Detecting a disc bending wave in a barred-spiral galaxy at redshift 4.4

MNRAS 527, 8941–8949 (2024) https://doi.org/10.1093/mnras/stad3588
Advance Access publication 2023 November 23
Detecting a disc bending wave in a barred-spiral galaxy at redshift 4.4
Takafumi Tsukui ,1,2,3,4‹
Emily Wisnioski ,1,2
Joss Bland-Hawthorn,2,5
Yifan Mai,2,5
Satoru Iguchi ,3,4
Junichi Baba3,4,6
and Ken Freeman1,2
1Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston Creek, ACT 2611, Australia
2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
3National Astronomical Observatory of Japan, National Institute of Natural Sciences, 2-21-1 Osawa, Mitaka, 181-8588 Tokyo, Japan
4Department of Astronomical Science, SOKENDAI (The Graduate University for Advanced Studies), 2-21-1 Osawa, Mitaka, 181-8588 Tokyo, Japan
5Sydney Institute for Astronomy, School of Physics, A28, The University of Sydney, NSW 2006, Australia
6Amanogawa Galaxy Astronomy Research Center, Kagoshima University, 1-21-35 Korimoto, 890-0065 Kagoshima, Japan
Accepted 2023 November 13. Received 2023 October 12; in original form 2023 August 30
ABSTRACT
The recent discovery of barred spiral galaxies in the early Universe (z > 2) poses questions of how these structures form and
how they influence galaxy evolution in the early Universe. In this study, we investigate the morphology and kinematics of the
far-infrared (FIR) continuum and [C II] emission in BRI1335-0417 at z ≈ 4.4 from ALMA observations. The variations in
position angle and ellipticity of the isophotes show the characteristic signature of a barred galaxy. The bar, 3.3+0.2
−0.2 kpc long in
radius and bridging the previously identified two-armed spiral, is evident in both [C II] and FIR images, driving the galaxy’s rapid
evolution by channelling gas towards the nucleus. Fourier analysis of the [C II] velocity field reveals an unambiguous kinematic
m = 2 mode with a line-of-sight velocity amplitude of up to ∼30–40 km s−1
; a plausible explanation is the disc’s vertical bending
mode triggered by external perturbation, which presumably induced the high star formation rate and the bar/spiral structure. The
bar identified in [C II] and FIR images of the gas-rich disc galaxy ( 70 per cent of the total mass within radius R ≈ 2.2 disc
scale lengths) suggests a new perspective of early bar formation in high redshift gas-rich galaxies – a gravitationally unstable
gas-rich disc creating a star-forming gaseous bar, rather than a stellar bar emerging from a pre-existing stellar disc. This may
explain the prevalent bar-like structures seen in FIR images of high-redshift submillimeter galaxies.
Key words: galaxies: bar – galaxies: disc – galaxies: kinematics and dynamics – galaxies: spiral.
1 INTRODUCTION
Bar structure plays a crucial role in driving galaxy evolution and
shaping disc structure. In galaxies an axisymmetric stellar bar exerts
gravitational torque on the gas, driving it towards the galactic centre
and forming a centralized stellar structure such as a bulge and nuclear
disc (Athanassoula 1992; Wada Habe 1992). This process may also
promote gas accretion onto the black hole observed as active galactic
nuclei (AGN; Hopkins Quataert 2010; Emsellem et al. 2015). Bars
can also drive radial migration of gas and stars, which is essential
for explaining the observed stellar kinematics in Milky Way galaxies
(e.g. Kawata et al. 2021).
Numerical simulation suggests that stellar bar formation in galax-
ies leads to an immediate gas inflow into the central region and the
formation of a nuclear disc, making the stellar age of the nuclear disc a
good indicator of the epoch when the bar first formed (Baba Kawata
2020). Rather earlier however, the idea was applied to observations
for estimating bar formation age in Gadotti et al. (2015).
Recent observations using integral field spectroscopy (IFS) have
provided insight into the stellar populations of nuclear discs in barred
E-mail: tsukuitk23@gmail.com
galaxies (Gadotti et al. 2015; Bittner et al. 2020; de Sá-Freitas et al.
2023), suggesting that the oldest nuclear discs in barred galaxies
are at least 10 Gyr old (z 2; de Sá-Freitas, Gadotti Fragkoudi
2023). The findings, pointing to early bar formations, align with
the latest high redshift observations. For instance, recent Atacama
Large Millimeter/submillimeter Array (ALMA) observations show
gas discs already formed at z 4 (e.g. Neeleman et al. 2020; Rizzo
et al. 2020; Lelli et al. 2021; Tsukui Iguchi 2021), while James
Webb Space Telescope (JWST) observations recently discovered early
barred galaxies at redshift 1 z 3 (Guo et al. 2023; Le Conte et al.
2023) and at z = 4.2 (Smail et al. 2023). In addition, numerous
disc-like systems (∼ 50 per cent) have been found at 3 z 6
by JWST (Ferreira et al. 2022; Nelson et al. 2023). While these
recent discoveries are consistent with some pre-JWST and ALMA
studies showing disc prevalence already at z ∼ 2.6 (Wuyts et al.
