example, for
hR, we first derive the covariance Cov(log hR, log M∗) and variance
Var(log M∗) and find the slope β = Cov(log hR, log M∗)/Var(log M∗)
of the linear relationship between log hR and log M∗. Then, we
subtract the mass dependency log hR,corr = log hR − β(log M∗ −
log
M∗) for the single disc sample with a median stellar mass
log
M∗ = 9.2. After making a correction for the M∗ dependency
with z0 and hR (red diamonds), both hR (left) and z0 (middle) show
a mild increasing trend from 12 Gyr to present.
The mild rising trend in the median values of hR towards the
present are consistent with the result of Wel et al. (2014). We compare
our measurements with their median evolutionary trends, rather than
with the absolute values (which are typically about 1.7 times smaller
than ours on average), for the following reasons. The evolutionary
trend and absolute values from Wel et al. (2014) shown in Fig. 7
correspond to effective radii derived from fitting a single 2D Sérsic
profile to galaxies with a wide range of inclinations. If we convert
these values to disc scale radii by dividing by 1.678, appropriate for
an exponential profile, their measurements fall significantly below
those presented here. As discussed in the previous section (Section
3.1), radii measured for face-on galaxies tend to be ∼2 times shorter
than those measured for edge-on galaxies (Boardman et al. 2020).
Additionally, the combination of a disc and a young compact bulge
fitted with a single Sérsic can result in a shorter measured radius,
whereas in this study, we use multiple components to mitigate the
effects of the bulge in edge-on galaxies.
7We use the BOOTSTRAP function from PYTHONSCIPY package with 104
samples to derive the uncertainty on median values. For the upper bound
of the first and final bin, 68th confidence interval provides the same value as
the median, so we instead use the upper bound of 95th confidence interval
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Figure 7. The properties of single discs, hR (left), z0 (middle) and hR/z0 (right) are plotted against galaxies’ lookback time τlookback. This figure includes only
galaxies classified as having a single disc or single disc with a bulge. Black circles show individual measurements with associated 1σ statistical uncertainty.
The large black diamonds indicate the median in each lookback time bin of 2 Gyr widths, with confidence intervals estimated via bootstrap resampling. The
red diamonds show the same but linearly corrected for the relation seen in log M∗ − log hR and log M∗ − log z0 to a median log(M∗[M]) = 9.2 in each bin.
The evolutionary trend from van der Wel et al. (2014) for galaxies with stellar mass log(M∗[M]) = 9 − 9.5 is shown by a black line with an associated 1σ
confidence interval for the median. The grey shading near τlookback ∼ 0 shows the range of values derived by Yoachim Dalcanton (2006) for z ∼ 0 sample.
The lookback time evolution of z0 from Lian Luo (2024) is shown in blue.
Figure 8. The properties of the thick and thin discs plotted against a galaxy’s lookback time. The individual measurements for thin and thick discs are shown
in blue and red points, respectively. The black and blue triangles are the median trends of thin disc without and with M∗ dependency correction to the stellar
mass log(M∗/M) = 9.5. The black and red squares are the same for thick discs. There is no significant evolution in all properties.
The increasing trend in z0 towards the present is consistent
with similar studies using local galaxies (Yoachim Dalcanton
2006), but contrasts with the declining trend reported by Lian
Luo (2024). This discrepancy can be attributed to the sequential
formation of the thick disc followed by the thin disc and the use
of shorter wavebands in Lian Luo (2024), which are sensitive
to younger stellar populations. Consequently, their measurements
capture the thickness associated with the ongoing formation of
thick discs at earlier times and the subsequent formation of thin
discs at later times. This is further clarified in the next subsection
(Section 3.2.2), which examines the evolution of thin and thick
discs.
No median evolution is seen for the ratio of scale length to scale
height (hR/z0, Fig. 7 right). This suggests that the discs at all of our
explored epochs, τlookback ∼ 1.6–11.4 Gyr, have already developed
geometrically similar structures to present-day galaxies (as denoted
by the grey band at z = 0).
3.2.2 Thick and thin discs
Fig. 8 shows equivalent plots to those presented in Fig. 7, i.e. disc
properties as a function of lookback time, but for the double disc
subsample, showing both thin and thick discs. The measured scale
lengths and heights for discs are almost constant as a function of
lookback time after correcting the M∗ dependency. This indicates
that there is no significant structural evolution in thin and thick discs.
One notable exception is a mild decrease in scale lengths for the
thin disc components towards late times. This trend is of interest
as thin discs may be preferentially affected by scattering processes
that reduce their scale radius by decreasing angular momentum, or
because we observe the effect of reduced pressure support in the
thin disc, causing it to shrink (see more discussion in Section 4.3).
However, measuring the scale length of thinner discs is subject to
larger uncertainties (see Appendix C), and low number statistics at
the bin at the latest lookback time.
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Lian Luo (2024), fitting a single disc component to the F115W
(rest-frame ∼1.2/(1 + z)μm) images, show a strong decrease in
scale height towards the present, which contrasts with the mild
increase shown in Fig. 7 (middle). Their thickness measurements are,
however, aligned with the thick disc at early times and then aligned
with the thin disc at later times towards the present Fig. 8 (middle).
The shorter wavelength bands used in Lian Luo (2024) trace young
stellar populations that likely outshine the main mass component
of the galaxy. At early times, ∼ 6–12 Gyr ago, their thickness
measurements in short bands aligned well with our measurements
for single disc galaxies, indicating that early young thick discs shone
brightly across wave bands [λ ∼ 0.3 μm and λ ∼ 1.1 μm at z = 3 for
Lian Luo (2024) and this work, respectively]. In the recent ∼ 6 Gyr,
due to the increasing prevalence of thin discs which outshine older
thick discs, their measurements in short bands effectively measure
the thin disc scale height [λ ∼ 0.8 μm and λ ∼ 2.4μm at z = 0.5 for
Lian Luo (2024) and this work, respectively]. Those align with
our measurements for thin discs decomposed from thick discs in our
rest-frame IR band. The rest-frame IR band used in this study traces
stellar mass, less sensitive to the age of the stars, thus providing better
contrast to see the fainter thick disc remaining from early formation
against the thin discs which will dominate in the shorter bands.
3.2.3 Interpreting evolutionary trends in disc formation
Single discs show a mild increase in both scale length (hR) and
height (z0) towards the present, whereas the thin and thick discs in
two-disc galaxies show no significant evolution. It is important to
note that the median evolution of disc structural parameters at a
given galaxy mass does not reflect the specific evolutionary tracks of
individual galaxies–galaxies in different time bins are not the same
progenitor populations. With the mass dependency already removed,
the evolution in radius and height is primarily determined by angular
momentum and vertical energy, respectively.
In the context of cosmic downsizing, for galaxies of the same
mass, those observed at early times formed rapidly (Behroozi,
Wechsler Conroy 2013) and completed their thick disc formation
earlier (Comerón 2021) compared to galaxies observed at later times.
The mild increase in hR at given galaxy mass can be attributed
to halo evolution in the CDM universe, where halo virial radii
grow larger towards the present. Gas accreting from more extended
regions carries larger specific angular momentum, so discs that form
later tend to be larger (Mo et al. 1998). Meanwhile, lower halo
concentrations at earlier epochs (Bullock et al. 2001) partially offsets
this effect, resulting in a modest overall size increase (Somerville
et al. 2008). Additional crucial processes, such as outflows removing
low angular momentum material (Brook et al. 2011; Guedes et al.
2011), radial migration that move stars to outer radii on average
(Minchev et al. 2012), and mergers also affect disc sizes (Governato
et al. 2009). The increase in disc thickness z0 is expected because stars
do not cool and are continuously thickened by satellite perturbations;
consequently, discs observed at later times have more chance to be
heated by such events. Moreover, for a given velocity dispersion,
a disc with a larger scale length at the same mass has a lower
surface mass density, leading to a larger scale height in gravitational
equilibrium. The absence of an increase in z0 for the thick disc in two-
disc galaxies (the middle panel of Fig. 8) could be due to the presence
of the thin disc. Simulations have shown that gas in a thin disc can
reduce heating from minor mergers and thin disc growth can lead
to the adiabatic vertical contraction of the thick disc (Moster et al.
2010). In our disc sample, the mechanisms responsible for radial and
Figure 9. Distribution of two-disc (red-blue points) and single-disc galaxies
(black circles) in lookback time and stellar mass. The top and right panels
display the fraction of the two disc galaxies as a function of lookback time
and stellar mass, with associated 1σ statistical uncertainties7. For two-disc
galaxies, grey lines indicate the range of lookback times at which galaxies can
be identified as having two discs when artificially redshifted. The averaged
evolutionary track of Milky Way mass galaxies (van Dokkum et al. 2013) is
shown by a blue-red line, where the red part marks the thick disc formation
period, and the blue part marks the thin disc formation, with a transition
estimated to be around 9 Gyr ago based on stellar age measurements.
vertical height growth seem to maintain the geometrical proportion
of the discs (see constant hR/z0 in Figs 7 and 8).
For evolutionary tracks of individual galaxies, it is more informa-
tive to examine their size and mass relations. As galaxies and discs
grow in mass, both their radii (hR) and heights (z0) tend to increase
on average, aligning with the scaling relations in Figs 5 and 6. An
increase of about two orders of magnitude in mass can roughly triple
these sizes. In contrast, the redshift evolution affects the sizes by a
factor of at most 1.5, contributing to the observed scatter in the scaling
relation. The relatively constant or mildly evolving mass-corrected
medians shown in Figs 7 and 8 indicate that the fundamental scaling
relations remain largely unchanged over time.
3.3 Emerging thin discs at later epochs
Fig. 9 shows the distribution of two-disc and single-disc galaxies
in stellar mass and lookback time, along with fractions of two-
disc galaxies as a function of each variable. Two-disc galaxies are
prevalently found at high stellar masses at earlier times, extending
back to ∼10 Gyr ago (z ∼ 2). At later times (i.e. shorter lookback
times), they are increasingly found at lower stellar masses, resulting
in an increasing fraction of two-disc galaxies with cosmic time
and stellar mass. The distribution includes observational biases:
identifying a two-disc structure becomes more difficult for more
distant galaxies or lower mass galaxies. To dissect observational
effects from the onset of thin disc formation, Fig. 9 shows the range
of lookback times at which two discs can be identified when a galaxy
(of similar properties) with two discs is artificially redshifted (grey
line for each data point).
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To find the maximum lookback time, we calculate redshifted
surface brightness, disc radius (hR), and disc height (z0) by redshift
increments (dz = 0.02) using galaxies’ best-fitting model parameters
for galaxies categorised as having two discs (Section 3). We consider
the surface brightness evolution including not only the surface
brightness dimming (∝ (1 + z)−4
) but also k-correction and intrinsic
evolution (see Fig. E2 in Appendix E). We then generate simulated
images with noise added and the identical PSF, and refit the images
using both a two-disc model and one-disc model. The noise incor-
porates variance from sky noise, read noise, and Poisson variance
due to photon counting from the object itself. Bulge components
are subject to redshifting but fixed during the refit. We consider the
two-discs to be detectable if the BIC difference between the two-
disc fit and one-disc fit is conservatively more than 1008
We visually
inspect the fitting results to confirm that the two-discs are identifiable
with clarity comparable to the visual inspection process described in
Section 2.4.
By examining the lookback time ranges where two-disc structures
are detectable, we find that identifying two-disc galaxies becomes
increasingly difficult for those with masses below 109
M, making it
challenging to assess their fractional changes over time. In contrast,
galaxies with masses above 109
M extend well over some single
disc galaxies, which allowed us to see the onset of two disc galaxies.
For the most massive galaxies above 109.75
M, there is evidence
of a transition from single discs to two discs around 8 Gyr ago.
Lower mass galaxies with masses between 109
M and 109.75
M, on
the other hand, begin forming thin discs approximately 4 Gyr ago.
This shift in the onset of two disc formation suggests that thin disc
formation proceeds in a ‘downsizing’ manner, where more massive
galaxies develop thin discs at earlier epochs.
The averaged evolutionary track of Milky Way mass galaxies
(Dokkum et al. 2013) crosses the detectable lookback time ranges
of two-disc galaxies, demonstrating the power of JWST to directly
constrain the thin disc onset of MW-sized galaxies. The thin disc
formation for high-mass galaxies, ∼8 Gyr, aligns with the thin disc
formation period, starting ∼ 9 Gyr, for Milky Way (Kilic et al. 2017;
Conroy et al. 2022; Wu et al. 2023; Ciucă et al. 2024).
3.4 The mass ratio of thin and thick discs
In this section, we explore the mass fraction of thick and thin discs
in galaxies that host two disc structures. The mass ratio is calculated
multiplying the luminosity ratio with the ratio of mass-to-light ratios
for thick and thin discs, Mthick/Mthin = ϒthick
ϒthin
Lthick
Lthin
. We adopt the
fiducial ratio of thin and thick mass-to-light ratio, ϒthick/ϒthin = 1.2,
derived by Comerón et al. (2011) assuming the SFH of the Milky
Way’s thin and thick discs at the F356W band (Pilyugin Edmunds
1996; Nykytyuk Mishenina 2006, but see additional assumptions
made in Comerón et al. 2011). Fig. 10 shows the mass ratio of thick
to thin discs for our sample, as a function of the total stellar mass,
compared with z = 0 galaxies from Comerón et al. (2014) using
Spitzer3.5 μm band (equivalent to F356W used in this study).
8Compared to a difference of 15 used in Section 2.4. In this simulation, we
fit a perfect model (two discs) to a noisy version of itself, so the model fit
is already near optimal, resulting in a high likelihood contrast with the case
of fitting an imperfect model (single disc). Consequently, we need to adopt
a higher BIC threshold compared to fitting models to real data, where both
