# DUVET: Spatially Resolved Observations of Star Formation Regulation via
Galactic Outflows in a Starbursting Disk Galaxy

Bronwyn Reichardt Chu Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, Hawthorn, VIC 3122, Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)  Deanne B.
Fisher Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, VIC 3122, Australia  ARC Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D)  Alberto D. Bolatto Department of
Astronomy, University of Maryland, College Park, MD 20742, USA  John Chisholm
Department of Astronomy, University of Texas, Austin, TX 78712, USA  Drummond
Fielding Center for Computational Astrophysics, Flatiron Institute, 162 Fifth
Avenue, New York, NY 10010, USA  Danielle Berg Department of Astronomy,
University of Texas, Austin, TX 78712, USA  Alex J. Cameron Department of
Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford,
OX1 4RH, UK  Karl Glazebrook Centre for Astrophysics and Supercomputing,
Swinburne University of Technology, Hawthorn, VIC 3122, Australia  ARC Centre
of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)  Rodrigo
Herrera-Camus Departamento de Astronomía, Universidad de Concepción, Barrio
Universitario, Concepción, Chile  Glenn G. Kacprzak Centre for Astrophysics
and Supercomputing, Swinburne University of Technology, Hawthorn, VIC 3122,
Australia  ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO 3D)  Laura Lenkić SOFIA Science Center, USRA, NASA Ames Research
Center, M.S. N232-12, Moffett Field, CA 94035, USA  Miao Li  Department of
Physics, Zhejiang University, 866 Yuhangtang Road, Hangzhou, 310058, China
Daniel K. McPherson Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, Hawthorn, VIC 3122, Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)  Nikole M.
Nielsen Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, VIC 3122, Australia  ARC Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D)  Danail Obreschkow International
Centre for Radio Astronomy Research (ICRAR), M468, University of Western
Australia,
35 Stirling Hwy, Crawley, WA 6009, Australia  Ryan J. Rickards Vaught Center
for Astrophysics and Space Sciences, Department of Physics, University of
California, San Diego, CA, USA  Karin Sandstrom Center for Astrophysics and
Space Sciences, Department of Physics, University of California, San Diego,
CA, USA

###### Abstract

We compare 500 pc scale, resolved observations of ionised and molecular gas
for the $z\sim 0.02$ starbursting disk galaxy IRAS08339+6517, using
measurements from KCWI and NOEMA. We explore the relationship of the star
formation driven ionised gas outflows with colocated galaxy properties. We
find a roughly linear relationship between the outflow mass flux
($\dot{\Sigma}_{\rm out}$) and star formation rate surface density
($\Sigma_{\rm SFR}$), $\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm SFR}^{1.06\pm
0.10}$, and a strong correlation between $\dot{\Sigma}_{\rm out}$ and the gas
depletion time, such that $\dot{\Sigma}_{\rm out}\propto t_{dep}^{-1.1\pm
0.06}$. Moreover, we find these outflows are so-called “breakout” outflows,
according to the relationship between the gas fraction and disk kinematics.
Assuming that ionised outflow mass scales with total outflow mass, our
observations suggest that the regions of highest $\Sigma_{\rm SFR}$ in IRAS08
are removing more gas via the outflow than through the conversion of gas into
stars. Our results are consistent with a picture in which the outflow limits
the ability for a region of a disk to maintain short depletion times. Our
results underline the need for resolved observations of outflows in more
galaxies.

Galaxy winds (626) — Galaxy evolution (594) — Starburst galaxies (1570)

††facilities: Keck:II (KCWI), IRAM:NOEMA††software: koffee (Reichardt Chu et
al., 2022, https://github.com/bronreichardtchu/koffee/tree/PaperI-code),
astropy (Astropy Collaboration et al., 2013, 2018)

##  1 Introduction

Galactic outflows are observed ubiquitously in star-forming galaxies across
cosmic time (Heckman et al., 2000; Chen et al., 2010; Steidel et al., 2010;
Newman et al., 2012; Rubin et al., 2014; Arribas et al., 2014; Rodríguez del
Pino et al., 2019; Bolatto et al., 2021; Veilleux et al., 2020) and have a
critical role in galaxy evolution models (e.g. Somerville & Davé, 2015). When
star formation driven outflows are not included, models are unable to
reproduce basic galaxy properties such as the galaxy mass function, galaxy
sizes, and the Kennicutt-Schmidt Law (see review by Somerville & Davé, 2015).
The most energetic winds are observed coming from active galactic nuclei
(Veilleux et al., 2005; Fluetsch et al., 2019; Förster Schreiber et al.,
2019), which send gas into the halo (Nelson et al., 2019; Oppenheimer et al.,
2020). Galactic fountains arising from clusters of intense star formation
remove gas from their local region (e.g. Bolatto et al., 2013b; Leroy et al.,
2015a; Salak et al., 2020), which is then recycled into the disk after moving
through the lower regions of the halo.

Star formation driven outflows are widely thought to play multiple roles in
regulating star formation. One such role is to directly remove gas from
regions of active star formation, for example as observed in nearby starbursts
NGC 253 (Bolatto et al., 2013b) and M 82 (Leroy et al., 2015b). In such
environments the mass loss rate due to the wind can be comparable to the rate
at which gas is converted into stars.

Moreover, theory argues that the energy and momentum injected from supernovae
driven winds plays a regulatory role by increasing the turbulence of the
interstellar medium (e.g Ostriker et al., 2010; Faucher-Giguère et al., 2013;
Hayward & Hopkins, 2017; Krumholz et al., 2018). The increased turbulence is
critical to providing pressure support in galaxies, setting the thickness of
the gas disk and preventing runaway star formation, and is known as star
formation feedback. This regulation generates a local balance between the
inward gravitational pressure on the disk, characterised by the molecular and
stellar mass surface densities, and the outward pressure provided by the
feedback, which is typically characterised by the star formation rate (SFR)
surface density multiplied by an efficiency factor (for description see Kim et
al., 2013). Observations do recover positive correlations of gravitational
pressure with SFR surface density over 6 orders-of-magnitude (Fisher et al.,
2019; Barrera-Ballesteros et al., 2021; Sun et al., 2020; Girard et al.,
2021), albeit those published thus far find shallower power-law slopes than
theory predicts. Ostriker & Kim (2022) argued that this may be due to
systematics in the estimations of pressure. Lenkić et al. in prep will
investigate this. It is not clear how outflows may impact feedback regulated
star formation theory. Theoretical work employing results from supernova
clustering suggest that clustering may lead to increases in the momentum input
into the ISM (Gentry et al., 2020; Fielding et al., 2018). Conversely, Orr et
al. (2022) argued that if winds leave the disk they carry momentum with them,
which might reduce turbulence.

Current theory therefore implies that supernova driven winds (or outflows)
play multiple roles (1) removing gas directly from disks and (2) injecting
turbulence into the ISM. Resolved observations of outflows are, however,
challenging due to the intrinsic faintness of the spectral features of the
wind. We use data from the DUVET sample (Fisher et al. in prep) that uses high
signal-to-noise observations from the Keck Cosmic Web Imager (KCWI) to study
resolved properties of outflows in rare starburst disk galaxies at $z\approx
0.01-0.03$ (e.g Cameron et al., 2021; Reichardt Chu et al., 2022). In this
paper, we focus on using resolved outflow observations of IRAS 08339+6517 from
the DUVET sample to compare the properties of molecular gas and star
formation.

The paper is organised as follows. We describe our target galaxy, IRAS
08339+6517 (hereafter IRAS08), in Section 2.1. Our observations and data
reduction of IRAS08 for ionised gas are described in Section 2.2, and for
molecular gas in Section 2.3, together with our methods. In Section 2.4 we
find resolved stellar masses for IRAS08. In Sections 3.1, 3.2 and 3.3 we
explore the relationship between outflows and the star formation rate surface
density and the molecular gas surface density. In Sections 3.4 and 3.5 we
compare our resolved outflow observations to models. A summary of our results
and conclusions is presented in Section 4. We assume a flat $\Lambda$CDM
cosmology with
$H_{0}~{}=~{}69.3~{}\mathrm{km}~{}\mathrm{Mpc}^{-1}~{}\mathrm{s}^{-1}$ and
$\Omega_{0}=0.3$ (Hinshaw et al., 2013).

Figure 1: Maps of IRAS08. (Left) Map of H$\alpha$ flux from HST. (Right) Mass
outflow flux, $\dot{\Sigma}_{\rm out}$, found in each spaxel using [OIII]
$\lambda$5007 and H$\beta$ emission line flux from observations with KCWI on
Keck II (Reichardt Chu et al., 2022). Only spaxels where an outflow was
detected are included. The $\dot{\Sigma}_{\rm out}$ values were scaled to
assume electron densities of $n_{e}=100~{}\mathrm{cm^{-3}}$. Outflowing gas
driven by star formation has been resolved across the disk of IRAS08.

