benchmark Model A with coupling constant $g_{\text{V}}=1$. For Model B with
coupling constant $g_{\text{V}}=3$, $W^{\prime}$ masses below
$3.3\leavevmode\nobreak\ \text{TeV}$ are excluded. The $W^{\prime}$ cross-
section limits are also converted into constraints on the couplings in the
$g_{\mathrm{F}}$ vs $g_{\mathrm{H}}$ plane for resonance mass hypotheses of
$2$, $3$ and $4$ TeV.

The 95% CL upper limits on the cross section for $ggA$ production multiplied
by the $A$ boson’s branching fraction to $Zh$ range from
$0.6\leavevmode\nobreak\ \mathrm{pb}$ for $m_{A}=220\leavevmode\nobreak\
\text{GeV}$ to $3\leavevmode\nobreak\ \mathrm{fb}$ for
$m_{A}=2\leavevmode\nobreak\ \text{TeV}$. The 95% CL upper limits on the cross
section for $b\mathit{{\mkern 0.0mu\overline{\mkern
0.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}A$
production multiplied by the $A$ boson’s branching fraction to $Zh$ range from
$0.5\leavevmode\nobreak\ \mathrm{pb}$ for $m_{A}=220\leavevmode\nobreak\
\text{GeV}$ to $2.5\leavevmode\nobreak\ \mathrm{fb}$ for
$m_{A}=2\leavevmode\nobreak\ \text{TeV}$. The limits on the $ggA$ and
$b\mathit{{\mkern 0.0mu\overline{\mkern
0.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}A$
production cross sections are converted into constraints on the parameters
$\tan\beta$, $\cos(\beta-\alpha)$ and $m_{A}$ in the Type-I, Type-II, Lepton-
specific and Flipped 2HDM scenarios.

The cross-section limits improve on the results from the ATLAS analysis of the
partial Run 2 dataset. The improvements range from about $50\%$ for a
resonance mass of $220\leavevmode\nobreak\ \text{GeV}$ to about $400\%$ for a
mass of $5\leavevmode\nobreak\ \text{TeV}$. The improvements at low resonance
masses are mainly due to the larger dataset, while at high resonance masses
the improvements are mostly due to refined $b$-tagging techniques, including
the use of variable-radius track-jets instead of track-jets clustered with a
fixed radius parameter of $R=0.2$.

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# Translators of galaxy morphology indicators between observation and
simulation

J. K. Jang  Department of Astronomy and Yonsei University Observatory, Yonsei
University, Seoul 03722, Korea  Sukyoung K. Yi  Department of Astronomy and
Yonsei University Observatory, Yonsei University, Seoul 03722, Korea
<EMAIL_ADDRESS>Yohan Dubois  Institut d’Astrophysique de Paris, Sorbonne
Université, CNRS, UMR 7095, 98 bis bd Arago, 75014 Paris, France  Jinsu Rhee
Department of Astronomy and Yonsei University Observatory, Yonsei University,
Seoul 03722, Korea  Christophe Pichon  Institut d’Astrophysique de Paris,
Sorbonne Université, CNRS, UMR 7095, 98 bis bd Arago, 75014 Paris, France
Taysun Kimm  Department of Astronomy and Yonsei University Observatory, Yonsei
University, Seoul 03722, Korea  Julien Devriendt  Dept of Physics, University
of Oxford, Keble Road, Oxford OX1 3RH, UK  Marta Volonteri  Institut
d’Astrophysique de Paris, Sorbonne Université, CNRS, UMR 7095, 98 bis bd
Arago, 75014 Paris, France  Sugata Kaviraj  University of Hertfordshire,
Hatfield, Hertfordshire, United Kingdom  Sebastien Peirani  Université Côte
d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice,
France  Sree Oh  Department of Astronomy and Yonsei University Observatory,
Yonsei University, Seoul 03722, Korea  Research School of Astronomy and
Astrophysics, Australian National University, Canberra, ACT 2611, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia  Scott Croom  ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), Australia  Sydney Institute for Astronomy (SIfA),
School of Physics, The University of Sydney, NSW 2006, Australia

(Received XX; Revised YY; Accepted ZZ)

###### Abstract

Based on the recent advancements in the numerical simulations of galaxy
formation, we anticipate the achievement of realistic models of galaxies in
the near future. Morphology is the most basic and fundamental property of
galaxies, yet observations and simulations still use different methods to
determine galaxy morphology, making it difficult to compare them. We hereby
perform a test on the recent NewHorizon simulation which has spatial and mass
resolutions that are remarkably high for a large-volume simulation, to resolve
the situation. We generate mock images for the simulated galaxies using SKIRT
that calculates complex radiative transfer processes in each galaxy. We
measure morphological indicators using photometric and spectroscopic methods
following observer’s techniques. We also measure the kinematic disk-to-total
ratios using the Gaussian mixture model and assume that they represent the
true structural composition of galaxies. We found that spectroscopic
indicators such as $V/\sigma$ and $\lambda_{\rm R}$ closely trace the
kinematic disk-to-total ratios. In contrast, photometric disk-to-total ratios
based on the radial profile fitting method often fail to recover the true
kinematic structure of galaxies, especially for small galaxies. We provide
translating equations between various morphological indicators.

††journal: ApJ

##  1 Introduction

In the era of modern astronomy, various observations have been made with
regard to external galaxies. From the local to the high-redshift Universe,
many observations have suggested that galaxies exhibit various morphological
properties. Such diversity indicates that galaxies comprise a complex mixture
of kinematic components rather than a single structure. Multiple structures
may provide an essential clue to the formation process of galaxies. Based on
this idea, an independent field of study exists for morphological
classification (Hubble, 1926; Shapley & Paraskevopoulos, 1940; Holmberg, 1958;
De Vaucouleurs, 1959; van den Bergh, 1960; Sandage, 1975). The simplest
exercise is based on visual inspection. However, with the improvement of the
surface photometric technique we can now perform radial profile fitting for
the structural decomposition of the galaxy often using Sérsic parameterization
(Sérsic, 1963).

