11institutetext: Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan
281 S9, B-9000 Gent, Belgium
11email<EMAIL_ADDRESS>22institutetext: Department of Physics and
Astronomy, N283 ESC, Brigham Young University, Provo, UT 84602, USA
33institutetext: Center for Astrophysical Sciences, Department of Physics and
Astronomy, The Johns Hopkins University, 3400 N Charles St., Baltimore, MD
21218, USA 44institutetext: Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA 55institutetext: Physics Department, College
of Natural Sciences, Jimma University, PO Box 378, Jimma, Ethiopia
66institutetext: Instituto de Radioastronomía y Astrofísica, Universidad
Nacional Autónoma de México, Morelia, Michoacán 58089, Mexico 77institutetext:
SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD,
Groningen, The Netherlands 88institutetext: Kapteyn Astronomical Institute,
University of Groningen, Postbus 800, 9700 AV, Groningen, The Netherlands
99institutetext: INAF – Osservatorio Astronomico di Capodimonte, Salita
Moiariello 16, I-80131 Napoli, Italy

# The TNG50-SKIRT Atlas:
wavelength dependence of the effective radius

Maarten Baes The TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Aleksandr Mosenkov The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radius Raymond Kelly The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radius Abdurro’uf The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius Nick
Andreadis The TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Sena Bokona Tulu The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Peter Camps The TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Abdissa Tassama Emana The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius Jacopo Fritz
The TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius Andrea Gebek
The TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius Inja Kovačić
The TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius Antonio La
Marca The TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Marco Martorano The TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Angelos Nersesian The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radius Vicente Rodriguez-Gomez The TNG50-SKIRT Atlas:  wavelength dependence
of the effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the
effective radius Crescenzo Tortora The TNG50-SKIRT Atlas:  wavelength
dependence of the effective radiusThe TNG50-SKIRT Atlas:  wavelength
dependence of the effective radius
Ana Trčka The TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radius
Bert Vander Meulen The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radius Arjen van der Wel The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radius Lingyu Wang The TNG50-SKIRT Atlas:  wavelength dependence of the
effective radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective
radiusThe TNG50-SKIRT Atlas:  wavelength dependence of the effective radiusThe
TNG50-SKIRT Atlas:  wavelength dependence of the effective radius

Galaxy sizes correlate with many other important properties of galaxies, and
the cosmic evolution of galaxy sizes is an important observational diagnostic
for constraining galaxy evolution models. The effective radius is probably the
most widely used indicator of galaxy size. We used the TNG50-SKIRT Atlas to
investigate the wavelength dependence of the effective radius of galaxies at
optical and near-infrared (NIR) wavelengths. We find that, on average, the
effective radius in every band exceeds the stellar mass effective radius, and
that this excess systematically decreases with increasing wavelength. The
optical g-band (NIR ${\textit{K}}_{\text{s}}$-band) effective radius is on
average 58% (13%) larger than the stellar mass effective radius. Effective
radii measured from dust-obscured images are systematically larger than those
measured from dust-free images, although the effect is limited (8.7% in the
g-band, 2.1% in the ${\textit{K}}_{\text{s}}$-band). We find that stellar
population gradients are the dominant factor (about 80%) in driving the
wavelength dependence of the effective radius, and that differential dust
attenuation is a secondary factor (20%). Comparing our results to recent
observational data, we find offsets in the absolute values of the median
effective radii, up to 50% for the population of blue galaxies. We find better
agreement in the slope of the wavelength dependence of the effective radius,
with red galaxies having a slightly steeper slope than green–blue galaxies.
Comparing our effective radii with those of galaxies from the Siena Galaxy
Atlas in separate bins in z-band absolute magnitude and
${\textit{g}}-{\textit{z}}$ colour, we find excellent agreement for the
reddest galaxies, but again significant offsets for the blue populations: up
to 70% for galaxies around $M_{z}=-21.5$. This difference in median effective
radius for the bluer galaxies is most probably due to intrinsic differences in
the morphological structure of observed and TNG50 simulated galaxies. Finally,
we find that the median effective radius in any broadband filter increases
systematically with decreasing ${\textit{u}}-{\textit{r}}$ colour and with
increasing galaxy stellar mass, total SFR, sSFR, and dust-to-stellar-mass
ratio. For the slope of the wavelength dependence of $R_{\text{e}}$, however,
there does not seem to be a systematic, monotonic correlation with any of
these global properties.

###### Key Words.:

dust: extinction – galaxies: fundamental parameters – galaxies: stellar
content – galaxies: structure

##  1 Introduction

Of all the morphological characteristics of a galaxy, size is arguably the
most important one. Galaxy sizes correlate with many other important
properties of galaxies, such as stellar mass, surface brightness, and stellar
density (Kormendy 1977; Roberts & Haynes 1994; Shen et al. 2003; van der Wel
et al. 2014). The cosmic evolution of galaxy sizes is an important
observational diagnostic for constraining galaxy evolution models (Trujillo et
al. 2006, 2007; van der Wel et al. 2008, 2014; Roy et al. 2018; Costantin et
al. 2023). Galaxy sizes are also important to define central dark matter
fractions, and can be used together with these dark matter fractions to test
galaxy evolution models (e.g. Tortora et al. 2018).

There are different ways to characterise the size of a galaxy (Petrosian 1976;
Kron 1980; Graham 2019; Trujillo et al. 2020). The effective or half-light
radius is probably the most widely used one. One of the main advantages of the
effective radius as an indicator of galaxy size is its robustness against many
observational issues, such as the depth of images (e.g. Trujillo et al. 2001).
On the other hand, the effective radius is an on-sky property and not an
intrinsic 3D property of a galaxy, and its value is expected to depend on the
orientation and the band in which we observe the galaxy (Möllenhoff et al.
2006; Graham & Worley 2008; Pastrav et al. 2013; Devour & Bell 2017).

Several teams demonstrated observationally that the effective radius is indeed
wavelength-dependent. Ko & Im (2005) and La Barbera et al. (2010) found a 30%
decrease in the effective radius of early-type galaxies when moving from the
optical g\- or V-bands to the near-infrared (NIR) K-band. Kelvin et al. (2012)
and Vulcani et al. (2014) extended these studies by including late-type
galaxies, and found an overall $\sim$30% decrease in effective radius when
moving from g\- to K-band values, with the decrease slightly depending on
galaxy colour or Sérsic index. Other studies indicating a similar dependence
of effective radius on wavelength include Lange et al. (2015), Kennedy et al.
(2015, 2016), Casasola et al. (2017), Dimauro et al. (2018), Psychogyios et
al. (2020), Baes et al. (2020), and Nersesian et al. (2023). Advanced studies
considering multi-wavelength bulge-disc composition of large galaxy samples
include Häußler et al. (2022) and Casura et al. (2022).

The systematic wavelength dependence is generally understood to be a
combination of two distinct effects: stellar population gradients and
differential dust attenuation. Both early-type and late-type galaxies
generally show negative metallicity and age gradients (Tortora et al. 2010;
Sánchez-Blázquez et al. 2014; Ibarra-Medel et al. 2016; García-Benito et al.
2017; Zheng et al. 2017; López Fernández et al. 2018; Zhuang et al. 2019; Dale
et al. 2020; Parikh et al. 2021; Pessa et al. 2023). These stellar population
gradients naturally lead to colour gradients, and thus a systematic decrease
in the half-light radius for increasing wavelength. On the other hand, dust
attenuation primarily obscures the central regions of galaxies, as evidenced
from spatially resolved imaging of galaxies at far-infrared wavelengths
(Muñoz-Mateos et al. 2009; Pohlen et al. 2010; González Delgado et al. 2015;
Casasola et al. 2017; Greener et al. 2020) and studies of overlapping galaxies
(Keel & White 2001a, b; Holwerda et al. 2009). This differential dust
attenuation leads to a flattening of the surface brightness profile, and hence
to an increase in the half-light radius. Dust attenuation, being strongly
wavelength-dependent (Mathis 1990; Draine 2003; Burgarella et al. 2005),
automatically generates a decrease in half-light radius with increasing
wavelength.