2011; Wisnioski et al. 2015, but see Conselice 2014), they show
surprisingly numerous discs up to z ∼ 6 and earlier spiral and bars
than expected (Elmegreen Elmegreen 2014).
Numerical simulations motivated by these discoveries show that
baryon-dominated disc galaxies promptly form a bar (Fujii et al.
2018; Bland-Hawthorn et al. 2023). It remains an open question if
this rule applies to galaxies with high gas fractions (more than ∼ 50
per cent of total baryonic mass at z 3; Carilli Walter 2013), as
© The Author(s) 2023.
Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium,
provided the original work is properly cited.
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8942 T. Tsukui et al.
MNRAS 527, 8941–8949 (2024)
some simulations suggest molecular gas can suppress bar formation
or result in a weaker bar (Athanassoula, Machado Rodionov 2013;
Łokas 2020). Conversely, ALMA observations reveal prevalent bar
morphologies in dust continuum images of gas-rich submillimeter
galaxies (Gullberg et al. 2019; Hodge et al. 2019; Smail et al.
2023). Tidal interaction is another promising avenue to form bars
(e.g. Noguchi 1996; Łokas et al. 2014, 2016), even for gas-rich
systems (Gajda, Łokas Athanassoula 2018). Recent cosmological
simulations, including a realistic high gas fraction of high-redshift
galaxies and external effects such as mergers, suggest a high bar
fraction out to z ∼ 4 (Rosas-Guevara et al. 2022). Different sub-grid
physics implementations in simulations can result in different galaxy
properties and bar dynamics (Fragkoudi et al. 2021).
Recently, Tsukui Iguchi 2021 revealed a spiral morphology
in BRI 1335–0417 at z = 4.4074 (Guilloteau et al. 1997), hosting
an optical quasar initially identified in Automatic Plate Measuring
(APM) survey (Storrie-Lombardi et al. 1996). The galaxy exhibits a
high star formation rate (SFR) ∼1700 M yr−1
estimated from the
spectral energy distribution modelling with the AGN contribution
being corrected using spatially resolved information (point source
and extended source separation; Tsukui et al. 2023b), making it one
of the brightest unlensed submillimeter source at z 4 (Jones et al.
2016). The [C II] and dust continuum maps of the galaxy revealed a
two-armed structure with a pitch angle of 26.7+4.1
−1.6
◦
(Tsukui Iguchi
2021). These arms extend from 2 to 5 kpc and appear to start at the
end of an elongated bar-like structure that bridges them.
Despite new observational and theoretical results, it remains
unclear what was the dominant cause for early bar and spiral
formation – internal or external processes. As the brightest and
earliest barred spiral example, BRI 1335–0417 allows us to study the
detailed [C II] line and FIR continuum morphology in unprecedented
detail and without uncertainties due to lens model reconstruction.
The spatially resolved [C II] line kinematics together with numerical
simulations provide an excellent laboratory to provide new insights
into early bar formation.
Gas disc kinematics tell us not only the dynamics of the galaxy,
such as disc stability and underlying mass distribution of the galaxy.
Subtracting the overall rotation and examining the more subtle
residual velocity field allows us to explore further: gas inflows (e.g. Di
Teodoro Peek 2021; Genzel et al. 2023), bar and dynamical effect
of the bar/spiral structure (e.g. Grand et al. 2016; Monari et al. 2016;
Gómez et al. 2021), and even bending waves of the disc – seismic
ripple propagating through the disc due to perturbation by a recent
interaction with satellites (Bland-Hawthorn Tepper-Garcı́a 2021;
Tepper-Garcı́a, Bland-Hawthorn Freeman 2022; Urrejola-Mora
et al. 2022) or misaligned gas accretion (Khachaturyants et al. 2022).
In this paper, we report a new analysis of the bar structure in the
quasar host galaxy BRI 1335–0417 using ALMA Band 7 data of
the far-infrared (FIR) continuum (observed frame ∼ 869 μm or rest-
frame ∼ 160 μm) and ionized carbon [C II]. We also demonstrate that
the rotation-subtracted residual velocity field is consistent with the
dynamical imprint of a recent interaction by an external perturber,
which likely induced the bar and spiral density wave in the gas disc.
Throughout this paper, we assume a flat -dominated cold dark
matter cosmology with a present-day Hubble constant of H0 =
70 km s−1
Mpc−1
, and a density parameter of pressureless matter
M = 0.3.
2 OBSERVATION AND DATA REDUCTION
This study uses rest-frame 160 μm FIR continuum image and
[C II] line cube from the observation program #2017.1.00394.S
(PI = González López, Jorge), which was carried out on 2018 January
21. The data calibration and reduction details were described in
(Tsukui Iguchi 2021; Tsukui et al. 2023b). In order to accurately
quantify the elongated bar structure, both [C II] and FIR intensity
maps were convolved to have a circular-shaped beam (point spread
function; PSF) with the same resolution [full width half-maximum
(FWHM) = 0.195 arcsec = 1.3 kpc]. The [C II] line data are binned
in the spectral axis to have a spectral resolution of 20 km s−1
.