The profile fitting results suggest the presence of “disk” and “bulge”
components in a galaxy, which provides the most widely used morphology index,
i.e., the bulge-to-total ratio ($B/T$) or disk-to-total ratio ($D/T$). In
addition, an extended stellar halo and/or an extra component in the nuclear
region is often implied. Disks are often expressed with the $n=1$ Sérsic
index, that is, the so called exponential disk. Classical bulges are generally
referred to as Sérsic with $n=4$ components, whereas pseudo-bulges show $n<2$
(Carollo et al., 1997; Kormendy et al., 2006). Photometric decomposition is
usually performed using open-source software tools: e.g., IRAF, GALFIT (Peng
et al., 2010), or PROFIT (Robotham et al., 2017). While photometric
decomposition is based on profile fitting, Zhu et al. (2018b); Santucci et al.
(2022) attempted to conduct kinematic decomposition using integral field
spectroscopic data, e.g., CALIFA and SAMI (González Delgado et al., 2015; S.
F. Sanchez et al., 2016; van de Sande J., et al., 2017; Rawlings et al.,
2020).

In numerical simulations, galaxy properties, including morphology, are
sensitive to the cosmology adopted mainly because of the dark matter and thus
galaxy assembly history is determined by cosmology. Moreover, understanding
astrophysical processes, such as stellar and AGN feedback, is crucial for
generating the galaxy morphology distribution realistically (Übler et al.,
2014). As we possess a “concordant” cosmological understanding of the Universe
(Komatsu et al., 2011) and a reasonable consensus for the feedback effect, it
is an urgent task to see if state-of-the-art simulations reproduce the
critical properties of galaxies, in particular, morphology. Indeed, recent
simulations have provided an array of beautiful and seemingly-realistic images
of galaxies (Vogelsberger et al., 2014; Schaye, J., et al., 2015; Dubois et
al., 2016; Pillepich et al., 2019; Dubois et al., 2021).

Different techniques are used to determine the morphology of galaxies through
simulations. For instance, a widely-used property is the ratio between the
speeds of ordered (rotating) motion and random motion, that is, $V/\sigma$ or
kappa parameter (${\kappa}_{\rm rot}$) (Sales, 2010). These parameters may be
effective for separating early- from late-type galaxies in a large sample;
however, the demarcation cut is still arbitrary. For example, Dubois et al.
(2016) found that a cut of $V/\sigma$ $=1$ roughly satisfied the observed
fractions of early and late-type galaxies.

The circularity parameter is another way to measure the degree of rotational
dominance of a galaxy. Abadi et al. (2003) introduced it using the angular
momentum and the binding energy of the stellar particles in a galaxy. As the
circularity parameter is measured for all the star particles of the simulated
galaxy, we can express the “kinematic morphology” based on the circularity
distribution. Thus, the use of circularity distribution may reduce the degree
of uncertainty compared to $V/\sigma$ but is still subject to the same problem
of arbitrariness. An important concern is how well visual or morphological
classifications trace the kinematics of galaxies ($V/\sigma$ or circularity).
Scannapieco et al. (2010) have indeed demonstrated that the morphology
indicator $D/T$ from photometry and kinematics based on circularity do not
agree well with each other for their simulated galaxies. This is a severe
issue for the galaxy community. Their claim was based on eight simulated
galaxies with spatial resolutions of roughly 1 kpc. We aim to verify this
claim using a larger sample of galaxies based on a more up-to-date simulation
with much higher resolution.

All these issues originate from one question. Can we identify the pivotal
structures of galaxies distinctively and reliably? With its high spatial and
mass resolution, the hydrodynamical cosmological simulation NewHorizon (Dubois
et al., 2021) is a excellent testbed for answering this question. To directly
compare with observational data, we generate mock images using SKIRT, a
radiative transfer pipeline (Baes & Camps, 2015; Camps & Baes, 2020). We
measure the weights of the disk and spheroid components following the standard
observational technique. We compare the photometric and kinematic values of
$D/T$ of every galaxy with a stellar mass of over $10^{9.5}\,\rm M_{\odot}$
and attempt to find or quantify the correlation between them. We then discuss
the degree of (dis)agreement between the two. Finally, we provide a translator
between observation and the NewHorizon simulation.

Figure 1:  Eight sets of the face-on and edge-on mock images created using the
SKIRT pipeline for various values of disk-to-total ratios. Red, green, and
blue colors are corresponding to SDSS $i$-, $r$-, and $g$-band fluxes,
respectively. The kinematic disk-to-total ratios (see Section 2.3.1 for
definition) of the sample galaxies are given in the face-on images.

##  2 Methodology

###  2.1 The Sample

We use NewHorizon (Dubois et al., 2021), a high-resolution cosmological
hydrodynamic zoom-in simulation of galaxy formation. It covers a spherical
“field” region in Horizon-AGN (Dubois et al., 2016) with a radius of $10\,{\rm
Mpc}$. Both simulations were performed with RAMSES (Teyssier et al., 2002), an
adaptive mesh refinement (AMR) code. The maximum spatial resolution of
NewHorizon considering the AMR structure is $\Delta x=34\,\rm{pc}$, and the
mass resolutions are $10^{4}$ and $10^{6}\,\rm M_{\rm\odot}$ for stellar and
dark matter particles, respectively. The simulation was executed with the
following cosmological parameters, consistent with the WMAP-7 data (Komatsu et
al., 2011): Hubble constant, $H_{0}=70.4\,{\rm km\,s}^{-1}\,{\rm Mpc}^{-1}$;
total mass density, $\Omega_{\rm m}=0.272$; total baryon density, $\Omega_{\rm
b}=0.0455$; dark energy density, $\Omega_{\rm\Lambda}=0.728$; the amplitude of
power spectrum, ${\sigma}_{\rm 8}=0.809$; the spectral index, $n_{\rm
s}=0.967$. A detailed description of NewHorizon can be found in Dubois et al.
(2021).

