# K-Band Imaging of the Nearby, Clumpy Turbulent Disk Galaxy DYNAMO G04-1

Heidi A. White Department of Astronomy and Astrophysics, University of
Toronto, 50 St. George St., Toronto, ON, M5S 3H8, Canada  Dunlap Institute for
Astronomy and Astrophysics, University of Toronto, 50 St. George St., Toronto,
ON, M5S 3H8, Canada  Deanne B. Fisher Centre for Astrophysics and
Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn,
VIC 3122, Australia  ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), Australia  Roberto G. Abraham  Department of Astronomy
and Astrophysics, University of Toronto, 50 St. George St., Toronto, ON, M5S
3H8, Canada  Dunlap Institute for Astronomy and Astrophysics, University of
Toronto, 50 St. George St., Toronto, ON, M5S 3H8, Canada  Karl Glazebrook
Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
Danail Obreschkow  International Centre for Radio Astronomy Research (ICRAR),
University of Western Australia, M468, Crawley, WA 6009, Australia

###### Abstract

We present a case study of stellar clumps in G04-1, a clumpy, turbulent disk
galaxy located at $z$ = 0.13 from the DYNAMO sample, using adaptive optics
enabled K-band imaging ($\sim 2.25$ kpc/arcsec) with Keck/NIRC2. We identify
15 stellar clumps in G04-1 with a range of masses from $3.6\times 10^{6}$ to
$2.7\times 10^{8}\ {\rm M}_{\odot}$, and with a median mass of $\sim 2.9\times
10^{7}\ {\rm M}_{\odot}$. Note that these masses decrease by about one-half
when we apply a light correction for the underlying stellar disk. A majority
(12 of 15) of clumps observed in the $K_{P}$-band imaging have associated
components in H$\alpha$ maps ($\sim 2.75$ kpc/arcsec; $<$R${}_{clump}>\
\sim$500 pc) and appear co-located ($\overline{\Delta x}\sim 0.1\arcsec$).
Using Hubble Space Telescope WFC/ACS observations with the F336W and F467M
filters, we also find evidence of radial trends in clump stellar properties:
clumps closer to the centre of G04-1 are more massive (consistent with
observations at high-$z$) and appear more red, suggesting they may be more
evolved. Using our high-resolution data, we construct a star forming main
sequence for G04-1 in terms of spatially-resolved quantities and find that all
regions (both clump and intra-clump) within the galaxy are experiencing an
enhanced mode of star formation routinely observed in galaxies at high-$z$. In
comparison to recent simulations, our observations of a number of clumps with
masses $10^{7}-10^{8}\ {\rm M}_{\odot}$ is not consistent with strong
radiative feedback in this galaxy.

##  1 Introduction

The morphology of star forming galaxies at $1\leq z\leq 3$ is often dominated
by giant ($\sim$1 kpc) and massive ($\gtrsim$10${}^{8-9}\ {\rm M}_{\odot}$)
clumps which contribute a significant fraction ($\sim$20-30%) of the total
system’s star formation. These clumpy structures are consistently observed via
tracers of young stars, e.g. in the rest-UV and -optical (Cowie et al. 1995;
Elmegreen et al. 2004; Elmegreen & Elmegreen 2005; Elmegreen et al. 2007; Guo
et al. 2012) and in ionized gas observations (Genzel et al., 2008). This
irregular morphology was initially attributed to galaxy merger activity and
some work examining $z>1$ samples has indicated gravitational interactions can
drive clumpiness in galaxies (e.g. Puech 2010; Calabrò et al. 2019). However,
resolved kinematic studies (e.g. Genzel et al. 2006; Förster Schreiber et al.
2006; Tacconi et al. 2008; Förster Schreiber et al. 2009; Shapiro et al. 2008;
Epinat et al. 2012) have shown that a large fraction of systems ($>60\%$) do
not appear to be mergers. Instead, such systems are often identified as
orderly rotators, with clumps thought to form in situ via Toomre instabilities
in a gas-rich ($f_{gas}\sim$50-60%) disk (Tacconi et al., 2020).

There is a long standing concept, motivated largely by simulations (Noguchi,
1999; Elmegreen et al., 2008; Immeli et al., 2004a, b; Dekel et al., 2009)
that these observed clumps could contribute significantly to the formation of
bulges in disk galaxies. The processes which allow for this migration (e.g.
decreasing angular momentum due to dynamical friction) require clump in-spiral
timescales of order a few 108 yr. However, the degree to which clumps can
contribute to bulge growth via this mechanism depends on their viability, e.g.
whether or not they are disrupted by their own stellar feedback within a few
orbital times. Observations of normal $1<z<3$ star forming galaxies observe a
range of lifetimes for clumps (100 - 650 Myr; Zanella et al. 2019; Förster
Schreiber & Wuyts 2020) suggest that some appear sufficiently long-lived to
migrate. This is typically the case for higher mass clumps with
$M_{\star}>10^{9}{\rm M}_{\odot}$. If clumps survive long enough to in-spiral,
one should expect a radial gradient within the galaxy, in particular with age.
Evidence for a radial gradient of clump properties is seen in observations
(such as in SINS and CANDELS galaxies; e.g. Förster Schreiber et al. 2011;
Förster Schreiber & Wuyts 2020; Guo et al. 2012; Ginzburg et al. 2021) and
these observations appear consistent with simulations (Bournaud et al., 2014;
Mandelker et al., 2017; Dekel et al., 2021) where clumps closer to the galaxy
nucleus appear redder, older, denser, and more massive. Other studies at
high-$z$ (e.g. Guo et al. 2018; Förster Schreiber et al. 2011; Zanella et al.
2019) report little or only slight evidence of a trend between age and
galactocentric radius, although small number statistics may influence some of
these findings. However, there may be some ambiguity in using radial trends as
evidence for long-lived clumps as radial trends are also predicted as a result
of inside-out disk formation (Murray et al., 2010; Genel et al., 2012). More
recent theoretical work suggests that though clumps may play a role in bulge
formation, significant contributions from large gaseous inflows within these
disks is likely very important for bulge formation as well (Dekel & Burkert,
2014; Zolotov et al., 2015). Moreover, galaxies at $z=1-3$ likely experience
multiple periods of instability, and one set of clumps need not explain the
full mass of bulges at $z=0$ (Tacchella et al., 2016).

As the star formation rate densities of massive clumps are observed to be very
high, stellar feedback effects are predicted to play a crucial role in
determining the fate of these clumps and how they contribute to their host
galaxy (i.e. in building bulges). Consequently, the stellar masses of clumps
are both a strong indicator of their viability and an important clue into the
dominant forms of feedback at play. Observations of clumps in $1<z<3$ galaxies
suggest they are characteristically massive, upwards of $10^{8-9}{\rm
M}_{\odot}$ (Elmegreen et al., 2007; Guo et al., 2012; Soto et al., 2017). The
true sizes and masses of these clumps remain uncertain, however due to the
inherent resolution limits imposed on observations at high-$z$. Work probing
different spatial scales (for example $\sim 1$ kpc as in Förster Schreiber et
al. 2011 to a few hundred pc Livermore et al. 2012, 2015) consistently find
derived clump properties are resolution-dependent and vary with spatial scale.
This is supported by investigations of the resolution dependence of clump mass
using cosmological simulations (e.g. Huertas-Company et al. 2020; Meng &
Gnedin 2020). Dessauges-Zavadsky et al. (2017) examined clumps in both lensed
and unlensed star-forming galaxies at $1.1<z<3.6$ and find masses ranging
$10^{7}-10^{9}{\rm M}_{\odot}$. They also show that the limited resolution
available in observations of non-lensed systems works along side clump
clustering and projection effects to artificially enhance derived mass
estimates. This is also supported by some studies at lower redshift: Larson et
al. (2020) study clumpy star formation in $z<0.1$ luminous infrared galaxies
(LIRGs) and find clumps are overall much less massive ($\sim 10^{5}{\rm
M}_{\odot}$).

Results from numerical work indicate that the details of feedback models have
a significant impact on the resulting stellar masses of clumps (Tamburello et
al., 2015; Mayer et al., 2016; Mandelker et al., 2017; Dekel et al., 2021).
Studies where feedback effects are primarily modeled via radiation pressure
and supernovae (e.g. Bournaud et al. 2007, 2014) routinely find long-lived
clumps which migrate inward and contribute to bulge growth. Mandelker et al.
(2017) find that including radiation pressure increases the surface density
and mass thresholds for clumps remaining undisrupted for a few free-fall
times. Alternatively, Hopkins et al. (2012) uses a feedback recipe that
includes radiation pressure and high photon trapping fractions. These combined
effects produce star forming clumps which are short-lived ($10-100$ Myr) and
rapidly disrupted, transforming $\sim$10% of their gas into stars (Hopkins et
al., 2012). Indeed, Hopkins et al. predict that the distribution of older
stellar populations within clumpy star forming galaxies should be smooth in
comparison to that of the gas and young stars. Using this feedback
prescription Oklopčić et al. (2017) perform a case study of giant clumps in a
massive, $z=2$ disk galaxy and, similarly, find no evidence in their
simulations for net inward migration of clumps and predict by $z=1$ a smooth,
stellar morphology. Using the NIHAO simulation, Buck et al. (2017) find a
similar lack of long-lived clumps and suggest that clumps in high-z galaxies
are merely the consequence of variable extinction. The similarity between
these simulations is that both incorporate early radiative feedback with high
photon trapping coefficients in the dust (Hopkins et al., 2012; Stinson et
al., 2013).

