# [Cii] Spectral Mapping of the Galactic Wind and Starbursting Disk of M82
with SOFIA

Rebecca C. Levy NSF Astronomy and Astrophysics Postdoctoral Fellow  Steward
Observatory, University of Arizona, Tucson, AZ 85721, USA  Alberto D. Bolatto
Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Joint Space-Science Institute, University of Maryland, College Park, MD 20742,
USA  Elizabeth Tarantino Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA  Department of Astronomy, University of
Maryland, College Park, MD 20742, USA  Adam K. Leroy Department of Astronomy,
The Ohio State University, Columbus, OH 43210, USA  Lee Armus IPAC, California
Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125,
USA  Kimberly L. Emig Jansky Fellow of the National Radio Astronomy
Observatory  National Radio Astronomy Observatory, 520 Edgemont Road,
Charlottesville, VA 22903  Rodrigo Herrera-Camus Departamento de Astronomía,
Universidad de Concepción, Barrio Universitario, Concepción, Chile  Daniel P.
Marrone Steward Observatory, University of Arizona, Tucson, AZ 85721, USA
Elisabeth Mills Department of Physics and Astronomy, University of Kansas,
1251 Wescoe Hall Dr., Lawrence, KS 66045, USA  Oliver Ricken Max-Planck-
Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany  Juergen
Stutzki I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77,
D-50937 Köln, Germany  Sylvain Veilleux Department of Astronomy, University of
Maryland, College Park, MD 20742, USA  Joint Space-Science Institute,
University of Maryland, College Park, MD 20742, USA  Fabian Walter Max-Planck-
Institut für Astronomie, Königstuhl 17, 69120 Heidelberg, Germany

###### Abstract

M 82 is an archetypal starburst galaxy in the local Universe. The central
burst of star formation, thought to be triggered by M 82’s interaction with
other members in the M 81 group, is driving a multiphase galaxy-scale wind
away from the plane of the disk that has been studied across the
electromagnetic spectrum. Here, we present new velocity-resolved observations
of the [Cii] 158$\mu$m line in the central disk and the southern outflow of M
82 using the upGREAT instrument onboard SOFIA. We also report the first
detections of velocity-resolved ($\Delta V=10$ km s-1) [Cii] emission in the
outflow of M 82 at projected distances of $\approx 1-2$ kpc south of the
galaxy center. We compare the [Cii] line profiles to observations of CO and Hi
and find that likely the majority ($>55$%) of the [Cii] emission in the
outflow is associated with the neutral atomic medium. We find that the
fraction of [Cii] actually outflowing from M 82 is small compared to the bulk
gas outside the midplane (which may be in a halo or tidal streamers), which
has important implications for observations of [Cii] outflows at higher
redshift. Finally, by comparing the observed ratio of the [Cii] and CO
intensities to models of photodissociation regions, we estimate that the far-
ultraviolet (FUV) radiation field in the disk is $\sim
10^{3.5}\leavevmode\nobreak\ G_{0}$, in agreement with previous estimates. In
the outflow, however, the FUV radiation field is 2-3 orders of magnitudes
lower, which may explain the high fraction of [Cii] arising from the neutral
medium in the wind.

††facilities: SOFIA (upGREAT), IRAM:30m, VLA, GBT††software: Astropy (Astropy
Collaboration et al., 2018, 2022), kalibrate (Guan et al., 2012), MatPlotLib
(Caswell et al., 2020), NumPy (Harris et al., 2020), pandas (Reback et al.,
2020), photutils (Bradley et al., 2021), SciPy (Virtanen et al., 2020),
seaborn (Waskom et al., 2014), spectral-cube (Ginsburg et al., 2019),
WebPlotDigitizer (Rohatgi, 2021)

##  1 Introduction

Stars inject energy and momentum into their surrounding environments over
their entire lifetimes. This so-called stellar feedback can result in massive
outflows of gas and dust from the centers of galaxies, where there are high
concentrations of stars and star clusters. In these dense environments, energy
and momentum injected by supernova explosions and winds from massive stars
that are clustered in space and time push material out of the midplane of a
galaxy, leading to the observed biconical outflows and superwinds (e.g.,
Heckman et al., 1990; Veilleux et al., 2005, 2020, and references therein).
These outflows are inherently multiphase, with the cool neutral phases of the
winds potentially carrying away the bulk of the outflowing mass and the fuel
for future star formation (e.g., Veilleux et al., 2020).

The [Cii] 158µm line in the far-infrared (FIR) is one of the brightest lines
in star forming galaxies. It is a major cooling channel of the neutral
interstellar medium (ISM) and can contribute 0.1-1% of the total FIR emission
from a galaxy (e.g., Crawford et al., 1985; Stacey et al., 1991). Owing to its
low ionization potential (11.2 eV), neutral carbon can be singly ionized in a
range of conditions and ISM phases, making the [Cii] 158µm line an excellent
tracer of multiphase gas (e.g., Madden et al., 1993; Goldsmith et al., 2012;
Pineda et al., 2013). In the disks and centers of nearby star forming
galaxies, [Cii] tends to be most closely associated with the neutral atomic
component, but a substantial fraction can also arise from the molecular
component (Mookerjea et al., 2016; Röllig et al., 2016; Fahrion et al., 2017;
Tarantino et al., 2021). It is unknown, however, how the origin and
distribution of [Cii] may change in a starburst-driven superwind.

M 82 is an archetypal starburst galaxy, located at a distance of $3.63\pm
0.34$ Mpc (Freedman et al., 1994) in the M 81 group. M 82 is interacting with
the other group members (Yun et al., 1994; de Blok et al., 2018). It is
thought that this tidal interaction triggered a central burst of star
formation 10 Myr ago, followed by a second bar-driven burst 5 Myr ago (Förster
Schreiber et al., 2003). The central starburst has launched a multiphase,
galaxy-scale wind, which has been studied across the electromagnetic spectrum
(e.g., Lynds & Sandage, 1963; Heckman et al., 1990; Strickland et al., 1997;
Walter et al., 2002; Engelbracht et al., 2006; Strickland & Heckman, 2009;
Veilleux et al., 2009; Yoshida et al., 2011; Yamagishi et al., 2012; Contursi
et al., 2013; Beirão et al., 2015; Leroy et al., 2015; Martini et al., 2018;
Yoshida et al., 2019; Krieger et al., 2021). It is unclear whether the
material in the wind has sufficient energy to escape into the intergalactic
medium or whether it will fall back onto the galaxy as a fountain (e.g., Leroy
et al., 2015; Martini et al., 2018; Yuan et al., 2023).

Because M 82 is such an important laboratory for studying the multiphase ISM
in a starburst environment, its center has previously been observed in the
[Cii] 158µm line by the Kuiper Airborne Observatory (KAO; Stacey et al. 1991)
and Herschel HIFI and PACS (Loenen et al., 2010; Contursi et al., 2013;
Herrera-Camus et al., 2018). While the PACS data extend into the base of the
outflow, [Cii] has not been detected in the outflow at distances greater than
$\sim 1$ kpc from the midplane. Moreover, because of the low velocity
resolution of PACS, the [Cii] data from that instrument are not velocity-
resolved.

In this paper, we present new observations of the [Cii] 158µm line taken with
the upgraded German REceiver for Astronomy at Terahertz Frequencies (upGREAT;
Risacher et al. 2018) on board the Stratospheric Observatory for Infrared
Astronomy (SOFIA; Temi et al. 2018). These velocity-resolved observations
measured [Cii] at 10 km s-1 velocity resolution in the inner disk of M 82 and
the southern side of the superwind at distances of $1-2$ kpc from the
midplane.

This paper is organized as follows. We describe the data used in this study in
Section 2. In Section 3, we discuss the main results from the [Cii] detections
in the outflow of M 82. The main results from the [Cii] map in the disk are
discussed in Section 4. A discussion of the disk and wind together is
presented in Section 5. We discuss constraints on the far-ultraviolet (FUV)
radiation field in both the disk and outflow in Section 6. We summarize our
main conclusions in Section 7.

Throughout, we use CO to refer to 12C16O($J=1-0$). We use
$(\alpha,\delta)=(09^{\rm h}55^{\rm m}52.72^{\rm s},+69^{\circ}40^{\rm
m}45.8^{\rm s})$ as the J2000 right ascension and declination of the center of
M 82 (Martini et al., 2018). We assume a central recessional velocity of 210
km s-1 LSRK (Krieger et al., 2021). We assume that the major axis position
angle111The PA is measured counterclockwise from north to the receding side of
the galaxy. (PA) of M 82 is 67∘; therefore, the PA of the southern side of the
wind is 157∘ (e.g., Martini et al., 2018). We adopt an inclination of 80∘ for
the disk (e.g., Lynds & Sandage, 1963; McKeith et al., 1993; Martini et al.,
2018; Krieger et al., 2021). The data and code for the analysis presented here
are available online222https://github.com/rclevy/M82_CII.

