# A minimal model for structure, dynamics, and tension of monolayered cell
colonies

Debarati Sarkar<EMAIL_ADDRESS>Gerhard Gompper  g.gompper@fz-
juelich.de Jens Elgeti<EMAIL_ADDRESS>Theoretical Physics of Living
Matter, Institute of Biological Information Processing and Institute for
Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany

###### Abstract

The motion of cells in tissues is an ubiquitous phenomenon. In particular, in
monolayered cell colonies in vitro, pronounced collective behavior with swirl-
like motion has been observed deep within a cell colony, while at the same
time, the colony remains cohesive, with not a single cell escaping at the
edge. Thus, the colony displays liquid-like properties inside, in coexistence
with a cell-free “vacuum” outside. How can adhesion be strong enough to keep
cells together, while at the same time not jam the system in a glassy state?
What kind of minimal model can describe such a behavior? Which other
signatures of activity arise from the internal fluidity? We propose a novel
active Brownian particle model with attraction, in which the interaction
potential has a broad minimum to give particles enough wiggling space to be
collectively in the fluid state. We demonstrate that for moderate propulsion,
this model can generate the fluid-vacuum coexistence described above. In
addition, the combination of the fluid nature of the colony with cohesion
leads to preferred orientation of the cell polarity, pointing outward, at the
edge, which in turn gives rise to a tensile stress in the colony – as observed
experimentally for epithelial sheets. For stronger propulsion, collective
detachment of cell clusters is predicted. Further addition of an alignment
preference of cell polarity and velocity direction results in enhanced
coordinated, swirl-like motion, increased tensile stress and cell-cluster
detachment.

collective cell migration $|$ liquid-vacuum coexistence $|$ tensile stress $|$
cellular velocity alignment $|$ coordinated motion

###### pacs:

Valid PACS appear here

##  I Introduction

Many fundamental biological processes, like embryogenesis, wound healing or
cancer/tumor invasion require cells to move collectively within tissues [1, 2,
3]. The physics underlying these processes ranges from understanding actin
polymerization and tread-milling for force generation [4, 5] and single cell
migration [6, 7], to the collective behavior of many migrating cells [8, 9,
10]. Here, we focus on an observation from monolayers of migrating Madin-Darby
canine kidney (MDCK) cells on surfaces, a prototypical model system for
collective cell migration. Experimental observations reveal large-scale
collective motion, like swirls, within the bulk of young monolayers [11, 12],
thus the display of fluid-like properties, before jamming occurs as the
epithelial sheet matures [13, 14, 15, 16]. Interestingly, as an initial colony
expands, no cells detach from the boundary — even though the bulk of the
tissue remains clearly fluid-like [9]. Cohesion is strong enough that fingers
of many cells can protrude at the propagating tissue front without cell
detachment. Even stronger-pulling “leader cells” do not detach [17, 18, 19,
20]. Cells are thus in a ’liquid-vacuum’ 111We use the term ’vacuum’ here
somewhat loosely to represent a phase of extremely low cell density
coexistence regime. Even more surprising, pioneering experiments have revealed
that these expanding colonies are under tensile stress [22, 23]. This raises
the question how this liquid-vacuum coexistence, in combination with strong
collective motion and tensile stress, can be captured and understood from a
minimal physical model.

An active Brownian particle (ABP) model [24, 25, 26, 27] for cells with
standard attractive Lennard-Jones (LJ) interactions has been proposed to study
cell colonies [28, 29, 30]. However, only solid-vacuum (no fluidity of the
condensed phase), or liquid-gas (finite cell density in the dilute phase)
coexistence has been obtained. The coexistence of liquids with a very-low-
density gas phase is of course well known in many equilibrium systems. In the
biological context, for example, lipid-bilayer membranes are liquid in nature,
but the critical-micelle concentration is very low, so that lipids essentially
never detach from the membrane. In the modelling and simulation of lipid
membranes, a similar problem of attractive interactions and fluidity exists as
for cell monolayers – too strong attraction leads to solidification. In
coarse-grained simulations of lipid bilayers, this problem was overcome by an
interaction potential with an extended range compared with the standard
Lennard-Jones potential, which provides strong adhesion while still giving
enough wiggle room for the molecules that the membrane to remains the fluid
phase [31]. In the spirit of minimal modeling, we propose an active Brownian
particle (ABP) model for the cells, combined with a similar longer-range
interaction potential as employed successfully for the membrane lipids. We
demonstrate that the LJ potential with a wider attractive basin indeed opens
up a region in phase space that displays liquid-vacuum coexistence. The size
of the liquid-vacuum region expands as the basin width of LJ potential
increases. The fluidity of the condensed phase implies the emergence of
several interesting behaviors, like a tensile stress within the colony due to
a preferred orientation of the boundary cells to the outside, as awell as the
detachment of cell cluster above a size threshold. When a coupling of cell
polarity to the instantaneous direction of motion – which is significantly
affected by the interactions with the neighboring cells – is introduced, the
formation of swirls and collective cell detachment is strongly enhanced.

##  II Results and Discussion

###  II.1 Active Brownian particles with attraction

Liquid-vacuum coexistence requires strong inter-particle adhesion, so that
cells can not detach from the main colony. Concurrently, the adhesion has to
provide enough wiggling room that the cells remain locally mobile inside the
condensed phase and provide fluidity to the colony. A long-range coordinated
motion of cells, like fingering or swirls, then already emerges to some extent
from the self-organized motion of cells which all vary their propulsion
direction independently and diffusively. However, pronounced correlations are
found to require additional alignment interactions of cell orientation and
direction of motions. Here, the effect of neighbors pushing (or pulling) a
cell in a certain direction is assumed to induce a reaction in the cell to
reorient and align its propulsion direction with its instantaneous velocity
direction.

The ABP model, where each particle is a sphere (in 3D) or a disc (in 2D) which
undergoes rotational Brownian motion and additionally experiences a body-fixed
driving force of constant magnitude, was developed to describe active motion
on the microscale [15, 32]. This model displays a rich phase behavior, most
notably motility-induced phase separation [24, 25, 33, 26], where persistence
of motion and short-range repulsion induce cluster formation. Addition of a
Lennard-Jones attraction leads to the formation of arrested clusters for small
propulsion [28, 34, 29]. In order to obtain liquid-like properties at strong
adhesion, we follow the spirit of Ref. [31] and propose an interaction
potential with an extended basin of width $\bar{\sigma}$, so that

$V_{m}=\left\\{\begin{array}[]{lr}4\epsilon\left[(\sigma/r)^{12}-(\sigma/r)^{6}\right],&0<r\leq
2^{1/6}\sigma\\\ -\epsilon,&2^{1/6}\sigma<r\leq\tilde{r}\\\
4\epsilon\left[(\sigma/(r-\bar{\sigma}))^{12}-(\sigma/(r-\bar{\sigma}))^{6}\right],&\tilde{r}<r\leq
r_{cut}\end{array}\right.$

(see Appendix A Fig. 6). Here, $\sigma$ is the particle diameter,
$\tilde{r}=(2^{1/6}\sigma+\bar{\sigma})$, and $\epsilon$ is the interaction
strength. This modified interaction provides a short-range repulsion or volume
exclusion for the particles with separation $r<2^{1/6}\sigma$, a force-free
regime for $2^{1/6}\sigma<r\leq\tilde{r}$, and a long-range attraction for
particle separation, $\tilde{r}<r<r_{cut}=2.5\sigma$.

For activity, each ABP is subjected to a constant active force $f_{0}$ along a
body-fixed propulsion direction
${\bf\hat{n}}_{i}=(\cos\theta_{i},\sin\theta_{i})$. The orientation $\theta$
undergoes diffusive reorientation, and may additionally experience alignment
forces. Time evolution follows a Langevin dynamics,

$\begin{split}m\ddot{\bf r}_{i}&=-\gamma\dot{\bf r}_{i}+{\bf F}_{i}({\bf
r}_{i})+f_{0}{\bf\hat{n}}_{i}+\sqrt{2D}{\bf\eta}_{i}^{T},\\\
\dot{\theta}_{i}&=\sqrt{2D_{r}}\eta_{i}^{R}.\end{split}$ (1)

Here, ${\bf F}_{i}=-\nabla_{i}V$ describes the interaction with other cells
with the total potential $V$ as a sum of all pair interactions, and
$f_{0}=v_{0}\gamma$ is the driving force which results in a self-propulsion
velocity $v_{0}$ for an isolated cell experiencing a drag force due to
substrate friction with drag coefficient $\gamma$, which is related to the
thermal translational diffusion coefficient $D=k_{B}T/\gamma$ by the Einstein
relation. Similarly, $D_{r}$ is the rotational diffusion coefficient. The
noise forces $\eta$ are assumed to be Gaussian white-noise variables with
$\langle\eta_{i}(t)=0\rangle$ and
$\langle\eta_{i}(t)\eta_{j}(t^{\prime})\rangle=\delta_{ij}\delta(t-t^{\prime})$.
However, note that this is an active system, and thus both diffusion processes
can in principle be independent active processes with different amplitudes,
and thus do not need to satisfy the Einstein relation or fluctuation-
dissipation theorem. In order to emphasize the importance of rotational over
translational diffusion, we choose $D_{r}\sigma^{2}/D=3$.

The cohesive nature of modeled cell colonies depends on the competition
between adhesion and self-propulsion. A key parameter is the potential width
$\bar{\sigma}$, which controls the fluid-like consistency of the colony.
Further details about model parameters can be found in the supporting
information. In the simulation results described below, all quantities are
reported in dimensionless units based on thermal energy $k_{B}T$, particle
diameter $\sigma$, and rotational diffusion time $\tau_{r}=1/D_{r}$. We
characterize the system by three dimensionless numbers, the Péclet number,
$Pe=v_{0}\sigma^{2}/D=3v_{0}\tau_{r}/\sigma$ which quantifies the activity of
the system, the adhesion strength $U=\epsilon/(k_{B}T)$, and the potential
width $\bar{\sigma}/\sigma$ which determines the wiggle room of the cells.

In order to introduce local velocity-orientation alignment, we assume
alignment between propulsion direction and velocity for each cell individually
[35, 36, 37]. In our simple stochastic model, Eq. 1, the orientation dynamics
in this case is determined by

$\dot{\theta}_{i}=\sqrt{2D_{r}}\eta_{i}^{R}-k_{e}D_{r}\frac{\partial}{\partial\theta}({\bf{n}}_{i}.{\bf{v}}_{i})$
(2)

Here, $k_{e}$ is the strength of particle alignment. The alignment force can
be interpreted as arising from a pseudo potential $V_{a}=-(k_{e}/2)({\bf
v}\cdot{\bf n})$, acting only on the orientation $\bf n$, but not on $\bf v$.
Unless noted otherwise, results concern systems withouth velocity-alignment
interactions (i.e. $k_{e}=0$).

