11institutetext: Department of Physics, Imperial College London, London, SW7
2AZ, UK 22institutetext: Physics and Astronomy, The Johns Hopkins University,
3400 N. Charles Street, Baltimore, MD 21218, USA 33institutetext: Department
of Physics, Umeå University, 901 87 Umeå, Sweden 44institutetext:
Physikalisches Institut, University of Bern, Sidlerstrasse 5, 3012 Bern,
Switzerland 55institutetext: LESIA, Observatoire de Paris, Université PSL,
CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195
Meudon, France 66institutetext: Southwest Research Institute, Department of
Space Studies, Suite 300, 1050 Walnut Street, Boulder, CO 80302, USA
77institutetext: SouthWest Research Institute, P.O. Drawer 28510, San Antonio,
TX 78228-0510, USA 88institutetext: Swedish Institute of Space Physics,
Ångström Laboratory, Lägerhyddsvägen1, 75237 Uppsala, 20 Sweden

# Multi-instrument analysis of far-ultraviolet aurora in the southern
hemisphere of comet 67P/Churyumov-Gerasimenko

P. Stephenson 11 M. Galand 11 P. D. Feldman 22 A. Beth 33 M. Rubin 44 D.
Bockelée-Morvan 55 N. Biver 55 Y.-C Cheng 55 J. Parker 66 J. Burch 77 F. L.
Johansson 88 A. Eriksson 88

(Received XXXX / Accepted XXXX)

###### Abstract

Aims. We aim to determine whether dissociative excitation of cometary neutrals
by electron impact is the major source of far-ultraviolet (FUV) emissions at
comet 67P/Churyumov-Gerasimenko in the southern hemisphere at large
heliocentric distances, both during quiet conditions and impacts of corotating
interaction regions observed in the summer of 2016.

Methods. We combined multiple datasets from the Rosetta mission through a
multi-instrument analysis to complete the first forward modelling of FUV
emissions in the southern hemisphere of comet 67P and compared modelled
brightnesses to observations with the Alice FUV imaging spectrograph. We
modelled the brightness of OI1356, OI1304, Lyman-$\beta$, CI1657, and CII1335
emissions, which are associated with the dissociation products of the four
major neutral species in the coma: CO2, H2O, CO, and O2. The suprathermal
electron population was probed by the Ion and Electron Sensor of the Rosetta
Plasma Consortium (RPC/IES) and the neutral column density was constrained by
several instruments: the Rosetta Orbiter Spectrometer for Ion and Neutral
Analysis (ROSINA), the Microwave Instrument for the Rosetta Orbiter (MIRO) and
the Visual InfraRed Thermal Imaging Spectrometer (VIRTIS).

Results. The modelled and observed brightnesses of the FUV emission lines
agree closely when viewing nadir and dissociative excitation by electron
impact is shown to be the dominant source of emissions away from perihelion.
The CII1335 emissions are shown to be consistent with the volume mixing ratio
of CO derived from ROSINA. When viewing the limb during the impacts of
corotating interaction regions, the model reproduces brightnesses of OI1356
and CI1657 well, but resonance scattering in the extended coma may contribute
significantly to the observed Lyman-$\beta$ and OI1304 emissions. The
correlation between variations in the suprathermal electron flux and the
observed FUV line brightnesses when viewing the comet’s limb suggests
electrons are accelerated on large scales and that they originate in the solar
wind. This means that the FUV emissions are auroral in nature.

###### Key Words.:

Comets: individual: 67P/CG - Ultraviolet: planetary systems - Planets and
satellites: aurorae

##  1 Introduction

Auroras, most familiarly observed at high latitudes over the northern and
southern regions of Earth, have been detected at several bodies in the Solar
System. Auroral emissions are generated by (usually charged) extra-atmospheric
particles colliding with an atmosphere, causing excitation (Galand &
Chakrabarti 2002). At Earth, other magnetised planets, and the Jovian moon
Ganymede, the magnetospheric structure restricts entry of these extra-
atmospheric particles into the atmosphere, confining auroras to regions with
open field lines. However, comets are unmagnetised (Heinisch et al. 2019), so
they exhibit more similarities to regions of Mars with no crustal
magnetisation, where diffuse auroras have been seen (Schneider et al. 2015).
The Rosetta mission (Glassmeier et al. 2007) observed comet 67P/Churyumov-
Gerasimenko (hereafter 67P) from within the coma throughout the two-year
escort phase, allowing measurement of cometary emissions from a new, close
perspective. Earth-based observations of comets in the far-ultraviolet (FUV)
with the Hubble Space Telescope (HST; Lupu et al. 2007; Weaver et al. 2011)
and the Far Ultraviolet Spectroscopic Explorer (FUSE; Feldman et al. 2002;
Weaver et al. 2002) have not seen evidence of aurora at comets. The analysis
of FUV emission spectra from HST and FUSE indicated that photodissociation and
resonance scattering were the dominant sources of emissions at these
wavelengths. However, these Earth-based observations are limited to active
comets, with an outgassing rate of $Q>10^{28}$ ${\mathrm{s}}^{-1}$, which are
close to the Sun ($<2$ $\mathrm{ua}$). Rosetta provided an opportunity to
observe a comet further from the Sun ($>3$ $\mathrm{ua}$) and at much lower
levels of activity ($Q<10^{26}$ ${\mathrm{s}}^{-1}$) than was previously
possible (Läuter et al. 2018).
The Alice FUV imaging spectrograph (Stern et al. 2007) onboard Rosetta was
used to measure emission spectra from within the coma of 67P, which contrasted
with the Earth-based measurements of cometary emissions. An analysis of the
emission line ratios in FUV spectra has suggested that the dissociative
excitation of cometary neutrals by electron impact (e + X for a cometary
molecule - X) was a significant source of FUV emissions (Feldman et al. 2015).
Dissociative excitation is driven by suprathermal electrons which have
energies greater than the high threshold energies ($>14$ $\mathrm{eV}$) for
these processes (McConkey et al. 2008; Ajello 1971; Mumma et al. 1972).
Suprathermal electrons have been observed in the coma of 67P throughout the
escort phase with the electron spectrometer (Burch et al. 2007) and do not
follow a Maxwellian distribution (Clark et al. 2015; Broiles et al. 2016).
There is also a thermal population of cold electrons ($<1$ $\mathrm{eV}$)
which have been observed throughout the escort phase (Eriksson et al. 2017;
Gilet, N. et al. 2020) but their energy is too low to be able to contribute to
the FUV emissions.
Early FUV spectra taken in the northern hemisphere summer were consistent with
the impact of electrons on water (Feldman et al. 2018). The outgassing of H2O
is closely linked to the illumination conditions of the nucleus and exhibits
seasonal trends in its production rate (Fink et al. 2016; Läuter et al. 2018).
Pre-perihelion, in the northern hemisphere summer, H2O is the dominant
outgassed neutral species (Hässig et al. 2015; Läuter et al. 2018; Bockelée-
Morvan et al. 2016), whilst there is also a significant presence of O2 (Bieler
et al. 2015a).
Unlike over the northern hemisphere, the post-perihelion spectra analysed over
the southern hemisphere summer exhibit strong carbon lines and hence they are
driven mostly by electron impact on CO2. This reflects the hemispherical
asymmetry in the composition of 67P’s coma that has been observed at large
heliocentric distances with the mass spectrometer (Balsiger et al. 2007) as
well as with the infrared (Coradini et al. 2007) and sub-mm (Gulkis et al.
2007) spectrometers onboard Rosetta. Throughout the mission, the outgassing of
CO2 and, to a lesser extent, CO were larger in the southern hemisphere than in
the northern hemisphere (Läuter et al. 2018), which reflects an inhomogeneity
in the surface of the nucleus. The significant increase in the outgassing of
both CO2 and CO post-perihelion (Gasc et al. 2017a; Biver et al. 2019) may
also result from the exposure of a more pristine surface layer of the nucleus,
due to erosion around perihelion (Fink et al. 2016; Filacchione et al. 2016).
Chaufray et al. (2017) showed that HI-Ly-$\beta$ emissions observed by the
Alice FUV spectrograph exhibit some correlation with remote measurements of
the water column density from the IR spectrometer on Rosetta. This
demonstrated the dependence of FUV emission brightness on the column density
of water along the line of sight. They also calculated the Ly-$\beta$
brightness, assuming a Maxwellian distribution of suprathermal electrons with
a constant temperature (17 $\mathrm{eV}$) and density (20
${\mathrm{cm}}^{-3}$). However, this does not account for large variations (by
a factor of 100) that have been observed in the suprathermal electron flux or
the non-thermal distribution of electrons. Chaufray et al. (2017) also found
that away from perihelion the suprathermal electron flux does not seem to vary
with cometocentric distance, in contrast to the total electron density which
varies approximately with $1/r$ (Galand et al. 2016; Heritier et al. 2017b).
Raghuram & Bhardwaj (2020) have analysed the brightness of FUV emissions using
a photochemical model, with application to a high outgassing regime
($Q>10^{27}$ s-1). However, they model significant emissions from several
photodissociation processes that require spin-forbidden transitions, and
therefore do not occur. When the analysis is applied to a larger heliocentric
distance (1.99 $\mathrm{ua}$), they cannot explain the observed FUV emission
brightnesses.
Galand et al. (2020) employed a multi-instrument analysis to combine FUV
brightnesses with in situ or remote neutral gas observations and in situ
measurements of the suprathermal electron flux. This work focused on the
northern, summer hemisphere of comet 67P at large helicoentric distances where
H2O is the major neutral species, demonstrating that electron impact on H2O
and O2 are the dominant sources of emissions. Galand et al. (2020) concluded
that emissions are driven by electrons which have been accelerated on large
scales rather than locally heated. Acceleration of solar wind electrons by an
ambipolar field is the most likely candidate (Deca et al. 2017, 2019), meaning
these emissions are auroras, a phenomenon which had not previously been
observed at a comet in the FUV.
In the non-illuminated southern hemisphere, the FUV emission spectra are very
different to those in the northern hemisphere, with much stronger emissions of
atomic carbon lines and molecular bands of CO (Feldman et al. 2018). There has
been no forward modelling to determine whether the FUV emissions in the
southern hemisphere are also driven by dissociative excitation of cometary
neutrals or to understand which neutral species are key to each emission line.
We propose to apply an extension of the multi-instrument analysis of Galand et
al. (2020) to model the FUV emissions in the southern hemisphere of comet 67P
at large heliocentric distances.
The brightest emission from the coma is Ly-$\alpha$ at 1216
$\mathrm{\SIUnitSymbolAngstrom}$ but due to the high flux of Ly-$\alpha$
photons during the mission, the detector degraded significantly at this
wavelength throughout the mission. We model the brightness of emissions in the
strongest remaining atomic emission lines. These are associated with atomic
transitions of oxygen (OI1356, OI1304), hydrogen (Ly-$\beta$), and carbon
(CI1657 and CII1335), which are the dissociation products of the four major
neutral species in the coma (CO2, H2O, CO, O2; Gasc et al. 2017a; Läuter et
al. 2018).
Throughout the duration of Rosetta’s escort phase, many solar events, such as
Coronal Mass Ejections (CMEs) and Corotating Interaction Regions (CIRs)
reached 67P, generating enhancements in the suprathermal electron population
in the coma (Edberg et al. 2016; Witasse et al. 2017; Hajra et al. 2018; Goetz
et al. 2019). The variation of emissions during these events has been observed
by Feldman et al. (2015) and Noonan et al. (2018), although the solar event
which Feldman et al. (2015) analysed was not identified until after
publication (Witasse et al. 2017). Both of these events were observed in the
northern hemisphere when H2O was the dominant outgassing species, with the CIR
of Feldman et al. (2015) occurring early in the mission and the CME of Noonan
et al. (2018) arriving when 67P was close to perihelion. Noonan et al. (2018)
qualitatively compared the ’warm’ (5-100 $\mathrm{eV}$) electron density to
the brightness of several atomic FUV lines (OI1356, OI1304, Ly-$\beta$ and
CI1657) during the arrival of a CME near perihelion.
In the present study, we focus on CIRs observed at 67P throughout the summer
of 2016 (Hajra et al. 2018). These are formed when a fast solar wind stream
interacts with the slow solar wind that precedes it, generating a region of
compression. The compression causes an increase in the electron number
density, while shock structures can lead to further heating of electrons at
large heliocentric distances (Smith & Wolfe 1976). The CIR is seen
periodically ($\sim\\!25$$\mathrm{d}$) from June to September 2016, because of
its solar corotation. Electron impact is the dominant ionisation process
during these CIRs and contributes significantly to the total plasma density
(Heritier et al. 2018b), but there has not been a quantitative assessment of
their impact on FUV emissions so far.
In this paper, we utilise a multi-instrument analysis to model the brightness
of FUV emission lines in the southern hemisphere of comet 67P at large
heliocentric distances, with direct comparison to observed brightnesses from
the FUV spectrograph onboard Rosetta. In Section 2, we introduce the
methodology used in the study to calculate the brightness of each emission
line, using measurements of neutral gas composition and density as well as
measurements of the suprathermal electron flux. In Section 3, we apply this
analysis in the southern hemisphere during quiet periods, outside of solar
events, both pre- and post-perihelion. We then model FUV emissions from the
coma during the August and July occurrences of the CIR in the summer of 2016
in Section 4. In Section 5, we compare our results with those obtained in the
northern hemisphere and discuss the implications of our findings on our
understanding of the cometary environment and on future analysis of cometary
FUV emissions.

