# Kinematics of Galactic Centre clouds shaped by shear-seeded solenoidal
turbulence

Maya A. Petkova,1,2 J. M. Diederik Kruijssen,3 Jonathan D. Henshaw,4,5 Steven
N. Longmore,4,3 Simon C. O. Glover,6 Mattia C. Sormani,6 Lucia Armillotta,7
Ashley T. Barnes,8 Ralf S. Klessen,6 Francisco Nogueras-Lara,5 Robin G.
Tress,9 Jairo Armijos-Abendaño,10 Laura Colzi,11 Christoph Federrath,12,13
Pablo García,14,15 Adam Ginsburg,16 Christian Henkel,17,18 Sergio Martín,19,20
Denise Riquelme17 and Víctor M. Rivilla11
Affiliations are listed at the end of the paper E-mail:
<EMAIL_ADDRESS>(MAP)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The Central Molecular Zone (CMZ) is a kinematically unusual environment
relative to the Galactic disc, with high velocity dispersions and a steep
size-linewidth relation of the molecular clouds. In addition, the CMZ region
has a significantly lower star formation rate (SFR) than expected by its large
amount of dense gas. An important factor in explaining the low SFR is the
turbulent state of the star-forming gas, which seems to be dominated by
rotational modes. However, the turbulence driving mechanism remains unclear.
In this work, we investigate how the Galactic gravitational potential affects
the turbulence in CMZ clouds. We demonstrate that several kinematic properties
of the CMZ cloud G0.253+0.016 (‘the Brick’) arise naturally in a cloud-scale
hydrodynamics simulation that takes into account the Galactic gravitational
potential. These properties include the line-of-sight velocity distribution,
the steepened size-linewidth relation, and the predominantly solenoidal nature
of the turbulence. Within the simulation, these properties result from the
Galactic shear in combination with the cloud’s gravitational collapse. This is
a strong indication that the Galactic gravitational potential plays a crucial
role in shaping the CMZ gas kinematics, and is a major contributor to
suppressing the SFR by inducing predominantly solenoidal turbulent modes.

###### keywords:

stars: formation – ISM: clouds – ISM: evolution – ISM: kinematics and dynamics
– Galaxy: centre – galaxies: ISM

††pubyear: 2022††pagerange: Kinematics of Galactic Centre clouds shaped by
shear-seeded solenoidal turbulence–Kinematics of Galactic Centre clouds shaped
by shear-seeded solenoidal turbulence

##  1 Introduction

The Central Molecular Zone (CMZ) is one of the most extreme star-forming
environments in the Milky Way. The region contains a large reservoir of
molecular gas ($\sim 10^{7}~{}\rm{M_{\odot}}$; Dahmen et al. 1998) within the
innermost few hundred parsecs of the Galaxy, with temperatures ($\sim
100~{}\rm{K}$; Ao et al. 2013; Ginsburg et al. 2016; Krieger et al. 2017),
column densities ($\sim 10^{23}~{}\rm{cm^{-2}}$; Molinari et al. 2011) and
pressures ($P/k>10^{7}~{}\rm{K~{}cm^{-3}}$; Rathborne et al. 2014; Walker et
al. 2018; Myers et al. 2022) much higher than in the Solar neighbourhood
(Kruijssen & Longmore, 2013). Despite that, the region as a whole has a star
formation rate (SFR) which is an order of magnitude lower than expected based
on the large amount of dense gas (e.g. traced by NH3; Longmore et al., 2013),
and is likely due to a current minimum within an episodic star formation cycle
(Kruijssen et al., 2014; Armillotta et al., 2019; Callanan et al., 2021). Sgr
B2 accounts for at least 50% of all star formation activity in the CMZ
(possibly up to 89%; Barnes et al. 2017; Ginsburg et al. 2018), leaving the
rest of the clouds with quiescent to intermediate levels of star formation (Lu
et al., 2019; Walker et al., 2021; Williams et al., 2022).

Interstellar medium (ISM) structure and star formation arise in response to
the kinematic state of the gas (Henshaw et al., 2020). Therefore, the
kinematics of the star-forming gas in the CMZ could help us understand the low
SFR. The kinematics in the CMZ are also unususal, with high line-of-sight
velocity dispersions and reports of a steep size-linewidth relation relative
to the solar neighbourhood (Shetty et al., 2012; Kauffmann et al., 2017).
These phenomena are (at least partially) attributed to the effects of
turbulence, which is known to play an important role in shaping the ISM
(Elmegreen & Scalo, 2004; Mac Low & Klessen, 2004). Turbulent motions consist
of solenoidal and compressive modes that coexist at varied relative strength
(see e.g. Federrath et al., 2010). The compressive turbulent modes can lead to
fragmentation and star formation by creating shocks and overdensities, while
the solenoidal modes can prevent gravitational collapse. Within the CMZ we
have an indication of predominantly solenoidal turbulence driving (Federrath
et al., 2016), which is likely linked to the suppressed SFR. Orkisz et al.
(2017) found an inverse relation between the fraction of solenoidal modes in
the velocity field of the gas and SFR within Orion B. A later work by Rani et
al. (2022) found the same type of relation for a large sample of Milky Way
clouds at Galactocentric radii between $3{-}12$ kpc.