##  2 Observations and Methods

Our analysis combines observations of outflows from Reichardt Chu et al.
(2022) (hereafter RC22) with observations of molecular gas from Fisher et al.
(2022) (hereafter F22). All data have been published, and the data reduction
methods are described in more detail in those papers. We briefly summarise
these data and methods here.

###  2.1 IRAS 08339+6517

IRAS08 is a face-on, UV-bright, blue-compact galaxy at $z\approx 0.0191$. It
is a $10\times$ outlier from the $z=0$ star forming main sequence. In Figure 1
we show the H$\alpha$ flux map from $HST$, which shows IRAS08’s star forming
ring. IRAS08’s young stellar population has been shown to be consistent with
containing super-star clusters in $HST$/COS spectra (Otí-Floranes et al.,
2014). For more physical properties of IRAS08, see Table 1.

Table 1: Galaxy properties for IRAS 08339+6517. Property |  | Value | Reference
---|---|---|---
Redshift | $z$ | 0.0191 | Kim et al. (1995)
Inclination | $i$ | $13^{\circ}$ | Leitherer et al. (2013)
Stellar mass | $\mathrm{M}_{*}$ | $1.1\pm 0.3\times 10^{10}~{}\mathrm{M}_{\odot}$ | F22
Star formation rate | SFR | $12.1\pm 1~{}\mathrm{M}_{\odot}~{}\mathrm{yr}^{-1}$ | F22
Stellar population age |  | 10 Myr | Leitherer et al. (2002)
Molecular gas fraction | $f_{\rm gas}$ | 17% | F22
Toomre stability parameter | $Q_{\rm gas}$ | 0.5 | F22
Resolved ionised gas mass outflow rate ($n_{e}=100$ cm-3) | $\dot{\rm M}_{\rm out}$ | 34.7 $\mathrm{M_{\odot}~{}yr^{-1}}$ | RC22
Resolved ionised gas mass outflow rate ($n_{e}=300$ cm-3) | $\dot{\rm M}_{\rm out}$ | 11.6 $\mathrm{M_{\odot}~{}yr^{-1}}$ | RC22
Total galaxy ionised gas mass loading factor (from absorption) | $\dot{\rm M}_{\rm out}/{\rm SFR}_{\rm COS}$ | 0.07 | Chisholm et al. (2017)
Resolved ionised gas mass loading factor ($n_{e}=100$ cm-3) | $\eta$ | 3.2 | RC22

IRAS08 is well known to host a strong outflow (Leitherer et al., 2013;
Chisholm et al., 2015; Reichardt Chu et al., 2022). The benefit of studying
IRAS08 is that since it is mostly face-on, we can make point-to-point
comparisons between outflow properties and the molecular gas.

###  2.2 KCWI observations of SFR and outflows

IRAS08 was observed with the Keck Cosmic Web Imager (KCWI, Morrissey et al.,
2018) using the BM grating in the Large Slicer mode (FOV: $33\farcs\times
20\farcs 4$) for 20 minutes with the central wavelength setting at
$\lambda=4800$Å. These observations are described in both RC22 and F22. The
data were reduced using the standard IDL pipeline (Version 1.1.0) and in-frame
sky subtraction. A continuum fit and subtraction was applied using pPXF
(Cappellari, 2017) with BPASS templates (Version 2.2.1 Stanway & Eldridge,
2018).

To measure SFR and outflow properties we follow a very similar procedure as
described in RC22. The most significant adjustment is that we modify the
adopted electron density (discussed below).

KCWI spaxels are non-square, with dimensions $0\farcs 29\times 1\farcs 36$ for
the large slicer. RC22 carried out an analysis in which outflows were fit in
various spatial bin sizes. They found that correlations of outflow physical
properties are more stable for bin sizes of 5$\times$1 spatial sampling of the
KCWI data and larger, summing the spectra in each set of 5$\times$1 spaxels.
In order to more easily interpret the data, we resample all data sets to match
this 5$\times$1 spatial sampling of the KCWI data. This binning corresponds to
sizes of $1\farcs 46\times 1\farcs 36$, which in physical scale is 0.57
kpc$\times$0.53 kpc.

Following the method described in RC22, to identify outflows we fit both a
single and a double Gaussian profile to the H$\beta$ emission lines in spaxels
where the continuum has a signal-to-noise greater than 10 per pixel. We used
the Bayesian Information Criterion (BIC) to decide whether the extra
parameters in the double Gaussian fit are required. When two Gaussians are
required, we assume that the broad second Gaussian represents the outflowing
gas (see RC22 for more detail).

Using the double Gaussian fits, we calculated the outflow velocity

$v_{\rm out}=|v_{\rm narrow}-v_{\rm broad}|+2\sigma_{\rm broad},$ (1)

where $v_{\rm narrow}$ and $v_{\rm broad}$ are the velocities at the centre of
the narrow and broad Gaussians respectively, and $\sigma_{\rm broad}$ is the
standard deviation of the broad Gaussian. This definition of $v_{\rm out}$ is
comparable to the velocity at 90% of the continuum, $v_{90}$, measured from
absorption line studies (e.g. Rupke et al., 2005; Chisholm et al., 2015,
2016), and similar to previous emission line studies (e.g. Genzel et al.,
2011; Davies et al., 2019; Fluetsch et al., 2019).

The mass outflow rate is defined as

$\dot{M}_{\rm
out}=\frac{1.36m_{\mathrm{H}}}{\gamma_{\mathrm{H}\beta}n_{e}}\left(\frac{v_{\rm
out}}{R_{\rm out}}\right)L_{\rm H\beta,broad},$ (2)

where $m_{\mathrm{H}}$ is the atomic mass of Hydrogen,
$\gamma_{\mathrm{H}\beta}$ is the H$\beta$ emissivity at electron temperature
$T_{e}=10^{4}$ K for case B recombination
($\gamma_{\mathrm{H}\beta}=1.24~{}\times~{}10^{-25}~{}\mathrm{erg~{}cm}^{3}~{}\mathrm{s}^{-1}$,
Osterbrock & Ferland, 2006), $n_{e}$ is the local electron density in the
outflow, $R_{\rm out}$ is the radial extent of the outflow, and $L_{\rm
H\beta,broad}$ is the extinction-corrected H$\beta$ luminosity of the broad
component. We assume $R_{\rm out}=0.5$ kpc; see the discussion in RC22 for
motivation and the likely systematic uncertainty on $R_{\rm out}$.

RC22 showed that the main driver of $\dot{M}_{\rm out}$ is the luminosity of
the broad component, with only a small dependence on the outflow velocity. In
IRAS08 there is a $\sim 2$ order-of-magnitude variation in the broad-component
luminosity, but only a factor of a few change in velocity.

There is an explicit inverse dependence of $\dot{M}_{\rm out}$ on
$\gamma_{\mathrm{H}\beta}$. Since $\gamma_{\mathrm{H}\beta}$ depends inversely
on $T_{e}$, different assumptions in $T_{e}$ directly change derived
$\dot{M}_{\rm out}$. Cameron et al. (2021) provides a direct measurement of Te
from the [OIII] $\lambda$4363 line for MRK 1486. They found that Te decreases
in the outflow compared to the disk by an order of $\sim$1000 K, with a
typical outflow $T_{e}$ of $\sim$12,000-14,000 K. IRAS08 has a higher
metallicity than MRK 1486, (0.7 $Z_{\odot}$, López-Sánchez et al., 2006),
which corresponds to a lower $T_{e}$ (Kewley et al., 2019). Indeed, López-
Sánchez et al. (2006) derives T${}_{e}\sim 8,000$ K for IRAS08. There is no
evidence that the metallicity varies across the disk of IRAS08 (López-Sánchez
et al., 2006; Fisher et al., 2022). We, therefore, assume a constant $T_{e}$
throughout our outflow. Using the code PyNeb (Luridiana et al., 2015) we find
that if we assume an electron temperature for the outflow of $T_{e}=7000$ K,
the derived $\dot{M}_{\rm out}$ would be 1.4$\times$ higher than we find for
our standard assumption of $T_{e}=10^{4}$ K. Conversely, if we assume a high
electron temperature of $T_{e}=14,000$ K, the $\dot{M}_{\rm out}$ would be
0.7$\times$ lower.