3 RESULTS AND DISCUSSION
In this section, we present the results of structural investigations in
the first two subsections and then investigations from the dynamical
point of view using first-order and higher-order [C II] kinematics in
the subsequent subsections.
3.1 Bar identification by the ellipse fitting
We employ the commonly used ellipse-fitting method to examine the
photometric structure of the disc (e.g. Jedrzejewski 1987; Wozniak
et al. 1995; Erwin 2005; Gadotti et al. 2007). We fit ellipses to
isophotes of the [C II] and FIR intensity images, with position angle
(PA) and ellipticity () allowed to vary for each ellipse and the central
position fixed to the best fit of the smallest ellipse. To estimate the
statistical uncertainty in our measurements, we performed the fitting
procedure 300 times, each time adding realistic correlated noise to
the original images. The noise properties are measured using the
noise auto-correlation function (Tsukui et al. 2023a).
The left column of Fig. 1 shows the ellipticity and PA of
the best-fitting ellipses as a function of radius. The right column
presents the best-fitting isophote ellipses overlaid on [C II] and FIR
images. The ellipticity profile of the best-fitting ellipses exhibits
a characteristic profile common to barred galaxies (Wozniak et al.
1995). At smaller radii, the ellipticity is small as the ellipses trace the
centrally concentrated light. Then the ellipticity reaches a maximum
as the ellipse aligns with the elongated bar shape. Subsequently, the
ellipticity decreases as the ellipse traces the disc more circular than
the bar. The PA changes slowly as the ellipse traces the bar and
rapidly changes at the end of the bar as the ellipse starts tracing the
disc because the disc PA is offset from the bar in most cases.1
In both [C II] and FIR continuum, the ellipticity reaches a max-
imum at the same radius within some uncertainty. Therefore, we
adopt the radius of the maximum ellipticity of [C II] as a fiducial
sky-projected bar length, R
sky
bar,max
= 3.1+0.2
−0.1 kpc. This bar length
is larger than the 2×FWHM of the beam, which is the required
minimum criterion for detecting the bar (Erwin 2018). Another way
to define the bar length from the ellipse fitting is the radius where
the PA changes by 5◦
relative to its value at the radius of maximum
ellipticity. This alternative definition provides slightly larger values,
R
sky
bar,PA=5deg = 3.5+0.3
−0.1 kpc yet similar to our adopted fiducial value,
confirming that the choice of the definition does not affect the
conclusion.
We find the intrinsic bar length Rint
bar,max
= 3.3+0.2
−0.2 kpc by the
analytical deprojection assuming a planer bar ellipse (Gadotti et al.
2007) and the disc inclination (37.3◦
) and PA (7.6◦
) estimated by
Tsukui Iguchi (2021). The bar length relative to the [C II] disc
scale length Rd = 1.83 ± 0.04 kpc (Tsukui Iguchi 2021) is larger
than stellar bars seen in nearby galaxies (Erwin 2019; their derived
1The elongated bar structure has a random orientation relative to the disc PA.
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Figure 1. Left column: Ellipticity (top) and PA (bottom) of isophote ellipses as a function of the ellipse radius (semimajor axis) of [C II] (blue) and FIR
(orange) images of BRI 1335–0417. The vertical lines indicate the radii of the maximum ellipticity for [C II] (blue) and FIR (orange). For each measurement,
1σ uncertainty is shown with a shaded region. The grey-shaded region indicates the PSF FWHM, where accurate ellipticity and PA estimates are not possible.
Right column: [C II] and FIR images of BRI 1335–0417 overlaid with the best-fitting isophote ellipses (black ellipses), the bar ellipse (a blue ellipse) and its
PA in the solid blue line. The disc kinematic PA (Tsukui Iguchi 2021) is also shown in the dashed blue line. The FWHM of PSF is shown in the bottom left
corner of both images.
scaling relation predicts a bar length of 1.7 ± 0.1 kpc given the same
disc scale length).
We note that the PA of the outermost isophote is misaligned with
the kinematic disc PA. The outer ellipses are influenced not only by
noise, as evidenced by the increased uncertainty shown in the bottom
left panel of Fig. 1, but also by the spiral structure and faint tidal tail-
like structure extending from north-east to south-west. Therefore,
in later analysis, we will use the kinematic disc PA rather than the
photometric isophote PA as the disc’s PA.
3.2 Interpretation of [C II] and FIR continuum bars
The [C II] line traces not only overall star formation but also multi-
phase gas distribution, from neutral gas (Herrera-Camus et al. 2018)
to molecular and ionized gas (Pineda et al. 2013). On the other hand,
the FIR continuum represents thermal emission from dust heated by
ultraviolet emission produced by young massive stars. Although the
FIR continuum is commonly used as the tracer for dust mass and SFR
(young massive stars heating the dust), the relationships of the single
band FIR continuum to these two quantities are complex depending
on the spatial temperature and opacity variation (da Cunha et al.
