# DUVET: sub-kiloparsec resolved star formation driven outflows in a sample of
local starbursting disk galaxies

Bronwyn Reichardt Chu,1,2,3,4 Deanne B. Fisher,1,2 John Chisholm,5 Danielle
Berg,5 Alberto Bolatto,6 Alex J. Cameron,7 Drummond B. Fielding,8 Rodrigo
Herrera-Camus,9 Glenn G. Kacprzak,1,2 Miao Li,10 Anna F. McLeod,3,4 Daniel K.
McPherson,1,2 Nikole M. Nielsen,1,2 Ryan Rickards Vaught,11 Sophia G.
Ridolfo,12,1,2 and Karin Sandstrom11
1Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, VIC 3122, Australia
2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia
3Centre for Extragalactic Astronomy, Department of Physics, Durham University,
South Road, Durham DH1 3LE, UK
4Institute for Computational Cosmology, Department of Physics, Durham
University, South Road, Durham DH1 3LE, UK
5Department of Astronomy, University of Texas, Austin, TX 78712, USA
6University of Maryland, College Park, MD 20742, USA
7Sub-department of Astrophysics, University of Oxford, Keble Road, Oxford, OX1
3RH, UK
8Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue,
New York, NY 10010, USA
9Departamento de Astronomía, Universidad de Concepción, Barrio Universitario,
Concepción 4070032, Chile
10Institute for Astronomy, School of Physics, Zhejiang University, 866
Yuhangtang Road, Hangzhou, 310027, China
11Department of Astronomy & Astrophysics, University of California, San Diego,
CA, USA
12Research School of Astronomy and Astrophysics, Australian National
University, Canberra, ACT 2611, Australia
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We measure resolved (kiloparsec-scale) outflow properties in a sample of 10
starburst galaxies from the DUVET sample, using Keck/KCWI observations of
H$\beta$ and [OIII] $\lambda$5007\. We measure $\sim 450$ lines-of-sight that
contain outflows, and use these to study scaling relationships of outflow
velocity ($v_{\rm out}$), mass-loading factor ($\eta$; mass outflow rate per
SFR) and mass flux ($\dot{\Sigma}_{\rm out}$; mass outflow rate per area) with
co-located SFR surface density ($\Sigma_{\rm SFR}$) and stellar mass surface
density ($\Sigma_{\ast}$). We find strong, positive correlations of
$\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm SFR}^{1.2}$ and $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\ast}^{1.7}$. We also find shallow correlations between
$v_{\rm out}$ and both $\Sigma_{\rm SFR}$ and $\Sigma_{\ast}$. Our resolved
observations do not suggest a threshold in outflows with $\Sigma_{\rm SFR}$,
but rather we find that the local specific SFR ($\Sigma_{\rm
SFR}/\Sigma_{\ast}$) is a better predictor of where outflows are detected. We
find that outflows are very common above $\Sigma_{\rm
SFR}/\Sigma_{\ast}\gtrsim 0.1$ Gyr-1 and rare below this value. We argue that
our results are consistent with a picture in which outflows are driven by
supernovae, and require more significant injected energy in higher mass
surface density environments to overcome local gravity. The correlations we
present here provide a statistically robust, direct comparison for simulations
and higher redshift results from JWST.

###### keywords:

galaxies: evolution – galaxies: starburst – galaxies: star formation –
galaxies: ISM

††pubyear: 2023††pagerange: DUVET: sub-kiloparsec resolved star formation
driven outflows in a sample of local starbursting disk galaxies–B

##  1 Introduction

The evolution of galaxies is shaped by the baryon cycle. Cold gas is accreted
onto galaxies, used as fuel in star formation which in turn enriches the gas,
and is then ejected from the galaxy to enrich the surrounding environment
(Somerville & Davé, 2015). Star formation-driven outflows are a necessary
component of this cycle, contributing to the enrichment of the circumgalactic
medium (CGM) (Tumlinson et al., 2017; Cameron et al., 2021), and suppressing
star formation through the removal of gas (Veilleux et al., 2005; Bolatto et
al., 2013; Reichardt Chu et al., 2022b). Galaxy-wide outflows are required for
simulations to reproduce basic galaxy properties including the galaxy mass
function, typical galaxy sizes, and the Kennicutt-Schmidt Law (e.g Springel &
Hernquist, 2003; Oppenheimer & Davé, 2006; Hopkins et al., 2012, 2014). To
constrain the implementation of galaxy-wide outflows in simulations, the
simulations need to be compared to empirical measurements of outflow
quantities. It is, therefore, necessary that we understand the observational
properties of outflows and their driving mechanisms.

Star formation-driven outflows have been observed across cosmic time (e.g.
Heckman et al., 2000; Chen et al., 2010; Rubin et al., 2010; Davies et al.,
2019). Outflows are an observational tracer of the feedback process that
regulates star formation, preventing runaway star formation in multiple ways.
First, it is expected that the gravitational weight of the disk creates
pressure in the interstellar medium (ISM) which is balanced by the energy and
momentum injected into the ISM by young massive stars and supernovae. This
injected energy and momentum creates turbulence, suppressing the star
formation occurring within the galaxy disk (e.g. Ostriker et al., 2010;
Faucher-Giguère et al., 2013; Hayward & Hopkins, 2017; Krumholz et al., 2018;
Ostriker & Kim, 2022). Recent observations that compare velocity dispersion to
the star formation properties find correlations that are consistent with
feedback-based regulation of star formation in disks (Fisher et al., 2019;
Girard et al., 2021). Pre-supernova feedback from young massive stars affects
the density of the ISM gas that the supernovae then explode into, regulating
the impact of the supernova feedback (McLeod et al., 2021; Chevance et al.,
2022). In more extreme starburst environments, clustered supernovae create
expanding “superbubbles” which drive galactic winds when they break out of the
disk (Fielding et al., 2018; Kim & Ostriker, 2018; Vijayan et al., 2020; Orr
et al., 2022). Once these expanding gas bubbles break out of the disk, the gas
they drive out of the galaxy is no longer available for star formation.
Scaling relations are useful for identifying where this occurs, and in which
local regions the outflow dominates over turbulence as the main method of star
formation regulation. Moreover, establishing observational scaling relations
provides direct tests for simulations (e.g. Kim et al., 2020; Rathjen et al.,
2023).

Simulations make direct predictions of outflow properties such as the outflow
velocity $v_{\rm out}$, the outflow mass flux $\dot{\Sigma}_{\rm out}$, and
the mass loading factor $\eta$ as a function of the star formation rate
surface density $\Sigma_{\rm SFR}$ (e.g. Nelson et al., 2019; Kim et al.,
2020; Pandya et al., 2021). Characterising these scaling relationships
provides constraints on our understanding of the physical drivers of outflows.
For example, the relationship between the star formation rate surface density
and the outflow velocity provides constraints on the primary driving mechanism
of the outflows. Outflows primarily driven by mechanical energy from
supernovae are expected to have a shallow relationship as $v_{\rm
out}\propto\Sigma_{\rm SFR}^{0.1}$ (Chen et al., 2010; Li et al., 2017; Kim et
al., 2020). However, if the outflows are primarily driven by momentum given to
the gas by radiation from young massive stars, then the expected relationship
has a steeper dependence as $v_{\rm out}\propto\Sigma_{\rm SFR}^{2}$ (Murray
et al., 2005; Kornei et al., 2012; Hopkins et al., 2012). Outflows are almost
certainly driven by a combination of both of these mechanisms. Spatial and
temporal differences in the preprocessing of the ISM material that SNe explode
into and entrain will contribute to the observed $v_{\rm out}-\Sigma_{\rm
SFR}$ relationship. In addition, supernovae generate cosmic rays which are
also expected to play a role in driving outflows (e.g. Girichidis et al.,
2016, 2024). The extent to which this is important is unclear due to
uncertainties in the parameters of cosmic ray transport (e.g. Naab & Ostriker,
2017; Crocker et al., 2021; Kim et al., 2023). To drive realistic galaxy-wide
outflows, simulations need to include empirically motivated prescriptions that
include the effects from all of the relevant feedback processes. As an initial
constraint, these very different power-laws make observational tests of the
primary contributor of the two models possible.

Observations of outflows have historically been limited by their low surface
brightness to studies of either integrated galaxy samples, or stacked galaxy
samples. Trends between the outflow velocity and global galaxy measurements of
stellar mass, SFR and $\Sigma_{\rm SFR}$ of galaxies have been reported by
many studies (e.g. Martin, 2005; Rupke et al., 2005; Steidel et al., 2010;
Chen et al., 2010; Newman et al., 2012; Kornei et al., 2012; Arribas et al.,
2014; Bordoloi et al., 2014; Rubin et al., 2014; Chisholm et al., 2015, 2017;
Förster Schreiber et al., 2019). However, galaxy-wide observations have an
underlying dependence on the stellar mass of the galaxy (Newman et al., 2012;
Chisholm et al., 2015; Nelson et al., 2019), making it difficult to test the
predicted local correlations. Moreover, it has not been established how the
resolved measurements may alter empirical correlations between outflow and the
galaxy from which they launched. For example, if outflows are launched from
small-scale regions in a galaxy, then global averages may wash out any
existing local relationships. Alternatively, it may be that aggregate effects
of the wind dominate the outflow energetics, and thus global averages are more
important.

Resolved observations of face-on galaxies allow the comparison of outflow
properties to co-located galaxy properties. Using resolved observations, we
can trace the outflowing kinematics back to the local energy and momentum
injected by star formation to test on which scales the star formation drives
galaxy-scale outflows. Recently developed sensitive IFUs, such as KCWI, MUSE
and JWST/NIRSpec, have made this possible. In Reichardt Chu et al. (2022a)
(hereafter RC22a) we studied resolved ionised outflows in the pilot target for
the DUVET sample, IRAS 08339+6517. We found a shallow correlation between the
local co-located $\Sigma_{\rm SFR}$ and $v_{\rm out}$, consistent with trends
expected from supernovae being the primary outflow driving mechanism. In our
follow-up paper, Reichardt Chu et al. (2022b) (hereafter RC22b), we found a
relationship between the star formation rate surface density and outflow mass
flux of $\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm SFR}^{1.06\pm 0.1}$. In this
paper, we extend this analysis to a sample of ten face-on galaxies from the
DUVET survey.

The paper is organised as follows. We describe our galaxy sample in Section
2.1, and our observations and data reduction of the sample in Sections 2.2 and
3.1. We describe our method to fit for outflows in Section 3.2. The resulting
relationships of the maximum outflow velocity, mass outflow flux, and mass
loading factor with SFR surface density and stellar mass surface density are
explored in Section 4. Conclusions are presented in Section 5. Throughout the
paper, we assume a flat $\Lambda$CDM cosmology with $H_{0}=69.3$ km Mpc-1 s-1
and $\Omega_{0}=0.3$ (Hinshaw et al., 2013).

##  2 Observations and Data Reduction

###  2.1 DUVET sample

DUVET (Deep near-UV observations of Entrained gas in Turbulent galaxies) is a
sample of starbursting disk galaxies at $z\sim 0.02-0.04$. The sample contains
both face-on and edge-on galaxies so that we can build a three-dimensional
understanding of the impact of stellar feedback and star formation-driven
outflows on galaxies with high star formation rate surface densities,
$\Sigma_{\rm SFR}$, and their environments (e.g. face-on: ; ; edge-on: Cameron
et al. 2021; McPherson et al. 2023, McPherson et al. in prep). The galaxies
are chosen to have total SFRs at minimum $5\times$ the main sequence value for
their total stellar mass. The galaxies are also required to have the
morphology and kinematics of a disk so that we can remove the underlying
velocity field. The total sample has 27 galaxies and a stellar mass range of
$10^{9}-10^{11}$ M⊙.