We do not know a priori what electron density $n_{e}$ should be adopted for
the outflows. We only have access to the [OII] density tracer, but the broad
outflow components are blended in the spectrum such that we do not have
sufficient spectral resolution to measure the electron density of the outflow
in IRAS08. We therefore must adopt a value. The electron density of IRAS08
based on the total integrated [OII] emission line ratio from the galaxy and
outflow, together, is of order $\sim 300-400~{}\mathrm{cm^{-3}}$. Standard
assumptions expect $n_{e}$ to decline in the outflow compared to the disk,
though recent work suggests this may not be the case (Förster Schreiber et
al., 2019; Fluetsch et al., 2021). In the current paper, we are specifically
focused on the amount of mass in the outflow. We therefore adopt the electron
density scaling as done by Veilleux & Rupke (2002), where the mass outflow is
normalised to $n_{e}=100~{}\mathrm{cm^{-3}}$. We estimate that $n_{e}$
introduces a systematic uncertainty of order 0.4-0.5 dex on the outflow mass.
In a previous work, RC22 made a different assumption for $n_{e}$ in order to
compare with other observations. We discuss this further in Sections 3.3 and
3.4. To illustrate this systematic uncertainty, in Figures 2, 4 and 6 we
include points that represent a higher $n_{e}$ assumption as well as the
$n_{e}=100~{}\mathrm{cm^{-3}}$ assumption, as described in associated
captions.

To calculate the star formation rate of each spaxel in IRAS08, we use the
narrow line flux from the H$\beta$ fits, according to the conversion

${\rm
SFR}=\mathrm{C}_{\mathrm{H}\alpha}\left(\frac{L_{\mathrm{H}\alpha}}{L_{\mathrm{H}\beta}}\right)10^{-0.4A_{\mathrm{H}\beta}}L_{\mathrm{H}\beta}.$
(3)

Here C${}_{\mathrm{H}\alpha}=5.5335\times 10^{-42}$ M⊙ yr-1 (erg s-1)-1, which
assumes a Kroupa & Weidner (2003) Initial Mass Function (Hao et al., 2011).
$L_{\mathrm{H}\alpha}/L_{\mathrm{H}\beta}=2.87$ is the luminosity ratio for
electron temperature $T_{e}=10^{4}$ K and case B recombination (Osterbrock &
Ferland, 2006). $A_{\mathrm{H}\beta}$ is the extinction derived from the
observed H$\beta/$H$\gamma$ ratios and a Calzetti (2001) attenuation curve.
$L_{\mathrm{H}\beta}$ is the observed H$\beta$ luminosity.

RC22 found the spatially resolved velocity, $v_{\rm out}$, of the ionised gas
outflow to be consistent with a shallow slope in $v_{\rm
out}\propto\Sigma_{\rm SFR}^{N}$, with $N\propto 0.1-0.2$, similar to
simulations (e.g. Kim et al., 2020). IRAS08 has an integrated mass outflow
rate in ionised gas of $\dot{M}_{\rm out}$$\approx
7.9~{}\mathrm{M_{\odot}~{}yr^{-1}}$ and a corresponding ionised gas mass
loading factor of $\eta_{\rm ion}=\dot{M}_{\rm out}/{\rm SFR}\approx 0.8$ when
assuming $n_{e}=380~{}{\rm cm}^{-3}$ (RC22). In RC22 the integrated mass
loading factor $\eta_{\rm ion}$ was calculated using SFRs from only those
regions of IRAS08 where evidence of outflows is observed. These values of
$v_{\rm out}$, $\dot{M}_{\rm out}$ and $\eta$ are comparable to strong winds
in well studied local galaxies like NGC 253 (Bolatto et al., 2013b) and M 82
(Shopbell & Bland-Hawthorn, 1998), and suggest that the outflow is removing
gas from the galaxy at comparable rates to the star formation.

###  2.3 NOEMA CO(2-1) observations of molecular gas

CO(2-1) was observed in IRAS08 using the NOrthern Extended Millimeter Array
(NOEMA) for 13 hours in A configuration and 5.5 hours in C configuration.
Observations used the PolyFix correlator tuned to a sky frequency of 226.215
GHz in USB with a channel width of 2.7 km s-1 using 9 antennas. We recover CO
emission over twice the half-light radius of the stars in IRAS08 ($r_{50}\sim
1$ kpc or 2.5″) with a point source sensitivity of 1.4 mJy beam-1 in 20 km s-1
of bandwidth, and with a beam size of $0.52\times 0.47$ arcsec2 ($\sim
197\times 178$ pc2). For further details on the observations and data
reduction, see F22.

To convert CO to H2, we consider both the metallicity and compactness of
IRAS08 in selecting the appropriate conversion factor, $\alpha_{\rm CO}$.
IRAS08 has a low metallicity (0.7 $Z_{\odot}$, López-Sánchez et al., 2006),
indicating that a higher $\alpha_{\rm CO}$ should be used. On the other hand,
IRAS08 is also a compact and starbursting galaxy, suggesting a lower
$\alpha_{\rm CO}$. Following the parametrisations from Bolatto et al. (2013a)
these two properties offset each other in IRAS08. For simplicity’s sake we use
a Milky Way $\alpha_{\rm
CO}=4.36~{}\mathrm{M_{\odot}~{}(K~{}km~{}s^{-1}~{}pc^{2})^{-1}}$ corrected to
the CO(2-1) transition using a line ratio of $R_{12}=$CO(2-1)/CO(1-0)=0.7 such
that $\alpha_{\rm CO}^{2-1}=\alpha_{\rm
CO}/R_{12}=6.23~{}\mathrm{M_{\odot}~{}(K~{}km~{}s^{-1}~{}pc^{2})^{-1}}$. The
assumption of $\alpha_{CO}$ introduces a factor of $\sim$2-3 systematic
uncertainty in the gas mass surface density that is difficult to characterise
further due to the competing effects of the metallicity and the starburst.

The molecular gas fraction of IRAS08 has been measured to be of order $f_{\rm
gas}\equiv M_{\rm mol}/(M_{\rm star}+M_{\rm mol})\sim 20$% (F22). Toomre’s
$Q_{\rm gas}$ characterises the stability of a self-gravitating disk, where
disks with high velocity dispersion are unstable if $Q_{\rm gas}\leq 0.7$
(Romeo et al., 2010). Dynamically, F22 show that IRAS08 is consistent with a
galaxy wide violent disk instability (Dekel et al., 2009) with $Q_{\rm
gas}\sim 0.5$ across most of the disk, and high molecular gas velocity
dispersions of $\sim 25-30$ km s-1.

F22 used NOEMA A+C observations of IRAS08 to study the star formation
efficiency per free-fall time, $\epsilon_{\rm ff}\equiv{\rm SFR}/(M_{\rm
gas}\times t_{\rm ff})$, where the free-fall time is $t_{\rm
ff}\equiv\sqrt{3\pi/(32\mathrm{G}\rho)}$. They found at the 100 pc scale that
$\epsilon_{\rm ff}$ reaches high values in the galaxy center of $\sim
10-100\%$, which translates to a variable gas depletion time that decreases
from $t_{\rm dep,SF}\sim 1-2$ Gyr in the disk to $\sim$0.1 Gyr in the galaxy
center. The $\epsilon_{\rm ff}$ found for IRAS08 by F22 is in the range of
values expected from the models of Grudić et al. (2018), which we will discuss
further in the context of outflows later in this paper. A strongly variable
$\epsilon_{\rm ff}$ is not well explained by current theory, and motivates our
comparison to the impact that outflows may have on the star formation
regulation.

###  2.4 Stellar Mass

We determine the stellar masses in 0.53 kpc$\times$0.57 kpc regions by
applying stellar population fits using the CIGALE code (Boquien et al., 2019)
to HST/ACS image filters HRC F330W, WFC F435W, WFC F550M and Spitzer/IRAC Ch1.
Before fitting, all stellar continuum images are rotated, convolved to matched
PSF and resampled to match the sampling of the KCWI data using Python
routines. We remove backgrounds in all images by the standard process of
fitting a simple surface to the images in galaxy emission free regions. In the
case of the HST images the background is near to zero. We only measure the
stellar mass in regions of the image with significant detections of CO(2-1)
and the outflow. This restricts the measurement to regions of the stellar
continuum images with $S/N\sim 50$ or higher in individual resolution
elements.

To carry out the fitting, we assume the Calzetti et al. (2000) extinction law,
allowing for a range of extinctions between $A_{V}\approx 0.05-2.0$ We note
the typical extinction in IRAS08 is quite low, $A_{V}\approx 0.2-0.5$ similar
to derivations from the Balmer decrement. We follow the standard prescription
for starburst galaxies as outlined in CIGALE papers (e.g. Boquien et al.,
2019), and fit the star formation history with a delayed starburst
superimposed on an exponentially decaying star formation rate. The burst in
each pixel is restricted to be less than 15% of the mass. Ambachew et al.
(2022) studied the impact of the choice of SFH parametrisation using CIGALE on
derived stellar masses in galaxies similar to IRAS08, and find that it has
only a small effect. Although we calculate the SFR assuming a Kroupa IMF,
CIGALE only implements the Chabrier IMF, which has been shown to under
estimate stellar mass-to-light ratios by 5-10% in the ages that we expect for
IRAS08 (Conroy et al., 2009). We, therefore, scale the derived masses by 1.08
to match the expected mass-to-light ratio of Kroupa IMFs (Conroy et al.,
2009). We note that this is a minor adjustment compared to the systematic
uncertainty in point-to-point measurements of stellar masses in high SFR
galaxies. The typical mass-to-light ratio derived from this is of order
$M/L_{3.6}\approx 0.1-0.3$, which is consistent with similarly young, high SFR
surface density systems (Ambachew et al., 2022). We find that the overall fit
recovers a stellar mass of $\sim$1.1$\times 10^{10}$ M⊙ for the entire galaxy,
which is similar as reported elsewhere (e.g. Leitherer et al., 2013; López-
Sánchez et al., 2006).