2021; Tsukui et al. 2023b). The FIR continuum is proportional to
the dust mass and SFR2
specifically in a limiting case of dust being
optically thin with a spatially constant temperature.
The ellipse fitting result confirms both [C II] and FIR continuum
images have elliptical elongated bar shapes, which are shown in
Fig. 2 along with the two-armed spiral confirmed in Tsukui Iguchi
2021 (projected on the sky). The configuration of the bar and spiral
2With several assumptions such that the dust is solely heated by the young
massive stars and archived single equilibrium temperature. Stellar initial mass
function and dust geometry are known.
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Figure 2. [C II] and FIR images of BRI 1335–0417 overlaid with our
identified bar ellipses (blue ellipse) and two-armed spiral structure identified
in Tsukui Iguchi (2021, black solid line). Contours start at 2σ in both maps
but are linearly spaced by 2σ for [C II] map and logarithmically spaced in
powers of 2 for FIR map (2σ, 4σ, 8σ,...).
is similar to the nearby grand-design spiral galaxies observed (e.g.
Stuber et al. 2023) and found in simulations (e.g. Baba 2015).
In the nearby Universe, not all barred galaxies show star formation
and gas reservoirs in the bar region. Star formation or gas lanes
along the bar region are preferentially found in gas-rich late-type
barred galaxies (Dı́az-Garcı́a et al. 2020; Fraser-McKelvie et al.
2020) and more massive gas-rich barred systems (Stuber et al.
2023). FIR continuum bars are often seen in high redshift (z ∼ 2–4)
submillimeter galaxies (Gullberg et al. 2019; Hodge et al. 2019),
implying that the star-forming gasious bar may be common in the
gas-rich early galaxies (Carilli Walter 2013).
Interestingly, there is a slight yet statistically significant offset in
PA of the bar ellipses between [C II] and FIR continuum (PA[C II] =
−15.9+4.0
−3.1, PAFIR = −6.9+4.2
−4.7). Also, the bar ellipse of [C II] is
more elongated than that of the FIR continuum ([C II] = 0.27+0.02
−0.02,
FIR = 0.39+0.03
−0.02). Although the rounder shape of the FIR bar may
be attributed to the significant AGN contribution to the FIR image
suggested by Tsukui et al. (2023b) these morphological differences,
if further confirmed by higher resolution data, may tell the dynamics
of the bar.
These differences may be consistent with the bar characteristics
commonly confirmed in local observations (Fraser-McKelvie et al.
2020) and simulation (Emsellem et al. 2015) – the compressed gas
flow (traced by [C II]) which usually forms a straight line into the
centre of the galaxy along the leading edge of the bar made up by
the stellar components (traced by FIR emission), making the [C II]
bar thinner than the FIR bar. The [C II] bar is also inclined towards
the leading edge of the FIR bar.
This interpretation requires two assumptions. (1) The spiral arm
in this galaxy is trailing as the majority of spiral galaxies are trailing
(e.g. Iye, Tadaki Fukumoto 2019). If so, the right (west) side in
Fig. 2 is the far side of the disc, and the disc rotates clockwise, given
that the north/south is the receding/approaching side of the disc (see
Fig. 3a). The bar ellipse of the [C II] line is displaced towards the
leading edge of the bar (on the downstream side of the gas motion). (2)
The FIR emission may trace more towards young stellar components
than interstellar medium (ISM) traced by [C II], as the FIR emission
can depend on the distribution of the dust (ISM) and young massive
stars which heat the dust. Especially in the early universe, ∼ 1 Gyr,
the main producers of dust grains are asymptotic giant branch (AGB)
stars or core-collapse supernovae (Gall, Hjorth Andersen 2011).
AGB stars start contributing at 10–100 Myr after the stellar evolution
of stars with the mass of 3–8 M while core-collapse supernovae
contribute after the lifetime of 10 Myr. Within the relatively longer
dynamical time-scale of the disc, 120 Myr, the stellar distribution
producing the dust would not have displaced relative to the dust
distribution.
As discussed in the next section, the stellar content is quite small
relative to gas, so the bar dynamics and formation may differ from
the nearby stellar-dominated bar paradigm.
3.3 Dynamical constraint from [C II] rotation curve
The detailed mass distribution within galaxies is an essential factor
for bar formation (e.g. Efstathiou, Lake Negroponte 1982; Fujii
et al. 2018; Bland-Hawthorn et al. 2023; Romeo, Agertz Renaud
2023). A disc-dominated system is prone to instability and bar
formation, while spherical structures such as dark matter and bulges
as well as the presence of gas can suppress the bar formation. In
this section, we derive a lower boundary on the disc fraction and
gas fraction using (1) the dynamical mass distribution estimated
by Tsukui Iguchi (2021) whose rotation curve is consistent with
the independent modelling by Roman-Oliveira, Fraternali Rizzo
(2023) and (2) the CO(2-1) line luminosity which traces molecular
gas mass (Jones et al. 2016). Then, we discuss the implication for
the bar formation in this galaxy.
