# EXPANDING ACCESS TO MUSIC TECHNOLOGY
Rapid Prototyping Accessible Instrument Solutions For Musicians With
Intellectual Disabilities

Quinn Jarvis-Holland

Crystal Cortez

Station

PCC Adaptive
Instruments Project  705 N Killingsworth St  Portland, OR 97217
<EMAIL_ADDRESS>PCC Adaptive
Instruments Project  705 N Killingsworth St  Portland, OR 97217
<EMAIL_ADDRESS>PCC Adaptive
Instruments Project  705 N Killingsworth St  Portland, OR 97217
<EMAIL_ADDRESS>Francisco Botello

PCC Adaptive
Instruments Project  705 N Killingsworth St,  Portland, OR 97217
<EMAIL_ADDRESS>
###### Abstract

Using open-source and creative coding frameworks, a team of artist-engineers
from Portland Community College working with artists who experience
Intellectual/Developmental disabilities prototyped an ensemble of adapted
instruments and synthesizers that facilitate real-time in-key collaboration.
The instruments employ a variety of sensors, sending the resulting musical
controls to software sound generators via MIDI. Careful consideration was
given to the balance between freedom of expression, and curating the possible
sonic outcomes as adaptation. Evaluation of adapted instrument design may
differ greatly from frameworks for evaluating traditional instruments or
products intended for mass-market, though the results of such focused and
individualised design have a variety of possible applications.

###### keywords:

NIME, proceedings, rapid prototyping, adaptive, inclusive, music, controller,
MIDI, microcontrollers, creative coding, intellectual disabilities

††conference: NIME’20, July 21-25, 2020, Royal Birmingham Conservatoire,
Birmingham City University, Birmingham, United Kingdom.††titlenote: N. Gammill

[500]Human-centered computing Interface design prototyping [500]Human-centered
computing Accessibility design and evaluation methods [300]Applied computing
Sound and music computing

##  1 Introduction

Innovative Digital Musical Instruments (DMIs) and audio effects can often
bypass some presumed necessary abilities or talents. For example, autotuning
algorithms allow untrained vocalists to hit perfect pitches and “all in one”
mixing effects hide a variety of complex DSP tasks behind a single “macro”
knob. New technology that is widely accessible consistently gains traction and
constantly reshapes the professional landscape of music. Increasingly, even
highly technical professions such as mastering have been challenged by AI
assisted DSP.[3]

To remain hopeful in this fast changing climate it is important that we
harness and celebrate the ways that these technologies increase access to, and
facilitate hyper-localized design and musical expression for under-served
populations including people with intellectual/ developmental disabilities.

The idea for a project building adapted instruments was brought forth by
Daniel Rolnik (an outsider art critic and curator, who at the time was working
with Portland Art and Learning Studios [7]) and Dan Wenger111PCC Cascade
Campus Arts & Professions Dean at PCC. The Portland Community College Cascade
campus interactivity lab222part of the Music and Sonic Arts program [8]
provides an audio-oriented makerspace and classes teaching microcontrollers
and programming to musicians. In contrast to more traditional engineering
environments, the lab has empowered many queer, trans, and neuro-divergent
artists to utilize electronics and programming. The group of engineers -
experienced students and lab techs -all employ a variety of code, sensors,
microcontrollers, and midi devices in their own respective installation art
and musical performances.

In the initial meeting Mx Rolnik discussed possible outcomes for the project
as well as the needs and current equipment of the artists with cognitive
disabilities at PALS. Many artists at the Studios enjoyed making music, but
due to the layout of the Studios and the traditional non-adapted instruments
(piano, guitar, drumkit) at their disposal, “jamming” could become
cacophonous. It was suggested that the instruments in question could somehow
connect to each other as artists frequently collaborated in the open-floor
Studios space. For more consonant improvisation the designs could employ
adaptive constraints to pitch and timing. Mx Rolnik also gave the team a sense
of the ways some artists at PALS prefer expressing themselves (eg, vocally-
loud, vocally quiet, small sign language, large gestures). Notably, different
individuals with the same diagnosis had vastly different preferred range of
movements and methods of self expression. This observation is at odds with
design processes that rely on broader user-demographic data or designing for
all people with a specific intellectual disability. The initial meeting gave
the team a chance to learn important information relating to disability
rights, people first language, and the social model of disability-