NewHorizon contains a substantially smaller number of massive galaxies than
the parent simulation, Horizon-AGN, simply because of the volume difference
(roughly a factor of 543). In order to resolve kinematic structure, we used
only the most massive galaxies in the NewHorizon simulation. To secure a large
sample size we used the data from three different snapshots assuming that the
morphology and kinematic structure of a galaxy at different snapshots are
independently determined.

We used the AdaptaHOP algorithm (Aubert et al., 2004) with the most massive
sub-node mode method (Tweed et al., 2009) for stellar particles. For the
initial detection of a galaxy, a cut of $N_{\rm ptcl}>50$ was used. The center
of a galaxy is defined using the density distribution, that is, the position
of the stellar particles on the highest density peak. We sample the galaxies
with the total stellar mass greater than $10^{9.5}\,\rm M_{\rm\odot}$, which
corresponds to $N_{\rm ptcl}\gtrsim 3.6\times 10^{5}$ (75 galaxies at $z=0.7$,
92 galaxies at $z=0.3$ and 107 galaxies at $z=0.17$). Also, we exclude the
irregular or merging galaxy samples (38 galaxies) based on the visual
morphology classification.

###  2.2 Mock Imaging

For visual inspection and photometric classification following the oberver’s
approach, we first generate the mock images of the NewHorizon galaxies using
SKIRT. Assuming that a certain number of photon packets are radiated from each
light source, SKIRT traces each ray and calculates the attenuation from the
gas cells along its path. We used the “BC03” simple stellar population models
(Bruzual & Charlot, 2003) to calculate the light from the sources. We assume
that only the gas cells with the temperature under $10,000\,\rm K$ can have
the dust content in it. We use the dust population model of Zubko et al.
(2004), allowing each gas cell to include silicate, graphite, and PAH
populations each of which has 15 size varieties. We estimate the dust
abundance of each cell as $M_{\rm dust}=M_{\rm cell}\times Z\times f_{\rm
dust}$, where $Z$ denotes the metallicity and $f_{\rm dust}$ denotes the dust-
to-metal ratio. We set $f_{\rm dust}$ to 0.3 as a fixed value for every gas
cell. The quality of the image basically depends on the number of photon
packets per wavelength. We assume the number of photon packets to be $8\times
10^{7}\times(M_{\rm gal}\,/\,10^{10}\,\rm M_{\rm\odot})$ photon packets
depending on the galaxy mass, where $M_{\rm gal}$ denotes the total stellar
mass of a galaxy. Other studies have adopted adaptive photon packet number
scaling with pixel size (Rodriguez-Gomez et al., 2019). In this study, the
pixel scale of the resultant image is $\Delta x$ (i.e., $34\,\rm pc\,\rm
pix^{-1}$). SKIRT can provide the calculation of a second (cascade) radiation,
i.e., the thermal radiation from each gas (dust) cell, and characteristic
emission lines from star-forming regions; however, they were not considered in
our analysis because we focus on optical bands in this study.

We include seeing effects by adding Gaussian dispersion with a standard
deviation of 3 pixel lengths but not the background noise. The outermost part
of the galaxy’s surface brightness is obviously more affected by the noise.
However, with logarithmic radial binning and a strict radius cut for radial
profile we can achieve reasonably-robust measurements against the uncertainty
in the background noise. Figure 1 shows the mock images of eight sample
galaxies for various values of disk-to-total ratios. The color scheme is the
same as that of Lupton et al. (2004).

###  2.3 Decomposition

####  2.3.1 Kinematic Decomposition

Figure 2:  An example of the phase-space distribution of a disk galaxy. While
three parameters are used for component detection as described in the text, we
hereby show only the energy and circularity parameters. The GMM clustering
result with Ncomp = 6 is also marked in the figure. Y-axis shows the specific
binding energy normalized with the most bound particle’s specific binding
energy, and X-axis shows circularity parameter. Ellipses show 1-${\sigma}$ of
multivariate Gaussian distribution, and the numbers are ordered with their
mass weight.  Figure 3:  The face-on $r$-band flux density map of each GMM
component shown in Figure 2.

The kinematic decomposition of the NewHorizon galaxies was performed based on
three key parameters. The first is circularity. The circularity (${\epsilon}$)
of each stellar particle can be defined in two different ways, using the
radial distance or the binding energy of a particle. We adopt the latter.
Circularity is defined as

$\epsilon=J_{\rm z}\,/\,J_{\rm cir}({e}),$ (1)

where $J_{\rm z}$ denotes the angular momentum of each star particle along the
bulk rotation axis of a galaxy, and $J_{\rm cir}({e})$ denotes the maximum
angular momentum that a stellar particle can have with a specific binding
energy ($e$). We assumed a spherically symmetric potential for calculating the
binding energy to perform a fair comparison with the circularity parameters
derived from spectroscopy (e.g., Zhu et al., 2018a, b). The circularity
parameter (${\epsilon}$) is widely used to decompose the kinematic structures
of simulated galaxies (see e.g., Park et al., 2019, 2020). Furthermore, we use
two additional parameters for kinematic decomposition as considered in recent
studies (e.g., Obreja et al., 2018; Du et al., 2019, 2020). The first is the
remaining angular momentum, i.e., $J_{\rm p}\,/\,J_{\rm cir}(e)$, where
$\vec{J_{\rm p}}=\vec{J}-\vec{J_{\rm z}}$. The second parameter (namely,
“energy parameter”) is the specific binding energy of a particle normalized by
the value of the most bound particle, i.e., $e\,/\,|e_{\rm max}|$.