###  II.2 Liquid-Vacuum Coexistence

We begin our analysis by exploring the available phase space spanned by
activity $Pe$ and adhesive strength $U$. The system is initialized with a
circular cell colony with $N=7851$ particles and a diameter $100\sigma$
(packing fraction $\phi=0.79$) in a square simulation box of linear size
$150\sigma$. The resulting phase behavior as a function of $Pe$ and $U$ is
displayed in Fig. 1. Here, snapshots of particle conformation after long
simulation time ($t=3300\tau_{r}$), together with particle mobility, measured
by the mean squared displacement

$d_{m}^{2}=({\bf r}_{i}(t+t^{\prime})-{\bf r}_{i}(t))^{2}$ (3)

averaged over several reorientation times $t^{\prime}=12\tau_{r}$, are
employed to characterize the phases. Figure 1 shows that a line $Pe\simeq U$
separates a homogeneous gas phase at $Pe>U$ from a two-phase coexistence
regime for $Pe<U$. For low activity ($Pe\ll U$), the condensed phase is solid,
where particles do not show any significant movement, i.e. $d_{m}^{2}\approx
0$. As activity increases and approaches $Pe\simeq U$, cells become mobile
($d_{m}^{2}>1$). Finally, for large $Pe\gtrsim 100\gg U$, attraction becomes
negligible and conventional motility-induced phase separation is observed. A
simple calculation, which equates the propulsion force with the maximum of the
attraction force, reveals that the detachment of particle pairs occurs at
$Pe=2.4U$; for larger $Pe$ the adhesive force is no longer strong enough to
keep particles together. Note that thermal fluctuations are usually rather
small in this study (because $U\gg 1$).

Figure 1: Phase diagram illustrated by snapshots at the end of simulation.
Here we plot the mobility profile as a function of attractive interaction $U$
and activity $P_{e}$. We start the simulation with initial circular patch. The
colour code defines the magnitude of mobility. Blue means immobile and red
means highly mobile colony. ($\bar{\sigma}/\sigma=0.3$; overall packing
fraction is $0.274$). See SI Movies S1 and S2 for the formation and dynamics
of the cohesive colony at liquid vacuum coexistence for $U=40$, $Pe=30$.

For $Pe\lesssim U$, cells are unable to detach from the colony, and the colony
coexists with a cell vacuum outside. If $P_{e}\ll U$ and $U\gtrsim 8$, the
system is clearly kinetically arrested, but as activity increases, the “wiggle
room” of the potential allows particles to break the neighbor cage and move,
resulting in liquid-vacuum (L-V) coexistence. This state of a single cohesive
colony is not induced by the initial conditions of a single circular patch,
but also emerges from an initial random distribution of particles due to
particle aggregation and cluster coarsening. To quantitatively characterize
and clearly distinguish mobile cohesive colonies from the kinetically-arrested
colonies, we employ the ”mean squared particle separation” (MSPS). We choose
random pairs of cells $m$ and $n$ inside the colony at time $t_{p}$, which are
initially at contact with a center-center distance $1.1\,\sigma$, and measure
the squared separation of this pair over time. n average over $N_{p}$ such
pairs at different initial times $t_{p}$ yields

$MSPS(t)=\frac{1}{N_{p}}\sum_{N_{p}}({\bf r}_{m}(t_{p}+t)-{\bf
r}_{n}(t_{p}+t))^{2}.$ (4)

A characteristic feature of the arrested dynamics in a solid phase is that
particles do not exchange neighbors, so that the MSPS plateaus at
$MSPS<(1.2\sigma)^{2}$. In a fluid phase, particles exchange neighbors at a
constant rate, and MSPS increases linearly with time (see also Appendix B,
Fig. 8). Thus the MSPS is good indicator of fluid-like behavior. Here, we
choose $MSPS>(1.2\sigma)^{2}$ at time $t=12\tau_{r}$ as a definition of fluid-
like behavior. To quantify cohesiveness, we turn to a cluster analysis, where
particles are identified to be in the same cluster if their distance is less
than the cutoff distance $r_{cut}$. The condensed phase-vacuum coexistence is
then signaled by cluster number $N_{cl}=1$. Figure 2(A) displays
$MSPS(t=12\tau_{r})$ and $N_{cl}$ as a function of $Pe/U$. For $Pe\lesssim
0.55U$, the system remains cohesive and solid. As activity increases, MSPS
increases as well, but the colony remains cohesive, clearly identifying the
liquid-vacuum (L-V) coexistence region. Further increasing activity
($Pe\gtrsim 0.75U$) leads to the occasional detachment of small clusters
(above a threshold size) from the parent colony (see discussion below).
Interestingly, occasional cluster detachment is not sufficient to disintegrate
the parent colony, as detached cluster can rejoin the parent colony, which
thereby coexists with a gas of small clusters.

Figure 2(B,C) display different cuts through the phase space, to elucidate the
region of stability of different regimes. The results in Fig. 2(B) show that a
minimum width $\bar{\sigma}/\sigma\simeq 0.1$ of the potential well is
necessary to observe a liquid-vacuum coexisting phase. Thus, the width
$\bar{\sigma}/\sigma$ plays a crucial role to achieve a cell colony with
fluid-like dynamics at strong adhesion. The importance of $Pe/U$ as the
relevant variable to distinguish two-phase coexistence from a one-phase gas-
like region, is emphasized by Fig. 2(C), which demonstrates that the
boundaries between the different regimes occur at $Pe/U\simeq 0.55$, 0.75, and
0.875, for $U\gtrsim 20$. Note that all these boundaries appear at $Pe/U$
values, which are much smaller than the unbinding threshold $Pe/U\simeq 2.4$
of particle pairs.

Figure 2: (A) ”MSPS” (left axis) and $N_{cl}$ (right axis) as a function of
$P_{e}/U$, for fixed $U=40$ with increasing activity. changing $Pe$ value.
$MSPS(t)$ is calculated at time separation $t=12\tau_{r}$. The orange area
indicates $S-V$ coexistence, the blue area $L-V$ coexistence, the green area
$L-G$ coexistence with small detached cell clusters in the gas phase, and the
red area a homogeneous phase of many small clusters. Results are for
$\bar{\sigma}/\sigma=0.3$. (B) Phase diagram as a function of the potential
width $\bar{\sigma}$ for fixed $U=40$. (C) Phase diagram various $U$ as a
function of rescaled Péclet number, $Pe/U$, for fixed
$\bar{\sigma}/\sigma=0.3$. (D) Cluster-size distribution of detached clusters,
of size $n_{pc}$, at $\bar{\sigma}/\sigma=0.3$, $U=40$, and $Pe=32$. Inset:
Same data in log-log representations, which also includes the parent colony
along with the detached clusters.

For Péclet numbers $Pe\gtrsim 0.75U$, small clusters are able to detach from
the parent colony. This process can be characterized by the cluster-size
distribution $P(n_{pc})$, see Fig. 2(D). The peak of the distribution for
clusters in the size range from 10 to 100 indicates that particles escape
collectively. We do not observe the escape of any single cell from the colony
in this regime. This can be understood from a simple argument, which considers
a small semi-circular patch of $n_{pc}$ particles at the boundary of the
colony (see Appendix B, Fig. 9). The patch has an interface with the colony of
length proportional to $\sqrt{n_{pc}}$. If all particle orientations point in
roughly the same direction (outwards), then the patch can unbind when
$n_{pc}>n_{pc}^{*}\simeq 12.7(U/Pe)^{2}$, i.e. for sufficiently large patch
size, a size which decreases rapidly with increasing $Pe$ (see Appendix B for
details, in particular Fig. 10). The probability for all particles in such a
cluster to be roughly aligned depends on the Péclet number, as particles move
toward the boundary with preferred outward orientation [38]. However, the
particle mobility in the fluid phase is very small due to the dense packing of
neighbors, so that the characteristic ballistic motion of ABPs for times less
than $\tau_{r}$ is completely suppressed (see Appendix B, Fig. 7). Therefore,
polar ordering is mainly seen at the edge of the colony, see Fig. 3(A).
Cluster formation therefore arises mainly from the increased mobility of pre-
aligned particles at the boundary.

###  II.3 Stress Profile - Tensile Colonies

Figure 3: (A) Averaged polarization vector of the circular patch at
$\bar{\sigma}=0.3\sigma$ at $L-V$ coexisting state for two different activity
and (B) Different components of the stress at $\bar{\sigma}=0.3\sigma$ and
$U=40$, $Pe=30$. ”Violet” represents the ”virial” stress profile, yellow color
represents the stress profile due to activity, ”sky-blue” represents the
kinetic contribution of the stress profile and ”red” represents the sum of all
these three contributions. (C) The total stress profile for different adhesive
strength in $L-V$ coexisting states at $U=15,40$. The stress starts generated
at the boundary region of the colony and outside of it, the stress vanishes.
Figure 4: Total central stress calculated in the area starting from the center
to a radius $30\sigma$ as a function of activity, $Pe$, for $U=40$ and
$\bar{\sigma}=0.3\sigma$. The transition from S-V to L-V coexistence occurs at
$Pe=23$ (compare Fig. 2(C)), which essentially coincides with Péclet number
where central stress changes sign.

To gain a better understanding of the properties of the liquid-like cohesive
colony, we analyze the polarization field of the active force and the stress
profile. Figure 3(A) shows that the averaged local polarization is zero inside
the colony, but points outwards at the boundary. This is in contrast to what
is typically found for motility-induced clustering [24, 39, 26, 40, 41]. The
reason is that the attractive interactions keep outward-oriented particles at
the boundary of the colony – which would otherwise move away – combined with
the fluidity of the colony which allows local particle sorting near the
boundary, similar to the behavior of isolated self-propelled particles in
confinement [38, 42].

The alignment of motility forces at the boundary should lead to an increase of
tensile stress. For the liquid colonies in coexistence with the vacuum phase,
we find significant tensile stress in the center (see Fig. 3(C)). As expected
from force balance, the stress is nearly constant inside the colony, but
rapidly decreases in the boundary region where the tension is generated. The
total stress in the colony has three contributions: the inter-particle force,
kinetic contribution, and swim stress. At liquid-vacuum coexistence, the
inter-particle contributions plays the dominant role, whereas the swim stress
is comparatively small (Fig. 3(B)). Figure 4 shows the dependence of the total
central stress in the colony on the activity $Pe$. In the solid regime, the
central stress is negative due to the passive surface tension, resulting in a
Laplace pressure proportional to $U$. Increasing activity leads to more
liquid-like consistency, facilitating enhanced outward particle orientation at
the edge, and hence tensile stress. Interestingly, the stress is found to be a
linearly increasing function of $Pe$ over the whole investigated range,
$0<Pe\leq 30$, i.e. both in the solid and liquid regime of the colony. This
indicates that the enhanced particle sorting occurs mainly near the edge, and
an increased edge mobility exists already in the solid phase near the S-L
phase boundary. A tensile stress in cell colonies is observed similarly in
experiments, where the average stress within a spreading cell sheet increases
as a function of distance from the leading edge [22]. In a quasi-one-
dimensional (rectangular channel) geometry, the total stress in the colony is
obtained by integration of the net active forces, and increases from zero
outside to a finite tensile stress in the center (see Appendix B, Fig. 11).