This work uses 10 targets from the DUVET sample that have low inclinations.
Inclination is estimated photometrically using the ratio of the major-to-minor
axis in near-IR broadband images from 2MASS and Spitzer/IRAC ch1. Nine of
these targets have inclinations of $i<15^{\circ}$, and one target is
moderately inclined (CGCG 453-062: $i=54^{\circ}$). The inclined target was
observed due to a range in LST at the time of observation that did not have
sufficient targets available that meet the DUVET sample selection criterion.
We will highlight CGCG 453-062 in our discussion of results and in the main
results plots.

The ten galaxies chosen for this work span four orders-of-magnitude in
$\Sigma_{\rm SFR}$ ($\sim 0.001-10$ M⊙ yr-1 kpc-2) in $\sim 500$ pc scale
regions, while keeping the total galaxy stellar mass $10-200\times 10^{10}$
M⊙. Properties for all 10 galaxies examined here are given in Table 1, in
order of increasing total stellar mass. We have calculated the infrared SFR
(Column 5) using the standard Band 4 photometry from the WISE Telescope
(Wright et al., 2010) given in the AllWISE Source Catalog (Cutri et al.,
2021), following the relationship from Cluver et al. (2017, their Eq. 7). The
profile-fit magnitudes from the AllWISE Catalog systematically underestimate
the brightness of extended sources with respect to the WISE point spread
function, and so the SFRs we calculate here are lower bounds.

Name | $z$ | M∗ | SFR${}_{\rm IFU,H\beta}^{*}$ | SFRtotal,IR | $A_{v}$ | $r_{50}$ | $r_{90}$ |  $\log$ [OIII]/H$\beta$ | References
---|---|---|---|---|---|---|---|---|---
|  | ($10^{10}~{}M_{\odot}$) | ($M_{\odot}$ yr-1) | ($M_{\odot}$ yr-1) | (mag) | ($\arcsec$) | ($\arcsec$) |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
IRAS 08339+6517 | 0.019 | 1.10 | 11.1 | 20.5 | $0.5^{+2.4}_{-0.5}$ | 2.6 | 5.9 | $0.14\pm 0.05$ | 1
IRAS 15229+0511 | 0.036 | 3.02 | 4.7 | 20.6 | $0.9^{+1.0}_{-0.9}$ | 3.7 | 9.1 | $-0.34\pm 0.03$ | 2
KISSR 1084 | 0.032 | 3.05 | 3.5∗ | 5.4 | $1.1\pm 0.5$ | 4.8 | 8.2 | $-0.39\pm 0.03$ | 3
NGC 7316 | 0.019 | 4.17 | 3.8∗ | 2.9 | $0.5^{+0.6}_{-0.5}$ | 6.8 | 12.3 | $-0.24\pm 0.02$ | 4
UGC 01385 | 0.019 | 4.74 | 7.1 | 16.8 | $1.2\pm 0.9$ | 2.8 | 7.6 | $-0.32\pm 0.06$ | 5
UGC 10099 | 0.035 | 5.73 | 5.1 | 12.8 | $0.3\pm 0.3$ | 2.5 | 6.2 | $-0.06\pm 0.02$ | 6
CGCG 453-062 | 0.025 | 8.99 | 22.4∗ | 13.9 | $1.9\pm 0.6$ | 7.2 | 13.2 | $-0.48\pm 0.02$ | 5
UGC 12150 | 0.021 | 11.0 | 20.2∗ | 18.5 | $4.0\pm 1.1$ | 5.3 | 11.1 | $-0.40\pm 0.04$ | 5
IRAS 20351+2521 | 0.034 | 11.2 | 26.1∗ | 38.1 | $1.3\pm 0.8$ | 7.3 | 12.1 | $-0.19\pm 0.02$ | 7
NGC 0695 | 0.032 | 20.1 | 42.1∗ | 41.4 | $1.8\pm 0.6$ | 5.9 | 11.2 | $-0.23\pm 0.03$ | 5
Table 1:  Columns are: (1) Galaxy name. (2) Redshift. (3) Stellar mass from
literature, references given in Column 10. (4) Star formation rate from
ionised gas using the H$\beta$ line. (5) Star formation rate from WISE Band 4
data, following Cluver et al. (2017, their Eq.7). (6) Average extinction in
the disk gas based on the H$\gamma$/H$\beta$ flux ratio. (7) and (8) effective
radius and 90% radius in arcseconds from g-band PanSTARRS data respectively.
(9) Median $\log_{10}($[OIII] $\lambda 5007/$H$\beta)$ flux ratio. (10)
References: 1–Fisher et al. (2022), 2–Bik et al. (2022), 3–Cook et al. (2019)
4–Fernández Lorenzo et al. (2013), 5–Howell et al. (2010), 6–Kouroumpatzakis
et al. (2021), 7–Shangguan et al. (2019).
∗ We use the total flux measured in H$\beta$ to calculate SFRIFU,Hβ, however,
some galaxies in our sample extend beyond the FOV of our observations and so
this is a lower limit of the total SFR for the galaxy. The affected SFR values
are indicated using an asterisk.

###  2.2 Observations

The galaxies were observed with KCWI/Keck II (Morrissey et al., 2018) over a
range of nights given in Table 2, with sub-arcsecond seeing conditions. We
used the BM grating in the large IFU slicer mode, giving a field of view of
$20\aas@@fstack{\prime\prime}4\times 33\aas@@fstack{\prime\prime}$ with
spatial sampling of $0\aas@@fstack{\prime\prime}29\times
1\aas@@fstack{\prime\prime}35$, which is seeing limited in the short spaxel
side direction. The galaxies were observed using a half-slice dither pattern
in the direction of the long side of the spaxel to allow for better spatial
sampling. The exposure time and number of exposures for each galaxy are given
in Column 3 of Table 2. All galaxies are observed with multiple grating
settings a “blue" and “red" setting. In this paper we only use the red
setting. The central wavelength set for the BM grating of the red setting is
given in Column 4 of Table 2 for each galaxy and was chosen to include all
wavelengths from H$\gamma$ to [OIII] $\lambda 5007$. The galaxies were also
observed with a “blue” configuration, to extend the wavelength coverage from
H$\gamma$ to below the [OII] doublet. The observations using the “blue"
configuration are described in McPherson et al. in prep. A separate sky field
was observed beyond the virial radius for each galaxy either directly before
or after the science exposures. The observations and data reduction for the
pilot target, IRAS 08339+6517 were discussed in detail in RC22a and Fisher et
al. (2022). The observations and data reduction for the remaining nine
galaxies follow a similar method.

The data were reduced using the standard IDL KCWI Data Extraction and
Reduction Pipeline (Version 1.1.0)111https://github.com/Keck-
DataReductionPipelines/KcwiDRP. Before combining the images, small-scale
imperfections in the WCS were accounted for by a re-alignment based on the
H$\gamma$ emission line, which is detected in all images and allows for
alignment with bluer wavelength settings taken on each galaxy not used in this
work. The H$\gamma$ flux was compared in each pixel using an iterative
minimisation method, and the WCS of the images was adjusted to result in the
minimum average residual across each galaxy. The python package
Montage222http://montage.ipac.caltech.edu/ was then used to reproject the
images to produce square spaxels of $0\aas@@fstack{\prime\prime}29\times
0\aas@@fstack{\prime\prime}29$, based on the shorter side length of the
original rectangular spaxels. The resulting reprojected images of each galaxy
were co-added in Montage using the adjusted WCS coordinates. The variance
cubes were similarly reprojected and coadded. The number of images and their
exposure times are given in Column 3 of Table 2 for each galaxy. The reduction
process for DUVET galaxies is described in more detail in McPherson et al.
(2023).

To account for the (on average) $0\aas@@fstack{\prime\prime}7$ seeing
conditions, the resulting realigned, reprojected and coadded cubes were binned
$3\times 3$ to obtain cubes with a final spaxel size of
$0\aas@@fstack{\prime\prime}87\times 0\aas@@fstack{\prime\prime}87$, which is
comparable to the typical seeing FWHM. The dither pattern of the observations
in the direction of the long side of the original spaxels
($0\aas@@fstack{\prime\prime}29\times 1\aas@@fstack{\prime\prime}35$) allows
for the reconstructed images to better sample the seeing. RC22a found stronger
correlations between outflow and co-located galaxy parameters above a re-
binned spaxel size of ${\sim 0.5}$ kpc, and discussed possible geometric and
temporal causes (see RC22a for a discussion). The reprojected spaxel size for
the galaxies in this work is equivalent to $0.34$ kpc $\times~{}0.34$ kpc at
$z=0.019$ for our closest galaxies and $0.63$ kpc $\times~{}0.63$ kpc at
$z=0.036$ for our furthest galaxy. Our pilot target IRAS 08339+6517 is the
exception to this, retaining its original data reduction from RC22a resulting
in rectangular spaxels of $0\aas@@fstack{\prime\prime}3\times
1\aas@@fstack{\prime\prime}35$ ($0.1$ kpc$\times 0.5$ kpc at $z=0.019$).

Name | RA | Dec | Obs date | Exp times | Central wavelength
---|---|---|---|---|---
| (J2000) | (J2000) |  | (s) | (Å)
(1) | (2) | (3) | (4) | (5) | (6)
IRAS 08339+6517 | 08:38:23.18s | +65:07:15.2s | 15 Feb 2018 | 1200, 600, 300, 100 | 4800
CGCG 453-062 | 23:04:56.53s | +19:33:08.0s | 20 Oct 2019 | $6\times 300$ | 4800
UGC 01385 | 01:54:53.79s | +36:55:04.6s | 20 Oct 2019 | $6\times 300$ | 4800
UGC 12150 | 22:41:12.26s | +34:14:57.0s | 21 Oct 2019 | $6\times 300$ | 4800
NGC 0695 | 01:51:14.24s | +22:34:56.5s | 21 Oct 2019 | $4\times 300$ | 4800
NGC 7316 | 22:35:56.34s | +20:19:20.1s | 20 & 21 Oct 2019 | $1\times 200,6\times 300,3\times 500$ | 4800
IRAS 15229+0511 | 15:25:27.49s | +05:00:29.9s | 22 March 2020 | $6\times 300$ | 4850
UGC 10099 | 15:56:36.40s | +41:52:50.5s | 22 March 2020 | $6\times 300$ | 4850
IRAS 20351+2521 | 20:37:17.72s | +25:31:37.7s | 16 May 2020 | $6\times 300$ | 4820
KISSR 1084 | 16:49:05.27s | +29:45:31.6s | 16 May 2020 | $6\times 300$ | 4820
Table 2: Columns are: (1) Galaxy name. (2) and (3) RA and Dec from NED*. (4)
The date the galaxy was observed with KCWI/Keck II. (5) Number and length of
exposure times in seconds. (6) is the set central wavelength of the BM
grating.
*The NASA/IPAC Extragalactic Database (NED) is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology.

##  3 Methods

###  3.1 Continuum Subtraction

Before each cube was continuum subtracted, foreground extinction due to the
Milky Way was corrected using the Cardelli et al. (1989) law and a galactic
extinction value of 0.251 mag (Schlafly & Finkbeiner, 2011).