Considering these parameters ($J_{\rm z}\,/\,J_{\rm cir}(e)$, $J_{\rm
p}\,/\,J_{\rm cir}(e)$, and $e\,/\,|e_{\rm max}|$), we can decompose the
kinematic structures of a galaxy based on their three-dimensional phase-space
distributions. The specific locations of structures in the phase-space vary
especially along the energy parameter axis, depending on galaxies and the
presence of a centrally-concentrated component (e.g., bulge). However, the
distribution is so smooth that it is challenging to group (“cluster”) stellar
particles into various kinematic components.

We use a Gaussian mixture model (GMM), an un-supervised machine learning
clustering technique, to overcome this difficulty. Recent studies have used
GMM to decompose galaxies into detailed structural components (e.g., Du et
al., 2019, 2020). For instance, Du et al. (2019) suggests that for the TNG100
simulation (Nelson et al., 2018), the mean positions of clusters identified
with GMM are located in four different regions in the energy versus
circularity space: two for the spheroidal component (${\epsilon}<0.5$, bulge &
halo) and the other two for the (thin and thick) disk components
(${\epsilon}>0.5$) (refer to Fig. 3 in Du et al. 2020). We apply GMM to
NewHorizon galaxies. The number of components is a free parameter in GMM, and
we have tried various numbers up to 15. We set it to be 6 ($N_{\rm
comp}\,=\,6$) in this study so that the comparison with observations becomes
simple and intuitive. To be more specific, we wanted to detect the structural
components that observers often detect and discuss: e.g., thin and thick disks
for rotating components, and bulge, inner and outer halos for dispersion
components. In order to detect these five components using GMM, the minimum
value of $N_{\rm comp}$ was found to be 6 in most cases.

Figure 2 shows the GMM “components” in the energy-circularity space for a
sample galaxy. Each component is assigned an ID in the order of mass weight,
where 1 corresponds to the highest weight. The detailed spatial distributions
of the components are presented in Figure 3. We classify the six components
into five structural components that observers often refer to: the warm disk
(components 1 and 2), cold disk (component 3), inner spheroid (component 4),
outer spheroid (component 5), and nucleus (component 6), although the direct
comparison between the GMM-detected structures and observational structures
may not be straightforward.

We note that 38% of our galaxies possess a kinematically distinct component
near the galactic center. Their size (the mean distance of all the star
particles of the component) is roughly 12% of the half mass radius ($R_{\rm
50}$) of the galaxy, or 0.2 kpc, and their mass fraction is about 11%. Since
they appear to be more centrally concentrated than typical bulges, we call
them a “nucleus” in this study. If it is real, conventional bulges may be a
combination of the nucleus and (part of) the inner spheroid. The detailed
distribution of star particles in the phase space varies substantially from
galaxy to galaxy. We present the phase-space diagram of other galaxy in
Appendix for reference. The existence of such a nucleus in galaxies as a
kinematically-distinct structure is an interesting issue. It will be a subject
of future investigations.

Figure 4:  Visual morphology versus kinematic disk-to-total ratio for the
sample galaxies at $z=0.17$. Visual morphology classification was performed by
four members of the authors, and each index value is a mean value of the four.
Individual members classified galaxies into early-type (index 0), lenticular
(1), late-type (2), and unclear (3) galaxies. Except for the unclear galaxies
(morphology index $>2$), visual morphology and $[D/T]_{\rm kin}$ shows a good
correlation (Pearson correlation coefficient r $\sim$ 0.80). The red line with
shade shows the linear fit and 1-$\sigma$ error. The color key on the side
shows the stellar mass information for the galaxies.

The kinematic disk-to-total ratio, $[D/T]_{\rm kin}$, is defined as the mass
ratio between the combined mass of the disk components and the total stellar
mass:

$[D/T]_{\rm kin}=M_{\rm disk}\,/\,M_{\rm total}.$ (2)

where $M_{\rm disk}$ is a total mass of GMM components with mean circularity
$\bar{\epsilon}\,>\,0.5$. We assume $[D/T]_{\rm kin}$ as “ground truth”, a
representative structural property of a galaxy in this study. We compare it
with the visual morphology based on the face-on and the edge-on projection
determined by four members of the authors in Figure 4. We used an arbitrary
digital scheme: 0 for early-type, 1 for lenticular, 2 for late-type, and 3 for
unclear type. The Pearson correlation coefficient ($r$) was measured in the
range of 0 to 2, as 3 for the unclear type is an irrelevant value. The
correlation is reasonably good with $r$ of 0.80, thereby confirming that the
kinematic disk-to-total ratio agrees with the visual morphology.

####  2.3.2 Photometric Decomposition

Figure 5:  Examples of photometric decomposition result. Each column shows the
optimal fitting result based on BIC, best-fitted by one, two, and three
component respectively. The first row shows the face-on mock image of a galaxy
created using sdss g, r, i flux. The second row shows the surface brightness
profile fitting result. The disk (blue), inner spheroid (red), nucleus
(orange), and total galaxy (green)’s surface brightness profiles are shown.
The last row shows the surface mass profile. The disk (blue), spheroid (red)
are divided using the kinematic decomposition, and total (black) surface
density profile is the sum of the two. The black dashed vertical lines are the
$R_{\rm 90}$ of the galaxies.  Figure 6:  Spin parameter estimation for a
galaxy with different inclinations: 0, 30, 60 degree for each row. The first
column shows the mock images of the galaxy based on the SDSS
$g$-,$r$-,$i$-band magnitudes. The second and the third columns are a velocity
and dispersion maps. The last column is the spin parameter measured as a
function of radial distance. The red dashed line indicates the effective
radius.