###  2.5 Prototype Outflow Galaxies For Comparison

We will compare the molecular gas surface density, $\Sigma_{\rm mol}$, and the
star formation rate surface density, $\Sigma_{\rm SFR}$, from IRAS08 to
literature values for outflow galaxies in the local Universe (M82, NGC 253 and
NGC 1482). For these galaxies throughout this work we adopt values of
$\Sigma_{\rm mol}$ and $\Sigma_{\rm SFR}$ that are intended to be from the
area of the galaxy near the base of and likely driving the outflow, rather
than the global galaxy integrated quantity. For M82, this corresponds to a
kiloparsec wide region, which has a molecular gas surface density of
$\Sigma_{\rm mol}\sim 250$ M⊙ pc-2 and SFR surface density of $\Sigma_{\rm
SFR}\sim$2.5-3 M⊙ yr-1 kpc-2 (Leroy et al., 2015b; Kennicutt, 1989).

For NGC 253, we use the values given by Leroy et al. (2015a) for the
starbursting nuclear disk, $\Sigma_{\rm mol}\sim 560$ M⊙ pc-2 and $\Sigma_{\rm
SFR}\sim 2.9$ M⊙ yr-1 kpc-2.

For NGC 1482, we use the central kiloparsec values from Salak et al. (2020),
$\Sigma_{\rm mol}\sim 490$ M⊙ pc-2 and $\Sigma_{\rm SFR}\sim 1.3$ M⊙ yr-1
kpc-2.

Note that values of the local outflows (M 82, NGC 253, & NGC 1482) are only
used for context. We never include them in fitting relationships.

##  3 Relationship between molecular gas depletion and outflows

###  3.1 $\dot{\Sigma}_{\rm out}$ and $\Sigma_{\rm SFR}$

The outflow mass flux is defined as the mass outflow rate normalised by the
surface area of the measurement, $\dot{\Sigma}_{\rm out}=\dot{\rm M}_{\rm
out}/{\rm Area}$. This quantity is described in Kim & Ostriker (2017), and is
useful for resolved outflow studies. We show the ionised gas outflow mass
flux, $\dot{\Sigma}_{\rm out}$, for IRAS08 found using observations with KCWI
on Keck II in Figure 1. Our NOEMA observations were not deep enough to detect
broad line emission that could be associated with the molecular component of
the outflow.

It is commonly expected that a higher star formation rate surface density,
$\Sigma_{\rm SFR}$, drives a higher mass outflow rate, $\dot{M}_{\rm out}$
(e.g. Hopkins et al., 2012; Hayward & Hopkins, 2017; Arribas et al., 2014;
Heckman et al., 2015; Muratov et al., 2015; Roberts-Borsani et al., 2020). In
Figure 2 we plot $\dot{\Sigma}_{\rm out}$ against $\Sigma_{\rm SFR}$ for
IRAS08 at $\sim 500$ pc sampling scale.

Figure 2: Ionised gas outflow mass flux ($\dot{\Sigma}_{\rm out}$) compared to
star formation rate surface density ($\Sigma_{\rm SFR}$) for $\sim 500$ pc
resolution pixels in IRAS08 where we have observed an outflow. The blue points
are calculated assuming an $n_{e}$ normalised to 100 cm-3, and the faint grey
points use an assumed $n_{e}$=300 cm-3. A typical error bar is shown in the
top left corner. We fit a relationship to the two quantities, which returns a
slight non-linear correlation. Yet, within the scatter, the data is also
consistent with a linear correlation (within 1.5$\sigma$).

In IRAS08 we measure $\dot{\Sigma}_{\rm out}$ $\sim 0.1$ M⊙ yr-1 kpc-2 to
$\sim 15~{}\mathrm{M_{\odot}~{}yr^{-1}}$ kpc-2 over 2 orders of magnitude in
$\Sigma_{\rm SFR}$(Fig. 2). We find a Pearson correlation coefficient of
$r=0.8$ (p-value $=6\times 10^{-13}$) for log($\Sigma_{\rm
SFR}$)-log($\dot{\Sigma}_{\rm out}$). There is a large range in errorbars on
$\dot{\Sigma}_{\rm out}$, which would bias the fit to those few points at high
signal-to-noise. We, therefore, place a minimum uncertainty of 0.15 dex on
$\dot{\Sigma}_{\rm out}$ for the fit. Using the method of orthogonal distance
regression, we find the fit to be

$\dot{\Sigma}_{\rm out}=10^{0.43\pm 0.06}~{}\Sigma_{\rm SFR}^{1.06\pm 0.10}.$
(4)

In Fig. 2 we also show the linear bisector. If we do not constrain the
errorbars the fit returns a slightly non-linear powerlaw of $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\rm SFR}^{1.12\pm 0.09}$. The root-mean-squared (RMS)
deviation of the fit is essentially equivalent to the RMS of the bisecting
line, at 0.36 dex. Therefore, while the regression to the unconstrained
errorbars returns a slightly nonlinear fit, our results are consistent with a
linear relationship $\dot{M}_{\rm out}\propto\Sigma_{\rm SFR}$ (within
1.5$\sigma$).

While there are no observational measurements that we are aware of that
compare $\dot{\Sigma}_{\rm out}$ to $\Sigma_{\rm SFR}$, there are some studies
that investigate correlations between the integrated star formation and
outflow mass rates (e.g. Heckman et al., 2015). We note that there are
significant differences between these measurements. We are measuring
$\dot{\Sigma}_{\rm out}$ and $\Sigma_{\rm SFR}$ in ionised gas in equally
sized areas in a single galaxy at a fixed distance. Fluetsch et al. (2019)
found a slightly non-linear relationship $\dot{M}_{\rm out}\propto
SFR^{1.19\pm 0.16}$ for molecular gas outflows in local star forming galaxies.
Avery et al. (2021) found a similarly linear slope of $\dot{M}_{\rm
out}\propto SFR^{0.97\pm 0.07}$ for integrated outflows on MaNGA galaxies
using H$\alpha$ to measure outflows.

To compare to our results from IRAS08, we calculate the mass outflow rate in
ionised gas of M 82 and NGC 1482 from the total H$\alpha$ luminosity and
outflow velocity using values from Shopbell & Bland-Hawthorn (1998) and
Veilleux & Rupke (2002) respectively. For each of these, we assume, as we do
for IRAS08, $n_{e}\approx 100$ cm-3 and an $R_{out}=0.5$ kpc. We find ionised
gas mass outflow rates of $\sim$2 M⊙ yr-1 for M 82 (Shopbell & Bland-Hawthorn,
1998) and $\sim$0.6 M⊙ yr-1 for NGC 1482 (Veilleux & Rupke, 2002). These
$\dot{M}_{\rm out}$ values translate to $\dot{\Sigma}_{\rm out}\approx 2.5$ M⊙
yr-1 kpc-2 for M 82, and $\sim$0.75 M⊙ yr-1 kpc-2 for NGC 1482. We note these
are measured in edge-on systems and are thus quite different methods of
estimating the mass outflow rate. Nonetheless they are in the range of what we
measure for the high $\Sigma_{\rm SFR}$ regions in IRAS08 (see Fig. 2).

The relationship between $\Sigma_{\rm SFR}$ and $\Sigma_{\rm mol}$ we observe
in IRAS08 is broadly consistent with both theoretical expectations and
observations of entire galaxies. In the subsequent analysis it will be
important to keep track of when the fundamental driver of any relationship may
be a reflection of this strong correlation in Fig. 2.