A social model of disability presents the individual as needing access to
support and assistance in the same way as any other person. For example, in a
lecture hall chairs are provided for the audience to sit. These are not
considered aids or specialist devices; they are normalised as part of the
expectation that people would become tired if they had to stand up for any
length of time. Chairs are provided for the comfort and assistance of the
audience in a completely unremarked way. Yet if someone needs special access
to a room or venue this can sometimes be presented as a difficulty and
problematised. The principles of inclusive design recommend that it is not
only people who walk into a venue who should be considered but all members of
society including wheelchair users and parents with prams/buggies. [5] The
parallels that can be drawn to considerations for DMI’s are rather clear. In
order to best care for people in our communities who experience disabilities
we must think of them in the design of things that will be in use in their
community. Failing to make accessible designs, according to the social model,
is equivalent to building in impairment. “A person might be very musical and
enjoy the violin, saxophone, or piano. But if the individual does not have the
use of both arms, he or she is unable to play these instruments. And like
buildings, instruments are created by human artisans. So, from a social model
perspective, because these instruments are not designed with a person with an
impairment in mind, they prevent some individuals from making music with them
even though their impairments do not inhibit them from enjoying music.” [1]
Abramo makes an excellent point here applying the social model of disability
to instrument design. However the example given doesn’t encompass the variety
of experiences and impairments faced by people with disabilities, particularly
those experiencing intellectual disabilities. Abramo’s example does not
challenge the prevalence of “meritocracy” and a marked penchant for valuing
skill or virtuosity above self-expression. Intellectual disabilities do not
inhibit people who experience them from enjoying music, or desiring to play
music. Aspects that may be inhibiting are having a vast number of controls,
requiring precision rhythmic timing, reading quickly, or having too many
pitches to choose from. Coincidentally, these are also aspects of an
instrument’s design that inhibit non-musicians, children, and the elderly. In
turn- building interfaces with the intent of avoiding impairments can serve
multiple populations.

##  2 Project Parameters

The team was given a hardware parts budget of 400 USD to build the control
surfaces and to design a standalone application(s) in Cycling 74’s Max 8.
Keeping a relatively small budget for developing four instruments, and
designing freely redistributable applications were both important
considerations in order for the project to possibly seed similar efforts at
other makerspaces or studios. The most important project parameters were
decided on as follows:

  * •

400 budget for parts and materials

  * •

Four or more controllers connected to their respective sound generating
softwares

  * •

Utilize a variety of sensors

  * •

Empower artists artists with musical expression, choice

  * •

Intuitive and sonically inspiring for skilled or non-disabled musicians

  * •

Consonant or in-key improvisation

  * •

Facilitate some form of quantized rhythm as well as real-time playing

  * •

Sounds complement each other when played together

  * •

Low-cost materials

  * •

Documentation of designs for DIY re-use

Control surfaces were developed using PJRC’s Teensy and Adafruit’s Feather
uControllers with the arduino IDE. Both microcontrollers have excellent
diagrams, open source schematics, libraries, and other resources online. In
particular PJRC’s website has extensive documentation and guides on using
usbMIDI in projects. For instruments that benefit from being wireless, the
Feather was the preferred dev board due to the built-in (and simple to
program) atwinc WIFI chip. MAX/msp was chosen for developing the sound
generation side of the instruments- in part due to the engineers’ familiarity
but also because of the immediacy of prototyping with visual and object
oriented programming. Routing patches in MAX saves time compared to writing
the same DSP operations in openFrameworks, faust, or other lower level
languages. Having visual representations of operations and signal flow is
particularly useful for members of the team who are visual artists and visual
learners. While not open source, MAX can publish executables of a patch,
allowing for free distribution of our completed programs. While this has
worked for the project parameters with PALS, fully open source alternatives
should be explored for further development of the software.

