# Extreme Variation in Star Formation Efficiency Across a Compact,
Starbursting Disk Galaxy

Fisher, D.B.11affiliation: Centre for Astrophysics and Supercomputing,
Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122,
Australia 22affiliation: ARC Centre of Excellence for All Sky Astrophysics in
3 Dimensions (ASTRO 3D) , Bolatto, A.D.33affiliation: Laboratory of Millimeter
Astronomy, University of Maryland, College Park, MD 29742 , Glazebrook,
K11affiliation: Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia
22affiliation: ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D) , Obreschkow, D44affiliation: International Centre for
Radio Astronomy Research (ICRAR), M468, University of Western Australia, 35
Stirling Hwy, Crawley, WA 6009, Australia , Abraham, R.G.55affiliation:
Department of Astronomy & Astrophysics, University of Toronto, 50 St. George
St., Toronto, ON M5S 3H8, Canada , Kacprzak, G.G.11affiliation: Centre for
Astrophysics and Supercomputing, Swinburne University of Technology, P.O. Box
218, Hawthorn, VIC 3122, Australia 22affiliation: ARC Centre of Excellence for
All Sky Astrophysics in 3 Dimensions (ASTRO 3D) , & Nielsen,
N.M.11affiliation: Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia
22affiliation: ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D)

###### Abstract

We report on the internal distribution of star formation efficiency in IRAS
08339+6517 (hereafter IRAS08), using $\sim$200 pc resolution CO(2-1)
observations from NOEMA. The molecular gas depletion time changes by 2 orders-
of-magnitude from disk-like values in the outer parts to less than 108 yr
inside the half-light radius. This translates to a star formation efficiency
per free-fall time that also changes by 2 orders-of-magnitude, reaching
50-100%, different than local spiral galaxies and typical assumption of
constant, low star formation efficiencies. Our target is a compact, massive
disk galaxy that has SFR 10$\times$ above the $z=0$ main-sequence; Toomre
$Q\approx 0.5-0.7$ and high gas velocity dispersion ($\sigma_{mol}\approx 25$
km s-1). We find that IRAS08 is similar to other rotating, starburst galaxies
from the literature in the resolved $\Sigma_{SFR}\propto\Sigma_{mol}^{N}$
relation. By combining resolved literature studies we find that distance from
the main-sequence is a strong indicator of the Kennicutt-Schmidt powerlaw
slope, with slopes of $N\approx 1.6$ for starbursts from 100-104 M⊙ pc-2. Our
target is consistent with a scenario in which violent disk instabilities drive
rapid inflows of gas. It has low values of Toomre-$Q$, and also at all radii
the inflow timescale of the gas is less than the depletion time, which is
consistent with the flat metallicity gradients in IRAS08. We consider these
results in light of popular star formation theories, in general observations
of IRAS08 find the most tension with theories in which star formation
efficiency is a constant. Our results argue for the need of high spatial
resolution CO observations are a larger number of similar targets.

###### Subject headings:

galaxies: evolution — galaxies: star formation — galaxies: starburst
—galaxies: individual(IRAS08339+6517 (catalog ))

##  1\. Introduction

The connection between gas and star formation rate in galaxies, either
measured as the depletion time or the star formation efficiency, provides
direct test to star formation theories and is a direct input to models of
galaxy evolution (for review Kennicutt & Evans, 2012; Tacconi et al., 2020;
Hodge & da Cunha, 2020). The last decade has had a wealth of such studies in
large disk galaxies of the local Universe (e.g. Bigiel et al., 2008; Leroy et
al., 2008; Rahman et al., 2012; Leroy et al., 2013; Fisher et al., 2013; Utomo
et al., 2017; Leroy et al., 2017). Local Universe studies find that in the
main bodies of disks (R${}_{gal}>0.1R_{25}$) the ratio of molecular gas to
star formation rate (SFR) surface density, the so-called depletion time, is
consistently found to be $t_{dep}\sim$1-2 Gyr with statistically significant
scatter at the 0.3 dex level. This behavior extends into atomic gas dominated
regions of galaxies (Schruba et al., 2011). Utomo et al. (2017) reports a
trend toward lower $t_{dep}$ in the central 10% of the galaxy disk in 14 of 54
galaxies from the CARMA-EDGE survey, yet this variation is rarely larger than
a factor of $\sim 2-3\times$. In general the picture of star formation in the
disks of $z=0$ is for the most part a regular process, with variation in
molecular gas depletion time typically no greater than the 0.3 dex level.

We know much less about the resolved relationship between gas and SFR surface
density in starbursting systems, which are typically found in either advanced
stage mergers or turbulent disks of the $z>1$ Universe. Pioneering
observations have been made of gas mostly in the brightest star-bursting
systems at $z>1$ (e.g. Genzel et al., 2013; Hodge et al., 2015; Swinbank et
al., 2011; Chen et al., 2017; Tadaki et al., 2018; Sharon et al., 2019).
Unlike like with local spirals, the combined data set of these individual
target studies does not show a simple single power-law in the $\sim$1 kpc
resolved relationship between $\Sigma_{SFR}$ and $\Sigma_{mol}$, nor is
$t_{dep}$ always found to be constant inside $z>1$ disks (e.g. Hodge et al.,
2015; Tadaki et al., 2018). The few observations we have imply a far more
complex picture at the peak of cosmic star formation. Recently, kiloparsec-
scale resolved observations of advanced stage mergers have found a range
molecular gas depletion times that are typically shorter than in local spirals
(Saito et al., 2015, 2016; Bemis & Wilson, 2019; Wilson et al., 2019), and the
relationship between $\Sigma_{SFR}$ and $\Sigma_{mol}$ is steeper than unity.
However, as a class it is critical to consider the diversity of merger stages
when considering its gas and star-formation content (Sanders & Mirabel, 1996;
Combes et al., 1994; Larson et al., 2016). Espada et al. (2018) finds that for
wide separation merging systems this relationship can be shallower than in
local spirals, and the depletion time can be longer toward galaxy centers.

In the local Universe recent technical advances now make it possible to
measure the star formation efficiency per free-fall time,

$\epsilon_{ff}=\frac{\Sigma_{SFR}}{\Sigma_{gas}/t_{ff}},$ (1)

at spatial scales of $\sim$100 pc in nearby galaxies (Leroy et al., 2015;
Hirota et al., 2018; Utomo et al., 2018). When isolating the star forming
regions it is typically safe to assume that the gas mass surface density,
$\Sigma_{gas}$, can be approximated by the molecular gas mass surface density,
and therefore later in this work we will use $\Sigma_{mol}$ as an
approximation of the star forming gas. The star formation efficiency per free-
fall time takes the three-dimensional shape of the cloud through the
estimation of the free-fall time,

$t_{ff}\equiv\sqrt{\frac{3\pi}{32G\rho}}.$ (2)

Where $\rho$ is the volume density of the region being measured. Utomo et al.
(2018) measures $\epsilon_{ff}$ in local spirals at $\sim 120$ pc resolution
with a method that is similar to what we use. They find a typical
$\epsilon_{ff}\approx 0.5$%. Detailed studies of nearby spiral galaxies M 51
(Leroy et al., 2017) and M 83 (Hirota et al., 2018) find low values,
consistent with Utomo et al. (2018). Yet, those studies also show there may be
systematic variation in the values of $\epsilon_{ff}$ at the 0.3 dex level,
suggesting a completely universal value may not be a correct assumption.

The amount of variation of $\epsilon_{ff}$ both from galaxy-to-galaxy and
within galaxies is important to star formation models. A number of theories
make the explicit assumption that star formation proceeds at a constant, “low”
efficiency with $\epsilon_{ff}\approx 1$% (Krumholz et al., 2012; Salim et
al., 2015). Other theories that do not explicitly assume this find very little
variation in simulations (Shetty & Ostriker, 2012; Kim et al., 2013). If
$\epsilon_{ff}$ varies significantly in different types of galaxies, this
would limit the applicability to those theories. Some theory and simulation
predict that in very active regions, with very dense clouds, the efficiency
can reach 10-30% (Murray et al., 2010; Faucher-Giguère et al., 2013; Grudić et
al., 2019).

In this paper we present a map of CO(2-1) with $\sim$200 pc resolution in a
starbursting face-on galaxy, IRAS08339+6517. The galaxy exhibits many
properties in stellar populations, structure and kinematics that are similar
to compact, turbulent disks more commonly found at $z\approx 1-2$. We measure
the internal distribution of $t_{dep}$ and $\epsilon_{ff}$, as well as the
$\sim$1 kpc resolved star-formation law, and consider these results in light
of star formation models.

Figure 1.— The NOEMA CO(2-1) emission is shown in 5 velocity channels of width
21.6 km s-1. These channel widths are used for display purposes only and are
chosen to isolate the clumps of CO gas. We span the velocity range of the
galaxy. In the bottom left panel we plot the star light (HST F550M). The white
bar indicates 10 arcsec, which is roughly equivalenth to 4 kpc. In the bottom
row, right panel we also overplot the CO(2-1) contours from a moment zero map
onto the HST H$\alpha$ map convolved to matching spatial resolution as the CO
data.

##  2\. Methods

###  2.1. CO Observations and Molecular Gas Mass

We obtained CO(2-1) observations (Fig. 1) with the NOrthern Extended
Millimeter Array (NOEMA). All observations use the new PolyFiX correlator
tuned to sky frequency of 226.215 GHz in USB with a channel width of 2.7 km
s-1 utilizing all 9 antennas. IRAS08 was observed for 13 hours in A
configuration on 18-Feb-2018, and on 01-Apr-2018 for 5.5 hr in
C-configuration. By including the C-configuration data, and also considering
the relative compactness of our source, we are likely not missing a
significant amount of low-spatial frequency data, and are rather more strongly
affected by point source sensitivity. The maximum recoverable scale of the
C-configuration data is $\sim$6 arcseconds, which corresponds to $\sim$2.5
kpc. We can compare this to the half-light radius of the starlight, which is
$\sim 1$ kpc, or roughly 2.5 arcseconds. We should therefore recover twice the
half-light radius of the stars.

Observations were calibrated using GILDAS routines in CLIC, and then cleaned
with the MAPPING pipeline routine during an on-site visit to IRAM. We achieve
a point source sensitivity of 1.4 mJy beam-1 in 20 km s-1 of bandwidth, and
beam size of $0.52\times 0.47$ arcsec2 ($\sim 197\times 178$ pc2).

In this paper we consider two scenarios for CO-to-H2 conversion. First, we use
the standard Milky Way conversion of $\alpha_{CO}=4.36$ M⊙ (K km s-1 pc-2)-1
and a line ratio of $R_{12}$=CO(2-1)/CO(1-0) = 0.7
($\alpha_{CO}^{2-1}=\alpha_{CO}/R_{12}$). The metallicity (0.7 Z⊙, López-
Sánchez et al., 2006) and morphology (Fig. 1) both suggest a Milky Way like
conversion factor. Second, the large IR flux ratio, $f_{60}/f_{100}\approx
0.8$ (Wiklind, 1989) suggests a value of $\alpha_{CO}\approx 1.8-2.5$ M⊙ (K km
s-1 pc-2)-1 (Magnelli et al., 2012). We find a total molecular gas mass of
2.1$\times 10^{9}$ M⊙, using the Milky Way CO-H2 conversion factor. This is
similar to the total flux estimated from single dish observations by Wiklind
(1989), and we are thus not likely missing significant amounts of flux.

Using the kinematics from Cannon et al. (2004) observations of HI gas we can
estimate the total mass of the system. There is, however, an added source of
uncertainty in that the disk is relatively face-on, which makes estimating the
circular velocity uncertain by the inclination angle. Moreover, the large
radius HI gas is interacting with a companinion (described below) and is
likely not a good indicator of the total mass. Nonetheless, we can determine
if derived mass from CO strongly disagrees with this, as a sanity check on our
measurement. The velocity of the HI does cleanly assymptote to a flat curve,
but rather turns around at 15 kpc due to the interaction. It is not clear what
appropriate $v_{circ}$ to assume. We opt for a value closer to the galaxy of
$\sim 100$ kpc, though we note that total mass depends strongly on $v_{circ}$,
and even slightly larger values give significantly larger total masses. We
assume an inclination angle of 20o based on the average of the F550M
isophotes. Using the HI kinematics derived in López-Sánchez et al. (2006) and
a galaxy size of $2\times R_{1/2}\approx 2$ kpc, based on the star light. This
gives a total mass of $\sim 1.2\times 10^{10}$ M⊙. The total stellar mass is
$\sim 10^{10}$ M⊙ (described below). Cannon et al. (2004) finds that the HI
mass associated to the galaxy of IRAS08 is $\sim 0.11\times 10^{10}$ M⊙.
Therefore, our derived molecular gas mass of 2.1$\times 10^{9}$ M⊙ is roughly
consistent with kinematic observations.

We note that even the bimodal assumption of $\alpha_{CO}$ as either Milky Way
value or star burst may be an over-simplification for high $\Sigma_{mol}$
galaxies. These galaxies may possibly have an $\alpha_{CO}$ that varies with
local mass surface density (Narayanan et al., 2011; Bolatto et al., 2013a). In
the text, we will consider the impact of this on our results.

We measure the resolved properties of the CO(2-1) map using the moments of the
data cube. These are measured on the 2.7 km s-1 spectral resolution data cube,
and the spaxels are binned to 0.51 arcsec, matching the circularised FWHM. We
use an interpolation intended to conserve flux when regridding. We check this
by measuring the flux in an identical circular region 6 arcsec in radius. We
find the flux is the same to 99%. Using the CASA task immoments we determine
the integrated intensity, velocity and velocity dispersion of the CO(2-1) line
in each resolution element. To calculate the velocity moments we only include
data with $S/N>3$, and in a region of the spectrum that is restricted to
contain the emission line of the galaxy.