##  2 Methods

###  2.1 Multi-instrument analysis

In this study, we employed an extension of a multi-instrument analysis
developed by Galand et al. (2020) to model the emissions driven by
dissociative excitation of cometary neutrals by electron impact. The analysis
brings together distinct datasets from several instruments onboard Rosetta.
The process of dissociative excitation by electron impact is outlined in Fig.
1, along with a qualitative description of how each instrument contributes to
the analysis.

DissociativeExcitationDe-excitation(a) Suprathermal Electron(b) Cometary
Molecules CO2, H2O, CO, O2(c) Excited AtomicFragments(d) Auroral FUV Emissions
HI, OI, CI & CIIRPC/IESROSINA, VIRTIS & MIROAlice* Figure 1: Schematic of the
multi-instrument analysis used in this study to model FUV emissions driven by
electron impact on cometary neutrals. From left to right: (a) Suprathermal
electrons present within the coma were measured using RPC/IES (see Section
2.4.2). (b) Neutral gas molecules in the coma. There were four major neutral
species seen at 67P: CO2, H2O, CO, and O2 (see Section 2.3). (c) A collision
between a suprathermal electron and a cometary molecule causes the molecule to
dissociate. A neutral fragment and an excited atom are produced. (d) The
excited atom de-excites, releasing a photon in the FUV. These photons were
observed with the Alice FUV imaging spectrograph (see Section 2.2).

The equation underlying the methodology allows direct comparison of the
brightness derived from the observations, by the Alice FUV imaging
spectrograph (see Section 2.2), with the brightness, $B^{X}$ [R, 1 rayleigh
$=10^{6}/4\pi$ photons cm-2s-1sr-1], of the atomic emission line, X (OI, CI,
CII, HI), calculated as follows:

$B^{X}=10^{-6}\sum\limits_{l}N_{l}\int\limits_{E_{Th,l}}^{E_{Max}}\\!\sigma^{X}_{l}(E)J(E)\,\mathrm{d}E=10^{-6}\sum\limits_{l}N_{l}\nu_{l}^{X}$
(1)

where $N_{l}$ [cm-2] is the column density of each neutral species, $l$ (CO2,
H2O, CO and O2), along the line of sight of the FUV spectrograph and the
summation is over each of the major species found in the coma of 67P (see
Section 2.3). Equation 1 is predicated on the assumption that the suprathermal
electron particle flux, $J(E)$ [cm-2s-1eV-1], is constant throughout the
column in question (see Section 2.4.2). The emission frequency, $\nu_{l}^{X}$
[s-1], is derived from the emission cross-section, $\sigma^{X}_{l}(E)$ [cm2],
for each emission line, $X$, and neutral species, $l$, and from the
suprathermal electron particle flux (see Section 2.4).

###  2.2 Observed brightness of FUV emission lines

The Alice FUV imaging spectrograph (Stern et al. 2007) observed emissions in
the range 700 Å - 2050 Å, with a spectral resolution of 8 Å in the slit
centre. The slit comprised 32 rows (0 to 31) with Row 15 at the centre, each
row subtending $0.3^{\circ}$ along the slit axis. The slit had a dogbone-like
shape as the central rows (13 to 17) have a width of $0.05^{\circ}$, whereas
the outer rows ($\geq 19$ and $\leq 12$) had a width of $0.10^{\circ}$
(Feldman et al. 2015). Rows 12 and 18 were transitional between these two
widths, hence they have been avoided in the present analysis. Typically, the
spectrograph scans lasted either approximately five or ten minutes, but to
improve the signal-to-noise ratio (S/N), several consecutive spectra can be
co-added.
The emission spectra exhibit an odd-even oscillation between rows (Chaufray et
al. 2017), so even numbers of rows were co-added to minimise the impact of
this aberration. When using a nadir viewing, during quiet periods, 67P was
fairly stationary in the Alice field-of-view over several scans. As such, the
co-added scans, ranging from 20 to 100 $\mathrm{min}$, probed a small region
of the coma within each viewing period.
In the cases of solar events, the temporal variation in the brightness of each
emission line is highly relevant. Therefore, each spectrum retrieved from
Alice has been considered individually, whilst several adjacent rows were
combined. To capture some of the spatial variability in the emissions, the
brightness was evaluated in three different regions of the Alice viewing slit.
In the present study, we considered emissions from five multiplets (as
illustrated in Fig. 2): Lyman-$\beta$, OI1304, OI1356, CI1657 and CII1335. We
have not considered emissions of Lyman-$\alpha$ as the contribution to this
line from the interplanetary medium (IPM) is very strong, and the detector of
the FUV spectrograph degraded significantly at this wavelength throughout the
mission. The contribution of the IPM to the Lyman-$\beta$ brightness is of the
order of 2 R when looking off-limb, whereas the strength of the IPM
Ly-$\alpha$ is 300 times larger (Feldman et al. 2015).
There are also other emission features that overlap with the lines of interest
and which, therefore, must be considered. The oxygen line at 1027
$\mathrm{\SIUnitSymbolAngstrom}$ is not well resolved from the emissions of
Ly-$\beta$. The CO Fourth Positive Group (4PG) emits in the range $1400-1800$Å
and has several bands which can contribute to the emissions observed at 1657Å.
Those bands which emit significantly in this range are (3,4) at 1648Å, (0,2)
at 1653Å and (1,3) at 1670Å (Beegle et al. 1999).

Ly-$\beta$CII1335CI1657OI1304OI1356 Figure 2: FUV spectrum measured by Alice
during two nadir scans during quiet periods. The spectra have been coadded
over four rows in the Alice slit and smoothed with a five point moving average
to minimise the noise in the spectra. The key emissions selected in this study
have been highlighted.

###  2.3 Neutral column density

The column density of the neutral gas along the line-of-sight of the FUV
spectrograph can be calculated with several different methods depending on the
viewing geometry of Rosetta. When observing nadir, we can extrapolate from in-
situ total neutral density measurements by the Rosetta Orbiter Spectrometer
for Ion and Neutral Analysis (ROSINA, Balsiger et al. 2007). We derived the
neutral composition from measurements by the Double Focusing Mass Spectrometer
(ROSINA/DFMS) but this was not available at all times. Therefore, FUV scans
were only selected if DFMS was measuring at similar times. The total neutral
density at Rosetta was probed by the COmet Pressure Sensor (ROSINA/COPS) and
has been corrected for the composition of the gas in line with Gasc et al.
(2017b).
The neutral gas moves approximately radially away from the comet, which is
along the line-of-sight when Alice is looking nadir. As a result, the whole
column should originate from a similar region of the nucleus and have a
constant composition throughout.
The local neutral density measurements, $n(r_{Rosetta})$, at the cometocentric
distance, $r_{Rosetta}$, of Rosetta can be converted to a radial column
density from the nucleus surface to Rosetta as the neutral density has been
observed to follow a $r^{-2}$-dependence (Hässig et al. 2015; Bieler et al.
2015a):

$N_{Tot}=n(r_{Rosetta})r_{Rosetta}\bigg{(}\frac{r_{Rosetta}}{r_{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\text{67P}}}}-1\bigg{)}.$
(2)

However, under this model, the total column density, $N_{Tot}$, is highly
dependent on the radius of the comet, $r_{\text{67P}}$, at the foot-print of
the column, which varies significantly across the surface (Jorda et al. 2016).
We have taken $r_{\text{67P}}=1.7\text{\leavevmode\nobreak\ $\mathrm{km}$}$
and assumed that the expansion velocity of the neutral gas is constant, which
both introduce uncertainty to the neutral column density. The standard
deviation of the cometoradius is approximately $0.26\times r_{67P}$ (Gaskell
et al. 2017), which translates to a 30% uncertainty in the column density,
increasing to 35% at low cometoradii ($\sim 10$km). The assumption of a
constant expansion velocity results in an underestimate of the column density
as the gas undergoes acceleration near the nucleus surface (Heritier et al.
2017b; Bykov & Zakharov 2020). When looking off-limb, the neutral gas column
probed by the FUV spectrograph may have very different properties to the gas
measured locally by the pressure gauge, so the in situ neutral density was
only used to derive the column density when looking close to nadir.
The column density of several of the major neutral species could be measured
remotely using other instruments onboard Rosetta. The Visual InfraRed Thermal
Imaging Spectrometer (VIRTIS, Coradini et al. 2007) observed emissions from
the $\nu_{3}$ vibrational bands of H2O and CO2 at 2.67
$\mathrm{\SIUnitSymbolMicro m}$ and 4.27 $\mathrm{\SIUnitSymbolMicro m}$
respectively (Bockelée-Morvan et al. 2015). The calculations used to derive
the H2O and CO2 column densities are the same as those outlined in Bockelée-
Morvan et al. (2015). Emission from the $\nu$(1-0) band of CO was also
observed by the IR spectrometer, but the emission in this band is much weaker
than that of the $\nu_{3}$ bands of H2O and CO2, so the S/N was too low to be
useable at the large heliocentric distances under focus here. VIRTIS comprised
2 channels, M and H, operating at similar wavelengths in the infrared but
VIRTIS-M stopped working in May 2015 (Bockelée-Morvan et al. 2016), so in the
present study we used only VIRTIS-H measurements.
The Microwave Instrument for Rosetta Orbiter (MIRO; Gulkis et al. 2007)
observed emissions from H2O and CO lines in the sub-mm wavelengths. The
(110-101) rotational lines of H2O (H2^18O) at 557 $\mathrm{GHz}$ (548
$\mathrm{GHz}$) and the CO (5-4) rotational line at 576 $\mathrm{GHz}$ a were
seen in emission spectra when observing the limb and in absorption spectra
when viewing nadir (Biver et al. 2015, 2019). The CO line was more difficult
to observe due to its intrinsic low strength and the small abundance of CO.
The IR and sub-mm spectrometers were aligned with the FUV spectrograph line-
of-sight and their fields of view were located close to Row 15 of the viewing
slit. Thus, they probed approximately the same neutral column as the FUV
spectrograph (near the centre of the slit). This is particularly useful when
observing off-limb, as the composition may vary significantly along the column
and the source of gas is far more dispersed. Column densities derived from
MIRO data in nadir pointing are less reliable when viewing the nucleus due to
low contrast between the near surface warm gas emission and background
radiation emitted from the surface. The IR spectrometer could be used when
looking nadir if the surface is in shadow but it acquired little data in this
configuration throughout the mission. Each of these instruments has been used
to constrain the column density when the data are available.

###  2.4 Calculation of the emission frequency from dissociative excitation

The emission frequency, $\nu_{l}^{X}$, of a given neutral species, $l$, and
emission line, $X$, is driven by only two physical quantities (Eq. 1): the
emission cross-section (see Section 2.4.1) and the suprathermal electron
particle flux (see Section 2.4.2).