The full spectrum fitting code pPXF (Cappellari, 2017) was used to fit the
stellar continuum. For this fitting to occur, the continuum was required to
have a signal-to-noise greater than 3 in a continuum band (4600 Å
$<\lambda<4800$ Å) for each galaxy data cube. For nine of the ten galaxies in
this work, the continuum fitting used semi-empirical templates from Walcher et
al. (2009). Emission line ratios of the galaxies suggest that IRAS 08339+6517
López-Sánchez et al. (2006) has a lower metallicity than the remainder of the
sample. Due to this difference, and to keep consistency with the results from
RC22a and RC22b, the continuum subtraction for IRAS 08339+6517 used the BPASS
templates (Version 2.2.1, Stanway & Eldridge, 2018), including binary systems
with a broken power-law initial mass function with a slope of -1.3 between
$0.1~{}M_{\odot}$ and $1.0~{}M_{\odot}$, a slope of -2.35 above
$1.0~{}M_{\odot}$, and an upper limit of $300~{}M_{\odot}$. The BPASS
templates were built to cover younger ages and lower metallicities than the
Walcher et al. (2009) templates.

Post continuum subtraction, we identified some spaxels where a wide residual
absorption feature near H$\beta$ is not fully removed through the continuum
subtraction process. This does not occur in all spaxels, and appears to be
more common in more heavily extincted systems. The continuum subtraction of
starburst galaxies is unreliable, due to well-known issues in creating stellar
population libraries to model the continuum in these environments (Conroy,
2013). We therefore address any regions that were poorly fit by fitting any
remaining residuals. Using short wavelength bands on either side of the
emission lines, we fit a linear function across [OIII] $\lambda 5007$ and a
quadratic across H$\beta$ such that the corrected spectrum has a flat
baseline. The quadratic across H$\beta$ is fit at least 10 Å away from the
emission line, and the correction is interpolated across the baseline. We use
a quadratic function across H$\beta$ as it is more likely to be affected by
residual hydrogen absorption in stellar photospheres. The resulting baselines
are visually inspected for a subset of spaxels in each galaxy. We tested our
results with and without this additional baseline correction and found the
change fell within the error bars for the difference in both median outflow
velocity and median outflow mass flux. Including the baseline correction
decreased the median mass loading factor by $\sim 7\%$.

Finally, an internal extinction correction was calculated on a spaxel-by-
spaxel basis for all galaxies using the emission line ratio H$\beta$/H$\gamma$
and the Calzetti (2001) extinction curve. This extinction correction was
applied when calculating the star formation rate and the mass outflow rate.
The impacts of including an extinction correction within the outflow mass
calculation are discussed further in Section 4.2.

###  3.2 Emission-line Fitting Method

Figure 1: Example fits from DUVET target UGC 01385. Left panel: an RGB image
of UGC 01385 (R: Pan-STARRS z-band, G: Pan-STARRS r-band, B: Pan-STARRS
g-band). Large green rectangle shows the footprint of our KCWI observations.
Blue, purple and orange small squares show highlighted KCWI spaxels, for which
the H$\beta$ emission line fits are shown in the right-hand panels. Right-hand
panels: for each panel, data is in blue, purple or orange corresponding to the
squares in the left panel. The variance is shown as a grey band. Dashed black
lines show the two-component Gaussian fits. Dotted red line shows the complete
fitted model. The signal-to-noise and $\delta_{\rm BIC}$ are given for each
spaxel (see Sec. 3.2 and Appendix A for more discussion of the $\delta_{\rm
BIC}$).

To identify outflows we follow the method developed in previous DUVET papers
(Reichardt Chu et al., 2022a; McPherson et al., 2023). We implement multi-
component Gaussian fitting using the Python package
threadcount333https://github.com/astrodee/threadcount, which uses the Python
fitting package lmfit (Newville et al., 2019) with a Nelder-Mead simplex
minimisation algorithm. We fit both a single and a double Gaussian to the
H$\beta$ and [OIII] $\lambda$5007 emission lines independently in spaxels
where we measure a signal-to-noise greater than 10 in the emission line. To
determine whether the extra Gaussian component is necessary, we use the
Bayesian information criterion (BIC). The form of the BIC we use here is the
Aikake information creiterion, the special case where each model is fit to the
same number of data points, defined as

$BIC=\chi^{2}+2N_{\rm variables},$ (1)

where $\chi^{2}=\sum(f_{\rm data}-f_{\rm model})^{2}/\sigma^{2}$, and $\sigma$
is the data uncertainty. $N_{\rm variables}$ is the number of variables
included in the fit, which is 4 for single Gaussian fits and 7 for double
Gaussian fits. Some example fits are shown for one of our targets, UGC 01385,
in Fig. 1.

The double Gaussian model is only chosen where it gives a lower BIC value than
the single Gaussian model minus a threshold value such that $BIC_{\rm
doubleGaussian}<BIC_{\rm singleGaussian}-\delta_{\rm BIC}$. The threshold
value, $\delta_{\rm BIC}=-200$, is discussed further in Appendix A. We
restrict the double Gaussian fits such that the bluer component must have a
smaller amplitude and larger velocity dispersion than the redder component.
When a double Gaussian model is the statistically preferred fit, we assume the
broad, blue-shifted component measures flux from outflowing gas and the
narrower, higher amplitude component measures flux from gas within the galaxy
disk (see ;  and McPherson et al. 2023 for more detail). A visual inspection
of the data did not find any redshifted secondary peaks. The software prompts
the user to confirm fits with marginal BIC values or those in which the
central velocity shift of the second component is small. Likewise, we visually
inspect a large fraction of resulting fits, and generally find good fits.

We restrict the spaxels in our results to those within $r_{90}$ of each galaxy
(given in Table 1) to exclude any spaxels on the edge of the galaxy that may
have more complicated kinematics due to inflowing gas. We restrict the
velocity dispersion of both components to be greater than the instrument
dispersion of KCWI, $\sigma_{\rm inst}=41.9$ km s-1, such that all outflows
have resolved dispersions, and the outflow velocity dispersion is greater than
the galaxy dispersion. We additionally exclude 130 spaxels in a spiral arm of
IRAS 20351+2521, and 12 spaxels in the centre of CGCG 453-062 which have
evidence of recent accretion, making decomposing the outflow component
unreliable.

##  4 Results: Star formation driven outflow scaling relations

Figure 2: Summed total galaxy quantities for our 10 face-on DUVET galaxies
(blue circles) and 5 DUVET edge-on galaxies (blue squares, McPherson et. al.
in prep) compared with entire galaxy measurements from nearby dwarf galaxies
measured in emission (down triangles, up triangles: McQuinn et al., 2019;
Marasco et al., 2023, respectively), nearby star-forming galaxies measured in
absorption (crosses, Chisholm et al., 2017), main-sequence star-forming
galaxies at cosmic noon measured in emission (diamonds, Concas et al., 2022),
and nearby starburst M 82 (red star; Greco et al., 2012; Xu et al., 2023). The
panels show total galaxy measurements for mass outflow rate $\dot{M}_{\rm
out}$ against total stellar mass $M_{\ast}$ (top left), and total star
formation rate (top right); and the mass loading factor $\eta$ against total
stellar mass $M_{\ast}$ (bottom left), and total star formation rate (bottom
right). Dashed lines in the top right panel show lines of constant mass
loading factor. Our DUVET targets fall within the expected scatter for total
galaxy measurements. The outlier is UGC 12150, which we found had a very weak
outflowing ionised gas signal.

In this section, we compare results from fitting for outflows in each spaxel
to the co-located galaxy properties. We derive scaling relationships for the
maximum outflow velocity, the outflow mass flux and the mass loading factor
with star formation rate surface density and stellar mass surface density. A
summary of these correlations is given in Table 3. We also discuss the
relationship of the fraction of spaxels containing outflows with total galaxy
stellar mass and global star formation rate surface density.

In Fig. 2 we compare our summed total galaxy results to literature values for
total galaxy measurements of mass outflow rate, mass loading factor, total
stellar mass and star formation rate. We compare our local starbursting disk
galaxies to two samples of nearby dwarf galaxies (McQuinn et al., 2019;
Marasco et al., 2023), a sample of nearby star-forming galaxies extending from
dwarfs to Milky-Way mass galaxies (Chisholm et al., 2017), a sample of star-
forming galaxies at cosmic noon (Concas et al., 2022), and the well-studied
local starbursting system M 82 (e.g. Greco et al., 2012; Xu et al., 2023). We
have also included results from 5 DUVET edge-on outflow systems (McPherson et
al. in prep.). We note that a variety of different methods were used within
the literature to obtain these values, causing scatter. For example, McQuinn
et al. (2019), Marasco et al. (2023) and Concas et al. (2022) all used
emission lines to trace the ionised gas outflows, where Chisholm et al. (2017)
used absorption line measurements. Nevertheless, our DUVET targets fall within
the range covered by the literature values. The outlier is UGC 12150, which we
find has a very weak signal for outflowing ionised gas, as can be seen in the
individual outflow scaling relations in Appendix B. Total galaxy outflow
measurements for our 10 face-on DUVET galaxies can be found in Table 4.

$x$ | $y$ | $\alpha$ | $\beta$ | $R_{P}$ |  $p$-value | $R_{S}$ |  $p$-value
---|---|---|---|---|---|---|---
$\Sigma_{\rm SFR}$ | $v_{\rm out,H\beta}$ | 2.44$\pm$0.01 | 0.19$\pm$0.01 | 0.44 | $2\times 10^{-22}$ | 0.44 | $1\times 10^{-22}$
$\Sigma_{\rm SFR}$ | $v_{\rm out,[OIII]}$ | 2.48$\pm$0.01 | 0.10$\pm$0.02 | 0.16 | $8\times 10^{-3}$ | 0.29 | $6\times 10^{-7}$
$\Sigma_{\rm SFR}$ | $\dot{\Sigma}_{\rm out,extcorr}$ | 0.57$\pm$0.03 | 1.25$\pm$0.03 | 0.86 | $3\times 10^{-134}$ | 0.83 | $3\times 10^{-116}$
$\Sigma_{\rm SFR}$ | $\dot{\Sigma}_{\rm out,nocorr}$ | 0.27$\pm$0.04 | 1.20$\pm$0.04 | 0.76 | $1\times 10^{-83}$ | 0.69 | $3\times 10^{-63}$
$\Sigma_{\rm SFR}$ | $\eta$ | 0.17$\pm$0.04 | 0.04$\pm$0.04 | 0.04 | $0.42$ | 0.05 | $0.26$
$\Sigma_{\ast}$ | $v_{\rm out,H\beta}$ | 1.74$\pm$0.06 | 0.18$\pm$0.02 | 0.36 | $2\times 10^{-15}$ | 0.35 | $2\times 10^{-14}$
$\Sigma_{\ast}$ | $v_{\rm out,[OIII]}$ | 2.04$\pm$0.10 | 0.11$\pm$0.03 | 0.18 | $2\times 10^{-3}$ | 0.34 | $5\times 10^{-9}$
$\Sigma_{\ast}$ | $\dot{\Sigma}_{\rm out,nocorr}$ |  $-5.63\pm$0.15 | 1.68$\pm$0.05 | 0.84 | $8\times 10^{-123}$ | 0.83 | $2\times 10^{-113}$
$\Sigma_{\ast}$ | $\eta$ |  $-2.03\pm$0.16 | 0.71$\pm$0.05 | 0.55 | $3\times 10^{-}36$ | 0.56 | $5\times 10^{-38}$
Table 3: Power law fits to the given parameters for spatially resolved data
from all 10 galaxies in our sample, of the form
$\log_{10}(y)=\alpha+\beta\log_{10}(x)$, using the method of orthogonal
distance regression. $R_{P}$ is the Pearson correlation coefficient, with its
$p$-value in the next column to the right. $R_{S}$ is the Spearman’s Rank
correlation coefficient for the given correlation, with its $p$-value in the
next column to the right. The subscripts ‘extcorr’ and ‘nocorr’ indicate where
the outflow has been extinction corrected the same as the disk gas, or not
extinction corrected, respectively.