##  3 Prototypes And Client Interaction

The team visited the studio space at PALS to meet some of the artists as well
as staff members who were excited about getting new instruments. This served
as a time to brainstorm possible form factors and to observe the challenges
they currently face with non-adapted instruments. The team spoke with artists
there as well as staff facilitators who all had a variety of perspectives and
ideas about new instrument solutions. Using the parameters given at the
beginning of the project, communicating with artists and staff clients, and
making our own observations, prototype controllers using various sensors were
developed for the clients to play and for the engineers to get a better sense
of what kinds of movement and interaction the clients prefer to use. These
controllers, paired with sound generation patches in software, quickly found
their place as DMI’s.

###  3.1 Initial Designs

Auto Scaling Touch Synth
A box with small stripes of etched copper on a PCB panel that sends note-on
messages when touched. The sound generation is done in a MAX patch with a
simple Karplus/Strong implementation to give a plucked string sound.
Interactive Drum Sequencer
A GUI and set of sensor pads that control a drum machine, tempo, and
modulation. The software GUI shows accompanying visual feedback of the 4
sensor pads and shows when they have activated one or committed to a sequence.
The drum sounds were samples triggered in MAX that would be affected more
intensely or less intensely with filters depending on how hard the pad was
pressed. With a computer vision script, the computer camera tracked bodies
moving to the left or right to speed up or slow down the sequence. This was
represented by a slider on the screen as well as shown in a video of
themselves in the camera embedded in the GUI.
Rotation Detecting Headband Synth
An accelerometer embedded in a wearable headband, programmed to track the
rotation and movement of the head. Sound generation is done in a MAX with a
subtractive synthesizer, letting the controller move the notes of a synth up
and down in accordance to the degree of rotation of the head left or right.
Moving the head side to side triggered an added harmony, and up and down added
more or less reverb to the synth.
Handheld 9 Degrees Of Freedom Controller
Compact and wireless handheld device containing a 9 Degrees of Freedom sensor
detecting orientation and rotation of the device. The handheld controller
drives the same sound generating patch as the headband synth, but with up and
down tilting controlling the pitch in glissando, and left and right tilt
controlling filter cutoff.
Xbox Kinect Air Harp
An Xbox Kinect IR camera feed is interpreted in a Processing sketch to detect
human bodies. The Processing sketch provides visual feedback from what its
camera is capturing, through a colored filter, to the GUI. The rectangular
area captured by the IR camera is divided into columns and rows of cells. A
detected body part moving from one cell to another triggers a note-on at a
specific pitch, sent as OSC to MAX - triggering a guitar-like Karplus Strong
patch

###  3.2 Evaluation & Observations

There is a vast amount of study into HCI and DMI evaluation, however most
traditional or commercially oriented frameworks do not serve minority
populations such as people with intellectual disabilities. For this
application the team opted for a mostly unstructured client-instrument
interaction time. Thought was given to the project goals of musical
expression, immediacy, performance, and collaboration. Making calls on whether
an instrument performance is bad or good is challenging when working with a
population that subverts traditional concepts of intellectual hierarchy. For
most instruments, those traditional values are a central focus above
accessibility.

“[…] there may be many perspectives from which to view the effectiveness of
the instruments we build. For most performers, performance on an instrument
becomes a means of evaluating how well it functions in the context of live
music making, and their measure of success is the response of the audience to
their performance. Audiences evaluate performances on the basis of how engaged
they feel by what they have seen and heard. When questioned, they are likely
to describe good performances as " exciting” "skillful" "musical." Bad
performances are "boring," and those which are marred by technical malfunction
are often dismissed out of hand. If performance is considered to be a valid
means of evaluating a musical instrument, then it follows that, for the field
of DMI design, a much broader definition of the term "evaluation" than that
typically used in human-computer interaction (HCI) is required to reflect the
fact that there are a number of stakeholders involved in the design and
evaluation of DMIs.” [6]

With instrument prototypes functioning, the team and clients met again to beta
test and collect observations. For the testing, the instruments were connected
to a mixer and PA and initialized to the same key and scale. The engineers
then stepped back to observe what sorts of interactions arise naturally. Later
the engineers took a more hands-on position with the artists to collect
feedback and to explore any intended uses of an instrument the clients had not
harnessed yet. Artists preferred to play all of our instruments collectively.
While the sound modules were different there wasn’t enough sonic space between
the sounds we chose for each synth to be fully distinguishable from other
instruments in the room, especially because all sounds are emitted from the
same speakers.