Because this gas-rich, turbulent mode of star formation occurs primarily in
distant galaxies the effects of redshift must be considered. Distance affects
observations in three ways: (1) generating native limits to resolution with
current instrumentation, (2) creating practical limits to sensitivity, and (3)
shifting spectral features to longer wavelengths, making them impractical to
observe with current and near-future instruments. The first two effects,
resolution and sensitivity, are assuaged by lensed galaxies (Jones et al.,
2010; Livermore et al., 2012, 2015; Cava et al., 2018; Dessauges-Zavadsky et
al., 2017). However, in the vast majority of lensed systems the magnification
occurs in only one direction, which complicates structural analysis.
Furthermore, observations of lensed galaxies can still be impacted by
redshift-related effects. For example, resolved measurements of galaxies at
$z>2$ cannot be undertaken at $\lambda>500$nm using current facilities, which
significantly challenges efforts to measure the stellar masses of clumps, even
in lensed systems.

The optimal wavelength for constraining the masses of clumps is the near
infrared (IR). Mass-to-light ratios estimated from near-IR observations are
less sensitive to degeneracies in extinction, age and metallicity than are
rest-frame visible wavelength observations (Bell & de Jong, 2001). High-
resolution imaging of very clumpy star-forming galaxies at low redshifts would
provide a robust (and highly complementary) viewpoint on the physics of the
high-redshift population. Green et al. (2014) presented the DYnamics of Newly-
Assembled Massive Objects (DYNAMO) Survey, which is comprised of 95 nearby
($z\sim 0.06-0.08$ & $0.12-0.16$) galaxies which closely resemble high-$z$
clumpy systems in terms of their kinematic and star formation properties. The
DYNAMO sample has been the subject of a number of follow-on investigations
(for example, Green et al. 2014; Bassett et al. 2014, 2017; Fisher et al.
2014, 2017b, 2017a; White et al. 2017; Oliva-Altamirano et al. 2018; Fisher et
al. 2019) which test the similarity of these local galaxies to their potential
high-redshift counterparts. The most notable exploration of this theme is
presented in Fisher et al. (2017b), who used high-resolution H$\alpha$ maps
(from Hubble Space Telescope; hereafter, HST) to confirm that DYNAMO galaxies
exhibit the same clumpy morphology observed at high-redshift. As is the case
with massive galaxies at high-redshift, a large fraction of DYNAMO systems
appear kinematically to be turbulent disks ($\sigma_{gas}\sim$20-100 km/s;
Green et al. 2014; Bassett et al. 2014; Bekiaris et al. 2016) with high
molecular gas fractions ($f_{gas}\sim$0.2 - 0.6; Fisher et al. 2014, 2019;
White et al. 2017).

In this paper, we build on the work of Fisher et al. (2017a) by investigating
the existence and properties of stellar clumps in G04-1, a galaxy from DYNAMO,
using adaptive optics (AO)-enabled NIRC2 $K_{P}$-band observations111In this
manuscript, the term “$K$-band” refers to observations taken with the NIRC2
$K_{P}$ filter ($\rm\Delta\lambda=1.948-2.299\mu m$). Due to its wealth of
previous observations and its clear classification as a highly star forming,
clumpy, turbulent, gas-rich disk, G04-1 makes an ideal candidate for probing
the nature of stellar clumps.

This paper is structured as follows: in §2, we provide an overview of these
targets and describe the new NIRC2 and HST observations. In §3, we describe
the methods we have used for identifying stellar clumps and calculating clump
properties (such as mass and color) in our imaging data. In §4, we present our
results and discuss them in context. §5 summarizes our findings.

Throughout this paper, we assume a cosmology where $H_{0}$ = 67 km s-1 Mpc-1,
$\Omega_{M}=0.31$, and $\Omega_{\Lambda}=0.69$.

##  2 Observations

###  2.1 Known properties of G04-1

Galaxy G04-1 is a member of the greater DYNAMO sample (originally presented in
Green et al., 2014, hereafter referred to as DYNAMO-I). DYNAMO is an H$\alpha$
IFU survey of local ($z\sim 0.07$ and $z\sim 0.12$) galaxies which have been
selected from the Sloan Digital Sky Survey (SDSS, York et al. 2000; Blanton et
al. 2017) to be H$\alpha$-luminous (in the top 1% of H$\alpha$ emitters in the
local universe, based on fiber luminosity; $\overline{SFR}\sim$ 11 ${\rm
M}_{\odot}$ yr-1). Located at $z\sim 0.1298$, G04-1 has an integrated stellar
mass of 6.47$\times 10^{10}$ ${\rm M}_{\odot}$ and H$\alpha$-derived SFR of
about 15 ${\rm M}_{\odot}$yr-1 (DYNAMO-I). As is the case for G04-1, a large
fraction ($\sim$84%) of DYNAMO galaxies appear disk-like and about half are
located on the Tully-Fisher relation (Green et al., 2014). Fisher et al.
(2017b) produce a surface brightness profile from a high-resolution HST
continuum map for G04-1 and find that the system is well-fit by an exponential
disk + bulge model. Based on the data presented in DYNAMO-I and on follow-up
kinematic fitting by Bekiaris et al. (2016), G04-1 is classified as a
turbulent rotating disk ($V_{\rm circ}=264\pm 6\,{\rm km\,s}^{-1}$ and
$\sigma_{gas}=34\,{\rm km\,s}^{-1}$). Recently, Oliva-Altamirano et al. (2018)
have published high-resolution (100 - 400 pc scale) AO-assisted kinematic maps
of DYNAMO galaxies imaged in P$\alpha$ with Keck-OSIRIS. For G04-1, these
authors find an integrated velocity dispersion of $\sigma\sim 51\,{\rm
km\,s}^{-1}$. In addition, these authors observe multiple high-dispersion
($\rm\sigma_{max}\sim 71\,{\rm km\,s}^{-1}$) peaks in the P$\alpha$ map. G04-1
is also observed to be gas-rich; CO line fluxes reported by Fisher et al.
(2014) (using the Plateau de Bure Interferometer observations of the CO[1-0]
transition) estimate a baryonic gas mass fraction of $\sim$31% and a depletion
time of about 1.9 Gyr (White et al., 2017). Like many of the systems commonly
observed at high-$z$, G04-1 is morphologically clumpy. Using 100pc resolution
HST $H\alpha$ maps, Fisher et al. (2017b) identify 13 massive star forming
clump regions within the galaxy.

###  2.2 NIRC2 K-band imaging

G04-1 was observed with the NIRC2 imaging camera on Keck II using widecam4
($\sim$0.04”/pix scale) with laser guide star adaptive optics correction and
with the $K_{P}$ filter ($\rm\lambda_{c}=2.124\ \mu m$). Observations took
place on 2016-21OCT as part of the 2016B observing cycle (program W140N2L) for
1.75 hours.

Observations were reduced using fairly standard methods. First, all raw frames
were corrected for known bad pixels using the Keck-NIRC2 bad pixel map. Dark
current was removed from science and flat frames by subtracting off a scaled
master dark frame. Both lamp-on and lamp-off flat frames (8 each) were
recorded on the night of observation, and these frames were median-combined
separately (with sigma-clipping) and then subtracted (on-off) to construct a
flat field frame. This was divided through all science frames to flat-correct
the data.

Keck/NIRC2 images show interference fringes, which are easily detected in
flat-corrected frames. We modeled this pattern by first selecting all co-
temporal science frames within which all sources were masked. In most cases
this corresponded with the three frames associated with a single dither
pattern. These masked frames were median-combined and scaled (to an
appropriate background level) to produce frames which were subtracted off the
individual images to perform removal of sky and fringes in a single step. The
reduced science frames were individually corrected for distortion effects
using IRAF’s drizzle task in combination with X & Y wide camera distortion
solutions provided by H.
Fu.222https://www2.keck.hawaii.edu/inst/nirc2/dewarp.html Image registration
and sub-pixel offsets between the dithered frames were calculated with IRAF’s
xregister task. Finally, these offset values were used with drizzle once again
to produce a final co-added image.

Our G04-1 frames contained a ghost image of the Keck primary mirror positioned
in the lower-right quadrant of the array. In some cases ($<30\%$ of frames)
this image (which appeared static over the course of the night’s observations)
overlapped partially with the dithered position of the galaxy. Where possible
(i.e. where the source is in a different quadrant) the region with this
feature was left unmasked so as to remove it during the sky subtraction
process described above.