Figure 2.— We plot the velocity of CO(2-1), showing rotation (left) and
velocity dispersion (right) of IRAS08. The galaxy is rotating and as shown
later the velocity dispersion is relatively flat with respect to position int
he galaxy. We note that due to our sensitivity limits the observations are
biased toward the bright CO emission line sources. We cannot say if the
velocity dispersion is significantly different off of the arms.

###  2.2. Resolved Star Formation Rate

To measure the star formation (SFR) in IRAS08 we use H$\alpha$ image produced
from Hubble Space Telescope observations (Östlin et al., 2009), convolved to
the beam of our CO observations. Continuum subtraction was performed by
modelling the stellar continuum with multi-band photometry (Hayes et al.,
2009). The measurement uncertainty of H$\alpha$ flux for individual clumps is
less than 1% in all cases.

We determine the extinction by stellar population fits using the CYGALE
(Boquien et al., 2018) fitting code to HST/ACS image filters SBC F140LP , HRC
F220W, HRC F330W, WFC F435W, and WFC F550M. We measure, and correct for, the
extinction in individual regions that are set to match the resolution of the
CO(2-1) map. Averaged over the whole galaxy our fits recover
A${}_{H\alpha}\approx 0.2$ mag, which similar to previous results using line
ratios (Leitherer et al., 2002; López-Sánchez et al., 2006; Östlin et al.,
2009). To correct the H$\alpha$+[NII] narrow-band images to H$\alpha$, we use
the median [NII]/H$\alpha$ ratio from the longslit data in López-Sánchez et
al. (2006), which is [NII]/H$\alpha\approx 10$%. This is consistent with
expectations for a moderately low metallicity galaxy (Kewley et al., 2019).

To convert the ionized gas flux to SFR we use the calibration (Hao et al.,
2011) $SFR=5.53\times 10^{-42}L_{H\alpha}$, where $L_{H\alpha}$ is the
extinction corrected luminosity of H$\alpha$ gas in units of ergs s-1, which
assumes a Kroupa IMF.

A particular concern in deriving resolved star formation rates of both LIRG
and UV bright galaxies is the possible presence of AGNs in the central parts
of the galaxy. There have been a number of works that have analysed the
optical and UV spectra of IRAS08, which we can use to motivate our
interpretation of the H$\alpha$ flux as coming from star formation. Otí-
Floranes et al. (2014) carries out extensive modelling of the X-ray, UV and
optical data from the center of IRAS08, and finds it consistent with a super-
star cluster with age 4-5 Myr. Similar, López-Sánchez et al. (2006) does not
find elevated, nonthermal line ratios in the galaxy center with respect to the
rest of the galaxy. Similarly, in out KCWI data (described below) we do not
see a significant change in line ratios, for example [OIII]/H$\beta$, in the
galaxy center that would suggest the driving mechanism of the emission line is
changing. We find that [OIII]/H$\beta$ in the galaxy center is similar to that
of the outer disk, at the 0.1-0.2 dex level. Future observations that can
compare directly [OIII]/H$\beta$ to [NII]/H$\alpha$ would be definitive, see
Kewley et al. (2019) for recent review. Nonetheless, at present there is not
any evidence to suggest a prominent AGN in the center of IRAS08.

###  2.3. Metallicity Measurement

In this paper we will use the metallicity profile as a signature of possible
gas inflows (Kewley et al., 2010). To calculate the metallicity in IRAS08 we
use [OII], [OIII] and H$\beta$ observations take from the Keck Cosmic Web
Imager (Morrissey et al., 2018). The galaxy was observed for 20 minutes, using
the BM grating in Large Field mode with two central wavelength settings of 405
& 480 nm. Data was reduced with standard KCWI pipeline
methods111https://github.com/Keck-DataReductionPipelines/KCWI_DRP/ using in-
frame sky subtraction. Before the sky subtraction step, we masked out all
galaxy continuum and emission features for accurate sky estimates. Field-of-
view of the Large slicer is 33”$\times$20.4”. KCWI is seeing limited and
spaxels have a dimensions of 0.7$\times$1.35 arcsec2 (279$\times$600 pc2).

The metallicity was derived in each spaxel using the so-called R23 method, as
described in Kobulnicky & Kewley (2004). The metallicity of IRAS08 is near the
branching point of the R23-metallicity calibration. We therefore take an
iterative approach to solving for metallicity. We start by assuming that each
spaxel is on the “upper branch” ($12+log(O/H)>8.5$) and solve for the
metallicity. If the derived metallicity is less than 8.5, we then recalculate
that spaxel on the lower branch. This is carried on for a 3 iterations. We
then re-do the procedure starting on the lower branch. We find that the
absolute value of the metallicity changes by $\pm 0.4$ dex depending on the
branch choice, but the gradient of the metallicity across the disk is the same
whether we start on the upper or lower branch. We restrict our analysis to the
gradient of metallicity, and only make direct, quantitative comparison to
other measurements using the same emission lines, as different metallicity
indicators may yield different gradients.

##  3\. Properties of IRAS08339+6517

IRAS08339+6517 (hereafter IRAS08) is a face-on galaxy with redshift of
$z\approx 0.0191$, which translates to a luminosity distance of $\sim$83 Mpc.
The galaxy is known to be UV-bright, compact, and have young stellar
populations (Leitherer et al., 2002; López-Sánchez et al., 2006; Overzier et
al., 2008). The global mass-weighted age of IRAS08 is quite young compared to
local spirals with published age estimates varying between 10-50 Myr
(Leitherer et al., 2002; López-Sánchez et al., 2006). In this section we
discuss the resolved properties of the gas morphology and kinematic state of
IRAS08, with emphasis on how IRAS08 is an outlier for local galaxies, and
often is more similar to galaxies at $z\approx 1.5$. We also discuss the
interaction that IRAS08 is experiencing with a distant, smaller companion
galaxy.

The basic properties described in this section are summarized in Table 1.

###  3.1. Total Mass, Size and SFR

Using the optical colors from López-Sánchez et al. (2006), and assuming a
Kroupa IMF, we estimate a K-band mass-to-light ratio of
$log(M/L_{K})\approx$0.3-0.4, depending on the model assumptions (Bell, 2003;
Zibetti et al., 2009). Using the K-band magnitude of 11.88 mag and
log($M/L_{K}$)$\approx$0.35, the total stellar mass of IRAS08 to be
$M_{star}\approx$1.1$\pm 0.3\times 10^{10}$ Msun.

The size of the galaxy is determined by measuring the surface photometry of
the F550M ACS/WFC image, which is roughly V-band. We use the same software and
technique as developed in Fisher & Drory (2008). We find that the half-light
radius of IRAS08 is 2.54 arcseconds, which translates almost exactly to 1.0
kpc. This makes IRAS08 a $\sim$2-3$\sigma$ outlier toward smaller sizes (more
compact) than what is expected from the $r_{e}-M_{*}$ relationship measured on
$z\approx 0$ galaxies (Mosleh et al., 2013). We can also compare the size of
IRAS08 to local Universe galaxies of similar IR brightness. Arribas et al.
(2012) finds that LIRGS in general have a median H$\alpha$ half-light radius
of $\sim$2 kpc. They show that the largest LIRGs are pre-coalescence systems,
like IRAS08, the median H$\alpha$ half-light radius of pre-coalescence LIRGs
is closer to $\sim 3$ kpc. IRAS08 is thus more compact than the median LIRG,
especially those that are pre-coalescence.

Table 1Basic Properties of IRAS08339+6517

Total Stellar Mass | 1.1$\pm 0.3\times 10^{10}$ M⊙
---|---
Total SFR | 12.1$\pm 1$ M⊙ yr-1
Stellar $R_{1/2}$ | 1 kpc
Molecular Gas Massa | 2.1$\times 10^{9}$ M⊙
HI Gas Mass | 1.1$\times$109 M⊙
Molecular gas velocity dispersion | 25$\pm 6$ km s-1
Molecular gas depletion time | 0.12 Gyr
SFR/SFRMS | 12$\times$
Toomre $Q_{gas}$ | 0.5

aafootnotetext: $\alpha_{CO}=4.36$ M⊙ (K km s-1 pc-2)-1

We estimate the total SFR using the integrated H$\alpha$ luminosity of
1.8$\times 10^{42}$ erg s-1 and $A_{H\alpha}=0.19$ (Östlin et al., 2009).
Using the calibration from Hao et al. (2011), assuming a Kroupa IMF, we find
SFR=12.1 M⊙ yr-1. Sanders et al. (2003) finds a 25 $\mu$m flux of 1.13 Jy. We
can thus also estimate the total SFR from the combined H$\alpha$ and 25 $\mu$m
fluxes using the calibration from Kennicutt et al. (2009), which gives a very
similar value of 11.1 M⊙ yr-1. For consistency with resolved SFR measurements
we will use the H$\alpha$ only value for calculations. The SFR for IRAS08 is
12 times the value of the $z=0$ main-sequence for a similar mass galaxy
(Popesso et al., 2019).

The global, galaxy-averaged molecular gas depletion time of
$t_{dep}\equiv\Sigma_{gas}/\Sigma_{SFR}\approx 0.12$ Gyr. Tacconi et al.
(2018) find a relationship between offset from the main-sequence such that
$t_{dep}$ $t_{dep}(\delta MS)\approx(1+z)^{-0.6}\times\delta MS^{-0.44}$. For
$\delta MS\approx 12$ and $z=0$, this translates to a value of 0.33 Gyr.
Interestingly, in spite of its many idiosyncrasitic properties, IRAS08 is
behaving similar to other star-bursting galaxies (in terms of $t_{dep}$).

The molecular gas fraction for IRAS08 is $f_{gas}\equiv
M_{mol}/(M_{star}+M_{mol})\approx 0.17$. This gas fraction is in the top 95th
percentile of gas rich galaxies in the local Universe, using COLD GASS survey
as a $z\approx 0$ benchmark (Saintonge et al., 2011).

####  3.1.1 Large Gas Velocity Dispersion & Low Toomre Q

Here we discuss the internal kinematic state of IRAS08. In IRAS08 we find
through direct, resolved measurement that the disk is consistent with being
marginally stable to unstable ($Q\approx 0.5-1.0$), and has elevated molecular
gas velocity dispersion, compared to local spirals, across all radii.

Figure 3.—  The radial profile of Toomre Q for the molecular gas disk in
IRAS08 is shown. The solid line represents the profile for the Milky Way
$\alpha_{CO}$, and the dashed blue line for the star burst conversion factor.
The Q-profile suggests that IRAS08 is most likely consistent with an unstable
disk ($Q\approx 0.5-1.3$) for almost all radii across the molecular disk. Note
that the upper bound for stable versus marginally stable is arbitrarily
defined to guide the eye. We set this line at $Q\approx 1.3$ based on typical
systematic and measurement uncertainties in the value of Q (e.g. Genzel et
al., 2011).

Figure 4.— The velocity dispersion, $\sigma$, is plotted as a function of
galactocentric radius for IRAS08 for all lines of sight within the area of the
galaxy (squares), as well as the average (dark line) within 0.5 arcsec
($\sim$200 pc) bins. The shaded region represents the standard deviation about
the running average. The measured $\sigma$ in IRAS08 is significantly larger
than is typical for local spirals, which is indicated by the grey horizontal
bar (Ianjamasimanana et al., 2012) , and only mildly changes with radius.

The stability of a self-gravitating disk is characterised by Toomre’s $Q$
(Toomre, 1964; Binney & Tremaine, 1987), where

$Q_{gas}\equiv\frac{\kappa\sigma_{gas}}{\pi G\Sigma_{gas}}.$ (3)

The quantity $\kappa$ is the epicyclic frequency. We measure it directly as
$\kappa^{2}=4(v/R)^{2}+Rd(v/R)^{2}/dR$. We determine the velocity, $v$, by
fitting the flat disk model, $v(R)=v_{flat}[1-exp(-R/r_{flat})]$, to the
velocity map, shown in Fig. 2. We assume an inclination of 20o based on the
average ellipticity of the isophotes in F550M image. We note that for low
inclination galaxies the rotation field is particularly uncertain, and should
not be used on its own be a deciding factor in determining the physical state
of the galaxy. We take the $Q$ value only as one aspect of the IRAS08. The
velocity dispersion, $\sigma$, is measured from the CO moment map. An
infinitely thin disk is considered unstable if $Q<1$. Disks of non-zero
thickness, like those with high velocity dispersion, are unstable if
$Q\lesssim 0.7$ (Romeo et al., 2010).

In IRAS08 we find that the median $Q\approx 0.5$, assuming the Milky Way
$\alpha_{CO}$. In Fig. 4 we show that $Q(R)$ remains marginally unstable
across all radii except the very center of the galaxy, where $\kappa$ becomes
very large. Though $Q\approx 0.5$ may seem extreme by local Universe
standards, we reiterate that for galaxies with a thicker disk, as indicated by
high gas velocity dispersion, the critical value of stability using Equation 3
is 0.7. Moreover, this value of $Q$ is similar to the values of $Q$ in the
DYNAMO galaxies (Fisher et al., 2017a), which have similarly high SFR and gas
content. Moreover, it is essentially the same calculation using CO kinematics
and surface density as observations of a CO disk at both $z\approx 1.5$
(Genzel et al., 2013) and $z\approx 4$ (Tadaki et al., 2018), and find a very
similar value of $Q_{gas}\approx 0.5-1.0$. Conversely, Toomre-$Q$ measured on
local spirals produces $Q_{gas}\approx 2-10$ (Leroy et al., 2008) over a wide-
range in radius. For IRAS08, the assumption of lower $\alpha_{CO}$, motivated
by the high dust temperature, still keeps the galaxy in the “stable” regime.
It remains lower than $Q_{gas}$ values seen in THINGS survey spiral galaxies.