The artists had vastly varying levels of comfort with each instrument, as with
general expression. The most outgoing and physically energetic artists tended
to appreciate the instruments using sensors that captured a lot of movement,
such as the air harp or 9DOF controller. Artists who were more physically or
socially reserved gravitated to the more predictable and involved instruments
- the drum sequencer and touch synth Notable observations by instrument:

Auto Scaling Touch Synth

  * •

Thin copper strips are too small an area for artists to easily “return” to a
desired pitch

  * •

Sonic range of such a small number of keys is too limited

  * •

Note-on triggers from the controller, and the string-pluck sound module are
momentary, sustained key presses do not yield sustained sound

  * •

Very immediate and repeatable action to sound reaction

Interactive Drum Sequencer

  * •

The artists were very engaged with the visual feedback program and were
interested in seeing their own image transformed by the choices they were
making while playing the instrument.

  * •

The artists were utilizing the face tracking speed control by moving their
bodies left to right but it became obvious that the group of artists preferred
collaborative creation with the instrument, and the camera’s computer vision
was not programmed to track multiple faces and send erroneous control
messages.

  * •

Different ranges of dexterity and styles of playing became apparent. Some
artists preferred lightly touching the pads while others preferred to push
hard on them. The sensors in the pads did not allow for this range of pressure
application.

Headband Synth

  * •

The artists took to playing this instrument intuitively, however there wasn’t
an obvious connection between action and sound reaction aside from turning the
head left and right and the parameters they were controlling.

Handheld 9DOF Controller

  * •

Most artists were very comfortable coming up and grabbing the instrument.

  * •

Since it was small enough to be comfortably held they were able to really move
it around freely and discover all kinds of sounds.

Kinect Air Harp

  * •

Popular with more physically energetic or expressive artists.

  * •

Artists enjoyed visual feedback from the camera feed.

###  3.3 Revision & Further Development

After client interaction and testing the team shared observations, and made
revisions where appropriate. Roughly halfway through the process from initial
tests to final working prototype, the team hosted another testing session with
their in-development instruments. This allowed another round of client
observation, and strengthened the iterative feedback loops between the artists
and instruments, and the observations and design. These are the revisions and
developments for each instrument:
Auto Scaling Touch Synth

  * •

Pluck sound generation patch layered with a polyphonic multi- oscillator
synthesizer with sustain and diverse set of possible timbres (programmed into
presets)

  * •

Blank PCB panels hand painted and etched to yield organic-edged keys

  * •

Keyboard expanded from 12 to 24 keys by wiring the etched PCB panels to two
MPR121 cap-touch sensing chips

  * •

Added two momentary buttons to cycle the scale and cycle through presets

  * •

Enclosure designed to house the electronics of the keyboard, to be milled out
of plywood

Interactive Drum Sequencer

  * •

Replaced the piezo sensors with pressure sensors that could detect a greater
range of touch

  * •

Sample drum sounds were replaced with synthesized drum sounds in Max which
provided a wider range of parameters to manipulate

  * •

Added a button to switch between effected and dry drums

  * •

Removed the face tracking component and replaced it with a touch capacitive
strip on the sequencer itself to set the rate of the sequence, avoiding
multiple player bug

  * •

Laser cut an enclosure that could be either a handheld or table top instrument

Headband Synth

  * •

Added the capability to change the key and scale of the synth to fit with
other instruments that might be playing as well.