###  4.1 SFR surface density and maximum outflow velocity

The kinematics of the outflow and their relationship to the SFR surface
density can be used to distinguish between subgrid physical models describing
the primary launching mechanism of the outflow. RC22a found a shallow
relationship between the SFR surface density and the maximum outflow velocity,
$v_{\rm out}\propto\Sigma_{\rm SFR}^{0.1-0.2}$, consistent with outflows
driven by the energy from supernovae for IRAS 08339+6517. In this paper, we
extend this analysis to nine more face-on galaxies from the DUVET sample.

We measure the star formation rate, SFR, in each spaxel using the narrow line
flux from fits to the extinction corrected H$\beta$ emission line and scale
them using the $L_{\rm H\alpha}/L_{\rm H\beta}$ luminosity ratio such that

${\rm SFR}=C_{\rm H\alpha}\left(\frac{L_{\rm H\alpha}}{L_{\rm
H\beta}}\right)10^{0.4A_{\rm H\beta}}L_{\rm H\beta},$ (2)

where $C_{\rm H\alpha}=5.5335\times 10^{-42}~{}M_{\odot}~{}$yr${}^{-1}~{}($erg
s${}^{-1})^{-1}$ is the scale parameter assuming a Kroupa & Weidner (2003)
initial mass function (IMF; Hao et al., 2011). $L_{\rm H\alpha}/L_{\rm
H\beta}=2.87$ is the luminosity ratio ($T_{e}=10^{4}$ K and Case B
recombination, Osterbrock & Ferland, 2006). $A_{\rm H\beta}$ is the extinction
derived from the observed H$\beta$/H$\gamma$ ratio and a Calzetti (2001)
attenuation curve (see Section 3.1). $L_{\rm H\beta}$ is the observed H$\beta$
luminosity, using flux from the narrow component of the fits. This assumes
that emission from the broad component is due to outflowing gas, and is not
caused by star formation. RC22a found that including flux associated with
outflowing gas causes an average increase in the measured $\Sigma_{\rm SFR}$
of $\sim 25\%$.

We report the total SFR for each galaxy from the H$\beta$ emission line in
Column 4 of Table 1. We note that for six of the galaxies in our sample (CGCG
453-062, UGC 12150, NGC 0695, NGC 7316, IRAS 20351+2521 and KISSR 1084) the
galaxy extends beyond the FOV of our KCWI pointing. The SFR that we measure is
therefore a lower limit for the total SFR of these galaxies.

Star formation rate surface density, $\Sigma_{\rm SFR}$, is calculated using
the spaxel size for each measurement. We find that the average spaxel within
$r_{90}$ across all galaxies in the sample has a median $\log(\Sigma_{\rm
SFR}[$M⊙ yr-1 kpc${}^{-2}])$ of -1.2 with a root-mean-square range of $\pm
0.08$ dex. Spaxels across all galaxies where we find evidence for outflows in
both [OIII] $\lambda 5007$ and H$\beta$ have a median $\log(\Sigma_{\rm
SFR}[$M⊙ yr-1 kpc${}^{-2}])$ of -0.6 with a root-mean-square range of $\pm
0.14$ dex. The typical sub-kpc region hosting outflows has, therefore, roughly
half an order-of-magnitude higher $\Sigma_{\rm SFR}$ than the median across
all 10 galaxies.

Following RC22a, we define the maximum outflow velocity as

$v_{\rm out}=|v_{\rm narrow}-v_{\rm broad}|+2\sigma_{\rm broad},$ (3)

where $v_{\rm narrow}$ and $v_{\rm broad}$ are the fitted Gaussian centres in
velocity space for narrow and broad Gaussians respectively. $\sigma_{\rm
broad}$ is the standard deviation of the broad Gaussian. The instrumental
velocity dispersion of 0.7Å (41.9 km s-1) is removed in quadrature. The
average spaxel has a $v_{\rm out}$ measurement error of order $10-30$ km s-1.
We note that by construction of how we fit the data, this velocity should
implicitly be assumed to have a negative sign, as it is the blue-shifted
outflow component of the emission lines.

All of the galaxies in our sample except for IRAS 08339+6517 are brighter in
H$\beta$ than in [OIII] $\lambda 5007$, with the median $\log_{10}($[OIII]
$\lambda 5007/$H$\beta)$ ratio for the galaxy emission (excluding outflows)
given in Table 1.

We note that CGCG 453-062 has a high inclination angle ($i\approx
54^{\circ}$), and therefore the measured outflow velocities require
correction. We deproject the velocities by dividing by $\cos{i}$. For more
detail on the velocity deprojection, see Appendix B. We use the deprojected
velocity in the remainder of this work for CGCG 453-062. The difference in
velocities after correction for galaxies with inclinations $<15^{\circ}$ is of
order $\sim 5$ km s-1, which is negligible. We, therefore, do not deproject
the velocities of the rest of the galaxies as their inclination angles are
below $15^{\circ}$.

Figure 3: The maximum outflow velocity, $v_{\rm out}$, plotted against the
star formation rate surface density, $\Sigma_{\rm SFR}$, for spaxels of sub-
kpc resolution in 10 local starbursting disk galaxies which required a double
Gaussian fit for H$\beta$ (left panel) and [OIII] $\lambda 5007$ (right panel)
emission lines. For relations for individual galaxies, see Appendix B. The fit
to the data is given in the top left corner and shown as a solid red line in
each panel. The dashed line represents a model where outflows are primarily
driven by momentum injected from young massive stars ($v_{\rm
out}\propto\Sigma_{\rm SFR}^{2}$; Murray et al., 2011). The dotted line
represents a model where outflows are primarily driven by energy injected from
supernovae ($v_{\rm out}\propto\Sigma_{\rm SFR}^{0.1}$; Chen et al., 2010).
For observations of both H$\beta$ and [OIII] $\lambda 5007$, the fitted
correlation is not consistent with the momentum-driven model.

In Fig. 3 we show the results from our full sample for both the H$\beta$ and
[OIII] $\lambda 5007$ emission lines, which were fit independently. For
figures for individual galaxies, see Appendix B (Figures 9 and 10). In both
H$\beta$ and [OIII] $\lambda 5007$ we measure the outflow velocity $v_{\rm
out}$ across almost three orders of magnitude in $\Sigma_{\rm SFR}$. We find
median outflow velocities of $213$ km s-1 with a root-mean-square scatter of
234 km s-1, and $262$ km s-1 with a root-mean-square scatter of 279 km s-1 for
the H$\beta$ and [OIII] $\lambda 5007$ velocities respectively. We find a
Pearson correlation coefficient of $R_{P}=0.44$ ($p-$value$\ll 10^{-3}$) for
the relationship between $\log(\Sigma_{\rm SFR})$ and $\log(v_{\rm out})$ for
H$\beta$, and $R_{P}=0.16$ ($p-$value$=0.008$) for [OIII] $\lambda 5007$.

Using the method of orthogonal distance regression444Scipy’s ODR fitter, see
https://docs.scipy.org/doc/scipy/reference/odr.html we fit a relationship
between $\Sigma_{\rm SFR}$ and $v_{\rm out}$ for the results from H$\beta$ and
[OIII] $\lambda 5007$ separately, and find

$v_{\rm out,H\beta}=10^{2.44\pm 0.01}\Sigma_{\rm SFR}^{0.19\pm 0.01}$ (4)

for velocities found from fitting the H$\beta$ emission lines, and

$v_{\rm out,OIII}=10^{2.48\pm 0.01}\Sigma_{\rm SFR}^{0.10\pm 0.02}$ (5)

for velocities found from fitting the [OIII] $\lambda 5007$ emission lines.
These fits are shown in Fig. 3 as solid red lines. We compare these to two
models commonly used for the relationship between $v_{\rm out}$ and
$\Sigma_{\rm SFR}$ in simulations. The dashed line shows the expected
correlation if the outflows are primarily driven by the radiation pressure
giving momentum to the gas surrounding young massive stars ($v_{\rm
out}\propto\Sigma_{\rm SFR}^{2}$; Murray et al., 2011). The dotted line shows
the expected correlation if the outflows are primarily driven by the energy
injected from supernovae ($v_{\rm out}\propto\Sigma_{\rm SFR}^{0.1}$; Chen et
al., 2010). We recover shallow relationships for both [OIII] $\lambda 5007$
and H$\beta$ maximum outflow velocities, which are not consistent with the
model for a purely “momentum-driven” outflow.

Avery et al. (2021) fitted for ionised gas outflows using kinematically tied
fits to H$\beta$, H$\alpha$, and the [OIII] $\lambda\lambda 4959,5007$, [NII]
$\lambda\lambda 6548,6583$, and [SII] $\lambda\lambda 6716,6731$ doublets in
radially binned star-forming galaxies with disk morphologies from the MaNGA
Survey. Excluding galaxies with AGN-driven outflows, they found a shallow
negative relationship of $v_{\rm out}\propto\Sigma_{\rm SFR}^{-0.07\pm 0.02}$.
On the other hand, using fits to the H$\alpha$ and [NII] $\lambda\lambda
6548,6583$ emission lines, Davies et al. (2019) found a steeper relationship
of $v_{\rm out}\propto\Sigma_{\rm SFR}^{0.34\pm 0.10}$ for $z\sim 2.3$
galaxies from the SINs/zC-SINF AO Survey stacked by $\Sigma_{\rm SFR}$. Our
results lie between these two studies. We, however, have allowed H$\beta$ and
[OIII] $\lambda 5007$ to be fit with kinematically independent fits. We note
that the MaNGA galaxies cover a wide range of $\Sigma_{\rm SFR}$, but are not
chosen to be starbursting as our sample of galaxies. The sample of SINs
galaxies in Davies et al. (2019) has a median offset of 2$\times$ the main
sequence SFR at $z=2-2.5$, and covers a similar range of $\Sigma_{\rm SFR}$ as
the sample of galaxies studied here.

The galaxies in our sample do not have the same signal-to-noise in H$\beta$ as
in [OIII] $\lambda 5007$ and are on average brighter in H$\beta$. The higher
S/N enables us to fit the outflow component more reliably in H$\beta$. The
outflow component is unresolved in [OIII] $\lambda 5007$ for the galaxies NGC
7316, CGCG 453-062 and IRAS 15229+0511. Note that excluding spaxels where we
observe an outflow in only one emission line restricts the results to spaxels
with ${\Sigma_{\rm SFR}>10^{-1.5}~{}M_{\odot}}$ yr-1 kpc-2. The fits for
$v_{\rm out}-\Sigma_{\rm SFR}$ are consistent regardless of whether we
restrict our data. We do find that the Pearson correlation coefficient for the
outflow velocities measured in H$\beta$ increases from $R_{P}=0.44$ to
$R_{P}=0.51$ ($p-$value$\ll 10^{-3}$), however, it stays the same for the
[OIII] $\lambda 5007$ results at $R_{P}=0.17$ ($p-$value$=0.006$).

For those spaxels with both H$\beta$ and [OIII] broad components, the outflow
velocities measured for [OIII] $\lambda 5007$ are on average $\sim 40$ km s-1
higher than those measured for H$\beta$. The velocity is measured to be 220 km
s-1 with a root-mean-square scatter of 238 km s-1 in H$\beta$ and 262 km s-1
with a root-mean-square scatter of 279 km s-1 in [OIII] $\lambda 5007$. This
velocity difference is more apparent at lower $\Sigma_{\rm SFR}$. This
difference could be due to systematics introduced by the absorption line
around H$\beta$. Alternatively, it is plausible that [OIII] $\lambda 5007$ is
associated with a higher ionisation state than H$\beta$, and this gas is
intrinsically moving faster.