Even though turbulence is likely responsible for the kinematic and physical
state of the CMZ clouds, it is currently not understood what drives it. Based
on energetic analysis of common turbulence driving mechanisms, the CMZ
turbulence is most likely driven by supernova feedback, followed by gas inflow
from the galactic bar and magnetorotational instabilities (Kruijssen et al.,
2014; Henshaw et al., 2022a). However, this type of analysis is sensitive to
coupling parameters that determine what fraction of the total energy goes into
turbulent motions, and these parameters are not very well constrained. Recent
work by Tassis & Pavlidou (2022) suggested that the CMZ turbulence can be
explained by feedback from massive stars with high vertical velocity
dispersion that cross the clouds and deposit energy via stellar winds. The
authors also demonstrated that this type of energy injection results in a
steep size-linewidth relation.

An additional contribution to the gas turbulence may come from the strong
orbital shear resulting from the Galactic gravitational potential (Kruijssen
et al., 2014; Krumholz & Kruijssen, 2015; Federrath et al., 2016; Meidt et
al., 2018; Keto et al., 2020). This mechanism is expected to drive solenoidal
turbulence within the gas, which is consistent with observational estimates
(Federrath et al., 2016).

In this Letter, we investigate how the Galactic gravitational potential
affects the turbulence in the CMZ clouds. In particular, we focus on the
G0.253+0.016 cloud, also known as ‘the Brick’ (Longmore et al., 2012). This
cloud is in the very early stages of star formation (e.g. Lis et al., 1994; Lu
et al., 2019; Walker et al., 2021) and even though there is evidence that it
may contain an H II region (Henshaw et al., 2022b), its kinematics are not
dominated by in-situ stellar feedback. We use a recent cloud-scale
hydrodynamics simulation (Dale et al., 2019; Kruijssen et al., 2019; Petkova
et al., 2021) which includes a model for the Galactic gravitational potential,
and demonstrate that it matches very well the kinematic properties of the
Brick. This analysis provides key predictions for the ongoing ALMA CMZ
Exploration Survey (ACES) on the Atacama Large Millimeter/submillimeter Array
(Longmore et al. in prep.), which will be able to characterise the driving
mechanism(s) of turbulence in molecular clouds throughout the CMZ.

##  2 Simulation setup

We use the high-density (HDens) tidally-virialised simulation from Dale et al.
(2019) (see their sect. 3 and tab. 1). Kruijssen et al. (2019) and Petkova et
al. (2021) selected this particular model to represent the Brick as it best
matches the properties of the cloud (i.e. size, column density and velocity
dispersion). The simulation is performed with the smoothed particle
hydrodynamics (SPH) code gandalf (Hubber et al., 2018). The simulation is
three-dimensional, unmagnetised, and assumes an isothermal equation of state
with temperature $65~{}{\rm K}$ (Ao et al., 2013; Ginsburg et al., 2016;
Krieger et al., 2017) and a mean molecular weight $\mu=2.35$, corresponding to
fully molecular gas. Self-gravity of the gas is included, whereas the field
stars are included in the background potential (see below). The cloud is
initialised as a sphere with total mass $\sim 4.5\times
10^{5}~{}\rm{M}_{\odot}$ and $10^{6}$ SPH particles. The initial velocity
field is turbulent with a power spectrum $P(k)\propto k^{-4}$, and virial
parameter $\alpha_{\rm vir}=3.2$. These initial conditions are selected from a
set of randomly generated velocity fields to have negative spin angular
momentum with respect to the orbital motion, consistent with the shear
observed upstream from the Brick.

The simulated cloud is evolved on an eccentric orbit around the Galactic
Centre starting $0.41~{}{\rm Myr}$ before the pericentre passage (see fig. 3
of Kruijssen et al. 2019) in the gravitational potential described in Appendix
A of Kruijssen et al. (2015), which is based on the photometric model of
Launhardt et al. (2002). Since no turbulence driving is included, the initial
turbulent velocity field of the cloud is quickly dissipated (on a timescale
$\approx 0.56~{}{\rm Myr}$; Kruijssen et al., 2019). Turbulence is generated
during the simulation through gravitational collapse and shearing motions. Due
to the lack of sufficient pressure support, the cloud fragments and forms sink
particles (with threshold density of $\rho_{\rm
sink}=10^{-17}\mathrm{g~{}cm}^{-3}$). By the time the present-day position of
the Brick is reached (after 0.74 Myr of evolution), $\sim 55\%$ of the gas
mass is transformed into sink particles.