These two effects, stellar population gradients and differential dust
attenuation, are hard to disentangle for observed galaxies. They can be
disentangled, however, for simulated galaxies. In this work we use the
TNG50-SKIRT Atlas (TSA, Baes et al. 2024), a large multi-wavelength synthetic
image atlas based on simulated galaxies extracted from the TNG50 cosmological
hydrodynamics simulation (Pillepich et al. 2019; Nelson et al. 2019b), to
investigate the origin of the wavelength dependence of the effective radius in
the optical–NIR wavelength domain. Since dust attenuation can artificially be
turned on and off, the relative contribution of the two contributors can be
determined. Disentangling these two effects is the main goal of this work.

This paper is organised as follows. In Sect. 2 we discuss the data we use and
the methods we adopt to determine the effective radius. In Sect. 3 we present
the results of our analysis. More specifically we show how the effective
radius of the simulated galaxies in our sample depends on wavelength and we
discuss the origin of this wavelength dependence. In Sect. 4 we discuss our
findings: we compare our results to observations and we investigate how the
effective radius and its wavelength dependence depend on global galaxy
parameters. We present a summary and our conclusions in Sect. 5.

##  2 Sample and methods

In this section we describe the sample of simulated galaxies we use for our
analysis (Sect. 2.1) and the methods we adopt to determine effective radii
(Sect. 2.2) and half-mass radii (Sect. 2.3) for each simulated galaxy.

Figure 1: Histograms of a number of global properties of the galaxies in our
sample: stellar mass, star formation rate, specific star formation rate,
${\textit{u}}-{\textit{r}}$ colour, and dust mass. The dashed lines indicate
the median values of the sample. The peaks at low values in the SFR and sSFR
histograms correspond to galaxies without ongoing star formation. Similarly,
the peak at low dust mass corresponds to galaxies without interstellar dust
content. Figure 2: Illustration of the curve-of-growth analysis described in
Sect. 2.2, here applied to the 2MASS H-band image of simulated galaxy TNG
000001 in orientation O1. The 2D surface brightness distribution is fitted
with a series of concentric ellipses, and the total integrated flux within
each ellipse is determined. The effective radius is the semi-major axis of the
ellipse that contains half of the total flux.

###  2.1 The TNG50-SKIRT Atlas

The TSA (Baes et al. 2024) is a synthetic image atlas for a complete stellar-
mass selected sample of 1154 galaxies extracted from the TNG50 simulation
(Pillepich et al. 2019; Nelson et al. 2019b). TNG50 is the highest-resolution
version of the IllustrisTNG suite of cosmological hydrodynamical simulations
(Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et
al. 2018b; Springel et al. 2018). The simulation has a baryonic mass
resolution of $8.5\times 10^{4}\leavevmode\nobreak\ {\text{M}}_{\odot}$ and a
spatial resolution of 70–140 pc.

We selected all 1154 galaxies with total stellar mass between $10^{9.8}$ and
$10^{12}\leavevmode\nobreak\ {\text{M}}_{\odot}$ from the $z=0$ snapshot of
the TNG50 simulation. For each of these simulated galaxies, the TSA contains
high-resolution images in 18 broadband filters covering the UV to NIR
wavelength range111More specifically, we generated images in the GALEX FUV-
and NUV-bands, the Johnson UBVRI-bands, the LSST ugrizy-bands, the 2MASS
JHK${}_{\text{s}}$-bands, and the WISE W1- and W2-bands.. All images are
generated with the SKIRT radiative transfer code (Camps & Baes 2015, 2020) and
account for different stellar populations and absorption and scattering by
interstellar dust in a realistic 3D setting. The SKIRT post-processing
simulations were based on the prescriptions by Camps et al. (2016, 2018,
2022), Kapoor et al. (2021), and Trčka et al. (2022). For each galaxy, the
image atlas contains images for five different random observer positions (with
observing positions O4 and O5 antipodal). In addition to the dust-obscured
images, the atlas contains, for each observer position, synthetic dust-free
images in all 18 bands, and stellar mass surface density, mean stellar age,
mean stellar metallicity, and dust mass surface density maps. All images and
parameter maps contain 1600 $\times$ 1600 pixels with a pixel scale of 100 pc,
corresponding to a field of view of 160 kpc.

The TSA sample contains 869 star-forming and 285 quiescent galaxies when the
value ${\text{sSFR}}=10^{-11}\leavevmode\nobreak\ {\text{yr}}^{-1}$ is used as
the dividing line between the two populations. Figure 1 shows histograms of a
number of physical characteristics of the sample. The stellar masses, star
formation rates (SFR), and specific star formation rates (sSFR) are directly
taken from the TNG50 public database (Nelson et al. 2019a). The
${\textit{u}}-{\textit{r}}$ colours are calculated from the SKIRT-generated
maps, and take into account the effects of dust attenuation. The dust masses
are calculated by integrating the dust mass surface density maps. We note that
the TNG50 hydrodynamical simulations do not explicitly contain a prescription
for interstellar dust, so dust was added to the galaxies in post-processing
using the assumption that the dust density is proportional to the gas
metallicity in cold, dense gas (for details, see Trčka et al. 2022; Baes et
al. 2024).

The distribution of stellar masses follows the typical Schechter distribution
with a strong decline for increasing stellar mass. While our sample consists
of all galaxies with stellar masses between $10^{9.8}$ and
$10^{12}\leavevmode\nobreak\ {\text{M}}_{\odot}$, the median stellar mass is
only $10^{10.3}\leavevmode\nobreak\ {\text{M}}_{\odot}$. The sample contains
galaxies with a variety in SFR, ranging from totally quiescent galaxies to
actively star-forming galaxies with ${\text{SFR}}>20\leavevmode\nobreak\
{\text{M}}_{\odot}\leavevmode\nobreak\ {\text{yr}}^{-1}$ and
${\text{sSFR}}>10^{-9.5}\leavevmode\nobreak\ {\text{yr}}^{-1}$. The median
values for the sample are $\langle{\text{SFR}}\rangle=1\leavevmode\nobreak\
{\text{M}}_{\odot}\leavevmode\nobreak\ {\text{yr}}^{-1}$ and
$\langle{\text{sSFR}}\rangle=10^{-10.3}\leavevmode\nobreak\ {\text{yr}}^{-1}$,
indicating that most of the galaxies in our sample are star-forming. The
distribution of ${\textit{u}}-{\textit{r}}$ colour covers the range between
0.9 and 2.7 and is bimodal, as also noted in observed samples of galaxies in
the local Universe (Strateva et al. 2001; Baldry et al. 2004; Balogh et al.
2004). The median value is 1.72. Finally, the distribution of dust mass is
clearly peaked with a long tail towards low dust masses and with a median dust
mass of $10^{7.5}\leavevmode\nobreak\ {\text{M}}_{\odot}$. Such a distribution
is consistent with the typical dust masses found in nearby galaxies (Auld et
al. 2013; Ciesla et al. 2014; Nersesian et al. 2019; Aniano et al. 2020;
Galliano et al. 2021).

###  2.2 Determination of the effective radii

Figure 3: Histograms of the relative difference between the effective radius
measured from the antipodal O4 and O5 observer positions in the LSST u\- and
i-bands and the 2MASS ${\textit{K}}_{\text{s}}$-band. The dashed red lines
represent the 16% and 86% quantiles of the distribution. Half of the width of
this confidence interval can be used as an upper limit for the relative
uncertainty on our $R_{\text{e}}$ measurements.