##  2 Observations and Data Reduction

###  2.1 [CII] Data from upGREAT

Figure 1: Composite maps of M 82. In all panels, the teal rectangle shows the
fully-sampled region of the upGREAT [Cii] map of the disk (3 kpc $\times$ 1
kpc). The footprints of the upGREAT single pointing along the southern outflow
are shown as the teal circles, where the size of each circle is the upGREAT
beam size (14.1″). Top left: An $r$-band image of M 82 from the SINGS Survey
(Kennicutt et al., 2003). Top right: The Hi integrated intensity is shown in
orange-purple filled contours, with values linearly spanning $4-1500$ K km s-1
(Martini et al., 2018). The missing Hi data in the center reflects where
accurate Hi information cannot be obtained due to strong absorption against
the continuum; this region fully covers the region detected with SNR $>2$ in
the [Cii] map. The CO integrated intensity is shown in grayscale contours,
with values logarithmically spanning $20-600$ K km s-1 (Krieger et al., 2021).
The FWHM beam sizes of the Hi and CO data are shown in the lower right corner
in magenta and black respectively. Bottom left: A zoom in, showing the [Cii]
integrated intensity in green-blue, with values logarithmically spanning
$200-1200$ K km s-1. The Hi integrated intensity is shown as the orange-purple
filled contours over the same range of values as in the top right panel. The
FWHM beam sizes of the Hi and [Cii] data are shown in the lower right corner
in magenta and teal respectively. The numbers in each of the teal circles give
the pixel numbers of the LFA. The white $\times$ marks the galaxy center.
Bottom right: The same as the bottom left, but showing the CO integrated
intensity (in grayscale contours over the same range of values as in the top
right panel) instead of the Hi.

These observations of the [Cii] 158µm line in M 82 were taken using the low
frequency array (LFA) of the upGREAT333upGREAT is a development by the MPI für
Radioastronmie and KOSMA/Universität zu Köln, in cooperation with the MPI für
Sonnensystemforschung and the DLR Institut für Optische Systeme. instrument
(Risacher et al., 2018) onboard SOFIA (Temi et al., 2018). These data were
taken in cycle 8 as part of project 08_0225 (PI: R. Levy) on 2021 February 19,
February 23, February 25, March 10, and March 11.

The upGREAT LFA consists of a seven-pixel hexagonal array for each
polarization; the polarizations were averaged for these data. It was tuned to
the [Cii] line at 158µm (1.9005 THz). At this frequency, each upGREAT LFA
pixel has a half-power beam width of 14.1″ ($\approx 250$ pc). The bandwidth
of the observations ranged from -150$-$430 km s-1 (1.8996$-$1.9033 THz,
$\Delta\nu=3.6$ GHz), with a native velocity resolution of 0.04 km s-1
($R\approx 7.5\times 10^{6}$).

The observing time was split between making an on-the-fly (OTF) map of the
inner 3′$\times$1′ of the disk and a single pointing of the upGREAT LFA along
the southern outflow. Both observing strategies used a dual-beam-switching
mode to measure the OFF positions to maximize baseline stability. More details
pertaining to the OTF map and single pointing are given in Sections 2.1.1 and
2.1.2. The footprints of the OTF map and single pointing are shown in Figure
1.

All observations were pipeline calibrated (in particular: correction for
atmospheric transmission) with the GREAT kalibrate software (Guan et al.,
2012) by the upGREAT team and further processed to level-2 data using the
class software in gildas. As part of the calibration, a first-order baseline
was removed, the final spectra were smoothed to 10 km s-1 channels, and the
spectra were converted to a main-beam temperature (${\rm T_{mb}}$) scale,
where $\eta_{\rm mb}\approx\ 0.67$.

####  2.1.1 Disk Map

To map the inner region of the disk, the LFA was scanned across the central
4.3′$\times$2.3′, centered on the galaxy center given in Section 1, at an
angle of -20∘ so that the long-axis of the map is aligned with the galaxy’s
major axis. With this strategy, the fully-sampled region of the map covers the
inner 3.1′$\times$1.1′ (3 kpc $\times$ 1 kpc) as shown in Figure 1. Two
tunings (centered at 250 km s-1 and 290 km s-1 LSRK) were used to capture the
full extent of the [Cii] emission in the disk. The spectra were weighted by
1/$\sigma_{\rm rms}^{2}$, where $\sigma_{\rm rms}$ is the root-mean-square
(rms) noise of the baseline. The 3D data cube of the disk has an rms noise of
307 mK in 10 km s-1 channels away from the emission. Spatial pixels are
7″$\times$7″ and hence oversample the beam by a factor of $\approx 3$ (in
area).

Figure 2: The upGREAT [Cii] maps of the central 3 kpc $\times$ 1 kpc of M 82,
showing the [Cii] peak intensity (top left), integrated intensity (Moment 0;
top right), mean velocity (Moment 1; bottom left), and linewidth (Moment 2;
bottom right). Spaxels with SNR $<2$ (relative to the rms noise of the cube)
are masked out of the 3D cube before the 2D maps are made. The black rectangle
shows the boundaries of the fully-sampled map. The black-outlined circles
below the maps show the same values for the single pointings along the
outflow. The numbers in each of the circles in the upper left panel give the
pixel numbers of the LFA. The solid black circles in the lower left corners
show the 14.1″ ($\approx 250$ pc) beam. The black $\times$ marks the galaxy
center (Martini et al., 2018). In the lower left panel, the gray horizontal
line in the color bar marks the systemic velocity ($V_{\rm sys}$) of M 82 (210
km s-1; Krieger et al. 2021).

We make 2D maps of the [Cii] peak intensity, integrated intensity, mean
velocity, and linewidth using moments444In both the disk and outflow, the
[CII] lines are often not Gaussian and so deriving these quantities using a
Gaussian fit may lead to biased results.. We restrict the velocity range to
$-100-400$ km s-1 in the calculation of these quantities. For the disk maps,
we mask out elements in the cube where the intensity is less than 2$\times$
rms noise ($2\times 307=614$ mK). These moment maps are shown in Figure 2,
with the integrated intensity map also being shown in Figure 1.

As noted in Section 1, the [Cii] 158µm line has been previously observed in
the center of M 82 using the KAO (Stacey et al., 1991) and Herschel PACS
(Contursi et al., 2013; Herrera-Camus et al., 2018) and HIFI (Loenen et al.,
2010). In this article, we compare the upGREAT map to that from PACS (Contursi
et al., 2013)555The level-2 PACS data were downloaded from the Herschel
Science Archive, observation ID 1342187205.. To robustly compare these
measurements, we convolve the PACS cube to the 14″ Gaussian beam of upGREAT
using the kernels provided by Aniano et al. (2011). In single beams (not
maps), Tarantino et al. (2021) found that not properly accounting for the
different point-spread-function (PSF) shapes can lead to 40% discrepancies
between fluxes measured by PACS and upGREAT. We compute the integrated
intensity using a moment analysis over the same velocity range as the upGREAT
data. We measure the flux from the matched upGREAT and PACS maps in a 1′
$\times$ 1′ box (rotated by -20∘) centered on the center of M 82 (Martini et
al., 2018). This box optimizes the overlapping regions of the upGREAT and PACS
maps. Over this region, the integrated [Cii] line intensity measured from the
upGREAT map is $2.0\times 10^{-13}{\rm\leavevmode\nobreak\
W\leavevmode\nobreak\ m^{-2}}$. The matched PACS map yields $1.9\times
10^{-13}{\rm\leavevmode\nobreak\ W\leavevmode\nobreak\ m^{-2}}$. These two
values agree to within 5%, well within the 30% PACS calibration uncertainty
(Contursi et al., 2013).

####  2.1.2 Outflow Pointings

To measure [Cii] in the outflow, a single pointing of the upGREAT LFA was
used. A location on the southern (brighter) side of the outflow was chosen
such that the central pixel of the upGREAT array (Pixel 0) was located 1.5 kpc
from the galaxy center along the outflow (i.e., the galaxy minor axis with
${\rm PA}=157$∘). The LFA array was rotated by 70∘ to maximize the extent
along the southern outflow. The footprint of the LFA is shown is Figures 1 and
2. The spectra in the outflow, shown in Figure 3, have rms noise of $7-12$ mK
in 10 km s-1 channels.

Figure 3: SOFIA upGREAT [Cii] spectra in the southern outflow of M 82, with 10
km s-1 channels (teal filled). The panels are arranged as shown in Figure 1,
where the pixel number is shown in the top-left of each panel. The distance of
the center of each LFA pixel to the galaxy center is shown in the top-right
corner. The panels all have the same axis scaling, as shown in the lower-left
panel. Scaled versions of the CO (dark gray) and Hi (magenta) profiles are
overplotted. The CO and Hi spectra are simply normalized to the peak of the
[Cii] spectrum, and the values by which the CO and Hi spectra are scaled are
listed in each panel.

We calculate moments of the spectra to measure the peak and integrated
intensity, the mean velocity, and the linewidth. As with the disk map, we
restrict the velocity range to $-100-400$ km s-1 in the calculation of these
quantities. We report these values in Table 1 and show these quantities in
Figure 2.