###  3.2 Connecting $\Sigma_{\rm mol}-\Sigma_{\rm SFR}$ relationship to
outflows

Figure 3: The resolved relationship between star formation rate surface
density, $\Sigma_{\rm SFR}$, and molecular gas surface density, $\Sigma_{\rm
mol}$. The circles of IRAS08 are coloured according to the mass outflow flux,
$\dot{\Sigma}_{\rm out}$. Note that the vertical blue line is the largest of
the $\Sigma_{\rm SFR}$ error bars, the rest of the error bars are smaller than
the points. A typical error bar is shown in the top left corner. The grey
points represent data from the HERACLES sample of local spirals (Leroy et al.,
2013). NGC253 (Bolatto et al., 2013b), M82 (Leroy et al., 2015b) and NGC1482
(Veilleux & Rupke, 2002; Salak et al., 2020) are represented as a dark red
square, a black diamond and a green triangle respectively. The dashed lines
indicate where the time it takes to deplete the molecular gas through star
formation, $t_{\rm dep,SF}$, would be 0.1 Gyr (top line) and 1.0 Gyr (bottom
line). In IRAS08, a greater distance from the spiral sequence (grey points) in
$\Sigma_{\rm SFR}-\Sigma_{\rm mol}$ corresponds to outflows with higher mass
outflow rates and higher momentum flux.

There is a long history of literature discussing the resolved observations of
the relationship between $\Sigma_{\rm SFR}$ and the molecular gas surface
density, $\Sigma_{\rm mol}$, in galaxies (Kennicutt, 1989; Bigiel et al.,
2008; Genzel et al., 2011; Leroy et al., 2013; Kennicutt Jr & Evans, 2012) and
theories explaining it (Ostriker et al., 2010; Faucher-Giguère et al., 2013;
Krumholz et al., 2018; Hayward & Hopkins, 2017). F22 recently analysed the
resolved molecular gas depletion timescale for IRAS08. They find it is
consistent with a steep power-law slope for $\Sigma_{\rm SFR}$ $\propto$
$\Sigma_{\rm mol}$N, with $N\approx 1.5-1.6$, similar to starburst outflow
systems like NGC 253, M 82 and NGC 1482.

In Figure 3 we show the relation between $\Sigma_{\rm SFR}$ and the molecular
gas surface density, $\Sigma_{\rm mol}$, for IRAS08 in $\sim$0.5 kpc sampling
scale. The high $\Sigma_{\rm SFR}$ center of IRAS08 is comparable in both
$\Sigma_{\rm SFR}$ and $\Sigma_{\rm mol}$ to other well-known outflow galaxies
in the local Universe (NGC 253, M 82 and NGC 1482).

Figure 4: The outflow efficiency $\dot{\Sigma}_{\rm out}/\Sigma_{\rm mol}$ of
IRAS08 plotted against the star formation efficiency $\Sigma_{\rm
SFR}/\Sigma_{\rm mol}$ (left), and star formation rate surface density
$\Sigma_{\rm SFR}$ (right). In both panels, the blue circles represent our
IRAS08 data using $n_{e}=100~{}\mathrm{cm^{-3}}$. Fainter grey circles
represent IRAS08 if an electron density of $n_{e}=300~{}\mathrm{cm^{-3}}$ were
used. A typical error bar is shown in the top left corner. M 82, the central
kiloparsec of NGC 1482, and the centre of NGC 253 are the black diamond, green
triangle, and dark red square respectively. Open symbols for these galaxies
indicate the results for the molecular gas mass outflow rate, and filled in
symbols indicate the ionised gas mass outflow rate. In the left panel, the
one-to-one and ten-to-one ratios of the outflow efficiency to star formation
efficiency are plotted as grey dashed lines. A fit to the IRAS08 data is given
by the solid black line. In the right panel, the solid black line shows a fit
of the outflow efficiency to $\Sigma_{\rm SFR}$. In high $\Sigma_{\rm SFR}$
regions, IRAS08 drives more efficient outflows.

We colour the IRAS08 points by $\dot{\Sigma}_{\rm out}$. In Fig. 2 we showed a
tight correlation between $\dot{\Sigma}_{\rm out}$ and $\Sigma_{\rm SFR}$.
However, it is clear from Fig. 3 that there is a large spread in $\Sigma_{\rm
mol}$ for a given value of $\dot{\Sigma}_{\rm out}$. The Pearson correlation
coefficient is $r=0.8$ (p-value $=6\times 10^{-13}$) for
log($\dot{\Sigma}_{\rm out}$)-log($\Sigma_{\rm SFR}$). This reduces
significantly to $r=0.5$ (p-value $=4\times 10^{-4}$) for
log($\dot{\Sigma}_{\rm out}$)-log($\Sigma_{\rm mol}$).

The average error on the $\Sigma_{\rm SFR}$ points is 0.06 dex. This typically
small value is due to the very high S/N of the KCWI data. One point in Figures
2 and 3 shows a much larger error, and comes from a measurement made with
lower S/N than the remainder of the galaxy.

Figure 3 shows a clear trend that regions of IRAS08 with shorter molecular gas
depletion times (indicated by the dashed lines) have larger values of
$\dot{\Sigma}_{\rm out}$, as indicated by the coloured points. A powerlaw fit
to the relationship yields a power-law slope that is close-to-linear, and is
likely driven by the correlation in Fig. 2. We find

$\dot{\Sigma}_{\rm out}=10^{9.2\pm 0.5}t_{dep}^{-1.1\pm 0.06}$ (5)

with a correlation coefficient of $r=-0.85$ and a p-value of roughly
$10^{-16}$.

We can also estimate the momentum flux, defined as $dp/dt\equiv v_{\rm
out}\dot{M}_{\rm out}$. We do not plot these values, because $dp/dt$ is
primarily determined by $\dot{M}_{\rm out}$ and therefore has nearly identical
dependency as $\dot{\Sigma}_{\rm out}$. The momentum flux we measure increases
from $\sim 10^{0.7}~{}\mathrm{M_{\odot}~{}km~{}s^{-1}~{}yr^{-1}}$ to $\sim
10^{3.2}~{}\mathrm{M_{\odot}~{}km~{}s^{-1}~{}yr^{-1}}$. The highest values of
$dp/dt$ are similar to what is derived for molecular gas in M 82 (Leroy et
al., 2015b). The correlation for IRAS08 between the momentum flux and the star
formation depletion time is significant and non-linear (Pearson correlation
coefficient $r=-0.7$, p-value $=2\times 10^{-9}$), implying that regions in
IRAS08 which are more efficient at turning gas into stars are increasingly
more efficient at generating significant momentum in the outflow.

###  3.3 Outflow Efficiency

In Figure 4, we compare $\dot{\Sigma}_{\rm out}/\Sigma_{\rm mol}$, which we
refer to as the “outflow efficiency” of ionised gas, to $\Sigma_{\rm
SFR}/\Sigma_{\rm mol}$ and to the unnormalised star formation rate surface
density ($\Sigma_{\rm SFR}$). The outflow efficiency may be interpreted as the
rate at which the outflow exhausts the gas mass with the measured mass outflow
rate (assuming there is no supply of fresh gas). We will refer to $\Sigma_{\rm
SFR}/\Sigma_{\rm mol}$ as the star formation efficiency for ease of
discussion, noting the important distinction between this quantity and the
star formation efficiency per free fall time (discussed in F22, ).

In the left panel of Fig. 4 we compare the outflow efficiency to the star
formation efficiency. When outflow efficiency is greater than star formation
efficiency this suggests that outflows more rapidly remove gas from the local
region than does the conversion of gas into new stars. We note that the ratio
of these two quantities gives the more well-known metric, the mass loading
factor $\eta$, which we will consider in Section 3.4. In IRAS08 the average
log($\dot{\Sigma}_{\rm out}/\Sigma_{\rm mol}$ [yr-1])$=-8.4$ with standard
deviation of 0.55 dex. We find that 87% of measured regions in IRAS08 fall
above the one-to-one line in this space, with a median ratio of $\sim$2.4,
when assuming $n_{e}=100$ cm-3. This is similar to unresolved observations of
similar quantities, $t_{\rm dep,out}$ and $t_{\rm dep,SF}$, in Fluetsch et al.
(2019). For star formation driven winds in 8 galaxies they found that the
galaxies have longer star formation depletion times (smaller SFR/$M_{\rm
mol}$) in those galaxies with longer outflow depletion times (smaller
$\dot{M}_{\rm out}/M_{\rm mol}$).

We find the outflow efficiency and star formation efficiency are correlated
with a Pearson correlation coefficient of $r=0.7$ (p-value $=6\times
10^{-10}$). We find the resulting fit, by method of error-weighted orthogonal
distance regression, to be

$\frac{\dot{\Sigma}_{\rm out}}{\Sigma_{\rm mol}}=10^{3.5\pm
1.2}\left(\frac{\rm\Sigma_{\rm SFR}}{\Sigma_{\rm mol}}\right)^{1.35\pm 0.14}.$
(6)

This steeper than linear slope suggests that in regions of high star formation
efficiency, the outflow dominates slightly more than it does in regions with
star formation similar to that in typical spiral disks. Note that a typical
depletion time of $\sim 2$ Gyr, as is found in spirals (Leroy et al., 2013),
corresponds to a star formation efficiency of $-9.3$ dex in Fig. 4. It is
technically challenging, with present day instrumentation, to observe outflows
in typical spirals due to the lower $\dot{M}_{\rm out}$ and smaller velocity
offset (e.g. Roberts-Borsani et al., 2020). Moreover, in the main disks of
spirals the ratio of $\Sigma_{\rm SFR}/\Sigma_{\rm mol}$ changes by less than
20% with galactocentric distance within 8 kpc, not including the galactic
nucleus (Leroy et al., 2013). It is, therefore, not clear how this
relationship would behave in the disks of spiral galaxies.