For our analysis we focus mainly on the snapshot that corresponds to the
present-day location of the Brick. We label this snapshot as being at
$t=0~{}{\rm Myr}$. To facilitate analysis we bin SPH particles onto a 3D
Cartesian grid with cell size $0.1~{}{\rm pc}$ using splash (Price, 2007) and
the exact mapping method of Petkova et al. (2018). For reference, the sink
accretion radius is $0.035~{}\mathrm{pc}$, and the median particle smoothing
length is $0.096~{}\mathrm{pc}$. With the exception of Figure 1, which uses
the synthetic HNCO moment 1 map from Petkova et al. (2021), all of the
analysis is performed on these mapped simulation density outputs.

##  3 Comparison to the Brick

Figure 1: The distribution of line-of-sight velocities in the first velocity
moment map of HNCO ($4_{04}-3_{03}$) emission in the Brick. The blue histogram
is obtained from synthetic observations (Petkova et al., 2021). The black data
points shows the observed distribution in the Brick (Federrath et al., 2016).

In order to compare the kinematic state of the simulated and the observed
cloud, we first consider their line-of-sight (LoS) velocities. Kruijssen et
al. (2019) found that the simulation matches the LoS velocity dispersion of
the real Brick, indicating a kinematic similarity between the clouds. In
addition, the synthetic HNCO ($4_{04}-3_{03}$; 87.925 GHz) moment 1 map
constructed by Petkova et al. (2021) shows a clear gradient and a matching LoS
velocity range to the Brick (see their Appendix B). Figure 1 presents
histograms of the synthetic moment 1 map and of the observed HNCO moment 1 map
of the Brick (Federrath et al., 2016). The two distributions span the same
velocity range and have a double-peaked profile, with a minimum at $\approx
20~{}{\rm km~{}s^{-1}}$. The results remain unchanged if we consider a
synthetic moment 1 map that uses the density structure of the simulation
instead of modelled HNCO emission. Note that both the spin angular momentum
and the LoS velocity gradient of the simulation evolve with time (fig. 4 of
Kruijssen et al., 2019), and the presented velocity distribution is not
identical to the initial conditions. Furthermore, earlier simulation snapshots
have very different LoS velocities.

The double-peaked velocity profile in Figure 1 is indicative of rotation along
an axis perpendicular to the line-of-sight. However, the rotation is not
necessarily global but it may be present in multiple structures within the
Brick which are overlapping along the LoS Henshaw et al. (2019). This is
consistent with the velocity structure of the simulation, where the rotation
is multi-axial, and broken down into spatially-coherent regions.

The LoS velocities can be used to construct the size-linewidth relation
(Larson, 1981). We defer a full exploration of this observable in our
simulations to a future study (Petkova et al. in prep.), but mention our
finding that the simulated and observed cloud both exhibit the same size-
linewidth slope ($\approx 0.7$). This is consistent with other CMZ studies
(Shetty et al., 2012; Kauffmann et al., 2017), but is steeper than in the
Solar neighbourhood ($0.5$; Heyer & Dame, 2015). Our analysis considers the
entire Brick cloud and follows the procedure of Shetty et al. (2012), which
identifies structures in position-position-velocity space with a dendrogram.
In contrast, Henshaw et al. (2020) performed a Gaussian decomposition of HNCO
emission lines, and found a much shallower size-linewidth slope within
identified sub-structures of the Brick. This suggests that the steeper
relation may be due to rotational motions on the cloud scale.

The similar (yet atypical) size-linewidth relation in the simulation and in
the Brick is suggestive of a similar kinematic state, which is likely due to a
combination of rotation and turbulence. Federrath et al. (2016) estimated the
turbulence driving parameter of the Brick to be $b=0.22\pm 0.12$, which is
consistent with having predominantly solenoidal driving. In order to compare
this result with the simulation, we split the 3D velocity field into a
compressive (curl-free) and a solenoidal (divergence-free) component using
Helmholtz decomposition (see e.g. Federrath et al. 2010), and calculate the
power spectrum of each component multiplied by the square root of the local
density ($E_{\rm comp}$ and $E_{\rm sol}$, respectively). We then find the
compressive ratio, $E_{\rm comp}/(E_{\rm comp}+E_{\rm sol})$, which represents
the fraction of kinetic energy stored in the compressive modes of the velocity
field. For suprsonic clouds, the compressive ratio is always greater than 0,
even if the driving force is purely solenoidal (Federrath et al., 2010;
Federrath et al., 2011). Figure 2 shows the compressive ratio of the
simulation as a function of spatial scale ($k$), compared to the results of
Federrath et al. (2011) for a Mach number of $\approx 11$. For most spatial
scales our simulation has a cmpressive ratio of $0.2-0.3$, which is consistent
with having predominantly solenoidal turbulence driving. This is also in
agreement with the results of Federrath et al. (2016) for the Brick. Similar
results are seen for earlier simulation snapshots.