models are imperfect representations of reality. In the real case, unaccounted
structures in the data contribute to the χ2, reducing the likelihood contrast
between the models.
Figure 10. The mass ratio of thick-to-thin discs plotted against the total
stellar mass for two disc galaxies. The red-blue points represent measurements
of this work, spanning a redshift range of z ∼ 0.1 to 2.0. These measurements
are taken in bands approximately overlapping rest Ks band at z 1.45
and H band at 1.45 z 2.25. Black points denote measurements from
Comerón, Salo Knapen (2018) for galaxies at z ≈ 0, obtained using Spitzer
3.5 and 4.5μm bands. Error bars indicate the uncertainties associated with
each measurements. For visual reference, the dashed line marks the ratio
Mthick/Mthin = 1.
The value ϒthick/ϒthin = 1.2 is applied to galaxies with a assumed
specific SFH (observed at z = 0 with the F356W band). Using
the same SFH, we consider the spectral energy distribution (SED)
evolution of galaxies and rest-frame band shifting with redshift and
find that ϒthick/ϒthin does not significantly change across redshifts of
the sample and the bands used in this study (F227W, F356W, F444W:
see Appendix E). Therefore, we can safely assume ϒthick/ϒthin = 1.2
for comparison between our measurement with the z = 0 sample
(Comerón et al. 2011). Comerón et al. (2011) also varied the
assumption on the SFHs of thin and thick discs and found values
ranging from 1.2 to 2.4. We tested the constancy across redshift,
z = 0–3, for the same set of SFHs. While a delayed formation of
thin disc relative to thick disc provides higher values, all cases show
a constant ϒthick/ϒthin across redshifts and observed bands, with
differences among the three bands being small, less than 0.25.
The thick and thin disc mass ratios Mthick/Mthin for our two disc
galaxies at z ∼ 0.1–2 show a decreasing trend as a function of stellar
mass. This result is well aligned with massive galaxies at z = 0
(Yoachim Dalcanton 2006; Comerón et al. 2011, 2012, 2014).
Yoachim Dalcanton (2006) also derived the mass ratio for their
z = 0 sample using the R band, where the mass-to-light ratios are
strongly influenced by galaxies’ SFH. Therefore, we do not make a
comparison, but a similar decreasing trend is observed.
To further explore what drives the decreasing trend of thick-to-thin
disc luminosity with stellar mass, Fig. 11 shows the individual disc
mass of thin and thick discs plotted against total stellar mass. The
best-fitting slopes M∗ − Mdisc for thin and thick discs are shown. Fits
are derived from the two best-fitting relations M∗ − z0 and Mdisc − z0
(Table 1), demonstrating that a single power law can describe the thin
and thick disc sequences separately. The thin and thick disc sequences
are consistent with the local results (Comerón et al. 2018), showing
two clear distinct sequences with a shallow slope for Mthick − M∗ and
a steep slope for Mthin − M∗ that cross at a log(M∗[M]) ∼ 10. The
different slopes of the thin and thick disc sequences are responsible
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Figure 11. The decomposed thin and thick disc masses of two disc galaxies
are plotted against their total stellar masses. Blue triangles represent thin
disc measurements, and red squares represent thick disc measurements from
this study spanning the redshift range of 0.1–2. For comparison, blue and
red points indicate thin and thick disc measurements at redshift z ≈ 0 from
Comerón et al. (2018), respectively.
for the decreasing disc mass ratio as a function of galaxy masses seen
in Fig. 10.
Figs 10 and 11 demonstrate that higher mass galaxies tend to
have more massive thin discs compared to their thick discs. This
aligns with the downsizing formation trend shown in the previous
section (Section 3.3), where thin discs begin to form earlier in more
massive galaxies. Supporting this, numerical simulations of Milky
Way-sized galaxies suggest that an earlier transition from a bursty
thick disc phase to a steady thin disc formation phase results in higher
thin disc-fractions (Yu et al. 2021).
The different slopes may also reflect the efficiency with which
the thin and thick discs gain mass along with total galaxy mass
growth. For instance, it is expected that Milky Way-sized galaxies
have increased its mass by approximately 0.6 dex on average from
redshift z = 2 to z = 0.1, which spans the redshift range of our
two-disc galaxy sample (Dokkum et al. 2013). While this 0.6 dex
growth is relatively modest compared to the mass range we explored,
the slopes for both the thick and thin discs appear to align those
at redshift z = 0. For this relationship to remain unchanged as
galaxies grow, both the thick and thin discs must continue to gain
mass. Therefore, even after a galaxy possesses both a thick and a
thin disc, the thick disc continues to grow, albeit less efficiently
than the thin disc. This ongoing growth of the thick disc may be
driven by the variable gravitational stability of gas discs modulating
between thin and thick disc regimes due to episodic events such
as merging or accretion, which is discussed in next Section 4.1.
Additionally, satellite accretion or gradual scattering and heating
from thin disc stars could contribute to the growth of thick discs. This
overlapping formation could explain the continuous age populations
seen in the Milky Way (Bovy, Rix Hogg 2012; Ciucă et al. 2021;
Beraldo e Silva et al. 2021). This contrasts with a purely sequential
scenario where the two discs would form in entirely separate
epochs.
Disentangling the initial ratio of the two discs when they first
become observationally distinguishable from the later build-up
process requires additional information, such as SFHs and stellar
kinematics of these galaxies.
Figure 12. The measured axial ratios for the single disc (black circle), thin
discs (blue triangles), and thick discs (red square). The black dots represent
the v/σ values for gas discs (Übler et al. 2019, and others9), or the expected
axial ratios for stellar discs that form from the gas discs in the simplified
scenario where the gas disc is entirely converted into a stellar disc while
conserving v/σ. The black line indicates the predicted curve for a Toomre Q-
regulated gas disc, with Qcrit = 1 and fgas(M∗) for a main-sequence galaxy
at z = 1 (Tacconi et al. 2020). A 2 Gyr time evolution is illustrated by the blue
arrow, which horizontally shifts the curve to the left, allowing more low-mass
galaxies to enter the thin-disc formation regime. Variations in the predicted
curve, resulting from doubling or halving Qcrit, fgas, or the product Qcritfgas,
are shown by dashed and dash–dotted lines.
4 DISCUSSION
We confirm the presence of single discs up to z ∼ 3 and two discs
up to z ∼ 2, which already exhibit radial and vertical size-mass
relations (Section 3.1). The edge-on confirmation of stellar discs
complements the identification of spiral structures in face-on stellar
discs (Kuhn et al. 2024) at redshift up to z ∼ 3. Well-developed stellar
discs are internally unstable or dynamically responsive to external
perturbations, forming spiral patterns (Byrd Howard 1992; Law
et al. 2012; Pettitt, Tasker Wadsley 2016; Bland-Hawthorn et al.
2023; Tsukui et al. 2024). Spiral-inducing mechanisms driven by
external perturbations are presumably more significant at higher
redshifts, where merger rates are elevated (Rodriguez-Gomez et al.
2015).
In this section, building on the main observational findings in
preceding sections we discuss the evolution from gaseous to stellar
discs and the emergence of thick and thin discs across cosmic history,
linking gaseous disc measurements with the structural measurements
of stellar discs in hand.
4.1 Toomre Q self-regulated disc formation
The kinematics of gaseous discs have been systematically charac-
terized up to redshift z ∼ 2.7 (e.g. Wisnioski et al. 2015; Übler
et al. 2019), with more recent studies extending this exploration to
redshifts beyond z ∼ 4 (e.g. Neeleman et al. 2020; Rizzo et al. 2020;
Lelli et al. 2021; Tsukui Iguchi 2021). The commonly measured
kinematic parameter, v/σ, serves as a proxy for the dynamical support
of gas discs and provides insights into the geometric proportion of
the resulting stellar disc formed from star formation in the gas disc.
Fig. 12 shows the intrinsic vertical to radial ‘axial ratio’ of the discs,
hR/z0, for all disc categories as a function of total stellar mass,
as shown in Fig. 5 (right). We compare these measured geometrical
proportions with v/σ values from the literature for galaxies at similar
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redshifts z ∼ 0.1 − 2.7, mainly measured using optical emission
lines (Übler et al. 2019), and for galaxies at earlier redshifts
( 2) primarily using far-infrared (FIR) emission lines (e.g. [CII],
[CI]; sources in the footnote9
). Although measurements by optical
emission lines outnumber those using FIR emission measurements,
both distributions appear similar when plotted separately in the
diagram.
Assuming stellar components inherit the same v/σ of the gas
disc they form out of, a simple application of the tensor virial
theorem (Binney 2005; Binney Tremaine 2008) predicts a relation
between hR/z0 and v/σ of self-gravitating axisymmetric stellar
structure. Under the assumption of an isotropic velocity dispersion,
the approximate relation is given by Kormendy (1982) as
hR/z0 =
π2
16
v
σ
2
+ 1. (2)
We assume an isotropic velocity dispersion as we do not have
evidence to the contrary at high redshift (Genzel et al. 2017).
Gas discs exhibit a weak correlation between v/σ (or the expected
hR/z0) and stellar mass, with more massive galaxies typically located
in the thin disc regime and less massive galaxies in the thick
disc regime or below. This trend is consistent with results from
simulations (Pillepich et al. 2019; Kohandel et al. 2024) and can be
explained by self-regulated star formation of gas discs, supporting
the downsizing thin disc formation discussed earlier. The Toomre
stability criterion for gas-dominated discs (Toomre 1964) is
Qgas =
σ
v
a
fgas
, (3)
where a is a constant depends on the shape of rotation curve
(a =
√
2 for a constant rotation curve), and fgas is the gas mass
fraction within the disc (see Genzel et al. 2011). In models where
disc star formation is self-regulated by gravitational instability
and star-formation feedback, Toomre Qgas is maintained around a
critical value (Qcrit ≈ 1), keeping the disc marginally unstable. Thus,
v/σ ≈ a/fgas/Qcrit, which links v/σ to the gas mass fraction fgas.
More massive galaxies, which have lower gas fractions (Mc-
Gaugh Blok 1997; Tacconi et al. 2013, 2020) due to efficient
star formation (Behroozi et al. 2013), achieve high v/σ values
earlier, leading to the earlier onset of thin discs in these galaxies.
Conversely, less massive galaxies, with higher gas fractions, exhibit
lower v/σ and cannot form thin discs until their stellar component
develops sufficiently to reduce the gas fraction and support higher
v/σ. To illustrate this, in Fig. 12, we overplot the v/σ expected
for gas discs from equation (3), using the averaged gas fraction
fgas(M∗) for main-sequence galaxies at z = 1 (Tacconi et al. 2020)
and assuming Qcrit = 1. This predicted curve shows that high-
mass galaxies ( 1010
M) lie in the thin disc formation regime,
while low-mass galaxies lie in thick disc regime. The blue arrow
indicates the 2 Gyr evolution of the curve from z = 1, which shifts
the curve horizontally, allowing less massive galaxies to enter the
thin disc formation regime as their gas fraction decrease over time.
This explains the earlier thin disc formation in massive galaxies
(downsizing thin disc formation) hinted by Fig. 9, explaining the
dominance of thin discs in high-mass galaxies and thick discs in
low-mass galaxies (Fig. 11).
9Neeleman et al. (2020), Rizzo et al. (2020), Fraternali et al. (2021), Lelli et al.
(2021), Rizzo et al. (2021), Tsukui Iguchi (2021), Amvrosiadis et al. (2025),
Parlanti et al. (2023), Rizzo et al. (2023), Roman-Oliveira, Fraternali Rizzo
(2023), Fujimoto et al. (2024), Rowland et al. (2024).
The expected hR/z0 ratio for gas discs shows a broader range
than observed in stellar discs, indicating that gas discs are subject
to significant temporal variation of the Toomre Qgas parameter.
These fluctuations in Qgas are driven by episodic events such as
gas accretion and mergers, which increase the gas fraction (fgas),
and subsequent starburst that enhance turbulent energy (σ), and its
dissipation (see e.g. Tacchella et al. 2016). As a result, the Qgas
parameter for gas discs can vary widely, oscillating around the
marginal stable value (Qcrit). Also, Qcrit itself is variable; it can
decrease to about 0.7 when the finite scale height stabilizes a disc
(Kim, Ostriker Stone 2002; Bacchini et al. 2024, as opposed
to an infinitesimally thin disc), but can increase to 2–3 under a
condition that gas turbulence efficiently dissipates (Elmegreen 2011).
In Fig. 12, we show the variations in v/σ expected from the averaged
population by assuming either a 2× higher or lower value for fgas or
Qcrit, or the product fgasQcrit, which encompasses the range of gas
disc measurements.
In contrast, stellar distributions are shaped by the cumulative effect
of star formation, occurring under the variable conditions of the gas
disc, presumably leading to a convergence towards a narrower range
of axial ratios over time. As the stellar component develops in gas
discs, the total disc Toomre parameter, Q−1
tot = Q−1
∗ + Q−1
gas, is subject
to the disc stability criterion. This is valid if all components have
similar velocity dispersions (Romeo Wiegert 2011). Considering
a simple scenario, where the gas distribution and stellar distribution
are coupled with the same velocity structure and distribution and
fgas + fstar = 1, the marginally unstable disc would have hR/z0 ∼
(v/σ)2
= (a/Qcrit)2
, which does not depend on galaxy stellar mass,
consistent with no correlation seen in hR/z for stellar discs in Fig. 12.
Note also that during or after their formation from gaseous discs,
stellar discs undergo distinct processes from gaseous discs such as
heating by disc substructure or mergers. Unlike gaseous discs, once
heated, the stellar components do not cool.
Finally, note that stellar masses of galaxies with available optical
line kinematics, derived using the same methods (3D-HST; Übler
et al. 2019), are larger than those in our sample. This reflects the
current sensitivity limitations of spectroscopic observations and the
challenge of obtaining kinematics for low-mass galaxies.
4.2 Vertical equilibrium of the disc
In the previous section (Section 4.1), we demonstrated that a gas disc
with widely varying gas fractions fgas, can form stellar thin and thick
discs with similar geometric proportions − the relative height to the
radial length hR/z0. However, this does not necessarily mean that tur-
bulent gaseous discs are sufficiently thick or thin to directly produce
thick or thin stellar discs. In this section, we address this question by
examining the vertical equilibrium of these system. Fig. 13 shows
the expected velocity dispersion of the stellar disc assuming vertical
equilibrium. The scale height z0 of a self-gravitating isothermal sheet
is given by z0 = σ2
∗ /(2πG∗) (Binney Tremaine 2008), where
σ∗ is the stellar velocity dispersion, and ∗ is the surface density
of the stellar disc. Using measurements of the scale height z0 and
the surface density ∗ = M∗/(2πh2
R), we compute the expected
velocity dispersion for a single disc in vertical equilibrium as
σ =