###  II.4 Coordinated Motion – Motion Alignment

In experimental observations, long-range velocity correlations are often
visible in the bulk of spreading epithelial sheets [11, 12]. ABPs with
adhesion display significant velocity correlations even without explicit
alignment interactions (see Appendix Fig. 13, and Refs. [15, 43]). However, as
ABPs display independent orientational diffusion, it is evident that realistic
long-range correlations require some type of velocity alignment. We employ a
local velocity-orientation alignment mechanism, in which cell propulsion
direction (=cell polarity) relaxes toward the instantaneous cell velocity,
resulting from the forces induced by its neighbors [35, 36, 37], as introduced
in Eq. 2. Without alignment, correlations arise from a small group of cells
pointing in the same direction by chance, and thus moving collectively more
easily and furthermore dragging other cells along. The alignment interaction
stabilizes and enhances this effect. In presence of velocity alignment, the
velocity field shows an enhanced coordinated motion with prominent swirls in
the bulk of the colony and fingering at the edge (see Fig. 5(A)).

Figure 5: Dynamics of cell colony with orientation-velocity alignment
interactions. (A) Velocity fluctuation field of the full cell colony for
$U=40$, $Pe=25$ and $k_{e}v_{0}=1.25$ at $\bar{\sigma}=0.3\sigma$, which
displays prominent swirls in the bulk and finger-like structures at the edge.
See also Appendix B, Fig. 13. (B) Characteristic correlation length
$\xi_{vv}$, extracted from velocity correlation, as a function of alignment
strength $k_{e}$, for different attractive interactions $U$ and activities
$Pe$, as indicated, with $\bar{\sigma}=0.3$. The colony is in the fluid state
for $k_{e}v_{0}=0$. Inset: Variation of total central stress as a function of
alignment strength $k_{e}$, for adhesive strength $U=25,40$
($\bar{\sigma}=0.3$). For both data sets, the colony is in the solid state for
$k_{e}=0$, and transits to a liquid state at $k_{e}v_{0}\simeq 0.65$ and
$k_{e}v_{0}\simeq 1.3$ for $U=25$ and $U=40$, respectively.

We quantify the spatial correlations by the velocity-velocity correlation
function

$C_{vv}(r)=\Bigg{\langle}\frac{\sum_{r_{i}}\delta{\textbf{v}}({\textbf{r}}_{i})\cdot\delta{\textbf{v}}({\textbf{r}}_{i}+{\textbf{r}})}{\sum_{r_{i}}\delta{\textbf{v}}({\textbf{r}}_{i})\cdot\delta{\textbf{v}}({\textbf{r}}_{i})}\Bigg{\rangle},$
(5)

as a function of distance $r$, where the brackets denote an average over all
directions and time. Here, velocities are measured relative to the average
velocity $\bar{\textbf{v}}$, of the whole colony, i.e.
$\delta{\textbf{v}(\textbf{r})}={\textbf{v}(\textbf{r})}-\bar{\textbf{v}}$, to
avoid finite-size effects. The correlations decay exponentially with a
characteristic length scale, $\xi_{vv}$ (see Appendix B, Fig. 14). Figure 5(B)
displays the correlation length $\xi_{vv}$ as a function of alignment strength
$k_{e}$ for various adhesive interactions. For fixed adhesion and activity,
increasing alignment strength $k_{e}$ facilitates a transition from the solid
to the liquid state of the colony. Furthermore, the alignment coupling leads
to stronger correlations, as indicated by the monotonic increase of $\xi_{vv}$
with $k_{e}v_{0}$, and thus to swirls and fingers. Eventually, fingering is so
strong that clusters detach, and the colony is no longer cohesive. However,
correlation lengths up to $\xi_{vv}=10\sigma$ can be achieved, quite
comparable to the 5 to 10 times cell size obtainable in experiments [11, 15].
Also, the tensile stress at the colony center increases (see inset of Fig.
5(B)) and becomes positive at sufficiently large $k_{e}v_{0}$. The critical
alignment strength $k_{e}v_{0}$, where the colony is liquefied and the tensile
stress becomes positive, increases with attraction strength $U$.

##  III Conclusions and Outlook

We have presented a minimal model for the fluidization of cell colonies, which
consists of active Brownian particles with adhesion. An attractive potential
with increased basin width yields non-equilibrium structures, phase behavior
and dynamics, which capture relevant features of biological cell colonies. The
main observation is that for moderate adhesion and propulsion, the system
exhibits liquid-vacuum coexistence, i.e. all particles agglomerate into a
single colony displaying liquid-like properties, while the outside remains
devoid of any particles. This is reminiscent of in vitro experiments of MDCK
colonies, where cells show strong motion, while remaining perfectly cohesive.
Furthermore, the fluidity of the colony in our model results in outward
ordering of particle orientations at the edge, thus leading to tension in the
colony. This is consistent with the results of traction force microscopy,
which show that MDCK colonies are typically under tension [22]. Our model
demonstrates that no alignment interaction or growth mechanism need to be
evoked to explain such tensile forces – the motility of the cells combined
with liquid properties of the colony suffice. As motility force increases,
particles start to detach from the parent colony, however not as single cells
but collectively in small clusters of cells. Finally, we have demonstrated how
velocity-polarity alignment can further enhance fluidity, tension, and
fingering of the colony, and collective cell detachment. Indeed, with
velocity-polarity alignment, simulations look very reminiscent of real MDCK
colonies, displaying strong fingering at the edge, high tension and long-
ranged velocity correlations.

Our model also provides a tentative explanation for another biological
phenomenon. When metastatic cells detach from a tumor, they typically detach
collectively, as small groups of five cells or large aggregates [44, 45, 46],
into the stroma and migrate to reach blood or lymph vessels. At the edge of
the liquid-vapor region of our model, particles show exactly this type of
behavior; the colony is no longer perfectly cohesive, but clusters of cells
begin to detach.

An interesting next question is how these results will be affected by cell
growth. Of course, if growth is slow, the dynamics will be independent of
growth and the phenomenology will be unchanged. However, when time scales of
growth and motion become comparable, novel phenomena may arise.

###### Acknowledgements.

Financial support by the Deutsche Forschungsgemeinschaft (DFG) through the
priority program SPP1726 “Microswimmers – from single particle motion to
collective behavior” is gratefully acknowledged. The authors also gratefully
acknowledge the computing time granted through JARA-HPC on the supercomputer
JURECA [47] at Forschungszentrum Jülich.

##  Appendix A Attractive Brownian Particles: Model and Analysis of Simulation
Data

###  A.1 Simulation parameters

For numerical implementation of our model, we use the LAMMPS molecular
simulation package, with in-house modifications to describe the angle
potential and the propulsion forces, as described in the main text. The system
consists of $N=7851$ particles (cells) in a 2D square simulation box of size
$L_{x}=L_{y}=150\sigma$ with periodic boundary conditions, unless noted
otherwise. With velocity-orientation-alignment interaction, the simulation is
carried out in a box of size $L_{x}=L_{y}=250\sigma$. For the extended LJ
interaction potential, see Fig. 6, we use the cut-off distance
$r_{cut}=2.5\sigma$. For numerical efficiency, we chose a finite mass $m=1$
and drag coefficient $\gamma=100$ such that the velocity relaxation time
$m/\gamma$ is much smaller than all physical time scales. The equations of
motion are integrated with a velocity Verlet algorithm, with time step $\Delta
t=0.001$. Each simulation is run for at least $11\times 10^{7}$ time steps,
with rotational diffusion coefficient $D_{r}=0.03$ this corresponds to a total
simulation time longer than $3000\tau_{r}$, where $\tau_{r}$ is the rotational
decorrelation time.

###  A.2 Polarization Vector

We define the spatial-temporal average polarization $p$ for the quasi-circular
cell colony by the projection of the orientation vector $\bf\hat{n}$ of the
particle on the radial direction from the center of mass of the colony, i.e.,

$\langle
p(r^{\prime},t)\rangle=\sum_{i=1}^{N}({\bf\hat{n}}_{i}\cdot{\bf\hat{r}}_{i}^{\prime})\,\delta(r^{\prime}-|{\bf
r}^{\prime}_{i}|)/\sum_{i=1}^{N}\delta(r^{\prime}-|{\bf r}^{\prime}_{i}|)$ (6)

where ${\textbf{r}}_{i}^{\prime}={\textbf{r}}_{i}-{\textbf{r}}_{cm}$, and
${\textbf{r}}_{cm}$ is the center-of-mass position at a particular time $t$.
Here, $\delta(r)$ is a smeared-out $\delta$-function of width $\sigma$.
$\langle p\rangle$ is further averaged over time.

###  A.3 Stress calculation

In ABP systems with short-range repulsion, it has been shown that the pressure
is a state function, depending only on activity, particle density, and
interaction potential, but not on the interaction with confining walls [48,
49, 50, 41]. In comparison to passive systems, activity implies a new
contribution to pressure, which is called the swim pressure. The calculation
of the local stress in an ABP system is a matter of an ongoing debate, which
mainly concerns the form of the active term. We follow Ref. [41], and define
the stress in a volume $\Delta V$ by

$\displaystyle\Delta V\Sigma_{\alpha\alpha}=$
$\displaystyle\\-\sum_{i=1}^{N}m\langle\dot{\bf
r}_{i}^{2}\Lambda_{i}\rangle-\frac{\gamma}{\gamma_{R}}\sum_{i=1}^{N}\langle
v_{0}{\bf n}_{i}\cdot\dot{\bf r}_{i}\Lambda_{i}\rangle$ (7)
$\displaystyle\\-\frac{1}{2}\sum_{i=1}^{N}\sum_{j=1}^{N}\langle\lambda_{ij}{\bf
r}_{ij}\cdot{\bf F}_{ij}\rangle$

where $\dot{\bf r}_{i}$, ${\bf F}_{i}(i=1,...,N)$ denote the velocity and
force of particle $i$, respectively. ${\bf F}_{ij}$ represents the pair wise
interaction between particle $i$ and $j$ and
${\textbf{r}}_{ij}={\textbf{r}}_{i}-{\textbf{r}}_{j}$. Here
$\Sigma_{\alpha\alpha}$ are the diagonal stress-tensor components.
$\gamma_{R}$ is the damping factor which is related to the rotational
diffusion coefficient as $\gamma_{R}=2D_{r}$. $\Lambda_{i}$ determines the
volume $\Delta V$, where $\Lambda_{i}(\textbf{r})$ is unity when particle $i$
is within $\Delta V$ and zero otherwise. $\lambda_{ij}$ denotes the fraction
of the line connecting particle $i$ and $j$ inside of the volume $\Delta V$.
The first and the last term in (7) are the classic kinetic contribution and
the contribution of inter-particle interactions. The second term denotes the
active-force contribution in the stress calculation. Notably, in the fluid-
vacuum state we are focusing on in this work, the active stress component is
negligible compared to the inter particle interaction contribution. This is in
line with results for the pressure contributions in repulsive ABP systems at
coexistence between a high-density and a low-density phase, where the swim
pressure in the high-density phase is negligible [41].