In Fig. 4 we show that the galaxy averaged velocity dispersion in IRAS08 is
$\sigma\approx 25$ km s-1 with a root-mean-squared deviation (RMS) of $\pm 6$
km s-1. The velocity dispersion is taken from the moment map, with the channel
width removed in quadrature. This however has a very small effect as the
channels are less than 5% of the typical FWHM of the line. Because the galaxy
is face-on, well resolved ($\sim$200 pc), and has a relatively low rotation
velocity the velocity gradient across individual spaxels due to rotation is
small. Using the velocity model fit to the moment 1 map, we find that in the
central resolution element the line dispersion introduced by velocity
gradients is $\sigma_{vel}\sim 6$ km s-1. This is calculated by taking the
model fit to the velocity field and resampling it to match our beam size. The
velocity field begins with an assumption of infinitely thin emission lines,
and when sampled at the beam resolution the width reflects the range of
velocities in the beam. Removing this in quadrature would alter the measured
$\sigma$ by less than 1 km s-1. We, therefore, do not make a correction for
beam smearing as it is a small effect, and likely introduces its own
systematic uncertainties.

Ianjamasimanana et al. (2012) find that the average CO velocity dispersion of
galaxies in the HERACLES sample is 6 km s-1 with a standard deviation of 1.5
km s-1. The velocity dispersion of IRAS08 is 4$\times$ what is measured in
local spirals, making it a $\sim$10$\sigma$ outlier. Work using stacking of CO
spectra uncovers a secondary broad component of dispersion with $12\pm 4$ km
s-1 (Caldu-Primo et al., 2013). The unstacked velocity dispersion of IRAS08
remains a 3$\sigma$ outlier from the broad component in local spirals.

It is difficult to compare the velocity dispersions to that of LIRGS, as there
are not many studies of the resolved gas velocity disperion, especially
targeting molecular gas in LIRGS. Also, LIRGs represent a very diverse set of
objects when considering morpho-kinematic properties (e.g. Larson et al.,
2016), and it is, thus, challenging to make a well-posed comparison. Espada et
al. (2018) makes similar resolution maps of two LIRGs with wide-seperation
interactions. They found that $\sigma_{mol}$ varies much more in their targets
than we find in IRAS08. In their targets the disk has a low dispersion, with
$\sigma_{mol}\sim 10-20$ km s-1 and the center is higher, $\sim$40 km s-1.
Zaragoza-Cardiel et al. (2015) studies resolved kinematics in samples of
interacting, though not advanced, merging galaxies. They find the intercting
systems have a median $\sigma\sim 10-15$ km s-1. There is, therefore, a range
of velocity dispersions in local Universe LIRGs galaxies and it is difficult
to make any conclusive statement about the comparison.

###  3.2. Distant Interaction

There is a plume of HI gas that extends from IRAS08 in the direction of a
nearby companion (Cannon et al., 2004). The stellar light of the companion
galaxy is quite low compared to IRAS08($\sim$1/10-1/20; López-Sánchez et al.,
2006) and the separation is $\sim$60 kpc. For this separation and mass ratio
the merger classifications developed on GOALS sample galaxies (Larson et al.,
2016) places IRAS08 in the minor-merger category. We do not observe signs that
the interaction in IRAS08 (Cannon et al., 2004; López-Sánchez et al., 2006) is
directly altering either the morphology or kinematics of IRAS08 inside the 90%
radius of the F550M image. (1) The morphology of starlight (Fig. 1) does not,
show signs of significant disturbances (such as in advanced mergers like
Antennae galaxies). There is an asymmetry to the spiral arms. We measure the
asymmetry value of 0.17-0.2 depending on whether we use the 50% or 90% radius,
respectively. Conselice (2014) reviews galaxy morphology and finds asymmetries
of 0.15$\pm$0.06 for typical late-type disks, and 0.32$\pm$0.19 for ULIRGs.
IRAS08 falls in between the two values. It is on the high side, but within the
distribution of late-type disks, and on the low-side of ULIRGS. It is below
the range of asymmetries that are quoted as “typical” for starbursts. (2) The
stellar light profile is well described as a smooth exponential decay (López-
Sánchez et al., 2006). (3) The kinematics inside the radius of the galaxy are
well-fit with a rotating disk model (Fig. 1). (4) There is not a significant
off-center rise in the velocity dispersion. These are similar criteria as used
in studies of galaxies at $z\approx 1-3$ to classify mergers and rotating
galaxies (e.g. Förster Schreiber et al., 2009; Genzel et al., 2011). Based on
these observations, it does not appear appropriate to categorize IRAS08 with
advanced stage mergers. The main impact of this interaction could be that it
provides the disk of IRAS08 with a supply of gas that is of order the gas mass
inside the disk $\sim 4\times 10^{9}$ M⊙ (Cannon et al., 2004). We note that
the plume HI gas could be an outflow from the star burst of IRAS08, however,
this would open the question as to why there is not a symmetric flow on the
opposite side, as expected from biconical flows. In the Appendix we consider
the interaction as possible driver of the $t_{dep}$ properties of IRAS08,
though we find it behaves differently than other galaxies with similar
interaction parameters.

Figure 5.— The radial profile of the molecular gas mass surface density (top),
SFR surface density (top) and molecular gas depletion time (bottom) in IRAS08
is shown. For the depletion time measurements of individual beams are shown as
the blue squares. In both panels, the radial average in 200 pc increments is
shown as a solid line, with the standard deviation shown as a shaded region.
The uncertainty on $t_{dep}$ due to $\alpha_{CO}$ is shown as the errorbar.
For comparison, we also show data from the HERACLES survey (Leroy et al.,
2013) for the central 4 kpc of galaxies, and in a compressed panel to the
right we show $R_{gal}=5-10$ kpc for HERACLES galaxies. We display the
HERACLES data in this manner to emphasize the extreme nature of IRAS08, not
only is the gradient strong compared to typical spirals, but this occurs over
a very compact radius, despite have a similar total mass. In IRAS08 $t_{dep}$
is a strong function of radius, compared to local spirals which are
essentially constant over 10 kpc in radius. In the top panel we show that the
decrease in $t_{dep}$ is does not monotonically correlate with an increase
$\Sigma_{mol}$.

##  4\. Spatial Variation in molecular gas depletion time

In this section we investigate the spatial variation of $t_{dep}$. We find
that in IRAS08 $t_{dep}$ is of order $\sim$1.5-2 dex lower in the galaxy
center than the outer parts of the disk. In large samples of spiral galaxies
the most extreme variation observed is only of order $\sim$0.5 dex (Utomo et
al., 2017; Leroy et al., 2013).

In Fig. 5 we show that there is a clear gradient in $t_{dep}$ within IRAS08
that is mush stronger than what is observed in HERACLES disk galaxies (Leroy
et al., 2013). We find that $t_{dep}$ increases from less than 0.1 Gyr in the
central kiloparsec to greater than 3 Gyr at radii beyond the 80% radius of the
star light ($\sim$2.5 kpc). We measure a total gradient in the depletion time
of $\Delta t_{dep}/\Delta R\approx 7$ Gyr kpc-1. The local increase in
$t_{dep}$ at $R_{gal}\sim 1$ kpc by 0.2 dex is associated with an H$\alpha$
ring that contains high surface densities of CO. In Fig. 5 spirals are
represented by HERACLES galaxies (Leroy et al., 2013). We measure a gradient
in $t_{dep}$ of HERACLES galaxies from 0 to 3 kpc of $\Delta t_{dep}/\Delta
R\approx 0.3$ Gyr kpc-1. From $\sim$1-10 kpc the gradient is consistent with
$\sim$0.

We find in IRAS08 that $t_{dep}$ is more strongly coupled to $\Sigma_{SFR}$
than to $\Sigma_{mol}$. In the top panel of Fig. 5 we show the radially
averaged profiles of $\Sigma_{SFR}$ and $\Sigma_{mol}$, the constituent
components of $t_{dep}$. The profiles are plotted such that they overlap at
large radius. The profile for $\Sigma_{SFR}$, is to low order approximation
decreasing with radius at all points to the edge of the disk. Conversely,
molecular gas shows a peak at $\sim$0.8 kpc and decrease in the galaxy center.
We measure a correlation coefficient and $p$-value for both
$t_{dep}-\Sigma_{SFR}$ and $t_{dep}-\Sigma_{mol}$. Of course both are strong
correlations as they are circularly dependent, however we find that
$\Sigma_{SFR}$ has a stronger correlation with $r=-0.98$ and $p\approx
10^{-11}$, where molecular gas surface density has $r=-0.79$ and $p\approx
10^{-5}$.

The mostly likely impact of systematic uncertainties in the measurement of
$\Sigma_{mol}$ would steepen the gradient of $t_{dep}$ for IRAS08. Bolatto et
al. (2013a) argues that $\alpha_{CO}\propto\Sigma_{gas}^{-2}$ for values above
$\sim$100 M⊙ pc-2 (also see Sandstrom et al., 2013; Narayanan et al., 2011).
This would lead to increasingly lower values of $\Sigma_{mol}$ than what is
shown in Fig. 5 at radii $\lesssim$2.5 kpc, and thus even lower values of
$t_{dep}$. We can also consider missing low-spatial frequency emission from
interferometic data. Though our NOEMA C-configuration observations likely
assuage this, there could be an extremely flat distribution of CO gas that is
filtered out by the interferometric observations. One would expect the low
surface brightness extended emission to become more prominent at lower
$\Sigma_{mol}$, i.e. larger radius, and thus this effect would also likely
steepen the gradient of $t_{dep}$ in IRAS08. The decrease in $t_{dep}$ in the
very center of the galaxy, from the ring at $R_{gal}\sim 0.5$ kpc inward,
could be due to the presence of an AGN increasing the H$\alpha$ flux. However,
as we have discussed in the § 2.2, there is not strong evidence for non-
thermal emission from the currently observed emission lines. Moreover, the
rise in H$\alpha$ flux in Fig. 5 covers an area that is larger than a single
resolution element. Future, spatially resolved observations of the
[NII]/H$\alpha$ ratio, combined with our current KCWI data would allow us to
definitively determine what is driving the emission in each resolution element
of IRAS08. Also, in comparison to the global trend in $t_{dep}$, the central
part of the gradient is only a very small change. Overall, our estimates of
the gradient in $t_{dep}$ err toward conservative estimates with respect to
the systematic uncertainties.

We find that degrading the resolution acts to soften the gradient of $t_{dep}$
in IRAS08. We convolved the IRAS08 data cube to $\sim$800 pc resolution (4
beams). This resolution is chosen to be more similar to the resolution of the
HERACLES data, while still being sufficient to sample the small size of
IRAS08. We find across the same radial range $\Delta t_{dep}/\Delta R\approx
2$ Gyr kpc-1. This is still nearly an order-of-magnitude steeper than what is
observed in HERACLES disks, and the central 800 pc has $t_{dep}$ in the range
60-140 Myr. Utomo et al. (2017) shows with a sample of spiral galaxies in the
CARMA-EDGE that similarly the most common scenario is that $t_{dep}$ profiles
are flat. They measure the ratio of $t_{dep}$ inside 1 kpc to the average of
the rest of the disk, $t_{dep}^{cen}/t_{dep}^{disk}$. The most common value is
unity. The most extreme targets have $t_{dep}^{cen}/t_{dep}^{disk}\approx
0.1$. If we measure the same quantity in IRAS08 we find
$t_{dep}^{cen}/t_{dep}^{disk}\approx 0.008$, implying a much steeper decline
toward the galaxy center.

The radial gradient of $t_{dep}$ in IRAS08 is therefore in the range of
7-20$\times$ larger than in a typical local Universe disk galaxy from the
HERACLES survey, and reaches depletion times that are $\sim$30$\times$ lower
in the galaxy center than in the region surrounding the 90% radius of the
optical light.

##  5\. Star Formation efficiency per free fall time in IRAS08

###  5.1. Estimating free-fall time

In IRAS08 we find values of $t_{ff}$ vary across the disk. The central values
are $\sim$3 Myr and largest are $\sim$12 Myr. The central values skew to lower
values than observed in local spirals (Utomo et al., 2018), but outer parts
are similar. We discuss below that the systematic uncertainties here are of
order 0.2 dex, and is enough to affect the comparison with local spirals.

As defined in Equation 2, $t_{ff}\propto\rho^{-1/2}$. Measuring the volume
density at or near the scale of clouds introduces a significant source of
uncertainty. We follow the common approach to let
$\rho=\Sigma_{gas}/(2h_{z})$, where $h_{z}$ is the scale height. If the
gravitational potential is balanced by the kinetic energy then one can
estimate that $h_{z}\propto\sigma_{z}^{2}/\Sigma$, and thus
$\rho\propto(\Sigma/\sigma_{z})^{2}$. Since IRAS08 is near to face-on, we can
safely assume that $\sigma_{z}\approx\sigma$.

One must, however, account for all sources of pressure support, such as
magnetic fields and cosmic rays. Multiple prescriptions for this exist in the
literature. To generate an estimate of the systematic uncertainty, we consider
three recent calculations of the scale-height, and hence density. That of
Krumholz et al. (2018), their Equation 22, such that $\rho\approx
2.8G(\Sigma_{g}/\sigma)^{2}$, and that of Wilson et al. (2019), their equation
7. Thirdly, we also consider the simple spherical-cloud assumption in which
the galaxy has a constant disk thickness, and in each beam the gas is a sphere
of radius $R_{cloud}\approx FWHM/2\approx 100$ pc, similar to other studies of
star formation efficiency (e.g. Utomo et al., 2018).