Figure 2: Compressive ratio as a function of spatial scale. The black line
shows the ratio for our simulation, while the red and blue lines (and shaded
areas) show the compressive ratio of simulations with purely solenoidal and
compressive turbulence driving, respectively (Federrath et al., 2011). The
arrow indicates the (inverse of the) initial cloud size.

All of the above measurements are consistent with the hypothesis that the
Galactic shear is influencing the cloud kinematics. We explore this hypothesis
further in the following section.

##  4 The role of the Galactic potential

Figure 3: Top-down view ($xy$-plane) of three snapshots of the simulated cloud
(see time stamps). The column density is shown in grey scale, while the
$xy$-velocities (mass-weighted averages along the $z$-axis) are shown as
arrows. The length of each arrow indicates the magnitude of the corresponding
velocity, with a $10~{}\rm{km}~{}\rm{s}^{-1}$ arrow drawn at the top of each
panel for reference. Each arrow shows the velocity average within squares of
$10\times 10$ pixels. The cyan cross in each panel marks the location of the
local minimum of the gravitational potential within the cloud, and the cyan
circle shows the size of the tidal radius (see eq. 3) around the cyan cross.
The arrows are coloured based on the ratio of azimuthal to radial kinetic
energy with respect to the position of the cyan cross. In this coordinate
system, Sgr A∗ is located at $(8.08,0.00,-6.68)~{}{\rm pc}$, and an observer
on Earth is looking along the $y$-axis (see Dale et al. 2019, fig. 2).

The Galactic gravitational potential can influence the evolution and dynamics
of the CMZ clouds through two main effects: shear and tidal forces. The
simulated cloud uses the Launhardt et al. (2002) potential, which has a
scaling of $M\propto R^{2.2}$ between the enclosed mass $M$, and the
Galactocentric radius $R$ for radii between 60 pc and 100 pc (Kruijssen et
al., 2015). Using this dependence, Kruijssen et al. (2019) derived the
velocity differential due to shear:

$\delta v_{\rm shear}=0.67~{}\rm{km}~{}\rm{s}^{-1}\left(\frac{\Omega_{\rm
rot}}{1.7~{}\rm{Myr}^{-1}}\right)\left(\frac{\delta R}{1~{}\rm{pc}}\right),$
(1)

where $\Omega_{\rm rot}$ is the mean orbital angular velocity of a cloud (for
our simulation $\Omega_{\rm rot}=1.7~{}\rm{Myr}^{-1}$; Kruijssen et al.,
2015), and $\delta R$ is the difference in Galactocentric radius between two
points in the cloud. While an updated potential (Sormani et al., 2022) has
been constructed since the simulation run, the shape of the new potential
within the orbit of the simulation is consistent with that of Launhardt et al.
(2002), and hence the results of this paper remain unchanged.

The tidal radius of the cloud is (Mo et al., 2010, eq. 12.21):

$r_{\rm tidal}=\left(\frac{m(r_{\rm tidal})/M(R)}{2+\frac{\Omega_{\rm
rot}^{2}R^{3}}{GM(R)}-\frac{\mathrm{d}\ln M}{\mathrm{d}\ln
R}\bigg{\rvert}_{R}}\right)^{1/3}R,$ (2)

where $m(r_{\rm tidal})$ is the cloud mass enclosed within the tidal radius.
By assuming that $\Omega_{\rm rot}^{2}R^{3}/GM(R)=1$ (true for circular motion
where $m\ll M$), and $\mathrm{d}\ln M/\mathrm{d}\ln R|_{R}=2.2$ (Launhardt et
al., 2002; Kruijssen et al., 2015), we simplify the above expression to the
following:

$r_{\rm
tidal}=5.36~{}\mathrm{pc}\left(\frac{R}{70~{}\rm{pc}}\right)\left(\frac{m(r_{\rm
tidal})}{10^{5}~{}\rm{M}_{\odot}}\right)^{1/3}\left(\frac{M(R)}{2.8\times
10^{8}~{}\rm{M}_{\odot}}\right)^{-1/3}.$ (3)

In eq. 3 we express the dependence of the tidal radius on $m(r_{\rm tidal})$.
This allows us to find $r_{\rm tidal}$ iteratively within the simulation. Note
that due to the adopted gravitational potential, the tidal field is fully
compressive (Dale et al., 2019; Kruijssen et al., 2019).