Table 1: Properties of [Cii] spectra in the outflow

Pixel Number | R.A. | Decl. | ${\rm I_{peak}}$ | ${\rm I_{int}}$ | ${\rm V_{0}}$ | $\sigma_{\rm V}$ | rms | ${\rm log_{10}M_{C^{+}}}$
---|---|---|---|---|---|---|---|---
| (J2000 hours) | (J2000 degrees) | (mK) | (K km s-1) | (km s-1) | (km s-1) | (mK) | (${\rm log_{10}M_{\odot}}$)
0 | $9^{\mathrm{h}}55^{\mathrm{m}}54.6^{\mathrm{s}}$ | $+69^{\circ}39{}^{\prime}24.3{}^{\prime\prime}$ | 72.0 $\pm$ 14.8 | 10.8 $\pm$ 1.0 | 143.3 $\pm$ 10.2 | 94.2 $\pm$ 16.9 | 5.8 | 3.5 $\pm 0.2$
1 | $9^{\mathrm{h}}55^{\mathrm{m}}56.2^{\mathrm{s}}$ | $+69^{\circ}39{}^{\prime}46.9{}^{\prime\prime}$ | 98.6 $\pm$ 33.4 | 21.2 $\pm$ 2.4 | 141.2 $\pm$ 10.3 | 96.0 $\pm$ 19.7 | 9.4 | 3.8 $\pm 0.1$
2 | $9^{\mathrm{h}}55^{\mathrm{m}}56.9^{\mathrm{s}}$ | $+69^{\circ}39{}^{\prime}19.8{}^{\prime\prime}$ | 88.9 $\pm$ 28.2 | 13.7 $\pm$ 2.0 | 144.9 $\pm$ 10.5 | 89.3 $\pm$ 17.5 | 9.6 | 3.6 $\pm 0.2$
3 | $9^{\mathrm{h}}55^{\mathrm{m}}55.3^{\mathrm{s}}$ | $+69^{\circ}38{}^{\prime}59.1{}^{\prime\prime}$ | 77.5 $\pm$ 31.0 | 16.4 $\pm$ 2.2 | 165.1 $\pm$ 10.6 | 111.8 $\pm$ 93.8 | 6.9 | 3.7 $\pm 0.1$
4 | $9^{\mathrm{h}}55^{\mathrm{m}}53.4^{\mathrm{s}}$ | $+69^{\circ}39{}^{\prime}00.0{}^{\prime\prime}$ | — | — | — | — | 6.8 | —
5 | $9^{\mathrm{h}}55^{\mathrm{m}}52.5^{\mathrm{s}}$ | $+69^{\circ}39{}^{\prime}30.1{}^{\prime\prime}$ | — | — | — | — | 16.8 | —
6 | $9^{\mathrm{h}}55^{\mathrm{m}}54.1^{\mathrm{s}}$ | $+69^{\circ}39{}^{\prime}52.3{}^{\prime\prime}$ | 203.0 $\pm$ 27.4 | 23.3 $\pm$ 1.9 | 180.2 $\pm$ 10.3 | 77.4 $\pm$ 247.0 | 11.5 | 3.8 $\pm 0.1$

Note. — The R.A. and Decl. of the center of each pixel are given. The other
columns show the moments of the spectra including the peak intensity (${\rm
I_{peak}}$), the integrated intensity (moment 0; ${\rm I_{int}}$), the mean
velocity (moment 1; ${\rm V_{0}}$), the linewidth (moment 2, $\sigma_{\rm
V}$), and corresponding uncertainties. The moments are calculated over a fixed
velocity range spanning -$100-400$ km s-1. rms is the root-mean-square noise
of the spectrum calculated outside of the velocity range used for the moments.
If the moments cannot be calculated because the line is not detected, then the
rms is calculated over the entire bandpass. All temperatures refer to Tmb.
${\rm M_{C^{+}}}$ is the mass in C+ inferred from the spectrum considering
only collisions with the atomic gas; see Appendix A for details of this
calculation.

As a check, we compare the flux we measure in outflow Pixels 1 and 6 to the
Herschel PACS map (Contursi et al., 2013) convolved to a 14″ Gaussian PSF as
described in Section 2.1.1. Pixels 1 and 6 are the only upGREAT pointings that
overlap with the PACS coverage. From the PACS map, we measure a total [Cii]
integrated line intensity of 4.8 K km s-1 (12.0 K km s-1) in Pixel 1 (6). This
is lower than the [Cii] integrated intensity of 21.2 K km s-1 (23.3 K km s-1)
measured in the upGREAT map (Table 1). We note, however, that these pixels are
at the edges of the PACS map and there may be substantial flux loss due to
edge effects and undersampling. When these PACS maps were reprocessed by
Herrera-Camus et al. (2018), for example, these edge regions were excluded.

###  2.2 Ancillary Data

Because [Cii] can be excited in many conditions, we compare the [Cii] emission
with the molecular and atomic ISM components. We use ancillary CO and Hi data
as tracers of those respective components.

####  2.2.1 CO(1-0) Tracing the Molecular Gas

The CO data used in this study is from the Institut de Radioastronomie
Millimétrique (IRAM) 30-m telescope. These data were presented by Krieger et
al. (2021), and we direct the reader to that paper for details on the
observations, calibration, and imaging. We note that while the data presented
by Krieger et al. (2021) include both interferometric and single-dish
observations, we find that there are significant interferometric artifacts
(absorption) in the spectra that hinder the comparison to the [Cii] data in
this work. Therefore, we use only the single-dish data, which do not show
these spectral artifacts. The final CO cube has a spatial resolution of 22″
($\approx 385$ pc) and a velocity resolution of 5 km s-1. For this work, we
smooth the CO cube to a velocity resolution of 10 km s-1 to match the [Cii]
data. We show the CO integrated intensity in Figure 1.

####  2.2.2 HI Tracing the Atomic Gas

The Hi data used in this study is from the Karl G. Jansky Very Large Array
(VLA) which has been combined with single-dish data from the Robert C. Byrd
Green Bank Telescope (GBT). These data were presented by Martini et al.
(2018), and we direct the reader to that paper for details on the
observations, calibration, and imaging. The Hi cube has a native velocity
resolution of 5 km s-1. We spectrally smooth this data to a velocity
resolution of 10 km s-1 to match the [Cii] data. The Hi data used here have a
spatial resolution of 17″ ($\approx 300$ pc), slightly higher than that
presented by Martini et al. (2018). In the center of M 82, the Hi is heavily
absorbed against the bright continuum (Martini et al., 2018), so the Hi cannot
be compared to the [Cii] in the disk; this is not a problem in the outflow
pointings. To produce the integrated intensity map (Figure 1), we create a
mask to exclude the absorption and to exclude channels where the Hi intensity
$<2.3$ K (SNR$<3$). We note that our analysis is performed on the Hi cube
itself, and the Hi integrated intensity map is to aid in the visualization.

####  2.2.3 $r$-band Image

For visualization purposes, we show an $r$-band image of M 82 in Figure 1.
This image was taken with as part of the SINGS Survey (Kennicutt et al., 2003;
SINGS Team, 2020) and was downloaded from the NASA/IPAC Extragalactic
Database.

####  2.2.4 Matching the Datasets

In the outflow, we extract the CO and Hi from the central pixel of each
upGREAT pointing. As noted above, the CO and Hi data are smoothed to a
velocity resolution of 10 km s-1, to match the [Cii]. To make the most
accurate comparison, the data should be convolved to the 22″ resolution of the
CO data. Because, however, the upGREAT data in the outflow are single
pointings (not a map), they cannot be convolved to lower resolution.
Therefore, we do not match the beam sizes of the CO, Hi, and [Cii] data in the
outflow. As we will discuss in Section 4, we do match the resolutions and
pixel scales of the [Cii] and CO datasets in the disk.

We show the [Cii], CO, and Hi spectra in Figure 3, where the CO and Hi are
simply normalized to the peak intensity of the [Cii]. We derive the CO and Hi
integrated intensities (moment 0) in the same way as for the [Cii] spectra and
over the same velocity range. In Table 2, we give the ratios of the integrated
intensities of Hi/[Cii] and CO/[Cii], where all integrated intensities are in
K km s-1 units.

Table 2: Ratios of the integrated intensities and luminosities in the outflow.

Pixel Number | ${\rm I_{int,HI}/I_{int,[CII]}}$ | ${\rm I_{int,CO}/I_{int,[CII]}}$ | ${\rm L_{[CII]}/L_{CO}}$
---|---|---|---
0 | 1372.9 $\pm$ 140.5 | 12.0 $\pm$ 1.3 | 154 $\pm$ 6
1 | 779.1 $\pm$ 91.1 | 12.0 $\pm$ 1.4 | 154 $\pm$ 6
2 | 944.4 $\pm$ 141.2 | 11.4 $\pm$ 1.7 | 163 $\pm$ 7
3 | 498.5 $\pm$ 69.5 | 3.5 $\pm$ 0.5 | 535 $\pm$ 30
4 | — | — | —
5 | — | — | —
6 | 718.3 $\pm$ 65.7 | 14.8 $\pm$ 1.3 | 125 $\pm$ 5

Note. — To form the ratios, all integrated intensities are in K km s-1 units
and all luminosities are in $L_{\odot}$ units.

##  3 [CII] in the Wind of M 82

We robustly detect the [Cii] 158µm line in five of the seven LFA pixels in the
southern outflow of M 82, as shown in Figure 3. As described in Section 2.1.2,
we calculate moments of these spectra which are listed in Table 1 and shown in
Figure 2. The ratios of the peak CO to [Cii] intensities (in K brightness
temperature units) are $\sim 1$, in agreement with previous work (Stacey et
al., 1991). We present the integrated intensity ratios (on a K km s-1
intensity scale) in each LFA pixel in Table 2.

From the [Cii] spectra in the outflow, we calculate the column density and
mass of C+ in each outflow pointing. These calculations are detailed in
Appendix A. Briefly, the C+ column density as a function of velocity ($N_{\rm
C^{+}}$) is calculated the following Equation A5, assuming that the [Cii] is
only excited in the cold neutral medium (CNM; e.g., Pineda et al., 2013;
Fahrion et al., 2017; Herrera-Camus et al., 2017). For this calculation, we
must assume a kinetic temperature, $T$, and a gas density, $n$. Our assumed
temperature and density come from inspecting the spatially-resolved
photodissociation region (PDR) modeling results presented by Contursi et al.
(2013). Though they do not probe out as far into the outflow as our
measurements, they find temperature of $T\sim 200-300$ K and densities of
$n\sim 10-150$ cm-3 along the southern outflow away from the disk (uncorrected
for the effects of the ionized gas; see their Figures 15 and 16). We note that
these values differ from those presented in their Table 1. The "southern
outflow" macro region they define is likely contaminated by the starburst (see
their Figure 18) and hence the average temperature and density reported in
that table are likely too high to apply to the part of the outflow we are
studying. From these results, we take a representative temperature of
$T=250\pm 50$ K and a representative density of $n=100\pm 50$ cm-3.