The constant thickness assumption yields an average $<t_{ff}>=6.47$ Myr with a
standard deviation of 1.2 Myr. This is a factor of 2$\times$ shorter than the
free-fall times measured in a similar fashion on local spirals (Utomo et al.,
2018). The prescription used in Wilson et al. (2019) yields similar values of
$t_{ff}$, with the constant thickness model on average shorter by a factor of
1.5-2$\times$. The method of Krumholz et al. (2018) gives larger values of
$t_{ff}$, that are typically 3$\times$ what we estimate with the constant
thickness model.

Figure 6.—  The quantity $\Sigma_{mol}/\sigma^{2}$ is plotted against radius
for IRAS08 (blue) and M 51 (teal). The M 51 data is radial averages using data
from Leroy et al. (2017). These observables are assumed to correlate with the
inverse of the disk scale-height. The lower values of
$\Sigma_{mol}/\sigma^{2}$ in IRAS08 imply that, under the same assumptions,
the IRAS08 disk is thicker than that of M51 by nearly an order-of-magnitude.
The gradient in IRAS08 implies also that the disk scale height does not vary
by more than $\pm$0.3 dex across IRAS08.

Figure 7.—  The free-fall time of all beams is shown for IRAS08. Here we plot
$t_{ff}$ using the same prescription as in Wilson et al. (2019) for the disk
scale-height. We find that across the disk the free-fall time varies by a
factor of $\sim$3.5$\times$ from the center to the outer radii. This is not
sufficient to account for the large change in $\epsilon_{ff}$.

Figure 8.—  The radial distribution of star formation efficiency per free-fall
time, $\epsilon_{ff}$, in IRAS08 for the circular cloud model. As before, the
solid line represents the running average in 0.5 arcsec bins, and the shaded
region represents the RMS logarithmic scatter. As with $t_{dep}$ there is a
strong gradient in $\epsilon_{ff}$ within this galaxy, in this case spanning
multiple orders of magnitude. As discussed above, this gradient cannot be
accounted for by variation in the disk thickness.

Those methods that estimate the scale-height with $\sigma$ and $\Sigma_{gas}$
both show an increase in $t_{ff}$ by a factor of 3$\times$ from the center of
IRAS08 to the outskirts, whereas the circular cloud model finds an increase of
roughly $\sim 1.7\times$. To study $\epsilon_{ff}$ we adopt $h_{z}$ as
described in Wilson et al. (2019) as this formulation is specifically derived
for star-bursting environments, like IRAS08.

This prescription for disk thickness is

$h_{z}\approx 0.2\frac{\sigma^{2}}{\pi G\Sigma_{mol}}$ (4)

(adopted from Equation 7 in Wilson et al., 2019). The factor of 0.2 in front
takes into account sources of pressure support from magnetic and cosmic ray
sources, as described in Kim & Ostriker (2015). It has been scaled from the
value in Wilson et al., 2019 for the fraction of gas-to-total mass in IRAS08.
It also considers non-local sources of gravity, as in the vertical component
of the three-dimensional gravitational acceleration toward the inner part of
the galaxy. It is here that we assume the higher surface density environment,
which is appropriate for IRAS08. For a full description of their derivation
see Wilson et al. (2019).

Since the free-fall time varies as $h_{z}^{1/2}$, even in the most extreme
limit, this particular assumption could not account for more than a 20% change
in the free-fall time. In Fig. 6 we show the radial profile of
$\Sigma_{mol}/\sigma^{2}$, which scales inversely with the scale-height. This
quantity is discussed in detail in Leroy et al. (2017) in a study of nearby
spiral galaxy, M 51. As we show in the figure, IRAS08 has significantly lower
values of $\Sigma_{mol}/\sigma^{2}$ than what is found in M 51, typically at
the order of magnitude level. This implies that under similar assumptions
about the calculation of $h_{z}$, IRAS08 has a thicker disk.

We can use the result in Fig. 6 to estimate the variation in the disk
thickness of IRAS08. There is considerable point-to-point scatter, but the
radial averages are fairly flat. The average value of
$\Sigma_{mol}/\sigma^{2}$ decreases by $\sim$0.4 dex from the highest value at
$\sim$0.6 kpc to the region around $2\times R_{1/2}$ (2 kpc).

We remind the reader that the variation the free-fall timescale is related to
the square root of $h_{z}$, $t_{ff}\propto h_{z}^{1/2}$, which means that the
changes in scale height of order $2\times$ only impact $t_{ff}$ and
$\epsilon_{ff}$ by $\sim$0.15 dex. Combining this with alternatives to the
adopted prescription, we estimate that choices for deriving $h_{z}$ in IRAS08
generates a systematic uncertainty of order $\pm$0.2 dex on $\epsilon_{ff}$.

In Fig. 8 we show that $t_{ff}$ increases from $\sim$3-5 Myr in the galaxy
center to values of order 10-15 Myr at the 90% radius, roughly a factor of
$3\times$ increase. Note the low values of $t_{ff}$ at $\sim$1 kpc and 2 kpc
are associated to peaks, likely clumps of CO gas.

###  5.2. Distribution of $\epsilon_{{ff}}$ in IRAS08

In Fig. 8 we compare the radial distribution of $\epsilon_{ff}$ to local
spiral galaxies (M 83 Hirota et al., 2018 & M 51 Leroy et al., 2017). We find
in IRAS08 that there is a very strong correlation of galactic radius with
$\epsilon_{ff}$. At large radii in IRAS08 $\epsilon_{ff}$ is similar to what
is found in local spirals, $\epsilon_{ff}\approx 0.3\%$. Inside $R\sim 2$ kpc
the profile of $\epsilon_{ff}$ shows a strong decrease of $\epsilon_{ff}$ with
radius, that is not matched in either local spiral. The full range of
variation of $\epsilon_{ff}$ in M 51 and M 83 is at the $\pm$0.3 dex level,
where IRAS08 experiences a difference of roughly 2 orders-of-magnitude from
the center to the outer disk.

We note the caveat that our study and that of Hirota et al. (2018) (M 83) use
H$\alpha$ to trace SFR, while Leroy et al. (2017) (M 51) uses total IR
luminosity. This may introduce a bias in derived $\epsilon_{ff}$ values.
Different tracers reflect different time-scales of star formation, though this
is very unlikely to account for the multiple order of magnitude difference
that we observe (for review Kennicutt & Evans, 2012). CO-to-H2 conversion is
another important systematic uncertainty. Using a starburst $\alpha_{CO}$
would have the effect of making a significant fraction of lines-of-sight in
the central $\sim$50% of the galaxy reach $\epsilon_{ff}\approx 100\%$.
Alternatively, $\alpha_{CO}$ could vary with local surface density, as
described in the results on $t_{dep}$. In IRAS08 this would yield act to
steepen the correlation in both $t_{dep}$ and $\epsilon_{ff}$, with disk-like
efficiency at large radius and extreme efficiencies of order
$\epsilon_{ff}\approx 100\%$ in the central few kpc. Our constant Milky Way
$\alpha_{CO}$ assumption is therefore a conservative estimate of the value and
gradient of $\epsilon_{ff}$ in IRAS08.

Very high $\epsilon_{ff}$ are rare in the local Universe, and are more similar
to those observed in super-star clusters (SSCs) in local galaxies (Turner et
al., 2015). There are only a handful of observations capable of measuring the
efficiency in SSCs. The center of NGC 253 offers a rich starbust environment
in which Leroy et al. (2018) observes an overall efficiency of star formation
of $\sim$50% in SSCs and an efficiency per free-fall time that is similar to
the central kiloparsec of IRAS08 (when using a Milky Way $\alpha_{CO}$),
$\epsilon_{ff}\sim 10$%. Similar results are found in the SSC Mrk 71A (Oey et
al., 2017). Indeed, Otí-Floranes et al. (2014) carries out a multiwavelength
study of IRAS08, and finds that the center is consistent with containing SSC.

Recently, Utomo et al. (2018) measured $\epsilon_{ff}$ at a similar resolution
to ours in a sample of local spiral galaxies from PHANGs. They do not study
the radial variation of $\epsilon_{ff}$, but do provide mean and RMS values.
The key difference between $\epsilon_{ff}$ measured in IRAS08 to that of the
local spirals in Utomo et al. (2018) is that IRAS08 has a much larger RMS, and
that that spread is skewed to higher $\epsilon_{ff}$. The RMS of
$\epsilon_{ff}$ is 0.76 dex in IRAS08 compared to 0.25 dex in the disks from
PHANGS.

Using a standard, unweighted, median yields a $<\epsilon_{ff}>\approx 0.3\%$,
similar to Utomo et al. (2018). An unweighted average implicitly weights the
average $\epsilon_{ff}$ to the larger radius regions, where there are more
lines-of-sight. An average that is weighted by SFR yields
$<\epsilon_{ff}>_{SFR}\approx 8-10\%$ and weighting by CO flux yields
$<\epsilon_{ff}>_{CO}\approx 1\%$.

The weighted averages imply that, like $t_{dep}$, higher $\epsilon_{ff}$ in
IRAS08 is more strongly correlated with $\Sigma_{SFR}$ than with
$\Sigma_{mol}$. We find that the Spearman rank correlation coefficient of
$\epsilon_{ff}$ with $\Sigma_{H\alpha}$ is stronger ($r\approx 0.60$) than
with $\Sigma_{mol}$ ($r\approx 0.45$). We note that the strong correlation of
$\epsilon_{ff}$ with $\Sigma_{SFR}$ is also different from what is observed in
M 51 and M 83. There is not a statistically significant correlation of
$\epsilon_{ff}$ with $\sigma$ ($r\approx 0.15)$.

Figure 9.— The resolved (kiloparsec-scale) relationship between $\Sigma_{SFR}$
and $\Sigma_{mol}$ is shown above. In each panel we fit a subset of targets,
which are indicated as having blue (left), green (middle) or blue & violet
(right) colors. In all panels the points that are grey color are not included
in the respective fit. The powerlaw of each fit is given in the lower right
corner of each panel. The left panel shows a fit to the blue points (light and
dark), which are rotating disks that have SFR that is at least 2$\times$
higher than the main-sequence value for their respective mass, including
IRAS08. The middle panel shows a fit to the green points, which are disks – at
both low and high redshift– that are on the main-sequence. The right panel
shows a fit to both the blue and violet points, which are star bursting disks
(blue) and those systems that from morpho-kinematic analysis are likely to be
significantly affected by their merging (violet). The $\sim 1\sigma$ scatter
around the weighted average in all panels is shown as a shaded region. The
full range in $\Sigma_{SFR}-\Sigma_{mol}$ parameter space has significant
complexity. There are two sequences, that appear to be more closely connected
to distance to the main-sequence than morpho-kinematic state (i.e. merging or
rotating). We point out the very considerable scatter of all points in the
range $\Sigma_{mol}\approx 10^{2}-10^{3}$ M⊙ pc-2 implies a lack of single
$\Sigma_{mol}$ at which the separation of starburst occurs.

##  6\. The $\Sigma_{SFR}-\Sigma_{mol}$ scaling relationship at kiloparsec
resolution

To place IRAS08 into context with other $z>1$ and high $\Sigma_{mol}$ star
forming galaxies we use the relationship between SFR surface density and gas
mass surface density at roughly kiloparsec scale resolution. We highlight 2
results from IRAS08. First, it further illustrates that there is not a simple
cut-off at $\Sigma_{mol}\sim 100-200$ M⊙ pc-2 separating all starburst from
non-starburst galaxies in this parameter space; the separation is more
complex. Secondly, despites its highly variable $\epsilon_{ff}$, IRAS08 is not
an outlier, implying that variable $\epsilon_{ff}$ could be common in $z>1$
starburst galaxies.

This relationship is typically characterised by a power-law where

$\Sigma_{SFR}=A_{\ }\Sigma_{mol}^{N},$ (5)

where $A$ and $N$ are fitted parameters (Kennicutt, 1998a; Kennicutt & Evans,
2012). The power-law slope, $N$ in Equation 5, has been interpreted as a
constraint on physical models of star formation (e.g. Ostriker et al., 2010;
Krumholz et al., 2018; Elmegreen, 2018; Semenov et al., 2019), and is
therefore of particular interest. There is a large amount of literature on
this correlation across a range of surface brightness, for recent reviews see
Tacconi et al. (2020) and also Hodge & da Cunha (2020).

To compare IRAS08 to measurements of $t_{dep}$ for galaxies in the literature
we must degrade the resolution of our data cube to a similar resolution (800
pc) and remeasure the integrated intensity map. We note the well-known biases
of of how spatial scale affects $\Sigma_{mol}-\Sigma_{SFR}$ relationship are
described in literature (e.g. Calzetti, 2012; Leroy et al., 2013; Kruijssen &
Longmore, 2014). The comparison sample includes the following galaxies: local
disks from the HERACLES project (Leroy et al., 2013); local Universe wide-
seperation interacting galaxies NGC 232 and NGC 3110 (Espada et al., 2010);
local Universe advanced merging galaxies VV 114 (Saito et al., 2015), NGC 1614
(Saito et al., 2016) and the Antenna System (Bemis & Wilson, 2019); rotating
$z=1-4$ galaxies EGS 13011166 (z$\approx$1.5; Genzel et al., 2013), GN20
($z\approx 4$; Hodge et al., 2015), AzTEC-1 ($z\approx 4$; Tadaki et al.,
2018), SHIZELS-19 ($z\approx 1.5$; Molina et al., 2019), SDSS J0901+1814
($z\approx 2.3$; Sharon et al., 2019) and $z>1$ systems that are more
consistent with being merging galaxies HATLAS J084933 ($z\approx 2.4$; Gómez
et al., 2018), ALESS67.1 ($z\approx 2.1$; Chen et al., 2017). Due to the
biases in sampling size discussed above, we refrain from plotting measurements
of entire galaxies, and also refrain from plotting measurements less that 0.4
kpc.