We now study the effects of shear and tidal forces on the kinematics of the
simulation. Figure 3 shows a top-down view of the simulated cloud with
superimposed $xy$-velocity vectors, where the bulk motion of the gas has been
subtracted. We include three snapshots of the cloud – one at the present
location of the Brick (right), and two at earlier positions along the cloud’s
orbit. We find that as the cloud evolves it undergoes collapse towards a
central dense region, which can be seen both in the more enhanced gas column
density (grey scale in Figure 3), and in the gas velocities. The velocity
vectors are coloured based on the ratio of their tangential and radial
components with respect to the local minimum of the gravitational potential
along the orbit (cyan cross; hereafter ‘cloud centre’). Figure 3 shows that as
the cloud evolves, there is more radial motion of the gas (blue arrows)
concentrated within the tidal radius (cyan circle; see eq. 3), and the regions
outside the tidal radius move predominantly in a tangential direction (red
arrows). This is consistent with the interpretation that the periphery of the
cloud is stretched due to shear, while its central region is collapsing
(possibly with the help of tidal compression).

In order to quantify the effect of the shear, we consider the tangential
velocity components of the gas with respect to the cloud centre, $v_{\phi}$,
and their dependence on the distance from this centre, $r$ (see Figure 4). We
also include the velocity ranges that we expect from a simple model of shear
(outside the tidal radius) and collapse (inside the tidal radius). For the
shear we consider two limiting cases. In the first case (lower estimate) we
take each pixel from Figure 3 and we compute its shear velocity using eq. 1.
This approach does not give axisymmetric results with respect to the cloud
centre. We then divide the pixels in radial distance bin and compute the mean
$v_{\phi}$ in each bin. In the second case, we assume that a parcel of gas
will maintain its tangential speed set by shear as the cloud rotates. This
approach assumes that the effects of shear are effectively axisymmetric with
respect to the cloud centre. To compute the upper velocity estimates, we use
eq. 1 where we replace $\delta R$ with $r$. The grey shaded area is then
continued within the tidal radius by assuming $r^{-1}$ dependence for the
upper and the lower velocity estimate. This is equivalent to a parcel of gas
moving with the shear velocity at the tidal radius, and then being accreted
while it conserves its angular momentum.

Figure 4 shows that for all snapshots our lower theoretical prediction for the
contribution of the shear (i.e. outside the tidal radius) overlaps with a
prominent feature in the data. This feature is better defined in the early
snapshots where the spread of velocities is smaller and there is less ongoing
gravitational collapse. We also see an average increase of $v_{\phi}$ inside
the tidal radius in all snapshots, consistent with spin-up due to collapse.
This effect is most prominent at $t=0~{}\rm{Myr}$ where we have a better
defined centre of cloud rotation.

##  5 Summary and Discussion

In this Letter, we demonstrated that several kinematic properties of the CMZ
cloud known as the Brick arise naturally in a hydrodynamics simulation which
takes into account the Galactic gravitational potential. These properties
include the line-of-sight velocity distribution, the steep slope of the size-
linewidth relation and the solenoidally-driven turbulence. Within the
simulation, we explain these through the effect of shear. In the outskirts of
the simulated cloud, shear stretches the gas, boosts the velocity dispersion
and seeds solenoidal turbulence. Due to the kinematic similarities between the
simulation and the Brick, we conclude that the dynamical state of the Brick is
likely strongly influenced by the Galactic gravitational potential. Our
findings trigger several important follow-up questions.

Figure 4: Tangential velocity component as a function of radial distance from
the cloud centre. The 2D histogram in blue presents the data from Figure 3.
The vertical dotted line marks the size of the tidal radius. The grey shaded
area outside the tidal radius shows the expected tangential velocity based on
shear (see Sec. 4). Inside the tidal radius, the boundaries of the grey shaded
area follow $r^{-1}$ profiles, consistent with conservation of angular
momentum during collapse.