  * •

Added preset options to provide a range of sounds

  * •

Exaggerated the effects associated with the up and down and side to side
movement of the head to make interaction clearer

  * •

Developed a GUI in Max for artists to adjust presets, scale, and key

Handheld 9DOF Controller

  * •

Upgraded the 9-DOF sensor to one that allowed for more reliable reading of
heading (yaw).

  * •

Developed a smaller form factor to allow for it to be attached to the hand and
allow for more people to use the instrument.

  * •

Installed a battery and wifi chip to make the device un-tethered

Kinect Air Harp

  * •

Refined note-on detection to produce fewer clustered triggers

  * •

Updated the index of note values to include the same scales and keys as the
other instruments

  * •

Re-arranged the scale degree placement in the camera’s rectangular grid to a
more musically and harmonically rewarding pattern

One of the most apparent observations from visiting the PALS Studios was that
playing music can be difficult when many people with various non-adapted
instruments are playing together in close quarters. To play “in sync” with
other musicians can require lightning fast perception and solid timing.
Fortunately, computers are well adept at both tasks: our team built a master
sync patch in max that sends OSC over wifi, any other instruments plugged into
laptops running their app can connect to the same wifi network in order to
receive the OSC. The primary OSC message controls the variable that picks a
particular scale on the “scaler” pre-build in max. Rigid mapping of each
instrument to the same scale does restrict a lot of possible musical choices -
however the simple setup seemed effective almost immediately. For additional
musical variation, the OSC reception can be turned off to manually select a
scale. This is notable for vastly increasing the variety of possible harmonies
and intervals intervals between two different modes.

##  4 Conclusions

The instruments after revisions and further development, began to serve their
intended purposes well. More notably, the sound generators all compliment each
other nicely, with certain instruments providing higher notes and others
filling in the lows. If there were no budget or time restraints it would be
valuable to repeat the testing and revision phases with various client groups.
With all the instruments locked to the same key “wrong” notes are mostly
omitted. While this diminishes an individual player’s choices and freedom, it
also serves to empower the player by lessening the fear of failure, and
increasing the musical cohesion of the player’s resulting sounds with the
group’s. While it’s important to consider the freedom in failure and
limitlessness, restrictions may not be opposite to creative expression. As
explored by Thor Manussen in “Designing Constraints:” “Margaret A. Boden
defines constraints as one of the fundamental sources for creativity: "[F]ar
from being the antithesis of creativity, constraints on thinking are what make
it possible. . . . Constraints map out a territory of structural possibilities
which can then be explored, and perhaps transformed to give another one"
(Boden 1990, p. 95). For Boden, the continuity of cultural constraints
constitutes the possibility to evaluate creative work, or to recognize ideas
as creative. All cultures are founded on constraints,- they are the rule-sets
that maintain dynamic unity.” [4] Magnussen and Boden both make a compelling
case for constraints empowering expression and creativity here. In this
project the greatest success was found in letting artists with disabilities
play the instruments together and the result being a traditionally “in tune”
and sonically pleasing tapestry. When evaluated against the primary goals, the
instrument ensemble designed through this project was a success as it empowers
players with the unity of collaborative music making regardless of ability or
musical knowledge. Further, the hyper-localized rapid development process used
can be applied to similar design issues for minority populations that
traditional design processes and evaluation frameworks may not serve.

###  4.1 Links

Documentation and project files will be made available on github:
https://github.com/pccadaptiveinstrumentsteam/PCC-Adaptive-Instruments-
Project.

##  5 Acknowledgments

Thanks to ACM SIGCHI and NIME for allowing us to modify templates they have
developed. Our thanks to Daniel Rolnik, the artists and assistants we worked
with at PALS, Dean Wenger, PCC, Jesse Mejia, Darcy O’neal, Paul Stoffregen,
and Cycling 74[2]

##  6 Ethical Standards

Funding for the project - 400 USD, came from Cycling 74, the publisher of
MAX/MSP[2]. To avoid conflict of interest we have avoided claiming their
product as better than another, or comparing various commercial products, but
rather share why it was useful to us. We also acknowledge that the commercial
nature of the software is a drawback and are working on - and encourage others
to develop - fully open source platforms. Engineers were compensated for hours
spent meeting and building the instruments as PCC “casual hire” at 15 USD an
hour. Mx. Rolnik led a discussion for the team around best practices for
interacting with the clients with disabilities without disrespecting,
overlooking, or misinterpreting their reactions. Mx. Jarvis-Holland also
provided information on “People First Language”[9] and the social model of
disability to inform the team’s vocabulary and to encourage a musical rather
than medical approach.