####  2.4.1 Dissociative excitation cross-sections

The emission cross-sections for each spectral line, $X$, and neutral species,
$l$, are outlined in Table $2$. The current set of laboratory measurements of
the emission cross-sections due to electron impact are somewhat incomplete.
Many of the cross-sections have datapoints at only one or two energies so the
energy dependence of the cross-sections are not known. As such, several
assumptions about the energy dependence of the cross-sections have been made
and are summarised in Table $2$.
Several cross-sections were recently updated by Ajello et al. (2019), but we
do not use these in this study. The emission cross-sections of OI1356 from e +
CO2 in Ajello et al. (2019) are an order of magnitude smaller than those from
previous literature (Wells et al. 1972; Wells & Zipf 1974). The inferred
OI1304/OI1356 line ratio of $\sim 3.2$ is not consistent with emission spectra
from the Rosetta mission, when electron impact on CO2 was prevalent (Section
3.1 & Feldman et al. 2018). The 5S upper state of the OI1356 transition has a
long radiative lifetime (180 $\mu$s; Wells & Zipf 1974) and may have been
quenched through collisions. Wells et al. (1972) and Wells & Zipf (1974)
measured the production and radiative lifetime of the 5S state independently,
so the inferred emission cross section was not susceptible to collisions
experienced by the intermediate state. The experiments in Ajello et al. (2019)
were based on the emission spectra of CO2, which are more strongly impacted by
any quenching of the 5S state by the relatively dense neutral gas used ($\sim
3\times 10^{11}$ molecules cm-3). This is 3-4 orders of magnitude denser than
the neutral gas seen at 67P at the large heliocentric distances considered in
this study.

Table 1: Cross-sections for the dissociative excitation of cometary molecules by electron impact. . Emission Line | Species | Threshold Energy [$\mathrm{eV}$] |  Reference and Assumptions
---|---|---|---
Ly-$\beta$ & OI1027 |  H2O | 17.21 |  Makarov et al. (2004). Assume the same shape as Ly-$\alpha$ with ratio $7/55$ at 200 $\mathrm{eV}$. Includes coincident OI line.
CO2 |  $21\pm 2$11$1$Mumma et al. (1972)Mumma et al. (1972) |  Kanik et al. (1993) Assume the same shape as OI1304. Use ratio at 200 $\mathrm{eV}$.
CO | 23.17 |  James et al. (1992).
O2 | 20.6 |  Wilhelmi & Schartner (2000). Absolute value given at 200 $\mathrm{eV}$. Assume same shape as OI1304.
OI1304 |  H2O | 15.2 |  Makarov et al. (2004).
CO2 | $21\pm 2$ |  Mumma et al. (1972). Reduced by a factor of 0.59 due to updated measurements of H2 Ly-$\alpha$ (McConkey et al. 2008).
CO | 20.6 |  Ajello (1971). Some uncertainty at energies $>100$ $\mathrm{eV}$.
O2 | 14.622$2$McConkey et al. (2008)McConkey et al. (2008) |  Kanik et al. (2003). Scaled up by factor $2.93/2.90$ in line with the recommendation by McConkey et al. (2008).
OI1356 |  H2O | 15.2 |  Makarov et al. (2004). Assume same threshold and shape as OI1304.
CO2 |  $20.6$22$2$From MIRO. |  Feldman et al. (2015). Excitation rate of OI1356 33 times larger for CO2 than H2O (Wells et al. 1972), after revision of the lifetime of the ^5S^$\circ$ state (Wells & Zipf 1974). Assume the same shape as OI1304.
CO | 20.6 |  Ajello (1971). Ratio given at 100 $\mathrm{eV}$ (Wells & Zipf 1974; Wells et al. 1972). Assume the same shape as OI1304.
O2 | 14.6 |  Kanik et al. (2003). Scaled up by factor $6.47/6.40$ in line with recommendation by McConkey et al. (2008).
CI1657 |  CO2 | $25\pm 2$ |  Mumma et al. (1972).
CO |  |  Difficult to measure cross-section due to the strong overlapping CO4PG band. No contribution from dissociative excitation of CO considered for CI1657.
CO4PG |  CO2 | $25\pm 2$ |  Contribution of (0,2) bands included in CI1657 cross-section of Mumma et al. (1972).
CO | 8 |  Beegle et al. (1999). Absolute values for bands given at 100 $\mathrm{eV}$. Shape of (0,1) band given. Scaled down by factor 0.925 due to remeasurement of calibrating NI line (Ajello et al. 2019).
CII1335 |  CO2 | 44 |  Mumma et al. (1972).
CO | 33 |  Ajello (1971).

####  2.4.2 Suprathermal electron flux

The suprathermal electron flux during each scan of the FUV spectrograph has
been derived from measurements by the Rosetta Plasma Consortium (RPC; Carr et
al. 2007). The count rate measurements from the Ion and Electron Sensor
(RPC/IES; Burch et al. 2007) were converted to an electron particle flux using
the method outlined in Appendix A. Several of the RPC/IES anodes degraded
throughout the mission, resulting in limited angular coverage of the electron
flux (Broiles et al. 2016). In the correction for the field of view, we
assumed that the electron flux was isotropic.
We also assumed that the suprathermal electron flux was constant along the
line of sight of the Alice FUV spectrograph, which is consistent with the
findings of Chaufray et al. (2017). We consider the electron depth (Heritier
et al. 2018b)

$\tau^{e-}=\sum\limits_{l}\sigma_{l}^{e-,inel}N_{l}(r),$ (3)

where $\sigma_{l}^{e-,inel}$ is the total inelastic collision cross-section
for 30 $\mathrm{eV}$ electrons with the neutral species H2O ($2.32\times
10^{-16}$ ${\mathrm{cm}}^{2}$, Itikawa & Mason 2005) and CO2 ($1.6\times
10^{-16}$ ${\mathrm{cm}}^{2}$, Itikawa 2002). The electron depth is analogous
to an optical depth, so for $\tau^{e-}<1$ we expect little degradation of
suprathermal electrons along the line of sight. As expected at large
heliocentric distances, the electron depth was small ($\tau^{e}<0.35$) for all
cases in the present study so suprathermal electrons were unlikely to undergo
collisions in the coma.
RPC/IES measured electrons that have energies between 4.32 $\mathrm{eV}$ and
17.67 $\mathrm{keV}$ at the detector. However, throughout the mission, the
spacecraft was typically at a voltage of $-10$ $\mathrm{V}$, as measured by
the Rosetta Dual Langmuir Probes (RPC/LAP, Odelstad et al. 2015). The negative
spacecraft potential ($V_{S/C}$) repelled electrons, allowing only those with
higher energies to reach the sensor. The minimum energy, $E_{min}$, in
$\mathrm{eV}$ that electrons observed by RPC/IES has is:
$E_{min}\,\text{[$\mathrm{eV}$]}=4.32-V_{S/C}\,\text{[$\mathrm{V}$]}$.
The electron flux was corrected for this using the Liouville’s theorem, under
the assumption that the phase space density is conserved within the potential
of the spacecraft:

$\frac{J(E)}{E}=\frac{J_{IES}}{E_{IES}}\quad\text{where}\quad
E\,\text{[$\mathrm{eV}$]}=E_{IES}\,\text{[$\mathrm{eV}$]}-qV_{S/C}\,\text{[$\mathrm{V}$].}$
(4)

Within the duration of each FUV scan, there were several measurements of the
electron flux by RPC/IES, each of which was individually corrected for the
spacecraft potential at that time. The time-average and the standard deviation
of the electron flux were calculated at each energy as shown in Figure 3.
Although RPC/IES could not measure the electron population below the detection
threshold, there may still have been a large electron flux at low energies. As
such, we extended the mean particle flux to low energies assuming a constant
particle flux at low energies. We also considered extrapolating
logarithmically but the method of extrapolation had little impact on the
resulting emission frequency as the cross-sections decrease significantly near
the threshold energies (given in Table $2$). The emission cross-sections
decrease sharply near the threshold energies of each line (see Table $2$) and
electrons below the threshold are unable to generate FUV emissisons. Despite
large particle fluxes the low energy ($<20$ $\mathrm{eV}$) electrons
contributed little to the model brightness.

Figure 3: Suprathermal electron particle flux during two nadir Alice scans
during quiet periods. The solid line is the average particle flux during each
of the scans, while the shaded region corresponds to the standard deviation of
the electron flux in the same period. The extrapolation of the electron flux
to energies below which RPC/IES could not measure, due to the spacecraft
potential, is given by the dashed line.

###  2.5 Other sources of emission

Alongside dissociative excitation by electron impact, there are several other
sources of emission that are observed at comets. We have already referred to
the contribution to the Lyman series by the IPM (see Section 2.2), but this
should not have been visible when viewing the surface of the nucleus from
Rosetta.
We considered two main emission sources outside of electron impact: prompt-
photodissociation of H2O to produce Lyman-$\beta$ and fluorescence of CO to
emit in the Fourth Positive Group.
These emission features are driven by the solar flux incident on the column of
gas along the line of sight. The brightness of the emissions from these
sources is given by

$B^{X,h\nu}_{l}=10^{-6}N_{l}\int\limits_{\lambda_{min}}^{\lambda_{Th}}\\!\sigma_{l}^{X,h\nu}(\lambda)I(\lambda)\,\mathrm{d}\lambda,$
(5)

where $l$ is H2O for $X=\text{Ly-$\beta$}$ and CO for $X=\text{CO4PG}$
(contributing to the CI1657 emissions).
The photon flux, $I(\lambda)$, at comet 67P was driven by TIMED-SEE (Woods et
al. 2005) measurements at 1 $\mathrm{ua}$ taken at the same Carrington
longitude as comet 67P for each time interval. The cross-section for resonance
fluorescence of CO was based on the model of Lupu et al. (2007). For the
prompt-photodissociation of H2O, we use the emission cross-section from Hans
et al. (2015).
The modelled brightness of these photon-driven emissions are upper bounds as
we assumed that the entire column of neutral gas along the line of sight was
illuminated. In reality, the neutral column may have been partially shadowed
near the nucleus, where the neutral number density was highest, and the
emissions from fluorescence of CO and prompt-photodissociation of H2O will be
overestimated.

##  3 Nadir analysis during quiet periods

###  3.1 Selected cases

Table 2: Cases selected in the southern hemisphere, with nadir viewing at large heliocentric distances. The horizontal lines separate nadir cases with high (Cases 1-8) and low (Cases 9-13) electron fluxes. Case |  Date |  Start Time [UTC] |  Integration Time [$\mathrm{s}$] |  Cometocentric Distance [$\mathrm{km}$] |  Heliocentric Distance [$\mathrm{ua}$] |  Spacecraft Latitude [$\circ$] |  Spacecraft Longitude [$\circ$] |  Total Column Density [$10^{15}$ ${\mathrm{cm}}^{-2}$]
---|---|---|---|---|---|---|---|---
1 |  14/01/2015 |  11:38:40 |  3629 |  28.4 |  2.55 |  -23.4 |  -82.9 |  0.58
2 |  29/01/2015 |  18:40:49 |  6048 |  27.8 |  2.44 |  -63.8 |  5.4 |  0.27
3 |  30/01/2015 |  04:25:44 |  2419 |  27.8 |  2.43 |  -64.6 |  56.6 |  0.22
4 |  30/01/2015 |  06:34:42 |  2419 |  27.8 |  2.43 |  -64.2 |  -11.4 |  0.51
5 |  30/01/2015 |  07:17:41 |  1763 |  27.8 |  2.43 |  -64.0 |  -34.0 |  0.48
6 |  30/01/2015 |  11:32:18 |  2419 |  27.9 |  2.43 |  -62.5 |  -167.4 |  0.18
7 |  30/01/2015 |  15:25:50 |  2419 |  27.9 |  2.43 |  -60.5 |  71.35 |  0.28
8 |  26/04/2016 |  06:06:12 |  4452 |  21.2 |  2.9 |  -33.1 |  -107 |  1.88
9 |  29/01/2015 |  07:51:27 |  3629 |  27.8 |  2.44 |  -58.4 |  -17.1 |  0.75
10 |  21/04/2016 |  23:01:00 |  3398 |  30.9 |  2.85 |  -24.6 |  -57.7 |  1.24
11 |  21/03/2016 |  00:05:00 |  2603 |  12.2 |  2.62 |  -24.2 |  -36.8 |  1.43
12 |  14/05/2016 |  14:39:34 |  4613 |  9.8 |  3.0 |  -53.1 |  -111.7 |  1.13
13 |  27/05/2016 |  08:43:00 |  5592 |  7.0 |  3.09 |  -56.2 |  -42.3 |  1.32

In order to determine whether the FUV emissions over the southern hemisphere
are driven primarily by electron impact, cases with a nadir viewing geometry
over the shadowed nucleus are considered. By observing the shadowed nucleus,
there is no contribution from the IPM to the observed Lyman-$\beta$ brightness
and any contamination from solar photons reflected off the nucleus is
minimised. This geometry also provides the best constraint on the neutral
composition of the coma from the mass spectrometer (see Section 2.3).
We have considered 13 cases in the southern hemisphere and at large
heliocentric distances. The properties of each of these scans are outlined in
Table 2. The cases have been split into two sets, which have been approached
separately: nadir cases with a high suprathermal electron flux, as illustrated
by the blue spectrum in Fig. 3 (Cases 1-8; Section 3.2); and nadir cases with
a low suprathermal electron flux, as illustrated by the red spectrum in Fig. 3
(Cases 9-13; Section 3.3). The emission frequency for all the selected lines
and the column density of each neutral species are shown in Figs. 4 and 5,
respectively, for all cases in order to interpret the modelled brightnesses
presented in Fig. 6, along with the FUV spectrograph observations. The average
electron particle fluxes in two energy brackets are given in Table 3. The
distinction between the high and low suprathermal electron flux cases (see
Fig. 3) can be seen in both of the energy ranges, but to a greater extent from
$60-120$ $\mathrm{eV}$.