To measure the powerlaw relationship between star formation and molecular gas
mass surface density we carry out Monte Carlo fit of the data sets to Equation
5 using Ordinary Distance Regression in the Python package scipy. We weight
the data so that each galaxy has equal impact on the fit. Data points are also
weighted by the measurement uncertainty. For each fit, we run 1000
realizations in which the data points are shifted randomly within 0.3$~{}dex$
in both SFR and gas mass to account for systematic uncertainties. Increasing
the size of the range in which we shift points, within reasonable limits, only
has a minor impact on the derived powerlaw. The reported powerlaw slope and
scale factor are the median values from the iterations, and the uncertainty is
the 1$\sigma$ scatter around this value. We test our method first by fitting
the HERACLES data only in the range 10-100 M⊙ pc-2, and we recover a powerlaw
of $N=0.97$, which is very similar to values measured in Leroy et al. (2013).
Results of fits are shown in Fig. 9 and tabulated in Table 2.

For the fits in Fig. 9, we group galaxies together based on coarse galaxy
properties including: morpho-kinematic state (i.e. disks versus mergers) and
distance to the star forming main-sequence. We use the redshift evolution of
the main-sequence as defined in Whitaker et al. (2012). We define the distance
from the main-sequence as the ratio of the observed star-formation rate to the
main-sequence star formation rates ($\delta MS\equiv SFR/SFR_{MS}$). When
multiple estimates of star formation rate were available we opt for those made
from ionized gas for consistency.

We find $N\approx 1.2$ for main-sequence galaxies. This is marginally steeper
than what is found for fits to HERACLES disks alone ($N\approx 0.97$), but
similar to the steep slope found by Genzel et al. (2013) for the $z\sim 1.5$
main-sequence galaxy. Galaxies identified as having starbursts show powerlaws
with $N\sim 1.6$. We find that separating star-bursting galaxies between those
suspected of being mergers and those that are not mergers has very little
impact on the power-law slope derived from fitting Equation 9. IRAS08 is in
general agreement with the star-bursting sequence. It has a range
$\Sigma_{mol}\sim 100-400$ M⊙ pc-2 that overlaps with both the starbursting
and non-starbursting sequence. On its own it has a steeper power-law ($N\sim
1.8-2.0$). We note that because IRAS08 is compact (R${}_{1/2}\sim 1$ kpc),
when resampled to lower resolution there are only a few independent data
points, and thus the fit to only IRAS08 has significant uncertainty. Moreover,
we reiterate from Section 4 that the lower resolution averages soften the
gradient in $t_{dep}$. We do not find it useful to study higher spatial
resolution relationship of $\Sigma_{SFR}-\Sigma_{mol}$ for two reasons. First,
our purpose of studying the $\Sigma_{SFR}-\Sigma_{mol}$ relationship is for
comparison to other galaxies, and it is well established that such comparisons
must be carried out on a comparable spatial scale (Leroy et al., 2013).
Secondly, it is clear from Fig. 5 that there is considerable scatter of
individual beams. Fits using standard methods, as we use here, are heavily
dominated by uncertainty.

We find that there is not a simple threshold in behavior at a single
$\Sigma_{mol}$, as suggested previously in the literature (Bigiel et al.,
2008). IRAS08 has a similar range of $\Sigma_{mol}$ and both EGS 13011166 and
SHIZELS-19 but has a significantly steeper slope than both. The key parameter
that distinguishes galaxies on the two tracks, is distance from the main-
sequence. Similar arguments are discussed in Tacconi et al. (2020) describing
global depletion times. We argue $\Sigma_{mol}$ on its own should not be used
to discriminate between the two sequences in the $\Sigma_{SFR}-\Sigma_{mol}$
relationship.

Table 2Fits to $\Sigma_{SFR}=A\Sigma_{mol}^{N}$ Category | log($A$) | $N$
---|---|---
$\delta$MS$>2$ disks only | -4.14$\pm$0.27 | 1.63$\pm$0.09
$\delta$MS$>2$ All | -4.15$\pm$0.38 | 1.53$\pm$0.16
$\delta$MS$<2$ disks only | -3.85$\pm$0.12 | 1.20$\pm$0.04

In spite of its large high variability in $\epsilon_{ff}$ in IRAS08, Fig. 8,
the galaxy is not a significant outlier from other starbursting systems. It is
in fact less extreme in $\Sigma_{mol}$ and $\Sigma_{SFR}$, by an order-of-
magnitude, than AzTEC-1 (Tadaki et al., 2018) and GN20 (Hodge et al., 2015),
and has similar gas and SFR surface densities as $z\approx 1-2$ galaxies, e.g
SDSS J0901+1814 (Sharon et al., 2019). This implies that such extreme values
of $\epsilon_{ff}$ could be wide-spread in starbursting galaxies of the
distant Universe. Given its similarity to other star-bursting galaxies in the
subsequent section we consider the implications of the results in Figs. 8 and
9 on star formation models in the literature.

##  7\. Discussion

###  7.1. Implications for Galaxy-Scale Star Formation Theories

The combined results in Fig. 8 and Fig. 9 allow for a direct comparison to a
number of theories for how star formation evolves in galaxies. We note that
the extreme nature of star formation in IRAS08 does not preclude comparison to
these theories, as almost all explicitely discuss the relevancy for star-burst
regime (e.g. Shetty & Ostriker, 2012; Krumholz et al., 2018; Faucher-Giguère
et al., 2013; Elmegreen, 2018).

There is a clear tension between our results in Fig. 8 and those theories that
assume or derive a constant star formation efficiency per free fall-time (e.g.
Krumholz et al., 2012; Salim et al., 2015; Elmegreen, 2018). In such theories
$\Sigma_{SFR}=\epsilon_{ff}/t_{ff}\Sigma_{gas}$, and that $\epsilon_{ff}$ is
constant, but $t_{ff}$ varies. In IRAS08 we find that the opposite is true. We
find very little variation across the disk in $t_{ff}$ (of the order of a
factor of a few), but a variation in $\epsilon_{ff}$ of a factor of
$\sim$50$\times$. Moreover, recent observations (Fisher et al., 2019) have
established that on galaxy scales there is an inverse relationship of
$t_{dep}\propto\sigma_{gas}^{-1}$, which is opposite the prediction of
constant star formation efficiency models.

Elmegreen (2018) reviews how different physical regimes may lead to different
powerlaws in the Kennicutt-Schmidt diagram. They show that for a disk

$\Sigma_{SFR}\propto\epsilon_{ff}h_{z}^{-1/2}\Sigma_{gas}^{3/2}.$ (6)

While we do see that in starburst galaxies
$\Sigma_{SFR}\propto\Sigma_{mol}^{3/2}$, in order for Equation 6 to hold for
IRAS08 the change in $\epsilon_{ff}$ would need to be canceled by a greater
change in $h_{z}$. Under the assumption that variation in the scale height of
a disk is traced by $\sigma^{2}/\Sigma_{mol}$, we would need a factor of
$\sim$200$\times$ to cancel the change in $\epsilon_{ff}$. We find however, in
Fig. 6 that the ratio $\Sigma_{mol}/\sigma^{2}$ only changes by a factor of
$\sim$2$\times$ across the disk. This implies that $h_{z}$ is relatively
constant, while $\epsilon_{ff}$ systematically increases with $\Sigma_{SFR}$
by orders-of-magnitude. This formulation, therefore, appears inconsistent with
observations of star formation in IRAS08.

A third class of models predict that star formation is regulated by feedback
from newly formed stars (e.g. Ostriker et al., 2010; Shetty & Ostriker, 2012;
Kim et al., 2013; Faucher-Giguère et al., 2013). Shetty & Ostriker (2012)
specifically investigates the regime of maximally starbursting disks, and is
therefore applicable to our observations, they argue that

$\Sigma_{SFR}\propto(p_{*}/m_{*})^{-1}\Sigma_{gas}^{2}$ (7)

The quantity $p_{*}/m_{*}$, is the momentum input into the ISM from supernova
per mass of new stars formed, sometimes referred to as the “feedback
efficiency” (Kim et al., 2013). For comparison to IRAS08 this prediction has
the advantage of not simultaneously depending on both $\epsilon_{ff}$ and
$t_{dep}$. As we show in Fig. 8, the simulations of Shetty & Ostriker (2012),
which incorporate these concepts, find that, even at high $\Sigma_{mol}$, the
maximum $\epsilon_{ff}$ is $\sim$1%, and thus a factor of $\sim$50$\times$ too
low to describe the variability in IRAS08.

In order for Equation 7 to match the observations in Fig. 9 $p_{*}/m_{*}$
would have to increase with $\Sigma_{gas}$ (or $\Sigma_{SFR}$), at roughly
$p_{*}/m_{*}\propto\Sigma_{gas}^{1/2}$, but for starburst galaxies only. The
feedback efficiency is typically derived, or adopted, as a constant in star
formation theories (e.g. Ostriker et al., 2010; Faucher-Giguère et al., 2013;
Krumholz et al., 2018).

Fisher et al. (2019) shows that constant feedback efficiency models have
trouble describing the global relationships for both $\Sigma_{SFR}$ and
gravitational pressure (also see Sun et al., 2020; Girard et al., 2021). If
the value of $p_{*}/m_{*}$ were to increase with either $\Sigma_{SFR}$ or
$\Sigma_{mol}$, as described above, this would alleviate the discrepancies at
high $\Sigma_{SFR}$ with both the correlations of $\sigma-t_{dep}$ and
$\Sigma_{SFR}$ versus hydrostatic pressure.

Though debate still exist (Kim et al., 2017), some simulation work finds a
significant increase in $p_{*}/m_{*}$ is possible in regions of higher star
formation rate surface density, due to the effect of clustered supernova
driving more efficient feedback (Gentry et al., 2017, 2018; Martizzi, 2020).
Moreover, simulations of outflows in starbursting systems like M82 or $z\sim
2$ galaxies find that constant feedback efficiency models are not capable of
reproducing the high velocity winds, whereas clustered supernova are (Fielding
et al., 2018). We note that similarly in IRAS08 Chisholm et al. (2015)
observes very high velocity winds, $v_{out}\sim 1000$ km s-1, using UV
absorption lines. IRAS08 in fact has among the most rapid outflows in their
sample of 48 local Universe galaxies. The $\Sigma_{SFR}$ clumps we observe in
IRAS08 seem like an ideal location for the effects of clustered supernova.
Such a change could also act to increase the observed $\epsilon_{ff}$ as more
efficient feedback would decrease $\Sigma_{mol}$.

Alternative to varying the feedback efficiency others argue that star
formation is regulated by a combination of feedback and dynamical disk
stability (Faucher-Giguère et al., 2013; Krumholz et al., 2018). In these
theories the $\Sigma_{SFR}-\Sigma_{gas}$ relationship depends on both
$p_{*}/m_{*}$ and Toomre $Q$, such that

$\Sigma_{SFR}\propto Q(p_{*}/m_{*})^{-1}\Sigma_{gas}^{2}.$ (8)

To first approximation, this is consistent with a picture of galaxy evolution
in which main-sequence galaxies have high values of $Q$ and starburst
galaxies, which may be experiencing a violent disk instability, have low
values of $Q$. This would then explain why there are multiple sequences in
Fig. 9 at large $\Sigma_{mol}$, and is consistent with what we observe in Fig.
4 for IRAS08, as well as AzTEC-1 (Tadaki et al., 2018). We note that testing
the $Q$ dependance on high-$z$ galaxies is more difficult than it seems, as
systematic uncertainties can have very large effects on both how the velocity
dispersion is measured and the molecular gas is estimated (Girard et al.,
2021). We note that Girard et al. (2021) shows that when SFR is compared to
molecular gas velocity disperions, instead of ionized gas, the mixed feedback-
transport model from Krumholz et al. (2018) does not agree with data.

Faucher-Giguère et al. (2013) creates a similar feedback-regulated model of
star-formation, which incorporates dynamical regulation of the disk, such that
$Q\approx 1$ and in their model $\epsilon_{ff}$ is free to vary. They find a
range of $\epsilon_{ff}$ at all $\Sigma_{mol}>100$ M⊙ pc-2. They also make
predictions for global properties like $\Sigma_{gas}$, $f_{gas}$ and $\sigma$.
The predict a disk averaged $\epsilon_{ff}$ as high as 30% for a galaxy with
properties like IRAS08. Though it is not clear from their model if there is a
systematic variation of $\epsilon_{ff}$ like we see in IRAS08.

Similar to these gravitationally based prescriptions, there is a long known
result (Kennicutt, 1998b) that for total gas mass in galaxies normalising the
gas mass by the orbital time-scale creates a linear correlation that galaxies
obey well, such that $t_{dep}\propto t_{orb}$, where the orbital timescale is
defined as $t_{orb}=2\pi R/V$. This amounts to stating that galaxies convert a
constant fraction of gas into stars per orbit. In IRAS08 both $t_{dep}$ and
$t_{orb}$ become larger with radius, causing a positive correlation. The
change in $t_{orb}$, however, is insufficient to account for the two orders-
of-magnitude change in $t_{dep}$. We find that in the central kiloparsec in
IRAS08 $t_{orb}\approx 30-50$ Myr, rising to $\sim 150$ Myr in the outer disk,
an increase of a factor of 5.