Tsukui Iguchi (2021) decomposed the rotation curve into
contributions from the bulge and disc, assuming a de Vaucouleurs
mass distribution for the bulge and an exponential for the disc (with
the scale radius from the [C II] emission). The derived disc mass,
Mdisc = 4.9+1.7
−2.5 × 1010
M, is consistent with the lower limit of the
molecular gas mass, Mgas = 5.1 × 1010
M estimated by Jones et al.
(2016) assuming solar metalicity and a typical CO line ratio r21 =
LCO(2-1)/LCO(1-0) = 0.85 for submillimeter galaxies (Carilli Walter
2013), suggesting that the galaxy is baryon-dominated and gas-rich.
As Tsukui et al. (2023b) revealed the optical emission of BRI
1335–0417 is dominated by a quasar, using a typical r21 = 0.99
for quasars (Carilli Walter 2013) further reduces the estimated
molecular gas mass by 10 per cent to Mgas = 4.6 × 1010
M. Using
this lower limit on the molecular gas estimate, we derive a lower limit
for the disc mass fraction within the radius at which disc dynamics
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(a) (b) (c)
(d) (e)
Figure 3. (a) [C II] velocity field derived fitting a Gaussian at each spatial pixel of the data cube. (b) Best-fitting KINEMETRY model using odd Fourier series
(m = 1, 3, 5) to expand the azimuthal velocity profile. (c) Best-fitting KINEMETRY model using odd + even Fourier series (m = 1, 2, 3, 4, 5). (d) Residual map
subtracting the model with odd terms only (b) from the data velocity field (a). (e) Residual map subtracting the model with both odd and even terms (C) from
the data velocity field (a). In (a), (d), and (d), [C II] contours, bar ellipse, and two armed-spiral are overplotted in the same way as in Fig. 2.
dominates, 2.2Rd = 4.0 kpc,
fdisc =

vdisc(R)
vtotal(R)
2
R=2.2Rdisc

vgas(R)
vtotal(R)
2
R=2.2Rdisc
0.73 ± 0.07
(1)
where vtotal(2.2Rd) = 200 ± 10 km s−1
is the total circular velocity
at 2.2Rd (Tsukui Iguchi 2021), and vgas(2.2Rd) = 179 km s−1
is
the circular velocity of the exponential gas disc at 2.2Rd with the
lower limit mass.3
This lower limit on the disc mass fraction can
also be interpreted as a lower limit on the gas mass fraction and
baryon fraction in the disc, suggesting that the gravitational potential
of BRI 1335–0417 is dominated by gas rather than stars and dark
halo (see also Carilli et al. 2002; Riechers et al. 2008; suggesting gas
dominance in this galaxy).
Recent numerical studies have primarily focused on forming stellar
bars out of stellar discs alternating the orbits of disc stars (Bland-
Hawthorn et al. 2023) in which the gas delay the process. However,
a disc with such a high gas fraction as in BRI 1335–0417 may
behave differently. The dominant gas disc could potentially lead to
the formation of a gas bar (Barnes Tohline 2001), as opposed to
a dominant stellar disc forming a stellar bar, which then influences
the gas kinematics. Theoretically, an axisymmetric 100 per cent gas
disc is found to be able to form a self-gravitating stable gaseous bar
structure (Cazes Tohline 2000). This scenario seems plausible
explaining the prevalent high-redshift bar structures seen in far-
infrared emissions (Gullberg et al. 2019; Hodge et al. 2019) and
another high-z barred galaxy at z = 4.3 with an extreme gas fraction
3We assumed the dispersion supported disc with finite thickness and the scale
radius Rd of [C II] (Tsukui Iguchi 2021).
(Smail et al. 2023). However, whether the stars forming out of a
gaseous bar can lead to a stellar bar as we see in later epochs
(Guo et al. 2023; Le Conte et al. 2023) remains an open question,
as only idealised simulation experiments have been conducted
thus far.
3.4 Second order disc kinematics
We analyzed the [C II] gas velocity field of BRI 1335–0417 (Fig. 3a)
using KINEMETRY (Krajnović et al. 2006)4
to determine if there
is a dynamical imprint from a bar, recent interaction, and or in-
flow/outflow in the gas kinematics.KINEMETRY expands the velocity
field profile v(a, θ) along ellipses into Fourier series,
v(a, θ) = A0(a) +
N

m=1
Am(a) sin(mθ) + Bm(a) cos(mθ), (2)
where the ellipses are defined by the semimajor axis a, axis ratio
q, and PA from which azimuthal angle θ is measured. As the
velocity field of a rotating disc can be expressed by v(a, θ) = A0
+ B1(a)cos (θ) (Krajnović et al. 2006), the deviation from pure
rotational motion manifests as higher order coefficients (A1, A2,
B2,...). By this approach, we can investigate non-circular velocities
in a non-parametric manner, in contrast to the dynamical modelling
4See the derivation of [C II] velocity field (Tsukui et al. 2023b), Briefly, we
derived the velocity field by fitting a Gaussian function (including Hermite
parameters h3 and h4; Cappellari 2017) to the [C II] spectrum at each pixel,
where the three channels are available with the emission detected more than
3σ.