##  Appendix B Supporting Considerations and Results

###  B.1 Particle Mobility in Vacuum, Gas, and Fluid Phases

A single, isolated ABP has a characteristic mean square displacement, with
ballistic motion (MSD $\sim v_{0}^{2}t^{2}$) at short times $t<\tau_{r}$, and
a diffusive motion (MSD $\sim v_{0}^{2}\tau_{r}t$) for $t>\tau_{r}$ [51]. This
is the behavior we observe in the vacuum phase, see Fig. 7. A very similar
behavior is found in the gas phase, at packing fraction $\phi=0.274$, but now
the particle velocity is significantly reduced due to frequent collisions with
other particles, while the crossover time $\tau_{r}$ remains unaffected.
However, the behavior changes drastically in the fluid-like phase, where the
collisions and attractive interactions completely suppress the ballistic
regime, see Fig. 7.

A very similar dynamic behavior is observed in the mean squared particle
separation (MSPS), see Fig. 8. The time dependence in the fluid phase is
dominated by linear diffusion behavior, while in the solid (jammed) phase it
is strongly sublinear.

Figure 6: Modified Lennard-Jones (LJ) potential (red colored curve) is
modified by inserting a plateau of width $\bar{\sigma}$ at the minimum of this
potential. The usual LJ potential is shown by blue crosses. Figure 7:  Mean
square displacement (MSD) in three different states: (i) In the bulk of
”fluid-like” colony (purple circles) with $U=40$ and $Pe=30$, (ii) in the
”gas” phase (red squares) $U=40$ and $Pe=41$ and packing fraction
$\phi=0.274$, and (iii) in the ”vacuum” phase (brown triangles) with $Pe=41$.
Figure 8: Mean squared particle separation ($MSPS$) as a function of time for
two different $Pe$ numbers at $U=40$ and $\bar{\sigma}=0.3$. At $Pe/U=0.5$,
$MSPS$ remains constant at short times, indicative of no neighbor exchange,
and shows sub-diffusive behavior at longer time. However, at $Pe/U=0.57$, the
time evolution of $MSPS$ shows a long-time linear behavior, indicative of
constant neighbor exchange and liquid-like behavior.

###  B.2 Minimum Cluster Size for Detachment

For our model system, particles can only escape from the parent colony in the
form of a small cluster at larger adhesive strength ($U\geq 10$). Let us
consider the following simplified model. A semi-circular cluster of particles
has formed at the colony edge, where all particle orientations are aligned and
are pointing outwards normal to the interface. In this idealized situation, we
can address the question about the number of particles in the cluster, and the
${\rm Pe}$ number required to separate the cluster against the adhesive force
from the parent colony.

Let $n_{pc}$ be the number of particles in the cluster. For packing in a
roughly triangular lattice with lattice constant $a=\sigma+\bar{\sigma}/2$,
this implies a cluster radius $R_{cl}/a=(\sqrt{3}/\pi)^{1/2}n_{pc}^{1/2}$. The
length of the interface between cluster and parent colony is $L=2R$, see Fig.
9. Along the interface, there are $L/a$ bonds between particles on both sides
of the interface, which generate the same maximum force as for the detachment
of a single particle, where bond breakage occurs at $Pe/U=2.4$ (see main
text). Thus, we have the force balance for the cluster break-off,
$n_{pc}Pe=2.4(L/a)U=4.8(\sqrt{3}/\pi)^{1/2}Un_{pc}^{1/2}$, which implies

$n_{pc,min}=\frac{\sqrt{3}}{\pi}\left(\frac{4.8U}{Pe}\right)^{2}.$ (8)

Hence, with increasing activity $Pe$ at constant adhesive strength $U$, the
minimal size of detached clusters is expected to decrease rapidly. Figure 10
shows simulation results for the number of particles present in the smallest
cluster $n_{pc,min}$ as a function of $Pe/U$. This demonstrates that beyond
the liquid-vacuum region, $n_{pc}$ rapidly decreases with increasing activity
$Pe$ and eventually reaches a ”gas-like” phase, where single-particle
detachment from the parent colony, i.e. $n_{pc,min}=1$, is observed.

Furthermore, we can use Eq. (8) to estimate the cluster size when cluster
break-off first becomes possible, at $Pe/U\simeq 0.75$, which is about
$n_{pc}\simeq 20$, in reasonable agreement with the lower cutoff of the
cluster-size distribution in Fig. 2(D) of the main text.

Figure 9: A semi-circular cluster of particles formed at the colony edge. All
particles in this region are assumed to be aligned and to be oriented in the
outward direction, normal to the interface, as indicated by the arrows. The
length of the interface between parent colony and detaching cluster is $L$.
Figure 10: Average cluster size $\langle N_{cl}\rangle$ (left axis) and size
of smallest cluster $n_{pc,min}$ (right axis) as a function of $Pe/U$, for
fixed $U=40$ with increasing activity ($\bar{\sigma}/\sigma=0.3$). The blue
area indicates $L-V$ coexistence, the green area $L-V$ coexistence with small
detached clusters in the gas phase, and the red area a homogeneous phase of
many small clusters.

###  B.3 Probability Distributions of Aligned Particle Clusters at Colony Edge

For randomly oriented particles, the probability to find a cluster in which
the orientations of all particles have a positive projection into one chosen
direction is $2^{-N_{cl}}$, which is very small for clusters of size $10$ or
larger. However, there is a sorting mechanism which strongly enhances this
probability, which is the active motion of particles toward the colony edge,
where they arrive with roughly the right orientation [38]. However, due to the
diffusive motion in the bulk of the colony, see Fig. 7, this mechanism can
only operate very close to the colony edge. The polarization profile (Fig.
3(A) of the main text) shows a high polarization of $p=0.65$ at the boundary.
Thus, properly oriented particles only have to diffuse laterally along the
boundary to form clusters for detachment. This mechanism is supported by
simulations, which allow the tracking of the history of cluster development.

###  B.4 Stress Calculation in a Quasi-One-Dimensional Geometry

As a further test to our stress estimates, we use force balance to obtain an
independent measure of stress, similar to traction-force microscopy setups
[22]. Under the physical interpretation of our system that the particles are
cells which exert an active force $\gamma v_{0}$ on the substrate in order to
move against friction forces $-\gamma v$, the traction force of each particle
is $T=\gamma v_{0}\bf\hat{n}-\gamma\bf v$. In one dimension, force balance is
closed, and we can calculate a change of stress via force balance. We simulate
a quasi-one-dimensional geometry with a nearly flat interface. The system
consists of a 2D channel of dimensions $L_{x}=6*L_{y}$ and $L_{y}=20\sigma$,
filled with $N=1200$ particles arranged initially to fill half the channel.
This system is subjected to periodic boundary conditions in both $x$ and $y$
directions. The stress within the cell colony is calculated via integration of
force balance (assuming zero stress outside the colony).

With the parameters $\bar{\sigma}=0.3\sigma$, adhesive strength $U=15$ and
activity $Pe=13$, the cell colony is in liquid-vacuum coexistence, see Fig.
11(top). The stress profile in the direction ($x$) normal to the interface is
shown in Fig. 11(bottom), while the tangential stress vanishes. Figure 11 also
shows that the estimations of the stress profile calculated from the traction
forces and from the virial expression agree quite well.

Figure 11: Top: Snapshot from the simulation in a quasi-one-dimensional
rectangular channel, for a cell colony in liquid-vacuum coexistence. The
parameters are $\bar{\sigma}=0.3\sigma$, adhesive strength $U=15$ and activity
$Pe=13$. Bottom: Stress calculated from traction forces and virial
contribution.

###  B.5 Origin of Tension in Attractive ABP Clusters – a Toy Model

Why are colonies of attractive ABPs under tension, while cluster of repulsive
ABPs in the state of motility-induced phase separation are under pressure? A
simple toy model can elucidate the underlying mechanism. Consider two ABPs
which are connected by a harmonic bond [52]. This bond represents the
interaction between an ABP at the colony edge, and one (or more) ABP further
inside the bulk. In case of a sufficiently high Péclet number (large
propulsion, slow rotational diffusion), the dumbbell quickly reaches a quasi-
stationary, torque-free state, see Fig. 12(A,B). In this state, the force can
be separated into a propelling component with direction $({\bf n}_{1}+{\bf
n}_{2})$, normal to the instantaneous bond vector ${\bf r}\sim({\bf
n}_{1}-{\bf n}_{2})$, and a bond stretching component, see Fig. 12(B,C). The
stretching force is

$\displaystyle f_{ext}=$ $\displaystyle f_{0}|{\bf
n}_{1}\cdot\hat{\bf{r}}|=f_{0}|\cos(\theta_{1})|$ (9) $\displaystyle=$
$\displaystyle f_{0}\sqrt{(1-{\bf n}_{1}\cdot{\bf n}_{2})/2}$ $\displaystyle=$
$\displaystyle|\sin((\varphi_{1}-\varphi_{2})/2)|$

where $\varphi_{i}$ is the orientation angle of ${\bf n}_{i}$ with respect to
some fixed axis. This stretching force has to be averaged over all
orientations ${\bf n}_{1}$ and ${\bf n}_{2}$, which yields

$\langle f_{ext}\rangle=\frac{2}{\pi}f_{0}$ (10)

Stress $\Sigma_{\alpha\alpha}$ is force per length, i.e.
$\Sigma_{\alpha\alpha}\simeq\langle f_{ext}\rangle/a\simeq\langle
f_{ext}\rangle/\sigma$. We can thus use Eq. 10 to estimate the tensile stress
as a function of Péclet number. With $f_{0}=\gamma v_{0}$, $D=k_{B}T/\gamma$,
$D_{r}=3D/\sigma^{2}$, and $Pe=3v_{0}/(\sigma D_{r})$, we obtain $f_{0}=Pe$
(in our dimensionless units). Thus, we predict $\Sigma=\Sigma_{0}+(2/\pi)Pe$
from our toy-model calculation. The linear dependence agrees well with the
simulation results for the cell colony, see Fig. 4 of main text. However, the
slope estimated from Fig. 4 is $0.16$, about a factor 4 smaller than the toy-
model prediction. Two obvious reasons for this overestimation of the slope in
the toy model are that (i) the bond vector takes all orientations with equal
probability, but only orientations roughly perpendicular to the interface
contribute to the stress (factor 2), and (ii) the hard-core repulsion between
ABPs is neglected, which sometimes leads to a pressure (negative tension)
(maybe another factor 2) – so that the overall agreement is quite
satisfactory.