Figure 1: Multi-band Imaging of Stellar Clumps in G04-1. In the center panel,
we show the reduced, co-added (n=21) image of G04-1 from Keck NIRC2
observations in KP-band. White boxes within the center panel denote individual
clump regions with labels corresponding to the Clump ID numbers provided in
Tables 1 & 2. Surrounding this center panel, we include enlarged maps of each
clump region in K-band (with the disk light removed) and in our HST $H\alpha$
(from Fisher et al. 2017b), F336W, and F467M data sets. Due to the complex
structure near the center of G04-1, clumps 13, 14, & 15 are shown in a single
region labeled the ”nuclear ring”. The on-sky region depicted by white boxes
in the center panel match that of each of the corresponding clump’s enlarged
panels. For reference: cutouts for clumps 1, 2, 3, 5, 6, 7, 8, 9, & 12 are
represent on-sky sizes of $\sim 1$ kpc across. For clump 4, this cutout
represents a size of $\sim 1.4$ kpc and for clumps 10 & 11, about $\sim 1.5$
kpc. Finally, the width of the white box enclosing the nuclear ring (R) region
is $3.7$ kpc in size.

###  2.3 HST F336W and F467M Observations

We obtained observations (Proposal ID #15069) of G04-1 using the Wide Field
Camera on the Advanced Camera for Surveys (WFC/ACS) on the Hubble Space
Telescope. Observations were performed using the F336W ($U$) wide and F467M
(Stromgen $b$) medium filters on 2018-02-26 for a total integration time of
0.5 and 0.2 hrs, respectively. For further description of the broad-band HST
images we refer the reader to Lenkić et al. (2021). Charge transfer effects in
WFC images were mitigated both by placing the target close to the readout edge
of the image, and also by using a post-flash to raise the image background to
12 e-/pix. All images were reduced using the standard HST pipeline and
combined using drizzle.

##  3 Properties of Stellar Clumps in G04-1

###  3.1 Identification of Stellar Clumps

Clumps were identified in our galaxy maps as follows. First, we constructed a
model of our AO point-spread function (PSF) by combining all imaging of all
point sources from a single observing night (described in more detail in
§3.3). We then convolved the co-added K-band image with a Gaussian kernel with
a width of 10x the full-width-at-half-maximum (FWHM) of the PSF (determined by
a double Moffat function fit; details on this derivation are provided in
§3.3). This corresponds to a kernel size of $\sim$1.2 arcseconds. This
convolved galaxy image was then divided through the un-convolved image to
produce a ratio map from which we identified stellar clumps.

Next, all ratio map pixels above a given threshold (defined as 4x the standard
deviation of the the intraclump regions) were identified as peak-value pixels.
We then imposed the constraint that all peak-value pixels represented local
peaks in the flux map. Here, we defined the local regions surrounding the peak
values as boxes 10$\times$10 pixels ($\sim$1 kpc $\times$ 1 kpc at $z\sim$0.1;
motivated by the typical clump sizes observed in G04-1 by Fisher et al. 2017a)
in size. If higher-value pixels were found within in this local region, the
location of the flux peak was shifted accordingly. It is emphasized that this
technique assumes a minimum separation between candidate clumps (the box
size). Once local peaks were identified, we determined the center of the clump
candidates by centroid fitting a 2D Gaussian + constant to a cutout region of
the map surrounding the local peak pixel. We then imposed a final constraint
that all clump candidates were least as large in size as the FWHM of our
combined AO PSF (about 3$\times$3 pixels in area). Within G04-1, this process
identified the 15 stellar clumps. These clumps are shown in the center panel
of Fig 1, where individual clump regions are indicated by white boxes. In this
figure, we also include maps of each of the identified clumps in the HST
H$\alpha$ (from Fisher et al. 2017b), F336W, and F467M data sets.

The number of detected clumps is inherently connected to the detection
threshold. Decreasing the detection threshold of clumps to 3-$\sigma$ would
increase the number of potential clumps in G04-1 to $\sim$30 from 15. If we
make a more strict definition of clumps using a threshold of 5-$\sigma$ this
decreases the number of clumps to $\sim$10\. However, we observe that our
algorithm fails to identify fainter and smaller clumps (such as ID=1 and 9)
which are otherwise easily identified by eye. Of course, we acknowledge that
this illustrates there exists a systematic uncertainty in this choice.

We recognize that the clumps we report here in G04-1 do not likely represent a
full statistical sample of all star clusters in the galaxy. G04-1 is a galaxy
with diverse forms of structure, including multiple clumps (as identified in
this paper), spiral arms, and a bright nuclear ring. Our aim in this paper is
simply to determine if a rotating disk galaxy with large, observed clumps of
star formation likewise has larger structures (i.e. “clumps”) in maps of
starlight, and (if so) where are these masses located and to report their
corresponding masses. We acknowledge that constructing a catalog of all
observable structures within the galaxy, spanning a wide range of spatial
scales, is beyond the scope of this work.

In summary, in the present paper we define stellar “clumps” to be regions
within the galaxy disk which (1) represent local flux peaks (2) are entirely
comprised of pixels above a given threshold level (4x the background of the
disk) and (3) are at least 3$\times$3 pixels in size (the FWHM of the AO PSF).
A list of the photometric properties of all regions meeting these criteria for
G04-1 is given in Table 1.

Figure 2: Exploring AO PSF effects on clump photometry. In panel 2a the disk-
subtracted 1D brightness profile of the combined AO point-spread function
(black diamonds; see §3.3) is shown in comparison with the brightness profile
for a typical clump (in green; for Clump ID = 2) and the double Moffat best-
fit to the data (in blue). Panels 2b & 2c illustrate the effects of convolving
the observed point-spread function with a simulated stellar clump. Dashed
white circles show the regions defining the photometric aperture and
background annulus. These regions have been used to determine the fraction of
clump light lost due to the broad wing component of the AO PSF when performing
photometry ($\sim$30%).

###  3.2 Determination of Clump Fluxes

We calculated the flux of clumps in two ways. First, we simply integrated the
flux of all pixels within a defined aperture centered on each clump (apertures
were placed at the locations determined in the previous section). In most
cases (12 of 15), the clumps identified in our K-band map could be directly
associated with clumps observed in H$\alpha$ by Fisher et al. (2017b). In
these cases, we utilized the apertures described in that work in our flux
calculations. In four cases (Clump IDs: 4, 7, 11, & 15) we identified NIR
clumps with no obvious H$\alpha$ counterpart. For these clumps, appropriate
apertures were estimated using the observed sizes in the ratio map.

We note that while Clump ID = 7 is well-detected in K-band imaging it is
unique in that it has no observable counterpart (i.e. a feature with similar
morphology and position) in any of the HST data sets presented in this paper.
Suspecting that this object is not actually a clump in G04-1 but the
serendipitous detection of a background infrared source, we have performed a
sky coordinate search using the online search tool Vizier (Ochsenbein et al.,
2000) but were unable to find a known object for which we could directly
associate this emission. Unable rule out that this feature is indeed a stellar
clump (without significant $\rm H\alpha$ emission) in G04-1, we include it in
the analysis and discussion sections which follow.

Next, a local disk background subtraction was performed to remove light
contributed from the diffuse disk component. The local disk background value
was determined from a region surrounding each clump (an annular aperture of
area equal to that of the clump aperture). Nearby clump pixels that fell
within this annular region were omitted from the background estimate. This
local background component (defined as the mean background value multiplied by
the area of the clump aperture) was then subtracted off the flux of the clump,
$F_{K_{P}}$, to obtain a disk-subtracted flux estimate ($F_{K_{P},diskcorr}$).
These values are listed in Table 1. While disk subtraction is typically
performed via bulge-disk decomposition methods, attempts (using both GalFit
and ProFit softwares; Peng et al. 2002; Robotham et al. 2017) to fit a bulge
and disk component to the K-band image of G04-1 left substantial structure
within the galaxy (i.e. the ring, spiral arms, and bright peaks in flux
associated with clumps), which were difficult to model with tolerable
residuals. Therefore, we chose to adopt a more clump-centric approach to the
removal of the background component.

Figure 3: An assessment of Keck NIRC2 $K_{P}$-band and HST F336W and F467M
filter AB magnitudes (with and without local disk subtraction) for clumps in
G04-1 (unity slope reference lines shown in red). The near 1-to-1 relationship
between disk corrected and non-disk corrected magnitudes indicates effects of
correction for disk light are independent of clump position in the galaxy.

G04-1’s guide star was used to derive a zero-point value for converting
counts/s to flux. All images of the guide star were reduced using the methods
described above, aligned by centroiding, and combined to produce a final
image. The star (2MASS J04122098-0555104) has an entry in the Two Micron All-
Sky Survey Point-source Catalog (hereafter 2MASS; Skrutskie et al. 2006). We
derived a $K_{P}$ magnitude for the guide star using its $K_{S}$ magnitude
(from 2MASS) in combination with the flux ratio of the bandwidths between the
$K_{P}$ and $K_{S}$ filters. This, in combination with our imaging of the
star, was used to produce a conversion value between counts/s and flux.