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method used in Tsukui Iguchi (2021), where they assumed a pure
circular rotation and bulge-disc mass profile.
We performed the KINEMETRY expansion of the azimuthal velocity
profile up to the fifth-order Fourier terms (m = 5) along concentric
ellipses. We used ellipses with a PA 7.6◦
and an axis ratio q = 0.79,
which are determined as the global kinematic PA using KINEMETRY
and the photometric axis ratio of the dust continuum distribution in
Tsukui Iguchi (2021), consistent with the independent measure-
ments by Roman-Oliveira, Fraternali Rizzo (2023). The centre of
each ellipse is fixed at the peak position of the continuum image,
which matches with the centre of rotation [see Fig. 3A Tsukui
Iguchi (2021)] and the optical quasar position (Tsukui et al. 2023b).
Fig. 3(b) shows the best-fitting expansion with odd-term harmon-
ics m = 1, 3, 5. The data-model residual (Fig. 3d) reveals the
significant even (m = 2) component, with two redshifted regions
and two blueshifted regions in symmetric positions. The redshifted
residuals spatially coincide with the two-armed spiral morphology
in the [C II] and FIR continuum maps. The features are already
visible in the velocity field before subtraction in Fig. 3(a); the
redshifted/blueshifted high velocity/low velocity are aligned with
spiral arms.
By definition, the m = 2 mode cannot be compensated by any
odd modes which are the orthogonal basis. This is illustrated by
Figs A1–A3. Fig. A1 shows the ellipses along which the azimuthal
velocity profiles are extracted by KINEMETRY. Figs A2 and A3 show
(top) the azimuthal velocity profiles v(θ) for ellipses at radii 0.54 and
0.68 arcsec with the best-fitting circular velocity A0 + B1cos θ and
the circular velocity residual v(θ) − A0 + B1cos θ with higher order
expansion with only odds terms and odds plus even terms (bottom),
clearly showing that m = 2 mode is required to reproduce the data
profile.
We also confirm that the m = 2 mode, with the amplitude of up
to ∼ 30–40 km s−1
, cannot be diminished by changing the PA and
axis ratio of the kinematic ellipses by ±20◦
and ±0.1, respectively
(Fig. A4). The addition of the even components fully characterizes
the velocity field of the BRI 1335–0417 [see the best-fitting harmonic
expansion in Fig. 3(c)] leaving only a small data-model residual
over the disc shown in Fig. 3(e). Recently, Bagge et al. (2023) also
explored the importance of the even components in spatially resolved
gas kinematics for galaxies at intermediate redshift z ∼ 0.3.
3.5 Interpretation of the m = 2 mode in velocity field
We conclude that the observed m = 2 kinematic mode in the velocity
residual is less likely due to inflow or outflow, as symmetric flow
would show line of sight velocity residuals with the opposite sign in
symmetric positions (Di Teodoro Peek 2021; Genzel et al. 2023),
leaving the peculiar possibility where the residual on one side is due
to outflow while the opposite side is due to inflow. Similarly, it is
unlikely due to in-plane motion induced by the dynamical influence
of spiral and bar structures (e.g. Grand et al. 2016; Monari et al.
2016; Gómez et al. 2021). The analytical model suggests a m-fold
symmetric mass density structure would only induce m − 1 or m + 1
velocity field distortions (Canzian 1993; Schoenmakers, Franx de
Zeeuw 1997), inconsistent with the observed m = 2 mode velocity
residual for a m = 2 spiral and bar density structures in the galaxy.
Also, the m = 2 mode velocity residual cannot be attributed to a PA
change of the disc due to disc tilting.
Using an analytic model for a galaxy with similar rotational
velocity and inclination to BRI 1335–0417, Gómez et al. (2021)
show that the radial velocity induced by the spiral density structure
is small (10 km s−1
) compared to the disc vertical velocity caused
by an interaction. Assuming the line of sight velocity residual of
the m = 2 mode, ∼ 35 km s−1
(Fig. 3d), is purely due to in-plane
radial motion, the induced radial velocity would be 57 km s−1
after
inclination correction. With and without inclination correction the
magnitude of the velocity residual seems too large to attribute for the
radial motion caused by the spiral structure (e.g. Grand et al. 2016;
Monari et al. 2016).
A more plausible explanation for the observed m = 2 mode
signature is vertical motion relative to the disc (disc bending mode)
induced by external forces, such as recent interactions with satellite
galaxies (e.g. Gómez et al. 2017; Bland-Hawthorn Tepper-Garcı́a
2021) or misaligned gas accretions (Khachaturyants et al. 2022).