We measured the effective radius in all LSST and 2MASS wavebands using a
curve-of-growth analysis, similar to the approach applied to the galaxies from
the Siena Galaxy Atlas by Moustakas et al. (2023). Following most
observational studies of the wavelength dependence of the effective radius
(e.g. Ko & Im 2005; La Barbera et al. 2010; Kelvin et al. 2012; Vulcani et al.
2014; Lange et al. 2015), we focus on the optical and NIR regime, from the u\-
to the ${\textit{K}}_{\text{s}}$-band.

As a first step we first convolve each SKIRT post-processed galaxy image with
a Gaussian kernel with FWHM of 5 pixels. This step was taken to smooth out
fine details and Monte Carlo noise in our galaxy images. We experimented with
different values of the smoothing lengths and settled on 5 pix as a trade-off
between a significant degradation of the resolution and a sufficient noise
reduction. The second step consisted of fitting elliptical isophotes to the
individual images by means of the standard IRAF STSDAS/ELLIPSE routine
(Jedrzejewski 1987), with the galaxy centre fixed. We determined the total
integrated flux within each elliptical aperture, and plotting them as a
function of increasing semi-major axis yielded the curve-of-growth. This curve
was approximated with a cubic spline fit from which the half-light radius was
measured. This procedure was independently executed for every single image in
our atlas. Figure 2 illustrates our approach.

For a limited number of images this method did not converge, either because
the galaxies were extremely asymmetrical, or because there were technical
issues (for example, for galaxies located very close to the border of the
simulation volume). We discarded all measurements for a given galaxy and
observer position if the ellipse fitting routine failed for at least one band.
In total, we had to discard 129 sets of images out of a total of $5\times
1154=5770$ sets, corresponding to a 2.2% rejection rate.

To characterise the accuracy of our effective radius measurements, we compared
the values obtained independently for the antipodal O4 and O5 observer
positions (the images corresponding to observer position O5 were only used as
a check for the accuracy of our analysis but were not used in the statistical
analysis in the remainder of this work). Figure 3 shows the histograms of the
relative error between the two measurements for the u-, i-, and
${\textit{K}}_{\text{s}}$-bands. The relative difference between the O4 and O5
measurements decreases with increasing wavelength, which can be attributed to
the diminishing effect of dust attenuation and the smoother appearance of
galaxies at longer wavelengths. For each band, we calculated the 16% and 84%
quantiles of the distribution of the relative difference and considered half
of the width of this confidence interval as an upper limit for the relative
uncertainty on our $R_{\text{e}}$ measurements, as the O4 and O5 images are
not perfectly mirrored versions due to different levels of dust attenuation.
This value decreases from 7.0% in the u-band to 1.3% in the
${\textit{K}}_{\text{s}}$-band.

###  2.3 Determination of half-mass radii

Figure 4: Correlation between the 3D particle half-mass radius
$r_{\text{half}}$ and the half-mass radius $R_{\text{e}}^{\star}$ determined
as the semi-major axis of the elliptical iso-density contour that contains
half of the total projected stellar mass. Each galaxy is represented by four
dots, one for each of the four independent observer’s positions. The solid
yellow line is the best-fitting power-law relation.

We determined the effective radius in the stellar mass surface density maps in
the same way as for the synthetic images. The corresponding effective radius,
denoted as $R_{\text{e}}^{\star}$, is the semi-major axis of the elliptical
iso-density contour that contains half of the total projected stellar mass. In
Fig. 4 we compare $R_{\text{e}}^{\star}$ with the half-mass radius
$r_{\text{half}}$ obtained directly from the TNG50 stellar particle data as
the radius of the sphere that contains half of the total stellar mass. For
completely spherical models with realistic surface density profiles, we expect
a relation

$R_{\text{e}}^{\star}\approx\frac{3}{4}\,r_{\text{half}},$ (1)

as demonstrated by Ciotti (1991) and Wolf et al. (2010).

Fig. 4 shows the correlation between $r_{\text{half}}$ and
$R_{\text{e}}^{\star}$ for all galaxies in our image atlas. Every galaxy has,
by definition, a single value for $r_{\text{half}}$ and four different values
for $R_{\text{e}}^{\star}$, corresponding to each different observer position.
This figure shows that, for the majority of the galaxies, Eq. (1)
underestimates the stellar mass effective radius, particularly for the smaller
galaxies. The individual measurements are colour-coded by the inclination of
the galaxy for the given observer, defined as the angle between the direction
of the stellar angular momentum vector and the direction towards the observer.
For a given half-mass radius, galaxies observed nearly edge-on turn out to
have, on average, smaller values for $R_{\text{e}}^{\star}$ than galaxies
observed nearly face-on. The solid yellow line is a power-law fit to the
individual data points and is given by

$\frac{R_{\text{e}}^{\star}}{\text{kpc}}=0.999\left(\frac{r_{\text{half}}}{\text{kpc}}\right)^{0.922}.$
(2)

Most importantly, we have, for each galaxy and for each observer’s position, a
measurement of the half-mass radius determined in the exact same way as the
half-light radius in each of the broadband filters.

##  3 Results

###  3.1 Wavelength dependence of the effective radius

Figure 5: Comparison between the half-mass radius $R_{\text{e}}^{\star}$ and
the half-light radius $R_{\text{e}}$ in nine different optical–NIR broadband
filters. Thick red contours correspond to measurements of $R_{\text{e}}$ from
the dust-obscured images, slightly thinner blue contours to measurements from
dust-free images. The contour correspond to the 10, 40, 70 and 90% percentile
levels. The dashed lines represent a one-to-one relationship between
$R_{\text{e}}^{\star}$ and $R_{\text{e}}$.

In Figure 5 we compare the effective radius $R_{\text{e}}$ in each of the nine
considered bands with respect to the half-mass radius $R_{\text{e}}^{\star}$.
Focusing first on the blue contours, which correspond to the effective radii
obtained from the dust-free images, we see that the dust-free effective radius
is larger than the half-mass radius. This excess is largest in the u-band and
systematically decreases towards the ${\textit{K}}_{\text{s}}$-band. Looking
at the thicker red contours, which correspond to the images with dust
attenuation properly accounted for, we note similar but even more outspoken
trends. The effective radius as measured from the dust-obscured images
systematically exceeds both the half-mass radius and the dust-free effective
radius. The excess decreases with increasing wavelength.

Figure 6: Histograms of $R_{\text{e}}$ and $R_{\text{e}}/R_{\text{e}}^{\star}$
for nine different optical–NIR broadband filters, for both dust-obscured (red)
and dust-free (blue) images. The median values of the distributions are
indicated as vertical dotted lines.

Figure 6 shows the same data in an alternative way. The histograms on the left
column display a wide range of effective radii in any broadband filter, which
just reflects the variety of sizes in the galaxy population. In each
individual band, the distribution of effective radii approximates a lognormal
distribution, similar to the effective radius distributions at low redshift
shown by Vulcani et al. (2014) and at higher redshift by Shibuya et al.
(2015). Our distributions tend to be slightly skewed with a long tail towards
smaller effective radii, whereas the distributions presented by Vulcani et al.
(2014) are rather skewed towards larger effective radii.

More remarkable than the large spread in $R_{\text{e}}$ is that also the range
in $R_{\text{e}}/R_{\text{e}}^{\star}$ is relatively broad in all the bands.
At short wavelengths, this is not unexpected, as blue light is a poor
estimator for the stellar mass. We find that the width of the distribution in
$R_{\text{e}}/R_{\text{e}}^{\star}$ decreases when moving from shorter to
longer wavelengths. Interestingly, this width is still non-negligible even in
the ${\textit{K}}_{\text{s}}$-band that is generally considered as a good
proxy for stellar mass. The ratio between the ${\textit{K}}_{\text{s}}$-band
half-light ratio and half-mass ratio can be as small as 0.8 and as large as 2.

Figure 7: Wavelength dependence of the effective radius for our sample of
TNG50 galaxies. Top panel: median value of the half-light radius. Middle
panel: median ratio of the half-light radius to the g-band half-light radius.
Bottom panel: median ratio of the half-light radius and half-mass radius. In
all three panels, the black lines and markers correspond to the dust-affected
images, the blue ones to the dust-free images. The dotted lines represent
power-law fits to the data points.