2πG∗z0. (4)
For galaxies with two disc components, we approximate the surface
density as ∗ = thin + thick (refer to Aniyan et al. 2018 for
isothermal sheet solution with the presence of an additional thin
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Figure 13. Expected stellar velocity dispersion from vertical equilibrium
for single, thin and thick discs, with black circles, blue triangles, and red
squares, respectively. The arrows indicate upper limit measurements. Green
circles indicate stellar velocity dispersion measurements from the DiskMass
survey for face-on galaxies at z = 0 (Martinsson et al. 2013a, b). These stellar
velocity dispersions are compared with those of gas discs (black dots).
disc) to derive the expected velocity dispersion of thick disc:
σthick =

2πG(thin + thick)z0,thick. (5)
For thin disc, we use an approximate solution by Forbes, Krumholz
Burkert (2012), which accounts for the gravitational influence of the
thick disc:
σthin =

2πG(thin + thick × z0,thin/z0,thick)z0,thin. (6)
For simplicity, we exclude contributions from dark matter, as
baryons dominate in the disc mid-plane (Narayan Jog 2002), and
neglect small bulges, which contribute a median of 2 per cent to the
total disc luminosity in our sample. Their inclusion would marginally
increase the estimated σ. The expected velocity dispersion of thin
discs aligns with the measurements of vertical stellar velocity
dispersion by the DiskMass Survey for local galaxies (Martinsson
et al. 2013a, b). The light weighted dispersion of the literature sample
traces the thin disc stellar dispersion. This alignment suggests that
discs achieve vertical equilibrium, and their measured thickness
reflects the virialized state. The vertical equilibrium can be reached
rapidly: for instance, the crossing time of a stellar particle within a
typical vertical scale height of 0.5 kpc with a velocity dispersion of
50 km s−1
is approximately 10 Myr.
Gas velocity dispersions, from the high-redshift samples, span
a range similar to those expected for thin and thick stellar discs.
If galaxies of similar stellar mass have comparable disc density
structures (Fig. 5) and have reached vertical equilibrium, then
velocity dispersions serve as a good proxy for scale height and vice
versa. The roughly consistent velocity dispersions between stars and
gas suggest that gaseous discs are effectively forming corresponding
structures with similar scale heights. Together, Figs 12 and 13 confirm
that early gaseous discs are able to form both thick and thin stellar
discs.
4.3 On why thin discs are smaller than thick discs
The Milky Way’s thin disc is more radially extended than its thick
disc. This contrasts with our measurements, showing the thick disc
is often larger than the thin disc, which is also shown in local galaxy
Figure 14. The relative thickness and radial sizes of thin and thick discs
in individual two-disc galaxies. The ratio hthin/hthick is plotted against
zthin/zthick for each galaxy, represented by black circles filled with colour
to indicate galaxy mass. Galaxies at z = 0 (Yoachim Dalcanton 2006;
Comerón et al. 2018) and the Milky Way (Bland-Hawthorn Gerhard 2016)
are overplotted with black dots and a black star, respectively.
samples structurally (Yoachim Dalcanton 2006; Comerón et al.
2012) and chemically (Sattler et al. 2023; Sattler et al. 2024).
The larger size of thick discs in both radius and height than
that of thin discs suggests compaction and expansion processes
preferentially at work on the discs. One mechanism contributing
to larger thick discs could be the inwards radial flow of gas particles
as the proto-gas disc dissipates turbulent energy, conserving the
angular momentum. The less turbulent thin gas disc ends up having
a shorter radius to increase the centrifugal force against gravity with
less pressure support (Yoachim Dalcanton 2006).
There is another mechanism that may selectively expand thick
discs (or single thick discs before thin disc formation) in radius
and vertical height. Bland-Hawthorn et al. (2024) demonstrate the
gas-rich turbulent starburst phase involves significant mass ejection
which weakens disc potentials. Following the weakening of the
disc potential due to the mass loss with the axial ratio remaining
unchanged, the velocity dispersion ratio of the ensemble disc stars
σz/σR is conserved and thus existing stars subsequently adiabatically
expand vertically and radially. The episodic or continuous mass
ejection makes the thick disc longer and thicker. When the thinner
disc dominantly forms later with low gas fraction and less turbulence,
the mass loading of outflow decreases (Hayward Hopkins 2017),
making this process inefficient.
In addition to the mechanisms active during the proto-gaseous
disc phase, the thin disc is preferentially scattered by the density
fluctuations in the disc mid-plane, including GMCs, clumps, spiral,
bars, resulting in further compaction of the thin disc relative to the
thick disc (Bournaud et al. 2009). This may explain why the disc
scale length has a shallower slope with mass relative to the thick
discs and single discs (see the left figures of Figs 5 and 6). The
radial sizes of both thin and thick discs increase as the discs acquire
stellar mass, but the thin discs are more prone to compaction due to
heating, leading to smaller disc radial growth per unit mass increase
compared to the thick disc.
Fig. 14 compares the relative thickness and radial sizes of thin and
thick discs in galaxies, showing that thin discs are shorter in both
radius and vertical height compared to thick discs. Despite some
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outliers, galaxies appear to form a positive correlation, indicating that
thinner thin discs, relative to thick discs, within the same galaxies are
also radially shorter. However, the correlation of our measurements
alone is not statistically significant with a spearman rank coefficient
of r = 0.2 and p−value of 0.25. To confirm this correlation, we in-
clude z = 0 results from Yoachim Dalcanton (2006) and Comerón
et al. (2018), restricting the latter to galaxies without disc truncations.
This redshift z = 0 sample shows positive correlation (r = 0.40,
p−value = 0.01) and when combined with our data provide higher
statistical significance (r = 0.36, p−value = 0.001).
The values (zthin/zthick, hthin/hthick) are expected to be noisier
compared to (hthin/zthin, hthick/zthick) due to potential degeneracies
and correlations between the denominator and numerator in the fitting
process. This correlation may qualitatively support the disc evolution
scenario discussed above e.g. the selective compaction or expansion
of thin/thick discs. Galaxies may also move within this diagram over
time. As thick disc growth slows while the thin disc continues to gain
mass and expand in both height and radius (inside-out disc evolution;
Minchev, Chiappini Martig 2013), data points may shift from the
lower left to the upper right along the sequence. In the downsizing
thin disc formation, more massive galaxies might have had more
time for their thin discs to grow; however, such trends are not clearly
evident in the diagram. Constraining stellar ages could further help
test these scenarios by revealing how galaxies evolve within the
diagram.
The formation of a smaller thin disc within an existing thick disc
suggests an outside-in transformation when the thin disc emerges in
pre-existing thick disc. Tadaki et al. 2020 found that in massive star-
forming galaxies at z ∼ 2 (M∗ 1011
M), the star-forming region
is about half the size of the pre-existing stellar disc, possibly marking
the onset of thin disc formation. According to the downsizing
scenario, such massive galaxies may have formed thin discs earlier
than the most massive galaxies in our sample (∼ 8 Gyr ago; see
Fig. 9).
4.4 Origin of thick and thin discs
In this section, we discuss which formation scenarios of thin and thick
discs are supported by our findings. By directly observing galaxies in
the past, we confirm sequential stellar disc formation: galaxies first
form a thick disc and later evolve into two-disc composite galaxies
by forming a subsequent thin disc from within. The accretion of ex
situ stars from small satellites cannot be the primary mechanism for
the thick disc formation. Bringing satellites to the galactic disc scale
via dynamical friction, in the absence of a pre-existing disc, would
take longer (Pe˜
narrubia, Kroupa Boily 2002; Villalobos Helmi
2008) than the observed early appearance of dissipative gas discs at
z ∼ 4–7 (as early as 700 Myr, Neeleman et al. 2020; Rizzo et al.
2020; Lelli et al. 2021; Tsukui Iguchi 2021; Rowland et al. 2024).
These early discs likely form through gas-rich mergers and/or cold
gas accretion. Similarly, slow ‘progressive thickening’ is inconsistent
with our observations, as galaxies seem to have thick discs as early
as z ∼ 3. However, it may still be viable if the process occurs on a
much shorter timescale than our observations can capture.
Over the long term, these mechanisms may contribute to the
growth of the thick disc. Both thin and thick disc masses increase
with galaxy mass, following different power-law slopes (Fig. 11). If
we interpret this as galaxies evolving along the tracks, they continue
increasing their thick disc mass (albeit less efficiently than their thin
discs) after forming a thin disc. Satellite accretion and heating may
be a viable mechanism for thick disc growth at later stages (Pinna
et al. 2019a, b; Martig et al. 2021), driving the continuous growth of
thick discs as total galaxy mass increases.
We demonstrate that sequential formation, thick then thin, pro-
ceeds in a downsizing manner, where more massive galaxies form
thin discs earlier. By linking to high-z gas kinematics, we highlight
the role of ISM turbulence in determining the timing of thin disc
formation (Section 4.1). This is consistent with the scenario in
which thick discs rapidly form in chaotic gas-rich turbulent disc
and thin discs subsequently form from quiescent low gas-fraction
discs (Silva et al. 2021; Yu et al. 2023; Bland-Hawthorn et al.
2025).10
Under gravitational stability-regulated disc formation, the
gas turbulence is related to gas fraction fgas by v/σ ∝ 1/fgas (Genzel
et al. 2011), suggesting that higher fgas leads to higher turbulence
(lower v/σ). High turbulence pressure may prohibit the thin disc
formation (Donkelaar et al. 2022). In cosmic downsizing, more
massive galaxies convert gas into stars more efficiently (Behroozi
et al. 2013), forming thick discs earlier (Comerón 2021). As they
achieve lower fgas and lower turbulence, they transition to form thin
discs earlier.
Archaeological studies of nearby edge-on galaxies also support
the downsizing picture. More massive galaxies tend to have older
thick discs with higher [α/Fe] than low-mass galaxies, indicating
rapid and early thick disc formation in massive galaxies (Pinna et al.
2019a, b; Martig et al. 2021; Sattler et al. 2023; Sattler et al. 2024).
Ground-based observations support this view showing that disc
turbulence and fgas increases at higher redshifts (Förster Schreiber
et al. 2009; Genzel et al. 2011; Wisnioski et al. 2015; Übler et al.
2019; Tacconi et al. 2020; Rizzo et al. 2024). Although recent ALMA
observations have revealed surprisingly low relative turbulence, with
v/σ values as high as ∼ 10 at z∼ 4, this remain consistent with this
downsizing framework (Rizzo et al. 2020; Lelli et al. 2021). The
available spatially resolved kinematic measurements are generally
biased towards massive systems (Fig. 12), which may already host
substantial thick discs and thus exhibit lower fgas. Interestingly, some
ALMA detected lower mass galaxies (e.g. Neeleman et al. 2020;
Tsukui Iguchi 2021; Parlanti et al. 2023) show enhanced turbulence
(low v/σ) and high gas fractions, suggesting ongoing thick disc
formation. For example, BRI 1335–0417 has a high gas fraction of
∼70 per cent and turbulence v/σ ∼ 2.5 ± 0.5, corresponding to an
axial ratio q ∼ 5, clearly placing it in the thick disc formation regime
(Fig. 12). Additionally, it uniquely shows spiral and bar structures
(Tsukui Iguchi 2021; Tsukui et al. 2024).
Understanding the role of gas-rich turbulent discs in thick disc
formation – and the puzzling presence of spiral and bar in such
environments – has advanced significantly through numerical simula-
tions. Recent simulations of gas-dominated discs show that high gas-
fraction discs can rapidly develop spirals and bars, while young stellar
bars form through disc shear flows (Bland-Hawthorn et al. 2024).
These simulations also reveal an intriguing mechanism: stochastic
star formation within complex gas substructures induces bulk motion
(sloshing) of the gas disc relative to the halo potential, dispersing
stars. The energy from this bulk motion is transferred to the stars,
contributing to thick disc formation (Bland-Hawthorn et al. 2025).
10In gas-rich turbulent discs, Yu et al. (2023) suggest that thick disc stars form
in hot orbits (‘born-hot’), whereas Silva et al. (2021); Bland-Hawthorn et al.
(2025) propose that most stars form near the disc mid-plane and are quickly
heated (clumps and sloshing, ‘instant thickening’). The structural analysis in
this paper cannot distinguish them, but colour gradients or rest-frame ultra
violet (UV) observations for a single (thick) disc in high-z galaxies may help
differentiate them.
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In these early epochs, clumps may have also contributed to stellar
scattering (Silva et al. 2020, 2021).
A potential contradiction to our findings ‘thick disc first, thin
disc later’ is the presence of an old, metal-poor thin disc in the
Milky Way (Nepal et al. 2024). However, this low-mass component
may have formed through later satellite accretion events, where
dynamical friction drags satellites into the disc plane, preferentially
from prograde satellites (Walker, Mihos Hernquist 1996), or it
may consist of stars that survived heating in the gas-rich disc (Silva
et al. 2021; Yu et al. 2023; Bland-Hawthorn et al. 2025).
The relative importance of different growth mechanisms likely
depends on a galaxy’s properties (e.g. total mass at a given epoch)
and formation history (e.g. Yu et al. 2021; Pinna et al. 2024). This
study demonstrates the JWST potential to understand the Milky
Way’s formation history by directly examining Milky Way-sized
progenitors at earlier epochs (Fig. 9) and determine if the Milky Way
has a distinct formation history compared to others (e.g. Rey et al.
2023).
5 SUMMARY
We present the first systematic thin/thick disc decomposition of
high-redshift galaxies using a sample of 111 edge-on galaxies
from the flagship JWST imaging fields from JADES, FRESCO,
CEERS, COSMOS-Web, PRIMER, and NGDEEP. To create a robust
sample, we cross-match JWST detections with the 3D HST catalogue
for reliable redshifts and galaxy parameters. The sample covers a
wide redshift range, 0.1 z 3.0, encompassing ∼ 70 per cent of
cosmic history up to a lookback time of 11.4 Gyr.
We fit a 3D disc model, where the 3D luminosity density follows
a radially exponential and vertically sech2
function, to the JWST
galaxy images, corresponding to the rest-frame Ks band (z 1.45)
or H band (z 1.45). Most galaxies are well fit with a single disc
model, while 44 galaxies show systematic excess light above the disc
mid-plane, necessitating a second disc component. With Bayesian
Information Criteria (BIC) and visual inspection, we classify galaxies
into categories of (1) well-fitted by a single disc and (2) requiring
two discs (thin and thick discs). We also assessed the need for a bulge
component. We find 44 ‘two disc’ galaxies (25 with bulge and 19
without bulge) and 67 ‘single disc’ galaxies (39 with bulge and 28
without bulge). The most distant two disc galaxy we identify is at
redshift up to z = 1.96.
We identify well-defined correlations between some measured
disc parameters across our sample, despite the wide baseline across
cosmic time. The radial length, hR, and vertical height, z0, of all disc
categories (single disc, thin and thick discs) correlate strongly with
total stellar mass and disc mass, independent of the cosmic time.