Strikingly, the kinematic m = 2 mode in BRI 1335–0417 spatially
coincides with the spiral structure in the intensity map, as shown in
Fig. 3(d). This overlap is consistent with the vertical wave of stellar
and gas discs induced by satellite interactions in some simulations
(Tepper-Garcı́a, Bland-Hawthorn Freeman 2022). The simulations
reveal the m = 1 mode in the disc vertical velocity develops
∼100 Myr after the Milky-Way-like galaxy is perturbed by the high-
speed encounter of the Sagittarius dwarf system, followed by the
development of the m = 2 mode vertical velocity as soon as 200–
400 Myr (Bland-Hawthorn Tepper-Garcı́a 2021; Tepper-Garcı́a,
Bland-Hawthorn Freeman 2022). The vertical velocity pattern
initially aligns with the spiral pattern in density and then decouples.
The observed co-spatial spiral arm patterns in velocity residual
and intensity (Fig. 3d) are consistent with the simulation of bending
waves induced by interactions, or at least imply a common cause
for the two. Given that BRI 1335–0417 has a gas-rich, dynamically
hot disc with velocity dispersion of ∼70 km s−1
(Tsukui Iguchi
2021), conditions typically unfavourable for spontaneous spiral
arm formation (Elmegreen Elmegreen 2014), it is reasonable to
interpret that the external perturbation responsible for the m = 2
bending mode induced the observed spiral arms even in a dynamically
hot disc (Law et al. 2012) and potentially formed bar (Łokas et al.
2014, 2016). The disc is turbulent but still baryon-dominated and
gravitationally unstable (Tsukui Iguchi 2021), making it prone to
forming such substructures through perturbations (Law et al. 2012).
The gas velocity dispersion, σ, of BRI 1335–0417 is estimated to
be 71+14
−11 km s−1
(Tsukui Iguchi 2021). This value is relatively high
compared to average values at lower redshifts (45 km s−1
at z = 2.3,
30 km s−1
at z = 0.9; Übler et al. 2019) but is in agreement with the
scatter seen around cosmic noon (Kassin et al. 2012; Wisnioski et al.
2015; Übler et al. 2019; Wisnioski et al. 2019). Using the EAGLE
simulations, Jiménez et al. (2023) highlights the importance of the
gas accretion rate and its relative orientation to the disc in driving the
redshift evolution of disc velocity dispersion. The gas accretion (and
accompanying satellites) with a large angle relative to the disc plane
effectively increases the velocity dispersion of the disc. In general
bending mode (buckling instability) is suppressed for a disc with
isotropic velocity dispersion (Toomre 1964; Araki 1985; Merritt
Sellwood 1994, see for review Sellwood 2013) which may hold for
high-redshift galaxies (Genzel et al. 2017; Genzel et al. 2023). The
bending wave induced by the vertical perturbation of the high-angle
accreters may be immediately damped and contribute to the kinetic
energy of the disc velocity dispersion.
4 CONCLUSION
We identify an elongated bar-like structure in the z = 4.4 spiral
galaxy BRI 1335–0417 using both [C II] and rest-frame 160 μm
FIR images by fitting ellipses to the isophotes. The variation of
ellipticity and PA shows the characteristic profile of barred galaxies.
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The identified bar, 3.3+0.2
−0.2 kpc long in radius, appears to bridge the
two arm spirals identified in the previous study (Tsukui Iguchi
2021). When compared to the disc scale length, the bar length is
larger than stellar bars in nearby galaxies (Erwin 2019).
The [C II] bar is more elongated than the FIR bar and displaced
towards the leading edge of the FIR bar (at the downstream side of
the gas motion), assuming the spiral arms of BRI 1335–0417 are
trailing spiral arms. If we attribute the structural difference of FIR
and [C II] to the fact that FIR emission can depend on the distribution
of both dust (ISM roughly traced by [C II]) and young massive stars
heating the dust, the observations seem to align with the established
picture from both observations and simulations – the compressed
gas flow (traced by [C II]) forms a straight line into the centre of the
galaxy along the leading edge of the young stellar bar (more traced
by FIR emission).
The galaxy is shown to have a significant gas fraction (73
per cent), hosting the star-forming gas bar, which prevents us from
assuming the presence of a stellar bar dominating the gravitational
potential and influences the gas bar kinematics. Along with this
object, the abundant bar-like structures in FIR continuum observed
in bright sub-millimetre galaxies (Gullberg et al. 2019; Hodge et al.
2019) and another example high-redshift barred galaxy at z = 4.3
with an extremely high gas fraction (Smail et al. 2023) may prompt a
different perspective on the bar formation and dynamics rather than
simulations focused on how disc stars form stellar bars. The dominant
gas disc, by itself gravitationally unstable, potentially leads to the
formation of a gas bar (Barnes Tohline 2001), as an axisymmetric
100 per cent gas disc is theoretically proven to form a self-gravitating
stable gaseous bar structure (Cazes Tohline 2000).