We note that the systematic uncertainty introduced from $n_{e}$ would not
necessarily change the trend, however, it may imply that the ionised gas
outflow efficiency is more comparable to the star formation efficiency. If the
$n_{e}$ of the outflow changes with $\Sigma_{\rm SFR}$ within a galaxy, this
would alter the slope in Fig. 4, but we do not have any results to suggest
whether this occurs. Another large systematic uncertainty, however, is the
ratio of the outflow mass flux in different phases, specifically the ionised-
to-molecular gas ratio. Molecular gas is the more dominant phase of outflow
mass (review Veilleux et al., 2020), which increases the total $\dot{M}_{\rm
out}$ by a factor of $\sim$5-10$\times$ (Fluetsch et al., 2019; Herrera-Camus
et al., 2020). This suggests that even with a higher $n_{e}$, outflows likely
dominate over star formation in removing the gas in the starbursting center of
IRAS08. If the ratio of ions-to-molecules changes with $\Sigma_{\rm SFR}$ this
too would affect the relationship between the outflow efficiency and star
formation efficiency. In four galaxies, Fluetsch et al. (2019) found a
relatively constant relationship between the mass outflow rate measured in
ions compared to molecules.

In the right panel of Fig. 4 we compare outflow efficiency to the SFR surface
density. There is likewise a positive correlation between the quantities such
that outflows co-located with regions of high $\Sigma_{\rm SFR}$ have higher
efficiency. We find a correlation coefficient of $r\approx 0.5$ (p-value
$=8\times 10^{-5}$). We find that,

$\frac{\dot{\Sigma}_{\rm out}}{\Sigma_{\rm mol}}=10^{-7.86\pm
0.05}~{}\Sigma_{\rm SFR}^{0.83\pm 0.11}.$ (7)

We can compare this correlation to that of Fig. 2, which has a steeper power
law, higher correlation coefficient, and less scatter in the fit as indicated
by the fit uncertainties. The larger correlation coefficient implies that the
inclusion of the galactic disk molecular gas mass in the outflow efficiency
increases scatter in Fig. 4.

Figure 5: The combined $\Sigma_{\rm SFR}+\dot{\Sigma}_{\rm out}$ is compared
to $\Sigma_{\rm mol}$ for regions in IRAS08, and shown as the solid points.
Colours indicate the fraction of the total SFR in the corresponding area. A
typical error bar is shown in the top left corner. The combined SFR and
outflow mass flux represent a more complete view of gas removal. Open symbols
represent only $\Sigma_{\rm SFR}$, for comparison. In lower $\Sigma_{\rm SFR}$
regions the combination only makes a factor $\sim$2 change to the gas
depletion time (dashed lines), but at high $\Sigma_{\rm SFR}$ it decreases the
total depletion time by nearly an order of magnitude.

In Fig. 5 we compare the molecular gas surface density to the combination of
both the SFR surface density and outflow mass flux. The combination of
$\Sigma_{\rm SFR}+\dot{\Sigma}_{\rm out}$ can be thought of as a more complete
estimate of the removal of gas from the star forming region, noting of course
that the addition of molecular outflows are needed for a full accounting of
the outflow mass. The figure clearly demonstrates that the addition of both
the $\Sigma_{\rm SFR}$ and $\dot{\Sigma}_{\rm out}$, together, shortens the
depletion time significantly in the high $\Sigma_{\rm SFR}$ regions by nearly
an order-of-magnitude.

Similar to the depletion time measured with only the star formation, the
combination of outflow and star formation results in a depletion time that
varies within the galaxy and with local $\Sigma_{\rm SFR}$. This is not
surprising given our result in Fig. 2 that $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\rm SFR}$. We find for radii within 1 kpc the median
outflow+star formation depletion time ($\Sigma_{\rm mol}/(\dot{\Sigma}_{\rm
out}+\Sigma_{\rm SFR})$) is of order 0.05 Gyr. We find a similar value if we
select those regions with $\Sigma_{\rm SFR}>1$ M⊙ yr-1 kpc-2. This depletion
time increases to 0.3 Gyr for larger radii and lower $\Sigma_{\rm SFR}$. We
note that while 1 kpc is a small area, it represents over 50% of the total
star formation in the galaxy, as indicated by the colours in Fig. 5.

We reiterate that the main systematic uncertainty in our results is that the
observations of outflows are only of a single phase, and that the addition of
the molecular phase could increase the outflow mass rate by as much as an
order-of-magnitude. This would reduce the total depletion time to only
0.005-0.01 Gyr in the center of IRAS08, which is very short, and is comparable
to the free-fall time found for these regions (F22).

###  3.4 Mass-loading Factors

Figure 6: The mass loading factor of ionised gas, $\eta_{\mathrm{ion}}$, as a
function of the molecular gas surface density, $\Sigma_{\rm mol}$ (left panel)
and the star formation rate surface density, $\Sigma_{\rm SFR}$ (right panel).
Observational data from IRAS08 is given in circles coloured by outflow
efficiency using $n_{e}=100$ cm-1, with rescaled values for an electron
density of $n_{e}=300$ cm-1 as open circles. The black arrows show the
magnitude and direction the median $\eta_{\rm ion}$ value would move if we
assumed an outflow extent of $R_{\rm out}=0.1R_{\rm vir}$ (open arrow
represents the median with $n_{e}=300$ cm-1). Typical error bars for the
IRAS08 data are shown in the top right corner of each panel. We compare our
observational results from IRAS08 with results from the FIRE-2 (Pandya et al.,
2021, Figure 11) and TIGRESS (Kim et al., 2020, Figure 9) simulations. Results
from the warm-phase gas ($10^{3}<T<10^{5}$ K) from FIRE-2 are shown as grey
squares. The $\Sigma_{\rm mol}$-$\eta_{\mathrm{ion}}$ and $\Sigma_{\rm
SFR}$-$\eta_{\mathrm{ion}}$ relationships found in Kim et al. (2020) for the
cool gas component ($T<2\times 10^{4}~{}$K) are plotted with solid black
lines, and extrapolated past the parameter space they covered with the dashed
black lines. The simulation data is not inconsistent with our observational
results.

In Figure 6 we compare the mass loading factor, $\eta_{\rm
ion}=\dot{\Sigma}_{\rm out}/\Sigma_{\rm SFR}$, to $\Sigma_{\rm mol}$ and
$\Sigma_{\rm SFR}$ in IRAS08. We additionally overplot results from the recent
FIRE-2 simulations (Pandya et al., 2021) and the SMAUG-TIGRESS simulation (Kim
et al., 2020). A number of simulations and analytic theories predict a
decreasing $\eta_{\rm ion}$ with increasing $\Sigma_{\rm SFR}$ (recently
Fielding et al., 2017; Li et al., 2017; Kim et al., 2020; Pandya et al.,
2021). Observations are mixed as to how well these correlate (Arribas et al.,
2014; Roberts-Borsani et al., 2020).

In IRAS08 we find very little correlation between $\eta_{\rm ion}$ and
$\Sigma_{\rm mol}$. We find a Pearson correlation coefficient of $r=-0.23$
(p-value $=0.1$) for $\log(\Sigma_{\rm mol})-\log(\eta_{\rm ion})$. We note,
however, that values of $\Sigma_{\rm mol}$ in IRAS08 cover a fairly small
range compared to the FIRE-2 simulations. We also note that the FIRE-2
simulations calculate the total values of $\eta$ and $\Sigma_{\rm mol}$ for
entire galaxy halos, rather than resolved regions. Moreover, the values of
IRAS08, while being on the high side of the FIRE-2 data and over the Kim et
al. (2020) correlation, are not completely discrepant. Nevertheless, our data
are consistent with no correlation between $\eta$ and $\Sigma_{\rm mol}$. This
is in contrast to the steeper trend expected from both the TIGRESS and FIRE-2
simulations (Kim et al., 2020; Pandya et al., 2021). It could be that we
should expect different relations when comparing our resolved observations to
simulations on different spatial scales. In order to recover the high scatter
correlation which simulations predict between $\eta_{\rm ion}$ and
$\Sigma_{\rm mol}$, we may need to include observations of more galaxies
covering a larger range in $\Sigma_{\rm mol}$.