Table 3: Average electron flux in two energy ranges for each of the nadir cases outlined in Table 2. The distinction between cases with high and low suprathermal electron fluxes is clearer in the 60-120 $\mathrm{eV}$ range. Case |  Ave. Electron Flux for $20-60$ $\mathrm{eV}$ [$10^{7}$ ${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$] |  Ave. Electron Flux for $60-120$ $\mathrm{eV}$ [$10^{7}$ ${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$]
---|---|---
1 |  $23.2\pm 1.2$ |  $6.33\pm 0.85$
2 |  $30.4\pm 1.9$ |  $5.68\pm 1.34$
3 |  $27.7\pm 3.6$ |  $5.10\pm 2.62$
4 |  $20.5\pm 1.3$ |  $4.82\pm 0.95$
5 |  $16.9\pm 0.9$ |  $4.36\pm 0.65$
6 |  $22.2\pm 0.8$ |  $5.88\pm 0.56$
7 |  $10.5\pm 1.4$ |  $2.47\pm 1.01$
8 |  $\phantom{0}6.42\pm 0.51$ |  $2.60\pm 0.37$
9 |  $3.51\pm 0.84$ |  $0.05\pm 0.61$
10 |  $1.18\pm 0.05$ |  $0.22\pm 0.04$
11 |  $1.40\pm 0.12$ |  $0.06\pm 0.09$
12 |  $0.51\pm 0.09$ |  $0.01\pm 0.07$
13 |  $1.03\pm 0.11$ |  $0.03\pm 0.08$
(a)(b)(c)(d)(e) Figure 4: Emission frequency, $v_{l}^{X}$, of each neutral
species and emission line: (a) OI1356, (b) OI3014, (c) Ly-$\beta$ and OI1027,
(d) CI1657 and CO4PG, and (e) CII1335. Emissions due to electron impact (e +
X, Section 2.4) on CO2 (red), H2O (dark blue), CO (orange), and O2 (purple)
and other processes (hν \+ X, Section 2.5) have been included. The uncertainty
in the electron impact emission frequency is derived from the variability in
the electron flux during each scan of the FUV spectrograph (see Section
2.4.2). hν \+ CO refers to emissions from the fluorescence of CO (green),
while hν \+ H2O refers to the prompt-photodissociation of water (light blue)
to produce Lyman-$\beta$ (see Section 2.5).  Figure 5: Column density of the
four major neutral species in the coma during each of the spectrograph scans.
The volume mixing ratios are derived from ROSINA/DFMS measurements (see
Section 2.3).

###  3.2 Nadir cases 1-8

As mentioned in Section 2.3, we can derive the total neutral density in nadir
viewing from in situ measurements. However, the strong dependence of the
column density on the cometoradius means this method is quite uncertain.
Alternatively, we can constrain the total column density by setting the
modelled brightness of the OI1356 line such that it equals the observed
brightness of this line. OI1356 emissions are associated with a forbidden
transition (^5S - ^3P), so there are few sources of this emission line apart
from electron impact. The contributions of both resonance scattering and
fluorescence to this line are negligible.
There is a close agreement between the modelled and observed brightnesses for
all five FUV emission lines selected for cases 1-8 (see Fig. 6). This suggests
that our model represents the sources of FUV emissions in the coma well.
The emission of OI1356 is dominated by e + CO2 (red, Fig. 6a) across the high
suprathermal electron flux cases. This is a result of the high emission
frequency of e + CO2 ($1.08\times 10^{-8}$ ${\mathrm{s}}^{-1}$) compared to e
+ H2O ($4.0\times 10^{-10}$ ${\mathrm{s}}^{-1}$, see Fig. 4) in this line. The
small emission frequency from e + H2O means the brightness of the OI1356
emissions is not sensitive to the column density of water. e + O2 has an
OI1356 emission frequency of $5.98\times 10^{-8}$ ${\mathrm{s}}^{-1}$ in cases
1-8, larger than that from e + CO2, but the column density of O2 is
insufficient for this process to contribute significantly to the total
brightness (purple, Fig. 5). In case 1, e + O2 drives 0.69 R of OI1356
emission (purple, Fig. 6a), which is considerably more than the $0.1-0.2$ R of
emission from this source in cases 2-8. This results from the larger column
density of O2 ($8.9\times 10^{12}$ ${\mathrm{cm}}^{-2}$, Fig. 5) in case 1
than in cases 2-7 ($3.1\pm 0.9\times 10^{12}$ ${\mathrm{cm}}^{-2}$, Fig. 5),
due to the more equatorial latitude compared to the southerly cases 2-7 (see
Table 2). Case 8 occurred post-perihelion, when the outgassing rate of CO2
increased, resulting in a low volume mixing ratio of O2 (purple, Fig. 5),
despite having a similar latitude to case 1 (see Table 2).
The OI1304 emissions are mostly driven by electron impact on CO2 and H2O (see
Fig. 6b). The emission frequency of OI1304 from e + CO2 is only 1.5 times more
efficient than e + H2O, in contrast to the factor of 20 in the emission
frequencies of OI1356. Electron impact on CO and O2 are 1.5 and 10 times more
efficient at emitting OI1304 than e + CO2 (see Fig. 4b), respectively, but the
small volume mixing ratios of these molecules throughout cases 1-8
($\ce{O2}/\ce{CO2}=0.04$; $\ce{CO}/\ce{CO2}=0.11$; Fig. 5) limits their
contribution to the total OI1304 brightness. However, these processes can be a
significant source of OI1304, when the volume mixing ratio of each species
increases (see. Fig. 5) as seen in case 1 for e + O2 and case 8 for e + CO
(see Fig. 6b).
The emission feature near 1026 $\mathrm{\SIUnitSymbolAngstrom}$ is dominated
by electron impact on water throughout cases 1-8 (dark blue, Fig. 6c),
generating emissions of Ly-$\beta$. As seen with OI1356 and OI1304 emissions,
the largest emission frequency at this wavelength is from e + O2 at
$1.17\times 10^{-8}$ ${\mathrm{s}}^{-1}$ (purple, Fig. 4c), which produces
OI1027, but this is only twice that of e + H2O, so the small column density of
O2 with respect to that of water means it contributes negligibly to the
modelled brightness (purple, Fig. 6). Throughout these cases, we see a
sizeable contribution from e + CO2 ($<0.9$ R) to the OI1027 brightness that is
not seen in the northern hemisphere (Galand et al. 2020). This is especially
prominent in case 8, with a post-perihelion enhanced CO2 column density of
$8.66\times 10^{14}$ ${\mathrm{cm}}^{-2}$ (see Fig. 5). In cases 1-8, prompt-
photodissociation of H2O (light blue, Fig. 4c) has an emission frequency 5
times smaller than from e + H2O (dark blue, Fig. 4c), so photodissociation is
a minor source of emissions when the suprathermal electron flux is large (Fig.
6c). We show that e + H2O is the major source of the emissions near 1026
$\mathrm{\SIUnitSymbolAngstrom}$ in the southern hemisphere, but the
contribution from e + CO2 and prompt-photodissociation of H2O to this line are
not negligible.
Throughout cases 1-8, the emissions near 1657 $\mathrm{\SIUnitSymbolAngstrom}$
are dominated by CI1657 emission from electron impact on CO2 (red, Fig. 6d).
There is also a small contribution from e + CO (orange, Fig. 6d) to the
overlapping bands of the Fourth Positive Group, which has an emission
frequency ($4.58\times 10^{-8}$ ${\mathrm{s}}^{-1}$) twice that of e + CO2
(orange and red, respectively, Fig 4d). As the suprathermal electron flux is
high for these cases, fluorescence of CO (green, Fig. 4d) has a lower or
similar emission frequency to e + CO2. However, the low column density of CO
compared to that of CO2 (see Fig. 5) means the emissions from both electron
impact on and fluorescence of CO are only minor contributions to the total
brightness near 1657 $\mathrm{\SIUnitSymbolAngstrom}$ (see Fig. 6d), except in
case 8, when the column density of CO ($1.19\times 10^{14}$
${\mathrm{cm}}^{-2}$) is larger than seen in cases 1-7 (see Fig. 5).
The CII1335 emissions have significant contributions from electron impact on
both CO and CO2. The emission frequency of e + CO ($2.04\times 10^{-8}$
${\mathrm{s}}^{-1}$) is 8 times larger from e + CO2 for this line, which is
balanced by a ratio of 0.11 of CO to CO2 in column density. The two competing
effects result in the two species contributing approximately equally to the
brightness of the CII1335 line (see Fig. 6e). This emission line is primarily
driven by $60-120$ $\mathrm{eV}$ electrons due to the high threshold energies
of e + CO (33 $\mathrm{eV}$) and e + CO2 (44eV, Table $2$) for this process.
The electrons in this energy range vary little across cases 1-8 (see Table 3),
which is reflected in the roughly constant emission frequency (see Fig. 4e).
Therefore, the variations in the CII1335 brightness in cases 1-8 are driven by
changes in the column densities of CO and CO2 (see Fig. 5). The large emission
frequency of e + CO relative to e + CO2 (see Fig. 4e) in this line means the
observed brightness is highly sensitive to the column density of CO. The
volume mixing ratio of CO, derived from measurements by the mass spectrometer,
includes a significant correction for fragmentation of CO2 within the
instrument, which leads to a contribution to the CO signal (Dhooghe et al.
2014). The close agreement between the modelled and observed brightness of
this line across cases 1-8 (Fig. 6e) suggests that the corrected
$\ce{CO}/\ce{CO2}$ volume mixing ratio derived from the mass spectrometer
measurements is accurate.

(a)(b)(c)(d)(e) Figure 6: Comparison of the total modelled (black) and
observed brightness (magenta), $B^{X}$, of each emission line. The stacked
bars show the contribution from each neutral species and emission process. The
same colour code as Fig. 4 is used. The error on the observed brightness is
derived from the integration of the FUV spectra. The error on the modelled
brightness is from the temporal variation of the electron flux and column
density, as well as a 20% uncertainty in the neutral composition. In cases
1-8, where the observed OI1356 brightness is used to fit the total neutral
column density (see Section 3.2), the error on the modelled OI1356 brightness
is included in the error of the other modelled emission brightnesses.