Figure 12:  Arrangement and forces of ABP dumbbells. (A) Two connected ABPs
with randomly oriented propulsion forces ${\bf f}_{1}$ and ${\bf f}_{2}$. (B)
A short time $t$ later, with $\sigma/v_{0}<t<\tau_{r}$, the ABP orientations
remain essentially unchanged, but the particles have rearranged to form a
quasi-stationary, torque-free state, in which the bond is under tension. The
dumbbell also moves in direction ${\bf n}={\bf n}_{1}+{\bf n}_{2}$ normal to
the bond vector ${\bf r}$. (C) In the quasi-stationary state, the ABP
orientation vectors form angles $\theta_{1}$ and $\theta_{2}$ with the bond
vector ${\bf r}\sim({\bf n}_{1}-{\bf n}_{2})$, with $\theta_{1}=\theta_{2}$.

###  B.6 Velocity Correlation Function

To quantify collective cell migration, we map out the velocity field.
Snapshots of the simulations in Fig. 13 demonstrate that particles display
strongly coordinated motion. To further quantify the correlations, we
calculate the velocity correlation function $C_{vv}$ as described in Eq. 5 of
the main text. Figure 14 shows $C_{vv}(r)$. On short length scales, the
velocity correlations decay exponentially with a characteristic length scale
$\xi_{vv}$. We estimate $\xi_{vv}$ by fitting the simulation data by
$\exp(-r/\xi_{vv})$. The dependence of the $\xi_{vv}$ on $U$ and $Pe$ is
discussed in the main text, see Fig. 5(B).

Figure 14 shows $C_{vv}$ with and without alignment interaction. Velocity-
alignment interactions strengthen correlated motion and result in more swirl-
like patterns, as indicated by a small negative minimum in $C_{vv}$.

Figure 13: (Top) Velocity field (left) without and (right) with explicit
alignment interaction at $U=40$, $Pe=25$ $\bar{\sigma}=0.3$, and
$k_{e}v_{0}=1.25$. (Bottom) Velocity field in the finger-like structure of the
fluid-like in presence of alignment interaction ($k_{e}v_{0}=1.25$).

Figure 14: Velocity correlation function $C_{VV}(r/\sigma)$ for a system with
velocity-alignment interaction in the L-V region. (A) Spatial dependence for
various attraction strengths $U$, Péclet numbers $Pe$, and alignment
interaction strengths $k_{e}v_{0}$, and widths $\bar{\sigma}$ of the
attraction well, as indicated. (B) Same data as in (A), with exponential decay
demonstrated by log-lin representation. (C) Comparison of correlation
functions with (w-align) and without velocity alignment (wo-align).

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# PEARLS: Discovery of Point-Source Features Within Galaxies in the North
Ecliptic Pole Time Domain Field

Rafael Ortiz III School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Rogier A. Windhorst School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Seth H. Cohen School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  S. P. Willner Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138 USA  Rolf A. Jansen School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Timothy Carleton School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Patrick S. Kamieneski School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Michael J. Rutkowski Department of Physics and Astronomy, Minnesota State University, Mankato, MN 56001, USA  Brent Smith School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Jake Summers School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Tyler J. McCabe School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Rosalia O’Brien School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Jose M. Diego Instituto de Física de Cantabria (CSIC-UC). Avda. Los Castros s/n. 39005 Santander, Spain  Min S. Yun Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA  Jordan C. J. D’Silva International Centre for Radio Astronomy Research (ICRAR) and the International Space Centre (ISC), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia  ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Juno Li International Centre for Radio Astronomy Research (ICRAR) and the International Space Centre (ISC), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia  ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Hansung B. Gim Department of Physics, Montana State University, Bozeman, MT 59717, US  Nimish P. Hathi Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA.  Benne W. Holwerda Department of Physics, University of Louisville, Natural Science Building 102, Louisville KY 40292, USA  Adi Zitrin Department of Physics, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel  Cheng Cheng Chinese Academy of Sciences South America Center for Astronomy, National Astronomical Observatories, CAS, Beijing 100101, China  Noah J. McLeod School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Christopher J. Conselice Jodrell Bank Centre for Astrophysics, Alan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, UK  Simon P. Driver International Centre for Radio Astronomy Research (ICRAR) and the International Space Centre (ISC), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia  Haojing Yan Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA  Dan Coe AURA for the European Space Agency (ESA), Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21210, USA  Brenda Frye Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ, 85721-0009, USA  Norman Grogin Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21210, USA  Anton Koekemoer Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21210, USA  Madeline A. Marshall National Research Council of Canada, Herzberg Astronomy & Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada  ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Nor Pirzkal Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21210, USA  Aaron Robotham International Centre for Radio Astronomy Research (ICRAR) and the International Space Centre (ISC), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia  Russell E. Ryan, Jr. Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21210, USA  Christopher N. A. Willmer Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ, 85721-0009, USA Rafael Ortiz III<EMAIL_ADDRESS>
###### Abstract

The first public 0.9–4.4 $\mu$m NIRCam images of the North Ecliptic Pole (NEP)
Time Domain Field (TDF) uncovered many galaxies that display point-source
features in their cores as seen in the longer wavelength filters. We visually
identified a sample of 66 galaxies ($\sim$1 galaxy per arcmin2) with point-
like cores and fit their spectral energy distributions (SED)s using EAZY and
CIGALE to characterize the sample’s active galactic nucleus (AGN) and host
galaxy parameters. Single-template fitting best fits $70\%$ of the sample with
a Seyfert-blended SED. With CIGALE we compute the median fractional AGN
contribution to the 0.1–30.0 $\mu$m flux to be $0.30\pm 0.06$, and that 56% of
the 66 galaxies have star-formation rates in the starburst range whereas the
remainder are near the star-formation main sequence. There are Very Large
Array (VLA) 3 GHz detections for 24/66 galaxies, implying some combination of
AGN emission and vigorous star formation. We present a novel sample selection
procedure in tandem to the morphological sample selection based on objects’
light profiles at 4.4 $\mu$m. This procedure identifies a parameter space
which probes point-source features and automatically recovers our visual
sample with minimal contamination from both stars and brighter galaxies. This
procedure may be used in other extant and future NIRCam images to streamline
the search for galaxies with point-like cores. The morphological approach to
recognizing AGN is being resurrected by the James Webb Space Telescope (JWST)
by virtue of its superb angular resolution at infrared wavelengths.

Active Galactic Nuclei(16) — Seyfert Galaxies(1447) — James Webb Space
Telescope(2291) — Spectral Energy Distribution(2129)

††software: AstroPy (Astropy Collaboration et al., 2013, 2018, 2022); CIGALE
(Boquien et al., 2019); SExtractor (Bertin & Arnouts, 1996); EAZY (Brammer et
al., 2008)††facilities: James Webb Space Telescope (NIRCam); Very Large Array.

##  1 Introduction

More than eighty years ago, Carl Seyfert (1943) drew attention to 6
“extragalactic nebulae” with broad emission lines and “exceedingly luminous
stellar or semistellar” nuclei. Galaxies of this type became known as “Seyfert
galaxies” (Burbidge et al., 1963), and they are now recognized (e.g.,
Osterbrock, 1993) as members of the low-luminosity end of the population of
active galactic nuclei (AGN).

AGN are now thought to consist of an accretion disk around a supermassive
black hole (SBMH) within a wider, optically thick dust torus (e.g., Antonucci
& Miller, 1985). This central engine can achieve enormous luminosities and can
even outshine the entire host galaxy (e.g., Padovani et al., 2017). Modern
studies of AGN probe the relationship with their host galaxies and
intergalactic environments along with properties of the central SMBHs (e.g.,
Bollati et al., 2023; Costa-Souza et al., 2023; Sampaio et al., 2023).

AGN emit energy across the entire electromagnetic spectrum, and identification
and classifications of AGN are based on X-ray (e.g., Elvis et al., 1978),
UV–visible (e.g., Seyfert, 1943), infrared (e.g., Stern et al., 2005), and
radio (e.g., Fanaroff & Riley, 1974) observations. AGN are most often
identified via their spectral energy distributions (SED)s (e.g., Li et al.,
2023; Lyu et al., 2023; Yang et al., 2023), their colors (e.g., Stern et al.,
2005; Hwang et al., 2021; Juodžbalis et al., 2023; Furtak et al., 2023),
spectroscopy (e.g., Mehdipour et al., 2024; Burke et al., 2024), variability
(e.g., Pouliasis et al., 2019; O’Brien et al., 2024), radio (e.g., Hyun et
al., 2023), or X-ray emission (e.g., Masini et al., 2020; Zhao et al., 2021).
Identifying AGN by visual morphology has fallen out of favor in the “big data”
era of advanced instrumentation and vast surveys such as the Sloan Digital Sky
Survey (York et al., 2000). This is largely because dust obscuration can hide
the active nucleus (Hickox & Alexander, 2018) and at infrared wavelengths,
where the dust extinction is lower, wide-field surveys can only be done from
space. Until now, the angular resolution of infrared space observatories has
been low.

The James Webb Space Telescope (JWST), with its unprecedented resolution in
the infrared (e.g., Davies et al., 2024; Li et al., 2023; Yang et al., 2023),
offers the chance to revisit morphological AGN selection and analysis. This
paper is an initial exploration of the possibilities via characteristic
diffraction spikes of the telescopes’s PSF in the 0.9–4.4µm wavelengths that
suggest near-pointlike galaxy cores.

The North Ecliptic Pole (NEP) Time Domain Field (TDF) (Jansen & Windhorst,
2018) is located within _JWST_ ’s continuous viewing zone, making it a prime
target for AGN variability and other time-domain science. Because the ultimate
goal will be to compare morphological selection with other methods, we used
the now-public _JWST_ NEP TDF images (Windhorst et al., 2023) to visually
search for galaxies with point-like features in their center, i.e., potential
AGN, following the core morphology and Seyfert class relationship (e.g.,
Windhorst & Cohen, 2010; Rutkowski et al., 2013).

Section 2 describes the observations and construction of a morphologically
selected AGN catalog. Section 3 discusses the results, and Section 4 gives a
summary. All magnitudes are in AB units (Oke & Gunn, 1983). Where relevant, we
adopt a flat $\Lambda$CDM cosmology with $H_{0}=68$ km s-1 Mpc-1,
$\Omega_{M}=0.32$, and $\Omega_{\Lambda}=0.68$ (Planck Collaboration et al.,
2016, 2020).

##  2 Data & Cataloging

###  2.1 Observations

The _JWST_ NEP TDF is centered at (RA, DEC)J2000 = (17:22:47.896,
+65:49:21.54) (Jansen & Windhorst, 2018). The TDF was observed with _JWST_ as
part of the Prime Extragalactic Areas for Reionization and Lensing Science
(PEARLS) GTO program (Windhorst et al., 2023) in eight filters: F090W, F115W,
F150W, F200W, F277W, F356W, F410M, and F444W. The observations consisted of
four orthogonal spokes (illustrated by Figure 1 of both Willmer et al. 2023
and O’Brien et al. 2024) observed between 2022 Aug 25 and 2023 May 30. The
NIRCam image quality is diffraction-limited (Rigby et al., 2023; Windhorst et
al., 2023) at wavelengths $\gtrsim$1.3 µm with point source FWHM values
ranging from 60–160 milliarcseconds (mas) at wavelengths of 1.3–4.8$~{}\mu$m.