However, the ratio of radial length and vertical height (hR/z0) does
not correlate with host galaxy mass or individual disc mass. Single
discs occupy similar regions to thick discs rather than thin discs,
suggesting the sequential formation that thick discs dominantly form
first before galaxies develop a second, detectable thin disc (Figs 5
and 6).
The transition from single to double discs occurred around ∼
8 Gyr ago in high-mass galaxies (109.75
–1011
M), somewhat earlier
than the transition around ∼ 4 Gyr ago in low-mass galaxies
(109.0
–109.75
M). The shift of the onset indicates the sequential
thick then thin disc formation proceeds in a ‘downsizing’ manner,
where higher mass galaxies tend to form thin discs earlier and lower
mass galaxies increasingly form thin discs at later time (Fig. 9).
Lower mass galaxies have higher thick-to-thin disc mass ratios
(Fig. 10), consistent with the delayed formation of thin disc in
low mass galaxies and aligning with the results for z = 0 galaxies
(Yoachim Dalcanton 2006; Comerón et al. 2014). Both thin and
thick disc masses increase with total stellar mass, roughly described
by single slopes across a wide range of masses (2.5–3 dex, Fig. 11).
The slope for thin discs is steeper than for thick discs, crossing at a
log(M∗[M]) ∼ 10, creating the anticorrelation between the thick-
to-thin disc mass ratios and galaxy stellar masses.
Despite the dominant sequential picture of thick to thin disc
formation revealed in this study, Fig. 11 indicates the co-evolution
of the two discs, with the thick disc continuously growing as the
galaxy grows (although less efficient than thin disc growth). This is
in contrast to a simple sequential scenario where two discs form in
entirely separate epochs.
We propose that the Toomre-Q self-regulated star formation coher-
ently explains the above findings (Section 4.1), linking our structural
measurements for stellar discs with available gas kinematics of gas
discs from recent ALMA and ground-based IFU surveys (Fig. 12).
High-mass galaxies achieve lower gas fractions early on, enabling
them to host less turbulent gas discs and form thin discs earlier in
time. The declining gas fraction over time allows more lower-mass
galaxies to form thin discs at later epochs.
ACKNOWLEDGEMENTS
We are grateful to the anonymous reviewer for their constructive
feedback, which has significantly improved the clarity and quality of
this paper. TT is grateful to the conference organizers and financial
support of the ELT Science in Light of JWST meeting, held in Miyagi,
Japan in June 2024. Attending the conference helped to focus this
research and the eventual paper. TT thanks Bruce Elmegreen, Eric
Emsellem, Mark Krumholz, Andreas Burkert, Masashi Chiba, Trevor
Mendel, Lucas Kimmig, Lucas Valenzuela and Federico Lelli for
insightful discussions and Mahsa Kohandel and Hannah Übler for
sharing their data (Übler et al. 2019; Kohandel et al. 2024). This
research was supported by the Australian Research Council Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
through project number CE170100013. This work was supported in
part by Japan Foundation for Promotion of Astronomy. This work is
based on observations made with the NASA/ESA/CSA JWST. The
data were obtained from the Mikulski Archive for Space Telescopes
at the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under
NASA contract NAS 5–03127 for JWST. These observations are
associated with programme # 1180, 1210, 1895, 2079, 2514, 1181,
3577, 1345, 2750, 2279, 1727, 1837, 1283, 2198. The data products
presented herein were retrieved from the Dawn JWST Archive (DJA).
DJA is an initiative of the Cosmic Dawn Center, which is funded
by the Danish National Research Foundation under grant no. 140.
This work made use of the following software packages: ASTROPY
(Astropy Collaboration 2013, 2018, 2022), JUPYTER (Perez
Granger 2007; Kluyver et al. 2016), MATPLOTLIB (Hunter 2007),
NUMPY (Harris et al. 2020), PANDAS (Wes McKinney 2010; pandas
development team 2024), PYTHON (Van Rossum Drake 2009),
SCIPY (Virtanen et al. 2020; Gommers et al. 2025), CYTHON, and
SCIKIT-IMAGE (van der Walt et al. 2014). This research has made
use of NASA’s Astrophysics Data System. This research made use
of Photutils, an Astropy package for detection and photometry of
astronomical sources (Bradley et al. 2024) and MATHEMATICA (Wol-
fram Research 2024). Software citation information aggregated using
The Software Citation Station (Wagg Broekgaarden
2024; Wagg, Broekgaarden Gültekin 2024).
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DATA AVAILABILITY
The data products are available at DJA The DAWN JWST Archive
https://dawn-cph.github.io/dja/index.html. The specific observations
included in the mosaic images used in the paper can be accessed via
DOI: 10.17909/ehkk-th30
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APPENDIX A: OUR USED DATASETS AND
OBSERVATIONAL PROGRAMMES
Table A1 summarize the observational programmes used in this
studies.
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Table A1. Summaries of the JWST programmes included in the DJA mosaic images used in the paper. The
table lists: the mosaic field name defined by DJA, the version of the reduced mosaic images used in the paper,
JWST programme IDs used to produce the mosaic images, and PI names of the observation programme.
Mosaic field name DJA version JWST programme IDs PI names
GOODS-South (-SW) 7.1 (7.0) #1180/1210 D. Eisenstein/N. Luetzgendorf
#1895 P. Oesch
#2079 S. Finkelstein
#2514 C. Williams
GOODS-North 7.3 #1181 Eisenstein
#1895 P. Oesch
#2514 C. Williams
#3577 E. Egami
CEERS-full 7.2 #1345 S. Finkelstein
#2750 P. Arrabal Haro
#2514 C. Williams
#2279 R. Naidu
PRIMER-COSMOS-East 7.0 #1727 J. Kartaltepe
PRIMER-COSMOS-West #1837 J. Dunlop
PRIMER-UDS-South
PRIMER-UDS-North
7.0 #1837 J. Dunlop
NGDEEP 7.0 #2079 S. Finkelstein
#1283 G. Oestlin
#2198 L. Barrufet
APPENDIX B: COMPOSITE COLOUR IMAGES
OF GALAXIES
Figs B1–B3 show the thee colour composite JWST NIRCam
(F115W/F277W/F444W) images of our sample galaxies continued
from Fig. 1. For galaxies without those filter bands available, we
instead show other filter JWST NIRCam images which are indicated
in lower right corner. If fewer than three filters are available, we show
a grey scale image.
Figure B1. Continued from the Fig. 1. NIRCam F227W; F356W; F444W colour composite images unless noted by red texts which denote the filters used to
make the composite.
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Figure B2. Continued from the Fig. 1. 0.5 arcsec scale bar is shown instead of 1 arcsec.
Figure B3. Continued from the Fig. 1.
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Figure C1. Relative error in scale height as a function of input scale height
(in pixels). The shaded regions represent 1σ uncertainty for 16th percentile
of the SNR.
APPENDIX C: FITTING SYSTEMATICS AND
UNCERTAINTIES
In this section, we assessed systematic uncertainty on our structural
measurements.
C1 Minimum recoverable disc scale height
The first consideration is how reliably we can recover the scale
height relative to image pixel sizes. To demonstrate this, we generate
mock simulated images with a typical disc scale radius of ∼10 pixels
and a range of disc scale heights. We convolve the simulated disc
with the F444W PSF, which provides the most conservative estimate
of accuracy (as the F444W PSF is the largest compared to other
filters F277W, F356W). We then refit the simulated image using
an appropriate variance image, sky noise, read noise, and Poisson
variance of the source based on the typical effective gain. Fig. C1
shows the relative error in the recovered scale height as a function
of the input scale height for both the 16th percentile SNR, where
most of the sample (84 per cent) has a higher SNR and thus better
accuracy, and the median SNR for the sample. This demonstrates that
we can recover the scale height down to 0.2 pixels with ∼20 per cent
accuracy for most of the data. We adopt this value as a conservative
lower limit for galaxies that reach this boundary.
C2 Inclination deviation from a perfect edge-on
We quantify the bias introduced by deviations from a perfect edge-
on orientation. Slight inclination deviations, of 7 deg, expected
for our sample (64th percentile) has been shown to minimally affect
structural measurements (Grijs et al. 1997). However, this affect may
vary depending on the image quality, the intrinsic properties of the
discs, and the presence of a second disc or central bulge. To assess
whether inclination effects affect our results we generate simulated
images based on the measured structural parameters of our galaxy
sample (111 best-fitting models), varying the disc inclination over a
range of i = [0, 15 deg] in 0.5 deg intervals. The simulated images
were further convolved with the PSF and had Gaussian white noise
added from the original variance map. We then refit these convolved
simulated images using a model assuming a 90 degree inclination
(as adopted in our study) and obtained the fractional biases in the
structural parameters, shown in Fig. C2. We use the best fit model
classified in Section 3 (e.g. a disc, a disc + bulge, two discs, and
two discs + bulge), where single disc, thin disc, and thick disc are
denoted in black circle, blue triangle, red square respectively. The
error bar shows the standard deviation encompassing our sample of
galaxies, representing galaxy to galaxy variation due to the intrinsic
structure of disc and image quality for our sample.
As expected the bias is largest for thin disc structures and smallest
for thick disc structures. We found 30 per cent, 20 per cent and
10 per cent overestimation are expected for vertical scale height
measurements if galaxies have 5 deg deviation from the perfect edge-
on for thin, single, and thick discs, respectively. The same value of
30 per cent is found in Grijs et al. (1997) for a similar intrinsic axial
ratio q = 0.11 of a thin disc. For galaxies with q 0.3 adopted in
our sample (see Fig. 3), the assumption of 90 deg lead to median
bias of 0.1 per cent, 12 per cent, 1 per cent underestimation for disc
scale radii, 17 per cent, 27 per cent, 9 per cent overestimation for disc
scale height, and 13 per cent, 27 per cent, 6 per cent underestimation
for disc radii/height ratios (values are denoted for single disc, thin
disc, and thick disc, respectively). These variations contribute to the
measured scatter in the reported values.
C3 Systematics from nuisance disc substructures such as dust
lane, disc truncatiotingn, bulges
Figs C3 and C4 summarize our assessment of systematic uncer-
tainties in our modelling due to unaccounted disc substructures and
potential dust extinction. To evaluate how much our fiducial results
are affected by these substructures, we repeat the fitting procedure
using different masks. A ‘bulge mask (r 1.5 kpc)’, a circular mask
with a 1.5 kpc radius centred on the galaxy, is used to exclude the
Figure C2. Fractional change of the derived parameters are shown as a function of inclination deviation from 90 deg i (deg). The error bars denote the range
encompassed by our sample of galaxies (1 σ).
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Figure C3. The measurements for galaxies classified as ‘Single disc’ and ‘disc + bulge’ are compared against fitting results with different masks: mask 1
(‘bulge mask’), mask 2 (‘bulge mask’ + ‘mid-plane mask’) and, mask 3 (‘bulge mask’ + ‘disc truncation mask’). See the text for details. For visual aid, the
solid line shows the 1:1 relation and the dashed lines show 20 per cent range (of linear quantities) from the 1:1 relation.
Figure C4. The measurements for galaxies classified as ‘two discs’ and ‘two discs + bugle’ are compared against fitting results with different masks (same as
Fig. C3). For visual aid, solid line shows the one-to-one line and the dashed line shows +/– 20 per cent from the one-to-one line in linear scaled measurements.
central concentrated light. A ‘mid-plane mask (z z0)’, masks the
region where the latitude is less than the disc scale height z0, is
used to account for disc substructures and potential dust extinction.
Finally, ‘disc truncation mask (R 3hR)’ masks the unmodelled
outer truncation of the disc to assess the potential impact of this
omission. We use the combination of those masks: mask 1 (‘bulge
mask’), mask 2 (‘bulge mask’ + ‘mid-plane mask’) and, mask 3
(‘bulge mask’ + ‘disc truncation mask’) and refit a two disc model
for two disc galaxies and one disc for single disc galaxies without a
bulge component, which is masked in all cases.
Figs C3 and C4 compare the refit results with masking against our
fiducial fit results for galaxies classified as single- and double-disc
galaxies, respectively. The impact of masking results is summarized
by the Table C1. The scatter and mean values quantify the deviation
introduced by masking, relative to the fiducial (unmasked) fit. The
comparison shows that masking does not introduce a significant
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Table C1. Fractional scatter and mean deviation of measurements obtained using different masks relative to the fiducial (unmasked) fit.
Parameter Disc component Mask 1 (bulge) Mask 2 (bulge + mid-plane) Mask 3 (bulge + truncation)
Scatter/mean dev. (per cent) Scatter/mean dev. (per cent) Scatter/mean dev. (per cent)
zsingle Single disc 8.21/−2.59 8.78/−6.04 8.82/−3.09
zthin Thin disc 11.07/−1.30 22.29/−14.45 19.34/0.02
zthick Thick disc 6.79/−0.94 8.90/−3.40 7.37/1.34
hsingle Single disc 12.16/1.62 12.47/−0.49 21.92/−6.70
hthin Thin disc 7.62/0.47 11.61/−1.59 16.69/1.96
hthick Thick disc 3.01/0.79 4.54/−2.89 40.26/−14.31
systematic shift in the refit results, as the mean deviation is smaller
than the introduced scatter. This suggests that the reduced amount of
available data to constrain the structural parameters has a greater
effect than the structural differences in the masked regions. As
expected, the mid-plane mask primarily affects disc heights, while the
truncation mask has a greater impact on disc radii. This validates the
fiducial fit and confirms that the potential mid-plane disc structure
and disc truncations do not affect our measurements significantly.
The moderate mean deviation for height measurements using mid-
plane mask is consistent with the dust effect ∼ 11 per cent estimated
in similar bands (Bizyaev Mitronova 2009).
Considering the discussions in this section and Appendix C2, the
systematic uncertainty from the disc inclination dominates in our
measurements. The thin disc is most affected by the inclination
effect, introducing a median bias of approximately 12 per cent
underestimation and 27 per cent overestimation in the measured
disc size and height, with smaller biases for single and thick discs.
Therefore, the systematic uncertainty is minor compared to the
dynamic range of the measurements and seen trend (e.g. Figs 5
and 6). The visual exclusion of face-on discs with dust morphology
further reduce the uncertainty than this estimate. These uncertainties
contribute primarily to the scatter in the correlation, while the median
trends are less affected.
APPENDIX D: DISTRIBUTION OF GALAXY
AND DISC STRUCTURAL PARAMETERS
Table D1 presents the properties of the edge-on galaxies in this study,
including physical parameters extracted from 3D-HST (Skelton
et al. 2014; Momcheva et al. 2016) and measured disc structural
parameters. Fig. D1 shows the physical properties of host galaxies
and individual discs (single, thin, and thick discs) with scatter
plots illustrating the relationships between different parameters and
diagonal panel displaying the histogram of each parameter. The offset
from the galaxy main sequence is computed using the main sequence
defined by Popesso et al. (2023). Fig. D2 shows similar corner plot
showing the physical properties of two-disc galaxies, focusing on the
inter-correlation of thin and thick discs within the same galaxies.
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Table
D1.
Properties
of
edge-on
galaxies
in
our
sample:
galaxy
ID,
right
ascension
(RA),
declination
(Decl.),
redshift
(
z),
stellar
mass
(log
(
M
∗
/
M