###  3.3 AO-PSF Effects on Photometry

As described in $\S$2.2, our observations of G04-1 incorporate laser guide
star AO correction. The shape of the AO PSF is known to vary in both time and
with observing conditions and is generally modeled as a near diffraction-
limited core with a broad, seeing-limited halo/wing component. Except in cases
with very high Strehl ratios, a significant fraction of the light is shifted
into the wings. The impact of the multi-component PSF of AO systems may
therefore act to systematically reduce the measured flux of clumps. Assuming
standard performance of the Keck AO system, we expect a Strehl ratio of 0.25
in the $K_{P}$ filter, based on our tip-tilt star magnitude (R$\sim$17 mag and
2MASS $K_{S}=15.7$ mag) and distance to our target ($r_{\rm offset}\sim
28.4\arcsec$). The Strehl ratio associated with this set of observations was
independently estimated by comparing imaging of point sources observed the
same night with a model of the diffraction-limited PSF. We find Strehl ratios
are very similar (0.26, on average) to that supplied by Keck and therefore a
value of 0.25 is used in all of our flux-magnitude calculations. Here, we
explore some of the recovery biases associated with performing photometry on
our AO-enabled $K_{P}$-band maps.

In order to increase the signal-to-noise of the faint component, we have
constructed a model of the AO PSF through a median combination of all of the
point sources observed (scaled by exposure time) on 2016-21OCT. These 21
frames correspond to a combined integration time of 1.4 min. In Fig. 2a, we
provide a plot of the azimuthally-averaged 1D surface brightness profile of
the combined source (shown as black diamonds). We find that this AO PSF model
from our observations is well fit by a double Moffat function with best-fit
parameters (amplitude, core width, power index) of (0.91, 0.06$\arcsec$, 1.56)
and (0.08, 0.13$\arcsec$, 1.21) for the core and halo components, respectively
(shown as a blue solid line). Note: the centering of our double Moffat profile
was fixed to the source origin. For comparison, we also include in Fig. 2a a
scaled 1D profile of a characteristic clump (ID: 2) in G04-1. The FWHM
corresponding to this double Moffat profile is $\sim 0.1\arcsec$, which is
consistent with that expected in K-band at this observing site and given the
Strehl ratio assessed above.

Due to image construction effects (i.e. the Drizzle algorithm), the empirical
PSF of the final, co-added Keck-NIRC2 image is likely slightly underestimated
by this point-source FWHM value. Although, we expect the difference between
these two resolution metrics to be small ($<10\%$). One method of inferring
the spatial resolution of this image would be to assess features observed
within the galaxy which appear smaller than clumps. The dominance of star
light in the disk, however, makes the search for small structures in the
galaxy prohibitive. Nevertheless, in the field of the final image of G04-1 we
do observe one small source for which we estimate a FWHM of $\sim 0.15$
arcsec. This provides additional confidence in the FWHM estimate we utilize
here to explore the effects on flux loss on our K-band clump photometry. We
note that our HST F336W ($U$) and F467M ($b$) data sets are also processed by
Drizzle and PSF modeling using TinyTim predicts FWHM values in this bands of
$\sim 0.1$ arcsec.333TinyTim is a PSF modeling software package developed by
J. Krist and R. Hook. Access to this software is available through the Space
telescope Science Institute (STSCI) HST instrumentation website. Within our
final F336W image, we observe a number of point sources in the field
surrounding the galaxy. From averaging the on-sky sizes of a few of these
sources, we estimate a spatial resolution for our HST data of $\sim 0.09$
arcsec, which is slightly better in comparison to our K-band maps.

We are interested primarily in estimating the fraction of the light
originating from stellar clumps that is shifted beyond our flux apertures
(i.e. the “light loss”) due to the broad wing component of the AO PSF. We
perform a simple simulation of the effects of the PSF on a stellar clump,
which we show in Fig. 2. Here, we model our clump with a 2D Gaussian function
where the FWHM is set by an average, circularized clump radius ($\sim
0.13\arcsec$ or $\sim$300 pc) from our sample in Table 1 (Fig. 2b). We note
that many of the clump sizes are consistent with sizes from HST H$\alpha$
imaging, and do not suffer from broad components of the PSF. We then convolved
this 2D clump with the previously described double Moffat profile to mimic the
smearing effect of our empirical PSF (see Fig. 2c). To assess the fraction of
light lost, we use a fixed aperture size of $r=3\sigma$ (where $\sigma$ is
defined by the double Moffat FWHM) and annulus radii of $r_{in}=4\sigma$ and
$r_{out}=8\sigma$ (see Fig. 2b & c) for performing flux and background
photometry.

After convolution with our AO PSF model, approximately 66% of the clump light
remains within the 3$\sigma$ flux aperture, corresponding to a flux/mass
correction factor of 1.33. However, in reality these clumps are embedded
within the galaxy disk and the broad PSF wings also feed stellar light from
the surrounding disk back into our clump apertures. This is likely to reduce
flux lost from clumps. Since we have not included an underlying disk component
in our simulation, this correction factor of 1.33 represents an upper limit
for the fraction of light lost due to PSF effects.

In our simulation, we find that the per-pixel flux contribution to the local
background estimate (determined within the aforementioned annulus) is of order
$\sim$1% of the amplitude (i.e. peak pixel value) of the clump. Again, we
present this as a rough estimate; clump clustering and bright structures in
G04-1 requires estimations of the local disk background to be determined from
a range of annuli radii. Moreover, the morphology of stellar clumps is
observed in our maps to deviate from simple Gaussians. Nevertheless, we note
that clump peak pixel values range between 2-5$\times$ higher than their
corresponding local disk values, suggesting that this light represents a minor
contribution to our background estimates.

The authors highlight that the above consideration of the impact of AO-
correction on photometry measurements of clumps within G04-1 is really only
possible due to the galaxy’s location at relatively low redshift. The scale
length of star forming clumps in G04-1 is small when compared with the scale
length of the disk. This allows us to more cleanly separate out the clumps
from the underlying disk of the galaxy. This underscores another unique
advantage of studying processes at high-$z$ via targets in the DYNAMO sample.

###  3.4 Clump Stellar Masses

It is commonly assumed that stellar mass density varies in lock-step with
near-infrared surface flux density, but we have used our in-hand visible-
wavelength HST photometry to try to refine our mass estimates using population
synthesis models. Integrated and clump-scale mass-to-light ratios for G04-1
were estimated using the stellar population synthesis code galaxev, which
comprises a library of evolutionary models computed using the isochrone
synthesis codes of Bruzual & Charlot (2003). We used spectral energy
distribution (SED) models from the Bruzual & Charlot (2003) code base
(incorporating their 2011 update), assuming a Chabrier initial mass function
(Chabrier, 2003). As our goal was to derive mass-to-light ratios for isolated
clump regions, we modeled the star formation history of clumps as a simple
stellar population (i.e. a delta-burst). Galaxies in DYNAMO (including G04-1)
are observed to have metallicities which are slightly sub-solar (determined
from the [NII]/$H\alpha$ ratio (Pettini & Pagel, 2004) from SDSS spectra) and
an BC2003 SED model consistent with this was chosen from the BaSeL 3.1
spectral library (Bruzual & Charlot, 2003).

Clump colors vary to a small degree across the galaxy disk, and we have used
the HST data described in §2.3 to construct ($U-b$) maps (using F336W and
F467M). Using the apertures defined in calculating $K_{P}$-band magnitudes on
these maps, we calculated a ($U-b$) color index (with and without disk-
subtracted magnitudes) for each of the clumps in G04-1. The standard deviation
of the clump colors was 0.36 (in AB mag units). Using the BC03 software, we
then modeled the evolution of the $K_{P}$ mass-to-light ratio as a function of
observed ($U-b$) color to derive clump-specific mass-to-light ratios. The
stellar mass of each clump is then defined as simply the product of the NIR
flux and the BC03-derived mass-to-light ratio of the clump. Derived ($U-b$)
clump colors, mass-to-light ratios, and masses are all listed in Tables 1 & 2.

The simple stellar population’s observed magnitudes in our selected filters
are evaluated at equally spaced time steps ($\Delta log(\rm Age)=$ 0.05 yr,
beginning at $10^{5}$ yr) and thus we are able to track the color evolution of
the burst with time. This provides us a reasonable metric for estimating the
ages of the clumps, using simply their individual $U-b$ colors, which we
include on the right-hand axis of Fig. 6 (top panel). We note that a
particular age of a clump should be interpreted carefully in terms of the
clump lifetime. Bournaud et al. (2014) outlines the difficulties associated
with accurately measuring the lifetime of a clump based solely on photometric
ages. Clumps can have complex star formation histories and their simulations
show that if clumps are long lived, they will continually rejuvenate (i.e.
experience subsequent bursts) and young stars dominate the age measurement.
However, Bassett et al. (2014) reports (based on absorption line analysis) an
age range of $60-500$ Myr for the entire galaxy of G04-1 which is consistent
with the clump ages we derive here using stellar population synthesis
modeling.

Figure 4: In this figure, the observed $(U-b;F336W-F467M)$ and $(b-K)$ colors
of clumps in G04-1 are compared to those of two example synthetic stellar
populations (generated using galaxev and stellar models from Bruzual & Charlot
2003). Here, the positions of stellar clumps are shown as black stars. The
evolutionary tracks of two star formation histories, a simple delta-burst
(SSP) and an exponentially-declining SFR (Exp; with an e-folding timescale of
$t=500Myr$) are provided for reference. SSP and Exp tracks in red and blue,
respectively, include colors with extinction applied, assuming a Calzetti et
al. (2000) extinction law. Their counterparts plotted as grey do not account
for effects from extinction.