Another interesting characteristic of these histograms is the systematic shift
with increasing wavelength. Moving from top to bottom, one notes that the
histograms of both $R_{\text{e}}$ and $R_{\text{e}}/R_{\text{e}}^{\star}$
slightly but systematically shift towards smaller values. This shift is
present for both the dust-obscured and dust-free measurements of the effective
radius. The systematic shift with increasing wavelength can be characterised
by the median values of the histograms, indicated as dotted vertical lines in
Figure 6. One can immediately note that these median values systematically
decrease as a function of increasing wavelength.

In Figure 7 we show the median values of $R_{\text{e}}$ and
$R_{\text{e}}/R_{\text{e}}^{\star}$ explicitly as a function of wavelength. In
each panel, the red lines and markers correspond to the dust-obscured images,
the blue ones to the dust-free images. These plots confirm the general trends
noticeable in Figures 5 and 6 and allow to make more quantitative
observations. It shows that, across the optical–NIR range, the half-light
radius tends to exceed the half-mass radius, and the median effective radius
systematically decreases with increasing wavelength. In the optical g-band the
median ratio of $R_{\text{e}}/R_{\text{e}}^{\star}$ is 1.58, in the
${\textit{K}}_{\text{s}}$-band the median ratio is still 1.13. The two panels
of Figure 7 also show that the effective radii measured from dust-obscured
images are systematically larger than those measured from dust-free images.
The g-band half-light radii measured from dust-obscured images are, on
average, 8.7% larger than those measured from dust-free images. In the
${\textit{K}}_{\text{s}}$-band the median ratio of this excess reduces to
2.1%.

###  3.2 Origin of the wavelength dependence

These findings confirm the common understanding that the decrease in the
effective radius of galaxies with increasing wavelength is the combination of
two distinct effects: stellar population gradients and dust attenuation. We
note that, in the present study, we do not make an explicit distinction
between bulge and disc components. The half-light radius we measure is
determined using a curve-of-growth analysis and is a nonparametric measure of
the galaxy size. Any variation in the relative intrinsic luminosity of bulge
and disc components as a function of wavelength is incorporated in our stellar
population gradient.

The stellar population gradient contribution is evident from the fact that the
effective radius measured from the dust-free images shows this systematic
wavelength dependence. It can only be caused by differences in the intrinsic
colours of the stellar populations. Differential dust attenuation and the
corresponding flattening of the surface brightness profiles is responsible for
an additional contribution to the wavelength dependence of the half-light
radius.

Table 1: Parameters of power-law fits to the median wavelength dependence of the effective radius, $\log X=\alpha\log(\lambda/\mu{\text{m}})+\beta$. The second and third columns correspond to dust-obscured data, the fourth and fifth column to dust-free data.  $X$ | $\alpha$ | $\beta$ | $\alpha_{\text{df}}$ | $\beta_{\text{df}}$
---|---|---|---|---
$R_{\text{e}}/{\text{kpc}}$ | $-0.248$ | $0.767$ | $-0.194$ | $0.739$
$R_{\text{e}}/R_{\text{e}}^{\star}$ | $-0.249$ | $0.125$ | $-0.196$ | $0.099$

Contrary to purely observational imaging studies (e.g. Ko & Im 2005; La
Barbera et al. 2010; Kelvin et al. 2012; Vulcani et al. 2014), we can try to
disentangle the importance of the two effects to the observed wavelength
dependence of the half-light radius because we can artificially turn dust
attenuation on or off. We fitted power-law fits to the median trends in Figure
7, shown as the dotted lines in each panel. The parameters of the fits are
listed in Table 1. While the two contributions (stellar population gradients
and differential dust attenuation) do not linearly add up, we can take the
slope of the power-law as a qualitative measure of the importance of each
contributor. The joint contribution of stellar population gradients and
differential dust attenuation results in a slope of almost $-0.25$ for the two
power-law fits. When we consider only stellar population gradients, that is,
when we suppress dust attenuation, we find a slope of nearly $-0.20$ for the
two power-law fits. These numbers suggest that the stellar population
gradients are the dominant factor in driving the wavelength dependence of the
effective radius, and that differential dust attenuation is a minor, but non-
negligible, secondary factor. In the concise style of Trujillo et al. (2004)
we can summarise the wavelength dependence of galaxy sizes: 80% stellar
population, 20% dust attenuation.

##  4 Discussion

###  4.1 Comparison to Vulcani et al. (2014)

The results of the previous section are only valid if the TNG50 galaxies in
our sample are representative for the galaxies in the local Universe. In this
subsection we compare the wavelength dependence of the effective radius of our
TNG50 galaxies with the work by Vulcani et al. (2014). These authors presented
the wavelength dependence of the effective radius based on a large sample of
galaxies with available optical (SDSS ugriz) and NIR (UKIDSS YJHK) imaging
from the Galaxy And Mass Assembly (GAMA, Driver et al. 2011) survey.222The
SDSS ugriz \+ UKIDDS YJHK filter set is slightly different from the LSST
ugrizy \+ 2MASS JHK${}_{\text{s}}$ filter set that we used for our SKIRT post-
processing, but this does not fundamentally affect the conclusions of the
comparison. The authors considered a complete, volume-limited sample with an
absolute r-band magnitude limit of $M_{r}=-21.2$. They split their sample of
galaxies into three different populations based on ${\textit{u}}-{\textit{r}}$
colour: blue (${\textit{u}}-{\textit{r}}<1.6$), green
($1.6<{\textit{u}}-{\textit{r}}<2.1$), and red
(${\textit{u}}-{\textit{r}}>2.1$). They simultaneously fitted one wavelength-
dependent Sérsic model to the optical and NIR images with the GALFITM code
(Häußler et al. 2013). The dashed lines and open squares in Figure 8 represent
the median values for $R_{\text{e}}$ and
$R_{\text{e}}/R_{\text{e}}^{\text{g}}$ as a function of wavelength obtained by
Vulcani et al. (2014) for their three subpopulations.

Figure 8: Comparison of the wavelength dependence of the effective radius for
our sample of TNG50 galaxies to literature values from Vulcani et al. (2014).
Top panel: median value of the half-light radius. Bottom panel: median ratio
of the half-light radius to the g-band half-light radius. For the meaning of
the different colours, we refer to Sect. 4.1.

We attempted to mimic the sample selection criteria of Vulcani et al. (2014)
by excluding from our sample all the galaxies with $M_{r}>-21.2$ and
subsequently subdividing the resulting sample into three subpopulations using
the same ${\textit{u}}-{\textit{r}}$ colour criteria. The resulting median
values for $R_{\text{e}}$ and $R_{\text{e}}/R_{\text{e}}^{\text{g}}$ are shown
as the solid lines and filled circles in Figure 8.

The top panel of Figure 8 shows that there is a significant difference between
the absolute values of the effective radii for the different populations. For
the red population, there is a reasonable agreement, with our values, averaged
over the entire wavelength range, some 9% smaller than the values by Vulcani
et al. (2014). For the green and blue populations, however, there is a
significant difference: the median effective radii for our green population
are about 29% larger than theirs, and for the blue population this increases
to almost 50%.

We see three potential reasons that can contribute to these significant
differences. The first reason is we used different techniques to determine the
effective radii. Vulcani et al. (2014) use single-component Sérsic fits to the
images. Such fitting simultaneously determines the total magnitude, effective
radius, and Sérsic index as parameters of the parametric model that provides
the best description of the surface brightness distribution in a $\chi^{2}$
fitting. Our half-light radii, on the other hand, are determined using a
curve-of-growth analysis (see Sect. 2.2). It is well-known that different
measures for the effective radius can differ systematically, as also
demonstrated by Vulcani et al. (2014) in their Figure 1. Moreover, the spatial
resolution (i.e. PSF size and pixel size) of the observed imaging data may
also have a significant effect on the observed trends.