###  3.3 Nadir cases 9-13

In cases 9-13, the suprathermal electron flux was very low (see Table 3) in
both energy ranges. The electron flux was on average 11.8 times greater for
cases 1-8 than for cases 9-13 between 20 and 60 $\mathrm{eV}$, whereas in the
range $60-120$ $\mathrm{eV}$ the average flux ratio was $\sim\\!{60}$. The FUV
emission lines considered, except CII1335, are driven primarily by electrons
from $20-60$ $\mathrm{eV}$ so the emission frequencies are a factor of
$\sim\\!20$ smaller in cases 9-13 than in cases 1-8 (e.g. 26.6 for Ly-$\beta$
from e + H2O; dark blue, Fig. 4c). The threshold energies for emission of
CII1335 from electron impact on CO (33 $\mathrm{eV}$, see Table $2$) and CO2
(44 $\mathrm{eV}$) are much higher than for the other wavelengths considered,
and hence the emissions are more dependent on the electron flux between 60 and
120 $\mathrm{eV}$. This results in a ratio of $\sim\\!{50}$ in the emission
frequency of the process e + CO2 (red, Fig. 4e) between the high and low flux
cases.
Throughout the low flux cases, we observe no substantial emissions of OI1356
due to the low electron impact emission frequencies (see Fig. 6a). As a
result, we use the radial column density, derived from the in situ pressure
gauge measurements (see Section 2.3), to calculate the modelled emission
brightnesses. The radial column density is calculated assuming a constant
neutral gas velocity, which may result in an underestimate of the column
density.
We also observe negligible emissions of OI1304 throughout this time (see Fig.
6b). The column densities in cases 9-13 are similar to cases 1-8 (see Fig. 5),
so the lack of oxygen line emissions is a result of the lower electron flux
(Table 3). In addition, there are negligible emissions of CII1335 (see Fig.
6e), as there are few $60-120$ $\mathrm{eV}$ electrons in the coma (Table 3).
The lack of observed OI1356, OI1304, and CII1335 emissions (see Figs. 6a, 6b
and 6e) in these lines is replicated in the modelled brightnesses for the
cases associated with a low suprathermal electron flux. This demonstrates that
the only source of these emission lines in nadir viewing is dissociative
excitation by electron impact.
As shown in Fig. 6d, there are significant emissions near 1657
$\mathrm{\SIUnitSymbolAngstrom}$ for these cases, despite the small
populations of energetic electrons in the coma (Table 3) and the low emission
frequency of the processes e + CO ($3.96\times 10^{-9}$ ${\mathrm{s}}^{-1}$)
and e + CO2 ($1.07\times 10^{-9}$ ${\mathrm{s}}^{-1}$, see Fig. 4d). The
emission frequency of fluorescence of CO is $1.86\times 10^{-8}$
${\mathrm{s}}^{-1}$ through cases 9-13, and hence is the dominant source of
emissions at this wavelength. The dominance of CO fluorescence, compared to
case 8, results only from the decrease in the electron impact emission
frequency, as both the volume mixing ratio $\ce{CO}/\ce{CO2}=0.14\pm 0.05$ and
the emission frequency from CO fluorescence (green, Fig. 6d) are similar to
those in case 8. In cases 1-7, the total column density and the CO column
density are on average a factor 3 times smaller than in cases 9-13, which
result in a small absolute contribution from CO fluorescence (0.27 R). There
is some uncertainty in the source of the CO4PG emissions in the low flux
cases, as the Cameron bands, which are seen at long wavelengths, indicate that
there may be emissions from CO in the 4PG driven by a large flux of low energy
($\sim$10 eV) electrons. However, we have not seen evidence of this in the
measured electron flux as the spacecraft potential ($-23$ to $-17$ eV, as
measured by RPC/LAP) prevented measurements at such low electron energies.
Other emission lines are unaffected by these low energy electrons as these
lines have a much higher threshold energy ($>$15 eV) compared to 4PG emissions
from CO (8 eV, see Table $2$). Despite this, the modelled CI1657 and CO4PG
emissions well represent the observed emissions in these cases, given the
uncertainty in the column density, and dissociative excitation by electron
impact is not the major source of emissions when the suprathermal electron
flux is small.
In cases 9-13, the emission frequency of Ly-$\beta$ and OI1027 from electron
impact on all species drops below the emission frequency of prompt-
photodissociation of H2O ($8.6\times 10^{-10}$ ${\mathrm{s}}^{-1}$, Fig. 4c).
In these cases, prompt-photodissociation of H2O is the dominant source of
emissions as the process e + H2O has an emission frequency a factor four
smaller ($1.97\times 10^{-10}$ ${\mathrm{s}}^{-1}$, Fig. 4c).
Photodissociation of H2O is comparable in efficiency to electron impact on O2
near 1026 $\mathrm{\SIUnitSymbolAngstrom}$ but throughout these cases the
number density ratio of $\ce{O2}/\ce{H2O}$ is less than $0.02$, so the
contribution from electron impacts on O2 is small.
The observed and modelled brightnesses of Ly-$\beta$ and OI1027 agree closely
in cases 9 and 10 but for cases 11-13 the modelled brightness is smaller than
that observed (see Fig. 6c). The unexplained intense Lyman-$\beta$ emissions
are unlikely to be from electron impact emissions which would produce strong
signals in the other atomic lines, such as OI1304 from e + H2O at a factor
$\sim 2.9$ smaller than the Ly-$\beta$ brightness.
The Lyman-$\alpha$/Lyman-$\beta$ ratio can be used as an indicator of key
emission processes, with a ratio of 8 expected from pure e + H2O (Makarov et
al. 2004). On 29 Nov 2014, a spectrum of pure e + H2O (Galand et al. 2020) was
observed with a ratio Lyman-$\alpha$/Lyman-$\beta=4.4$. The disparity between
the observed ratio and the theoretical ratio may be a result of the difficult
calibration of Alice around Lyman-$\alpha$, variation in the shape of the
Lyman series cross-sections or differences in the cascade emissions. Case 8,
also in early 2016, has a ratio of 2.56 with a large electron flux, but the
1027Å line brightness has a large contribution of OI emissions from e + CO2.
The modelled Ly-$\beta$ emissions from e + H2O in case 8 are a factor 4.4
smaller than the Ly-$\alpha$ brightness, consistent with the line ratio in Nov
2014.
Cases 11-13 have Ly-$\alpha$/Ly-$\beta=$ 2.6, 3.2 and 3.3 respectively,
suggesting that a process with a small line ratio has contributed
significantly to the Ly-$\beta$ brightness. Electron impact on other neutral
species cannot be a strong source of OI1027 in these cases, as they would show
stronger emissions in other lines (e.g. OI1356 for O2 and CO2) which were not
observed. Resonant scattering of solar flux on atomic hydrogen would generate
Ly-$\alpha$ emissions 300 times brighter than Ly-$\beta$, greatly increasing
the line ratio. It is also very unlikely at the low cometocentric distances
($\sim 10$ km) as neutral molecules are advected away from the nucleus
(timescale of the order of seconds; Galand et al. 2016) before they can
undergo photodissociation (timescale $>10^{5}$ s; Huebner & Mukherjee 2015).
Prompt-photodissociation, which gives a Ly-$\alpha$/Ly-$\beta$ ratio of 1.4
(Hans et al. 2015), could generate the lower line ratio. The emission of
OI1304 from this process is also very weak, as a spin forbidden transition
would be required (Wu & Judge 1988). However, if we had significantly
underestimated the efficiency of this process in the model, a discrepancy
would be seen in the other cases. A large increase in the column of water in
cases 11-13 (by a factor of 8, 15 and 5, respectively) would bring the
modelled Ly-$\beta$ into agreement with the observed brightnesses, whilst
generating few emissions in the other atomic lines due to the low emission
frequencies (dark blue, Figs. 4a & b). However, this would result in a neutral
column comprising 80% water in cases 11 and 12 (50% in case 13), which is
inconsistent with the concurrent mass spectrometer measurements (see Fig
5).The required mixing ratio would also be incongruous with wider outgassing
trends, as the outgassing rate of CO2 in the southern hemisphere was larger
than that of H2O in Mar 2016 (Case 11) and was dominant over the outgassing of
H2O near the end of mission (Cases 12 and 13; Gasc et al. 2017a; Läuter et al.
2018). The source of the Lyman-$\beta$ emissions in cases 11-13 remains
unclear.

##  4 Corotating interaction regions in summer 2016

###  4.1 Selection of cases

Having confirmed that the impact of suprathermal electrons on cometary
neutrals is a major source of emissions during quiet periods in the southern
hemisphere in Section 3, we apply the multi-instrument analysis to the CIRs
observed in the summer of 2016. The CIR was observed over four solar rotations
throughout the summer of 2016 (Hajra et al. 2018), from the start of June
until the beginning of September. In the present study, we consider two
occurrences: one over the 9 and 10 July, and one on the 4 August. Enhanced FUV
emissions were observed on two additional solar rotations in early and late
September. However, observations in the FUV occurred infrequently during these
events, so we could not study the temporal variability of the emissions.
During these events, the suprathermal electron flux can vary by a factor of
100 within several hours, as seen during the first periods on 4 Aug and 9 July
(see Tables $3$ and 5 and Fig. 8). The brightness of the FUV emission lines
are also seen to vary by a factor of ten within the same time periods (see
Figs. 9 and 11). This scale of variation in the emission brightness has also
been observed by Galand et al. (2020) during a solar event in October 2014 and
Noonan et al. (2018) during a CME in summer 2015. To capture the variability,
we use the highest temporal resolution available for both the measurements of
the electron flux and the observed FUV brightness (10 $\mathrm{min}$). The
emission frequencies are calculated from individual electron flux
measurements, once the flux has been corrected for the spacecraft potential
(see Section 2.4.2). The modelled brightness is plotted in Figures 9 and 11 at
the time resolution of the electron spectrometer. We do not co-add consecutive
spectra from the FUV spectrograph, as in Section 2.2, but instead evaluate the
brightness at three distinct regions of the viewing slit for each spectrum.
The black vertical lines are therefore indicative of the spatial variability
of the emissions along the Alice slit. In Figures 9 and 11, the three regions
associated with rows 8-11, 13-16, and 18-21 are given by the red, black, and
blue crosses, respectively. The measurements taken simultaneously in the 3
regions of the FUV spectrograph slit are linked by vertical black lines.
Neither the case in July nor the one in August 2016 had a nadir viewing
geometry as was used in Section 3. On 4 August 2016, the FUV spectrograph was
viewing off the limb of the nucleus, whereas on the 9-10 July 2016 the
spectrograph was pointed at the nucleus but off-nadir. In both situations it
is not possible to derive the column density along the line of sight from the
ROSINA in-situ measurements as was done in cases 1-8 in Section 3.2. Variation
across the nucleus’ surface in both the density and composition of the
outgassing neutrals means we cannot extrapolate from in situ measurements to
calculate the column density along the line of sight. For the August case, the
column densities of CO2 and H2O are derived from remote observations by
VIRTIS-H and MIRO spectrometers, respectively, (see Section 2.3) over each of
the intervals of FUV observations.
In the July event, the surface of the nucleus was illuminated, which prevents
the estimation of reliable column densities using either of the spectrometers.
We, therefore, set the column density of CO2 during each interval such that
the scale of the modelled and observed brightnesses of the OI1356 within each
interval agree, which is consistent with the approach in cases 1-8 in Section
3.2.
The column density, taken constant with each interval during the CIR events
considered are given in Tables $3$ and 5. The different periods, with distinct
neutral column densities, are indicated by different coloured lines in Figures
9 and 11. During each interval the nucleus moved slowly within the field of
view of the spectrograph, justifying the constant column density during each
interval. However, between these periods the spacecraft underwent manoeuvres
in which the region of the coma observed changed rapidly, which justifies the
variation of the column density from one interval to the next. As the column
density is taken as constant in each interval, the variation of the modelled
brightness during the time periods is only due to the fluctuations of the
measured suprathermal electron flux. The average electron fluxes in each
period of the FUV spectra are shown in Figures 8 and 10 for August and July,
respectively. The electron flux in period 1 of the August case is split into
two parts, comprising the peaks (dark blue) and troughs (light blue) of the
electron flux as seen in the modelled brightness in Fig.9 (dark blue).

###  4.2 4 August 2016

####  4.2.1 Overview

Figure 7: OSIRIS WAC image (Keller et al. 2007) from 4 Aug 2016 02:00 UT
during period 1 (see Section 4.2.3) with the Alice viewing slit shown in
white. The line of sight passes within $\sim 500$ m of the comet nucleus.

On this day the viewing geometry was limb (Fig 7), so we have used column
density measurements from the VIRTIS-H and MIRO spectrometers (see Section
2.3). The column density measurements taken in the four time periods are
outlined in Table 5. This solar event occurred near the end of mission at 3.5
$\mathrm{ua}$, when CO2 was dominant over H2O in the southern hemisphere as
seen in Table $3$, which is consistent with a volume mixing ratio of
$\ce{H2O}/\ce{CO2}\sim 0.05$ from Läuter et al. (2018). During period 2, the
line of sight of the spectrograph passed over the neck region of the comet,
which had an increased abundance of water (Migliorini et al. 2016), resulting
in the enhanced water column density. CO was not detected during any of the
four periods and the 3$\sigma$ upper-limits of the column density derived from
the sub-mm spectrometer are given in Table $3$. The FUV emission spectra
display weak CO band emissions which indicates there is some CO in the coma,
although insufficient to be detected by MIRO. In Figure 9, we have assumed
that there is no CO present in the coma as we do not have a good constraint on
the CO mixing ratio throughout the column. The spectrometers could not measure
the column density of O2, so we have assumed there is no O2 present in the
column along the line of sight. Towards the end of mission, the mixing ratio
$\ce{O2}/\ce{CO2}$ decreased ($<1$%, Läuter et al. 2018) and O2 was less
abundant in the southern hemisphere (Hässig et al. 2015), so we would not
expect significant emissions from e + O2. Including a few percent of O2
relative to the H2O column density has negligible impact on the emission
brightness, as emissions of the atomic oxygen lines are dominated by electron
impact on CO2.