We summarise how our results compare to star formation:
$\bullet$ Constant Star Formation Efficiency Models: Our observations of
IRAS08 are inconsistent with theories in which the star formation efficiency
is held constant (Krumholz et al., 2012; Salim et al., 2015). Constant star
formation efficiency models also fail to recover the observed relationship of
$t_{dep}\propto\sigma^{-1}$ (Fisher et al., 2019).

$\bullet$ Feedback Regulated Models: Models in which star formation is
regulated only by the balance of feedback with local gravity (Shetty &
Ostriker, 2012, e.g.), excluding large scale galactic flows, could explain the
properties of galaxies like IRAS08 only if more freedom is given to both star
formation efficiency, and especially if the efficiency of feedback is allowed
to be higher in higher SFR surface density regions, perhaps due to supernova
clustering.

$\bullet$ Mixed Feedback+Toomre Regulation: Models in which feedback effects
are mixed with disk self-regulation via Toomre instabilities appear most
consistent with our observations (Faucher-Giguère et al., 2013; Krumholz et
al., 2018). Such models have a built-in explanation for the multiple sequences
in the $\Sigma_{SFR}-\Sigma_{mol}$ relationship. Moreover, the model of
Faucher-Giguère et al. (2013) does allow for larger disk averaged
$\epsilon_{ff}$. Though these models do not, as yet, give testable predictions
for the systematic variation in $t_{dep}$ and $\epsilon_{ff}$ within IRAS08,
and the correlation of SFR-$\sigma_{mol}$ for molecular gas velocity
dispersions does not match the data in samples of both low- and high-z
galaxies (Girard et al., 2021).

It is important to emphasize that our findings are based on only one galaxy.
The stark differences from what we observe and commonly accepted theories of
star formation seem to strongly argue for more observations of resolved maps
of molecular gas in high $\Sigma_{SFR}$ disk galaxies. Whether that be
directly at $z>1$ or with analogue samples such as DYNAMO (Fisher et al.,
2017b), it is now needed to determine if strong gradients in $\epsilon_{ff}$
are common in this mode of star formation.

###  7.2. Possible dynamical drivers of ${t_{dep}}$ gradient

If we assume that the gas flow which was responsible for the variation in
$\epsilon_{ff}$ and $t_{dep}$ is quasi-stable on a similar timescale as
$t_{dep}$ (100-500 Myr) we can expect that evidence for such an inflow may
still present in the galaxy. It is particularly interesting to consider the
similarity between IRAS08 and blue-compact galaxies at $z\approx 1-2$, which
are thought to experience very rapid inflows as an important component of
galaxy evolution (Dekel & Burkert, 2014; Tacchella et al., 2016).

We first look for independent evidence of inflow using the metallicity
profile. Flat metallicity gradients are frequently interpreted as indicators
of gas inflows within galaxies (Kewley et al., 2010; Jones et al., 2013). The
reason is straightforward. The higher density of star formation in the galaxy
center (Fig. 5) should pollute the ISM faster, and therefore in order to
maintain a flat metallicity profile the center must be replenished with less
metal rich gas.

The metallicity profile, shown in Fig. 11, is consistent with an inflow of gas
toward the galaxy center. The blue points indicate our measurements using the
R23 method from Kobulnicky & Kewley (2004) with KCWI data, and the black
points show the measurement from López-Sánchez et al. (2006), which uses the
Pilyugin & Thuan (2005) calibration for the same emisison lines. There are
very well known offsets between the metallicity of different calibrations (for
review see Kewley et al., 2019). The gradient of our measurement and López-
Sánchez et al. (2006) is similarly flat across the disk. A typical, massive
spiral galaxy has a metallicity gradient, using the R23 method, of order -0.4
dex $R_{25}^{-1}$ in log(O/H), see Ho et al. (2015) and reviewed in Bresolin
(2017). For an exponential disk $R_{25}$ is roughly equivalent to the 90%
radius. We measure a 90% radius of star light, using HST F550M image, of 3
kpc. Across this range the metallicity profile of IRAS08 shows no decrease at
all, consistent with inflow scenarios.

Figure 10.— The metallicity profile determined via the R23 method as described
in Kobulnicky & Kewley (2004). Note that we do not plot error bars because the
typical strong-line measurements across this region of the galaxy have
$S/N\sim 100$, as the data was intended for analysis of the fainter features
in outflows. A future paper Reichardt-Chu et al. submitted provides an in
depth analysis of the KCWI dataset. We also show the metallicity profile
measured by López-Sánchez et al. (2006) as a black dashed line. Across the
disk of IRAS08 we observed an essentially flat metallicity profile. Shallow,
or even negative, metallicity gradients are widely interpreted as indicating
gaseous inflows across the disk.

Figure 11.— The molecular gas depletion time,
$t_{dep}\equiv\Sigma_{mol}/\Sigma_{SFR}$ is plotted against the inflow
timescale, $t_{inf}$ (Equation 11), as determined from Dekel & Burkert (2014).
The squares represent individual beams in the CO(2-1) map. The error bar
indicates the uncertainty from $\alpha_{CO}$. The thick, blue solid line
represents the average determined as a function of radius in increments of 1
arcsec ($\sim 0.8$ kpc). The black line represents the line of equality
assuming a mass-loading factor of $\eta=0$ (bottom) and $\eta=1$ (top). In
IRAS08 $t_{dep}$ varies by 2 orders-of-magnitude from the outer disk to the
inner kiloparsec, however the average does not drop below the inflow
timescale.

We consider 3 possible mechanisms for gas inflows: galaxy wide “violent” disk
instability, a distant interaction with a neighboring galaxy, and the bar in
the galaxy center.

####  7.2.1 Violent Disk Instability as inflow driver

Typically, violent disk instabilities as drivers of inflow are connected to
the phenomena of “wet compaction” in $z\approx 1-2$ galaxies. In this scenario
rapid inflows of gas quickly build bulges in starbursting disks (see
discussion in Zolotov et al., 2015). Observations and simulations of high-$z$
galaxies associate the phenomenon of compactions with blue compact galaxies.
As described above, IRAS08 has historically been treated as a rare local
analogue of luminous blue-compact galaxies in the distant Universe López-
Sánchez et al. (2006); Östlin et al. (2009). We have also measured a low
Toomre Q in IRAS08. We therefore consider the possibility that a similar
phenomena is dominating the inflow of gas in IRAS08.

Zolotov et al. (2015), and also recently Dekel et al. (2020), describe the
properties of simulated galaxies experiencing these phenomena. The critical
properties are high specific SFR (SFR/Mstar) and high stellar mass surface
density in the central kiloparsec. In IRAS08 we observe a specific SFR in the
central kiloparsec of $\sim$1.1 Gyr-1 and a stellar mass surface density of
$\Sigma_{*}=2.9\times 10^{9}$ M⊙ kpc-2. These values place IRAS08 within the
range of values for galaxies experiencing compaction in the simulations
analysed by Zolotov et al. (2015). In Fig. 5 we show that in IRAS08 the
molecular gas surface brightness peaks at a radius of $\sim$0.5-0.7 kpc, and
then declines at larger radius. Dekel et al. (2020) finds that such gas
profiles are similar to pre-compaction or early-compaction galaxies. We note
that there are no observations of blue-compact galaxies at $z>1$ with sub-kpc
resolution, like our observations of IRAS08, it is therefore not possible to
determine if such rings are common or not in blue compact galaxies thought to
experience compaction.

Dekel & Burkert (2014) argue that wide-scale violent disk instabilities
naturally drive inflows of gas, and make a testable predicitions for the
internal distribution of $t_{dep}$. They develop a formalism in which the
inflow timescale can be estimated from the assumption that (1) the kinematics
are that of marginally stable/unstable disk, and (2) that energy gained from
inflow is equal to the energy dissipated via turbulence. These assumption
yield an inflow timescale, $t_{inflow}$ of

$t_{inflow}\approx 2\frac{R}{V}\left(\sqrt{2}\frac{\sigma}{V}\right)^{-2}.$
(9)

If the galaxy kinematics are dominated by the violent disk instability then
the inflow timescale is predicted to always be greater than the depletion time
of the gas, $t_{dep}^{\prime}$. Here we use a modified definition of gas
depletion time, $t_{dep}^{\prime}$ as

$t_{dep}^{\prime}\equiv\frac{M_{gas}}{SFR_{\ }(\eta+1)},$ (10)

where $\eta$ is the outflow mass-loading factor. If $t_{dep}^{\prime}\leq
t_{inflow}$ then gas will convert to stars before it reaches the galaxy
center. The inflow timescale, as described in Equation 9, is only relevant to
galaxies experiencing a violent disk instability.

The condition that $t_{dep}>t_{inflow}$, therefore, gives us a testable
condition for consistency with the wet-compaction scenario for IRAS08. A
system in which the gas inflow is driven by torques due to merging or
accretion would not need to obey the condition $t_{dep}>t_{inflow}$ (where
$t_{inflow}$ is derived from Equation 9) to maintain inward gas movement.

We note that using Equation 9 to estimate the inflow timescale makes an
explicit assumption that the galaxy wide disk instability is driving the gas
flow. In IRAS08 there is clearly a bar, and there is a significant amount of
literature on the impact of bars, and associated resonances impacting gas
inflows (see reviews Kormendy & Kennicutt, 2004; Athanassoula, 2005). We will
consider bars later as a driver of the gas inflow.

In Fig. 1 the molecular gas is preferentially located in spiral arms, this may
imply that the assumptions of linear Toomre instabilites are not applicable.
Under this case the formulation of $t_{inflow}$ in Equation 9 may not be
correct. We can make approximate estimates of the impact of the nonlinearity,
on the formulation of $t_{inflow}$. The presence of large clumps of gas with
masses of order 107 M⊙ implies that some instability must have recently
existed. One possibility is that our measurements of $Q$ which focus on clumps
under-estimate the $Q$ value of the disk gas. Simulations of clumpy galaxies
in the non-linear regime find that $Q$ can be as high as $Q\sim 1.8$ Inoue et
al. (2016). Under very simplistic assumptions, this would have the effect of
increasing $t_{inflow}$ by a factor of 3$\times$. Alternatively, the fact that
that the molecular gas favours the spiral arms may imply that a the clumps are
in response to a spiral arm instability, as described in Inoue & Yoshida
(2018). They show that many of the results of Toomre theory, have only minor
corrections to clumpy spiral arm instabilties.

In Fig. 11 we compare the molecular gas depletion time to the inflow timescale
determined at each CO beam in IRAS08. The straight lines indicate the lines of
equality for typical assumptions on the mass-loading factor of outflowing gas
from star bursting regions (e.g. Bolatto et al., 2013a; Veilleux et al.,
2020). We show that while $t_{dep}$ decreases as a function of radius within
IRAS08, very few of the measured beams have $t_{dep}^{\prime}<t_{inflow}$. We
also averaged both $t_{dep}$ and $t_{inflow}$ in radial bins of $\sim$0.8 kpc.
In Fig. 11 we show that the two timescales decrease in such a way that the
$t_{inflow}$ is never less than the depletion time. This galaxy therefore
satisfies the condition in Dekel & Burkert (2014) for gas driven inflows by
violent disk instabilities.

The result in Fig. 11 does not absolutely mean that the gas inflow in IRAS08
is driven by disk instabilities. Indeed as we have stated above the fact that
the gas is preferentially in spirals may imply that the disk may be in the
non-linear phase of an instability.

However, we take this with the low Toomre Q (Fig. 4), high gas velocity
dispersion, compact size and large clumps of star formation as holistically
fitting a picture that is outlined in theoretical and simulation work
describing galaxies in which the Toomre instability drives the internal
dynamics of those galaxies. Moreover, the location of the ring is consistent
with expectations from Toomre instability theory (e.g. Genzel et al., 2014).
The ring is located at a radius of $\sim$1 kpc, which is colocated with the
rise in Toomre Q at the same radius (Fig. 4). This is expected in a system in
which the galaxy wide instability is driving the flow of gas (Genzel et al.,
2014; Dekel & Burkert, 2014).

What Fig. 11 adds is a connection of the gradient in $t_{dep}$ and
$\epsilon_{ff}$ directly to the disk instability. Blue-compact disks, that are
similar in many properties to IRAS08, are thought to be a critical phase in
galaxy evolution (Tacchella et al., 2016). Our results suggest that the
extreme inflows could sustain extremely high star formation efficiencies, and
thus build bulges 20-50$\times$ faster than current prescriptions based on
lower assumptions of $\epsilon_{ff}$ than we observe in the center of IRAS08.

####  7.2.2 Outflow as a driver of low depletion times

Removal of gas via star formation driven winds could lead to an observed
decrease in the ratio of SFR to $M_{gas}$. The interpretation of depletion
time as the currently observed emission line flux of ionized gas (star
formation rate) to the current flux from CO (molecular gas) makes an implicit
assumption that the mass of molecular gas is similar to the historic mass,
which formed the present population of stars. However, star formation driven
winds could reduce the mass of molecular gas in the environment of more
extreme star formation. In this case the observed depletion time reflects both
the loss of cold gas due to star formation and the loss of cold gas due to
outflows, as described in Equation 10.