Point-source sensitivities in an aperture radius of 80 mas range from 28.1 to
29.1 mag (5$\sigma$), depending on the filter, and 29.0 mag in F200W
specifically. The images were drizzled on a 30 mas pixel scale. The parameters
per filter, the data reduction pipeline process, and further details are given
by Windhorst et al. (2023).

We used SExtractor (Bertin & Arnouts, 1996) to generate catalogs. The
detection threshold required 9 contiguous pixels 1.5$\sigma$ above the
background. We used 32 deblending sub-thresholds with a 0.06 minimum contrast
necessary for object deblending. We ran SExtractor on all eight filters in
dual-image mode using F444W as the detection filter to produce position-
matched catalogs. Magnitudes are MAG_AUTO except where indicated otherwise.

For an initial comparison with other wavelengths, we used the VLA 3 GHz radio
observations detailed by Hyun et al. (2023, their Appendix A).

Figure 1: RGB image cutouts for the 66 CPG sorted by $z_{phot}$ from CIGALE.
All image cutouts are 6″ square. The top left corner of each image gives the
image ID from Table 1, and $z_{phot}$ and $f_{\rm AGN}$ are in the bottom
left. The RGB scaling is R = 0.3$\cdot$F356W + 0.8$\cdot$F410M +
1.0$\cdot$F444W, G = 1$\cdot$F200W + 0.7$\cdot$F277W + 0.5$\cdot$F356W, B =
1$\cdot$F090W + 1$\cdot$F115W + 1$\cdot$F150W + 1$\cdot$F200W + 1$\cdot$F277W
+ 0.5$\cdot$F356W + 0.5$\cdot$F410M + 0.5$\cdot$F444W.

###  2.2 Visual Sample Selection

ROIII visually inspected an 8-filter color-composite of all NIRCam
observations within the _JWST_ NEP TDF to identify resolved galaxies with
unresolved point-like features in their cores. The color-composite was
constructed according to the
Trilogy111https://www.stsci.edu/$\sim$dcoe/trilogy prescription (Coe et al.,
2012). This visual inspection process involved observing each SExtractor-
detected galaxy in the four spokes of the NEP TDF by eye, and determining
whether there was a PSF effect in the galaxy core or an unresolved point
source within the galaxy. This identified 66 galaxies222We verified that no
objects in the sample are stars by applying a FWHM and magnitude cut similar
to that used by Windhorst et al. (2023) and/or by computing $z_{\rm phot}\neq
0$., which we refer as “CPGs” (central point-source galaxies) hereafter.
Figure 1 shows the sample and highlights the qualitative criteria, diversity,
and similarities of the CPGs. Several of objects within the CPG sample display
obvious point-like features in their cores (i.e., IDs 1/14/28/48), whereas the
vast majority show less distinct features of the characteristic PSF from
_JWST_.

The NIRCam images of the NEP TDF sampled an area of 65.4 arcmin2, and hence
our sample of 66 CPGs corresponds to $\sim$1 galaxy per arcmin2 to $m_{\rm
F444W}\lesssim 22$ AB mag. This is comparable to the WISE (W1–W2) color-
selected AGN density (e.g., Assef et al., 2013, their Table 1), $\sim$0.5 AGN
per arcmin2 to $m_{\rm W2}\lesssim 20.5$ AB mag.

###  2.3 Automated Sample Selection

Figure 2: F444W central surface brightness versus the surface brightness in a
surrounding annulus. The central surface brightness was measured in a circular
aperture with a radius 0$\farcs$18, and the outer annulus between circular
apertures of 0$\farcs$24 and 0$\farcs$36\. Circles represent galaxies, and
blue stars represent stars. CPGs are indicated with red squares. Only objects
with $m_{\rm F444W}<22$ AB mag, the limiting magnitude of the CPG sample, are
plotted. The greyscale bar (right) maps the galaxy total F444W magnitudes
(MAG_AUTO), with brighter galaxies plotted as darker.

While our initial sample was obtained through qualitative visual selection, it
would be useful to find a quantitative way to identify objects similar to
CPGs. The concentration index (e.g., Conselice, 2003) is one measure, but its
simple ratio finds sources that are peaky but not necessarily pointlike.
Instead, we used SExtractor to measure magnitudes in apertures at the cores of
objects in the _JWST_ NEP TDF. We ran SExtractor on the F444W image to compute
magnitudes in circular apertures with radii of 6, 8, and 10 pixels,
corresponding to radii 0$\farcs$18, 0$\farcs$24, and 0$\farcs$30,
respectively. We adopted these apertures to probe the surface brightness near
the core of the CPGs and identify objects that are morphologically similar to
stars out to a certain radius. We used the smallest aperture to measure the
average surface brightness within an inner area of $\sim$0.1 arcsec2 (SBINNER)
and used the two other apertures to measure the average surface brightness
within an outer annulus (SBOUTER), which has an area equal to that within the
inner circular aperture. Multiple aperture radii for SBINNER and SBOUTER were
tested, and the ones adopted provided the most effective way to probe point-
source features in galaxies with a productive CPG isolation.

Figure 2 plots SBINNER against SBOUTER. Stars are identified as straddling the
NIRCam diffraction limit with $\rm 150~{}mas\leq FWHM\leq 170~{}mas$ with
$m_{\rm F444W}\leq 28$ mag (Windhorst et al., 2023). CPGs near the stars in
Figure 2 are IDs 14/28/48. (ID 1 probably belongs in this group, but its
nucleus is saturated in the F444W observation). These objects prove that there
exists a parameter space where we can probe point sources within galaxies,
barring contamination from other stars. The longer wavelengths of the near-
infrared regime can probe both optically obscured and unobscured AGN (e.g.,
Assef et al., 2013) and both star-forming galaxies and weak-AGN (e.g., Kim et
al., 2019) via redder colors in the 3.5–3.6 µm and 4.4–4.5 µm bands. The
angular resolution of _JWST_ allows aperture photometry to be effective at
probing morphological signatures of AGN at these wavelengths, thus giving the
prominent separation from brighter galaxies. Obscured AGN in the UV–visible
are likely showing up in these images because of the much smaller dust
extinction at these wavelengths, and AGN are likely to be the point-like
features in our infrared CPGs.

The above prototype procedure provides a robust star–CPG separation and a CPG
separation from brighter galaxies that automatically recovers our CPG sample
and finds objects similar to it. Identifying galaxies that straddle the
morphology of stars without contamination would allow the search of CPG-like
galaxies in any _JWST_ /NIRCam image. We recognize that the automated method
does not pick up all of the weak-Seyferts in the _JWST_ NEP TDF; there will be
some that require higher signal-to-noise data to be identified by this
procedure. For the brighter galaxies that plot similar to our visual sample
but were not visually identified as CPGs in Figure 2, we defer work with two-
dimensional light profiling and/or NIRISS spectroscopy to classify what our
visual identification may have missed.

##  3 Results & Discussion

###  3.1 Seyfert Template Fitting with EAZY

In order to estimate AGN fractions and derive photometric redshifts, we used
EAZY333https://github.com/gbrammer/eazy-photoz (Brammer et al., 2008) to fit
the eight NIRCam magnitudes for each sample galaxy. For this single-component
template fitting procedure, we ran EAZY twice: one run allowing a single-
component fit from the 12 EAZY tweak_fsps_QSF_12_v3 templates, and a second
run fitting the AGN-ATLAS SEDs. The former templates are galaxy templates used
for stellar population synthesis and the latter templates (Brown et al., 2019)
are blends of AGN and host-galaxy SEDs covering 0.09–30.0 µm. The host/AGN
ratios available are powers of two from 0.5 to 64 normalized at 0.6 µm.

Figure 3: Chi-square of EAZY fits with and without an AGN. Each square
represents one CPG, and colors indicate each CPGs’ best-fit host/AGN ratio as
indicated in the color bar. The diagonal line indicates equality, i.e., no
preference for or against an AGN SED. IDs 1 and 29 are not plotted because
their fits failed to converge owing to the core’s extreme brightness.

As shown in Figure 3, 70% of the CPGs prefer an AGN-ATLAS template over a
standard EAZY template. Generally, the fits with the lower host/AGN ratios
(templates with the highest AGN contributions to the total SED) are still
fairly well fit with an AGN-Atlas SED, i.e., with no AGN at all (See 4). Even
when an AGN is indicated, for most galaxies in the sample, the host galaxy
outshines AGN emission. The fitting does not prove that our sample galaxies
are Seyferts. Offering more SED templates could just be adding free parameters
resulting in better fits. Nevertheless, the fitting done here is consistent
with the morphological selection.

The photometric redshifts generated from the AGN-ATLAS and standard EAZY
templates in this procedure show reasonable scatter, $\sigma_{\rm NMAD}=0.130$
(Eq. 7 of Brammer et al., 2008). This likely arises from the relatively small
wavelength range covered by the existing observations combined with the wide
wavelength range of the AGN SEDs having few spectral features that can
indicate redshift (e.g., Brown et al., 2019). This makes it more difficult to
constrain photometric redshifts for objects with an AGN (e.g., Assef et al.,
2013).

###  3.2 SED Parameter Estimation with CIGALE

To infer the galaxies’ physical properties, we used
CIGALE444https://cigale.lam.fr/ (Boquien et al., 2019), an SED-fitting code
relying on energy balance between the ultraviolet and infrared. The fitting
parameters incorporated a stellar continuum component from Bruzual & Charlot
(2003) models, a dust component from Dale et al. (2014) templates, a Calzetti
et al. (2000) dust attenuation law, nebular emission templates from Inoue
(2011), and a clumpy two-phase torus model from Stalevski et al. (2016). We
use CIGALE generated photometric redshift for the fits. The fits are good, as
expected with so many free parameters and so few photometric points, with
98.5% of the fits having $\chi^{2}_{\nu}\leq 0.5$. The online version of this
paper includes a Figure Set of all 66 CIGALE fits, and Figure 4 shows three
examples.

We verified the consistency of photometric redshifts generated from CIGALE
with photometric redshifts generated from single-component fits in §3.1.
$\sigma_{\rm NMAD}=0.1$ between photometric redshifts from CIGALE and EAZY
tweak_fsps_QSF_12_v3 templates. $\sigma_{\rm NMAD}=0.09$ between photometric
redshifts from CIGALE and AGN-ATLAS templates.