Table 4: Properties of the four intervals on 4 Aug 2016 at 3.5 $\mathrm{ua}$. The first period has been split into the peaks and troughs in the electron flux, which can be seen in Fig. 9. These are the same periods as shown in Fig. 8 in dark blue (peaks) and light blue (troughs). Period |  Start Time [UTC] |  End Time [UTC] |  CO2 Column Density11$1$From VIRTIS-H.From VIRTIS-H. [$10^{14}$ ${\mathrm{cm}}^{-2}$] |  H2O Column Density22$2$From MIRO. [$10^{14}$ ${\mathrm{cm}}^{-2}$] |  CO Column Density33$3$3$\sigma$ upper limits from MIRO. 3$\sigma$ upper limits from MIRO. [$10^{14}$ ${\mathrm{cm}}^{-2}$] |  Ave. Electron Flux for 20 - 60 $\mathrm{eV}$ [$10^{7}$ ${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$]
---|---|---|---|---|---|---
1 - Peaks |  01:38:59 |  05:42:30 |  $6.21\pm 0.16$ |  $0.5\pm 0.03$ |  ¡1.1 |  15.5 - 44.9
1 - Troughs |  |  |  |  |  |  0.56 - 10.1
2 |  07:25:24 |  10:59:15 |  $2.65\pm 0.17$ |  $2.24\pm 0.09$ |  – |  0.77 - 23.3
3 |  11:51:51 |  15:56:18 |  $8.43\pm 0.14$ |  $0.36\pm 0.02$ |  ¡1.3 |  3.16 - 20.4
4 |  17:38:16 |  21:12:03 |  $7.93\pm 0.23$ |  $0.31\pm 0.02$ |  – |  3.48 - 7.95
Figure 8: Average electron particle flux during the three periods listed in
Table $3$, with the standard deviation of the flux shown by the shaded
regions. The colour of each period is the same as in Fig. 9. The first period
has been split into the peaks (dark blue) and troughs (light blue) in the
electron flux to highlight the variability in this period. The dotted lines
indicate energies where some of the RPC/IES measurements during the period
could not probe, due to a high spacecraft potential (see Section 2.4.2). The
dashed lines denote energies that could not be probed by any of the RPC/IES
scans during the period. The electron flux from Case 1 in the nadir study (see
Section 3 & Fig. 3) is plotted for comparison (black).

During the CIR, the variation in the suprathermal electron flux is mirrored in
the brightness of the emissions in all four of the selected lines: OI1356
(Fig. 9a), CI1657 and CO4PG (Fig. 9b), Ly-$\beta$ and OI1027 (Fig. 9c), and
OI1304 (Fig. 9d). This suggests that all of these emissions are strongly
driven by electron impact on cometary neutrals. For limb viewing, the
emissions originate from a distant region of the coma, which cannot be probed
in situ. The observed correlation between the in situ measurements of the
electron flux and the remote measurements of the FUV spectrograph suggest that
the variations in the electron flux occur on large scales. The electron fluxes
during each period (see Fig. 8) peak at 40-50 eV, which is not seen in the
electron spectra during the nadir cases in quiet periods (see Fig. 3). This
may result from the higher density and more energetic solar wind electrons
entering the coma that are associated with the CIR.

(a)(b)(c)(d) Figure 9: Comparison of the observed (crosses) and modelled
(coloured lines) brightness of four emission features, OI1356 (a), CI1657 and
CO4PG (b), Lyman-$\beta$ and OI1027 (c) and OI1304 (d), during four time
periods, during which a CIR was observed at comet 67P, on 4 Aug 2016 (see
Table $3$). The observed brightnesses are from three regions of the FUV
spectrograph slit (Rows 8-11 [red], 13-16 [black] and 18-21 [blue]). Vertical
black lines link simultaneous measurements of the brightness.

####  4.2.2 Periods 2-4

The modelled brightness of the OI1356 emissions closely replicate both the
variations and the magnitude of the observed emissions in periods 2-4 (see
Fig. 9a). The emissions are dominated by e + CO2, which accounts for 98% of
the modelled emissions. This is consistent with our findings from the nadir
cases over the southern hemisphere (see Fig. 6a) for which the neutral
composition was derived from the mass spectrometer (see Section 3.2). The
close agreement in periods 2-4 suggests that there are no other significant
sources of OI1356 in these cases. The lower OI1356 brightness during the
second time period is a result of the lower column of CO2 compared to the
following period (see Table $3$). In period 3, the OI1356 emission frequency
from e + CO2 increases from $7.1\times 10^{-10}$ ${\mathrm{s}}^{-1}$ at 12:35
UT to $2.1\times 10^{-8}$ ${\mathrm{s}}^{-1}$ at 15:42UT, which causes the
concurrent rise in the OI1356 brightness.
Period 4 has fewer emissions due to the small electron flux (green, Fig. 8 &
Table $3$), which results in a lower emission frequency. In period 3 the
emission frequency of OI1356 from e + CO2 reached $2.1\times 10^{-8}$ s-1,
five times the peak frequency in period 4 ($3.9\times 10^{-9}$ s-1).
When looking nadir in Section 3.1, the CI1657 emissions were dominated by
electron impact on CO2, with only a small contribution from fluorescence of CO
(dark green, Fig. 6d) when the suprathermal electron flux was high. For limb
viewing, the modelled brightness of CI1657, driven only by electron impact on
CO2 (without any contribution from fluorescence of CO), well reproduces the
observed brightness throughout the periods 2 and 3 (see Fig. 9b), which is
consistent with there being no significant column of CO present along the line
of sight ($\ce{CO}/\ce{CO2}<0.05$). Furthermore, we would not expect any
significant contribution from fluorescence in this case, as e + CO is a more
efficient source of emissions when the suprathermal electron flux is large
(see cases 1-8, Fig. 4). In period 4, a slight underestimation of CI1657 by
the model may result from the lack of CO column included in the model. A
$\ce{CO}/\ce{CO2}$ ratio of 0.2 would explain the disparity, which is only
slightly larger than the ratio in production rates ($\ce{CO}/\ce{CO2}=0.1$) in
the southern hemisphere at this time (Läuter et al. 2018).
For limb viewing, emissions from the IPM contribute to the observed Ly-$\beta$
brightness, unlike in the nadir case (see Section 2.2). As such we include a
2-rayleigh background contribution from the IPM in this line. The Ly-$\beta$
brightness exhibits the same variations as measured in the electron flux
throughout the CIR (see Fig. 9c), suggesting that dissociative excitation by
electron impact is a significant source of this line.
The brightness of Ly-$\beta$ emissions is well captured throughout periods
2-4, which suggests there are no other major sources of emissions. The
contribution from prompt-photodissociation of H2O to the total brightness is
negligible throughout the CIR. In the limb viewing geometry, the extended coma
is also observed, in which photodissociation is a significant source of
neutral atoms. There could be some contribution from resonant scattering off
atomic hydrogen in the extended coma, but the agreement between the modelled
and observed brightnesses in Fig. 9b suggests there are not significant
emissions from this source. However, it is difficult to estimate it
independently as there is no constraint on the column of atomic hydrogen from
remote instrumentation on Rosetta.
Again, the fluctuations of the OI1304 emission brightness mirror the changes
in the suprathermal electron flux (see Fig. 9d), indicating that e + X is a
major source of emission. In the nadir cases, these emissions were driven by
electron impact on both CO2 and H2O (see Fig. 6b) and when the suprathermal
electron flux was low there were no emissions in this line (see cases 10-14,
Fig. 6). When looking at the limb, we observe substantial emissions
($\sim\\!3$ R) of OI1304 when the average electron flux from $20-60$
$\mathrm{eV}$ is less than $10^{7}$
${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$. The
disparity between the observed and modelled emissions in Fig. 9d is
approximately constant throughout periods 2-4, suggesting that the residual
emissions are not driven by electrons which showed strong fluctuations over
the same time period. Similar to Ly-$\beta$, there may be a contribution from
resonant scattering from atomic oxygen along the line of sight, but with a
lack of constraints we cannot determine whether this is sufficient to explain
the discrepancy.

####  4.2.3 Period 1

During the first period on 4 Aug 2016, the variations in the electron flux
with time are mirrored by the changes in the line brightnesses for all four
atomic lines. There are two strong peaks in the electron flux (dark blue, Fig.
8) from 01:45-02:20 UT and 02:40-03:40 UT during which all four of the atomic
lines considered also exhibit peaks in the brightnesses. From 03:40 UT until
05:20 UT, the electron flux is small (light blue, Fig. 8) and no significant
FUV emissions are observed in the atomic lines. The 2 rayleighs of Ly-$\beta$
emissions observed during this trough are attributed wholly to interplanetary
emissions that are seen with a limb viewing geometry. An increase in the
electron flux at the end of the first period (after 05:20 UT) also coincides
with a rise in the brightnesses of the atomic lines.
However, the scale of the fluctuations related to the two strong peaks in the
modelled emissions greatly exceeds those observed with the FUV spectrograph.
This disparity in scale could be attributed to either a poorly estimated
column density or in the electron flux along the line of sight. A reduction of
the CO2 column, which was the dominant emission source in period 1, by a
factor of 0.4 gives a close agreement between the modelled and observed
brightnesses for all four of the atomic lines. With this reduction, there is a
slight underestimation of the OI1304 brightness, which is consistent with the
results in the later periods. Variation of the CO2 column density within the
first period could drive the difference in scale, so we have considered higher
time resolution VIRTIS data, which splits the first period into four parts. A
slightly lower CO2 column is found during the first peak ($3.37\times 10^{14}$
cm-2, 01:40-02:40 UT), but during the second peak the CO2 column density is
found to be larger ($7.4\times 10^{14}$ cm-2, 02:40-03:40 UT). The result of
using these column is plotted with a dashed blue line in Figure 9.
Alternatively, the assumption that the suprathermal electron flux is constant
along the line of sight may break down when viewing the extended coma. The
electron flux is measured at a cometocentric distance of 12 km, but the limb
observed passes within roughly 500 m of the nucleus surface at the closest
point (see Fig. 7) so there could be some variation along the line of sight.
Using the higher time resolution CO2 columns from VIRTIS, the electron flux
would have to be reduced by a factor 0.6 during the first peak and 0.3 during
the second peak to reach a close agreement between the observed and modelled
brightnesses. However, if this assumption were invalid, a similar disparity to
that seen in period 1 would be expected in periods 2-4, which is not the case.
The viewing geometry has been compared between period 1 and periods 2-4 and
there is no obvious distinction (all four periods have a line of sight passing
within 1 km of the nucleus) that would cause a difference in the electron
behaviour.
As the temporal variations of the electron flux and the FUV emissions are well
correlated for all four atomic lines, these emissions are driven by electron
impact and generated by the variations in the CIR. However, it is not clear
why the brightness of the emission lines during the two large peaks in period
1 are overestimated in the model.