As described above, we derive mass-to-light ratios for clumps via a method
which assumes that 1) the observed colors reflect that of a single burst of
star formation and 2) that the clumps extinction values are similar to that of
the disk (e.g. in using disk-subtracted values). Note: the assumption that
clump extinction is similar to the disk is supported by observations of the
$H\alpha$-to-$P\alpha$ flux ratio in G04-1, which is found to be roughly
constant (Bassett et al 2017). Given the observed stability of the K-band
mass-to-light ratio, the uncertainties associated with estimating stellar
masses via ($U-b$) color are not expected to be significant (e.g. a small
variation in clump color is observed across the galaxy). However, as magnitude
information is available for clumps in three bands ($U$, $b$, and $K_{P}$) we
can compare the observed ($U-b$) and ($b-K$) colors with those generated from
stellar population synthesis modeling. This comparison with two, distinct star
formation histories (a “delta-burst” SSP and an exponentially-declining SFR)
is shown in Fig 4. In this comparison, we utilize colors calculated from disk-
subtracted magnitudes to minimize K-band reddening from the underlying stellar
disk in which the clumps are embedded. We incorporate the effects of
extinction and reddening via the Calzetti et al. (2000) dust extinction law
assuming $A_{H\alpha}\sim 1-1.6$ (derived for G04-1 by Bassett et al. 2017)
and $A_{V}\sim 1$. Tracks which account for extinction are shown for the SSP
and Exponential star formation histories in red and blue, respectively. We
find that four clumps exhibit both ($U-b$) and ($b-K$) colors which map well
to those generated by BC03 SSP modeling. Five clumps are within a magnitude in
color from either the SSP or Exp BC03 tracks. Three clumps are vertically
offset by $>$1 mag from both tracks, appearing much more red in ($b-K$) color
than predicted by BC03.

These results are challenging to interpret as it remains unclear how well-
represented these clump populations are by the simple star formation histories
presented here. Indeed, the star formation histories of clumps in high-$z$
turbulent disk galaxies are very poorly constrained. Results from simulation
work (e.g. Bournaud et al. 2014) suggest that some clumps may undergo multiple
bursts of star formation over the course of their lifetime. While actively
star forming clumps are dominated by young stars, they may be holding onto a
redder, more evolved stellar population which might explain them appearing
significantly more red. We note, however, that attempts to fine-tune our
models for different star formation histories (a SSP and exponential SFR with
timescales of $100<\tau<500$ Myr) result in an overall range in the average
K-band mass-to-light ratio of 0.1 - 0.15. Further efforts to fine-tune are
likely beyond the scope of this paper. Nonetheless, this shows that our
uncertainty in model results in a small addition to the overall systematic
uncertainty associated with stellar mass. This underscores the clear advantage
of estimating clump stellar masses using K-band photometry.

##  4 Results & Discussion

Figure 5 shows a histogram of the full range of clump masses, both before and
after background flux subtraction is performed. On average, subtraction of the
local disk component reduces clump masses by around 50%. The average stellar
mass of the clumps before (after) background subtraction for the 15 identified
clumps in G04-1 is $5.69\pm 1.8\times 10^{7}{\rm M}_{\odot}$ ($2.06\pm
0.7\times 10^{7}{\rm M}_{\odot}$). The highest and lowest mass clumps (Clump
IDs 14 & 9) correspond to disk-subtracted masses of 27.0 and 0.36 $\times
10^{7}{\rm M}_{\odot}$, respectively. If we incorporate the correction for
light-loss due to wings of the AO PSF (see §3.3), the maximum mass for clumps
within G04-1 may be as high as 3.6 $\times 10^{8}{\rm M}_{\odot}$. We note
that the fractional drop in mass from the background subtraction is quite
consistent across clumps (i.e. uncorrelated with clump brightness or position
in the disk), as shown in Fig. 3 where we directly assess the effect of disk-
subtraction on calculated magnitudes for clumps in the $K_{P}$, F336W ($U$),
and F467M ($b$) datasets.

Table 1: G04-1 Clump Photometry

Clump ID | $K_{P}^{\dagger}$ | $K_{P,diskcorr}^{\dagger}$ | $F_{K_{P}}$ | $F_{K_{P,diskcorr}}$ | $M_{\star}$ | $M_{\star,diskcorr}$
---|---|---|---|---|---|---
| (AB mag) | (AB mag) | ($10^{-14}$ erg/s/cm2) | ($10^{-14}$ erg/s/cm2) | ($10^{7}$ ${\rm M}_{\odot}$) | ($10^{7}$ ${\rm M}_{\odot}$)
1 | 21.08 | 22.77 | 2.01 $\pm$ 0.41 | 0.43 $\pm$ 0.10 | 2.59 $\pm$ 0.79 | 0.55 $\pm$ 0.18
2 | 21.19 | 22.38 | 1.81 $\pm$ 0.37 | 0.61 $\pm$ 0.13 | 0.85 $\pm$ 0.50 | 0.28 $\pm$ 0.19
3 | 20.52 | 21.82 | 3.38 $\pm$ 0.68 | 1.02 $\pm$ 0.21 | 1.98 $\pm$ 1.07 | 0.60 $\pm$ 0.30
4 | 19.70 | 21.26 | 7.22 $\pm$ 1.45 | 1.88 $\pm$ 0.39 | 12.7 $\pm$ 3.31 | 3.31 $\pm$ 0.89
5 | 19.52 | 21.14 | 8.47 $\pm$ 1.70 | 1.91 $\pm$ 0.40 | 14.9 $\pm$ 3.88 | 3.37 $\pm$ 0.89
6 | 21.53 | 23.11 | 1.33 $\pm$ 0.27 | 0.31 $\pm$ 0.07 | 1.56 $\pm$ 0.50 | 0.37 $\pm$ 0.12
7 | 20.72 | 22.07 | 2.80 $\pm$ 0.57 | 0.81 $\pm$ 0.19 | 3.28 $\pm$ 1.06 | 0.95 $\pm$ 0.33
8 | 23.00 | 24.16 | 0.34 $\pm$ 0.07 | 0.12 $\pm$ 0.04 | 0.36 $\pm$ 0.13 | 0.13 $\pm$ 0.05
9 | 22.57 | 23.48 | 0.51 $\pm$ 0.11 | 0.22 $\pm$ 0.05 | 0.36 $\pm$ 0.17 | 0.16 $\pm$ 0.08
10 | 20.85 | 21.47 | 2.50 $\pm$ 0.51 | 1.41 $\pm$ 0.30 | 2.64 $\pm$ 0.91 | 1.49 $\pm$ 0.52
11 | 20.74 | 21.65 | 2.75 $\pm$ 0.55 | 1.19 $\pm$ 0.25 | 2.90 $\pm$ 1.00 | 1.26 $\pm$ 0.44
12 | 20.99 | 22.33 | 2.19 $\pm$ 0.44 | 0.64 $\pm$ 0.13 | 3.35 $\pm$ 0.93 | 0.97 $\pm$ 0.27
13 | 19.22 | 20.28 | 11.2 $\pm$ 2.24 | 4.19 $\pm$ 0.84 | 5.25 $\pm$ 3.45 | 1.97 $\pm$ 1.29
14 | 18.58 | 19.38 | 20.1 $\pm$ 4.02 | 9.69 $\pm$ 1.94 | 26.6 $\pm$ 7.95 | 12.9 $\pm$ 3.83
15 | 20.21 | 21.09 | 4.50 $\pm$ 0.90 | 2.00 $\pm$ 0.40 | 5.96 $\pm$ 1.78 | 2.65 $\pm$ 0.79

††footnotetext: Errors on clump AB magnitudes are approximately 0.24 mag.

Figure 5: The distribution of clump stellar masses in G04-1. The red and blue
histograms represent stellar masses determined for the clumps described in
Table 1 both with and without local disk background subtraction. Table 2:
Observed Properties of Stellar Clumps in G04-1

Clump ID | HST ID | SFR⋆ | $\sigma^{\star}$ | F336W - F467M† |  $K_{P}$ MLR | $R_{GC}$
---|---|---|---|---|---|---
|  | (${\rm M}_{\odot}$/yr) | $\,{\rm km\,s}^{-1}$ | (AB mag) |  | (kpc)
1 | 12 | 0.85$\pm$0.15 | 51 | 0.68 | 0.11 | 3.61
2 | 13 | 0.62$\pm$0.14 | 51 | 0.30 | 0.04 | 3.35
3 | 14 | 0.93$\pm$0.22 | 51 | 0.41 | 0.05 | 2.81
4 | - | - | 51 | 1.15 | 0.15 | 2.47
5 | 6 | 1.36$\pm$0.22 | 48.24$\pm$19.8 | 1.15 | 0.15 | 1.90
6 | 4 | 0.29$\pm$0.07 | 51 | 0.65 | 0.10 | 3.18
7 | - | - | 51 | 0.65 | 0.10 | 4.60
8 | 1 | 0.19$\pm$0.04 | 51 | 0.58 | 0.09 | 5.46
9 | 2 | 0.28$\pm$0.05 | 51 | 0.47 | 0.06 | 4.90
10 | 3 | 0.43$\pm$0.12 | 51 | 0.55 | 0.09 | 4.06
11 | - | - | 51 | 0.58 | 0.09 | 2.93
12 | 10 | 0.39$\pm$0.10 | 51 | 0.74 | 0.13 | 2.36
13 | 5 | 1.36$\pm$0.31 | 55.7$\pm$27.62 | 0.30 | 0.04 | 1.05
14 | 9 | 2.1$\pm$0.39 | 41$\pm$14 | 0.88 | 0.11 | 0.79
15 | - | - | 51 | 0.87 | 0.11 | 1.16

††footnotetext: HST F336W-F467M AB color values represent non-disk subtracted
colors and have associated errors of on average 0.6 mag.