A second aspect that can at least be partly explain the differences are sample
selection affects. While we adopted the same absolute magnitude and colour
criteria, the sample considered by Vulcani et al. (2014) contains galaxies
with redshifts up to $z=0.3$, with a peak in the redshift distribution around
0.2. We only have access to simulated galaxies at $z=0$ as the TSA currently
only considers this single TNG50 snapshot. Since galaxy properties, including
galaxy sizes, do change as a function of cosmic time (e.g. Conselice 2014), we
cannot expect to have a perfect match at this stage.

Finally, we cannot exclude that the TNG50 galaxies have systematically larger
sizes than the galaxies considered by Vulcani et al. (2014). Checking this is
not straightforward without a detailed matched sample. We come back to this
issue in Sect. 4.2.

One would hope that sample selection effects and the differences between the
methods used to measure $R_{\text{e}}$ would be less important when
considering the systematic wavelength dependence of the effective radius
rather than its absolute value. This seems indeed the case, as shown in the
bottom panel of Figure 8. An interesting feature of this plot is the
difference between the red population on the one hand, and the green–blue
population on the other hand. The wavelength dependence of the former
population is steeper than the one of the latter, both for the observed
galaxies and for the simulated TNG50 galaxies. The wavelength dependence of
$R_{\text{e}}$ is due to a combination of stellar population gradients and
differential dust attenuation, but as red, bulge-dominated galaxies are
generally less dusty than blue, disc-dominated galaxies (e.g. da Cunha et al.
2010; Cortese et al. 2012; Smith et al. 2012; Nersesian et al. 2019), this
difference in slope must be caused by stronger stellar population gradients.
This result is in agreement with our conclusion from Sect. 3.1 that stellar
population gradients are the dominant factor in driving the wavelength
dependence of the effective radius.

###  4.2 Comparison to the Siena Galaxy Atlas

Figure 9: Comparison of the effective radii for our sample of simulated TSA
galaxies to effective radii of galaxies from the Siena Galaxy Atlas 2020
(Moustakas et al. 2023). The three different panels correspond to different
bins in ${\textit{g}}-{\textit{z}}$ colour, and each symbol represents the
median effective radius in a bin in z-band absolute magnitude of width $\Delta
M_{z}=0.2$. Measurements in the g-, r-, and z-bands are indicated by different
symbols, as indicated in the top panel. The symbols for the SGA-2020 are
plotted slightly offset for the sake of clarity.

Figure 10: Dependence of the effective radius on global physical properties.
Each column corresponds to a different global physical property:
${\textit{u}}-{\textit{r}}$ colour, stellar mass, star formation rate,
specific star formation rate, and specific dust mass. The entire sample is
split into six subpopulations based on each of these properties. Top row:
median effective radius for each subpopulation. Middle row: median ratio of
the effective radius and the g-band effective radius. Bottom row: scatter
plots relating the physical property to the g-band effective radius. All TNG50
galaxies without ongoing star-formation are plotted at
${\text{SFR}}=10^{-3}\leavevmode\nobreak\
{\text{M}}_{\odot}\leavevmode\nobreak\ {\text{yr}}^{-1}$ and
${\text{sSFR}}=10^{-12}\leavevmode\nobreak\ {\text{yr}}^{-1}$, and all dust-
free galaxies at $M_{\text{dust}}/M_{\star}=10^{-5}$. The blue curves
represent running medians.

As indicated in the previous section, we found a significant difference in the
absolute values of the effective radii of our TSA galaxies and the observed
galaxies considered by Vulcani et al. (2014). To investigate to which degree
the sample selection is responsible for these differences, we compare the
effective radii of our TSA galaxies to effective radii for galaxies from the
2020 version of the Siena Galaxy Atlas (SGA-2020 or simply SGA) presented by
Moustakas et al. (2023). The SGA is an angular-size-selected multi-wavelength
atlas of almost 400,000 nearby galaxies (out to $z<0.5$). The catalogue is
based on deep, wide-field grz imaging from the DESI Legacy Imaging Surveys DR9
(Dey et al. 2019).

For the vast majority of the galaxies in the SGA, the effective radius in each
of the grz-bands is determined using a method that is very similar to the
method we applied. Elliptical isophotes are fitted to the images and the
curve-of-growth is determined by integrating the flux within the subsequent
elliptical apertures. The main difference to our approach is that the curve-
of-growth is fitted by an empirical model from which the effective radius is
determined, whereas we use a spline interpolation.

Compared to the multi-wavelength study by Vulcani et al. (2014), which showed
the wavelength dependence of the effective radius in 8 bands from u to H, the
SGA only lists effective radii in three optical bands. On the other hand, this
sample has the advantages that we can construct galaxy samples that match more
closely, and that the methods used to measure the half-light radius are very
similar.

We started our selection by picking from the SGA sample all galaxies with
distances between 50 and 150 Mpc. By eliminating galaxies with very low
redshifts we ensure that the redshifts are dominated by the Hubble expansion
and not by peculiar velocities; by eliminating galaxies with high redshifts we
avoid a non-negligible effect of K-corrections and small angular sizes that
might make the determination of the effective radius from the DESI imaging
data more difficult. We further eliminate all galaxies without measurements of
the effective radius in all three bands, we converted the model magnitudes to
absolute magnitudes, and we calculated the effective radii in physical units.

To generate a matched sample, we subdivided the observed SGA and simulated TSA
samples into two-dimensional bins in z-band absolute magnitude and
${\textit{g}}-{\textit{z}}$ colour. We limited the sample to
$-23.1<M_{z}<-19.9$ and $0.8<{\textit{g}}-{\textit{z}}<1.4$ to ensure
sufficient galaxies in each bin. We considered 16 bins in absolute magnitude
with width $\Delta M_{z}=0.2$ and three bins in ${\textit{g}}-{\textit{z}}$
colour with $\Delta({\textit{g}}-{\textit{z}})=0.2$. In each bin we calculated
the median effective radii of the two galaxy samples in the g-, r-, and
z-bands. The comparison is shown in Figure 9.

In all 48 bins, we find that the effective radius decreases from the g\- to
the r\- to the z-band. This is in line with the results from our analysis,
namely that the effective radius systematically decreases with increasing
wavelength. For the reddest galaxies, i.e. with
$1.2<{\textit{g}}-{\textit{z}}<1.4$, we find excellent agreement between the
effective radii of the SGA-2020 and the TSA galaxies. The median r-band
effective radius systematically decreases from almost 9 kpc for $M_{z}=-22$ to
3 kpc for $M_{z}=-20$. For bluer galaxies with
${\textit{g}}-{\textit{z}}<1.2$, we find significant differences (the strong
decrease in the effective radius between r-band and z-band for the most
luminous blue galaxies in the SGA seems spurious). For both the SGA and the
TSA samples, the median effective radius systematically decreases for
decreasing luminosity, but the absolute values differ. For the fainter
galaxies with $M_{z}\approx-20$ the median effective radii agree fairly well,
but for more luminous galaxies the TSA galaxies are systematically larger than
the observed SGA galaxies. The largest differences are found for intermediate
luminosities ($M_{z}\approx-21.5$) and for the bluest colours
$(0.8<{\textit{g}}-{\textit{z}}<1.0$): in this case the median r-band
effective radius of simulated TSA galaxies exceeds the corresponding value of
the observed SGA galaxies by about 70%.