As we discuss in more detail below, our choice to assume that the [Cii] is
primarily excited in the CNM is well-justified. We sum this column density
over velocity and multiply by the area of each LFA pixel to measure the mass
in C+ ($M_{\rm C^{+}}$; Equation A11). We list $M_{\rm C^{+}}$ in each
pointing in Table 1. The total C+ mass in the part of the outflow covered by
these pointings is $2.4\times 10^{4}$ M⊙ (excluding Pixels 4 and 5 where the
[Cii] line is not detected).

###  3.1 Atomic Gas in the Outflow

From $N_{\rm C^{+}}$, we can estimate the effective CNM column density needed
to produce the observed [Cii] spectra (see details in Section A.1). To make
this conversion, we divide $N_{\rm C^{+}}$ by a C/H abundance ratio (${\rm
C/H}=1.5\times 10^{-4}$; Gerin et al. 2015). We show these effective CNM
column density profiles (per unit velocity, i.e., divided by the channel width
of 10 km s-1) based on the [Cii] ($N_{\rm CNM}^{\rm[CII]}$) in teal in Figure
4.

Figure 4: The Hi and CNM column densities (per unit velocity) in the outflow
of M 82. The teal curves show the CNM column density inferred from the [Cii]
spectrum ($N_{\rm CNM}^{\rm[CII]}$) assuming collisions with only the atomic
gas, $T=250$ K, $n=100$ cm-3, and ${\rm C/H=1.5\times 10^{-4}}$. The thick
magenta curves show $N_{\rm HI}$ measured directly from the Hi data. The thin
magenta curves show the CNM column density inferred from the Hi ($N_{\rm
CNM}^{\rm HI}$) assuming $f_{\rm CNM}$ =0.5. The LFA pixels are oriented as in
Figure 3, and the pixel numbers are given in the top left corner of each
panel. The number in the top right corner of each panel is the ratio of the
peaks of $N_{\rm CNM}^{\rm HI}$ and $N_{\rm CNM}^{\rm[CII]}$ over the shaded
portions of the profiles. The uncertainties come from a Monte Carlo over the
range of temperature and densities considered.  Figure 5: Similar to Figure 4,
but showing the H2 column densities (per unit velocity) in the outflow of M
82. The teal curves show the H2 column density inferred from the [Cii]
spectrum ($N_{\rm H_{2}}^{\rm[CII]}$) assuming collisions with only H2,
$T=250$ K, $n=100$ cm-3, and ${\rm C/H_{2}=3\times 10^{-4}}$. The gray curves
show the column density of H2 measured from the CO data ($N_{\rm H_{2}}^{\rm
CO}$) assuming $X_{\rm CO}=0.5\times 10^{20}$ cm-2 (K km s-1)-1. The number in
the top right corner of each panel is the ratio of the peaks of $N_{\rm
H_{2}}^{\rm CO}$ and $N_{\rm H_{2}}^{\rm[CII]}$ over the shaded portions of
the profiles. The uncertainties come from a Monte Carlo over the range of
temperature and densities considered.

In order to determine the ISM phase from which most of the [Cii] emission
originates, we compare our $N_{\rm CNM}^{\rm[CII]}$ profiles to the measured
total Hi column density profiles ($N_{\rm HI}$). Modulo optical depth effects,
the Hi profiles (measured directly from the Hi data) probe the total atomic
gas content from both the CNM and WNM. Following Martini et al. (2018), we
convert the Hi intensity to a column density where

$N_{\rm HI}=1.823\times 10^{18}\left[\frac{I_{\rm HI}}{\rm
K\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}}\right]\leavevmode\nobreak\ {\rm cm\leavevmode\nobreak\ s^{-2}}$ (1)

which assumes optically thin emission. These column density profiles (per unit
velocity) are shown in magenta in Figure 4. For all LFA pixels, $N_{\rm HI}$
$>$ $N_{\rm CNM}^{\rm[CII]}$, meaning there is sufficient Hi to fully explain
the [Cii] emission without the need to invoke optical depth effects.

A somewhat more direct comparison of the column densities can be made by
assuming some CNM fraction ($f_{\rm CNM}$) of the atomic component, since the
[Cii] emission is thought to only arise from the cold phase (e.g., Pineda et
al., 2013; Fahrion et al., 2017; Herrera-Camus et al., 2017). In Figure 4, we
show $N_{\rm CNM}^{\rm HI}$ $\equiv$$f_{\rm CNM}$$N_{\rm HI}$ for $f_{\rm
CNM}$ $=0.5$ (thin magenta lines). In all LFA pixels, $N_{\rm CNM}^{\rm HI}$
$\gtrsim$ $N_{\rm CNM}^{\rm[CII]}$, meaning that there is enough CNM to fully
explain all of the [Cii] emission. The ratio of $N_{\rm CNM}^{\rm HI}$ to
$N_{\rm CNM}^{\rm[CII]}$ at the peak of the Hi profile is given in the upper
right of each panel in Figure 4. By varying $f_{\rm CNM}$, we find that the
[Cii] emission can be fully explained by collisions with the atomic gas for
$f_{\rm CNM}$ $>0.2$.

To assess the impact of uncertainties in our assumed temperature and density,
we perform a Monte Carlo over both quantities. Using 500 trials, we allow both
$T$ and $n$ to vary uniformly over the uncertainty range when calculating the
column density. We define the uncertainty on the column density as the
standard deviation of the trials. We propagate this uncertainty through to the
ratio shown in the upper right of each panel in Figure 4.

There is evidence of a warm atomic phase in some of the spectra. Focusing
specifically on Pixel 1, the [Cii] profile is more "flat-topped" than the Hi
(both in Figure 3 and Figure 4). This peak in the Hi profile around ${\rm
V_{LSRK}}=200$ km s-1 may be indicative of an appreciable WNM component. A
similar WNM component is seen in Pixel 2 at a similar velocity. In Pixel 6,
however, the atomic gas appears to be dominated by a cold component. Thus
there are variations in the overall density and temperature of the atomic
component within the outflow of M 82, likely because the entrained material is
clumpy.

###  3.2 Molecular Gas in the Outflow

As the [Cii] emission can also arise from the molecular phase, we also
calculate $N_{\rm C^{+}}$ assuming collisions with only H2 (see details in
Section A.2). We assume the same temperature and density as for collisions
with the atomic gas and we assume an abundance ratio of ${\rm C/H_{2}=2\times
C/H=3.0\times 10^{-4}}$. We show these effective H2 column density profiles
(per unit velocity) based on the [Cii] ($N_{\rm H_{2}}^{\rm[CII]}$) in teal in
Figure 5. We repeat the Monte Carlo analysis over the uncertainties in $T$ and
$n$ as above.

To compare, we calculate the column density of H2 from the CO data ($N_{\rm
H_{2}}^{\rm CO}$). To convert from the CO intensity to column density (per
unit velocity), we assume a "starburst" CO-to-H2 conversion factor $X_{\rm
CO}=0.5\times 10^{20}$ cm-2 (K km s-1)-1 (e.g., Bolatto et al., 2013; Krieger
et al., 2021). The value is slightly smaller than the single value of $X_{\rm
CO}=0.7\times 10^{20}$ cm-2 (K km s-1)-1 used by Leroy et al. (2015), where we
have converted from CO(2-1) to CO(1-0) assuming $I_{\rm CO\leavevmode\nobreak\
2-1}/I_{\rm CO\leavevmode\nobreak\ 1-0}=0.7$. In their model of M 82, Yuan et
al. (2023) find $X_{\rm CO}\approx 0.2\times 10^{20}$ cm-2 (K km s-1)-1 for
this region of the southern outflow666In their Figure 13, Yuan et al. (2023)
report $X_{\rm CO\leavevmode\nobreak\ 2-1}$. We have converted this to $X_{\rm
CO\leavevmode\nobreak\ 1-0}$ assuming $I_{\rm CO\leavevmode\nobreak\
2-1}/I_{\rm CO\leavevmode\nobreak\ 1-0}=0.7$ (Leroy et al., 2015)..

We show these molecular gas column density profiles in gray in Figure 5,
assuming our fiducial $X_{\rm CO}=0.5\times 10^{20}$ cm-2 (K km s-1)-1. We
note that adopting the conversion factors used by Leroy et al. (2015) or Yuan
et al. (2023) produce negligible changes in the $N_{\rm H_{2}}^{\rm CO}$
profiles. In all LFA pixels, $N_{\rm H_{2}}^{\rm CO}$ $\sim 15-40$% $N_{\rm
H_{2}}^{\rm[CII]}$, with most pixels $\sim 20\%$, meaning that the molecular
gas (traced by CO) is not the dominant contributor to the overall [Cii]
emission. In summary, because only $\sim 20$% of the [Cii] can be excited by
the molecular ISM, we conclude that the majority of the [Cii] arises from the
CNM. This result has important connections to studies of [Cii] in dust star-
forming galaxies at higher redshifts, where the [Cii] 158µm line is visible
with interferometers such as ALMA. While it is tempting to use the [Cii] lines
as a tracer of molecular gas and/or hence star formation rate (e.g., Herrera-
Camus et al., 2015; Zanella et al., 2018; Dessauges-Zavadsky et al., 2020),
caution should be used as these results in M 82 suggest that the majority of
the [Cii] does not arise from the molecular, star-forming material.