We use the mock images described in Section 2.2 for photometric decomposition.
We assume that each photometric component follows Sérsic profile (Sérsic,
1963):

$I(R)=I_{\rm e}\,\exp(-b_{\rm n}\,[(R\,/\,R_{\rm e})^{1/n}\,-\,1]),$ (3)

where $R_{\rm e}$ denotes the effective (half-light) radius, $I_{\rm e}$ the
luminosity at $R_{\rm e}$, $n$ the Sérsic index, and $b_{\rm n}$ a function
that depends on the Sérsic index. The Sérsic profile is a well-known model
that can express both the disk and bulge components of galaxies with different
Sérsic index values ($n$), historically 1 for the former and 4 for the latter.
According to a recent study, the Sérsic profile may over-predicts the disk
component in the inner part of galaxies (Papaderos et al., 2022). However, due
to the overall wellness of the fit and difficulty of applying a more
complicated model to observed profiles that are often of limited quality, the
majority of observations and surveys still use Sérsic profile fitting.

For the photometric decomposition of the NewHorizon galaxies, we assume that
galaxies can have up to four components: “nucleus”, “inner spheroid”, “disk”,
and “outer spheroid”. We fit the profile with a one-dimensional surface
brightness radial profile. We use circular apertures for profile fitting
mainly because we only use the face-on images of galaxies. To simplify the
analysis and interpretation, we set the Sérsic index of the disk component to
1. We treat the Sérsic index as a free parameter for the other components. For
the radial extension, we use the data inside $R_{\rm 90}$, where $R_{\rm 90}$
denotes the radius within which 90% of the total stellar mass resides. For our
sample, $R_{\rm 90}$ is $2.70^{+1.03}_{-0.40}$ times the $R_{\rm 50}$ median.
We performed profile fitting to rest-frame $r$-band images. We assume that
galaxies are at a distance of 1 Mpc regardless of the redshift; and thus
considering the high resolution of NewHorizon, our images are of good quality
in terms of surface brightness per pixel.

While all the four components are used for radial fits, we select the best
model based on the Bayesian information criterion (BIC) as follows:

$\mathrm{BIC}=-2\,\mathrm{Log}\,\mathcal{L}\,+\,k\,\mathrm{Log}\,n_{\rm dat},$
(4)

where $\mathcal{L}$ denotes the likelihood of fit, $k$ denotes the number of
parameters, and $n_{\rm dat}$ denotes the number of data points. In practice,
none of our galaxies needed all four components for a BIC-based best fit.
Approximately 34% (80 out of 236) of galaxies were best fitted as single-
component disk galaxies, i.e., “pure disks”. 29% of galaxies were best fitted
by a combination of two components (disk and spheroid). The rest (37%)
required an additional “nucleus” component. Approximately 54% of the three-
component fitted galaxies were found to possess a nuclear component based on
the GMM kinematic decomposition in Section 2.3.1. Figure 5 shows galaxies
best-fitted by one, two, or three components. We provide in the bottom row the
radial mass profile of the galaxies derived from the GMM analysis for
reference.

We defined the photometric disk-to-total ratio as the luminosity fraction of
the disk component as follows:

$[D/T]_{\rm phot}=L_{\rm disk}\,/\,L_{\rm total}$ (5)

and we compare this parameter with the result from the kinematic decomposition
described in Section 3.

###  2.4 Spectroscopic Parameters

We measure spectroscopic parameters to assess the degree of correlation with
intrinsic kinematics. For this, we use two parameters, $\lambda_{R}$ and
$V/{\sigma}$. We used the definition of the spin parameter given in Emsellem
et al. (2007).

$\lambda_{\rm R}=\frac{\Sigma_{\rm i}F_{\rm i}R_{\rm i}|V_{\rm
i}|}{\Sigma_{\rm i}F_{\rm i}R_{\rm i}\sqrt{V_{\rm i}^{2}+\sigma_{\rm
i}^{2}}}.$ (6)

where $F_{\rm i}$, $R_{\rm i}$, $V_{\rm i}$, and $\sigma_{\rm i}$ are the
attenuated r-band flux, distance from the center, line-of-sight (los)
velocity, and los velocity dispersion of i-th spaxel.

We use the same axis ratio of the ellipse measured at $R_{\rm e}$ in the SDSS
$r$-band flux for all the radial bins. For each inclination, we generate
velocity and dispersion maps using the Voronoi tessellation algorithm based on
Cappellari & Copin (2003) to ensure that the $S/N$ ratios of the bins are
virtually the same. At least five stellar particles are present in each bin.
Figure 6 shows an example of the measurement. The first column exhibits RGB
color images using the SDSS $i$, $g$, and $r$-band fluxes. The red dashed
ellipse indicates the ellipse fit at $R_{\rm e}$. The second and third columns
show the velocity and velocity dispersion maps, respectively. The last column
shows the spin parameter measurements inside 3 $R_{\rm e}$. The rows
demonstrate the results for different inclinations.

The rotation-to-dispersion ratio, $V/\sigma$, was measured also considering
flux weights and within $R_{\rm e}$ using the following definition:

$(V/\sigma)^{\rm 2}\ =\ \frac{\Sigma_{\rm i}F_{\rm i}V_{\rm i}^{\rm
2}}{\Sigma_{\rm i}F_{\rm i}\sigma_{\rm i}^{\rm 2}},$ (7)

where $F_{\rm i}$, $V_{\rm i}$, and $\sigma_{\rm i}$ are the attenuated r-band
flux, los velocity, and los velocity dispersion of i-th spaxel. We choose
different inclinations to measure two spectroscopic parameters, $\theta$ =
$30^{\circ}$, $60^{\circ}$, and $90^{\circ}$.