Having constructed closely matched samples in which the effective radii are
measured in very similar ways, we conclude that difference in median effective
radius for the bluer galaxies is most probably due to intrinsic differences in
the morphological structure of observed and TNG50 simulated galaxies. On the
one hand, this seems surprising, as the IllustrisTNG model is by construction
designed to match galaxy sizes at low redshift (Pillepich et al. 2018a, Figs.
4 and 8). In their morphological comparison of TNG100 simulated galaxies and
Pan-STARRS observed galaxies, Rodriguez-Gomez et al. (2019) measured
systematically larger half-light radii at the massive end
($M_{\star}>10^{11}\leavevmode\nobreak\ {\text{M}}_{\odot}$), while the
apparent sizes of less massive galaxies agree very well with the observations.
On the other hand, the IllustrisTNG model is calibrated at the resolution of
the TNG100 simulation, and is known to generate slightly increased stellar
masses and SFRs at the increased resolution of the TNG50 simulation (Pillepich
et al. 2018a, b, 2019; Donnari et al. 2019; Trčka et al. 2022). Using
intrinsic half-mass radii extracted from the TNG public database, we find that
the median half-mass radius of TNG50 galaxies in the stellar mass range we
consider ($10^{9.8}\leavevmode\nobreak\
{\text{M}}_{\odot}<M_{\star}<10^{12}\leavevmode\nobreak\ {\text{M}}_{\odot}$)
is 20% larger than that of TNG100 galaxies in the stellar same mass range
(4.55 kpc versus 3.73 kpc).

In future work we will apply different techniques to investigate the
morphological structure of the TSA galaxies, including both parametric
modelling (one-component Sérsic fitting and bulge-disc decomposition) and
nonparametric methods.

###  4.3 Dependence of the effective radius on global physical properties

In the previous two subsections, we separated our galaxy sample in different
subpopulations according to ${\textit{u}}-{\textit{r}}$ colour (Sec. 4.1) and
z-band absolute magnitude and ${\textit{g}}-{\textit{z}}$ colour (Sec. 4.2).
In this subsection we want to generalise these results: we investigate how the
absolute value of $R_{\text{e}}$ and the wavelength dependence of
$R_{\text{e}}$ vary when we split our sample into different subpopulations by
means of different global physical properties. We only use the half-light
radii derived from the dust-obscured images in this subsection.

The result of this analysis is shown in Figure 10. Each column in this figure
corresponds to a different global physical property:
${\textit{u}}-{\textit{r}}$ colour, stellar mass, star formation rate,
specific star formation rate, and dust-to-stellar-mass ratio (specific dust
mass). The ${\textit{u}}-{\textit{r}}$ colour was calculated from the SKIRT-
generated dust-obscured images, while the other properties were calculated
directly from the TNG50 simulation particle data. For each of these five
properties, we split the galaxy sample into six bins with the same number of
galaxies in each bin. For the median value of the physical property per bin,
see the legend in Figure 10, middle row. For each bin, we calculate the median
value of $R_{\text{e}}$ (top row) and $R_{\text{e}}/R_{\text{e}}^{\text{g}}$
(middle row) in every band.

The bottom row shows a scatter plot of the r-band half-light radius against
each of the global physical properties. The solid blue curves represent
running medians for our sample. For the scatter plot that shows the effective
radius versus the stellar mass, i.e. the size–mass relation, we also show
results from two observational studies. The dotted lines show the linear fits
to the size–mass relation of early- and late-type galaxies from Lange et al.
(2015), where the Sérsic index is used to discriminate between the two
classes. The filled circles represent the mean values for the size-mass
relation from Casura et al. (2022) for the same two populations. The results
are largely compatible with our trends, although at fixed stellar mass, the
median effective radii from our TSA galaxies tend to exceed the observational
relations, in agreement with the findings from Sect. 4.2. A full analysis of
the size–mass relation of the galaxies in the TSA, including the dependence on
secondary galaxy parameters and the evolution with redshift, is beyond the
scope of this paper and will be the topic of future work. For the present
paper, the scatter plots at the bottom row of Figure 10 mainly serve to
interpret the results in the top two rows.

The panels in the first column expand upon the results from Figure 8 by now
splitting the sample into six different bins in u–r colour. At every
wavelength, the median effective radius decreases with increasing
${\textit{u}}-{\textit{r}}$ colour. The reddest galaxies in our sample with
${\textit{u}}-{\textit{r}}>2.1$ are more compact than bluer galaxies with
${\textit{u}}-{\textit{r}}<2.1$. This behaviour can be understood by looking
at the bottom left panel. The reddest galaxies are very compact: there are
virtually no large galaxies with ${\textit{u}}-{\textit{r}}>2.4$. Concerning
the slope of the wavelength dependence of $R_{\text{e}}$ our results are more
mixed: there does not seem to be a systematic and consistent change with
increasing colour.

In general, we find a similar behaviour with other global physical parameters.
Splitting the galaxies in different subpopulations, we find a systematic
change of the median half-light radius at every wavelength. More specifically,
the median effective radius in every single band increases with galaxy stellar
mass, total SFR, sSFR, and dust-to-stellar-mass ratio. In particular for SFR
and specific dust mass, the different subpopulations are clearly separated in
the panels on the top row, with positive correlations also clearly visible in
the panels on the bottom row.

There does not seem to be a systematic correlation with any global property
for the slope of the wavelength dependence of $R_{\text{e}}$. There is hardly
any difference in the median slope for the different subpopulations in stellar
mass, SFR, or sSFR. When we subdivide the sample according to specific dust
mass, we do find different median slopes, but they do not increase or decrease
systematically or monotonically over the entire parameter range.

We interpret this lack of a monotonic correlation between the slope of the
wavelength dependence of galaxy sizes and any physical property as the result
of the two different effects that contribute to this wavelength dependence:
stellar population gradients and dust attenuation (Sect. 3.1). The mean
metallicity and age gradients in both late-type and early-type galaxies vary
strongly with galaxy morphology, galaxy stellar mass and environment (e.g.
Tortora et al. 2010; Zheng et al. 2017; Zhuang et al. 2019). On the other
hand, also specific dust masses and the level of attenuation depends strongly
on galaxy morphology and stellar mass (Cortese et al. 2012; Smith et al. 2012;
Auld et al. 2013; Viaene et al. 2016; Bianchi et al. 2018; Nersesian et al.
2019). It is hence not surprising that we find no systematic correlation
between the slope of the $R_{\text{e}}(\lambda)$ relation and a single global
galaxy parameter.

##  5 Summary and conclusion

Based on the TSA, a multi-wavelength atlas of high-resolution synthetic images
of simulated galaxies extracted from the TNG50 cosmological simulation, we
investigated the wavelength dependence of the effective radius of galaxies at
optical and NIR wavelengths. We determined the half-light radius in each
individual image (and each stellar mass surface density map) using a curve-of-
growth analysis. The main results we obtained are the following:

  * •

The effective radius is, in every band, on average larger than the half-mass
radius. This excess is largest in the u-band and systematically decreases with
increasing wavelength. In the optical g-band the median ratio of
$R_{\text{e}}/R_{\text{e}}^{\star}$ is 1.58, in the
${\textit{K}}_{\text{s}}$-band the median ratio is still 1.13.

  * •

Effective radii measured from dust-obscured images are systematically larger
than those measured from dust-free images. The g-band half-light radii
measured from dust-obscured images are, on average, 8.7% larger than those
measured from dust-free images. In the ${\textit{K}}_{\text{s}}$-band the
median ratio is almost negligible at 2.1%.

  * •

The decrease in the effective radius of galaxies with increasing wavelength is
due to the combination of two distinct effects: stellar population gradients
and dust attenuation. Since we have both dust-obscured and dust-free images,
we can disentangle the importance of the two effects. Assuming that our recipe
to populate the galaxies with dust is appropriate, we find that stellar
population gradients are the dominant factor (about 80%) in driving the
wavelength dependence of the effective radius, followed by differential dust
attenuation (20%).