## References

  * [1] J. Abramo.  Disability in the classroom: Current trends and impacts on music education.  Music Educators Journal, 99(1):39–45, 2012.  JSTOR www.jstor.org/stable/41692695.
  * [2] Cycling 74.  https://cycling74.com/.
  * [3] J. Drake.  Ai and music.  Sound On Sound, 15(5):795–825, November 1993.
  * [4] T. Magnusson.  Designing constraints: Composing and performing with digital musical systems.  Computer Music Journal, 34(4):62–73, November 2010.  JSTOR www.jstor.org/stable/40962941.
  * [5] J. F. Noone.  The applications of mainstream music technology to facilitate access to creative musical experiences for people with disabilities., June 2018.  https://193.1.102.136/bitstream/handle/10344/7570/Noone_2018_Applications.pdf.
  * [6] S. O’Modhrain.  A framework for the evaluation of digital musical instruments.  Computer Music Journal, 35(1):28–42, 2011.  JSTOR www.jstor.org/stable/41241705.
  * [7] PALS.  Portland art and learning studio.  https://portlandartandlearningstudio.com/.
  * [8] PCC.  Creative coding program.  https://www.pcc.edu/programs/music-and-sonic-arts/creative-coding.html.
  * [9] K. Snow.  Disability is natural, 2009.  https://www.disabilityisnatural.com.


# The Wagging Plasma Tail of Comet C/2020 S3 (Erasmus)

Jing Li Department of Earth, Planetary and Space Sciences, University of
California, Los Angeles, CA 90095, USA  Yoonyoung Kim Department of Earth,
Planetary and Space Sciences, University of California, Los Angeles, CA 90095,
USA  David Jewitt Department of Earth, Planetary and Space Sciences,
University of California, Los Angeles, CA 90095, USA

(Accepted October 23, 2023)

###### Abstract

Long-period comet C/2020 S3 (Erasmus) reached perihelion at 0.398 au on UT
2020 December 12.67, making it a bright, near-Sun object. Images taken between
mid-November and December 2020 using the HI-1 camera and COR2 coronagraph
onboard STEREO-A, as well as the LASCO/C3 coronagraph onboard SoHO, show
significant variations in the plasma tail position angles. To analyze these
variations, a simple technique was developed to calculate the aberration
angles. These angles are defined as the angle between the sun-comet line and
the tail axis, measured in the orbital plane. The aberration angles were found
to range from $1.2^{\circ}$ to $46.8^{\circ}$, with an average (median) value
of approximately $20.3^{\circ}$ ($16.3^{\circ}$). By considering the
aberration angles, the solar wind radial velocities during the observations
were inferred to range from 73.9 km/s to 573.5 km/s, with mean (median) values
of approximately 205.5 km/s (182.3 km/s). Throughout the observations, two
periods were identified where the tails showed forward tilting, which cannot
be explained by aberration alone. In one case, this anomalous position angle
was sustained for at least 11 days and is possibly due to co-rotating
interaction regions. In the other case, the tail exhibited dramatic excursions
from 180∘ to 150∘ back to 210∘ over a limited period of around 34 hours. This
behavior is tentatively explained as a consequence of the interaction with a
halo Coronal Mass Ejection that was launched from NOAA 12786 and arrived at
comet C/2020 S3 during the time when the tail displayed its wagging behavior.