Figure 7:  The relation between the spectroscopic parameters and the kinematic
disk-to-total ratio, $[D/T]_{\rm kin}$. The upper panel shows the relation for
$\lambda_{\rm R}$, and the lower panel shows for $V/{\sigma}$. The lines with
shades show the linear fit and 1-$\sigma$ error to the data of different
inclinations. The general properties of correlations are given in Table 1.
Figure 8:  The spectroscopic spin parameters of the SAMI observational data
(Hess diagram) and the NewHorizon simulation data (crosses).

##  3 Results

In this section, we assess the validity of various morphological indicators by
comparing them with the kinematic disk-to-total ratio.

###  3.1 Spectroscopic parameters

Figure 7 shows the correlation of the spin parameter $\lambda_{\rm R}$ (upper
panel) and $V/\sigma$ (lower panel) against the kinematic $D/T$. The three
different symbols represent three different inclinations: $30^{\circ}$,
$60^{\circ}$, and $90^{\circ}$. The linear regression for each inclination is
shown with 1-${\sigma}$ standard deviation. We found a reasonably good
agreement between the spectroscopic parameters and $[D/T]_{\rm kin}$. The
general properties of linear regression are given in Table 1. This confirms
that the spectroscopic spin parameters trace the kinematic structure of
galaxies well.

For validation, we compare the SAMI-observed data (Casura et al., 2022) with
the NewHorizon simulation galaxies in the plane defined by the two
spectroscopic spin parameters, $V/\sigma$ and $\lambda_{\rm R}$, in Figure 8.
They indeed correlate well with each other. The simulated galaxies occupy a
region similar to that captured based on the observed data in this plane.
Therefore, it is safe to use spectroscopic spin parameters to extract the
kinematic structure or morphology of galaxies.

Table 1: Correlation between parameters and $[D/T]_{\rm kin}$ ($Y$ = $a$
${[D/T]}_{\rm kin}$ \+ $b$)

$Y$ |  ${\theta}$ (or Mgal) | $a$ | $b$ | $r-value$
---|---|---|---|---
${\lambda}_{\rm R,e}$ | 30∘ | 0.50 | 0.05 | 0.78
${\lambda}_{\rm R,e}$ | 60∘ | 0.76 | 0.07 | 0.83
${\lambda}_{\rm R,e}$ | 90∘ | 0.82 | 0.08 | 0.81
$(V/{\sigma})_{\rm e}$ | 30∘ | 0.54 | 0.05 | 0.76
$(V/{\sigma})_{\rm e}$ | 60∘ | 1.07 | 0.03 | 0.83
$(V/{\sigma})_{\rm e}$ | 90∘ | 1.28 | 0.03 | 0.80
${[D/T]}_{\rm phot}$ | $>10^{9.5}$ | 0.51 | 0.55 | 0.35
${[D/T]}_{\rm phot}$ | $\&\ w/o\ \rm PD^{\rm a}$ | 0.54 | 0.42 | 0.42
${[D/T]}_{\rm phot}$ | $>10^{10.3}$ | 0.67 | 0.41 | 0.65
${[D/T]}_{\rm phot}$ | $\&\ w/o\ \rm PD$ | 0.74 | 0.36 | 0.73

aafootnotetext: PD : pure disk galaxy

Figure 9: The comparison between $[D/T]_{\rm phot}$ and $[D/T]_{\rm kin}$. The
circles denote the galaxies with stellar mass greater than 109.5 M⊙ (upper
panel) and 1010.3 M⊙ (lower panel). The sizes of the circles are scaled with
their mass, between 109.5 and 1011.5 M⊙. The blue dashed line is a linear
regression for the whole sample, while the green dashed line is for the
galaxies with 0.01 $<$ $[D/T]_{\rm phot}$ $<$ 0.99, that is excluding “pure
disks”. The magenta diamonds are the data from Scannapieco et al. (2010). The
correlation and the Pearson coefficient are also shown in each panel. The
galaxies photometrically best-fitted by one, two, or three components are
color-coded as red, yellow, and blue, respectively.

###  3.2 Photometric parameter

Figure 9 shows our galaxy sample on the $[D/T]_{\rm phot}$ versus $[D/T]_{\rm
kin}$ plane. The symbol size was scaled considering the galaxy’s stellar mass.
Figure 9-(a) shows the entire sample of galaxies above $10^{9.5}\,$$\rm
M_{\rm\odot}$. The 1-${\sigma}$ errors were estimated in five equally-spaced
$[D/T]_{\rm kin}$ bins. We also present the 8 simulated galaxies from
Scannapieco et al. (2010) for comparison. Our data based on the NewHorizon
galaxies appear to be compatible to the results of Scannapieco et al. (2010).

As shown in the figure, there is a large scatter, thus leading to a poor (or,
at best “modest”) correlation. Assuming that $[D/T]_{\rm kin}$ traces the true
structure of galaxies, $[D/T]_{\rm phot}$ does not properly recover it: the
correlation coefficient is 0.35 (given inside Panel-a). Besides, $[D/T]_{\rm
phot}$ systematically overestimates the disk-to-total ratio. These facts make
it difficult to directly compare the simulated with the observed galaxies.

Furthermore, there are a number of galaxies with an extremely high value of
$[D/T]_{\rm phot}$ (essentially 1), although their kinematic disk-to-total
ratios are substantially lower. The profile fitting technique classifies them
as “pure disks” whereas GMM clearly detects a substantial dispersion
component. This happens more often for lower mass galaxies: note the small
symbol sizes for galaxies with $[D/T]_{\rm phot}$ $\approx 1$. This
demonstrates that the profile fitting technique tends to perform inaccurate
decomposition for small galaxies. If we assume that galaxies classified as
pure disks are incorrectly done so, we may want to exclude them and re-
estimate the correlation between $[D/T]_{\rm kin}$ and $[D/T]_{\rm phot}$. In
this case, we derived a slightly improved correlation coefficient (0.42). The
translation relations with and without pure disk galaxies are shown in the
figure. The presence or abundance of massive pure disks is an important issue
in terms of cosmology (Kormendy et al., 2010; Peebles, 2015), and it appears
that photometric fits tend to incorrectly classify galaxies as pure disks.
This issue deserves further investigations.