For $\log(\Sigma_{\rm SFR})-\log(\eta_{\rm ion})$ we similarly find a weak-to-
no trend (Pearson correlation coefficient of $r=-0.17$, p-value $=0.23$). We
note that below $\log(\Sigma_{\rm SFR}[$M⊙ yr-1 kpc${}^{-2}])\approx-0.5$ the
data in IRAS08 is much more consistent with theoretical expectations from Kim
et al. (2020) and is consistent with a negative correlation (correlation
coefficient of $r=-0.67$, p-value $=2.5\times 10^{-4}$). It is possible that
regions of the galaxy below this $\Sigma_{\rm SFR}$ follow the predicted
relationship, but that in regions with higher $\Sigma_{\rm SFR}$ the outflow
efficiency increases (see Fig. 4) and we therefore observe a flat $\eta_{\rm
ion}$. It is important to also point out that the simulations of Kim et al.
(2020) are only run to $\Sigma_{\rm SFR}\sim 1.0$ M⊙ yr-1 kpc-2 and to
$\Sigma_{\rm mol}\sim 100$ M⊙ pc-2. We have extrapolated their $\Sigma_{\rm
mol}$-$\eta_{\rm ion}$ and $\Sigma_{\rm SFR}$-$\eta_{\rm ion}$ relations past
this parameter space in order to compare to our observations of a starbursting
environment. It is unclear whether this extrapolation should hold in
starbursting environments.

We note that the systematic uncertainty of $n_{e}$ is such that assuming
higher values of $n_{e}$ would bring our observed $\Sigma_{\rm mol}-\eta_{\rm
ion}$ into better agreement with the Kim et al. (2020) prediction. This would,
however, simultaneously make the mass-loading factors too low in comparison to
$\Sigma_{\rm SFR}$.

While we observe the molecular gas surface density $\Sigma_{\rm mol}$, the
TIGRESS simulations measure the total ISM gas mass divided by the horizontal
area of the disk included in the box of the simulation. Their horizontal box
sizes range from 512 pc to 2048 pc. The largest of these is $\sim 4\times$ the
area of our pixels. Moreover, we need to be mindful that the comparison to the
FIRE-2 results is not an apples-to-apples comparison. Pandya et al. (2021)
defined particles as outflows if they flow away from the galaxy disk and reach
$0.1R_{\rm vir}$ with enough energy remaining to make it to a larger radius.
To convert the down-the-barrel observations of outflows into a mass outflow
rate we assume an “outflow radius” of $R_{\rm out}=500~{}\mathrm{pc}$ for our
target (for more details, see RC22, ). This is four times smaller than the
$0.1R_{\rm vir}$ used by Pandya et al. (2021), which would be $\sim
20~{}\mathrm{kpc}$ for a galaxy of IRAS08’s mass. We don’t know how the
velocity and density profiles of the outflow change with radius, however
assuming everything stays the same, we rescale our data to use $R_{\rm
out}=20~{}\mathrm{kpc}$. Rescaling our data decreases the median value of
$\eta_{\rm ion}$ from 2.5 to 0.06. This rescaling introduces significant
uncertainty. It would be useful in the future for simulations to estimate the
properties of outflows such as the mass loading factor of the warm ionised gas
in the region less than 10 kpc from the galaxy disk, where we observationally
measure outflow properties.

###  3.5 Breakout Outflows

Figure 7: The gas fraction, $f_{\rm gas}\equiv\Sigma_{\rm mol}/(\Sigma_{\rm
mol}+\Sigma_{\rm star})$, is compared to the orbital frequency, $\Omega$. Data
points for IRAS08 are coloured by the outflow momentum flux, $dp/dt$. A
typical error bar for the IRAS08 data is shown in the bottom left corner. The
dashed line shows the boundary predicted by Orr et al. (2022) between outflows
which break out of the disk, and outflows which are stalled within the disk
(see their Figures 1 and 2). Grey squares indicate resolved observations of
local spiral galaxies with no observed outflow. Red squares indicate the
resolved observations of the outflow in NGC 253. We find that $\sim 85\%$ of
our resolved regions are within the predicted region for breakout outflows.

In a series of papers, Orr et al. (2021, 2022) considered the impacts of
supernova clustering on the regulation of star formation by stellar feedback,
and the conditions in which supernovae leave the disk or impart their momentum
to the ISM. They outlined the scenarios in which a resulting superbubble
generated by a supernova explosion expands until it either breaks out of the
galaxy disk, or stalls within the galaxy. This simple, yet predictive, model
is motivated by and is consistent with simulations of outflows (Fielding et
al., 2018) and star cluster formation (Grudić et al., 2018). As the authors
define it, in the event of “breakout”, more than 60% of the momentum from the
subsequent supernovae transfers to the outflow rather than coupling to the
ISM.

Orr et al. (2021) put forward the prediction that a boundary line exists in
the parameter space between local gas fraction, $f_{\rm gas}\equiv\Sigma_{\rm
gas}/(\Sigma_{\rm gas}+\Sigma_{\rm star})$, and the orbital frequency,
$\Omega\equiv v(R)/R$, that determines whether an outflow travels beyond the
vertical scale-height of the disk (i.e. breakout) or stays bound inside the
disk (i.e. stalled) (see also Orr et al., 2022).

We compare our observations for IRAS08 to the predictions from Orr et al.
(2022) in Figure 7. We find that the vast majority ($\sim 85\%$) of our
resolved regions in IRAS08 have $f_{\rm gas}$ and $\Omega$ consistent with the
predicted region for breakout outflows. We take the velocity models used in
F22 for IRAS08, in which a flat rotation curve is fit to the CO(2-1) data,
such that $v(R)=v_{\rm flat}[1-\exp(-R/r_{\rm flat})]$. There is a significant
systematic uncertainty in IRAS08 due to the low inclination of the galaxy. We
adopt $i\approx 20^{\circ}$, which F22 derived from the HST/F550M isophotes at
large radius, which is similar to the assumed inclination in Leitherer et al.
(2013). An uncertainty in the inclination angle of $\pm 5^{\circ}$ would
result in an uncertainty in Figure 7 of $\pm 0.15$ dex in $\log(\Omega)$.
Observationally this produces a challenging balance, as outflows would become
more difficult to observe in more highly inclined systems. The figure also
compares the IRAS08 measurements to NGC 253, which is known to contain an
outflow. Given that we have thus far seen similar behaviour between NGC 253
and IRAS08, it is therefore further consistent that both are above the
breakout line. Moreover, as a control Orr et al. (2022, see their Fig. 1)
showed data for 4 spiral galaxies that are known to not have outflows, which
we show are not colocated with IRAS08.

We can compare the outflow velocity in IRAS08 to local velocity dispersion to
check if the Orr et al. (2021, 2022) breakout scenario is consistent with
outflows moving beyond the scale-height of the disk. The scale-height of a
disk is set by $h_{z}\propto\sigma^{2}/\Sigma_{\rm gas}$, where $\sigma$ is
the velocity dispersion (see discussion in Wilson et al., 2019). For standard
scenarios, if an outflow is moving faster than $\sigma$ it will reach the
scale-height of the disk. F22 showed that the velocity dispersion of the
molecular gas is on average 25$\pm$6 km s-1, with the highest values being
$\sim$40 km s-1. The minimum of our estimated outflow velocities, $v_{\rm
out}$, is of order 130 km s-1, which is well above the dispersion of the disk,
even if we account for systematic differences between ionised and molecular
gas velocity dispersions (Girard et al., 2021). The position of IRAS08 in the
$f_{\rm gas}-\Omega$ diagram is therefore consistent with the theory put
forward in Orr et al. (2021). We can also argue that this implies the
depletion of gas discussed in previous sections is indeed leaving the plane of
the disk, and removing gas from star formation.

Orr et al. (2021) also predicted that at fixed $f_{gas}$ and larger $\Omega$
less momentum couples to the gas in the disk, and more momentum couples to the
outflow. For every unit of new stellar mass which is formed, there is an
amount of momentum which is available to be coupled to the surrounding gas
(ISM or outflow). We do not know the exact relationship between our observable
outflow momentum flux, $dp/dt$, and the amount of momentum per unit new
stellar mass formed, $p/m_{*}$. While we cannot observe the momentum which
couples to the ISM gas, we can observe the momentum flux of the outflow in
each region. In Figure 7 we colour the points of IRAS08 by their outflow
momentum flux. We find that increasing $\Omega$ corresponds with increasing
momentum flux within the outflow, i.e. outflows launched closer to the galaxy
center have greater momentum. Note that to first order $dp/dt$ simply traces
$\dot{M}_{\rm out}$, we therefore expect similar correlations with
$\dot{\Sigma}_{\rm out}$. There are a number of uncertainties, not the least
of which is likely the phase distribution of the momentum of the outflow (see
Fielding & Bryan, 2022 for an in-depth theoretical exploration of the momentum
content of multiphase galactic winds). Nonetheless, it is plausible that as
more momentum flux is incorporated in the outflow this would imply that less
is available to generate turbulence in the ISM. The effect is thus to decrease
the effective $p/m_{*}$ felt by the disk surrounding the outflow.