)),
and
the
best-fitting
model.
The
best-fitting
model
is
denoted
as
0:
a
disc,
1:
a
disc
+
bulge,
2:
two
discs,
3
two
discs
+
bulge
(see
details
in
Section
2.4
).
For
each
galaxy,
it
lists
the
radial
scale
length
h
R
,
vertical
scale
height
(
z
0
),
mid-plane
intensity
J
0
,
disc
stellar
mass
M
disc
for
either
the
single
or
thin
disc
(in
the
case
of
galaxies
with
two
discs),
followed
by
those
for
thick
disc.
R.A.
and
Decl.
are
sourced
from
the
DJA
photometric
catalogue
(Valentino
et
al.
2023
).
Redshift
and
stellar
mass
are
extracted
from
HST
-3D
catalogue
(Skelton
et
al.
2014
;
Momche
v
a
et
al.
2016
).
Indi
vidual
disc
masses
are
deri
ved
by
assuming
the
same
mass-to-light
ratio
for
all
components,
based
on
the
best-fitting
model
and
the
total
stellar
mass
(Section
3
).
Statistical
uncertainties
(1
σ
)
are
provided
for
individual
parameters,
and
systematic
uncertainties
are
discussed
in
Appendix
C
.
ID
R.A.
Decl.
z
log(
M
∗
)
Best
h
R,
single
/
thin
z
0
,
single
/
thin
J
0
,
single
/
thin
log
M
disc
,
single
/
thin
h
R,
thick
z
0
,
thick
J
0
,
thick
log
M
disc
,
thick
(deg)
(deg)
M