###  4.3 9 - 10 July 2016

During the CIR on 9-10 July 2016, the FUV spectrograph is viewing the
illuminated nucleus, which pollutes the FUV emission spectra at long
wavelengths ($>1500$ Å) and prevents reliable measurements of the column
density by either spectrometer. There are only a few periods when the
emissions driven by a CIR were observed by Alice, so despite the difficulties
in the analysis the reflected solar photons present, this period is still of
great interest.
In situ measurements do not provide a good constraint on the density and
composition of the neutral gas column due to the off nadir view. Therefore, we
adjust the column density during each of the periods to match the observed
OI1356 emission brightness, which is consistent with our findings of CO2
driving this line over the southern hemisphere (Sections 3.2 and 4.2). The
resulting column densities are given in Table 5, under the assumption of a
pure CO2 coma. The adjusted column densities of CO2 are between 0.88 and 1.6
times the radial column density derived from in situ measurements of the
neutral density (see Sec. 5). This is a good agreement given the variation in
the outgassing across the surface and the longer path through the coma due to
the viewing geometry. The off-nadir angle during periods 1-3 was roughly 10∘,
so the spatially variable outgassing is likely the major driver of the
difference in column density. The in situ measurements used for this
comparison have been corrected assuming the neutral gas is only CO2 (Gasc et
al. 2017a).
In Figure 11, we plot only the modelled and observed brightness of the OI1356
(a) and CI1657 (b) lines, as we have no constraint on the H2O column density.
The Ly-$\beta$ and OI1304 emissions both have significant contributions from e
+ H2O, which we cannot constrain with the OI1356 emissions (see Section 3.2).
Reflection of solar flux off the illuminated nucleus is seen in the Alice
spectra at long wavelengths, strongly contributing to the atomic line at 1657
Å. In order to distinguish the CI1657 emissions from the coma from those
reflected off the nucleus, we subtract the solar spectrum from the Alice
observations during this event as outlined in Appendix B. OI1356 is a weak
line in the solar spectrum due to the associated forbidden transition, so is
unaffected by this correction. Reflected solar flux would also contribute to
the Ly-$\beta$ and OI1304 brightnesses, but these lines are not considered in
this section.

Table 5: Properties of the three intervals on 9-10 July. Period |  Start Time [After 9 July 2016 00:00 UTC] |  End Time [After 9 July 2016 00:00 UTC] |  CO2 Column Density [$10^{14}$ ${\mathrm{cm}}^{-2}$] |  Total Radial Column Density [$10^{14}$ ${\mathrm{cm}}^{-2}$] |  Ave. Electron Flux for 20 - 60 $\mathrm{eV}$ [$10^{7}$ ${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$]
---|---|---|---|---|---
1 |  15:00:00 |  23:30:00 |  6.0 |  3.83 |  0.16 - 15.3
2 |  29:52:00 |  34:30:00 |  2.0 |  2.25 |  2.46 - 25.0
3 |  35:10:00 |  48:00:00 |  1.2 |  0.76 |  1.97 - 36.2
Figure 10: Average electron particle flux during the three periods listed in
Table 5, with the standard deviation of the flux shown by the shaded regions.
The colour of each period is the same as in Fig. 11. The format of the plot is
the same as outlined in Figure 8.

The OI1356 brightness closely matches the variation of the electron flux
during this event. Between 16:00 and 18:00 UT on 9 July, the emission
frequency of OI1356 from CO2 increases from $10^{-9}$ ${\mathrm{s}}^{-1}$ at
15:45 UT, plateaus at $9\times 10^{-9}$ ${\mathrm{s}}^{-1}$ until 17:30 UT,
and then drops to $4\times 10^{-10}$ ${\mathrm{s}}^{-1}$ at 17:45 UT. The
close agreement in the fine structure can be seen between 07:30 and 09:30UT on
10 July. The emission frequency of OI1356 from e + CO2 increases from
$5.7\times 10^{-9}$ ${\mathrm{s}}^{-1}$ to a maximum $1.3\times 10^{-8}$
${\mathrm{s}}^{-1}$ at 08:00 UT, followed by a decrease to $1.1\times 10^{-9}$
${\mathrm{s}}^{-1}$ at 08:40 UT. At 08:50 UT, the emission frequency and
brightness of the OI1356 line both increase rapidly to $2.0\times 10^{-8}$
${\mathrm{s}}^{-1}$ and 3.2 R, respectively, before plateauing.

(a)(b)July 9thJuly 10th Figure 11: Comparison of the observed and modelled
brightness of the OI1356 (a) and CI1657 emission lines from 9 July 15:00 UT to
11 July 00:00 UT 2016. The plots follow the same format as outlined in Figure
9. The modelled brightnesses shown here are only driven by electron impact on
CO2.

The observed CI1657 emissions display the same structures seen in the OI1356
brightness (e.g. between 16:00 and 18:00 UT on 9 July; Fig. 11b), capturing
both the magnitude and variability of the fluctuations. On 10 July, a peak in
the observed CI1657 brightness at 18:00 UT is mirrored by an increase in the
CI1657 emission frequency to $5.59\times 10^{-8}$ s-1, before a decrease in
both the observed emissions from the coma and the electron flux until 21:00
UT. When there are few suprathermal electrons around 21:00 UT 10 July, there
are almost no observed emissions from the coma, demonstrating that there are
no other major sources of emissions from the coma during this event. The good
agreement between the in situ electron measurement and remote FUV observations
strengthens the case that the electron variations occur over large scales.

##  5 Conclusion

The Rosetta spacecraft’s proximity to the nucleus of 67P, throughout the two-
year escort phase, provided us with the opportunity to observe FUV emissions
from within the coma. We have performed the first forward modelling of FUV
emissions in the southern hemisphere of comet 67P using an extension of the
multi-instrument analysis of Galand et al. (2020) and introducing carbon lines
for the first time. When observing the shadowed nucleus at large heliocentric
distances, the analysis we have applied well reproduces the observed
brightnesses of the selected FUV emission lines (OI1356, OI1304, Ly-$\beta$
and OI1027, CI1657 and CO4PG, and CII1335) for periods with large suprathermal
electron fluxes (see Section 3.2) . Therefore, dissociative excitation by
electron impact is a key source of the FUV emissions in the southern
hemisphere away from perihelion. When the suprathermal electron flux was small
(Averaged electron flux $<2\times 10^{7}$
${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$
between 20 and 60 $\mathrm{eV}$), no emission of either of the OI lines or the
CII line ($B^{\text{OI1304}}<0.55$R, $B^{\text{OI1356}}<0.79$R,
$B^{\text{CII1335}}<0.22$R) were observed, indicating that energetic electrons
in the coma are the dominant driver of these emissions (see Section 3.3). In
the low flux cases, fluorescence of CO was a larger source of emissions at
1657 Å compared to many of the cases with a high electron flux (see Fig. 6d),
due to the larger total column density (see Table 2). The relative
contribution of CO fluorescence in the low flux cases was also enhanced by the
small emission frequency from electron impact processes (see Fig. 4d), which
had dominated in the high flux cases (cases 1-8, Fig 6d).
Unlike other low suprathermal electron flux cases, in cases 11 & 12 there were
significant emissions at 1027Å (5 R & 3 R), the source of which remains
unclear. Electron impact on neutrals cannot be the source of the emissions as
the brightness of other atomic lines, such as OI1304 and OI1356 would be
significant as well. The low Lyman-$\alpha$/Lyman-$\beta$ ratios in these
cases (2.6 - 3.3) rules out resonant scattering as a source (expected ratio of
300) and suggests photo-dissociation could be a driver of these emissions
(expected ratio of 1.4). However, prompt-photodissociation would require
significantly more H2O along the line of sight (by a factor 5-15) to generate
emissions in agreement with those observed. Late in the Rosetta mission, as
these cases were, water was more weakly outgassing than CO2 in the southern
hemisphere (Gasc et al. 2017a; Läuter et al. 2018), so the required mixing
ratios (up to 80% water) are unlikely to have occurred and are inconsistent
with the in situ measurements. Therefore, the source of these unexplained
Ly-$\beta$ emissions remains an open question.
In the low electron flux cases (cases 9-13), the neutral column density is
derived from a very simple model (Eq. 2), where we have assumed a fixed comet
radius and constant neutral gas velocity. Using a constant expansion velocity
may underestimate the gas density near the nucleus by up to 50% (Heritier et
al. 2017a), but this has little impact on the conclusions in these low flux
cases. We have also neglected any lateral motion of the neutral gas in the
coma, which could impact the composition and density of the neutrals along the
line of sight. When deriving column densities from in situ measurements, a
more complete 3D structure of the neutral coma (e.g. Bieler et al. 2015b),
including expansion of the gas near the nucleus, could be incorporated into
the multi-instrument analysis.
At large heliocentric distances, the FUV spectra obtained in the southern
hemisphere are very different to those from the northern, summer hemisphere
due to the prominence of CO2 in the southern hemisphere (Hässig et al. 2015),
especially post perihelion (Gasc et al. 2017a). Consequently, the FUV spectra
contain much stronger atomic carbon lines (CI and CII) as well as molecular
bands of CO, such as the Fourth Positive Group (Feldman et al. 2018) compared
to the northern hemisphere where they are barely detected. The hemispherical
asymmetry in composition results in significantly different sources for
several emission lines between the northern and southern hemispheres.
OI1356 is produced primarily by e + CO2 in the southern hemisphere (see Fig.
6a), whereas, in the northern hemisphere, e + O2 plays a more significant role
(Galand et al. 2020). The OI1304 brightness had significant contributions from
electron impact on all four of the major neutral species in the coma (CO2,
H2O, CO and O2) across the selected cases over the shadowed nucleus in the
southern hemisphere(see Fig. 6b). The emissions near 1026
$\mathrm{\SIUnitSymbolAngstrom}$ correspond only to emissions of Lyman-$\beta$
from e + H2O during the northern hemisphere summer (Galand et al. 2020),
whereas for post-perihelion cases in the southern, winter hemisphere, there
can be a significant contribution of OI1027 from e + CO2 (see case 8, Fig.
2c). Therefore, it is important to account for all four of the major neutral
species when analysing FUV emission spectra over the southern hemisphere to
derive column densities or mixing ratios.
The CI1657 emissions are dominated by e + CO2, when there is a large
suprathermal electron flux (see Section 3.2). However when the population of
suprathermal electrons in the coma is small, fluorescence of CO in the
overlapping 4PG bands becomes a more significant driver of emissions near 1657
$\mathrm{\SIUnitSymbolAngstrom}$.
The brightness of the CII1335 emissions is highly sensitive to the column
density of CO, due to the large emission frequency of CO compared to CO2 in
this line (see Fig. 4e). The close agreement between the observed and modelled
brightness of the CII1335 line confirms that the volume mixing ratio of CO
derived from the ROSINA mass spectrometer is accurate, once the contribution
to the CO signal due to fragmentation of CO2 in the ion source is subtracted
from the CO signal on the detector (Dhooghe et al. 2014).
During the CIRs over the 9 and 10 July and on 4 August 2016, the OI1356 and
CI1657 emissions were dominated by e + CO2, as attested by the agreement
between the observed and modelled brightnesses (see Section 4). This is not
surprising as CO2 was the dominant species outgassing from the southern
hemisphere near the end of mission (Luspay-Kuti et al. 2019). For limb
viewing, the Lyman-$\beta$ (Fig. 9c) and OI1304 (Fig. 9d) emissions both have
significant contributions from electron impact, but the model underestimates
the brightness of these lines. As the extended coma is also observed in limb
viewing, resonant scattering of solar photons from atomic hydrogen and oxygen
present along the line of sight may account for the discrepancy between the
model and observations for these lines (Combi et al. 2004; Feldman et al.
2018). When viewing the illuminated nucleus, reflected solar flux from the
nucleus introduced significant noise to the brightness of the CI1657
emissions, but the OI1356 line was generated only by dissociative excitation.
Throughout the CIRs, the brightnesses of all the selected emission lines
exhibit the same temporal variation as measured in the suprathermal electron
flux (Section 4). For all the time periods except the first on 4 Aug 2016, the
modelled brightnesses agreed very closely with the observed line brightnesses,
although there is a slight underestimation of OI1304 throughout the limb
observations (see Figure 9d), which may be attributed to resonant scattering
from atomic oxygen in the extended coma. Resonant scattering off atomic
hydrogen may contribute to Ly-$\beta$ emissions, but this is less apparent as
the emissions are much weaker than those from the IPM, which have been
accounted for. It is difficult to constrain resonant scattering off atomic
oxygen or hydrogen as we do not have measurements of the density of these
neutrals throughout the column. The discrepancy in magnitude in the first
period in August may originate from some change in the electron flux
throughout the column. There should be no significant degradation of electrons
in the coma at the large heliocentric distances considered (see Section
2.4.2), but a large scale potential well (Deca et al. 2017) could cause a
variation of the electron flux over the extended column in limb viewing.
However, if the assumption of a constant electron flux were invalid, the
discrepancy should also arise in the other periods on 4 August, which have
similar viewing geometries.
In a limb or off-nadir viewing geometry, the emissions originate from a
distant region of the coma, which cannot be probed in situ. The observed
correlation between the in situ measurements of the electron flux and the
remote measurements of the FUV spectrograph suggests that any acceleration of
the electron flux occurs on large scales as suggested by Deca et al. (2017).
At times with low electron fluxes, such as period 4 and the troughs in period
1 on 4 August 2016, there were no strong emissions of the FUV lines, which
excludes any strong local heating of electrons in a distant region along the
column. These results support the findings of Galand et al. (2020) that these
are solar wind electrons, which undergo acceleration by several tens of
$\mathrm{eV}$ in the coma. Therefore, the FUV emissions are auroral in nature.
The close correlation observed between the observed FUV auroral brightness and
the electron flux allows FUV spectroscopy to be used as another measure of
structures in the solar wind.
The aurora observed in the southern hemisphere of 67P is similar to the
diffuse aurora at Mars in several ways. Both auroras are driven by solar wind
electrons on open draped field lines (Brain et al. 2007; Volwerk et al. 2019)
as shown in this study at comet 67P and by Schneider et al. (2015) at Mars.
However, at comet 67P the solar wind electrons are accelerated by an ambipolar
field (Deca et al. 2017, 2019), whereas at Mars the electrons driving diffuse
auroras are accelerated at the Sun rather than within the Martian system
(Schneider et al. 2015). Consequently, these auroras are persistent at comet
67P whereas at Mars the diffuse aurora is only observed during strong solar
events.