##  4 Summary & Discussion

###  4.1 Summary

We present resolved measurements of IRAS08 in ionised gas using KCWI/Keck and
molecular gas using NOEMA. We use these observations to relate the molecular
gas mass and star formation observed in the galaxy to the resolved outflow and
its properties. We have shown that the combined comparison of $\Sigma_{\rm
SFR}$, $\Sigma_{\rm mol}$ and $\dot{\Sigma}_{\rm out}$ allows for very direct
comparison to theory, in which three parameters that are thought to combine to
regulate star formation in disk galaxies are characterised.

We have shown direct correlation between the resolved $\Sigma_{\rm SFR}$ and
the co-located outflow mass flux, $\dot{\Sigma}_{\rm out}$, in regions of
$\sim$500 pc. We find that $\dot{\Sigma}_{\rm out}$ correlates much more
strongly with $\Sigma_{\rm SFR}$ than $\Sigma_{\rm mol}$. This leads to a
connection between outflow strength and location in the Kennicutt-Schmidt
relationship between $\Sigma_{\rm SFR}-\Sigma_{\rm mol}$, such that regions of
the galaxy with shorter molecular gas depletion times have stronger outflows.
There is therefore a strong, superlinear relationship between the outflow
efficiency $\dot{\Sigma}_{\rm out}/\Sigma_{\rm mol}$ and the inverse of the
gas depletion time $t_{\rm dep}^{-1}=\Sigma_{\rm SFR}/\Sigma_{\rm mol}$.

We find that the mass-loading factors we observe are consistent with
predictions from multiple simulations (Pandya et al., 2021; Kim et al., 2020).
The outflows we resolve are consistent with breakout outflows according to the
region in the $f_{\rm gas}-\Omega$ plane defined by Orr et al. (2021, 2022).
For our galaxy we can compare the velocity of the outflow to the local
velocity dispersion, which we indeed find is consistent with outflows
travelling fast enough to leave the disk.

###  4.2 Systematic Uncertainties

In this paper we attempt to derive physical quantities of outflows from
observations. This is necessary to compare to theory and simulation, however
the derivation is heavily impacted by assumptions that introduce systematic
uncertainties. We do not have strong constraints on how the $n_{e}$ of the
outflow changes across either a range of galaxies, or for regions within a
galaxy. Moreover, outflows are clearly multiphase phenomena (e.g Fluetsch et
al., 2021, 2019; Herrera-Camus et al., 2020). However, the ratio of the mass
outflow rate in ions to other phases of gas is not well constrained by
observations, especially on resolved scales within galaxies. Leroy et al.
(2015b) provided a heuristic model in which this ratio could change based on
the local region of the galaxy. More work constraining these properties with
ALMA, MUSE and KCWI is direly needed in order to reduce these systematics, and
confirm the results we have presented.

###  4.3 Implications for star formation regulation in high $\Sigma_{\rm SFR}$
galaxies

The superlinear relationship between outflow efficiency and star formation
efficiency (Fig. 4) has implications for how galaxies regulate their star
formation. This correlation suggests that in the disk-mode of star formation,
the outflow and the star formation are similarly effective at removing gas,
thus regulating the ability to form new stars. However, as the disk moves into
a starburst mode, this regulation becomes more dominated by the outflow.

We can therefore outline a picture in which the nature of the mechanism
regulating star formation may change with respect to location in the
$\Sigma_{\rm SFR}-\Sigma_{\rm mol}$ plane. At a fixed $\Sigma_{\rm mol}$, as
the $\Sigma_{\rm SFR}$ increases above the typical depletion time of $\sim
1-2$ Gyr, the outflows become the dominant mechanism in removing gas. Krumholz
et al. (2018) argues that gas inflow rates in disks are comparable to the SFR,
and therefore if the mass-outflow rate becomes significantly greater than
$\eta\sim 1$, as we show in Fig. 6, then the gas removal by the outflow will
reduce the gas surface density. This then causes the star formation rate
surface density to decline, and further gas removal is dominated by star
formation rather than outflows. Outflows in the center of starbursting disks,
such as observed here, may therefore act to reduce the impacts of other
effects that drive up the gas velocity dispersion. Theoretical work that
incorporates outflows into dynamical equilibrium models of star formation may
be necessary to explain high $\Sigma_{\rm SFR}$ disk galaxies.

We note that this is heuristically similar to a scenario in which feedback can
be overcome on short timescales by very efficient star formation (Torrey et
al., 2017). Orr et al. (2019) and Rathjen et al. (2021) made similar analyses
of simulation data, at lower $\Sigma_{\rm mol}$. The difference between IRAS08
and the conclusions in Torrey et al. (2017), however, is that in Torrey et al.
(2017) this phenomenon only occurs over the very central nuclei of a galaxy,
whereas in IRAS08 it extends to beyond the half-light radius of the star-
light. F22 reported short free-fall times, $\sim 1-5$ Myr in a very large
fraction of the galaxy, and high star formation efficiencies per free-fall
time. Taken together, the observations of F22 and the outflow observations
here are likewise conceptually consistent with the picture in which departures
from dynamical equilibrium are regulated by strong winds.

We note that there are many similarities between IRAS08 and $z\sim 1-2$
galaxies, including the higher gas fraction, high molecular gas velocity
dispersion and location in the $\Sigma_{\rm SFR}-\Sigma_{\rm mol}$ diagram
(for a full comparison see F22, ). Our results may therefore indicate that the
low molecular gas depletion times observed in galaxies at $z\sim 2$ (e.g.
Tacconi et al., 2018; Herrera-Camus et al., 2019) may be due more to outflows
depleting the local area of the disk, rather than conversion of gas into
stars. What we do not currently know is which relationship is more important,
that of $\dot{\Sigma}_{\rm out}-\Sigma_{\rm SFR}$ or the relationship between
outflow efficiency and star formation efficiency. For example, both Genzel et
al. (2011) and Molina et al. (2019) found galaxies with high $\Sigma_{\rm
mol}$ and $\Sigma_{\rm SFR}$ at sub-galactic resolution, but they have disk-
like depletion times. Observations of outflows in systems like this would be
informative.

Our work has shown the diagnostic power of comparing the properties of
outflows to both $\Sigma_{\rm SFR}$ and $\Sigma_{\rm mol}$ in resolved
observations. Tracking three of the parameters responsible for regulating star
formation in galaxy disks in resolved observations enables us to make unique
comparisons to theory. Yet we have examined only one galaxy. To repeat this on
multiple targets, however, requires a substantial investment of observing
time. Outflows are more easily detected on high efficiency spectrographs on
8-10 m class telescopes (such as Keck/KCWI and VLT/MUSE). This then must be
combined with data from millimeter-wave interferometers, such as ALMA, SMA and
NOEMA. Finally, observations of the ratio of $\dot{M}_{\rm out}({\rm
ions})$-to-$\dot{M}_{\rm out}({\rm molecules})$ vary significantly on the
handful of targets that have been measured (Fluetsch et al., 2019; Herrera-
Camus et al., 2020). Combining resolved observations from optical and
millimeter-wave instruments, we would ideally have much better constraints on
the phase distribution of outflows. Deep ALMA observations of molecular gas
outflows targeting galaxies with known ionised gas outflows would be very
informative, as ionised gas outflows are much easier to observe, especially in
more distant galaxies. We expect future work using DUVET galaxies to address
these concerns.

We are grateful to Viraj Pandya, for discussion and sharing FIRE-2 simulation
results, and to Matt Orr for helpful discussion. Parts of this research were
supported by the Australian Research Council Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.
D.B.F. acknowledges support from Australian Research Council (ARC) Future
Fellowship FT170100376 and ARC Discovery Program grant DP130101460. A.D.B.
acknowledges support from NSF-AST2108140. A.J.C. acknowledges funding from the
“FirstGalaxies” Advanced Grant from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (Grant
agreement No. 789056). R.H.-C. thanks the Max Planck Society for support under
the Partner Group project ”The Baryon Cycle in Galaxies” between the Max
Planck for Extraterrestrial Physics and the Universidad de Concepción. R.H-C
also acknowledges financial support from Millenium Nucleus NCN19058 (TITANs)
and support by the ANID BASAL projects ACE210002 and FB210003. D.O. is a
recipient of an Australian Research Council Future Fellowship (FT190100083)
funded by the Australian Government. R.R.V. and K.S. acknowledge funding
support from National Science Foundation Award No. 1816462.

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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