By applying a harmonic expansion of azimuthal profiles of the
[C II] velocity field with KINEMETRY we reveal a dominant m = 2
mode with the amplitude of up to ∼30–40 km s−1
in the velocity
residual. The m = 2 mode cannot be explained by large-scale
inflow/outflow or the non-circular motions caused by bar/spirals,
which generally produce odd-numbered modes (e.g. Canzian 1993;
Schoenmakers, Franx de Zeeuw 1997). Therefore we interpret
the m = 2 mode as vertical motion relative to the disc (disc bending
wave). The redshifted velocity regions contributing to the m = 2 mode
coincide spatially with the spiral arms, consistent with the scenario
where the galactic disc is perturbed by an interaction creating the
initially co-spatial spiral density wave and vertical bending mode
in the disc (e.g. Bland-Hawthorn Tepper-Garcı́a 2021; Tepper-
Garcı́a, Bland-Hawthorn Freeman 2022).
As it is assumed that a gas disc is stable for the bending mode
(buckling instability), the m = 2 mode velocity perturbation and
spiral arms are likely to be induced by a recent interaction and/or gas
accretion. It is natural to suppose that such an interaction would also
activate the high star formation activity.
For the first time, this study detects an unambiguous m = 2 mode
in a disc at high redshift (z 4), lending support to the use of
disc seismic ripple as evidence of a recent strong perturbation. With
further numerical simulations tuned for galaxies with realistic gas,
halo, and stellar masses and gas accretion histories, the m = 2 mode
may provide a useful constraint on the exact timing and primary
origin of external perturbations.
ACKNOWLEDGEMENTS
TT is grateful to the conference organizers of Galactic Bars: driving
and decoding galaxy evolution held in Granada, Spain in 2023 July,
which greatly helped in writing this paper and Trevor Mendel for
encouraging me to attend. TT also thanks Camila de Sá-Freitas, Karin
Menedez Delmestre, Ewa Luiza Lokas, and Andreas Burkert for
insightful discussions. This research was supported by the Australian
Research Council Centre of Excellence for All Sky Astrophysics in
3 Dimensions (ASTRO 3D), through project number CE170100013.
Data analysis was partly carried out on the Multi-wavelength Data
Analysis System operated by the Astronomy Data Center (ADC),
National Astronomical Observatory of Japan. This paper makes use
of the following ALMA data: ADS/JAO.ALMA#2017.1.00394.S.
ALMA is a partnership of ESO (representing its member states),
NSF (USA), and NINS (Japan), together with NRC (Canada), NSC
and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation
with the Republic of Chile. The Joint ALMA Observatory is operated
by ESO, AUI/NRAO, and NAOJ. Finally, TT thanks Takaho Masai
for his kind support at NAOJ.
DATA AVAILABILITY
The ALMA data we use in this work are publicly available in https:
//almascience.nrao.edu/aq/.
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APPENDIX A: SUPPLEMENTAL INFORMATION
OF KINEMETRY ANALYSIS
In this section, we provide the detailed results of the KINEMETRY
analysis to verify the presence of m = 2 mode. Fig. A1 shows
the ellipses to extract the azimuthal profile of the velocity field.
Figs A2 and A3 illustrate the harmonic expansion of the azimuthal
velocity profiles at two specific radii: 0.54 and 0.68 arcsec. For the
sake of visualization, the pure rotational motion (top: blue line) is
subtracted from the original velocity profile (top: black points) and
we have shown a higher-order expansion for the residual (bottom:
black points). The expansion involves odds terms with or without
even terms up to m = 5 modes (shown as red solid and dashed lines
respectively). Even terms, especially m = 2 mode are required to
reproduce the velocity fields. The dominance of the m = 2 relative
to the other modes obtained by expansion with full terms (odds plus
even) is shown in Fig. A4; the m = 2 is dominant after 0.4 arcsec and,
opposed to other odds modes, is not diminished by the vast change
of PA and ellipticity of sampling ellipses.
Figure A1. Blue points: Ellipses and azimuthal data sampling of each ellipse
used for KINEMETRY analysis overlain on the BRI 1335–0417 velocity field.
Black solid lines show ellipses with a radius of 0.54 arcsec and 0.68 arcsec
whose velocity profiles are shown in Figs A2 and A3.
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Figure A2. Top: Azimuthal velocity profile v(θ) at a radius of 0.54 arcsec
(black points) with the best-fitting circular velocity A0 + B1cos θ (blue solid
line). Bottom: The residual velocity after subtracting the circular velocity
v(θ) − A0 + B1cos θ (black points) and the best-fitting expansion with higher
order harmonics. The red dashed line is the best fitted with only odd terms
(m = 1, 3, 5) and the solid line is the best fit including even terms (m = 1, 2,
3, 4, 5).
Figure A3. Same as Fig. A2 but for a radius of 0.68 arcsec.
Figure A4. Solid lines; Fourier coefficients (m = 2, 3, 4, 5) of azimuthal
velocity profile as a function of the semimajor axis of the ellipse obtained
by KINEMETRY, using concentric ellipse with an axial ratio q = 0.79 and a
PA of 7.6◦. Shaded regions; the maximal variation allowed when varying the
axial ratio (±0.1) and PA (±20◦) of the ellipse used sampling the azimuthal
velocity profile.
This paper has been typeset from a TEX/L
ATEX file prepared by the author.
© The Author(s) 2023.
Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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