  * •

Comparing our results to the observational study by Vulcani et al. (2014), we
find significant offsets in the absolute values of the median effective radii.
In particular, the median effective radii for our green and blue populations
are about 30 to 50% larger than the median values obtained by Vulcani et al.
(2014). We also compare the effective radii of our galaxies to those of a
carefully matched sample of observed galaxies from the Siena Galaxy Atlas in
different bins in z-band absolute magnitude and ${\textit{g}}-{\textit{z}}$
colour. We find excellent agreement for the reddest galaxies, but significant
differences for the bluer galaxies. The difference in median r-band effective
radius peaks at about 70%. Since the samples match closely and the approaches
used to determine the effective radius are very similar, we interpret these
differences as due to intrinsic differences in the morphological structure of
observed and TNG50 simulated galaxies.

  * •

Contrary to the absolute values of the effective radii, we find that the slope
of the wavelength dependence of the half-light radius of our TSA galaxies
agrees more closely with the observational data from Vulcani et al. (2014). We
recover the observational result that the mean wavelength dependence for the
red galaxy population is steeper than that for the green–blue population.
Stronger stellar population gradients are probably the cause of this
difference.

  * •

We investigated how the absolute value of $R_{\text{e}}$ and the wavelength
dependence of $R_{\text{e}}$ vary when we split our sample into different
subpopulations by means of different global physical properties. We find that
the median effective radius in every single band increases systematically with
decreasing ${\textit{u}}-{\textit{r}}$ colour and with increasing galaxy
stellar mass, total SFR, sSFR, and dust-to-stellar-mass ratio. For the slope
of the wavelength dependence of $R_{\text{e}}$ there does not seem to be a
systematic, monotonic correlation with any global property. We interpret this
as the result of the complex dependence of both population gradients and
attenuation on galaxy morphology, stellar mass and environment.

As discussed in Baes et al. (2024), the TSA allows for a suite of
applications, in particular concerning the link between intrinsic galaxy
properties and galaxy morphology. In future papers we plan to use this image
atlas to systematically investigate the wavelength dependence and the effects
of dust attenuation on other morphological characteristics, derived from
single or multiple-component Sérsic fitting or from a non-parametric
morphological analysis. We also envision to extend the TSA by adding similar
images at different redshifts, which would allow a direct investigation of the
cosmic evolution of galaxy morphology in the TNG50 simulation and direct
apples-to-apples comparison to observational data. Specifically focusing on
the effective radius discussed in this paper, it would shed light on the
nature of the apparent size evolution of galaxies, the origin of which is
still under discussion (e.g. Suess et al. 2019; van der Wel et al. 2023).

###### Acknowledgements.

The authors thank the anonymous referee for comments and suggestions that
significantly improved the content and presentation of this work. MB, NA, IK,
and MM acknowledge financial support by the Flemish Fund for Scientific
Research (FWO-Vlaanderen) through the research projects G030319N, G0G0420N,
and G037822N. AG and BVM acknowledge the support by FWO-Vlaanderen through the
PhD Fellowship Grants 11H2121N and 1193222N, respectively. CT acknowledges the
INAF grant 2022 LEMON. This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation program (grant agreement No. 683184).