###  4.2 SFR surface density and outflow mass flux

It is expected that regions of galaxies with a higher SFR surface density will
drive a higher mass outflow rate, $\dot{M}_{\rm out}$, which has been observed
in resolved observations of one target (RC22b). The mass outflow rate is
defined as

$\dot{M}_{\rm out}=\frac{1.36m_{\rm H}}{\gamma_{\rm
H\beta}n_{e}}\left(\frac{v_{\rm out}}{R_{\rm out}}\right)L_{\rm
H\beta,broad}10^{0.4A_{\rm H\beta}},$ (6)

where $m_{\rm H}$ is the atomic mass of hydrogen. $\gamma_{\rm H\beta}$ is the
H$\beta$ emissivity for case B recombination with assumed electron temperature
${T_{e}=10^{4}}$ K ($\gamma_{\rm H\beta}=1.24\times 10^{-25}$ erg cm3 s-1;
Osterbrock & Ferland, 2006). $n_{e}$ is the local electron density in the
outflow, where we assume $n_{e}=100$ cm-3 (RC22b). $v_{\rm out}$ is the
maximum outflow velocity found from fitting the emission lines, here we use
the $v_{\rm out}$ from H$\beta$. $R_{\rm out}$ is the radial extent of the
outflow, where we assume $R_{\rm out}=0.5$ kpc. $L_{\rm H\beta}$ is the
H$\beta$ luminosity from the fitted broad Gaussian component. Finally, $A_{\rm
H\beta}$ is the extinction derived from the observed H$\beta$/H$\gamma$ ratio
for the narrow line component and a Calzetti (2001) attenuation curve (see
Section 3.1), which is discussed further below. For discussion of the
motivation and likely systematic uncertainty on $R_{\rm out}$ see RC22a, and
on $\gamma_{\rm H\beta}$ and $n_{e}$ see RC22b.

The outflow mass flux is the mass outflow rate divided by the surface area of
the measurement $\dot{\Sigma}_{\rm out}=\dot{M}_{\rm out}/{\rm Area}$. The
outflow mass flux is a more useful measurement in resolved outflow studies
than the outflow mass rate, and can be compared to results from simulations,
especially high-resolution box simulations (e.g. Kim & Ostriker, 2017; Rathjen
et al., 2023).

Figure 4: The ionised gas outflow mass flux, $\dot{\Sigma}_{\rm out}$,
compared to the SFR surface density, $\Sigma_{\rm SFR}$, for sub-kpc
resolution spaxels in local starbursting disk galaxies with evidence for
outflow components. We fit a relationship between the two quantities using the
method of orthogonal distance regression, which returns a nonlinear
correlation, given with the Pearson correlation coefficient in the top left
corner and plotted as a red solid line. Dashed black lines show constant mass
loading factors. The left panel shows no extinction correction on the outflow.
The right panel shows $\dot{\Sigma}_{\rm out}$ with the same extinction
correction applied as for gas in the disk.

We do not have sufficient S/N on H$\gamma$ to resolve the outflow component,
and then determine an extinction correction for the outflow. We therefore
compare our results assuming the same extinction correction that we applied
for the disk to the outflow, to our results when assuming no extinction in the
outflow. The assumptions of no extinction or the same extinction as in the
disk represent the extremes, where the actual value likely lies in between,
and may vary from galaxy to galaxy. We note that it is often an implicit
assumption that $\dot{M}_{\rm out}$ includes the same extinction as the ISM,
for example in calculating $\eta\propto F_{\rm broad}/F_{\rm narrow}$. While
dust certainly exists in outflows (e.g. Engelbracht et al., 2006; Roussel et
al., 2010), the extinction is likely not as high as in the midplane of the
galaxy. Xu et al. (2022) approximated the total dust extinction using
absorption-line outflows of CLASSY galaxies and found that most of the dust
responsible for extinction resides within the static ISM.

In the right-hand panel of Fig. 4 we plot the extinction-corrected outflow
mass flux against the SFR surface density for all galaxies in our sample. We
measure ${\dot{\Sigma}_{\rm out}\sim 0.01~{}M_{\odot}}$ yr-1 kpc-2 to $\sim
100~{}M_{\odot}$ yr-1 kpc-2 over three orders of magnitude in $\Sigma_{\rm
SFR}$. The median $\log(\dot{\Sigma}_{\rm out}[M_{\odot}$ yr-1 kpc${}^{-2}])$
for our sample was -0.25 with a root-mean-square of $\pm 0.83$ dex. We find a
Pearson correlation coefficient of $R_{P}=0.86$ ($p-$value$\ll 10^{-3}$) for
$\log\dot{\Sigma}_{\rm out}-\log\Sigma_{\rm SFR}$. Due to the large range of
error bars in outflow mass flux, fitting the data would be biased towards the
high S/N points at high SFR surface density. We, therefore, constrain the
error bars to have a minimum uncertainty of 0.15 dex in $\dot{\Sigma}_{\rm
out}$ for the fit. Fitting the data using the method of orthogonal distance
regression, we find a superlinear relationship of

$\dot{\Sigma}_{\rm out}=10^{0.57\pm 0.03}~{}\Sigma_{\rm SFR}^{1.25\pm 0.03}.$
(7)

We show this fit as a red line in the right-hand panel of Fig. 4. This is
slightly steeper than the relationship found in RC22b ($\dot{\Sigma}_{\rm
out}\propto\Sigma_{\rm SFR}^{1.06\pm 0.10}$). When the errorbars are used
without modification, we find a steeper correlation $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\rm SFR}^{1.33\pm 0.03}$, which is consistent with the
relationship found with unconstrained errorbars in RC22b. We observe values of
$\dot{\Sigma}_{\rm out}$ an order of magnitude lower than found in RC22b, and
these low S/N results may weight the fit towards low $\dot{\Sigma}_{\rm out}$
values when the error bars are unconstrained.

In the left panel of Fig. 4, we show the same relationship if we assume no
extinction in the outflow. With no extinction correction, we find a median
$\log(\dot{\Sigma}_{\rm out}[M_{\odot}$ yr-1 kpc${}^{-2}])$ of -0.57 with a
root-mean-square of $\pm 0.50$ dex. We also find a slightly shallower
relationship between the mass outflow flux and the SFR surface density, such
that $\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm SFR}^{1.20\pm 0.04}$. This is
consistent with the relationship found in RC22b within uncertainties. If we do
not apply an extinction correction to the outflows in the same manner as we do
to the SFR, we find mass loading factors a factor of 3 lower, with a median
mass loading factor of 1.55 with a root-mean-square scatter of 3.24. We use
the non-extinction corrected values of $\dot{\Sigma}_{\rm out}$ for the
remainder of the paper.

In Appendix B we show the same relationship as Fig. 4, but plotting each
galaxy in our sample individually. We find that each galaxy has a trend of
increasing outflow mass flux with increasing SFR surface density. We interpret
this to suggest that the important change from galaxy to galaxy is the overall
degree of star formation, yet roughly the same local relationship between
$\dot{\Sigma}_{\rm out}$ and $\Sigma_{\rm SFR}$ remains.

There is a wide range of results in the literature for the galaxy-integrated
relationship between the total outflow mass rate and SFR. Fluetsch et al.
(2019) found $\dot{M}_{\rm out}\propto$ SFR1.19±0.06 for molecular gas
outflows in local star-forming galaxies. Avery et al. (2021) found a shallower
relationship, $\dot{M}_{\rm out}\propto{\rm SFR}^{0.84\pm 0.08}$, for ionised
gas outflows using star-forming galaxies from MaNGA, excluding AGN from their
sample. In a follow-up paper of the same galaxies, Avery et al. (2022) found a
relationship of $\dot{M}_{\rm out}\propto{\rm SFR}^{0.74\pm 0.2}$ for the
neutral gas outflows. For a sample of dwarf starbursting galaxies from the
DWALIN survey, Marasco et al. (2023) found an even shallower result,
$\dot{M}_{\rm out}\propto$ SFR0.4. However, we caution that these galaxy-
averaged measurements almost certainly include regions that do not drive an
outflow but do contribute to the total SFR.

Using magnetohydrodynamic box simulations of the ISM and star formation-driven
outflows with the SILCC framework, Rathjen et al. (2023) found
$\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm SFR}^{0.81\pm 0.12}$ for the total
gas outflow mass flux. They suggested that more massive galaxies with higher
$\Sigma_{\rm SFR}$ have more difficulty driving outflows from their larger
potential wells, leading to a sublinear correlation. Considering only the warm
ionised gas, Rathjen et al. (2023) found a steeper relationship of
$\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm SFR}^{1.40\pm 0.24}$. This is
steeper than the slope which we fit in Fig. 4 (see also Eq. 7). However, our
galaxies cover a range of SFR surface densities that extends at least an order
of magnitude beyond the maximum SFR surface density ($\Sigma_{\rm SFR}\sim
0.2~{}M_{\odot}$ yr-1 kpc-2) modelled by Rathjen et al. (2023), and so a
complete comparison is difficult. It is possible that the less dense ionised
gas can be accelerated more efficiently than the cold phases of gas, leading
to a steeper correlation. This difference could explain the shallower slope
which Avery et al. (2022) observed for their molecular gas outflows than we
find for ionised gas outflows, although Avery et al. (2022) found agreement at
the $1\sigma$ level between their observations of ionised and neutral gas
outflows.

###  4.3 Mass loading factor

The mass loading factor describes the efficiency of a galaxy in driving
outflows. The resolved mass loading factor is the ratio between the mass
outflow flux and the star formation rate surface density

$\eta=\frac{\dot{\Sigma}_{\rm out}}{\Sigma_{\rm SFR}}.$ (8)

The mass loading factor relates the rate of gas leaving a region of the galaxy
to the underlying star formation driving the outflow. Regions of a galaxy with
a mass loading factor greater than 1 are driving more gas out of the galaxy
than they are turning into stars.

In Fig. 4 we show lines of constant mass loading factor as diagonal dashed
black lines. When we consider all galaxies in our sample, we find that for the
majority of spaxels we measure an ionised gas mass loading factor between 0.1
and 10. We find a median mass loading factor of 1.55 with a root-mean-square
scatter of 3.24. We did not find a statistically significant correlation
between the mass loading factor and the SFR surface density, with a Pearson
correlation value of $R_{P}=0.04$ ($p$-value$=0.42$) between $\log(\eta)$ and
$\log(\Sigma_{\rm SFR})$. This is expected, due to the almost linear
correlation we find between the mass outflow flux and the SFR surface density.
Our results suggest that in the majority of the regions where we observe an
outflow, the star formation is efficiently coupled to the gas to drive the
outflow.

Outflows are by nature multiphase. When calculating the mass loading factor
we, therefore, need to take into account the total mass budget of the outflow.
Fluetsch et al. (2019) found roughly comparable mass outflow rates from
ionised and molecular gas observations of outflows in four galaxies with a
similar specific star formation rates, sSFR$=$SFR/$M_{*}$, to the galaxies in
our sample. This would imply a total mass loading factor for our galaxies of
order $\eta\sim 2-20$. In contrast to this, Fluetsch et al. (2021) found that
for local ULIRGs, the mass of ionised gas in the galaxy wind is a very small
fraction ($<5\%$) of the total mass outflow, with neutral gas making up $\sim
10\%$ and molecular gas up to $\sim 95\%$ of the outflowing mass. Similarly,
Roberts-Borsani et al. (2020) found that ions contribute $<1\%$ of the mass to
the total outflowing gas mass. Following these studies, the total mass loading
factor for the galaxies we observe here could be anywhere from $\eta\sim
10-100$ or even greater.