Can the turbulence be driven by another mechanism? Within the simulation: In
addition to shear, turbulence can be driven by gravitational collapse within
the cloud. Dale et al. (2019) compared clouds evolved with the Galactic
potential to the same clouds evolved in isolation and found that the isolated
clouds undergo more rapid collapse, but after the initial period of turbulent
dissipation ($\approx 0.56$ Myr) their velocity dispersions remain lower than
in the clouds evolved within the potential (see fig. 14 and 15 of Dale et al.
2019). Together with the solenoidal nature of the turbulence (see Figure 2),
this indicates that the gravitational collapse on its own is not a sufficient
turbulence driver. However, CMZ simulations which include the Galactic
gravitational potential but no gas self-gravity also lack sufficient
turbulence (Hatchfield et al., 2021). Therefore, the most likely
interpretation is that shear seeds solenoidal turbulence which is amplified
through gravitational collapse. Within the Brick: we cannot be sure that shear
is the only factor contributing to the mode of the turbulence, but the
agreement between simulations and observations suggest that it is likely to be
an important factor. In addition to shearing motions within the cloud, there
should also be shear with respect to the warmer diffuse gas surrounding the
cloud, which can trigger Kelvin-Helmholtz instability. Other mechanisms can
(and likely do) inject energy into the gas (e.g. stellar feedback; Tassis &
Pavlidou 2022; Henshaw et al. 2022b), but this type of energy injection does
not typically trigger solenoidal motions (Menon et al., 2020).

Is the Galactic potential suppressing star formation in the Brick? Many
authors have argued in favour of the Galactic shear as the mechanism
responsible for suppressing star formation in the CMZ (Kruijssen et al., 2014,
2019; Krumholz & Kruijssen, 2015; Federrath et al., 2016; Meidt et al., 2018,
2020; Keto et al., 2020). However, the SFR in our simulation ($\sim
0.3~{}\rm{M_{\odot}~{}yr^{-1}}$; Dale et al. 2019) is much higher than that of
the Brick ($10^{-4}-10^{-3}~{}\rm{M_{\odot}~{}yr^{-1}}$; Rathborne et al.
2014; Walker et al. 2021). This discrepancy suggests that the low SFR in the
Brick may be partially caused by physical factors missing from the simulation,
such as magnetic and thermal support. Magnetic fields are known to delay star
formation and prevent fragmentation. Petkova et al. (2021) found a difference
in the width of the column density PDFs between the simulation and the Brick,
which can be accounted for with the estimated turbulent plasma $\beta$ of the
cloud (Federrath et al., 2016), indicating that magnetic fields are likely
important for shaping the cloud structure. Additionally, the high gas
temperature of the Brick is explained with shock heating (Ginsburg et al.,
2016), as well as high levels of cosmic rays and interstellar radiation (Clark
et al., 2013), that are not captured in our simulation.

Another reason for the different SFR in the simulation and the Brick may be
the idealised simulation assumptions. The simulation was initialised as a gas
sphere, which differs from the expected complex filamentary clouds that enter
the CMZ (Tress et al., 2020). The assumed spherical initial state is unstable
under the strong compressive tide in the vertical direction, and hence our
simulation flattens rapidly. This vertical collapse may be artificially
boosting the SFR, and the discrepancy with the Brick may be improved by
assuming more realistic initial conditions. Furthermore, the simulated cloud
exists in isolation and it is possible that the Brick has formed through
gradual accretion of (higher kinetic energy) material, shifting the timeline
of star formation to a later point along the Brick’s orbit.

Our analysis concludes that the dynamical state of the Brick is likely
strongly influenced by the Galactic gravitational potential. These findings
are extendable to the rest of the quiescent CMZ clouds and make predictions
for their turbulent state.

## Acknowledgements

This work was carried out by the ACES Collaboration as part of the ALMA CMZ
Exploration Survey. MAP and JMDK acknowledge funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 (ERC Starting
Grant MUSTANG; 714907). MAP, JMDK, and SCOG acknowledge financial support from
the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) via the
collaborative research center (SFB 881, Project-ID 138713538) “The Milky Way
System” (MAP, JMDK: subproj. B2; SCOG: subproj. A1, B1, B2, B8). JMDK
acknowledges funding from the DFG through an Emmy Noether Research Group
(KR4801/1-1). COOL Research DAO is a Decentralised Autonomous Organisation
supporting research in astrophysics aimed at uncovering our cosmic origins.
SCOG acknowledges subsidies from the Heidelberg Cluster of Excellence
STRUCTURES in the framework of Germany’s Excellence Strategy (EXC-2181/1 -
390900948) and funding from the ERC via the ERC Synergy Grant ECOGAL (855130).
AG acknowledges support from the NSF under grants AST 2008101, 2206511, and
CAREER 2142300, and from STSCI under grant JWST-GO-02221.001-A. JDH gratefully
acknowledges financial support from the Royal Society (University Research
Fellowship). VMR has received support from the project RYC2020-029387-I funded
by MCIN/AEI /10.13039/501100011033. C.F. acknowledges funding by the
Australian Research Council (Future Fellowship FT180100495 and Discovery
Projects DP230102280), and the Australia-Germany Joint Research Cooperation
Scheme (UA-DAAD). L.C. acknowledges financial support through the Spanish
grant PID2019-105552RB-C41 funded by MCIN/AEI/10.13039/501100011033.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