model
(kpc)
(pc)
(mag
arcsec
2
)
M

(kpc)
(pc)
(mag
arcsec
2
)
M

1
53
.0997
−27
.
7863
0
.731
9
.57
3
2.96
±0
.
01
237
±3
19.25
±0
.
01
9.45
±0
.
05
4.13
±0
.
08
915
±23
22.56
±0
.
09
8.86
±0
.
06
2
53
.1575
−27
.
7765
0
.84
8
.85
1
2.96
±0
.
05
314
±7
22.71
±0
.
04
8.82
±0
.
98
–
–
–
–
3
53
.0614
−27
.
7728
2
.632
10
.75
0
2.22
±0
.
02
395
±4
19.60
±0
.
02
–
–
–
–
–
4
53
.1368
−27
.
7689
0
.366
10
.02
3
3.67
±0
.
00
386
±0
18.89
±0
.
00
9.78
±0
.
01
5.28
±0
.
00
1281
±1
21.00
±0
.
00
9.61
±0
.
01
5
53
.1007
−27
.
7668
0
.893
9
.43
1
2.71
±0
.
03
346
±5
21.01
±0
.
03
9.42
±0
.
22
–
–
–
–
6
53
.1985
−27
.
7442
1
.155
10
.41
3
3.62
±0
.
02
256
±6
19.91
±0
.
02
10.24
±0
.
08
3.78
±0
.
05
632
±23
21.81
±0
.
14
9.89
±0
.
09
7
189
.22
62
.153
0
.457
8
.9
3
2.55
±0
.
02
169
±5
20.95
±0
.
03
8.69
±0
.
19
2.80
±0
.
04
397
±14
22.51
±0
.
15
8.48
±0
.
18
8
189
.217
62
.1614
0
.434
9
.11
1
2.88
±0
.
01
348
±1
21.09
±0
.
01
9.05
±0
.
10
–
–
–
–
9
189
.247
62
.1581
0
.866
8
.59
0
1.53
±0
.
03
178
±10
22.23
±0
.
06
–
–
–
–
–
10
189
.269
62
.1677
0
.226
8
.6
1
3.75
±0
.
01
318
±1
21.56
±0
.
00
8.52
±0
.
05
–
–
–
–
11
189
.275
62
.1695
0
.443
9
.04
2
1.65
±0
.
03
123
±11
20.71
±0
.
07
8.67
±0
.
05
1.84
±0
.
03
274
±11
21.38
±0
.
19
8.80
±0
.
04
12
189
.218
62
.1722
0
.457
9
.21
3
3.34
±0
.
05
174
±8
21.27
±0
.
04
8.65
±0
.
09
4.26
±0
.
03
444
±6
21.65
±0
.
06
9.01
±0
.
08
13
189
.295
62
.1914
0
.476
8
.98
1
2.21
±0
.
01
261
±1
20.92
±0
.
01
8.96
±0
.
19
–
–
–
–
14
189
.228
62
.1909
0
.254
9
.63
3
2.22
±0
.
00
114
±1
18.56
±0
.
01
9.29
±0
.
01
2.71
±0
.
00
334
±1
19.76
±0
.
01
9.36
±0
.
01
15
189
.048
62
.2236
0
.83
8
.53
0
1.90
±0
.
06
253
±16
22.47
±0
.
08
–
–
–
–
–
16
189
.155
62
.2262
0
.846
10
.49
3
3.39
±0
.
02
233
±3
19.07
±0
.
02
10.30
±0
.
04
4.18
±0
.
04
731
±10
21.23
±0
.
05
10.02
±0
.
04
17
189
.022
62
.2328
1
.332
9
.88
1
2.83
±0
.
08
390
±15
21.07
±0
.
08
9.82
±0
.
21
–
–
–
–
18
189
.354
62
.2369
1
.724
8
.75
0
3.13
±0
.
11
388
±20
23.05
±0
.
08
–
–
–
–
–
19
189
.096
62
.242
0
.191
8
.91
2
2.36
±0
.
11
66
±12
22.97
±0
.
15
7.46
±0
.
10
2.50
±0
.
01
345
±1
21.24
±0
.
01
8.89
±0
.
00
20
189
.281
62
.2533
1
.205
8
.83
0
2.24
±0
.
10
185
±27
22.10
±0
.
16
–
–
–
–
–
21
189
.263
62
.2741
0
.852
9
.02
0
1.76
±0
.
02
237
±7
21.15
±0
.
04
–
–
–
–
–
22
189
.177
62
.2777
2
.288
8
.72
0
1.97
±0
.
13
219
±36
22.57
±0
.
19
–
–
–
–
–
23
189
.134
62
.2792
1
.038
9
.85
3
3.88
±0
.
07
148
±18
19.97
±0
.
06
9.38
±0
.
09
4.51
±0
.
04
460
±12
20.70
±0
.
10
9.64
±0
.
08
24
189
.398
62
.2865
0
.64
10
.1237
3
3.77
±0
.
01
332
±3
18.97
±0
.
01
9.95
±0
.
02
4.93
±0
.
04
791
±11
21.03
±0
.
06
9.62
±0
.
03
25
189
.143
62
.2891
0
.446
9
.33
3
2.55
±0
.
02
168
±4
19.95
±0
.
02
8.97
±0
.
06
3.27
±0
.
02
514
±6
21.24
±0
.
04
9.05
±0
.
05
26
189
.392
62
.293
0
.531
8
.9
1
2.39
±0
.
02
359
±5
21.32
±0
.
04
8.83
±0
.
19
–
–
–
–
27
189
.199
62
.2983
0
.601
8
.83
0
1.99
±0
.
02
292
±5
21.50
±0
.
03
–
–
–
–
–
28
189
.332
62
.3023
2
.601
10
.1
0
2.60
±0
.
04
432
±8
21.72
±0
.
03
–
–
–
–
–
29
189
.135
62
.3049
1
.805
10
.02
1
3.70
±0
.
04
500
±7
21.67
±0
.
04
9.97
±0
.
22
–
–
–
–
30
189
.391
62
.3072
0
.545
9
.48
1
3.09
±0
.
01
413
±2
20.49
±0
.
02
9.45
±0
.
06
–
–
–
–
31
189
.26
62
.3136
1
.246
9
.55
1
2.61
±0
.
07
303
±15
21.23
±0
.
09
9.47
±0
.
32
–
–
–
–
32
214
.827
52
.7416
0
.903
8
.51
0
2.23
±0
.
13
242
±33
23.05
±0
.
16
–
–
–
–
–
33
214
.856
52
.7623
0
.244
8
.54
2
1.13
±0
.
03
174
±9
21.73
±0
.
05
8.02
±0
.
04
2.04
±0
.
04
431
±11
22.45
±0
.
11
8.38
±0
.
02
34
214
.833
52
.747
1
.764
9
.08
0
2.44
±0
.
13
302
±30
23.12
±0
.
13
–
–
–
–
–
35
215
.122
52
.9561
0
.65
9
.44
3
3.06
±0
.
08
220
±18
21.13
±0
.
08
8.90
±0
.
11
3.35
±0
.
04
517
±12
21.35
±0
.
10
9.22
±0
.
10
36
215
.074
52
.9248
0
.571
8
.79
3
1.72
±0
.
30
113
±78
22.22
±0
.
42
8.00
±0
.
59
2.19
±0
.
07
298
±22
21.83
±0
.
33
8.68
±0
.
46
37
215
.027
52
.8952
2
.211
9
.61
1
3.35
±0
.
09
515
±10
22.92
±0
.
07
9.49
±0
.
61
–
–
–
–
38
214
.876
52
.7871
1
.283
10
.07
2
3.03
±0
.
07
307
±36
20.31
±0
.
21
9.85
±0
.
12
3.18
±0
.
12
556
±73
21.44
±0
.
68
9.67
±0
.
18
39
214
.775
52
.7504
0
.733
9
.39
1
3.19
±0
.
01
395
±2
20.54
±0
.
01
9.38
±0
.
09
–
–
–
–
40
214
.92
52
.8747
1
.22
8
.82
0
2.35
±0
.
06
302
±16
22.39
±0
.
07
–
–
–
–
–
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MNRAS 540, 3493–3522 (2025)
Table
D1
–
continued
ID
R.A.
Decl.
z
log(
M
∗
)
Best
h
R,
single
/
thin
z
0
,
single
/
thin
J
0
,
single
/
thin
log
M
disc
,
single
/
thin
h
R,
thick
z
0
,
thick
J
0
,
thick
log
M
disc
,
thick
(deg)
(deg)
M