A CIGALE output parameter of immediate interest is $f_{\rm AGN}$, the
fractional contribution of AGN emission to the bolometric luminosity. We tuned
CIGALE to compute $f_{\rm AGN}$ based on AGN emission from 0.1 to 30 µm
following Assef et al. (2013, their Eq. 1) considering our NIRCam photometry.
The CPG median $f_{\rm AGN}\simeq 0.30$ with a median absolute deviation
$\pm$0.06. A control sample of the galaxy nearest in magnitude to each CPG has
$f_{\rm AGN}\simeq 0.16$ with a median absolute deviation $\pm$0.09. The
formal statistical separation here is only at the 1$\sigma$ level, though our
result suggests the CPG sample has measurable AGN emission in the infrared.
$f_{\rm AGN}$ can be better constrained with additional photometry in future
work, particularly in the UV and sub-mm (see, e.g., Ciesla et al., 2015).

Fig. Set1. CPG CIGALE SEDs

Figure 4: Example CIGALE model fits. The CPG ID is indidcated as a figure
title. The legend identifies model components included in the SED fitting, and
$z_{\rm phot}$, reduced $\chi^{2}$, and $f_{\rm AGN}$ are shown within each
panel. Fit residuals are shown below each SED panel. The online journal
includes a figure set showing all 66 CIGALE fits.

CIGALE also provides estimated stellar masses and star-formation rates (SFR)s,
which provide context for the CPGs. Typical galaxies fall on the star-
formation main sequence, which depends on both redshift and stellar mass
(Speagle et al., 2014, Eq. 28). As Figure 5 shows, the majority of our sample,
$\sim$56%, lies at or above the starburst boundary given by Rodighiero et al.
(2011), and the remainder of the sample lies near the star-formation main
sequence. An independent SFR estimate comes from radio observations (e.g.,
Condon, 1992; Tabatabaei et al., 2017). Positions for 24 CPGs match sources in
the VLA 3 GHz catalog (Hyun et al., 2023) (Table 1 identifies which CPGs have
radio counterparts). The most massive and highest-SFR CPGs are the ones having
radio detections. This could be attributed to either the synchrotron radiation
produced from remnants of Type II supernovae (e.g., Chevalier, 1982), i.e.,
star formation, or radio emission from the AGN (e.g., Kellermann, 1987), or
both. However, Willner et al. (2023, their Fig. 11) showed that few radio
sources in the TDF are in the starburst range.

The visual selection of these 66 CPGs is biased towards massive galaxies
because only bright galaxies could be examined for morphology. The CPGs’
active star formation, high stellar mass, and frequent radio loudness all
suggest that the near-infrared central point source is an AGN.

Figure 5: Star-formation rates from CIGALE relative to the respective star-
formation main sequence. The $y$-axis shows
$\Delta$SFR$\equiv$log10(SFR)/log10(SFRMS) with SFRMS defined by Speagle et
al. (2014, their Eq. 28). The horizontal dotted line and shaded region mark
the main sequence and the $\pm$0.2 dex range. The upper cyan, the middle
green, and the lower magenta dashed lines mark 0.6 dex above the main
sequence, commonly taken as the starburst boundary (e.g., Rodighiero et al.,
2011), the lower boundary to the main sequence, and the upper boundary to the
quiescent region (e.g., Renzini & Peng, 2015), respectively. CPG are denoted
as black squares, and squares with $\times$ symbols indicate sources with VLA
3 GHz matches.

###  3.3 ($m_{\rm F356W}$–$m_{\rm F444W}$) Colors

Another standard AGN selection method is red ($m_{\rm F356W}$–$m_{\rm F444W}$)
color (e.g., Stern et al., 2005). The NIRCam F356W and F444W filters are close
to the WISE W1 and W2 filters (Wright et al., 2010) and can replicate the
(W1–W2) $>$ 0.8 (Vega magnitudes) AGN color selection (e.g., Stern et al.,
2012). There are 19 CPGs with ($m_{\rm F356W,Vega}$–$m_{\rm F444W,Vega})>0.80$
as shown in Figure 6. (Table 1 gives the CPG colors). Other CPGs and all
galaxies in the control sample have integrated colors consistent with a pure
stellar population that formed early and evolved passively. However, these
colors do not preclude a modest AGN or star-formation contribution. At best,
reddening in Figure 6 can be attributed to dust.

Figure 6: ($m_{\rm F356W,AB}$–$m_{\rm F444W,AB}$) color versus CIGALE-computed
photometric redshift. Squares represent the CPGs with filled red squares
indicating the CPGs color-classified as AGN. Plus signs represent galaxies in
the control sample. The green and magenta lines show the colors of a galaxy
that formed at $z=5$ and has $A_{V}=0$ and $A_{V}=1$, respectively (Calzetti
et al. 2000 extinction law). The galaxy model is a Bruzual & Charlot (2003)
stellar population with Salpeter IMF, solar metallicity, and $\tau=0.5$ Gyr
exponentially declining star-formation history. The horizontal dotted line at
0.16 shows the $(m_{\rm F356W,Vega}$–$m_{\rm F444W,Vega})=0.8$ AGN color-
selection criterion in AB mag.

##  4 Summary & Future Prospects

The superb angular resolution of _JWST_ /NIRCam reveals galaxies (“CPGs”) with
pointlike cores at the redder wavelengths. Best-fit SEDs for 66 such galaxies
in the _JWST_ NEP TDF field suggest that the CPGs are massive and luminous,
and in most cases, the extended galaxy outshines the unresolved core. The SEDs
are well-characterized with AGN components, but the galaxies themselves appear
massive and star-forming. Photometry at additional wavelengths and
spectroscopy would aid in classifying these objects, confirming AGN presence,
constraining host-galaxy parameters, and characterizing the mechanisms driving
the semistellar galaxy cores. Additionally, cross correlation of our CPG with
X-ray detections will confirm their AGN nature and measure the nuclear
luminosity and absorption.

The initial visual sample selection revives the classical approach to AGN
identification via a bright, star-like nucleus. This simple selection method
is possible because of _JWST_ ’s superb angular resolution at long
wavelengths, where extinction is much lower than in visible light. Taking
advantage of the near-infrared surface brightness and morphology of our CPG
sample made it possible to quantify and automate the morphological approach.
This automated sample selection of brighter galaxies with point-source
features streamlines the search and analysis of CPG-like galaxies in current
and future _JWST_ /NIRCam imaging.

ROIII dedicates this work to the glory of God who makes all things possible.
ROIII acknowledges support from an undergraduate Arizona NASA Space Grant,
Cooperative Agreement 80NSSC20M0041. RAW, SHC, and RAJ acknowledge support
from NASA JWST Interdisciplinary Scientist grants NAG5-12460, NNX14AN10G, and
80NSSC18K0200 from GSFC. This work is based on observations made with the
NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the
Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These
observations are associated with JWST programs 1176, 2736, and 2738. AZ
acknowledges support by Grant No. 2020750 from the United States–Israel
Binational Science Foundation (BSF) and Grant No. 2109066 from the United
States National Science Foundation (NSF); by the Ministry of Science &
Technology, Israel; and by the Israel Science Foundation Grant No. 864/23. All
the _JWST_ data used in this paper can be found in MAST:
http://dx.doi.org/10.17909/jtd6-af15 (catalog 10.17909/jtd6-af15)

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Table 1 is the catalog of our morphologically identified CPG in the _JWST_ NEP
TDF.