####  3.2.1 CO-dark Molecular Gas

CO does not perfectly trace the total molecular gas content of the ISM, and
this component of missed gas is called CO-dark molecular gas (e.g., Grenier et
al., 2005; Langer et al., 2010; Wolfire et al., 2010). By its nature, this
phase is difficult to study. In the Milky Way, the fraction of molecular gas
not traced by CO varies with galactocentric radius and cloud density, dropping
below 20% within 4 kpc of the center and in dense clouds, but reaching nearly
80% in the diffuse ISM and beyond 10 kpc (Pineda et al., 2013; Langer et al.,
2014). From their models, Wolfire et al. (2010) found that the fraction of CO-
dark gas in PDRs is relatively constant with the ambient radiation field and
that the main driver is the cloud’s visual extinction, $A_{V}$ — a measure of
the dust shielding — where the fraction of CO-dark molecular gas decreases
steeply with increasing $A_{V}$. The fraction of CO-dark molecular gas
increases at lower metallicity as the CO molecule is more easily dissociated
due to a lack of shielding dust (e.g., Wolfire et al., 2010; Bolatto et al.,
2013).

Applying these previous results to the starburst-driven outflow of M 82, we
would expect a low CO-dark molecular gas fraction. The metallicity in this
region is solar (or slightly supersolar; e.g., Lopez et al., 2020). At the
resolution of these upGREAT observations, $A_{V}$ will vary substantially
within a beam. Over their entire field-of-view, which mainly covers the
central starburst, Förster Schreiber et al. (2001) found $A_{V}=36\pm 16$ mag.
Extending the models from Wolfire et al. (2010) would imply a CO-dark gas
fraction of $\sim 10-25$%. Because the shielding by dust in the outflow is
likely lower than in the nucleus, we estimate that $\sim 25$% of the molecular
gas may be in a CO-dark phase. Combining this with the fraction of the [Cii]
line attributed to the CO-emitting molecular gas ($\sim 20$%), we would expect
a $\sim 5$% contribution to the total [Cii] line from CO-dark molecular gas.

###  3.3 Ionized Gas in the Outflow

The [Cii] line can also be excited in the ionized phase of the ISM. It is
thought that, when [Cii] is excited in ionized conditions, the majority of the
[Cii] emission arises from regions of diffuse ionized gas rather than Hii
regions (e.g., Nagao et al., 2011; Contursi et al., 2013). In the KINGFISH
sample, Croxall et al. (2017) found that $25\pm 8$% of the [Cii] is associated
with the ionized gas. In star-forming regions in the center of the Milky Way,
Harris et al. (2021) found that PDRs and Hii regions contribute roughly
equally to the [Cii] flux. Therefore, while it is likely that the fraction of
[Cii] associated with the ionized gas changes with environment, the ionized
ISM is not the dominant contributor to the [Cii] emission.

Contursi et al. (2013) found that the ionized gas traced by H$\alpha$ in the
outflow of M 82 is kinematically decoupled from the neutral (atomic and
molecular) phases and from ionized gas traced by [Oiii] 88µm emission.
Moreover, they found that the ionized and neutral phases may not be co-spatial
in the outflow. They proposed a scenario where the H$\alpha$-emitting ionized
gas is more extended, is confined to the walls of the biconical outflow, has a
higher outflow velocity ($\sim$600 km s-1), and is ionized (at least in part)
by shocks between the outflowing X-ray-emitting plasma and the galaxy halo.
The [Oiii]-emitting ionized gas, on the other hand, is more collimated (even
narrower than the neutral material), has a slower outflow velocity ($\sim$75
km s-1), and is primarily photoionized by the starburst.

For the most part, the [Cii] lines we measure have similar spectral shapes to
the Hi and/or CO (e.g., Figures 4 and 5), indicating that the [Cii]-emitting
gas is likely coupled to the neutral material and photoionized by the
starburst. We do not see evidence for components of the [Cii] line that do not
correspond to either the Hi or CO, except perhaps the most redshifted edge of
the [Cii] profile in Pixel 1 (Figures 3, 4, and 4).

Another method to determine the fraction of [Cii] associated with the ionized
gas is to compare the [Cii] intensity to that of the [Nii] 205µm line. The
[Nii] 205µm line is only excited in the ionized ISM and it has a similar
critical density as the [Cii] 158µm line. Using this method, Tarantino et al.
(2021) found that the fraction of [Cii] arising from the ionized medium is
$<12$% in the disks of two normally star-forming galaxies. Unfortunately,
there are no observations of the [Nii] 205µm line from either Herschel or
SOFIA in M 82. Contursi et al. (2013) used the [Nii] 122µm line to place
limits on the fraction of [Cii] arising from the ionized medium in the outflow
at distances $<1$ kpc from the disk. Because the [Cii] and [Nii] 122µm lines
do not have similar critical densities, these results are dependent on the
electron density, which is largely unknown in the outflow of M 82 (e.g.,
Shopbell & Bland-Hawthorn, 1998; Yoshida et al., 2011). Nevertheless, Contursi
et al. (2013) were able to constrain that $\sim 11-40$% of [Cii] emission
arises from the ionized gas in the southern outflow of M 82 (at distances $<1$
kpc from the midplane). They note that these estimates will be even more
uncertain when applied to regions with a complex mix of different ISM
components, which is certainly the case in the outflow of M 82. We can
conclude, however, that the ionized gas is not the dominant contributor to the
[Cii] emission in the outflow of M 82.

Figure 6: A comparison of the [Cii] and CO spectra in the disk of M 82. The
grayscale filled contours show the CO integrated intensity. The blue-green
open contours show the [Cii] integrated intensities (see the lines in the
color bar). The black rectangle marks the fully-sampled region of the [Cii]
map. The subplots show the spectra of the CO (gray) and [Cii] (teal) extracted
at the galaxy center (yellow), at the peak of the [Cii] emission (cyan), and
on the redshifted and blueshifted sides of the galaxy (red, blue). Both the CO
and [Cii] intensities are reported as main-beam brightness temperatures, and
the data sets have been matched to the same spatial and spectral gridding and
convolved to the CO beam size (22″). The black vertical lines in the panels
show the $V_{\rm sys}$$\leavevmode\nobreak\ =\leavevmode\nobreak\ $210 km s-1.
Comparisons with Hi are not possible to due strong absorption over this region
(see Section 2.2.2).

###  3.4 Synthesis

We summarize the contributions to the [Cii] emission in the outflow of M 82
from various ISM phases as follows. From our comparison of the H2 column
density measured from CO compared to that predicted from [Cii], we find that
$\sim 20$% of the [Cii] emission may arise from CO-emitting molecular gas
(Figure 5). We attempt to quantify the contribution of CO-dark molecular gas,
finding $\sim 4$% of the total [Cii] emission may arise from this phase.
Therefore, $\sim 24$% of the [Cii] emission in the outflow of M 82 may arise
from the molecular ISM. For the contribution of ionized gas, we rely on
measurements by Contursi et al. (2013) and estimate that $\sim 20$% of the
total [Cii] emission may arise from the ionized ISM. Finally, we compare the
Hi column density measured from Hi data to that predicted from [Cii] and find
that there is sufficient Hi to fully explain the [Cii] emission (Figure 4).
Therefore, we can attribute the remaining $\sim 55$% of the [Cii] emission to
the atomic ISM.

##  4 [CII] in the Disk of M 82

As shown in Figures 1 and 2, we detect the [Cii] line at high significance in
the disk of M 82. We calculate a total [Cii] mass in the disk of $4\times
10^{6}$ M⊙, calculated where SNR $>2$ (Figure 2) following Equations A5 and
A11.

In Figure 6, we compare representative [Cii] and CO spectra in the disk of M
82 at the center, at the peak of the [Cii] emission, and on the redshifted and
blueshifted sides of the galaxy. For this figure, we have spectrally smoothed
the CO data to 10 km s-1 to match the [Cii], convolved the [Cii] data to the
larger 22″ CO beam, and matched the pixel sizes. Both the CO and [Cii] are
reported in main-beam brightness temperature units. We calculate the
integrated intensity (moment 0) of the [Cii] and CO on these matched data
sets, as shown in Figure 6. Comparisons with the Hi spectra are not possible
because of deep absorption features in the Hi over the region where the [Cii]
is detected in the disk (Section 2.2.2, Figure 1, and Martini et al., 2018).
In general, we find that the CO and [Cii] intensities and spectral shapes are
quite similar, in agreement with previous work in this galaxy at lower
resolution (e.g., Stacey et al., 1991).

Figure 7: A PV diagram of the [Cii] (filled colored contours) and CO (open
grayscale contours) in the center of M 82. This slice is extracted along the
galaxy major axis and covers the entire fully-sampled region of the [Cii] map
($3\times 1$ kpc). The CO and [Cii] data have the same beam size, pixel scale,
and velocity resolution. The $x$-axis shows the offset along the galaxy major
axis with respect to the center. The $y$-axis shows the velocity relative to
$V_{\rm sys}$ $=210$ km s-1 (Krieger et al., 2021). In general, the kinematics
of the CO and [Cii] agree, though the [Cii] velocity rises faster than the CO
in the center.