model
(kpc)
(pc)
(mag
arcsec
2
)
M

(kpc)
(pc)
(mag
arcsec
2
)
M

41
214
.814
52
.805
0
.778
9
.49
2
2.47
±0
.
03
214
±6
20.12
±0
.
02
9.15
±0
.
02
4.47
±0
.
06
666
±11
21.83
±0
.
07
9.22
±0
.
02
42
214
.895
52
.8719
0
.691
8
.66
2
1.98
±0
.
12
113
±58
21.99
±0
.
20
8.17
±0
.
19
2.20
±0
.
08
367
±36
22.59
±0
.
36
8.49
±0
.
09
43
214
.951
52
.9364
0
.713
9
.95
3
1.11
±0
.
01
58
17.66
±0
.
02
9.30
±0
.
03
6.04
±0
.
02
362
±1
20.48
±0
.
01
9.71
±0
.
03
44
214
.765
52
.8184
1
.616
9
.57
3
2.69
±0
.
17
239
±24
20.63
±0
.
19
9.16
±0
.
17
4.02
±0
.
19
668
±50
22.37
±0
.
31
9.08
±0
.
18
45
214
.845
52
.9024
0
.782
9
.16
1
2.86
±0
.
02
335
±3
21.22
±0
.
02
9.13
±0
.
23
–
–
–
–
46
150
.158
2
.30622
0
.886
9
.35
2
2.42
±0
.
09
62
20.02
±0
.
10
8.96
±0
.
04
2.71
±0
.
09
399
±15
21.74
±0
.
11
9.13
±0
.
03
47
150
.185
2
.30793
0
.339
9
.26
3
1.52
±0
.
01
158
±2
19.37
±0
.
02
8.96
±0
.
05
2.06
±0
.
02
507
±6
21.13
±0
.
04
8.90
±0
.
05
48
150
.168
2
.31407
0
.896
10
.06
3
3.47
±0
.
02
243
±4
19.23
±0
.
01
9.84
±0
.
04
5.60
±0
.
06
704
±11
21.39
±0
.
07
9.65
±0
.
04
49
150
.156
2
.34599
1
.961
9
.55
2
1.32
±0
.
08
139
±27
21.19
±0
.
23
9.06
±0
.
12
4.74
±0
.
33
644
±36
23.45
±0
.
24
9.38
±0
.
06
50
150
.143
2
.39619
1
.346
9
.54
2
2.96
±0
.
23
97
±120
21.21
±0
.
80
8.83
±0
.
51
3.08
±0
.
07
417
±26
21.30
±0
.
22
9.45
±0
.
12
51
150
.147
2
.39797
0
.574
9
.23
1
1.86
±0
.
02
197
±3
20.58
±0
.
03
9.20
±0
.
26
–
–
–
–
52
150
.175
2
.43063
0
.889
9
.14
1
3.98
±0
.
27
558
±27
23.25
±0
.
18
8.95
±0
.
48
–
–
–
–
53
150
.155
2
.44345
0
.34
10
.1267
3
3.20
±0
.
01
268
±3
18.70
±0
.
01
9.75
±0
.
01
3.76
±0
.
01
553
±3
19.41
±0
.
03
9.85
±0
.
01
54
150
.185
2
.44561
0
.679
9
.07
0
2.66
±0
.
03
433
±5
21.86
±0
.
02
–
–
–
–
–
55
150
.171
2
.44687
2
.085
8
.9
0
2.06
±0
.
10
229
±28
22.41
±0
.
15
–
–
–
–
–
56
150
.184
2
.45766
0
.378
9
.18
2
1.24
±0
.
07
102
±21
21.05
±0
.
19
8.25
±0
.
11
2.37
±0
.
03
477
±8
21.24
±0
.
06
9.13
±0
.
02
57
150
.15
2
.45979
0
.502
8
.56
1
2.19
±0
.
05
307
±9
22.20
±0
.
07
8.52
±0
.
54
–
–
–
–
58
150
.15
2
.4813
0
.683
9
.44
1
2.40
±0
.
01
305
±2
19.61
±0
.
01
9.42
±0
.
06
–
–
–
–
59
150
.058
2
.19537
0
.935
10
.01
1
3.66
±0
.
02
531
±3
20.32
±0
.
01
9.98
±0
.
06
–
–
–
–
60
150
.103
2
.22138
0
.651
9
.21
1
2.51
±0
.
03
390
±5
21.17
±0
.
04
9.14
±0
.
17
–
–
–
–
61
150
.086
2
.22929
1
.155
8
.72
0
2.78
±0
.
12
350
±33
22.71
±0
.
11
–
–
–
–
–
62
150
.057
2
.23075
0
.927
9
.71
2
2.76
±0
.
14
63
19.32
±0
.
15
9.06
±0
.
06
3.38
±0
.
06
488
±10
20.41
±0
.
06
9.60
±0
.
02
63
150
.062
2
.26762
0
.543
8
.98
1
4.47
±0
.
16
290
±12
22.33
±0
.
09
8.71
±0
.
20
–
–
–
–
64
150
.091
2
.28517
0
.751
10
.7412
3
2.93
±0
.
02
375
±3
18.93
±0
.
01
10.59
±0
.
03
5.58
±0
.
19
790
±27
22.16
±0
.
20
9.90
±0
.
08
65
150
.099
2
.29026
0
.362
10
.71
3
1.08
±0
.
00
477
±1
17.76
±0
.
01
10.36
±0
.
01
6.21
±0
.
01
773
±1
20.47
±0
.
00
10.25
±0
.
01
66
150
.089
2
.29717
0
.535
9
.58
2
1.65
±0
.
02
160
±5
19.66
±0
.
02
9.20
±0
.
02
3.09
±0
.
03
471
±7
21.16
±0
.
06
9.34
±0
.
01
67
150
.076
2
.30481
0
.123
9
.05642
3
1.82
±0
.
00
102
±0
18.33
±0
.
00
8.63
±0
.
00
4.50
±0
.
01
327
±0
20.09
±0
.
01
8.82
±0
.
00
68
150
.111
2
.31308
0
.482
9
.48
1
3.71
±0
.
01
405
±2
21.12
±0
.
01
9.45
±0
.
09
–
–
–
–
69
150
.08
2
.31392
0
.381
9
.38
3
2.77
±0
.
02
331
±4
20.25
±0
.
01
9.13
±0
.
04
4.12
±0
.
05
789
±14
22.16
±0
.
07
8.92
±0
.
04
70
150
.085
2
.31729
0
.944
9
.19
1
3.00
±0
.
06
358
±8
21.35
±0
.
07
9.14
±0
.
25
–
–
–
–
71
150
.062
2
.31874
0
.66
8
.87
1
1.93
±0
.
05
298
±9
21.22
±0
.
09
8.82
±0
.
32
–
–
–
–
72
150
.066
2
.35129
0
.34
8
.63
2
1.53
±0
.
09
88
±24
21.27
±0
.
15
8.06
±0
.
12
2.11
±0
.
06
273
±16
21.78
±0
.
22
8.49
±0
.
05
73
150
.087
2
.36566
1
.724
9
.53
0
3.91
±0
.
09
429
±14
22.42
±0
.
05
–
–
–
–
–
74
150
.087
2
.37173
0
.208
9
.68
2
1.88
±0
.
00
140
±1
18.99
±0
.
01
9.31
±0
.
00
2.76
±0
.
01
458
±2
20.39
±0
.
01
9.44
±0
.
00
75
150
.091
2
.37952
0
.454
8
.78
1
2.37
±0
.
06
277
±7
21.71
±0
.
07
8.74
±0
.
31
–
–
–
–
76
150
.091
2
.4093
0
.734
9
.26
2
2.67
±0
.
07
246
±21
21.10
±0
.
07
9.05
±0
.
07
3.21
±0
.
16
598
±64
22.76
±0
.
43
8.85
±0
.
11
77
150
.112
2
.47552
0
.794
9
.19
0
2.91
±0
.
04
507
±9
21.66
±0
.
03
–
–
–
–
–
78
34
.5301
−5
.
18858
0
.294
9
1
3.03
±0
.
07
417
±5
21.46
±0
.
08
8.90
±0
.
06
–
–
–
–
79
34
.3494
−5
.
18658
0
.633
9
.41
1
3.44
±0
.
02
449
±2
20.62
±0
.
01
9.38
±0
.
07
–
–
–
–
80
34
.3995
−5
.
18517
0
.725
9
.73
3
3.70
±0
.
04
168
±12
19.42
±0
.
04
9.26
±0
.
05
3.82
±0
.
03
431
±8
19.78
±0
.
08
9.53
±0
.
04
81
34
.5058
−5
.
18498
0
.466
9
.6
2
2.14
±0
.
02
128
±7
18.95
±0
.
03
9.27
±0
.
02
2.81
±0
.
03
414
±9
20.38
±0
.
09
9.33
±0
.
02
82
34
.305
−5
.
1816
0
.582
9
.02
0
2.67
±0
.
03
246
±5
21.31
±0
.
03
–
–
–
–
–
83
34
.4538
−5
.
18107
1
.745
9
.54
0
1.91
±0
.
06
241
±18
21.39
±0
.
09
–
–
–
–
–
84
34
.4177
−5
.
17535
1
.682
8
.6
0
1.51
±0
.
05
185
±18
21.37
±0
.
11
–
–
–
–
–
85
34
.436
−5
.
17003
0
.285
8
.93
1
2.53
±0
.
01
405
±1
20.95
±0
.
01
8.90
±0
.
06
–
–
–
–
Downloaded
from
by
guest
on
06
July
2025