Table 1: Catalog of CPG

ID | R.A. | Decl. | F090W | F115W | F150W | F200W | F277W | F356W | F410M | F444W | $z$ | $f_{\rm AGN}$ | (356–444) | H23 ID
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (∘) | (∘) | ——————————————AB mag—————————————– |  |  | AB mag |
1 | 260.671752 | 65.711688 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 16.69 | 17.07 | 17.05 | 17.32 | 0.48 | 0.08 | 0.39 | 194
2 | 260.756207 | 65.713177 | 23.11 | 22.16 | 21.61 | 21.44 | 20.92 | 20.72 | 20.46 | 20.37 | 1.63 | 0.44 | 0.99 | 314
3 | 260.694024 | 65.716929 | 20.74 | 20.14 | 19.63 | 19.27 | 19.15 | 19.66 | 19.78 | 19.78 | 0.38 | 0.09 | 0.52 | $\cdots$
4 | 260.751425 | 65.735378 | 19.21 | 18.90 | 18.71 | 18.61 | 19.13 | 19.50 | 19.63 | 19.74 | 0.13 | 0.02 | 0.40 | 308
5 | 260.690857 | 65.738085 | 22.90 | 21.76 | 21.22 | 20.80 | 20.29 | 20.15 | 20.06 | 20.08 | 1.51 | 0.33 | 0.71 | 218
6 | 260.701250 | 65.776180 | 22.79 | 22.02 | 21.52 | 21.14 | 20.59 | 20.26 | 19.99 | 19.91 | 1.84 | 0.50 | 0.99 | 232
7 | 260.697887 | 65.777933 | 24.22 | 22.84 | 21.98 | 21.31 | 20.89 | 20.57 | 20.34 | 20.20 | 1.66 | 0.46 | 1.01 | $\cdots$
8 | 260.659521 | 65.784555 | 20.74 | 20.18 | 19.78 | 19.41 | 19.18 | 19.19 | 19.32 | 19.55 | 0.74 | 0.18 | 0.28 | $\cdots$
9 | 260.695583 | 65.784352 | 23.31 | 22.80 | 22.43 | 21.92 | 21.55 | 21.22 | 21.04 | 20.88 | 2.12 | 0.46 | 0.98 | 223
10 | 260.746297 | 65.784221 | 25.07 | 23.94 | 22.74 | 22.13 | 21.58 | 21.11 | 20.94 | 20.82 | 2.01 | 0.49 | 0.93 | 300
11 | 260.719022 | 65.786260 | 22.53 | 21.59 | 21.15 | 20.81 | 20.48 | 20.34 | 20.28 | 20.36 | 1.44 | 0.32 | 0.62 | $\cdots$
12 | 260.773037 | 65.785647 | 21.27 | 20.79 | 20.45 | 20.14 | 19.98 | 20.16 | 20.52 | 20.60 | 0.44 | 0.10 | 0.20 | $\cdots$
13 | 260.641043 | 65.787557 | 23.04 | 22.02 | 21.45 | 21.02 | 20.65 | 20.45 | 20.46 | 20.52 | 1.36 | 0.31 | 0.57 | $\cdots$
14 | 260.536970 | 65.795297 | 20.97 | 20.80 | 20.73 | 20.53 | 20.58 | 20.27 | 19.95 | 19.78 | 1.22 | 0.69 | 1.13 | $\cdots$
15 | 260.733993 | 65.798508 | 19.04 | 18.64 | 18.29 | 18.06 | 18.17 | 18.59 | 18.66 | 18.56 | 0.31 | 0.11 | 0.67 | 283
16 | 260.758634 | 65.800809 | 18.11 | 17.84 | 17.67 | 17.52 | 17.94 | 18.06 | 17.95 | 18.11 | 0.22 | 0.10 | 0.59 | 319
17 | 260.639149 | 65.799387 | 20.00 | 19.53 | 19.21 | 18.87 | 18.67 | 18.55 | 18.66 | 18.79 | 1.02 | 0.25 | 0.40 | 141
18 | 260.507214 | 65.799489 | 22.30 | 21.64 | 21.13 | 20.64 | 20.31 | 20.43 | 20.58 | 20.73 | 0.72 | 0.18 | 0.34 | $\cdots$
19 | 260.684968 | 65.799834 | 22.16 | 21.56 | 21.09 | 20.69 | 20.42 | 20.52 | 20.74 | 20.92 | 0.67 | 0.15 | 0.24 | $\cdots$
20 | 260.722957 | 65.804355 | 19.41 | 18.95 | 18.56 | 18.30 | 18.28 | 18.71 | 18.93 | 18.99 | 0.36 | 0.06 | 0.36 | $\cdots$
21 | 260.473516 | 65.803032 | 21.35 | 20.85 | 20.50 | 20.19 | 19.98 | 20.22 | 20.46 | 20.60 | 0.47 | 0.11 | 0.26 | $\cdots$
22 | 260.536763 | 65.805280 | 22.70 | 21.89 | 21.33 | 20.90 | 20.59 | 20.46 | 20.56 | 20.60 | 1.14 | 0.28 | 0.50 | 64
23 | 260.456228 | 65.807676 | 22.62 | 21.55 | 21.08 | 20.70 | 20.35 | 20.26 | 20.24 | 20.29 | 1.40 | 0.30 | 0.61 | $\cdots$
24 | 260.524706 | 65.809982 | 22.34 | 21.23 | 20.74 | 20.36 | 20.00 | 19.89 | 19.82 | 19.89 | 1.45 | 0.31 | 0.64 | $\cdots$
25 | 260.483404 | 65.811818 | 23.52 | 22.87 | 22.22 | 21.37 | 20.82 | 21.15 | 21.03 | 20.88 | 1.59 | 0.37 | 0.91 | $\cdots$
26 | 260.486571 | 65.816233 | 20.15 | 19.64 | 19.24 | 18.91 | 18.71 | 18.99 | 19.34 | 19.39 | 0.44 | 0.09 | 0.24 | $\cdots$
27 | 260.531751 | 65.815627 | 22.60 | 21.85 | 21.12 | 20.57 | 20.01 | 19.76 | 19.72 | 19.79 | 1.64 | 0.33 | 0.61 | 63
28 | 260.896667 | 65.817463 | 20.54 | 19.84 | 19.54 | 19.11 | 18.67 | 18.49 | 18.33 | 18.22 | 1.67 | 0.39 | 0.91 | 497
29 | 260.905043 | 65.817563 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 18.72 | 19.31 | 19.45 | 19.50 | 0.39 | 0.05 | 0.45 | $\cdots$
30 | 260.814880 | 65.821168 | 24.78 | 23.62 | 22.99 | 22.60 | 22.18 | 22.04 | 21.96 | 21.87 | 1.60 | 0.36 | 0.81 | $\cdots$
31 | 260.851755 | 65.824977 | 20.05 | 19.60 | 19.27 | 18.96 | 18.74 | 18.90 | 19.16 | 19.31 | 0.54 | 0.12 | 0.23 | $\cdots$
32 | 260.898138 | 65.821819 | 23.92 | 22.53 | 21.99 | 21.69 | 21.33 | 21.25 | 21.14 | 21.10 | 1.64 | 0.35 | 0.79 | $\cdots$
33 | 260.423208 | 65.823911 | 22.44 | 21.63 | 21.18 | 20.82 | 20.44 | 20.33 | 20.25 | 20.32 | 1.47 | 0.33 | 0.65 | $\cdots$
34 | 260.768572 | 65.826200 | 23.12 | 21.65 | 21.05 | 20.73 | 20.37 | 20.18 | 20.08 | 20.06 | 1.62 | 0.36 | 0.76 | $\cdots$
35 | 260.538451 | 65.827557 | 22.05 | 21.51 | 21.19 | 20.85 | 20.53 | 20.42 | 20.44 | 20.49 | 1.31 | 0.32 | 0.57 | $\cdots$
36 | 260.942294 | 65.827685 | 21.87 | 21.19 | 20.73 | 20.34 | 20.03 | 20.09 | 20.21 | 20.39 | 0.75 | 0.20 | 0.34 | $\cdots$
37 | 260.924988 | 65.829837 | 19.69 | 19.22 | 18.86 | 18.62 | 18.74 | 19.31 | 19.45 | 19.49 | 0.29 | 0.04 | 0.46 | $\cdots$
38 | 260.919468 | 65.831341 | 20.38 | 20.03 | 19.72 | 19.52 | 19.56 | 19.92 | 19.88 | 19.75 | 0.37 | 0.17 | 0.81 | 528
39 | 260.965050 | 65.834642 | 20.87 | 20.34 | 20.03 | 19.68 | 19.46 | 19.60 | 19.72 | 19.74 | 0.61 | 0.22 | 0.50 | $\cdots$
40 | 260.661331 | 65.832686 | 23.97 | 22.52 | 21.86 | 21.42 | 21.01 | 20.81 | 20.67 | 20.68 | 1.60 | 0.36 | 0.77 | $\cdots$
41 | 260.886193 | 65.833875 | 22.27 | 21.59 | 21.08 | 20.64 | 20.28 | 20.32 | 20.40 | 20.55 | 0.85 | 0.23 | 0.41 | $\cdots$
42 | 260.498867 | 65.833758 | 22.56 | 22.07 | 21.71 | 21.42 | 21.13 | 21.00 | 20.86 | 20.71 | 1.60 | 0.44 | 0.93 | $\cdots$
43 | 260.661990 | 65.841400 | 21.45 | 20.29 | 19.84 | 19.51 | 19.14 | 18.98 | 18.86 | 18.95 | 1.51 | 0.33 | 0.67 | $\cdots$
44 | 260.673587 | 65.837855 | 22.42 | 21.72 | 21.20 | 20.80 | 20.50 | 20.36 | 20.49 | 20.58 | 1.02 | 0.25 | 0.42 | $\cdots$
45 | 260.894292 | 65.841649 | 18.77 | 18.35 | 18.06 | 17.87 | 18.37 | 18.64 | 18.73 | 18.85 | 0.15 | 0.05 | 0.43 | 492
46 | 260.679864 | 65.844673 | 21.20 | 20.56 | 20.11 | 19.69 | 19.36 | 19.25 | 19.34 | 19.46 | 1.01 | 0.25 | 0.43 | 205
47 | 260.745630 | 65.842305 | 21.31 | 20.67 | 20.19 | 19.69 | 19.31 | 19.20 | 19.26 | 19.44 | 0.99 | 0.24 | 0.40 | 299
48 | 260.639560 | 65.844960 | 20.17 | 19.76 | 19.42 | 19.25 | 18.90 | 18.51 | 18.25 | 18.15 | 1.46 | 0.58 | 1.00 | 142
49 | 260.626602 | 65.852172 | 21.51 | 20.75 | 20.23 | 19.82 | 19.52 | 19.39 | 19.52 | 19.61 | 1.02 | 0.25 | 0.42 | 124
50 | 260.756515 | 65.849021 | 21.63 | 21.00 | 20.64 | 20.34 | 20.10 | 19.98 | 20.08 | 20.16 | 1.12 | 0.27 | 0.46 | $\cdots$
51 | 260.692874 | 65.861906 | 18.89 | 18.41 | 17.98 | 17.64 | 17.74 | 18.15 | 18.20 | 18.24 | 0.32 | 0.10 | 0.55 | 222
52 | 260.624274 | 65.867878 | 20.75 | 20.16 | 19.66 | 19.15 | 18.79 | 18.56 | 18.59 | 18.69 | 1.31 | 0.30 | 0.51 | 121
53 | 260.681038 | 65.869282 | 22.22 | 21.58 | 21.01 | 20.43 | 19.94 | 19.50 | 19.19 | 18.97 | 2.56 | 0.67 | 1.17 | 207
54 | 260.701071 | 65.876123 | 21.86 | 21.33 | 20.93 | 20.62 | 20.39 | 20.61 | 20.94 | 21.05 | 0.47 | 0.10 | 0.20 | $\cdots$
55 | 260.738030 | 65.902876 | 24.04 | 22.76 | 22.16 | 21.71 | 21.23 | 20.97 | 20.73 | 20.51 | 1.62 | 0.49 | 1.10 | $\cdots$
56 | 260.708784 | 65.876954 | 24.01 | 22.44 | 21.85 | 21.55 | 21.26 | 21.15 | 21.10 | 21.02 | 1.72 | 0.35 | 0.77 | $\cdots$
57 | 260.651265 | 65.893590 | 23.50 | 22.60 | 22.07 | 21.68 | 21.37 | 21.24 | 21.27 | 21.33 | 1.27 | 0.30 | 0.55 | $\cdots$
58 | 260.668029 | 65.877818 | 23.65 | 22.46 | 21.76 | 21.16 | 20.62 | 20.29 | 20.15 | 20.03 | 1.66 | 0.41 | 0.90 | 187
59 | 260.665718 | 65.877257 | 24.78 | 23.24 | 22.31 | 21.92 | 21.59 | 21.42 | 21.32 | 21.25 | 1.80 | 0.38 | 0.81 | $\cdots$
60 | 260.690274 | 65.899640 | 22.37 | 21.40 | 20.99 | 20.67 | 20.29 | 20.24 | 20.23 | 20.28 | 1.37 | 0.30 | 0.60 | $\cdots$
61 | 260.668589 | 65.880723 | 21.78 | 21.16 | 20.74 | 20.43 | 20.04 | 19.88 | 19.83 | 19.87 | 1.54 | 0.34 | 0.65 | $\cdots$
62 | 260.709682 | 65.880570 | 24.22 | 23.03 | 22.44 | 21.95 | 21.43 | 21.23 | 21.05 | 21.04 | 1.58 | 0.37 | 0.83 | $\cdots$
63 | 260.629030 | 65.874101 | 24.68 | 23.15 | 22.42 | 21.91 | 21.40 | 21.17 | 21.00 | 21.03 | 1.60 | 0.38 | 0.78 | $\cdots$
64 | 260.649498 | 65.870951 | 22.85 | 21.98 | 21.72 | 21.58 | 21.39 | 21.21 | 21.02 | 20.95 | 1.55 | 0.42 | 0.90 | $\cdots$
65 | 260.739964 | 65.925101 | 21.89 | 21.15 | 20.62 | 20.04 | 19.59 | 19.68 | 19.93 | 19.99 | 0.81 | 0.19 | 0.33 | 292
66 | 260.672783 | 65.911116 | 24.73 | 23.24 | 22.45 | 21.93 | 21.51 | 21.38 | 21.29 | 21.20 | 1.70 | 0.37 | 0.82 | $\cdots$

Note. — Columns show ID number, J2000 positions, AB mag in eight _JWST_
/NIRCam filters, photometric redshift ($z$) as measured by CIGALE, $f_{\rm
AGN}$ from CIGALE, ($m_{\rm F356W}$–$m_{\rm F444W}$) color, and counterpart ID
in the Hyun et al. (2023) (H23) VLA 3 GHz source catalog.