Avery et al. (2022) compared the analysis of ionised gas outflows in the MaNGA
galaxies from Avery et al. (2021) to observations of neutral gas outflows
studied using the Na I D absorption feature. Avery et al. (2022) accounted for
the dust extinction in the outflow separately from that within the ISM of the
galaxy and found that this increased the fraction of the total gas mass
measured in ionised gas. Even with this correction, the ionised gas phase mass
they measured remained $\sim 1.2$ dex lower than the neutral gas phase mass.
They found an average neutral gas mass loading factor of order unity for non-
AGN MaNGA galaxies within a similar mass range to our galaxies. If our
galaxies follow a similar trend, then we could expect to observe neutral gas
mass loading factors of $\sim 10-100$, which is far higher than the neutral
gas mass loading factors that Avery et al. (2022) found. Alternatively, if we
expect the galaxies in our sample to have similar neutral gas mass loading
factors to those found by Avery et al. (2022), then it is possible that
neutral gas observations of the galaxies in our sample would find roughly
comparable ionised and neutral gas mass loading factors. This would then be
similar to the results from Fluetsch et al. (2019).

However, we urge caution when comparing observational results between resolved
studies such as this one and studies utilising stacked spectra or total galaxy
measurements such as Avery et al. (2022) and Fluetsch et al. (2019).
Normalising the mass outflow rate by the star formation rate may include star
formation from regions of the galaxy that do not drive an outflow in non-
resolved studies. This can result in an artificially low mass loading factor
for some observations.

Moreover, observations of the mass loading factor inherently include a large
number of assumptions about the geometry and electron density of the outflow.
These assumptions can vary dramatically between studies and can have a large
impact on the results. For example RC22b found that increasing the assumed
electron density from $n_{e}=100$ cm-1 to $n_{e}=300$ cm-1 decreased the mass
loading factor by $\sim 0.5$ dex. The electron density within the disk has
been observed to depend on the local SFR surface density (e.g. Kaasinen et
al., 2017; Davies et al., 2021). If the electron density of the outflow also
depends on the SFR surface density such that the electron density decreases
for brighter outflows, this would steepen the correlation between the mass
loading factor and SFR surface density, bringing our result closer to
predictions from simulations (e.g. Kim et al., 2020; Pandya et al., 2021).
Alternatively RC22b also found that increasing the assumed outflow radius from
$R_{\rm out}=0.5$ kpc to $R_{\rm out}=20$ kpc decreased the mass loading
factor by $\sim 1.5$ dex. If the $R_{\rm out}$ increases for outflows driven
by stronger star formation, this might offset a change in the electron
density. It is therefore difficult to definitively say how our assumptions
impact our results. High-resolution studies of outflows from edge-on galaxies
such as the MUSE/VLT GECKOS Large Program are likely to make progress on
understanding these systematics (Elliot in prep).

In addition, while we expect that there should be an order of magnitude more
molecular gas than ionised gas in the total outflow mass budget, regions of
the galaxy with higher SFR surface densities may well be ionising more gas,
increasing the fraction of ionised gas in the outflow. Simply assuming the
same ratio of ionised-to-molecular gas in the outflow for all SFR surface
densities may therefore lead us to overestimate the total mass loading factor.
For example, in the MHD stratified galaxy patch simulation SILCC, Rathjen et
al. (2023) found a steeper relationship between the warm and ionised outflow
mass rate and the SFR surface density than between the total outflow mass rate
and the SFR surface density. This suggests that for regions with higher SFR
surface densities, ionised gas may make up a larger fraction of the total
outflowing mass.

Simulations use the relationship between the mass loading factor and the SFR
surface density to test the driving mechanisms of outflows. A number of
simulations predict a negative relationship of $\eta_{\rm ion}$ with SFR
surface density (Fielding et al., 2017; Li et al., 2017; Kim et al., 2020;
Pandya et al., 2021). With our sample of galaxies, however, we find a very
shallow positive relationship between the mass loading factor and the SFR
surface density. We now compare the mass loading factor values from the
simulations to those measured in our observations. Using the FIRE suite of
cosmological zoom-in simulations, Anglés-Alcázar et al. (2017) found total gas
mass loading factors of $\eta\sim 2$ for galaxies in a similar galaxy mass
range to our sample. From the updated FIRE-2 simulations, Pandya et al. (2021)
found that the warm ($10^{3}~{}{\rm K}<T<10^{5}$ K) gas represents less than
10% of the total mass loading for galaxies with a similar stellar mass to our
sample. For $\Sigma_{\rm SFR}\sim 0.1-10~{}M_{\odot}$ yr-1 kpc-2 they find
warm gas mass loading factors ranging from $\eta\sim 0.04-10$. These values
are within the range of the mass loading factors we find for the ionised gas
phase observations in our galaxies. Using the SMAUG-TIGRESS simulations, Kim
et al. (2020) similarly found mass loading factors for the cool ($T\sim
10^{4}$ K) gas of $\eta\sim 0.2-10$ for $\Sigma_{\rm SFR}\sim
0.1-1~{}M_{\odot}$ yr-1 kpc-2. These values are consistent with the values we
observe in our galaxies at a similar SFR surface density.

We note that we are not comparing apples with apples. Kim et al. (2020)
simulate solar neighbourhood-like conditions and do not reach the high
$\Sigma_{\rm SFR}$ environments of some regions of our targets. In addition,
Pandya et al. (2021) calculate total values of $\eta$ and SFR surface density
for entire galaxy haloes, while we calculate these values for resolved
regions. While our extended sample covers a larger range of SFR surface
densities than RC22b, our results are however still within the scatter of
results returned for the warm ionised gas by Pandya et al. (2021).

###  4.4 Stellar mass surface density

Figure 5: The so-called “resolved main-sequence” for DUVET galaxies. The left
panel shows all spaxels within $r_{90}$. The right panel shows the same
region, but only for those spaxels with outflows. Grey points are kiloparsec-
scale measurements from the PHANGS sample. The line is an ad hoc seperation
showing that outflows become more common for $\Sigma_{\rm
SFR}/\Sigma_{\ast}>0.1$ Gyr-1. Outflow points are coloured by outflow mass
flux.  Figure 6: The relationship between the resolved stellar mass surface
density and the outflow mass flux (left), the mass loading factor (middle),
and the outflow velocity (right). We fit a relationship between the two
quantities for each panel using the method of orthogonal distance regression.
The resulting nonlinear correlations are given with the Pearson correlation
coefficient in the top left corner of each panel, and are plotted as solid red
lines. In the left panel, the dashed black line shows $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\ast}^{1.2}$, which would be the case if the
$\dot{\Sigma}_{\rm out}-\Sigma_{\ast}$ relation followed the
$\dot{\Sigma}_{\rm out}-\Sigma_{\rm SFR}$ relation.

In Fig. 5 we show the so-called “resolved main-sequence” relationship between
$\Sigma_{\rm SFR}$ and $\Sigma_{\ast}$ for DUVET targets in this work. We
derive stellar masses using 2MASS H-band observations, which are available for
all of our sources. The 2MASS data is convolved and resampled to match the
DUVET KCWI images. Our galaxies are selected to be starbursts, so to convert
to stellar mass we assume an LMC mass-to-light ($M/L$) ratio (Eskew et al.,
2012) of $M/L_{H}=0.11$ by scaling the 3.6 $\mu$m M/L to H-band, and the
Salpeter (1955) IMF to a Kroupa & Weidner (2003) IMF. We note that we tested
the Meidt et al. (2012) method using Spitzer 3.6 $\mu$m and 4.5 $\mu$m images,
and determined that Spitzer 3.6 $\mu$m images in our sample are likely to be
very strongly affected by 3.3 $\mu$m PAH feature, which varied significantly
across our targets. We, therefore, opted not to use methods like Meidt et al.
(2012) as the PAH feature introduced extra systematics to the conversion to
stellar mass. In Fig. 5 we compare our $\Sigma_{\rm SFR}$ and $\Sigma_{\ast}$
to those of the PHANGS sample (Sun et al., 2023), measured with comparable
resolution, and find that for regions of DUVET galaxies with $\Sigma_{\rm
SFR}$ that is similar to values of PHANGS targets the $\Sigma_{\ast}$ is
likewise comparable.

The DUVET sample is selected to have global SFR and M∗ that is nominally at
least 5$\times$ higher than the star-forming main sequence, and this is
reflected in Fig. 5. In the left panel of the figure, we show all lines of
sight, the majority of which have higher $\Sigma_{\rm SFR}/\Sigma_{\ast}$ than
PHANGS galaxies, which are more representative of the resolved star-forming
main sequence. Overall, the DUVET targets have a spread in $\Sigma_{\rm
SFR}/\Sigma_{\ast}$ that begins at the resolved main sequence and skews
upwards.

In the right panel of Fig. 5 we show only those lines of sight in which our
automatic detection method identifies outflows. Nearly 100% of the lines of
sight containing outflows are above the main sequence. We also plot a line
corresponding to $\Sigma_{\rm SFR}/\Sigma_{\ast}=0.1$ Gyr-1. Outflows are very
rare below this specific star formation rate, at any value of $\Sigma_{\ast}$.
We find that below $\Sigma_{\rm SFR}/\Sigma_{\ast}=0.1$ Gyr-1 only 9% of all
spaxels are determined to have outflows, and above this value 20% do have
outflows. Out of all the spaxels with outflows, 78% have $\Sigma_{\rm
SFR}/\Sigma_{\ast}>0.1$ Gyr-1.

A large number of studies conclude that outflows are more common at higher
specific SFR (Förster Schreiber et al., 2019; Avery et al., 2021; Roberts-
Borsani et al., 2020; Veilleux et al., 2020; Chen et al., 2010; Rubin et al.,
2014, e.g.). Our result in Fig. 5 shows that this extends down to sub-kpc
scales. More specifically, Förster Schreiber et al. (2019) showed that
$z\approx 2$ KMOS3D galaxies that are above the main sequence are much more
likely to host outflows, similar to our result. There are both theoretical and
observational arguments (Murray et al., 2011; Heckman et al., 2002) that a
minimum $\Sigma_{\rm SFR}\gtrsim 0.1$ M⊙ yr-1 kpc-2 is needed to drive
observable outflows. While we do find outflows become less common below this
threshold, it is clear from Figures 4 and 5 that they are still present and
seem to extend the correlations of higher $\Sigma_{\rm SFR}$ winds. We find
that 28% of the spaxels we observe to contain outflows fall below this
threshold. It is possible that any threshold value in $\Sigma_{\rm SFR}$ is
likely to increase at higher $\Sigma_{\ast}$. This can be understood by a
simple argument in which the higher $\Sigma_{\ast}$ exerts a greater
gravitational force on the outflow gas. The gas may require more energy, from
higher $\Sigma_{\rm SFR}$, to escape the local potential. This would be
consistent with where we find outflows in the DUVET targets.

In Fig. 6 we compare $\Sigma_{\ast}$ for individual spaxels to the outflow
properties ($\dot{\Sigma}_{\rm out}$, $\eta$ and $v_{\rm out}$). All three
show positive correlations. The correlation of $\dot{\Sigma}_{\rm
out}-\Sigma_{\ast}$ is similarly strong as that of $\dot{\Sigma}_{\rm
out}-\Sigma_{\rm SFR}$, with a Pearson correlation coefficient $R_{P}=0.84$
($p-$value$\ll 10^{-3}$). We find, however, that the powerlaw of this
relationship is steeper, such that $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\ast}^{1.68\pm 0.05}$, where the powerlaw index scaling
with $\Sigma_{\rm SFR}$ is closer to $\sim 1.2$. Similarly, the correlation of
$\eta-\Sigma_{\ast}$ is steeper than $\eta-\Sigma_{\rm SFR}$, such that
$\eta\propto\Sigma_{\ast}^{0.71\pm 0.05}$, with a Pearson correlation
coefficient of $R_{P}=0.55$ ($p-$value$\ll 10^{-3}$). The powerlaw index
scaling for $\eta-\Sigma_{\rm SFR}$ is closer to zero. The correlation of
$v_{\rm out}$ with $\Sigma_{\ast}$ is shallow and similar to that with
$\Sigma_{\rm SFR}$.