⋆⋆footnotetext: Values for clump star formation rates and velocity dispersions
have been taken from Fisher et al. (2017b) and Oliva-Altamirano et al. (2018),
respectively.

As described in §1, predictions from simulations for stellar clump masses in
turbulent, clumpy disk galaxies depend quite strongly on the detailed feedback
prescription assumed by the model. Observations of galaxy clumps (such as
those presented here) are therefore useful for testing these models and for
providing insight into the dominant forms of feedback. Strong radiative
feedback models predict that clumps of gas are disrupted so quickly that the
stellar morphology in these galaxies should be relatively smooth (Hopkins et
al., 2012; Oklopčić et al., 2017). Indeed, simulation work by Buck et al.
(2017) incorporating more moderate feedback models find little evidence for
clumps of stars after 200 Myr. Studies where feedback effects are modeled as
radiation pressure and supernovae, however, predict massive clumps
($>10^{8}{\rm M}_{\odot}$). We find that only a small fraction of the clump
masses (3 of 15; before disk-subtraction) observed in G04-1 are consistent
with this mass regime. While the present paper provides data for only a single
galaxy, at least in this case the majority of clumps (both before and after
disk-subtraction) observed in G04-1 appear to fall in the range $10^{6-8}{\rm
M}_{\odot}$, which is fairly near the middle of the mass spectrum observed in
high-redshift observations of lensed galaxies and in simulations.

Lenkić et al. (2021) recently studied the internal color gradients of clumps
in DYNAMO galaxies. They find that color gradients of clumps are more commonly
consistent with changes in age, rather than extinction. This is different than
the explanation by Buck et al. (2017) that clumps in turbulent galaxies are
the result of regions of lower extinction. They also find that DYNAMO clump
age gradients are consistent with an old clump of stars, with a young center.
This is consistent with our results, in which old stellar clumps co-exist with
high SFR surface densities. Together, these results give two independent lines
of evidence of DYNAMO galaxies contain long-lived clumps of stars.

The total mass of the clumps (after local disk subtraction) is approximately
3.1$\times 10^{8}{\rm M}_{\odot}$. Using high resolution HST continuum data,
Fisher et al. 2017b fit a surface brightness profile for G04-1 and estimate a
bulge-to-total ratio of about 11%. Given a total stellar mass of 6.47$\times
10^{10}{\rm M}_{\odot}$, this corresponds to a current bulge mass of about
7.1$\times 10^{9}{\rm M}_{\odot}$. If we assume that all of the clumps
observed in G04-1 survive sufficiently long to migrate inward, then the total
contribution of these clumps to the mass of the bulge would be of about 5%.
Assuming there is no further mass growth of the galaxy, this potential
contribution increases to 8.54$\times 10^{8}{\rm M}_{\odot}$ or about 12% when
considering non-disk subtracted mass estimates. Whether or not the current
observations lend support to the notion of bulge building from clump infall
clearly depends on the duty cycle of the process, because a single episode of
bulge growth from this process would only add incrementally to the present
bulge.

###  4.1 Placing Clump Masses and Sizes in Context

A number of recent observational studies have shown that the star forming
clumps observed in $1<z<3$ galaxies may not be as massive or large as
initially predicted due to observational challenges inherent to mapping light
in galaxies at high redshift. For example, studies examining systems with
strong gravitational lensing have been able to explore clumps at spatial
resolutions below 100 pc (e.g. Livermore et al. 2012, 2015; Wuyts et al. 2014)
and consistently find smaller clump sizes ranging 50 pc - 1 kpc. To explore
the effect of resolution on derived clump properties, Cava et al. (2018)
evaluated multiple images of a single galaxy with different lensing
magnifications (consistent with effective resolutions ranging from 30 to 300
pc) and found that at coarse resolution clump sizes and masses were
systematically overestimated. Their target galaxy, the Cosmic Snake, has
similar total mass and SFR as ours in this work. They find that when observed
at the finest spatial resolution that clumps in the Cosmic Snake galaxy have
masses ranging $\sim 10^{7}-10^{8.5}$ M⊙, a range quite comparable to ours.
Using machine learning methods to identify clumps in VELA zoom-in simulations,
Huertas-Company et al. 2020 find observational effects significantly impact
clump properties, leading to a factor of 10 over-estimation in stellar mass.
While it is becoming increasingly clear that observational constraints and
resolution limits have led to significant ambiguity in the true masses and
sizes of clumps, it’s difficult to ascertain to what degree these biases have
impacted the values we report here for clumps in G04-1. In this section, we
aim to contextualize our work by comparing our findings with similar studies
spatially resolving star formation in galaxies.

Using a combination of HST broad and narrow band imaging, Bastian et al.
(2005) explore star cluster populations in M51. M51 can be taken as a typical
star-forming spiral disks, and is therefore useful for comparison to the
extreme star formation in G04-1. They measure masses in complexes of star
formation with sizes from $\sim 100$ pc to a few hundred parcecs, comparable
to the sizes in G04-1. The key difference is the stellar masses associated to
the star forming associations in M51 are $3-30\ \times\ 10^{4}\ {\rm
M}_{\odot}$, which is multiple orders of magnitude lower than what we observe
in G04-1.

Ultra luminous infrared galaxies (U/LIRGs) are a class of local ($z<0.1$)
dusty systems with high IR luminosities ($L_{[8-1000\mu m]}>10^{11}{\rm
L}_{\odot}$) and associated SFRs which are comparable to our target and to
galaxies at $z\sim 1-3$ (of order $\rm 10^{2-3}\ {\rm M}_{\odot}\ yr^{-1}$)
(Małek et al., 2017; Larson et al., 2020). Looking at resolved star formation
(via Pa $\alpha$ and Pa $\beta$ line emission) in 48 galaxies from the Great
Observatories All-Sky LIRG Survey (GOALS) with HST, Larson et al. (2020) find
that while the typical sizes of clumps in LIRGs are comparable to that
observed in DYNAMO ($\sim 100-900$ pc), they appear generally less massive
($M_{*,median}\sim 5\times 10^{5}\ {\rm M}_{\odot}$) and exhibit individual
SFRs which are roughly an order of magnitude lower ($\sim 0.03\ {\rm
M}_{\odot}\rm yr^{-1}$).

Messa et al. (2019) examined star forming clumps in 14 galaxies from the
Lyman-Alpha Reference Sample (LARS; $z=0.03-0.2$) via UV/optical data from
HST. They find that for LARS galaxies (which are selected to be similar to
high-$z$ galaxies based on their $\rm H\alpha$ and UV fluxes) clump sizes
range from $20-600$ pc with a median clump size of about $d\sim 60$ pc. While
these reported clump sizes are smaller than that seen in DYNAMO
($<$R${}_{clump}>\ \sim$500 pc; Fisher et al. 2017b) it remains unclear
whether this indicates a significant difference in clump sizes or if it is due
to the clustering and resolution effects discussed above. For example, the
smallest clump sizes reported by Messa et al. (2019) are observed in the
lowest redshift LARS galaxies where the best resolution of their data ($\sim
10$ pc) is roughly 10$\times$ better than in the HST imaging presented in §2.3
for G04-1.

Global system dynamics are closely linked with theoretical formation pathways
for star forming clumps in galaxies and thus also provide a critical point of
comparison (discussion in Fisher et al., 2017a). Like other DYNAMO galaxies,
G04-1 has been shown to have a well ordered rotation field measured both in
ionized gas at AO-enabled high spatial resolution (Oliva-Altamirano et al.,
2018) and in stellar kinematics (Bassett et al., 2014). Moreover, Fisher et
al. (2017b) shows that the star-light profile is consistent with an
exponential model. While some fraction of ULIRGs are likely spirals, the
primary dynamical driving mechanism of the bulk of U/LIRGs is widely
considered to be merging (e.g. Larson et al. 2016). This has been shown to be
the true case of LIRG galaxies in GOALS, where the sample is dominated by
interacting systems (Larson et al., 2020). We highlight this important
kinematic distinction as it presents an important caveat when comparing the
observed properties of clumps in DYNAMO with other local high SFR samples.