## Acknowledgements

Rosetta is a European Space Agency (ESA) mission with contributions from its
member states and the National Aeronautics and Space Administration (NASA).We
acknowledge the continuous support of the Rosetta teams at the European Space
Operations Centre in Darmstadt and at the European Space Astronomy Centre. We
acknowledge the staff of CDDP and Imperial College for the use of AMDA and the
RPC Quicklook database. Work at Imperial College London was supported by STFC
of UK under grant ST/N000692/1 and ST/S505432/1. The Alice team acknowledges
support from NASA’s Jet Propulsion Laboratory through contract 1336850 to the
Southwest Research Institute. AB was supported by the Swedish National Space
Agency (grant 108/18). MR acknowledges the support of the State of Bern and
the Swiss National Science Foundation (200021 165869, 200020 182418). VIRTIS
was built by a consortium, which includes Italy, France, and Germany, under
the scientific responsibility of the Istituto di Astrofisica e Planetologia
Spaziali of INAF, Italy, which also guides the scientific operations. The
VIRTIS instrument development, led by the prime contractor Leonardo-
Finmeccanica (Florence, Italy), has been funded and managed by ASI, with
contributions from Observatoire de Meudon financed by CNES, and from DLR. We
thank the Rosetta Science Ground Segment and the Rosetta Mission Operations
Centre for their support throughout all the phases of the mission. The VIRTIS
calibrated data will be available through the ESAs Planetary Science Archive
(PSA) Website (www.rssd.esa.int) and is available upon request until posted to
the archive. We thank the following institutions and agencies for support of
this work: Italian Space Agency (ASI, Italy) contract number I/024/12/1,
Centre National d’Etudes Spatiales (CNES, France), DLR (Germany), NASA (USA)
Rosetta Program, and Science and Technology Facilities Council (UK). All
ROSINA data are the work of the international ROSINA team (scientists,
engineers and technicians from Switzerland, France, Germany, Belgium and the
US) over the past 25 years, which we herewith gratefully acknowledge.

## Supporting data

All of the primary data from Rosetta used in this study will be available
through ESA’s Planetary Science Archive (PSA) at www.rssd.esa.int or is
available on request until posted to the archive. The processed emission line
brightnesses, emission frequencies, column densities, and electron particle
fluxes are made available through the Centre de Donnés astronomiques de
Strasbourg (CDS) archives.

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##  Appendix A Calculating the suprathermal electron flux from the RPC/IES
counts

The Rosetta Plasma Consortium Ion and Electron Sensor (RPC/IES) was a top hat
electrostatic analyser which measured the number of electron counts in bins of
azimuthal angle, elevation angle and energy (Burch et al. 2007). The sensor
comprised $16\times 16\times 128$ bins in these dimensions with an angular
resolution of $$$\times$$$. The energy bins were distributed approximately
logarithmically with a bin width $\Delta E/E=8\%$. RPC/IES measured the
electron count rate in all 16 azimuthal bins simultaneously, whilst the
electron and energy bins were cycled through. During the mission, anodes from
the 8${}^{\text{th}}$ to 15${}^{\text{th}}$ azimuthal bins degraded (Broiles
et al. 2016), hence we only used anodes 0 to 7 in our analysis.
The electron particle flux was derived from RPC/IES measurements by Heritier
et al. (2018a), but here we provide an outline of each step in this
calculation. Within the Level 3 files on the PSA, the background count of
electrons, $C_{L3BG}$, is given for each scan of the electron spectrometer,
which is independent of the instrument bin. The background count must be
corrected as below before being subtracted from the counts in the measured
bins.

$C_{BG}=C_{L3BG}+\sqrt{5}C_{L3BG}$ (6)

When installed on Rosetta, the field of view of the instrument was obscured by
the main body of the spacecraft and other instruments (Clark et al. 2015).
This restricted field of view has been corrected with geometric factors,
$G(\theta_{0},\phi_{0},E_{0})$ (Broiles et al. 2016), where the subscript $0$
indicates that this has been evaluated on the underlying instrument grid of
$16\times 16\times 128$. However, in many of the operation modes, neighbouring
bins in all three dimensions were collapsed into one datapoint to reduce the
demand on telemetry. Combined azimuthal bins have already been separated in
the Level 2 datafiles, available on the PSA but the combined bins in elevation
and energy have not been separated. We refer to $N_{bins}$, the number of
combined energy bins multiplied by the number of combined elevation bins.
The counts, with background removed on the binned grid, were then un-binned
onto the instrumental $16\times 16\times 128$ grid, assuming the electrons
were distributed evenly between the combined bins.

$C^{\prime}(\theta_{0},\phi_{0},E_{0},t)=\frac{C(\theta_{b},\phi_{b},E_{b},t)-C_{BG}(t)}{N_{Bins}},$
(7)

where the subscript $b$ refers to the binned grid. The un-binned counts were
then divided by the geometric factor for each bin and the integration time
associated with the operation mode to convert to a differential energy flux,
$g^{\prime}(\theta_{0},\phi_{0},E_{0},t)$. The geometric factor of the
instrument used here is based on observations on 1 January 2015, as derived by
Broiles et al. (2016).

$g^{\prime}(\theta_{0},\phi_{0},E_{0},t)=\frac{C^{\prime}(\theta_{0},\phi_{0},E_{0},t)}{\Delta
t\times G(\theta_{0},\phi_{0},E_{0})}$ (8)

The differential flux above has not accounted for the efficiency,
$\epsilon(E)$, of the MicroChannel Plates (MCPs) in the instrument, which is
dependent on the impacting electron energy, E (in $\mathrm{eV}$; Kurz 1979).

$\begin{split}\epsilon(E)=0.52&\exp\Big{(}-[\log(E+37)-2.3]^{2}/0.82\Big{)}+0.071\\\
&+0.16\log(E+37)-0.028\log(E+37)^{2}\end{split}$ (9)

We returned to the binned energy grid, $E_{b}$, by summing over combined
energy bins, before dividing by the efficiency to give the differential
electron particle flux (DEF), $j(\theta_{b},\phi_{b},E_{b})$.

$j(\theta_{0},\phi_{0},E_{b},t)=\frac{\sum\limits_{\text{Comb.
Energies}}g^{\prime}(\theta_{0},\phi_{0},E_{0},t)}{N_{\text{Comb.
Energies}}\times\epsilon(\bar{E}_{b})\times\bar{E}_{b}},$ (10)

where the summation is over the energy bins which were combined in the binned
grid. $\bar{E_{b}}$ is the average energy of the combined energy bins. The DEF
was integrated over the field of view of RPC/IES to give the electron particle
flux, $J(E)$ (in
${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{eV}}^{-1}$;
Heritier et al. 2018a):

$J(E_{b})=\frac{4\pi}{2\pi\sin$$}\int_{\theta_{0}=$$}^{$$}\int_{\phi_{0}=$$}^{$$}\\!\cos\theta_{0}\times
j(\theta_{0},\phi_{0},E_{b})\,\mathrm{d}\phi_{0}\mathrm{d}\theta_{0}$ (11)

The term representing a geometric factor at the start of Eq. 11 is a
correction for the limited field of view of RPC/IES, under the assumption of
an isotropic electron particle flux at the detector.
We note that the electron particle flux at the detector was not representative
of the electron flux in the coma, as the Rosetta spacecraft was generally at a
spacecraft potential lower than -10 $\mathrm{V}$ (Odelstad et al. 2015). This
was corrected for using Liouville’s theorem (see Eq. 4) but this prevented
measurement of any electrons at low energies (see Section 2.4.2).

##  Appendix B Removing solar contamination from FUV emission spectra

Figure 12: Comparison of the photon flux observed by Alice at 15:58 UT 9 July
2016 to the solar photon flux, measured by TIMED-SEE at long wavelengths
(1500Å - 1800 Å). Three distinct regions of the Alice slit (Rows 8-11 [red],
Rows 13-16 [black] and Rows 18-21 [blue]) have been plotted which are the same
as those plotted in Figure 11. The linear fits are used to scale the solar
flux, so it can be subtracted from the observed Alice spectrum.

The emission spectra gathered on 9-10 July 2016 were strongly polluted by
reflected solar flux from the illuminated surface of the nucleus. As we are
only interested in the emissions from the coma, it was necessary to remove any
contribution of reflected solar photons. The shape of the solar spectrum was
taken from TIMED-SEE measurements on 16 July 2016 (green, Figure 13), which
was at the same Carrington longitude as the Alice observations. As this study
considers only cases at large heliocentric distances, the coma was optically
thin and there should not have been significant absorption of the solar flux
by cometary neutrals (Heritier et al. 2018b).

(a)(b)(c) Figure 13: Breakdown of the fitting procedure to retrieve the CI1657
and CO4PG line brightness for (a) Rows 8-11, (b) Rows 13-16 and (c) Rows
18-21. The solar spectrum from TIMED-SEE (green) is smoothed and then scaled
to the Alice photon flux (dark blue) at long wavelengths. The residual
observed flux, once the solar spectrum is subtracted, is shown in light blue
and with the CI1657 fit plotted in purple. The combination of the solar
background with the CI1657 line fit is plotted in orange.

As the solar flux was more intense at the long wavelength end of the Alice
spectral range (Feldman et al. 2018), the photon flux at 1au was compared to
the FUV emission spectra from Alice between 1500 Å and 1800 Å for each set of
co-added rows (see Figure. 12), with bright emission features around 1561 Å
and 1657 Å excluded. A clear linear correlation was seen for all three regions
of the Alice slit illustrating the strong presence of the solar spectrum. The
reflected solar flux was derived from the linear fit (green, Fig. 13) and was
subtracted from the observed Alice spectra. The residual FUV emission spectra
(light blue, Fig. 13) were then fitted with a linear combination of two
gaussian distributions (purple).
The CI1657 emission, measured by Alice (dark blue, Fig. 13), was more diffuse
than the atomic line measured at 1au by TIMED-SEE as a result of the lower
spectral resolution (8 -12 Å). The emission feature in the Alice spectra may
also contain several bands of the CO Fourth Positive Group (see Section 2.2)
leading to further broadening. We smoothed the TIMED-SEE flux over 10 Å to
broaden the peak at 1657 Å, which better captured the width of the peak in the
Alice dataset. If the adjusted goodness of fit exceeded 0.65, the line
brightness is given by

$B^{X}=(A_{1}+A_{2})\times
4\arcsin\Big{[}\sin\Big{(}\frac{\alpha}{2}\Big{)}\sin\Big{(}\frac{\beta}{2}\Big{)}\Big{]}\times\frac{10^{6}}{4\pi}$
(12)

where the line brightness $B^{X}$ is in rayleighs and the amplitudes of the
Gaussian distributions, $A_{1}$ and $A_{2}$, have units of photons cm-2s-1.
$\alpha$ and $\beta$ are the angles subtended by the coadded rows in the Alice
slit, and the numerical factor originates from the definition of 1 rayleigh
(see Equation 1).