We do not know why the correlation of $\dot{\Sigma}_{\rm out}$ with
$\Sigma_{\ast}$ should be so steep. For spaxels with outflows the correlation
of $\Sigma_{\rm SFR}$ with $\Sigma_{\ast}$ is roughly consistent with linear.
Therefore, if we assume that $\dot{\Sigma}_{\rm out}-\Sigma_{\ast}$ is a
secondary correlation between $\dot{\Sigma}_{\rm out}$ and $\Sigma_{\rm SFR}$
then we would expect the same powerlaw.

We note that the steep powerlaw of $\dot{\Sigma}_{\rm
out}\propto\Sigma_{*}^{1.68}$ may be a relic of systematic uncertainties. We
assumed a constant $M/L$ across our sample. However, if this changes due to
the local stellar populations or position in the galaxy, then this could
impact the powerlaw. In this case, however, the most likely scenario would be
that higher $\Sigma_{\rm SFR}$ would have younger stellar populations and thus
lower $M/L$. This would steepen the relationship.

There are also physical arguments for a steeper relationship with
$\Sigma_{\ast}$. For example, higher $\Sigma_{\ast}$ implies a stronger local
gravitational potential. In principle, this requires outflows to be stronger
for them to overcome the local gravity, and be observed in our sample.
Secondly, as the highest $\Sigma_{\ast}$ spaxels are preferentially in the
galaxy center, it may be that gas is preferentially built up in these regions
and thus able to drive stronger winds.

###  4.5 Outflow covering fraction

The covering fraction of outflows is defined by the total fraction of
starlight that is covered by outflowing gas. This quantity is necessary when
calculating the mass-outflow rate for entire galaxy outflow measurements (e.g.
at higher redshift; Rubin et al., 2014; Davies et al., 2019) or for edge-on
galaxy outflow measurements. In absorption line measurements it is typically
inferred from the depth of the absorption line. Our resolved outflow
measurements allow us to measure this directly via geometry. See McPherson et
al. (2023) for a similar calculation in an edge-on outflow galaxy.

Here we calculate the covering fraction as $f_{\rm cov}\equiv N_{\rm
outflow}/N_{\rm total}$, where $N_{\rm outflow}$ and $N_{\rm total}$ are,
respectively, the number of spaxels with an outflow and the total number of
spaxels. We calculate this for each galaxy within the 90% starlight radius
($r_{90}$) and half-light radius ($r_{50}$). In Fig. 7 we compare $f_{\rm
cov}$ within $r_{50}$ and $r_{90}$ to the total galaxy stellar mass, and the
median SFR surface density within $r_{50}$ and $r_{90}$ for outflows detected
in H$\beta$.

Figure 7: The fraction of spaxels with outflows detected in in H$\beta$ within
$r_{50}$ (coloured points) and $r_{90}$ (open points) for each galaxy is
plotted against the total stellar mass (left panel), and the median SFR
surface density (right panel) of the galaxies. We find the strongest
correlation is a dependence of the covering fraction on the median SFR surface
density.

Across our galaxy sample, we find a trend of decreasing covering fraction with
increasing stellar mass, shown in the left panel of Fig. 7. The correlation
between the covering fraction and the total galaxy stellar mass has a Pearson
correlation coefficient of $R_{P}=-0.60$ ($p-$value$=0.005$) for the
relationship $\log(f_{\rm cov})-\log(M_{*})$. For galaxies with $\log
M_{*}[M_{\odot}]=10.7-11.5$ we find a median covering fraction of 15% within
$r_{50}$. For the lower mass galaxies in the sample ($\log
M_{*}[M_{\odot}]=10-10.7$), we find the covering fraction increases to 34%.
The decrease in the fraction of outflow spaxels with increasing stellar mass
seems connected to our result in Fig. 5, where individual spaxels with higher
$\Sigma_{\ast}$ require higher $\Sigma_{\rm SFR}$ to be observed with an
outflow. Similarly, this can be understood given that galaxies with a higher
stellar mass have a larger gravitational potential well, making it harder to
accelerate outflows to the velocities necessary to leave the disk.

The right panel of Fig. 7 shows the relationship between the covering fraction
and the median value of the SFR surface density. This is calculated within
$r_{50}$ to compare to the covering fraction within $r_{50}$, and similarly
within $r_{90}$ to compare to the covering fraction within $r_{90}$. We find
an overall trend of increasing covering fraction with increasing median SFR
surface density. This trend has a higher statistical significance, with a
Pearson correlation coefficient of $R_{P}=0.76$ ($p-$value$=0.0001$) for
$\log(f_{\rm cov})-\log(\Sigma_{\rm SFR,median})$. Given the local
correlations between outflow properties and $\Sigma_{\rm SFR}$, this trend
seems straightforward to understand. If the typical $\Sigma_{\rm SFR}$ in a
galaxy is larger then this galaxy will have a larger area in which outflows
are present.

We also test the correlation of the covering fraction with stellar mass and
median SFR surface density for our results using [OIII] $\lambda 5007$. We
find the same correlation with stellar mass (Pearson correlation coefficent
$R_{P}=-0.60$, $p-$value$=0.02$), and a slightly less strong correlation with
median SFR surface density (Pearson correlation coefficent $R_{P}=0.51$,
$p-$value$=0.05$). However, overall fewer spaxels contain outflows.

Additionally, we also test the covering fraction out to $r_{90}$. We find that
the fraction of spaxels with outflows decreases between $r_{50}$ and $r_{90}$
by a median of 0.33 dex for H$\beta$ and 0.29 dex for [OIII] $\lambda 5007$,
suggesting that the majority of outflows are centrally located, although not
all outflows are launched from the centre of the galaxies. This is similar to
results from Avery et al. (2022) for the MaNGA galaxies, who found that most
neutral gas outflows are concentrated centrally within $\sim 0.25~{}R_{e}$.

Using absorption line measurements for 105 galaxies at $0.3<z<1.4$, Rubin et
al. (2014) found a median covering fraction of $\sim 0.65$ for both the Mg II
and Fe II absorption lines. This is far higher than what we find using
emission lines to trace the ionised gas. However, absorption line measurements
are sensitive to gas clouds at any distance along the line-of-sight to the
host galaxy. It is likely that they are able to probe outflowing gas that has
reached further from the galaxy than our emission line measurements, which
probe the base of the outflow. Their higher covering fractions could,
therefore, be caused by outflowing gas which has either been driven by
underlying star formation which is no longer observable, or has expanded
further across the face of the galaxy due to the outflow opening angle.

In addition, Rubin et al. (2014) found covering fractions $\gtrsim 0.5$ in 75%
of the absorption lines where they also measured equivalent widths for the
outflow component EW${}^{16\%}_{\rm flow}>0.2$ Å. They found a dependence of
the outflow equivalent width on the covering fraction. They also found that
the outflow equivalent width was correlated with the SFR, such that galaxies
with a higher SFR launch more material with a larger range of velocities.
Prusinski et al. (2021) also found a relationship between the equivalent width
and the covering fraction such that galaxies with more intense star formation
drive outflows with a higher covering fraction and a wider range of
velocities. These studies are in agreement with our result that galaxies with
a higher SFR surface density have a higher covering fraction.

##  5 Conclusions

In this paper we present sub-kpc spatially-resolved scaling relations for star
formation-driven outflows and properties of their host galaxies on 10 galaxies
from the DUVET sample. We fit multi-component Gaussians to the H$\beta$ and
[OIII] $\lambda 5007$ emission lines in 10 near-to-face-on galaxies. We find
the following main results.

  1. 1.

We find shallow relationships of the maximum outflow velocity with the SFR
surface density for both H$\beta$ ($v_{\rm out,H\beta}\propto\Sigma_{\rm
SFR}^{0.19\pm 0.01}$) and [OIII] $\lambda 5007$ ($v_{\rm
out,OIII}\propto\Sigma_{\rm SFR}^{0.10\pm 0.02}$). These fitted relationships
are not consistent with models of outflows that are dominated by momentum-
driven winds ($v_{\rm out}\propto\Sigma_{\rm SFR}^{2}$; Murray et al., 2011),
and suggests supernovae as the dominant energy source driving the wind (e.g.
Kim et al., 2020).

  2. 2.

We fit a nonlinear relationship between the mass outflow flux and the SFR
surface density such that $\dot{\Sigma}_{\rm out}\propto\Sigma_{\rm
SFR}^{1.20\pm 0.04}$.

  3. 3.

We find ionised gas mass loading factors between $\sim 0.1$ and $\sim 10$, and
approximate a total median mass loading factor of $\sim 2-100$. We fit an
almost flat relationship between the mass loading factor and the SFR surface
density which has no significant correlation.

  4. 4.

We make a direct comparison of outflow properties to the stellar mass surface
density and specific star formation rate. Outflows are much more common for
$\Sigma_{\rm SFR}/\Sigma_{\ast}\gtrsim 0.1$ Gyr-1. We note that outflows are
observed to lower $\Sigma_{\rm SFR}$ than previous threshold values. We also
find strong, positive correlations between outflow properties and co-located
$\Sigma_{\ast}$. In particular we find that outflow mass flux correlates with
the stellar mass surface density such that $\dot{\Sigma}_{\rm
out}\propto\Sigma_{\ast}^{1.68\pm 0.05}$.

  5. 5.

We compare the fraction of spaxels where we find evidence for outflows within
$r_{50}$ and $r_{90}$ to the total galaxy stellar mass, and the median galaxy
SFR surface density within $r_{50}$ and within $r_{90}$. We find a negative
correlation with stellar mass and a positive relationship with median SFR
surface density. This is consistent with the picture where galaxies of higher
mass have a larger gravitational potential well, and require more concentrated
star formation to drive gas out of the disk.

The observed scaling relations of outflow properties with the SFR surface
density suggest that outflows are primarily driven by energy from supernovae.
If supernovae are primarily driving the outflows, then the winds linearly
correlate to the SFR surface density. We should therefore expect that if you
change the spatial distribution of the starburst then the outflow distribution
will follow. Our covering fraction results are consistent with this picture.

This has multiple implications. Firstly, galaxies at higher redshift may have
a different outflow structure than local starburst galaxies (e.g. M 82 and NGC
253). While local starbursts are typically concentrated in the central
kiloparsec of the galaxy, galaxies at higher redshift have clumpier
morphologies, which may affect the structure of the outflowing gas. Secondly,
simulations suggest that outflows that have greater covering fractions may
have different energetics. Schneider et al. (2018) found that altering the
geometry of the simulated galaxy wind enables more gas cooling within the
outflow.

Our observation that outflows are more common in higher specific SFR regions
of galaxies seems straightforward to understand. Higher $\Sigma_{\rm SFR}$
provides more energy to the wind, and higher $\Sigma_{\ast}$ creates more
gravity reducing the outflow’s ability to break out of the disk. Therefore as
we increase the $\Sigma_{\ast}$ the $\Sigma_{SFR}$ required to drive an
outflow must also increase. We note that this boundary, $\Sigma_{\rm
SFR}/\Sigma_{\ast}\sim 0.1$ Gyr-1 is only a factor of $\sim$2$\times$ above
the resolved main-sequence for similar regions (Sánchez et al., 2021). It may
be that a combination of thresholds in both SFR surface density and specific
SFR is needed to predict the location of outflows.