Figure 6: The relationship between clump HST F336W - F467M (un-disk corrected)
color (top panel, solid red circles), mass (middle panel; green circles),
disk-subtracted mass (bottom panel; blue circles) and galactocentric radius.
Here, green points represent mass values uncorrected for disk contribution and
dark blue points represent mass estimates for which we have subtracted off the
local disk background. Radial distance values (horizontal axis) are calculated
as the offset between the individual clump aperture centroid and the galaxy
center. The Pearson’s correlation coefficients we calculate for these three
quantities indicate strong negative correlation: we find $r$-values of -0.65,
-0.64, and -0.61 for the clump colors, uncorrected masses, and disk-corrected
masses, respectively. The vertical grey dashed line represents the outer edge
of the ring region in G04-1 at $R_{GC}\sim 2.2$ kpc.

###  4.2 Radial Gradients in Clump Properties

In Fig. 6 we show the radial gradients in both clump stellar masses and clump
colors. We find that clumps inside $R<2$ kpc have average disk-corrected
masses of $5.2\times 10^{7}{\rm M}_{\odot}$ and average non-disk corrected
F336W-F467M colors of $\sim$0.8. Where clumps outside of this radius appear
smaller and bluer with masses $9.1\times 10^{6}{\rm M}_{\odot}$ and
F336W-F467M values of about $\sim$0.6. The trend with mass is roughly
consistent with a log-linear decline in mass with radius. The observable
properties of clumps: e.g. the number, mass, star formation rate (SFR), and
age, are fundamental for testing feedback models. In the case of G04-1, there
is clear evidence for a clump mass gradient across the galaxy. We have
computed Pearson’s correlation coefficients for the three derived quantities
in Fig. 6 and find $r$-values of -0.65, -0.64, and -0.61 for the clump colors,
uncorrected masses, and disk-corrected masses, respectively. This indicates
that all three quantities exhibit strong negative gradients across the galaxy
disk. This is shown in Fig. 6 (bottom panel) which illustrates the radial
dependence of clump mass (both before and after disk-subtraction). Clumps
closer to the galaxy’s nucleus are observed to be significantly (more than a
factor of ten) more massive than those at the outskirts. We note that galaxy
G04-1 is host to various structural features, including multiple spiral arms
and a prominent nuclear ring, which are clearly observed in the top row and
central panels in Fig. 1. This ring structure appears somewhat asymmetric and
varies radially in width due to the existence of bright knots of ongoing star
formation and (in some part) the slight inclination of the galaxy. We have
estimated the radial outer edge of this nuclear ring region to be located at a
distance of roughly $R_{GC}\sim 2.2$ kpc (the average value of four
measurements made at cardinal points in the HST $\rm H\alpha$ ratio map image)
from the galaxy centre. For spatial reference, we include a vertical dashed
line denoting the outer edge of this ring region in the panels of Fig. 6.

This clump mass gradient in G04-1 could have multiple origins. In particular,
it could be due to (i) the inward migration of clumps while gradually forming
more stars, (ii) an inside-out growth of the galaxy disk, or (iii) the Jeans
mass being larger at smaller radii. From spatially-resolved kinematic maps
(using Keck-OSIRIS observations of the Pa-$\alpha$ line; see Oliva-Altamirano
et al. 2018) it is known that the gas velocity dispersion in G04-1 declines
slightly with radius. While this would argue for a higher Jeans mass near the
galaxy centre, the declining surface density and age gradient make this
scenario (iii) unlikely. From Fig. 6, it is observed that from $r=5$ kpc to
$r=1$ kpc in the disk, clump age increases by about 150 Myr while the overall
clump mass increases by about $\sim 10^{8}{\rm M}_{\odot}$. Lenkić et al.
(2021) performs multi-band stellar population modelling of the spectral energy
distributions of clumps in G04-1 and finds a similar range in clump ages
($80-300$ Myr). If this variation is entirely due to star formation (e.g.
scenario i), this would imply that the mean SFR of clumps during migration
should be $\sim 0.7{\rm M}_{\odot}yr^{-1}$. This value is surprisingly
consistent with the average clump SFR for this galaxy reported by Fisher et
al. (2017b) using H$\alpha$-based measurements ($<$SFR$\rm{}_{clump}>$ $\sim
0.83\ {\rm M}_{\odot}\ yr^{-1}$). This also suggests that an upper-limit to
possible mass contributed by clumps in G04-1 to the bulge (assuming all clumps
complete migration) is of order $10^{9}{\rm M}_{\odot}$ or addition of roughly
$\sim 14\%$ to the bulge mass. The SFR of clumps is likely a more reliable
proxy for mass growth than mass flow rate, as more mass is likely to be lost
via feedback than star formation. Notably, the 150 Myr age-span observed for
clumps in G04-1 is well-matched to the minimum age predicted for clumps which
are able to survive long enough to complete in-spiral to the galaxy center
(Guo et al., 2012, 2017; Förster Schreiber et al., 2011; Shibuya et al., 2016;
Soto et al., 2017). However, we qualify this simple model by noting that it
assumes that 1) clumps originate in the outskirts of the disk, 2) clumps are
isolated from other clumps (i.e. they don’t merge) and 3) all clumps within
the galaxy survive long enough to complete their migration inward. It remains
unclear to what degree these assumptions are reasonable.

We find no clear evidence of a radial dependence on the number density of
clumps; Fig. 1 illustrates that stellar clumps are indeed evenly distributed
across the disk. Additionally, Fig. 6 (top panel) shows that stellar clumps
near the nuclear ring appear (albeit to a small degree) consistently more red,
suggesting that these stellar populations may be slightly older and more
evolved. Fisher et al. (2017b) report star formation rates (SFR) for these
clumps (§2, and listed in Table 2) and find higher SFRs for clumps located
near the inner ring (on average 1.6 ${\rm M}_{\odot}$/yr) when compared to the
arm (0.5 ${\rm M}_{\odot}$/yr).

Our measurements appear to be consistent with observations of clump properties
in high-redshift galaxies, as well as with numerical investigations. In their
simulations, Mandelker et al. (2014, 2017) and Dekel et al. (2021) find
significant gradients in clump properties across the disk. More specifically,
clumps closer to the galaxy center tend to be both more massive and comprised
of older stellar populations (i.e. longer-lived). Fig. 6 is consistent with
the investigation clump properties at high-redshift by Guo et al. (2018), who
examined UV-bright clumps in CANDELS galaxies and found significant gradients
in both stellar mass (with inner clumps on average being more massive than
outer clumps by 1-2 orders of magnitude) and color. They also found that inner
clumps appear redder (in $U-V$) than those observed in the outskirts of the
disks. Förster Schreiber et al. (2011) performed deep HST (NIC2/F160W and
ACS/F814W) imaging of clumps in six $z\sim 2$ star forming galaxies and also
found central clumps to be more massive and older. Positive color and stellar
mass gradients were similarly observed by Cava et al. (2018) in imaging of
clumps within the ‘Cosmic Snake’, a lensed system. Similar mass-radius
relations also appear at low redshift: observations of star clusters in local
galaxies such as $z<0.1$ star forming spirals (Sun et al., 2016) and major
merger Arp 299 (Randriamanakoto et al., 2019) find cluster mass increases with
decreasing galactocentric radius. Radial trends are often inferred to be an
observational basis for clump migration. If the clumps in G04-1 are long-
lived, however, and have survived long enough for in-spiral to establish these
gradients, then the masses we observe strongly argue against very strong
feedback effects (see §1).

It is emphasized that the clump mass results shown in Fig. 6 are quite robust;
these radial trends are certainly not due to uncertainties in mass-to-light
calculations, since our observations use K-band imaging where M/L is very
stable. Moreover, the high spatial resolution in two dimensions allows for an
accurate disk subtraction and, therefore, radial trends cannot be due to
background subtraction effects.

Figure 7: The resolved star forming main-sequence for G04-1. Here we show the
relationship between star formation rate (taken from Fisher et al. 2017b) and
stellar mass (from this work) for $\sim$400pc sized regions in G04-1. Galaxy
regions which can be directly associated with clumps (identified in our NIRC2
K-band maps) are identified in this figure by being either red or blue,
depending on whether they are positioned in the nuclear ring or disk regions
of the galaxy. The power-law fit to the data presented in this paper
(described in §4.2) is shown as a dashed cyan line. For comparison, we include
similar relations derived from observations at high-z (Wuyts et al., 2013) and
low-z (Cano-Díaz et al., 2016).

###  4.3 Resolved $\Sigma_{SFR}$ versus $\Sigma_{star}$

Observations at both high and low redshift have found a tight ($\sim$0.3 dex)
and roughly linear relationship (the so-called “star forming main-sequence”)
between the star formation rate and stellar mass surface densities in actively
star forming galaxies (Daddi et al., 2007; Noeske et al., 2007; Elbaz et al.,
2011). In Fig. 7, we plot the star forming main-sequence in terms of
spatially-resolved quantities for G04-1. To estimate the SFR and stellar mass
surface densities ($\Sigma_{SFR}\ \&\ \Sigma_{M_{star}}$, respectively) both
the $K_{P}$-band (this work) and the H$\alpha$ maps (presented in Fisher et
al. (2017b)) were re-gridded to a common scale of $\sim$400 pc/pixel. New
fluxes were calculated for each pixel in each of the re-gridded maps and used
to estimate corresponding SFRs and stellar mass surface density values. A
galaxy-averaged K-band mass-to-light ratio of 0.1 (corresponding to the
integrated F336W - F467M color for the galaxy) was used to calculate stellar
masses. As a reference, all pixels associated with the stellar clump regions
are plotted as red or blue points (depending on whether they correspond to
ring or disk/arm clumps; see Fig. 7). All non-clump region pixels (defined as
where $<$30% of the contributing flux originates from clumps) are shown as
black circles. We note that the two non-clump data points in Fig. 7 with high
(ring-like) $\Sigma_{SFR}$ values correspond to regions near the centre of
G04-1.