The mis-classified galaxies being typically small and low-mass, we tried
various values of mass cut in the range of $M_{\rm cut}=10^{9.5-10.5}$ $\rm
M_{\rm\odot}$. The correlation coefficient monotonically increases with
increasing mass cut until $M_{\rm cut}=10^{10.3}$ $\rm M_{\rm\odot}$ and
dramatically drops beyond that mainly due to the decrease in the sample size.
Therefore, we have decided that the most representative translation between
$[D/T]_{\rm phot}$ and $[D/T]_{\rm kin}$ can be achieved with $M_{\rm
cut}=10^{10.3}$ $\rm M_{\rm\odot}$. We show the result in Panel-b of Figure 9
and give the correlation between the two parameters for a mass cut of $M_{\rm
cut}=10^{10.3}$ $\rm M_{\rm\odot}$ as follows:

$\displaystyle[D/T]_{\rm phot}$ $\displaystyle=0.67\,[D/T]_{\rm kin}+0.41\
\rm(all)$ (8) $\displaystyle=0.74\,[D/T]_{\rm kin}+0.36\ \rm(exc.\ PD)$ (9)

with a correlation coefficient of 0.65 and 0.73 when pure disks are included
or excluded, respectively. It remains to be tested how galaxies simulated with
different physics and numerical approaches distribute along this relation.

###  3.3 Discussion

Figure 10:  The $\lambda_{\rm R}$ spin parameter vs. $[D/T]_{\rm phot}$ of the
SAMI and the NewHorizon data. The SAMI data are shown in the Hess diagram with
a linear fit (blue line) with 1-$\sigma$ errors (dashed lines). The NewHorizon
simulation data are also fitted with a linear regression (red lines).

We show in Figure 10 the SAMI observed data and NewHorizon simulation data in
the $\lambda_{\rm R}$ vs. $[D/T]_{\rm phot}$ plane. The $[D/T]_{\rm phot}$ for
the NewHorizon galaxies has been measured from face-on images, whereas
$\lambda_{\rm R}$ has been measured for the three values of inclinations as
mentioned in Section 2.4. In addition, for the $[D/T]_{\rm phot}$
measurements, two (disk and spheroid) components have been assumed for SAMI,
whereas up to three components have been used for NewHorizon, as described in
Section 2.3.2. As expected based on the discussion in Section 3.2, there is a
very poor correlation between the two parameters in both the observed and
simulation data.

It is important but not trivial to understand the cause of the difference
between $[D/T]_{\rm phot}$ and $[D/T]_{\rm kin}$. We can try to assess the
impact of technical issues in the measurement of $[D/T]_{\rm kin}$. We
mentioned earlier that the number of kinematic components in GMM is a free
parameter. The use of a large value can detect even small structures such as
tidal streams. We used $N_{\rm comp}=6$ in this study to simplify the analysis
but have tried other values as large as 15. Figure 11 shows the difference in
$[D/T]_{\rm kin}$ estimates when we use 6 and 15 as component numbers. When 15
is used instead of 6, $[D/T]_{\rm kin}$ is estimated to be larger by 0.08.
Thus, it is clear that the details of the analysis affect the estimates of
$[D/T]_{\rm kin}$. However, the component number accounts for only 20–30% of
the difference between $[D/T]_{\rm phot}$ and $[D/T]_{\rm kin}$.

The fact that $[D/T]_{\rm phot}$ is luminosity-weighted while $[D/T]_{\rm
kin}$ is mass-weighted could also cause some difference. It is easily
conceivable that disk stars being typically younger than other stars cause an
increase of $[D/T]_{\rm phot}$ in comparison to $[D/T]_{\rm kin}$. Figure 12
indeed shows it. The luminosity-weighted $[D/T]_{\rm kin}$ ratios are higher
than the mass-weighted values by roughly 0.1. However, this effect is so small
that when we tried the luminosity-weighted $[D/T]_{\rm kin}$ in Figure 9, the
discrepancy between $[D/T]_{\rm kin}$ and $[D/T]_{\rm phot}$ remained almost
the same.

Figure 11:  The difference between $[D/T]_{\rm kin,N=6}$ and $[D/T]_{\rm
kin,N=15}$. The red dashed line corresponds to the average offset between the
two, which is 0.08.

Multiple factors affect the measurement of $[D/T]_{\rm phot}$, too. As was the
case with GMM, the number of components can be a free parameter in the profile
fit, and the use of a different number may affect the measurement, as
mentioned in Section 2.3.1. Other factors may be as critical as the number of
components. The Sérsic index is one of them. Although we fixed the value for
the disk to be 1, we allowed a free value for the other components. However,
it is debatable whether this is the best decision. The size constraints of the
components are also influential. For instance, are disks always larger than
spheroids (in terms of scale length)? Moreover, the details of the mock-
imaging process also cause uncertainties. We know that galaxies can follow
significantly different dust attenuation laws (Fitzpatrick & Massa, 1990;
Calzetti et al., 2003; Gordon et al., 2003; Conroy et al., 2010) depending on
the gas fraction and metallicity. Our SKIRT mock imaging takes the metallicity
difference into account; however, the full consideration of attenuation is
probably much more complicated than what we have. It is not trivial to pin
down the cause of the departure of $[D/T]_{\rm phot}$ from $[D/T]_{\rm kin}$
at the moment; but it would be an important topic for future investigations.