We do not have a direct theoretical prediction for the steep scaling
relationship of $\dot{\Sigma}_{\rm out}\propto\Sigma_{\ast}^{1.68\pm 0.05}$.
We know that $\Sigma_{\rm SFR}$ correlates with both outflow properties and
stellar mass surface density. This may generate a secondary correlation
between the outflow and the stellar mass surface density, and the steep
scaling could simply be a result of uncertainties. Alternatively, it may be
that the higher stellar mass demands stronger outflows for gas to break out of
the plane of the disk and be observed as an outflow. More work relating the
resolved stellar mass properties, both stellar populations and kinematics,
with the feedback and gas properties is clearly warranted to understand this
correlation.

There are a number of limitations to our analysis. We must make many
assumptions about the outflow geometry and the electron density to calculate
some of these properties, particularly the mass outflow flux and the mass
loading factor. Future work obtaining resolved observations of outflows
capable of testing these assumptions is underway (Elliot et al. in prep) with
the GECKOS MUSE LP (van de Sande et al., 2023). It is also unclear whether the
constant mass loading we observe in our sample here persists in lower SFR
surface density environments. The mass that the star formation is able to lift
out of the galaxy may begin to decline more rapidly as the star formation
activity decreases.

More work adding observational constraints to the total mass loading
considering the multi-phase nature of outflows and its dependence on SFR
surface density and geometry is needed. In the future, with new facilities
such as the ELT, we will be able to test the contribution of underlying
stellar population parameters on star formation-driven feedback in
starbursting galaxies on the scale of stellar clusters.

## Acknowledgements

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.
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.
This publication makes use of data products from the Two Micron All Sky
Survey, which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation.
This work is based in part on observations made with the Spitzer Space
Telescope, which was operated by the Jet Propulsion Laboratory, California
Institute of Technology under a contract with NASA.
This research has made use of the NASA/IPAC Extragalactic Database (NED),
which is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology.

## Data Availability

Data underlying this article from the DUVET survey will be shared on
reasonable request to the PI, Deanne Fisher, at<EMAIL_ADDRESS>All other
data used within this article is archival and available publicly.

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##  Appendix A Choosing the $\delta_{\rm BIC}$ threshold

The typical literature value used for the BIC threshold is $\delta_{\rm
BIC}=-10$ (Kass & Raftery, 1995; Swinbank et al., 2019; Avery et al., 2021).
However, this threshold is based on the assumption that the model errors are
independent and distributed according to a normal distribution. Emission lines
in typical spiral galaxies have been shown to be better fit by multiple
Gaussian components (Ho et al., 2014). Observations of singular H II regions
also find emission lines require multiple Gaussian components (Rozas et al.,
2007) or a Voigt profile (Keto et al., 2008; Galván-Madrid et al., 2012). Our
data has extremely high signal-to-noise. We select only spaxels that have a
median signal-to-noise per wavelength channel of $\gtrsim 10$, implying a peak
signal-to-noise of 100-200 across many of the emission lines. This is
sufficiently high to identify any fluctuations away from a Gaussian shape in
the galaxy emission, even with the limited spectral resolution. In addition,
the models available for continuum subtraction are imperfect representations
of young, starburst populations, and residuals from this process may be
mistaken for a low-flux broad component if a lenient $\delta_{\rm BIC}$ is
used. In RC22a we found that using the typically adopted threshold value of
$\delta_{\rm BIC}$ results in all spaxels requiring multiple Gaussian
component models, even those spaxels in which a by-eye examination favours
only a single Gaussian component. We, therefore, choose a stricter value for
$\delta_{\rm BIC}$ using the following method.

Figure 8: The reduced $\chi^{2}$ value plotted against the difference in BIC
for fits to H$\beta$ (left) and [OIII] 5007 (right) emission lines. Purple
points represent fits using a simple 1 Gaussian model. Blue points represent
fits to the same data using a 2 Gaussian model. Solid lines of the same colour
show the rolling median of the points. The vertical black line is the
threshold value used for the whole sample, $\delta_{\rm BIC}=-200$. At this
threshold, the two populations of fits are statistically different.

To find the optimum threshold value to use with our data, we first ran
threadcount with a lenient threshold of $\delta_{\rm BIC}=-10$ for all
galaxies in our sample. We then compared the reduced $\chi^{2}$
($\chi^{2}_{red}=\chi^{2}/\nu$, where $\nu$ is the degrees of freedom) value
from fits to the emission lines using both a simple 1 Gaussian model and a 2
Gaussian model to the $\delta_{\rm BIC}$ returned comparing the two models.
There is some degree of circularity in this reasoning for any individual
emission line fit, as the $\chi^{2}$ value is calculated as part of the BIC.
However, we are using the comparative difference in $\chi^{2}_{red}$ value in
order to understand the BIC values. 8 shows the $\chi^{2}_{red}$ value plotted
against the $\delta_{\rm BIC}$ for all galaxies, with fits to H$\beta$
represented in the left, and [OIII] $\lambda 5007$ in the right panels
respectively.

For each galaxy, we determined the threshold to be the maximum $\delta_{\rm
BIC}$ where the running median of the $\chi^{2}_{red}$ for the 1 Gaussian
models becomes one standard deviation away from the running median of the
$\chi^{2}_{red}$ for the 2 Gaussian models. We then took the average across
all galaxies, finding an average H$\beta$ threshold of -161, and an average
[OIII] $\lambda 5007$ threshold of -132. We make a conservative choice to
round to $\delta_{\rm BIC}=-200$ for our threshold value across the sample,
and this is plotted as a black vertical line in Fig. 8. This conservative
choice may bias results by removing fits to low signal-to-noise spectra, as
well as fits suggesting low-velocity winds.

##  Appendix B Individual Galaxy Correlations

Galaxy Name | $v_{\rm out,[OIII]}$ | $v_{\rm out,H\beta}$ | $\dot{M}_{\rm out}$ | $\dot{\Sigma}_{\rm out}$ | $\eta$
---|---|---|---|---|---
|  (km s-1) |  (km s-1) |  ($M_{\odot}$ yr-1) |  ($M_{\odot}$ yr-1 kpc-2) |  |  |
| Median | RMS | Median | RMS | Total | Median | RMS | Median | RMS | Total | Median | RMS
IRAS 08339+6517 | 264 | 268 | 223 | 236 | 26.3 | 0.04 | 0.25 | 0.75 | 4.27 | 2.82 | 3.23 | 4.31
IRAS 15229+0511 | – | – | 218 | 219 | 0.74 | 0.05 | 0.07 | 0.12 | 0.19 | 0.16 | 0.42 | 0.60
KISSR 1084 | 353 | 355 | 299 | 286 | 0.64 | 0.01 | 0.06 | 0.04 | 0.18 | 0.19 | 0.47 | 1.21
NGC 7316 | 136 | 136 | 118 | 169 | 0.45 | 0.01 | 0.02 | 0.06 | 0.14 | 0.15 | 1.03 | 1.67
UGC 01385 | 377 | 361 | 307 | 320 | 12.23 | 0.18 | 0.55 | 1.68 | 5.04 | 1.72 | 2.81 | 4.58
UGC 10099 | 233 | 283 | 190 | 210 | 3.37 | 0.03 | 0.08 | 0.08 | 0.22 | 0.70 | 1.05 | 1.46
CGCG 453-062 | 299 | 299 | 231 | 265 | 0.81 | 0.03 | 0.04 | 0.14 | 0.20 | 0.04 | 0.48 | 1.28
UGC 12150 | – | – | 138 | 138 | 0.01 | 0.01 | 0.01 | 0.04 | 0.04 | 0.0003 | 0.06 | 0.06
IRAS 20351+2521 | 146 | 269 | 211 | 248 | 0.57 | 0.03 | 0.06 | 0.08 | 0.16 | 0.03 | 0.22 | 0.40
NGC 0695 | 215 | 219 | 190 | 199 | 2.89 | 0.04 | 0.07 | 0.12 | 0.20 | 0.07 | 0.61 | 1.16
Table 4: The median and root-mean-square for the maximum outflow velocity
$v_{\rm out}$ measured from the [OIII] $\lambda 5007$ and H$\beta$ emission
lines; the total, median and root-mean-square mass outflow rate $\dot{M}_{\rm
out}$; the median and root-mean-square mass outflow flux $\dot{\Sigma}_{\rm
out}$; and the total, median and root-mean-square mass loading factor $\eta$
within $r_{90}$ for 10 face-on galaxies in the DUVET sample.

In this appendix, we show the correlations between the SFR surface density and
the maximum outflow velocity from fits to the H$\beta$ and [OIII] $\lambda
5007$ emission lines, and the mass outflow flux for each individual galaxy in
our sample. In each figure, the panels are organised from left to right and
then top to bottom, such that the lowest total galaxy mass is in the top left
panel and the highest total galaxy mass in the bottom right panel. Total
galaxy masses for the galaxies are taken from literature values, and are given
in Table 1. The median and root-mean-square scatter values for the outflow
velocities and mass outflow flux, and the total, median and root-mean-square
scatter values for the mass outflow rate and mass loading factor within
$r_{90}$ for each galaxy are given in Table 4.

In Fig. 9 and Fig. 10 we compare the maximum outflow velocity to the SFR
surface density for H$\beta$ and [OIII] $\lambda 5007$ respectively for each
galaxy in our sample. All of the galaxies in our sample except for IRAS
08339+6517 are brighter in H$\beta$ than in [OIII] $\lambda 5007$. Three of
our galaxies (UGC 12150, NGC 7316 and IRAS 15229+0511) do not have the signal-
to-noise necessary to fit an outflow component in [OIII] $\lambda 5007$. In
fact, we find only one spaxel in UGC 12150 where H$\beta$ is fit with an
outflow component.

CGCG 453-062’s high inclination angle ($i\approx 54^{\circ}$) required that
the velocities be deprojected by dividing by $\cos{i}$. The originally
observed velocities are shown in the CGCG 453-062 panels of Fig. 9 and Fig. 10
as transparent orange circles. The deprojected velocities are shown as blue
points. The median H$\beta$ outflow velocity before correction is 125 km s-1,
and the inclination correction increases this to 213 km s-1.

In Fig. 4 we compare the ionised gas mass outflow flux to the SFR surface
density for each galaxy in our sample. We show here the results for the
outflow flux with no extinction correction applied (see Section 4.2 for more
information on the extinction correction). We find that the majority of
galaxies in our sample follow a trend of increasing outflow mass flux with
increasing SFR surface density. This suggests that the important global change
between galaxies is the degree of star formation driving the outflows, but on
smaller scales the same local relationship remains.

Figure 9: The maximum outflow velocity, $v_{\rm out}$, calculated using the
H$\beta$ line plotted against the star formation rate surface density,
$\Sigma_{\rm SFR}$ for individual galaxies in our sample, given in order of
increasing total stellar mass from left to right, top to bottom. Orange points
show the velocities we observe before reprojection. The dashed lines represent
a model where outflows are primarily driven by momentum injected into the gas
from young massive stars ($v_{\rm out}\propto\Sigma_{\rm SFR}^{2}$; Murray et
al., 2011). The dotted lines represent a model where outflows are primarily
driven by energy injected from supernovae ($v_{\rm out}\propto\Sigma_{\rm
SFR}^{0.1}$; Chen et al., 2010). Figure 10: As for Fig. 9, but using results
from fits to the [OIII] $\lambda 5007$ emission line. Figure 11: The ionised
gas outflow mass flux, $\dot{\Sigma}_{\rm out}$, compared to the SFR surface
density, $\Sigma_{\rm SFR}$, for spaxels of sub-kpc resolution pixels in local
starbursting disk galaxies with evidence for outflow components. Each panel
gives results for a different galaxy in our sample, given in order of
increasing total stellar mass from left to right, top to bottom. Dashed black
lines show constant mass loading factors.