## References

  * Ao et al. (2013) Ao Y., et al., 2013, A&A, 550, A135
  * Armillotta et al. (2019) Armillotta L., Krumholz M. R., Di Teodoro E. M., McClure-Griffiths N. M., 2019, MNRAS, 490, 4401
  * Barnes et al. (2017) Barnes A. T., Longmore S. N., Battersby C., Bally J., Kruijssen J. M. D., Henshaw J. D., Walker D. L., 2017, MNRAS, 469, 2263
  * Callanan et al. (2021) Callanan D., et al., 2021, MNRAS, 505, 4310
  * Clark et al. (2013) Clark P. C., Glover S. C. O., Ragan S. E., Shetty R., Klessen R. S., 2013, ApJ, 768, L34
  * Dahmen et al. (1998) Dahmen G., Huttemeister S., Wilson T. L., Mauersberger R., 1998, A&A, 331, 959
  * Dale et al. (2019) Dale J. E., Kruijssen J. M. D., Longmore S. N., 2019, MNRAS, 486, 3307
  * Elmegreen & Scalo (2004) Elmegreen B. G., Scalo J., 2004, ARA&A, 42, 211
  * Federrath et al. (2010) Federrath C., Roman-Duval J., Klessen R. S., Schmidt W., Mac Low M. M., 2010, A&A, 512, A81
  * Federrath et al. (2011) Federrath C., Chabrier G., Schober J., Banerjee R., Klessen R. S., Schleicher D. R. G., 2011, Phys. Rev. Lett., 107, 114504
  * Federrath et al. (2016) Federrath C., et al., 2016, ApJ, 832, 143
  * Ginsburg et al. (2016) Ginsburg A., et al., 2016, A&A, 586, A50
  * Ginsburg et al. (2018) Ginsburg A., et al., 2018, ApJ, 853, 171
  * Hatchfield et al. (2021) Hatchfield H. P., Sormani M. C., Tress R. G., Battersby C., Smith R. J., Glover S. C. O., Klessen R. S., 2021, ApJ, 922, 79
  * Henshaw et al. (2019) Henshaw J. D., et al., 2019, MNRAS, 485, 2457
  * Henshaw et al. (2020) Henshaw J. D., et al., 2020, Nature Astronomy, 4, 1064
  * Henshaw et al. (2022a) Henshaw J. D., Barnes A. T., Battersby C., Ginsburg A., Sormani M. C., Walker D. L., 2022a, arXiv e-prints, p. arXiv:2203.11223
  * Henshaw et al. (2022b) Henshaw J. D., et al., 2022b, MNRAS, 509, 4758
  * Heyer & Dame (2015) Heyer M., Dame T. M., 2015, ARA&A, 53, 583
  * Hubber et al. (2018) Hubber D. A., Rosotti G. P., Booth R. A., 2018, MNRAS, 473, 1603
  * Kauffmann et al. (2017) Kauffmann J., Pillai T., Zhang Q., Menten K. M., Goldsmith P. F., Lu X., Guzmán A. E., 2017, A&A, 603, A89
  * Keto et al. (2020) Keto E., Field G. B., Blackman E. G., 2020, MNRAS, 492, 5870
  * Krieger et al. (2017) Krieger N., et al., 2017, ApJ, 850, 77
  * Kruijssen & Longmore (2013) Kruijssen J. M. D., Longmore S. N., 2013, MNRAS, 435, 2598
  * Kruijssen et al. (2014) Kruijssen J. M. D., Longmore S. N., Elmegreen B. G., Murray N., Bally J., Testi L., Kennicutt R. C., 2014, MNRAS, 440, 3370
  * Kruijssen et al. (2015) Kruijssen J. M. D., Dale J. E., Longmore S. N., 2015, MNRAS, 447, 1059
  * Kruijssen et al. (2019) Kruijssen J. M. D., et al., 2019, MNRAS, 484, 5734
  * Krumholz & Kruijssen (2015) Krumholz M. R., Kruijssen J. M. D., 2015, MNRAS, 453, 739
  * Larson (1981) Larson R. B., 1981, MNRAS, 194, 809
  * Launhardt et al. (2002) Launhardt R., Zylka R., Mezger P. G., 2002, A&A, 384, 112
  * Lis et al. (1994) Lis D. C., Menten K. M., Serabyn E., Zylka R., 1994, ApJ, 423, L39
  * Longmore et al. (2012) Longmore S. N., et al., 2012, ApJ, 746, 117
  * Longmore et al. (2013) Longmore S. N., et al., 2013, MNRAS, 429, 987
  * Lu et al. (2019) Lu X., et al., 2019, ApJ, 872, 171
  * Mac Low & Klessen (2004) Mac Low M.-M., Klessen R. S., 2004, Reviews of Modern Physics, 76, 125
  * Meidt et al. (2018) Meidt S. E., et al., 2018, ApJ, 854, 100
  * Meidt et al. (2020) Meidt S. E., et al., 2020, ApJ, 892, 73
  * Menon et al. (2020) Menon S. H., Federrath C., Kuiper R., 2020, MNRAS, 493, 4643
  * Mo et al. (2010) Mo H., van den Bosch F. C., White S., 2010, Galaxy Formation and Evolution
  * Molinari et al. (2011) Molinari S., et al., 2011, ApJ, 735, L33
  * Myers et al. (2022) Myers P. C., Hatchfield H. P., Battersby C., 2022, ApJ, 929, 34
  * Orkisz et al. (2017) Orkisz J. H., et al., 2017, A&A, 599, A99
  * Petkova et al. (2018) Petkova M. A., Laibe G., Bonnell I. A., 2018, Journal of Computational Physics, 353, 300
  * Petkova et al. (2021) Petkova M. A., et al., 2021, arXiv e-prints, p. arXiv:2104.09558
  * Price (2007) Price D. J., 2007, PASA, 24, 159
  * Rani et al. (2022) Rani R., Moore T. J. T., Eden D. J., Rigby A. J., 2022, MNRAS, 515, 271
  * Rathborne et al. (2014) Rathborne J. M., et al., 2014, ApJ, 795, L25
  * Shetty et al. (2012) Shetty R., Beaumont C. N., Burton M. G., Kelly B. C., Klessen R. S., 2012, MNRAS, 425, 720
  * Sormani et al. (2022) Sormani M. C., et al., 2022, MNRAS, 512, 1857
  * Tassis & Pavlidou (2022) Tassis K., Pavlidou V., 2022, arXiv e-prints, p. arXiv:2205.06820
  * Tress et al. (2020) Tress R. G., Sormani M. C., Glover S. C. O., Klessen R. S., Battersby C. D., Clark P. C., Hatchfield H. P., Smith R. J., 2020, MNRAS, 499, 4455
  * Walker et al. (2018) Walker D. L., et al., 2018, MNRAS, 474, 2373
  * Walker et al. (2021) Walker D. L., et al., 2021, MNRAS, 503, 77
  * Williams et al. (2022) Williams B. A., et al., 2022, MNRAS, 514, 578

1Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität
Heidelberg, Mönchhofstr 12-14, D-69120 Heidelberg, DE
2Space, Earth and Environment Department, Chalmers University of Technology,
SE-412 96 Gothenburg, Sweden
3Cosmic Origins Of Life (COOL) Research DAO, coolresearch.io
4Astrophysics Research Institute, Liverpool John Moores University, IC2,
Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
5Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg,
Germany
6Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische
Astrophysik, Albert-Ueberle-Str 2, D-69120 Heidelberg, Germany
7Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA
8Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121, Bonn, DE
9 Institute of Physics, Laboratory for galaxy evolution and spectral
modelling, EPFL, Observatoire de Sauverny, Chemin Pegais 51, 1290 Versoix,
Switzerland
10 Observatorio Astronómico de Quito, Escuela Politécnica Nacional, 170136,
Quito, Ecuador
11 Centro de Astrobiología (CAB), CSIC-INTA, Ctra. de Ajalvir Km. 4, 28850,
Torrejón de Ardoz, Madrid, Spain
12 Research School of Astronomy and Astrophysics, Australian National
University, Canberra, ACT 2611, Australia
13 Australian Research Council Centre of Excellence in All Sky Astrophysics
(ASTRO3D), Canberra, ACT 2611, Australia
14 Instituto de Astronomía, Universidad Católica del Norte, Av. Angamos 0610,
Antofagasta 1270709, Chile
15 Chinese Academy of Sciences South America Center for Astronomy, National
Astronomical Observatories, CAS, Beijing 100101, China
16 Department of Astronomy, University of Florida 211 Bryant Space Science
Center P.O Box 112055, Gainesville, FL 32611-2055 USA
17 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn,
Germany
18 Astronomy Department, Faculty of Science, King Abdulaziz University, P. O.
Box 80203, Jeddah 21589, Saudi Arabia
19 European Southern Observatory, Alonso de Córdova, 3107, Vitacura, Santiago,
763-0355, Chile
20 Joint ALMA Observatory, Alonso de Córdova, 3107, Vitacura, Santiago,
763-0355, Chile