In IRAS08 we observed a lower depletion time in the galaxy center compared to
the outer parts. If the mass-loading factor (rate of mass outflow divided by
SFR) is higher in the galaxy center than the outskirts, then in principle this
could steepen the observed gradient in depletion time and $\epsilon_{ff}$. The
mass-loading factor in the galaxy center would need to be of order $\sim
20-50\times$ higher in the center for this to completely explain the gradient
in $t_{dep}$. Chisholm et al. (2017) observes very fast winds in the central
kiloparsec of IRAS08 ($v_{90}\approx 1000$ km s-1), which would be fast enough
to escape the disk easily, but the mass-loading factor is of order $\eta\sim
0.05$. This is not sufficient to account for the difference from a disk-value
of $t_{dep}\sim 1$ Gyr. There is little published work on internal gradients
of the mass-loading factor. In simulations, Kim et al. (2020) finds that mass-
loading factors are lower for shorter depletion times, which is opposite of
the trend needed to explain our results. Our team is using the KCWI data
described in this work to measure outflows of ionized gas. Reichardt Chu et
al. submitted finds that there is not strong variation of the mass-outflow
rate with $\Sigma_{SFR}$, which would imply that there is likewise not a
strong variation with $t_{dep}$. As discussed above, there is a strong
correlation of shorter depletion times with higher $\Sigma_{SFR}$. Moreover,
they find mass-loading factors of ionised gas that are similar to UV
absorption lines, of order unity $\dot{M}_{out}/SFR\sim 1$, which is not
sufficient to explain the low $t_{dep}$ in IRAS08. We intend a future paper
directly comparing the outflow kinematics to the molecular gas depletion time
and gas-mass fraction with the aim of testing models of feedback and star
formation regulation.

####  7.2.3 Bars or Mergers as inflow driver

IRAS08 does not behave similarly in its value nor gradient of $t_{dep}$ to
what is observed in either barred disks or merging galaxies (with similar
impact parameters and mass-ratios). The comparison of the depletion time of
IRAS08 to galaxies with bars and mergers is described in more detail in the
Appendix. Here we summarize the results.

Merging Galaxies: Using molecular gas data from the GOALS sample of merging
galaxies (Larson et al., 2016) we find that similar wide-separation
interacting galaxies do not show low global $t_{dep}$. Typically the very low
global depletion times are only observed in advanced stages of merging. We
also consider the internal gradient in molecular gas depletion times of wide
separation mergers. Espada et al. (2018) studies resolved $t_{dep}$ within
interacting galaxies with quite similar mass ratios and impact parameters as
IRAS08. Espada et al. (2018) finds that there is much less variation in
$t_{dep}$ in the interacting galaxies, than we see in IRAS08, and is shorter
at the edge of the galaxy, which is the opposite of IRAS08. Wide-separation,
interactions certainly drive gas inward, but this does not necessarily
translate to more efficient star formation in the galaxy center. We also use
the data from Espada et al. (2018) to show that in these merging galaxies the
depletion times are not consistent with predictions from disk instability
theory (Equation 9), and thus satisfying a null hypothesis.

Barred Disks: For bars there is not observational evidence that bars lead to
low central $t_{dep}$. Bars are well known to correlate with high central
densities of molecular gas (Sheth et al., 2005; Jogee et al., 2005; Fisher et
al., 2013), which are understood theoretically (e.g. Athanassoula, 1992;
Kormendy & Kennicutt, 2004). However, there is not a well known trend with
barred disks have significantly lower $t_{dep}$ in the galaxy center,
especially not more than a $\sim$0.2 dex level (Utomo et al., 2017). In IRAS08
there is a central decrease in gas mass surface density (Fig. 5), which is the
opposite of observed gas density profiles in barred disks. Moreover, the bar
in IRAS08 is on the small side of typical bars, and the gradient in $t_{dep}$
begins well outside the bar radius.

It is very important to state the caveat that none of these phenomenon
(instabilities, mergers, bars) are mutually exclusive. Simulations now
establish that minor-merger style interactions frequently drive the violent
disk instabilities (Zolotov et al., 2015). Moreover, rest-frame B-band surveys
find that 20-30% of galaxies at $z\sim 1$ are barred (Jogee et al., 2004). We
note that it is well known that blue-optical surveys significantly
underestimate the frequency of bars (Eskridge et al., 2002). It would thus
imply that significantly more that 30% of $z\sim 1$ galaxies are barred.
Indeed, recent studies of observations find bars, spirals and rings are common
features in galaxies at $z\sim 1.5-3$ (Hodge et al., 2019), and that the
historic absence of observations of such features may have been heavily biased
by resolution and sensitivity (Yuan et al., 2017).

###  7.3. Comparing IRAS08 to $z\approx 1-2$ galaxies

The observations of IRAS08 we describe in §3 and §5 correspond to a star-
forming compact rotating galaxy, with a high gas dispersion velocity
indicative of a thick disk of very high molecular surface density with low
enough Toomre Q to suggest large scale instabilities. This scenario is very
similar to the properties of galaxies at $z\sim 1-2$ (reviewed in Glazebrook,
2013; Tacconi et al., 2020). Other studies have reached similar conclusions
(Leitherer et al., 2002; López-Sánchez et al., 2006; Östlin et al., 2009). The
SFR and stellar mass of IRAS08 correspond to those of a main-sequence galaxy
at $z\sim 1-1.5$. This is also true for the compactness of its 500 nm half-
light radius.

A characteristic feature of galaxies (both main-sequence and bursting) at
$z\approx 1-2$ is the well known “clumpy” star forming regions (e.g. Elmegreen
& Elmegreen, 2005; Genzel et al., 2011; Guo et al., 2015). Fisher et al.
(2017b) includes IRAS08 in an analysis of local Universe clumpy galaxies from
the DYNAMO sample. The IRAS08 clumps are as bright as 18% of the total light
in H$\alpha$ and several are brighter than 12%. This galaxy therefore easily
passes quantitative literature definitions of “clumpy” galaxies (e.g. Guo et
al., 2015; Fisher et al., 2017b). This similarity to $z\sim 1-2$ galaxies, not
only in kinematic state (i.e. low-Q and high $\sigma$) but also
characteristics of star-forming complexes, suggests that such conditions in a
galaxy may facilitate high and/or variable $\epsilon_{ff}$. Moreover, these
observations also suggests a connection between this kinematic state and rapid
inflows. Given that these same conditions are very common at $z\approx 1-3$,
when most star formation in the Universe occurred (Madau & Dickinson, 2014;
Förster Schreiber & Wuyts, 2020) this motivates more study in this area.

Our results strongly argue for the need for more observations of more
turbulent, disk galaxies in which molecular gas and star formation rates can
be resolved to scales of $\sim$100 pc. This can only currently be achieved
with either local Universe analog samples, like DYNAMO, or lensed galaxies at
$z\sim 1$ (e.g. Dessauges-Zavadsky et al., 2019). Results from such projects
would directly inform models of galaxy evolution and possibly make a
significant step forward in understanding how bulges form in the early
Universe.

##  8\. Summary

Our main result is a two order-of-magnitude variation in the molecular gas
depletion time and $\epsilon_{ff}$ across a massive blue-compact disk galaxy.
We discuss the implications of this for both models of star formation and the
evolution of similar blue-compact disks at $z\sim 1-3$. We find that in the
central 50% of the galaxy typical $\epsilon_{ff}$ values are larger than 10%,
with extreme values as high as 100%. This variation is much larger than the
variation of $t_{ff}$, which accounts for a variable disk thickness. The
values and radial variation of $t_{dep}$ and $\epsilon_{ff}$ are very atypical
when compared to other disk galaxies in the local Universe (Leroy et al.,
2013, 2017; Utomo et al., 2017, 2018; Hirota et al., 2018).

IRAS08 is, however, similar in many properties to the turbulent, compact
starbusting disk galaxies of the distant Universe. While highly resolved
observations of distant galaxies remain elusive, we can interpret our high
spatial resolution observations or IRAS08 as possibly indicating that more
efficienct star formation is a common feature of $z\approx 1-2$ galaxy
evoution. We show, in Fig. 9, that this similarity also translates to a
consistency in the resolved Kennicutt-Schmidt relationship between
$\Sigma_{SFR}$ and $\Sigma_{mol}$. We find that the relationship between being
above the main-sequence and having a steeper $\Sigma_{SFR}-\Sigma_{mol}$
power-law slope is the same at $z\approx 0$ as at $z\approx 1-2$. This is
generically consistent with results showing that galaxies above the main-
sequence have short $t_{dep}$ (Tacconi et al., 2018, 2020), with which our
target is also consistent. Our results suggest that the steeper
$\Sigma_{SFR}-\Sigma_{mol}$ powerlaw may be driven by a higher $\epsilon_{ff}$
at the cloud scale, as suggested in theory developed in Faucher-Giguère et al.
(2013). Recent observations of molecular clouds in lensed galaxies do suggest
higher pressure clouds than what is observed in local spirals (e.g. Dessauges-
Zavadsky et al., 2019), which may indicate differences in the conversion to
stars.

As we have discussed in Section 6, it is hard to reconcile these observations
with models assuming constant $\epsilon_{ff}$. Models that do well at
describing properties of local spiral galaxies (e.g. Ostriker et al., 2010;
Krumholz et al., 2012; Salim et al., 2015) cannot match the observations of
IRAS08, or other star-bursting disk galaxies. Theories in which
$\epsilon_{ff}$ is variable (e.g. Faucher-Giguère et al., 2013) are more
consistent.

We note that for comparing to theory, there is some degeneracy between a truly
variable $\epsilon_{ff}$ and a variable feedback-efficiency. If the feedback
is more effective at removing molecular gas this could lead to an increase in
the observed $\epsilon_{ff}$. Fisher et al. (2019) argues that if the feedback
efficiency ($p_{*}/m_{*})$, in Equation 6, were larger in higher
$\Sigma_{SFR}$ disk galaxies this could reconcile a number of galaxy
properties with locally tested equilibrium star formation theories (e.g.
Ostriker et al., 2010; Kim et al., 2013). In IRAS08 it is not clear that
outflows alone can explain the gradient in $\epsilon_{ff}$. Chisholm et al.
(2015) measures very strong winds ($v_{90}\sim 1000$ km s-1) in the center of
IRAS08. The mass loading factor, however, in the center of the galaxy would
need to be of order $\eta\sim 20-50$ to account for the entire decrease
$t_{dep}$ below the typical disk value. Chisholm et al. (2017) finds, based on
UV-absorption lines, mass-loading factor of 5% in IRAS08 in photoionized gas.
This is for photoionized gas. The relationship between mass-loading factors of
different phases is not well-understood, and could be larger in molecular gas,
as suggested by Bolatto et al. (2013b). A detailed study of the resolved
outflows in IRAS08 is current in progress (Reichardt-Chu in prep).

We find that the internal properties of IRAS08 are most consistent with a gas
inflow being driven by a galaxy wide, violent disk instability (as described
in Dekel et al., 2009; Dekel & Burkert, 2014). Not only does IRAS08 exhibit
many of the properties similar to those in this theory (e.g. clumpy, high gas
velocity dispersion, compact), but we show for the first time, in Fig. 11, a
direct consistency with the prediction from Dekel & Burkert (2014) that in
unstable disks the inflow timescale must always be less than $t_{dep}$ in
order for an inflow to be maintained. If we interpret IRAS08 as a central
burst driven by a violent disk instability, then this galaxy has implications
for observations of compaction at high-$z$. As we show in Fig. 5, in IRAS08
there is no central pile-up of molecular gas, rather it is exhausted through
star-formation on very rapid timescales. Our results imply that high-$z$ blue
nugget galaxies could convert their gas very quickly, and make a high-
concentration of molecular gas absent.

We can also consider these extremely rapid growth scenarios in light of red-
nuggets at $z>4$ (Glazebrook et al., 2017), and the formation of early-type
galaxies. The $\alpha$/Fe abundances of early type galaxies can only be
reconciled with their IMFs if they have extremely short formation timescales,
in the 10’s of Myr (Martín-Navarro, 2016). The very short $t_{dep}$ and high
$\epsilon_{ff}$ we observed in the galaxy center of IRAS08, is approaching
those short times. These $t_{dep}$ are thus not inconsistent with the compact
size and short dynamical times of high-z red nuggets, and may provide an
avenue to explain the $\alpha$-enhancement of such galaxies (Kriek et al.,
2016).

Ultimately, IRAS08 is only one galaxy. Observations of more galaxies, and
observations with alternate methods of measuring star formation efficiency
(e.g. Onus et al., 2018), are needed to further confirm this scenario.
Moreover, studies that combine both resolved measurements of $t_{dep}$ with
metrics of the feedback, such as outflow kinematics, are needed. Such
comparison could determine if the variation in $\epsilon_{ff}$ is due to a
true change in star formation efficiency or if feedback is more efficiently
removing gas in those regions. We note that to observe sufficiently small
spatial scales to measure the $\epsilon_{ff}$ at high $\Sigma_{mol}$ will
require either observations of rare local galaxies like ours or lensed
galaxies at larger redshift.

We are thankful to Cinthya Herrera for help in reducing NOEMA data. This
manuscript was significantly improved due to conversations with Adam Leroy,
Mark Krumholz and Andreas Burkert, as well as thoughtful comments from the
referee. DBF is thankful to Sarah Busch for technical help. DBF acknowledges
support from Australian Research Council (ARC) Future Fellowship FT170100376
and ARC Discovery Program grant DP130101460. ADB acknowledges partial support
form AST1412419. GGK and NMN acknowledges support from ARC DP170103470. This
work is based on observations carried out under project number W17CB with the
IRAM NOEMA Interferometer. IRAM is supported by INSU/CNRS (France), MPG
(Germany) and IGN (Spain). 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.
Observations were supported by Swinburne Keck program 2018A_W185. The authors
wish to recognise 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.

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##  Appendix A Wide Separation Interaction & Possible Galactic Transfer of Gas

IRAS08 is currently experiencing an interaction with a nearby, lower mass
companion galaxy at a separation of $\sim$60 kpc. In interacting systems there
is a complex relationship between mass-ratio, interaction distance, gas
content and gas depletion timescale (e.g. Combes et al., 1994; Renaud et al.,
2019). Similar to the expectations from the violent disk instability we will
compare the properties of the interaction in IRAS08 to those observed in other
merging galaxies, to determine if IRAS08 exhbits a natural extension of the
behavior that is typical of mergers.