After flagging the clump regions as red and blue in Fig. 7, we note the
following: (1) the clump regions within the galaxy define the upper end of SFR
surface density for this galaxy and (2) support for the radial trends in clump
properties described in §4.1 at larger spatial-scales. Large-sample resolved
studies of galaxies (see Wuyts et al. 2013; Hemmati et al. 2014; Cano-Díaz et
al. 2016; Magdis et al. 2016) find that this spatially-resolved relation is
observed across redshifts and wavelengths, but the derived slopes and zero-
points vary. A power-law fit to all of the data points in Fig. 7 results in a
slope that is remarkably near unity:

$\rm log(\Sigma_{SFR})=-8.58\pm 0.21\ +\ 1.041\pm
0.03\log(\Sigma_{M_{star}}).$ (1)

A separate fit of only the data points associated with clumps results in a
flatter relation:

$\rm log(\Sigma_{SFR})=-3.69\pm 3.81\ +\ 0.44\pm 0.49\
log(\Sigma_{M_{star}}).$ (2)

We note that when computing these relations, we omitted a number of very low
signal-to-noise data points at large radii in both the H$\alpha$ and $K_{P}$
maps, because they were sufficiently near the sky background their errors were
likely dominated by systematics from sky subtraction.

Cano-Díaz et al. (2016) use integral field spectroscopy (IFS) observations of
306 local galaxies from the CALIFA survey ($0.005<z<0.03$) to derive this
relation and find $\rm log(\Sigma_{SFR})=-7.95+0.72\ log(\Sigma_{M_{*}})$.
This is significantly less steep than that observed at high-$z$: Wuyts et al.
(2013) use kpc-scale multi-wavelength broad-band imaging (from CANDELS) and
H$\alpha$ surface brightness profiles (from 3D-HST) for 473 star forming
galaxies ($0.7<z<1.5$) and find $\rm log(\Sigma_{SFR})=-8.4+0.95\
log(\Sigma_{M_{*}})$. For reference, we plot both of these observed relations
in Fig. 7.

Nearly all regions within G04-1 directly overlap with the star forming main-
sequence relation derived from observations of high-$z$ galaxies. Indeed, the
slope and intercept values are remarkably similar. In terms of its integrated
properties, G04-1 lies offset from the star forming main-sequence. However,
its location at $z\sim 0.1298$ results in some ambiguity as to the reason for
this offset. For example, one wonders whether G04-1 is a normal, local star
forming galaxy which simply hosts high-SFR clumps (i.e. a scenario where the
clumps were completely externally formed and then accreted). From this figure
we infer that this is likely not to be the case. Instead, Fig. 7 suggests that
all regions (both the clump and intra-clump regions) within the galaxy are
experiencing an enhanced mode of star formation, more like what is routinely
observed in galaxies at high-$z$.

###  4.4 Stellar clumps are co-located with Ha

Where possible, we calculated the spatial offsets between the locations of the
NIR clumps discussed in the present paper and their counterparts in the Fisher
et al. (2017b) H$\alpha$ maps. On average, clumps in K-band have centers
(determined via centroiding; see §3) which are displaced from their
corresponding H$\alpha$ centers (from Fisher et al. 2017b) by about 2.6 pixels
($\sim$0.1$\arcsec$). This close alignment of clumps can be visualized in the
enlarged clump multi-band panels provided in Fig. 1. As this average offset
between clumps is very similar to the width of our night’s AO PSF ($\sim$3
pix), we cannot infer whether this offset is indeed real or a manifestation of
the PSF associated with our night of data. Clumps in the ring region of G04-1
appear more offset from their H$\alpha$ counterpart than those in the galaxy’s
arms. However, as stated in §3, a number of the apertures (12, 13, & 14) taken
from Fisher et al. (2017a) for clumps in the ring region of the galaxy
required transformation (rotation and aperture-size modification) in order to
adequately encompass the K-band clump flux. Indeed, we identify fewer clumps
in the ring of G04-1 than Fisher et al. (2017b). These differences are a
likely consequence of the significant amount of additional light contributed
from the central disk component in the K-band imaging. This light may be
washing out the concentrated light from individual clumps within the ring and
blending structure. These effects would present reasonable explanations for
ring clumps exhibiting greater offsets.

In general, the stellar clumps appear well-aligned with the active star
forming regions observed in the H$\alpha$ map, implying that these more
evolved stellar populations maintain a link with regions of recent star
formation. If stellar clumps are long-lived structures then this would suggest
they don’t undergo a single burst and then shut off, but that they continue to
experience star formation. However, we observe a number of clumps (IDs: 4, 7,
11, & 15) for which we do not observe an obvious H$\alpha$ component. This is
quite interesting because, as seen in Fig. 5, we observe that all of the
regions in G04-1 associated with clumps exhibit high observed star formation
rate surface densities. This would imply that all stellar clumps should be
H$\alpha$-bright. We have identified two possible scenarios which may explain
this: the light from these HII regions may be obscured by the existence of a
molecular cloud situated along our line-of-sight. While this would certainly
be a very specific situation, it is statistically possible as typical HII
regions are of order a few tens of parsecs and only a few would be required to
produce something of order the scale of a clump. An alternative scenario would
be that these clumps have indeed turned off in terms of their star formation
and are now simply wandering through the gas rich disk. This second scenario
is quite interesting as numerical simulations (e.g. Bournaud et al. 2014)
suggest that clumps massive enough to survive as long-lived should eventually
re-accrete gas from the disk and re-ignite in star formation. Certainly, more
work teasing out the details of these stellar populations is required to
determine which of these scenarios is more likely.

##  5 Summary

In this paper, we present a case-study of stellar clumps in a gas-rich, clumpy
turbulent disk galaxy from the DYNAMO sample.

  * •

We present new K-band imaging of G04-1 using Keck-NIRC2 and Hubble Space
Telescope WFC/ACS observations using the F336W ($U$) and F467M (Stromgen $b$)
filters.

  * •

We identify 15 clumps in K-band light of G04-1 that are evenly distributed in
mass, ranging from 0.36 to $27.0\times 10^{7}\ {\rm M}_{\odot}$. These values
correspond to Clump IDs 14 & 9, respectively. Subtraction of the local disk
component from clump light results in a drop in clump mass estimates of around
50%. This corresponds to a median disk-corrected clump mass of $\sim 1.5\times
10^{7}\ {\rm M}_{\odot}$.

  * •

We find evidence of radial trends in clump stellar properties. Clumps closer
to the galaxy nucleus are observed to be more massive and appear consistently
more red, suggesting that these stellar populations may be more evolved. We do
not find evidence of a radial dependence on the number density of clumps.

  * •

We investigate the relationship between the star formation rate and stellar
mass surface densities using high-resolution maps in $K_{P}$ (from in this
paper) and H$\alpha$ (from HST; presented in Fisher et al. 2017a). A power-law
fit to the data results in slope and intercept values (1.041 $\pm$ 0.03 &
-8.58 $\pm$ 0.21, respectively) similar to that derived from populations of
high-$z$ galaxies. Indeed, nearly all regions in G04-1 appear to be undergoing
an enhanced mode of star formation.

## Acknowledgements

Some of the data presented herein were obtained at the W. M. Keck Observatory,
which is operated as a scientific partnership among the California Institute
of Technology, the University of California and the National Aeronautics and
Space Administration. The Observatory was made possible by the generous
financial support of the W. M. Keck Foundation.

The authors wish to recognize and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has always had within the
indigenous Hawaiian community. We are most fortunate to have the opportunity
to conduct observations from this mountain.

The above work is also partly based on observations made with the NASA/ESA
Hubble Space Telescope, obtained from the Data Archive at the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS 5-26555.

This publication makes use of data products from the Two Micron All Sky Survey
(2MASS), which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation.

This research made use of Astropy, a community-developed core Python package
for Astronomy (Astropy Collaboration, 2013).

HAW and RGA thank NSERC and the Dunlap Institute for Astronomy and
Astrophysics for financial support. The Dunlap Institute is funded through an
endowment established by the David Dunlap family and the University of
Toronto.

DBF acknowledges support from Australian Research Council (ARC) Future
Fellowship FT170100376 and ARC Discovery Program grant DP160102235. ADB
acknowledges partial support from AST1412419.

KG acknowledges support from Australian Research Council (ARC) Discovery
Program (DP) grant DP130101460. Support for this project is provided in part
by the Victorian Department of State Development, Business and Innovation
through the Victorian International Research Scholarship (VIRS).

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