In Figure 7, we make a position-velocity (PV) diagram of the matched-
resolution CO and [Cii] in the disk of M 82. The velocities for both datasets
are reported in the radio velocity convention and in the LSRK frame. We
extract the [Cii] and CO PV slices over the entire fully-sampled region of the
[Cii] map, covering the central $3{\rm\ kpc\ }\times 1{\rm\ kpc}$ of the
galaxy along its major axis (Section 2.1.1). We collapse the PV slice along
the minor axis by taking an average weighted by the intensity of each spaxel.
Spaxels with intensities less than the rms noise of the cube (in areas away
from emission) are removed.

As shown in Figure 7, the kinematics of the [Cii] and CO generally agree in
the inner regions of M 82. In detail, however, there are some differences. The
[Cii] velocity appears to rise faster in the center compared to the CO. This
disagreement is worse on the redshifted (i.e. eastern) side of the galaxy. The
CO on this side of the galaxy appears more kinematically disturbed (e.g.,
Figure 2 of Leroy et al. 2015 and Figure 2 of Krieger et al. 2021). The Hi on
the other hand appears less kinematically disturbed on this side of the galaxy
(e.g., Figure 1 of Martini et al. 2018). Therefore, if the [Cii] in the disk
primarily arises from the atomic gas (as it does in the outflow) then perhaps
this could explain the kinematic differences we see in the PV diagrams, though
this is somewhat speculative.

##  5 [CII] and CO throughout M 82

###  5.1 [CII] and CO Luminosity Ratios

Figure 8:  The CO and upGREAT [Cii] luminosities in the disk (green-blue
filled contours) and outflow (teal circles) of M 82. The teal numbers indicate
the pixel number of each outflow pointing. We compare our measurements to
those from PACS (Contursi et al., 2013) in the grayscale contours. For all
contours, the colors reflect the density of points. We also compare to
integrated measurements from the xCOLD GASS survey of star-forming galaxies
(red stars; Accurso et al., 2017).

A somewhat different angle to assess the contribution of the molecular gas to
the [Cii] emission than presented in Section 3.2 is to compare the luminosity
ratios of [Cii] and CO. In principle, this ratio is sensitive to the FUV
radiation field and the ability of CO to self-shield via dust from the FUV
radiation (e.g., Accurso et al., 2017). To calculate the luminosities from the
integrated intensities, we follow Equation 1 of Solomon et al. (1997):

$L=1.04\times 10^{-3}\left[\frac{\rm I_{int}}{\rm Jy\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}}\right]\left[\frac{\nu(1+z)^{-1}}{\rm
GHz}\right]\left[\frac{D_{L}}{\rm Mpc}\right]^{2}\leavevmode\nobreak\
L_{\odot}$ (2)

where $\nu$ is the line rest frequency, $z$ is the redshift, and $D_{L}$ is
the luminosity distance. Because M 82 is very nearby, we take $D_{L}=3.63$ Mpc
and calculate $z=V_{\rm sys}/c$ with $V_{\rm sys}$ $=210$ km s-1 as the
recessional velocity. We show these luminosities in Figure 8 for both the disk
(blue-green filled contours) and outflow (teal circles; Table 2) of M 82.

We compare the $L_{\rm[CII]}$ we infer from our measurements to those measured
by Contursi et al. (2013). The region mapped by PACS extends farther into the
outflow ($\sim 1$ kpc) compared to the upGREAT map ($\sim 0.5$ kpc), but not
as far as the upGREAT outflow pointings. We match the PACS [Cii] data to the
IRAM 30-m CO data by first convolving the PACS cube to a 22″ Gaussian beam
using the kernel provided by Aniano et al. (2011). We then match the pixel
scales of the [Cii] and CO cubes and re-derive the integrated intensities. We
show the PACS [Cii] and matched CO luminosities in Figure 8 as the grayscale
contours. The PACS and upGREAT data agree well (as expected from the analysis
in Section 2.1.1).

We compare the ratios we derive for M 82 to a sample of 24 normally star-
forming galaxies from the xCOLD GASS survey from Accurso et al. (2017) in
Figure 8. In the disk of M 82 we find somewhat lower $L_{\rm[CII]}$/$L_{\rm
CO}$ ratios than for normally star-forming galaxies (the median for M 82 is
0.4 dex lower). We note, however, that the measurements from Accurso et al.
(2017) are galaxy-integrated, whereas the measurements from the disk of M 82
are in ${\rm\approx(125\leavevmode\nobreak\ pc)^{2}}$ regions (one pixel).

Another important caveat is that the galaxies studied by Accurso et al. (2017)
tend to have metallicities less than solar, whereas M 82 has solar (or
slightly supersolar) metallicity (e.g., Lopez et al., 2020). Accurso et al.
(2017) found the strongest trend in $L_{\rm[CII]}$/$L_{\rm CO}$ with
metallicity (in 12+log(O/H) units), where higher metallicity systems have
lower $L_{\rm[CII]}$/$L_{\rm CO}$. They also found a strong trend with the
hardness of the radiation field (defined as the ratio of the FUV to near UV
(NUV) flux), where harder radiation environments have lower
$L_{\rm[CII]}$/$L_{\rm CO}$. Both of these trends may help explain why the
disk of M 82 has lower $L_{\rm[CII]}$/$L_{\rm CO}$ than the star-forming
galaxies analyzed by Accurso et al. (2017).

###  5.2 Fraction of [CII] in the Outflow of M 82

At ${z\sim 3-7}$, recent observations with ALMA have revealed extended [Cii]
halos around some galaxies extending up to ${\sim 10}$ kpc from the center and
containing $\sim 50$% of the [Cii] emission (e.g., Rybak et al., 2019;
Fujimoto et al., 2019, 2020; Ginolfi et al., 2020; Meyer et al., 2022, though
see also Novak et al. 2020 for counter-examples). We note that these studies
are a mix of detections from individual systems and stacks, as well as
spatially unresolved and marginally-resolved studies. Simulations have shown
that these extended [Cii] halos can be powered by supernova-driven cooling
outflows (e.g., Pizzati et al., 2020).

As M 82 is sometimes used as a local anchor for high-z star-forming galaxies,
it is interesting to constrain the fraction of [Cii] emission in the outflow
compared to the disk. The CO in the outflow of M 82 only extends for $\sim
2-3$ kpc above and below the midplane (Walter et al., 2002; Salak et al.,
2013; Leroy et al., 2015; Krieger et al., 2021). Martini et al. (2018) found
that the Hi is significantly more extended, reaching $\sim 5$ kpc above the
midplane and $\sim 10$ kpc below (in the direction of M 81 with which M 82 is
interacting; see also Yun et al. 1994). Based on lower resolution CO data,
Walter et al. (2002) measured $3.3\times 10^{8}$ M⊙ of molecular gas in the
halo and outflow of M 82, $2.3\times 10^{8}$ M⊙ in the disk, and $8.0\times
10^{8}$ M⊙ in the tidal streamers, for a total molecular gas mass of
$1.3\times 10^{9}$ M⊙. We note that this total molecular gas mass agrees with
other more recent measurements (Salak et al., 2013; Leroy et al., 2015;
Krieger et al., 2021). Overall, Walter et al. (2002) found that while $>70$%
of the molecular material resides outside of the disk of M 82, only $\sim 25$%
of the total molecular gas mass is swept up in the outflow/halo component with
the rest being in the tidal streamers.

For the measurements of the [Cii] halos at high-z, outflow/halo and streamer
components would be mixed together. However, as we know from M 82, not all of
this mass is outflowing so attributing all of the extended [Cii] emission to
the outflow can significantly overestimate the [Cii] mass outflow rates in
these high-z systems. This rough comparison assumes that the [Cii] and CO
masses in each component track one another.

Because our upGREAT observations do not cover the full extent of the outflow
of M 82, we cannot directly measure the total [Cii] extent, mass, or flux in
the outflow relative to the disk. We will instead extrapolate our [Cii]
measurements to infer the total fraction of [Cii] we might expect based on the
CO. In the outflow, the average ratio of the peak brightness of the CO and
[Cii] line (where [Cii] is detected) is $2.0\pm 0.8$, where the uncertainty is
the standard deviation (see Figure 3). In the central disk, the peak
brightness ratio is nearly the same, with an average and standard deviation of
$2.1\pm 1.1$ (see e.g., Figure 6). We note that Walter et al. (2002) define
the M 82 disk as the inner 1 kpc, which is very similar to the region of the
disk where we robustly detect [Cii] emission (e.g., Figure 2). Therefore,
since the ratio of the intensities in the central disk and outflow are roughly
the same, we might also expect the relative mass ratios to be the same as
well. This means that we would expect to find $\sim 25$% of the total [Cii] in
the outflow, $\sim 18$% in the inner disk, with the remaining [Cii]
distributed in the streamers. Given that we measure a [Cii] mass of $4\times
10^{6}$ M⊙ in the disk (Section 4), we would predict $\sim 5.5\times 10^{6}$
M⊙ of [Cii] in the entire outflow of M 82. This mass corresponds to a total
integrated intensity of $\sim 3.5\times 10^{4}$ K km s-1 (Equations A11 and
A5) and $L_{\rm[CII]}$ $\sim 1.7\times 10^{8}$ L⊙ (Equation 2).