Sun: solar wind - comet: individual (2020 S3)

††journal: Astronomical Journal

##  1 Introduction

Long-period comet C/2020 S3 (Erasmus) (hereafter “S3”) was discovered on UT
2020 September 17 by the Asteroid Terrestrial-impact Last Alert System (ATLAS)
sky survey111https://minorPlanetcenter.net/mpec/K20/K20SB9.html. It has
osculating semimajor axis $a$ = 194.9 au, eccentricity $e$ = 0.998 and
inclination $i$ = 19.9$\arcdeg$. (The barycentric elements are very similar at
$a$ = 190 au, $e$ = 0.998 and $i$ = 19.9°). As such, S3 has a likely origin in
the Oort cloud but it is not a dynamically new object (for which $a>10^{4}$ au
is required). Comet S3 reached its perihelion on UT 2020 December 12.67 at
0.398 au. The perihelion water production rate was $Q_{H_{2}O}=4\times
10^{29}$ s-1 (Combi et al., 2023), corresponding to a mass production rate in
gas $\sim$12,000 kg s-1. As the comet approached its perihelion, the solar
elongation as seen from Earth decreased from $46\arcdeg$ (mid-November) down
to $10\arcdeg$ (mid-December) rendering ground-based observation increasingly
difficult. However, the comet was captured by the Sun-observing STEREO-A and
SoHO spacecraft both before and after its perihelion, providing the dataset we
analyze here.

As is well known from the study of other comets, dust and gas move differently
once released from the nucleus. Cometary dust is expelled from the sublimating
nucleus by gas drag, typically attaining a size-dependent terminal speed small
compared to the thermal speed $V_{th}$ of gas molecules. Once ejected, the
motion of dust is controlled by solar gravity and radiation pressure. The
force due to solar wind drag is at least an order of magnitude smaller than
radiation pressure, and can be ignored (Ragot & Kahler, 2003). Comet dust
tails are usefully represented by syndynes marking the locus of positions of
particles of a given size released continuously from the comet and synchrones
which show the locus of positions of particles having a range of sizes but
released at a common time (Finson & Probstein, 1968).

Different forces influence the ion tails. Gas molecules become ionized
primarily by solar ultraviolet photons and are swept up by the passing solar
wind to form the comet’s plasma tail, as first explained by Biermann (1951).
In brief, gas molecules leave the comet nucleus with a speed comparable to the
thermal speed appropriate to the temperature of the sublimating surface,
typically $V_{th}\sim 1$ km s-1 at 1 au, while the orbital motion of the comet
is more comparable to the Kepler speed, $v_{K}\sim$ a few tens of km s-1 at 1
au. Both speeds are small compared to that of the solar wind, which sweeps
past the comet at a range $\sim 200$ to $\sim 750$ km s-1 (Hundhausen, 1968),
and expands outward from the Sun in a roughly radial direction. In
interplanetary space, the plasma pressure carried by the solar wind is bigger
than the magnetic field pressure so that the magnetic fields from the Sun are
frozen-in to and carried by the solar wind. As a result, cometary ions are
picked up by interplanetary magnetic fields (IMF) via the Lorentz force and
form a plasma tail that is characteristically aligned usually close to the
sun-comet line.

For these reasons, the dust and plasma tails are typically spatially separated
and appear distinct in the plane of the sky. Whereas the plasma tails are
straight and nearly radial to the Sun, dust tails are commonly diffuse and
curved in the plane of the sky as a result of the combined radiation pressure
and orbital motion. The directions of both types of tail should change
smoothly in response to the changing observer-sun-comet geometry. A third,
very narrow and typically faint type of tail has been associated with
resonance fluorescence from neutral sodium atoms (Cremonese et al., 2002).
Sodium atoms have very large solar radiation pressure acceleration (e.g. 100s
of times solar gravity), and so closely track the antisolar direction. For
example, a sodium tail was recently reported on asteroid 3200 Phaethon near
perihelion using the same instruments as we use in this work (Hui, 2023; Zhang
et al., 2023). However, our data provide no clear evidence for a neutral
sodium tail perhaps for the reason that the S3 is not as bright as comet
C/1995 O1 Hale-Bopp (Cremonese et al., 1997).