MNRAS 540, 3493–3522 (2025)
Table
D1
–
continued
ID
R.A.
Decl.
z
log(
M
∗
)
Best
h
R,
single
/
thin
z
0
,
single
/
thin
J
0
,
single
/
thin
log
M
disc
,
single
/
thin
h
R,
thick
z
0
,
thick
J
0
,
thick
log
M
disc
,
thick
(deg)
(deg)
M

model
(kpc)
(pc)
(mag
arcsec
2
)
M

(kpc)
(pc)
(mag
arcsec
2
)
M

86
34
.254
−5
.
1685
0
.907
9
.73
0
2.85
±0
.
03
325
±5
20.93
±0
.
02
–
–
–
–
–
87
34
.4198
−5
.
16491
0
.485
9
.09
1
2.80
±0
.
02
270
±2
20.95
±0
.
02
9.08
±0
.
16
–
–
–
–
88
34
.3024
−5
.
16273
1
.694
9
.61
0
2.50
±0
.
05
351
±12
21.31
±0
.
05
–
–
–
–
–
89
34
.2888
−5
.
14641
1
.821
8
.83
0
1.82
±0
.
16
341
±49
23.12
±0
.
20
–
–
–
–
–
90
34
.2943
−5
.
14363
0
.508
9
.42
1
3.44
±0
.
01
487
±2
20.55
±0
.
01
9.38
±0
.
05
–
–
–
–
91
34
.2498
−5
.
12784
1
.032
8
.96
1
2.52
±0
.
15
404
±24
22.54
±0
.
18
8.85
±0
.
71
–
–
–
–
92
34
.2577
−5
.
27481
0
.261
8
.58
1
1.35
±0
.
01
218
±3
20.88
±0
.
04
8.53
±0
.
15
–
–
–
–
93
34
.3184
−5
.
27302
0
.698
9
1
2.77
±0
.
13
406
±19
22.82
±0
.
13
8.88
±0
.
63
–
–
–
–
94
34
.3362
−5
.
27179
3
.051
9
.07
0
2.39
±0
.
12
295
±28
22.82
±0
.
13
–
–
–
–
–
95
34
.4907
−5
.
26951
0
.424
8
.51
2
2.67
±0
.
07
247
±14
22.16
±0
.
05
8.16
±0
.
05
3.72
±0
.
12
676
±33
23.40
±0
.
18
8.25
±0
.
04
96
34
.4726
−5
.
24115
1
.422
9
.34
1
2.70
±0
.
12
288
±23
22.03
±0
.
13
9.29
±0
.
73
–
–
–
–
97
34
.2925
−5
.
23886
0
.401
9
.27
1
2.05
±0
.
04
277
±3
20.57
±0
.
07
9.22
±0
.
11
–
–
–
–
98
34
.3119
−5
.
23517
1
10
.54
1
5.88
±0
.
02
621
±2
20.28
±0
.
01
10.46
±0
.
03
–
–
–
–
99
34
.3028
−5
.
23065
3
.012
10
.25
0
2.24
±0
.
13
320
±31
22.81
±0
.
13
–
–
–
–
–
100
34
.2416
−5
.
22803
0
.943
9
.67
2
1.26
±0
.
05
197
±15
20.46
±0
.
10
9.24
±0
.
06
4.57
±0
.
24
682
±28
22.63
±0
.
18
9.47
±0
.
04
101
34
.2535
−5
.
22677
2
.195
9
.16
0
1.46
±0
.
07
237
±27
21.56
±0
.
14
–
–
–
–
–
102
34
.2875
−5
.
2261
1
.033
9
.68
1
3.48
±0
.
07
335
±9
21.10
±0
.
08
9.57
±0
.
16
–
–
–
–
103
34
.4759
−5
.
22053
2
.128
9
.52
1
2.43
±0
.
11
347
±24
21.97
±0
.
11
9.48
±0
.
63
–
–
–
–
104
34
.2433
−5
.
22055
0
.345
8
.97
1
2.83
±0
.
01
286
±1
19.86
±0
.
01
8.93
±0
.
03
–
–
–
–
105
34
.2167
−5
.
2177
0
.317
8
.85
2
2.63
±0
.
13
146
±21
21.84
±0
.
11
8.41
±0
.
09
3.27
±0
.
13
422
±29
22.61
±0
.
23
8.66
±0
.
05
106
34
.4552
−5
.
21709
1
.408
8
.96
0
2.02
±0
.
14
255
±36
22.14
±0
.
18
–
–
–
–
–
107
34
.3351
−5
.
21707
0
.642
9
.47
3
2.59
±0
.
07
145
±22
19.90
±0
.
07
8.99
±0
.
11
2.85
±0
.
04
380
±13
20.30
±0
.
15
9.29
±0
.
08
108
34
.3845
−5
.
21452
0
.909
9
.5
1
2.93
±0
.
07
428
±10
21.54
±0
.
06
9.44
±0
.
24
–
–
–
–
109
53
.1022
−27
.
912
0
.123
9
.16
3
1.70
±0
.
00
133
±0
18.67
±0
.
00
8.83
±0
.
01
2.89
±0
.
00
387
±0
20.44
±0
.
00
8.82
±0
.
01
110
53
.0757
−27
.
8904
0
.333
8
.72
3
1.41
±0
.
04
146
±9
21.25
±0
.
08
8.19
±0
.
18
1.87
±0
.
02
314
±7
21.51
±0
.
10
8.54
±0
.
16
111
53
.2146
−27
.
8741
1
.533
9
.05
0
2.25
±0
.
11
242
±29
21.46
±0
.
15
–
–
–
–
–
Downloaded
from
by
guest
on
06
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MNRAS 540, 3493–3522 (2025)
Figure D1. A corner plot of physical properties of host galaxies and individual discs, with single, thin, and thick discs represented by black, blue, and red
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MNRAS 540, 3493–3522 (2025)
Figure D2. A corner plot of physical properties of two disc galaxies (blue-red points).
APPENDIX E: M/L VARIATION AT OBSERVED
BANDS F277W, F356W, AND F444W
In Section 3.4, We compare thin and thick discs mass ratios at
redshifts z = 0.1 − 2 in observed bands (F227W, F356W, F444W)
with a galaxy sample at z = 0 (Comerón et al. 2014, at Spitzer 3.5
μm band ≈ F356W). The derivation of the mass ratio depends on the
mass-to-light ratio of thick and thin discs, ϒthick/ϒthin, for which we
assumed a value of 1.2, as derived by Comerón et al. (2011) based
on a typical SFH of the Milky Way, and adopted in Comerón et al.
(2014).
A key question is whether this value can be used for galaxies
with different redshift and observed at different bands although
close to the band used in (Comerón et al. 2011). To address
this, we compute ϒthick/ϒthin as a function of redshift at each
observing band, with the same four SFHs for thin and thick discs
adopted in Comerón et al. (2011). For this computation, we use
the python implementation of FSPS (Flexible stellar Population
Synthesis) code (Conroy, Gunn White 2009; Conroy Gunn
2010; Johnson 2024). Fig. E1 shows that all ϒthick/ϒthin remains
nearly constant across the explored redshift range and exhibits similar
values in all three observing bands (F227W, F356W, F444W) with
difference being less than 0.25. This suggests that it is reasonable
to adopt the ϒthick/ϒthin value at z = 0 and F356W also for
our sample of galaxies at redshifts z = 0.1 − 2 in the observed
bands.
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MNRAS 540, 3493–3522 (2025)
Figure E1. The evolution of the ratio of thick and thin disc mass-to-light
ratios (ϒthick/ϒthin) as a function of redshift for the observing bands F227W,
F356W, and F444W. Different lines represent various SFHs, including models
from Pilyugin Edmunds (1996, see section 3.3.1 in Comerón et al. 2011)
with varying τstr and τtop, and an SFH from Nykytyuk Mishenina (2006, see
section 3.3.2 in Comerón et al. 2011). The ϒthick/ϒthin ratio remains nearly
constant across the explored redshift range, with variations of less than 0.25
among the different bands, supporting the use of ϒthick/ϒthin at z = 0 and
F356W for galaxies at redshifts 0.1–2.
Fig. E2 shows the disc mid-plane intensities of single-disc galaxies
plotted against their redshifts, with data points colour-coded by
galaxy mass. As expected, galaxies become fainter due to surface
brightness dimming, and higher-mass galaxies are brighter at a fixed
redshift. The expected surface brightness dimming trend, (1 + z)−4
,
appears to overpredict the evolution of our galaxies (solid line).
Incorporating an additional k-correction (accounting for rest-frame
Figure E2. Mid-plane disc surface brightness of single-disc galaxies plotted
against redshift, colour-coded by stellar mass. The solid and dashed lines
indicate the expected surface brightness dimming (1 + z)−4 and the combined
effect of dimming, k-correction (rest-frame band shifting), and evolutionary
correction (stellar population aging) derived from the SFH used to compute
Fig. E1. The observed trend shows that surface brightness dimming alone
overpredicts the observed evolution, whereas including k-correction and
evolutionary correction reproduces the data better. The errors are comparable
to or smaller than the size of the markers.
band shifting), and evolutionary correction (accounting for stellar
population aging), using the SFH used to derive Fig. E1 (see
section 3.3.2 in Comerón et al. 2011) more accurately reproduces
the observed trend (dashed line).
This paper has been typeset from a TEX/L
ATEX file prepared by the author.
© 2025 The Author(s).
Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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The emergence of galactic thin and thick discs across cosmic history

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