Figure 12:  $[D/T]_{\rm kin}$ $r$-band luminosity-weighted versus mass-
weighted. The dashed line shows the 1:1 relation, and the four adjacent lines
are simple vertical offsets by $\pm 0.1$ and 0.2.

##  4 Summary and Conclusion

This study aimed to inspect the validity of various morphological indicators
and, if possible, introduce translators between theoretical and observational
morphology indicators. We used the NewHorizon simulation, a hydrodynamic
cosmological zoom-in simulation with outstanding spatial and mass resolutions.
We considered galaxies of stellar mass $M_{\rm*}>10^{9.5}\ \rm M_{\rm\odot}$
sampled from three redshifts ranging from $z=0.17$ to $0.7$.

We measured the intrinsic kinematic structure using the GMM clustering in a
3-dimensional phase-space (including energy and angular momentum parameters)
to group each star particle into one of the six components. We classified the
components with a large mean value of circularity ($\epsilon>0.5$) as disks.
Then, we defined the kinematic disk-to-total ratio as the mass ratio between
the disk components and the total galaxy mass inside $R_{\rm 90}$.

We measured the photometric disk-to-total ratio on the mock images of the
galaxies, considering the attenuation from dust using the radiative transfer
pipeline SKIRT for a fair comparison of simulated galaxies with observations.
We performed multi-component fitting to radial surface brightness profiles
allowing up to four components (nucleus, inner spheroid, disk, and outer
spheroid). The optimal result was selected by comparing the Bayesian
information criterion values.

Moreover, we measured the spectroscopic parameters: $V/\sigma$ and
$\lambda_{\rm R}$. We generated the first and second moment velocity maps
using the Voronoi tesselation to ensure an equal $S/N$ ratio. We used three
values of inclinations to measure the following parameters.

The main results can be summarized as follows.

  * •

The kinematic disk-to-total ratio reasonably agrees with visual inspection.

  * •

The spectroscopic parameters exhibited tight correlations with the kinematic
disk-to-total ratio. The $\lambda_{\rm R}$ spin parameter indicated
correlation coefficients in the range of 0.7–0.8, depending on the
inclinations. Similarly-good correlations were found for $V/\sigma$. We
provide translators between different indicators.

  * •

The photometric disk-to-total ratio showed a poor correlation with the
kinematic ratio, and a substantial offset (0.2–0.5 in $D/T$) existed. The
photometric decomposition failed to accurately recover the structural
composition of galaxies, which seemed more serious for low-mass galaxies that
are often classified as pure disks. While the offsets did not change much, the
correlation between the kinematic and photometric disk-to-total ratios became
substantially stronger if we removed the low mass galaxies. We provide
translators between the kinematic and photometric disk-to-total ratios for
both cases.

Morphology is much more than just a first impression. Hubble (1926) correctly
noticed that it contains important information for the nature of galaxies.
Since then abundant information regarding the relationship between the
apparent morphology and true properties of galaxies has been obtained.
Galaxies are thought to be composed mainly of a rotation-dominant component
and dispersion-dominant component. However, it is almost certain that reality
is much more complex. While observational astronomy significantly contributed
to galaxy research in the last century, we have just succeeded in making
arguably-realistic models of galaxies in cosmological large-volume numerical
simulations. The question is how realistic they are. Observations and
simulations use different languages, and translators are required. In this
study, we attempted to find such a translator. We found that spectroscopic
indicators, such as $V/\sigma$ and $\lambda_{\rm R}$ closely traced the true
kinematic structure of galaxies. In contrast, the photometric profile fits
failed to recover it accurately, especially for small galaxies. We were able
to find mappings that could be useful for galaxies with good observational
quality. We hope that this translator will be useful when simulations are
tested against observations. There are a few open questions: for example, the
issue of pure disks and the implication of multiple components in the GMM
analysis, which require further investigation.

## Acknowledgements

This work was granted access to the HPC resources of CINES under the
allocations c2016047637, A0020407637 and A0070402192 by Genci,
KSC-2017-G2-0003 by KISTI, and as a “Grand Challenge” project granted by GENCI
on the AMD Rome extension of the Joliot Curie supercomputer at TGCC. This
research is part of the Spin(e) ANR-13-BS05-0005 (http://cosmicorigin.org),
Segal ANR-19-CE31-0017 (http://secular-evolution.org) and Infinity-UK
projects. This work has made use of the Horizon cluster on which the
simulation was post-processed, hosted by the Institut d’Astrophysique de
Paris. We warmly thank S. Rouberol for running it smoothly. The large data
transfer was supported by KREONET which is managed and operated by KISTI. The
radiative transfer pipeline, SKIRT, played a pivotal role in this study. We
sincerely thank its creators: Maarten Baes and Peter Camps. S.K.Y.
acknowledges support from the Korean National Research Foundation
(NRF-2020R1A2C3003769). TK was supported in part by the National Research
Foundation of Korea (NRF-2020R1C1C1007079). This study was in part funded by
the NRF-2022R1A6A1A03053472 grant and the BK21Plus program. Parts of this
research were supported by the Australian Research Council Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through
project number CE170100013.

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##  Appendix A Phase-space distribution

We select another sample galaxy from the NewHorizon simulation, this time
without a nucleus component. We present in Figure 13 the phase-space
distribution and the detected GMM components in the same format as in Figure
2. As we mentioned in section 2.3.1, the phase-space distribution of the
detected components is different from that shown in Figure 2. We also present
in Figure 14 the spatial distribution of corresponding GMM components in the
same format as Figure 3. Note that the GMM analysis detected two warm disks
but no nucleus in this galaxy. In addition, tidal features are clearly visible
in the outer spheroid.

Figure 13:  The phase-space distribution of a disk galaxy without a nucleus
component in the same format as Figure 2.  Figure 14:  The face-on $r$-band
flux density map of the GMM components detected in Figure A1, in the same
format as Figure 3.