Indeed, some observational studies of [Cii] halos at high-z do find evidence
of an extended component but without a broad [Cii] profile that would indicate
an outflow (e.g., Novak et al., 2020; Spilker et al., 2020; Meyer et al.,
2022). In particular, Spilker et al. (2020) studied molecular outflows in a
sample of lensed dusty star-forming galaxies at $z>4$. They found that $>70$%
of the galaxies in their sample had clear evidence for a molecular outflow
based on OH 119µm absorption. However, none of these galaxies with confirmed
molecular outflows had broad [Cii] emission line wings. This suggests that, at
least in this population of $z>4$ highly star-forming galaxies, that [Cii] is
not a robust tracer of outflowing molecular gas at high redshift.

In summary, in M 82 we clearly detect [Cii] in the starburst-driven outflow,
though we expect that the outflowing [Cii] accounts for only $\sim 25$% of the
total [Cii] of the system. This is somewhat different than is observed for
high redshift [Cii] outflows, where there is evidence for molecular outflows
in broad emission lines but that lack robust [Cii] (e.g., Novak et al., 2020;
Spilker et al., 2020; Meyer et al., 2022).

##  6 FUV Radiation Field

Figure 9: Left: The ratio of the [Cii] to CO integrated intensities (in units
of erg s-1 cm-2 sr-1 and K km s-1), in the same style as Figure 2. In the
disk, the [Cii] and CO data cubes, from which the integrated intensities are
calculated, have the same beam size, pixel scale, and velocity resolution (see
Section 4). Right: The estimated FUV radiation field strength based on the PDR
model by Kaufman et al. (1999) using the ratios from the left plot and
assuming a density of $10^{4}$ cm-3.

Within PDRs, photoelectric heating of small dust grains efficiently heats the
region and governs the chemistry, and this heating is primarily governed by
the density ($n$) and the far ultraviolet (FUV) radiation field strength
($G/G_{0}$777$G_{0}$ is the Habing field for radiation with energies from
$6-13.6$ eV, equivalent to $1.6\times 10^{-3}$ erg s-1 cm-2.; e.g., Tielens &
Hollenbach, 1985; Wolfire et al., 1990). The intensities of lines emitted in a
PDR are, therefore, sensitive to these properties as well, and line ratios of
FIR fine structure lines and CO can be used to constrain $n$ and $G$ (e.g.,
Wolfire et al., 1990; Kaufman et al., 1999). In the center of M 82, Kaufman et
al. (1999) applied their PDR model to integrated measurements of FIR lines,
finding $n\sim 10^{4}$ cm-3 and $G\sim 10^{3.5}\leavevmode\nobreak\ G_{0}$.
Contursi et al. (2013) also used the Kaufman et al. (1999) PDR model to
measure the FUV radiation field in the central starburst and southern outflow
of M 82 (within 1 kpc of the midplane), finding
$G=10^{3.1-3.4}\leavevmode\nobreak\ G_{0}$ in the starburst and $G\sim
10^{2.1}\leavevmode\nobreak\ G_{0}$ in the outflow.

###  6.1 Radiation Field Constraints from CO and [CII]

From their PDR model, Kaufman et al. (1999) find that, while the ratio of the
[Cii] to CO integrated intensities (where both quantities are in units of erg
s-1 cm-2 sr-1) is mostly sensitive to the column density of C+ and the
temperature, this ratio does also depend on $n$ and $G$ (see their Figure 9).
We, therefore, use the line ratios of [Cii] and CO that we measure in the disk
and outflow of M 82 to place new constraints on the FUV radiation field in
this region.

Figure 9 (left) shows the integrated intensity ratio of [Cii] to CO. Like has
been found previously (e.g., Stacey et al., 1991; Kaufman et al., 1999),
ratios range from $\sim\leavevmode\nobreak\ 3-7\times 10^{3}$ in the disk of M
82. Ratios in the outflow are substantially lower, with Pixels 0, 1, 2, and 6
(purple colors in Figure 9 left) having ratios of $300-400$.

Using the PDR model developed by Kaufman et al. (1999), we place limits on the
strength of the FUV radiation field assuming some density of the material. We
interpolate the predictions of the Kaufman et al. (1999) PDR model (their
Figure 9) to estimate $G$ for a given [Cii]-to-CO intensity ratio. This
estimation of $G$ is shown in Figure 9 (right). For a fiducial density of
$n=10^{4}$ cm-3 (following the results of Kaufman et al. 1999), the observed
[Cii]/CO ratios in the disk can be explained by $G\sim
10^{3-5}\leavevmode\nobreak\ G_{0}$, in agreement (though somewhat circularly)
with Kaufman et al. (1999) and Contursi et al. (2013).

In the outflow, we estimate a much lower FUV radiation field, with Pixels 0,
1, 2, and 6 (blue colors in Figure 9 right) having $G\sim
6\leavevmode\nobreak\ G_{0}$. Although the outflow is less dense than the disk
(e.g., Yuan et al., 2023), the result of a much smaller FUV radiation field
holds (see Section 6.2 for more discussion on the effect of uncertainties in
the assumed density).

###  6.2 Uncertainties on $G/G_{0}$ Due to the Assumed Density

A major source of uncertainty in these calculations is the assumed density
($n$). While we assume a fiducial $n=10^{4}$ cm-3 motivated by the results of
Kaufman et al. (1999) in the center of M 82, it is unlikely that the outflow
is this dense (as discussed in Section 3 and in Contursi et al. 2013).

In the disk, we allow the assumed density to vary by 0.5 dex (i.e.,
$n=10^{3.5-4.5}$ cm-3). Because the PDR models are not monotonic with density
(see Figure 9 of Kaufman et al. 1999), we perform a grid search in steps of
0.1 dex in density and find the minimum and maximum values of $G/G_{0}$ at
each disk pixel. For the disk, the uncertainty at each pixel is roughly the
same ($\log_{10}(G/G_{0})^{+0.5}_{-0.6}$).

In the outflow, the density is almost certainly much lower than $10^{4}$ cm-3.
We employ the same grid search as described above over a range of $n=10^{2-4}$
cm-3. The lower limit encompasses the density limits determined by Contursi et
al. (2013) and used in Section 3.1. We assume that our fiducial density is the
maximum density in the outflow. The lower uncertainty on $G/G_{0}$ in the
outflow comes from allowing the assumed density to be 2 dex lower than the
fiducial assumption (i.e., $n=10^{2-4}$ cm-3).

Accounting for the density uncertainties, we find $G/G_{0}\approx
10^{1.8-5.2}$ in the disk and $G/G_{0}\approx 10^{0.1-1.0}$ in the outflow
(excluding each green point in the disk and outflow). Therefore, even
considering the uncertainties from the density assumptions, the radiation
field in the outflow is substantially lower than in the disk.

##  7 Summary

M 82 is an archetypal example of a starburst-driven outflow and is an ideal
laboratory to study the detailed physics of superwinds. Here, we present new
velocity-resolved observations of the [Cii] 158µm emission line towards the
center and southern outflow of M 82, enabled by upGREAT onboard SOFIA. With
upGREAT, we mapped the central 3 kpc $\times$ 1 kpc of the disk of M 82. In
the southern outflow, we use one pointing of the seven-pixel upGREAT array to
measure [Cii] at distances of $1-2$ kpc from the midplane (Figure 1). Below we
summarize the main results of this analysis, indicating the relevant figures
and/or tables:

  1. 1.

We detect the [Cii] line out to 2 kpc from the midplane along the southern
outflow at 10 km s-1 velocity resolution (Figure 3). This twice as far as
previously probed by Herschel PACS (Contursi et al., 2013; Herrera-Camus et
al., 2018).

  2. 2.

We compare the column densities of the atomic medium measured from the Hi data
to the CNM column density measured from the [Cii] spectra (Figure 4).
Similarly, we compare the column densities of the molecular medium measured
from the CO data to the H2 column density measured from the [Cii] spectra
(Figure 5). From these comparisons, we find that the majority ($>55$%) of the
[Cii] arises from the atomic component. It is likely that the molecular gas
(including an estimate of the CO-dark molecular gas) contributes $\sim 25$%
and that the ionized gas contributes $\sim 20$% of the [Cii] emission.

  3. 3.

We are able to extend the results from Walter et al. (2002) from CO to
estimate the total fraction of [Cii] in the outflow of M 82. While the bulk of
the [Cii] emitting gas is likely outside of the main disk, only a small
fraction is actually outflowing (with the rest located in tidal streamers, for
example). This may help inform observations of [Cii] halos at higher
redshifts, which sometimes lack outflow signatures.

  4. 4.

We estimate the strength of the FUV radiation field in the disk and outflow of
M 82 using the PDR model developed by Kaufman et al. (1999). In the disk of M
82, we find $G\sim 10^{3-5}\leavevmode\nobreak\ G_{0}$, in agreement with
previous measurements (Figure 9; Kaufman et al., 1999; Contursi et al., 2013).
The FUV radiation field we measure $\sim 1.5$ kpc away from the disk in the
outflow, however, is 2-3 orders of magnitude lower than in the disk.

Owing to the sensitivity and wavelength coverage of ALMA, the [Cii] 158µm
emission line is routinely observed in galaxies at $z\gtrsim 2$. Because this
line is bright, it is a more attractive tracer of molecular gas than CO in
these systems. However, it is crucial to understand the contribution of the
various ISM phases to the [Cii] line in order to use this line as a tracer of
molecular gas and star formation. The galaxy systems studied so far at
$z\gtrsim 2$ tend to have high star formation rates, so understanding the
behavior of the [Cii] line in this starburst environment is critical to inform
these high-$z$ measurements. Unfortunately, with the end of the SOFIA mission,
observations of [Cii] and other FIR lines in the local Universe will be
possible only with balloon missions for at least the next few decades. Future
facilities in space are needed to more completely understand how the various
ISM phases contribute to the [Cii] 158µm line as a function of spatial
resolution, environment, and ISM conditions.