In the GOALS team classification system for mergers (Larson et al., 2016) the
IRAS08 system is a “minor merger” due to the mass-ratio. Minor mergers are
defined as having a ratio $>$4:1 of the galaxy to the companion that is likely
on the early-stage initial approach. IRAS08 has a ratio of at least
$\sim$10:1. Observations indicate that even large mass ratio, distant galaxy
interactions can increase the SFR of the larger galaxy (Ellison et al., 2008).
Simulations suggest that for those large mass ratios ($\sim$10:1) have only a
marginal impact on the structural and kinematic properties of the larger
galaxy (Cox et al., 2008).

Figure 12.— The galaxy averaged molecular gas depletion time of IRAS08 is
compared to interacting galaxies from the GOALS sample. Depletion time,
$t_{dep}$, is plotted against projected separation of the merging galaxies,
$d_{sep}$ for major mergers (mass ratio $<4:1$, filled dark red diamonds),
minor mergers (mass ratio $>4:1$, open red diamonds) and IRAS08 (blue square).
IRAS08 is a minor merger with a large separation, and a significant outlier
from the behavior of merging galaxies in the GOALS sample.

Figure 13.— Here we replot Fig. 5 adding wide-seperation early-stage merging
galaxies NGC 3110 & NGC 232 from Espada et al. (2018). The two interacting
systems are shown as brown and red symbols. The separations for these systems
are 38 kpc (NGC 3110) and 50 kpc (NGC 232). Neither of these galaxies exhibit
similar radial dependence of $t_{dep}$ as IRAS08.

Cannon et al. (2004) show in HI maps that there is a significant reservoir of
HI gas extending between the targets. The exact origin of the HI gas is not
wholly known. HST/COS observations of IRAS08 show very strong outflows of gas
coming out of the center of the galaxy (e.g. Chisholm et al., 2015). Indeed,
Cannon et al. (2004) hypothesize that the HI could be related to an outflow.
However, based on present observations it is equally likely that the gas has
been ejected from the companion, and may represent a transfer of mass from
companion to primary galaxy. Hafen et al. (2019) use simulations to argue that
this is one of the most common ways for galaxies to exchange gas. More work is
needed to characterise the nature of the large radius HI gas. Independent of
its origin the HI plume has a mass of $\sim 3\times 10^{9}$ M⊙, which is a few
percent of the baryonic mass of IRAS08. While by no means a major-merger, this
could provide a torquing force to the galaxy. Indeed, in Fig. 1 there is a
slight asymmetry to the spiral arms that may indicate an asymmetric
gravitational potential.

In Fig. 13 we show that the galaxy averaged $t_{dep}$ for IRAS08 is
significantly lower than other merging galaxies from the GOALS sample (Armus
et al., 2009). The GOALS sample is significantly well studied in a large
number of publications, with a comprehensive set of observations, and
therefore is a useful benchmark for properties of merging galaxies. Larson et
al. (2016) compares morphological merger classification and separation
distance to gas content of interacting galaxies. As we show in Fig. 13,
significantly low values of $t_{dep}$ is only observed in interacting galaxies
with small separations ($d_{sep}<10$ kpc). Even in major-mergers (mass-ratio
$<4:1$) with small separation it is not guaranteed that the depletion time is
always decreased in merging systems. When viewed as an interacting galaxy
IRAS08 is a significant outlier from the typical behavior of interacting
galaxies in the GOALS sample, and does not seem to follow the trends of other
interacting galaxies.

Local galaxy M 51 is also experiencing a minor-merger that is far more
advanced than IRAS08. The distribution of molecular gas in M 51 is very well
studied Leroy et al. (2013); Meidt et al. (2015); Leroy et al. (2017), and as
we show in Fig. 8 it does not have the same trend of $\epsilon_{ff}$ with
radius as in IRAS08.

In Fig. 13 we show that the radial profile of $t_{dep}$ in two similarly wide-
separation interacting galaxies (Espada et al., 2018) do not exhibit the same
gradient as IRAS08. The two galaxies studied by Espada et al. (2018) are well
matched in gas fraction, SFR, total stellar mass, and merger impact parameters
to IRAS08, and therefore provide a well controlled comparison. NGC 3110 has a
separation of $\sim$40 kpc as mass ratio of 14:1, making it a very early stage
minor-merger, like IRAS08. NGC 232 also has a wide-seperation of $\sim$50 kpc,
but with a much more significant mass-ratio of 4:5 with its companion. Both
galaxies are massive, M${}_{star}\approx 6\times 10^{10}$ M⊙ and star forming
$SFR\sim 15-28$ M⊙ yr-1. Neither galaxy shows the same strong decline in
$t_{dep}$ toward the galaxy center. Indeed, both NGC 3110 and NGC 232 show a
mild increase in $t_{dep}$ in the galaxy center. Other significant differences
exists between these two interacting systems and IRAS08. Both NGC 3110 and NGC
232 have very strong gradients in molecular gas velocity dispersion, and both
have a disk averaged surface density that is much lower,
$\Sigma_{mol}^{disk}\approx 8-21$ M⊙ pc-2. Whereas IRAS08 has a nearly
constant $\sigma(R_{gal})$, Fig. 4, and the surface density at the edge of the
disk of order $\sim$100 M⊙ pc-2. Espada et al. (2018) shows that the molecular
gas surface density in both NGC 232 & NGC 3110 is high in the center, and
provide arguments that this is driven by the interaction. However, in NGC 232
and NGC 3110 this does not translate to a lower $t_{dep}$ in the galaxy
center.

We can also find that NGC 232 and NGC 3110 do not satisfy predictions of the
violent disk instability model. Espada et al. (2018) used numerical
simulations to established that the gas flows in NGC 232 and NGC 3110 are most
likely due to the interaction from the host. These systems therefore offer a
good test to determine of the violent disk instability model. If these
galaxies have low $t_{inflow}$ and low $Q$ then this would weaken the case
that these metrics are meaningful for IRAS08. We consider the disk and central
values for these galaxies using data from Espada et al. (2018) as inputs into
Equations 3 & 4 of this paper. At large radius, in the disk, we find $Q\approx
2.9$ & 1.75 for NGC 232 and NGC 3110, respectively. We also find inflow
timescales of 7 Gyr and 12 Gyr. In both cases the Toomre parameter suggests
the disk is stable and $t_{inflow}>t_{dep}$. This is not consistent with
violent disk instabilities as drivers of the gas inflow in NGC 232 and NGC
3110. Even in the galaxy center the value for Toomre Q remains high; for both
targets $Q(R=1~{}kpc)\approx 2$. To be clear, this does not mean that IRAS08
is necessarily driven by the instability. It is however a useful to see that
$t_{inflow}$ and $Q$ do not result in “false positive” results when we have
independent evidence that a gas flow is not driven by an instability.

If the gas flow in IRAS08 is driven by its interaction, then this interaction
would be different from other interactions observed in the local Universe.
IRAS08 has a molecular gas depletion time that is as short as what is observed
in advanced stage mergers (Wilson et al., 2019; Bemis & Wilson, 2019), yet has
completely different morphology and kinematics from those systems. Moreover,
the strong gradient in $t_{dep}$ is not observed in other wide-separation
interacting systems (Espada et al., 2018).

##  Appendix B Stellar Bar

The F550M image of IRAS08 shows a stellar bar (Fig. 1) in the center of this
galaxy. Simulations clearly establish that bars can impact the distribution of
gas in galaxies (e.g. Athanassoula, 1992; Simkin et al., 1980). Here we
consider the possibility that this bar may contribute to the radial change in
$t_{dep}$ and $\epsilon_{ff}$.

The exact impact of bars on gaseous disks is somewhat complex. Along bars star
formation tends to be suppressed. This is thought to be due to strong shocks
(Athanassoula, 1992), which increase the velocity dispersion of the molecular
gas (Maeda et al., 2018). The gas then concentrates in the galaxy centers.
Indeed, observations of barred galaxies show preferentially higher molecular
gas mass surface densities than non-barred galaxies (Sheth et al., 2005; Jogee
et al., 2005; Fisher et al., 2013). However, observations do not show strong
evidence for a significant change in the $t_{dep}$ inside of bars (Fisher et
al., 2013). Indeed, the majority of disk galaxies in the HERACLES survey
(Leroy et al., 2013) are barred systems, as it draws from the general
population of star forming disk galaxies. It is this sample that we use for
comparison of the radial gradient in $t_{dep}$ (Fig. 5). If barred galaxies
showed a significant decrease in $t_{dep}$ in the central kiloparsec this
would be dected in Fig. 5, but we see only a slight change toward the center.

It is important to point out that there are substantial differences between
the properties of galaxies in most simulations of barred galaxies and in
IRAS08 (e.g. Athanassoula, 1992; Regan et al., 1997; Maciejewski et al.,
2002). The overall gas velocity dispersion and total gas fraction in IRAS08
are significantly larger than in simulations set to match the Milky Way.
Moreover, the bar in IRAS08 is only $\sim$2$\times$ larger that than the
Toomre length derived for this galaxy, which gives an expected size of
molecular clouds. Whereas in more typical local barred galaxies the
characteristic giant molecular cloud size is 10-100$\times$ smaller than the
bar. It is not clear how this might affect the interaction between bars and
gas. For example, Maciejewski et al. (2002) find that small-scale bars do not
produce shocks in galaxy centers, a similar phenomenon could occur in IRAS08.
To our knowledge there are no simulations of the impact of bars in a gas
medium that has a high velocity dispersion.

Figure 14.— The above figure compares the radial profile of $t_{dep}$ to the
ellipticity of the 500 nm flux. The rise in ellipticity of starlight indicates
the location of the bar. The bar in IRAS08 likely only impacts the gas at
radii $R_{gas}<1$ kpc, which is much smaller than the bulk trend in $t_{dep}$.

In Fig. 14 we compare the ellipticity of the star-light to the molecular gas
depletion time, both as function of radius within the galaxy. There is debate
in the literature about exactly where to place the bar length (see discussion
in Erwin et al., 2005; Marinova & Jogee, 2007). We use the ellipticity profile
of IRAS08 to identify the bar, and choose the bar length as the radius beyond
which the ellipticity decrease by 15% from the peak value. Numerical
simulations find that this radius is in good agreement with bar lengths as
defined by orbital analysis (Martinez-Valpuesta et al., 2006). Moreover, when
overlaying this ellipse on the F550M image we find that this radius
corresponds to the point at which the bar meets the ring of gas. Fig. 14 shows
that the decrease in $t_{dep}$ begins far beyond the radius of the bar.

We note that the ring just beyond the bar, identified as a minimum in the
ellipticity profile, is colocated with a relative increase in $t_{dep}$ and a
decrease in $\epsilon_{ff}$. Typically, in nearby spiral galaxies rings are
associated with more efficient star formation than in the surrounding disk
(e.g. Kormendy & Kennicutt, 2004). Rings are found to be very common in disk
galaxies at $z>1$ (Genzel et al., 2014), and 4 of 10 galaxies in the DYNAMO
sample of gas-rich, clumpy disks show evidence of rings (Fisher et al.,
2017b). If rings behave differently in gas-rich galaxies than in local spirals
this may be an interesting avenue for further research.

In general, there is not strong evidence that bars lead to enhanced star
formation efficiencies in their centers. In IRAS08 the general trend of
decreasing $t_{dep}$ begins at radii 3-4$\times$ the bar radius, also
suggesting this may be a galaxy wide phenomena rather than the bar.

Empirically speaking it is very difficult to determine if the presence of the
bar should impact our treatment of IRAS08 as a similar phenomenon as $z>1$
unstable disk galaxies. First, the bar length in IRAS08 is $\lesssim 1$ kpc.
If IRAS08 were observed at the same resolution as a $z\sim 2$ galaxy with HST
this bar would be covered by only 1-2 resolution elements. It would thus not
be so straightforward to identify the bar. Moreover, bars are far more easy to
identify in redder wavelengths (Eskridge et al., 2002), and observations of
restframe V-band light have significantly lower signal-to-noise at $z=2$, it
is conceivable that systematic uncertainties in observations lead to a lower
frequency of observed bars at $z>1$. Finally, bars, rings and spiral structure
in local Universe disks are known to be related phenomena (for review Kormendy
& Kennicutt, 2004). Sprials and rings are by no means absent from the high-$z$
universe. Spiral galaxies have been observed at $z>2$ (Yuan et al., 2017), and
recent work with ALMA identifies central concentrations of elongated
structures in galaxies at $z>2$ (Hodge et al., 2019). Inoue et al. (2016)
argues that massive star forming clumps in many galaxies at $z>1$ may be
intrinsically linked to spirals. As noted above, rings are likewise very
common at $z>1$. In short, we will not know if small scale bars (R$\lesssim$1
kpc) are common at $z>1$ until the advent of next-generation adaptive optics
instruments such as VLT-MAVIS, ELT-MICADO, or TMT-NFIRAOS come on-line in the
later part of the next decade.

In summary though bars are well known to drive high molecular gas mass surface
density in galaxy centers, the evidence from samples of barred galaxies is
that they do not lead to significant changes to the gradient of $t_{dep}$.
Moreover, in IRAS08 the bar is quite small, whereas the gradient in $t_{dep}$
and $\epsilon_{ff}$ is a phenomenon that covers the entire disk. At a finer
detail, the bar in IRAS08 is probably playing some role in gas redistribution
in the central $R_{gas}<0.5$ kpc, however, it does not seem to be the main-
driver of the full gradient in $t_{dep}$.