## References

  * Aniano et al. (2020) Aniano, G., Draine, B. T., Hunt, L. K., et al. 2020, ApJ, 889, 150
  * Auld et al. (2013) Auld, R., Bianchi, S., Smith, M. W. L., et al. 2013, MNRAS, 428, 1880
  * Baes et al. (2024) Baes, M., Gebek, A., Trčka, A., et al. 2024, A&A, in press
  * Baes et al. (2020) Baes, M., Nersesian, A., Casasola, V., et al. 2020, A&A, 641, A119
  * Baldry et al. (2004) Baldry, I. K., Glazebrook, K., Brinkmann, J., et al. 2004, ApJ, 600, 681
  * Balogh et al. (2004) Balogh, M. L., Baldry, I. K., Nichol, R., et al. 2004, ApJ, 615, L101
  * Bianchi et al. (2018) Bianchi, S., De Vis, P., Viaene, S., et al. 2018, A&A, 620, A112
  * Burgarella et al. (2005) Burgarella, D., Buat, V., & Iglesias-Páramo, J. 2005, MNRAS, 360, 1413
  * Camps & Baes (2015) Camps, P. & Baes, M. 2015, Astronomy and Computing, 9, 20
  * Camps & Baes (2020) Camps, P. & Baes, M. 2020, Astronomy and Computing, 31, 100381
  * Camps et al. (2022) Camps, P., Kapoor, A. U., Trcka, A., et al. 2022, MNRAS, 512, 2728
  * Camps et al. (2016) Camps, P., Trayford, J. W., Baes, M., et al. 2016, MNRAS, 462, 1057
  * Camps et al. (2018) Camps, P., Trčka, A., Trayford, J., et al. 2018, ApJS, 234, 20
  * Casasola et al. (2017) Casasola, V., Cassarà, L. P., Bianchi, S., et al. 2017, A&A, 605, A18
  * Casura et al. (2022) Casura, S., Liske, J., Robotham, A. S. G., et al. 2022, MNRAS, 516, 942
  * Ciesla et al. (2014) Ciesla, L., Boquien, M., Boselli, A., et al. 2014, A&A, 565, A128
  * Ciotti (1991) Ciotti, L. 1991, A&A, 249, 99
  * Conselice (2014) Conselice, C. J. 2014, ARA&A, 52, 291
  * Cortese et al. (2012) Cortese, L., Ciesla, L., Boselli, A., et al. 2012, A&A, 540, A52
  * Costantin et al. (2023) Costantin, L., Pérez-González, P. G., Vega-Ferrero, J., et al. 2023, ApJ, 946, 71
  * da Cunha et al. (2010) da Cunha, E., Eminian, C., Charlot, S., & Blaizot, J. 2010, MNRAS, 403, 1894
  * Dale et al. (2020) Dale, D. A., Anderson, K. R., Bran, L. M., et al. 2020, AJ, 159, 195
  * Devour & Bell (2017) Devour, B. M. & Bell, E. F. 2017, MNRAS, 468, L31
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168
  * Dimauro et al. (2018) Dimauro, P., Huertas-Company, M., Daddi, E., et al. 2018, MNRAS, 478, 5410
  * Donnari et al. (2019) Donnari, M., Pillepich, A., Nelson, D., et al. 2019, MNRAS, 485, 4817
  * Draine (2003) Draine, B. T. 2003, ARA&A, 41, 241
  * Driver et al. (2011) Driver, S. P., Hill, D. T., Kelvin, L. S., et al. 2011, MNRAS, 413, 971
  * Galliano et al. (2021) Galliano, F., Nersesian, A., Bianchi, S., et al. 2021, A&A, 649, A18
  * García-Benito et al. (2017) García-Benito, R., González Delgado, R. M., Pérez, E., et al. 2017, A&A, 608, A27
  * González Delgado et al. (2015) González Delgado, R. M., García-Benito, R., Pérez, E., et al. 2015, A&A, 581, A103
  * Graham (2019) Graham, A. W. 2019, PASA, 36, e035
  * Graham & Worley (2008) Graham, A. W. & Worley, C. C. 2008, MNRAS, 388, 1708
  * Greener et al. (2020) Greener, M. J., Aragón-Salamanca, A., Merrifield, M. R., et al. 2020, MNRAS, 495, 2305
  * Häußler et al. (2013) Häußler, B., Bamford, S. P., Vika, M., et al. 2013, MNRAS, 430, 330
  * Häußler et al. (2022) Häußler, B., Vika, M., Bamford, S. P., et al. 2022, A&A, 664, A92
  * Holwerda et al. (2009) Holwerda, B. W., Keel, W. C., Williams, B., Dalcanton, J. J., & de Jong, R. S. 2009, AJ, 137, 3000
  * Ibarra-Medel et al. (2016) Ibarra-Medel, H. J., Sánchez, S. F., Avila-Reese, V., et al. 2016, MNRAS, 463, 2799
  * Jedrzejewski (1987) Jedrzejewski, R. I. 1987, MNRAS, 226, 747
  * Kapoor et al. (2021) Kapoor, A. U., Camps, P., Baes, M., et al. 2021, MNRAS, 506, 5703
  * Keel & White (2001a) Keel, W. C. & White, Raymond E., I. 2001a, AJ, 121, 1442
  * Keel & White (2001b) Keel, W. C. & White, Raymond E., I. 2001b, AJ, 122, 1369
  * Kelvin et al. (2012) Kelvin, L. S., Driver, S. P., Robotham, A. S. G., et al. 2012, MNRAS, 421, 1007
  * Kennedy et al. (2015) Kennedy, R., Bamford, S. P., Baldry, I., et al. 2015, MNRAS, 454, 806
  * Kennedy et al. (2016) Kennedy, R., Bamford, S. P., Häußler, B., et al. 2016, MNRAS, 460, 3458
  * Ko & Im (2005) Ko, J. & Im, M. 2005, Journal of Korean Astronomical Society, 38, 149
  * Kormendy (1977) Kormendy, J. 1977, ApJ, 217, 406
  * Kron (1980) Kron, R. G. 1980, ApJS, 43, 305
  * La Barbera et al. (2010) La Barbera, F., de Carvalho, R. R., de La Rosa, I. G., et al. 2010, MNRAS, 408, 1313
  * Lange et al. (2015) Lange, R., Driver, S. P., Robotham, A. S. G., et al. 2015, MNRAS, 447, 2603
  * López Fernández et al. (2018) López Fernández, R., González Delgado, R. M., Pérez, E., et al. 2018, A&A, 615, A27
  * Marinacci et al. (2018) Marinacci, F., Vogelsberger, M., Pakmor, R., et al. 2018, MNRAS, 480, 5113
  * Mathis (1990) Mathis, J. S. 1990, ARA&A, 28, 37
  * Möllenhoff et al. (2006) Möllenhoff, C., Popescu, C. C., & Tuffs, R. J. 2006, A&A, 456, 941
  * Moustakas et al. (2023) Moustakas, J., Lang, D., Dey, A., et al. 2023, ApJS, 269, 3
  * Muñoz-Mateos et al. (2009) Muñoz-Mateos, J. C., Gil de Paz, A., Boissier, S., et al. 2009, ApJ, 701, 1965
  * Naiman et al. (2018) Naiman, J. P., Pillepich, A., Springel, V., et al. 2018, MNRAS, 477, 1206
  * Nelson et al. (2019a) Nelson, D., Springel, V., Pillepich, A., et al. 2019a, Computational Astrophysics and Cosmology, 6, 2
  * Nelson et al. (2019b) Nelson, D., Pillepich, A., Springel, V., et al. 2019b, MNRAS, 490, 3234
  * Nelson et al. (2018) Nelson, D., Pillepich, A., Springel, V., et al. 2018, MNRAS, 475, 624
  * Nersesian et al. (2019) Nersesian, A., Xilouris, E. M., Bianchi, S., et al. 2019, A&A, 624, A80
  * Nersesian et al. (2023) Nersesian, A., Zibetti, S., D’Eugenio, F., & Baes, M. 2023, A&A, 673, A63
  * Parikh et al. (2021) Parikh, T., Thomas, D., Maraston, C., et al. 2021, MNRAS, 502, 5508
  * Pastrav et al. (2013) Pastrav, B. A., Popescu, C. C., Tuffs, R. J., & Sansom, A. E. 2013, A&A, 557, A137
  * Pessa et al. (2023) Pessa, I., Schinnerer, E., Sanchez-Blazquez, P., et al. 2023, A&A, 673, A147
  * Petrosian (1976) Petrosian, V. 1976, ApJ, 210, L53
  * Pillepich et al. (2018a) Pillepich, A., Springel, V., Nelson, D., et al. 2018a, MNRAS, 473, 4077
  * Pillepich et al. (2018b) Pillepich, A., Nelson, D., Hernquist, L., et al. 2018b, MNRAS, 475, 648
  * Pillepich et al. (2019) Pillepich, A., Nelson, D., Springel, V., et al. 2019, MNRAS, 490, 3196
  * Pohlen et al. (2010) Pohlen, M., Cortese, L., Smith, M. W. L., et al. 2010, A&A, 518, L72
  * Psychogyios et al. (2020) Psychogyios, A., Vika, M., Charmandaris, V., et al. 2020, A&A, 633, A104
  * Roberts & Haynes (1994) Roberts, M. S. & Haynes, M. P. 1994, ARA&A, 32, 115
  * Rodriguez-Gomez et al. (2019) Rodriguez-Gomez, V., Snyder, G. F., Lotz, J. M., et al. 2019, MNRAS, 483, 4140
  * Roy et al. (2018) Roy, N., Napolitano, N. R., La Barbera, F., et al. 2018, MNRAS, 480, 1057
  * Sánchez-Blázquez et al. (2014) Sánchez-Blázquez, P., Rosales-Ortega, F. F., Méndez-Abreu, J., et al. 2014, A&A, 570, A6
  * Shen et al. (2003) Shen, S., Mo, H. J., White, S. D. M., et al. 2003, MNRAS, 343, 978
  * Shibuya et al. (2015) Shibuya, T., Ouchi, M., & Harikane, Y. 2015, ApJS, 219, 15
  * Smith et al. (2012) Smith, M. W. L., Gomez, H. L., Eales, S. A., et al. 2012, ApJ, 748, 123
  * Springel et al. (2018) Springel, V., Pakmor, R., Pillepich, A., et al. 2018, MNRAS, 475, 676
  * Strateva et al. (2001) Strateva, I., Ivezić, Ž., Knapp, G. R., et al. 2001, AJ, 122, 1861
  * Suess et al. (2019) Suess, K. A., Kriek, M., Price, S. H., & Barro, G. 2019, ApJ, 877, 103
  * Tortora et al. (2010) Tortora, C., Napolitano, N. R., Cardone, V. F., et al. 2010, MNRAS, 407, 144
  * Tortora et al. (2018) Tortora, C., Napolitano, N. R., Roy, N., et al. 2018, MNRAS, 473, 969
  * Trujillo et al. (2004) Trujillo, I., Burkert, A., & Bell, E. F. 2004, ApJ, 600, L39
  * Trujillo et al. (2020) Trujillo, I., Chamba, N., & Knapen, J. H. 2020, MNRAS, 493, 87
  * Trujillo et al. (2007) Trujillo, I., Conselice, C. J., Bundy, K., et al. 2007, MNRAS, 382, 109
  * Trujillo et al. (2006) Trujillo, I., Förster Schreiber, N. M., Rudnick, G., et al. 2006, ApJ, 650, 18
  * Trujillo et al. (2001) Trujillo, I., Graham, A. W., & Caon, N. 2001, MNRAS, 326, 869
  * Trčka et al. (2022) Trčka, A., Baes, M., Camps, P., et al. 2022, MNRAS, 516, 3728
  * van der Wel et al. (2014) van der Wel, A., Franx, M., van Dokkum, P. G., et al. 2014, ApJ, 788, 28
  * van der Wel et al. (2008) van der Wel, A., Holden, B. P., Zirm, A. W., et al. 2008, ApJ, 688, 48
  * van der Wel et al. (2023) van der Wel, A., Martorano, M., Haussler, B., et al. 2023, ApJ, submitted
  * Viaene et al. (2016) Viaene, S., Baes, M., Bendo, G., et al. 2016, A&A, 586, A13
  * Vulcani et al. (2014) Vulcani, B., Bamford, S. P., Häußler, B., et al. 2014, MNRAS, 441, 1340
  * Wolf et al. (2010) Wolf, J., Martinez, G. D., Bullock, J. S., et al. 2010, MNRAS, 406, 1220
  * Zheng et al. (2017) Zheng, Z., Wang, H., Ge, J., et al. 2017, MNRAS, 465, 4572
  * Zhuang et al. (2019) Zhuang, Y., Leaman, R., van de Ven, G., et al. 2019, MNRAS, 483, 1862