R.C.L. acknowledges support for this work provided by NASA through award
number 08-0225 issued by the Universities Space Research Association, Inc.
(USRA) and by a National Science Foundation (NSF) Astronomy and Astrophysics
Postdoctoral Fellowship under award AST-2102625. A.D.B. acknowledges support
from the NSF under award AST-2108140. R.H.-C. thanks the Max Planck Society
for support under the Partner Group project "The Baryon Cycle in Galaxies"
between the Max Planck for Extraterrestrial Physics and the Universidad de
Concepción. R.H-C. also gratefully acknowledge financial support from
Millenium Nucleus NCN19058 (TITANs), and ANID BASAL projects ACE210002 and
FB210003. This work is based on observations made with the NASA/DLR
Stratospheric Observatory for Infrared Astronomy (SOFIA), project #08_0225.
SOFIA is jointly operated by USRA, under NASA contract NNA17BF53C, and the
Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 2002 to the University
of Stuttgart. This work is based on observations carried out under project No.
107-19 with IRAM 30 m telescope. IRAM is supported by INSU/CNRS (France), MPG
(Germany), and IGN (Spain). The National Radio Astronomy Observatory is a
facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc. 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. This research has made use of NASA’s Astrophysics Data System
Bibliographic Services.

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##  Appendix A Calculating the C+ Density and Mass in the Outflow

We calculate the [Cii] density and mass in the outflow of M82 channel-by-
channel for the velocity-resolved [Cii] spectrum. We describe this calculation
below and direct the reader to Goldsmith et al. (2012) and Tarantino et al.
(2021, and references therein) for a much more complete discussion. We note
that these calculations assume the [Cii] is optically thin, which is well
supported by the results of Contursi et al. (2013).

First, we can relate the column density of C+ ($N_{\rm C^{+}}$) to the [Cii]
intensity ($I_{\rm[CII]}$) in each channel of the spectrum:

$\begin{split}N_{\rm C^{+}}=\frac{3.0\times
10^{15}}{B}\left[\frac{I_{\rm[CII]}}{\rm K}\right]\left[\frac{\Delta V}{\rm
km\leavevmode\nobreak\ s^{-1}}\right]{\rm\ cm^{-2}}\end{split}$ (A1)

where

$B=\frac{2e^{-91.2/T}}{1+2e^{-91.2/T}+A_{ul}/(\Sigma R_{ul}n_{i})}$ (A2)

and where $\Delta V$ is the channel width in km s-1, $T$ is the kinetic
temperature in K, $A_{ul}$ is the Einstein A spontaneous decay rate
($2.3\times 10^{-6}$ s-1 for the 158 µm transitions of [Cii]), and $\Sigma
R_{ul}n_{i}$ is the sum over all $i$ collisional partners with collisional
decay rates $R_{ul}$ and volume densities $n_{i}$ (Crawford et al., 1985;
Goldsmith et al., 2012; Tarantino et al., 2021).

###  A.1 Collisions with Atomic Gas

First, we focus on collisions with the atomic gas only. In particular, the
[Cii] is excited primarily in the cold neutral medium (CNM; e.g., Pineda et
al., 2013; Fahrion et al., 2017; Herrera-Camus et al., 2017; Tarantino et al.,
2021). Therefore, the sum over the collisional partners in Equation A2 can be
simplified to include only neutral hydrogen and helium:

$\begin{split}\Sigma R_{ul,i}n_{i}=n_{\rm CNM}\left[R_{ul}({\rm
H}^{0})+R_{ul}({\rm He}^{0})\right]{\leavevmode\nobreak\ \rm s^{-1}}\\\
=1.038R_{ul}({\rm H}^{0})n_{\rm CNM}{\leavevmode\nobreak\ \rm
s^{-1}}\end{split}$ (A3)

where we have made the final simplification because the collisional rate for
helium is 38% of that for hydrogen (Draine, 2011). Goldsmith et al. (2012)
calculated that

$R_{ul}({\rm H}^{0})=4.0\times
10^{-11}\left(16+0.35T^{0.5}+48T^{-1}\right){\rm cm^{3}\leavevmode\nobreak\
s^{-1}}.$ (A4)

We assume $T=250$ K and $n=100\leavevmode\nobreak\ {\rm cm^{-3}}$ following
the results of Contursi et al. (2013, the discussion in Section 3). Therefore,
$R_{ul}({\rm H}^{0})=9.1\times 10^{-10}\leavevmode\nobreak\ {\rm
cm^{3}\leavevmode\nobreak\ s^{-1}}$, $\Sigma R_{ul,i}n_{i}=9.4\times 10^{-8}$
s-1, and $B=5.7\times 10^{-2}$. With these assumptions, Equation A1 becomes

$N_{\rm C^{+};\,H^{0}}=5.2\times 10^{16}\left[\frac{I_{\rm[CII]}}{\rm
K}\right]\left[\frac{\Delta V}{\rm km\leavevmode\nobreak\ s^{-1}}\right]{\rm\
cm^{-2}}$ (A5)

considering only collisions with the atomic gas.

From $N_{\rm C^{+};\,H^{0}}$, we can estimate the effective CNM column density
($N_{\rm CNM}^{\rm[CII]}$) based on the relative abundance of carbon to
hydrogen (${\rm C/H}=1.5\times 10^{-4}$; Gerin et al. 2015) assuming all of
the carbon is singly-ionized and all the hydrogen is atomic:

$N_{\rm CNM}^{\rm[CII]}=\frac{N_{\rm C^{+};\,H^{0}}}{{\rm C/H}}.$ (A6)

The warm phase of the Hi accounts for $30-70$% of the Hi emission (Heiles &
Troland, 2003) but does not contribute to the [Cii] emission (e.g., Pineda et
al., 2013; Fahrion et al., 2017; Herrera-Camus et al., 2017). We show this
effective CNM column density profile based on the [Cii] in Figure 4 (teal).

###  A.2 Collisions with Molecular Gas

Next, we consider collisions with the molecular gas, H2. In this case, the sum
over the collisional partners in Equation A2 can be simplified to include only
molecular hydrogen:

$\Sigma R_{ul,i}n_{i}=n_{\rm mol}R_{ul}({\rm H}_{2}){\leavevmode\nobreak\ \rm
s^{-1}}.$ (A7)

Goldsmith et al. (2012) calculated that

$R_{ul}({\rm H}_{2})=3.8\times 10^{-10}\left(\frac{T}{100}\right)^{0.14}{\rm
cm^{3}\leavevmode\nobreak\ s^{-1}}$ (A8)

where $T$ is again the kinetic temperature. Using the same assume temperature
and density as above, $R_{ul}({\rm H}_{2})=4.5\times
10^{-10}\leavevmode\nobreak\ {\rm cm^{3}\leavevmode\nobreak\ s^{-1}}$, $\Sigma
R_{ul,i}n_{i}=4.5\times 10^{-8}$ s-1, and $B=2.9\times 10^{-2}$. With these
assumptions, Equation A1 becomes

$N_{\rm C^{+}}^{\rm H_{2}}=1.0\times 10^{17}\left[\frac{I_{\rm[CII]}}{\rm
K}\right]\left[\frac{\Delta V}{\rm km\leavevmode\nobreak\ s^{-1}}\right]{\rm\
cm^{-2}}$ (A9)

considering only collisions with the molecular gas.

From $N_{\rm C^{+};\,H_{2}}$, we can estimate the effective H2 column density
($N_{\rm H_{2}}^{\rm[CII]}$) based on the relative abundance of carbon to H2
(${\rm C/H_{2}}=7.5\times 10^{-5}$; i.e., half the C/H ratio from Gerin et al.
2015) assuming all of the carbon is singly-ionized and all the hydrogen is
molecular:

$N_{\rm H_{2}}^{\rm[CII]}=\frac{N_{\rm C^{+}}^{\rm H_{2}}}{{\rm C/H_{2}}}.$
(A10)

We show this effective H2 column density profile based on the [Cii] in Figure
5 (teal).

###  A.3 C+ Mass Estimate

From the C+ column density calculated from Equation A5 (since most of the
[Cii] is excited through collisions with atomic gas), we calculate the total
C+ mass ($M_{\rm C^{+}}$) in each upGREAT pointing in the outflow. In each LFA
pixel,

$M_{\rm C^{+}}=2.2\left[\frac{A_{\rm pix}}{\rm
arcsec^{2}}\right]\left[\frac{d}{\rm
Mpc}\right]^{2}\left[\frac{\sum_{v}{N_{\rm C^{+}}}}{\rm
10^{18}cm^{-2}}\right]{\rm\ M_{\odot}}$ (A11)

where $A_{\rm pix}$ is the area of each LFA pixel ($\approx 156$″2), $d$ is
the distance to the galaxy in Mpc, and $\sum_{v}{N_{\rm C^{+}}}$ is the sum of
the C+ column density over all of the channels. We report $M_{\rm C^{+}}$ in
each LFA pixel in the pointing along the outflow in Table 1. The total C+ mass
measured in these observations of the outflow is $4.2\times 10^{4}$ M⊙
(excluding Pixels 4 and 5 where the [Cii] line is not detected). $M_{\rm
C^{+}}$ changes by a factor of $\sim 2$ for a factor of 2 change in either the
assumed CNM temperature ($T$) or density ($n_{\rm CNM}$).