Although plasma tails are roughly aligned with sun-comet lines, they often
show dynamic fine structures imprinted by the local solar wind environment. In
fact, the existence of the solar wind was first realized from the appearance
of cometary plasma tails (Biermann, 1951; Alfven, 1957; Parker, 1958; Brandt,
1968). It is frequently observed that plasma tails appear cut-off in so-called
Disconnection Events (DEs) (Niedner & Brandt, 1978; Oyama & Hirao, 1985;
Wegmann, 2000; Voelzke, 2005). Suggested causes of DEs include variable ion
production rates in the cometary gas (Ip & Mendis, 1976), interplanetary shock
waves, the comet passing through a heliospheric current sheet (i.e. a sector
boundary (Niedner & Brandt, 1979)), and the impact of coronal mass ejections
(Vourlidas et al., 2007; Jia et al., 2009). For their visibly disturbed plasma
tails, sungrazing comets come close to the Sun within only a few tens of solar
radii. They are studied as probes to infer solar coronal physical conditions
(Uzzo et al., 2001; Bryans & Pesnell, 2012; Downs et al., 2013; Jones et al.,
2018; Cheng et al., 2020; Nisticò et al., 2022; Ramanjooloo & Jones, 2022).
These comets also provide good opportunities to study the constituents of the
cometary coma and plasma tails, for example, with the UltraViolet Coronagraph
Spectrometer (UVCS) (Kohl et al., 1995) onboard the SoHO satellite (Povich et
al., 2003; Raymond et al., 2018, 2022). These observations show that the
cometary emission lines, H I Ly$\alpha$ is the strongest UV emission line in
the cometary coma due to sunlight scattered by H atoms produced from H2O
photodissociation. An ion tail consisting of C III has also been observed by
UVCS as covered in the works by Povich et al. (2003); Raymond et al. (2018,
2022).

Because the plasma tail appearances reflect the local solar wind environment,
a direct application of the comet plasma tails is to infer the solar wind
radial velocity using the sky-plane position angles of the tails. Because of
the comet motion, the tail forms an angle with respect to the sun-comet line,
defining the so-called aberration angle, $\varepsilon$. In the comet orbital
plane, the angle is simply written as (Alfven, 1957) in the present of solar
wind,

$\varepsilon=tan^{-1}\left(\frac{v_{t}}{w_{r}-v_{r}}\right)$ (1)

where $v_{t}$ and $v_{r}$ represent the perpendicular and radial components of
the comet orbital velocities; $w_{r}$ represents the solar wind radial
velocity. Past measurements of 60 comets yield typical aberration angles
$\varepsilon\sim 5\arcdeg$ (Belton & Brandt, 1966; Brandt, 1968). However,
recent measurements show that $\varepsilon$ can span a wider range,
$5\arcdeg\lesssim\varepsilon\lesssim 30\arcdeg$ (Cheng et al., 2020).

The aberration angle can be obtained from the comet tail in various ways based
on the fact that the plasma tail orientation is dictated by the comet orbital
motion and the solar wind. One way is to fit to the tail position angles by
assuming solar wind velocity at the location of the comets. This is achieved
by a coordinate transfer from the orbital plane to the observer’s projected
sky plane (Belton & Brandt, 1966; Niedner et al., 1978). Several comets have
been observed by Solar Mass Ejection Imager (SMEI) on the Coriolis spacecraft,
which follows a polar orbit above the Earth’s terminator. The combined fisheye
sky map shows the entire sky, revealing comet tails as long as 0.5 au. The
aberration angles along with solar wind speeds are obtained at multiple
locations along the tail in a coordinate system originating at the comets
(Buffington et al., 2008; Clover et al., 2010; Jackson et al., 2013). Using
STEREO twin spacecraft, Cheng et al. (2020) reconstruct the comet images in
three dimensional space, and obtain the comet aberration angles and solar wind
velocities. They adapted their method to use single telescope measurements to
determine the aberration angles (Cheng et al., 2022). A different technique
using time-series images of the comet is employed by Ramanjooloo & Jones
(2022) to infer the solar wind radial velocity from the comet aberration
angles. In this paper, we report near-Sun observations of S3, focusing on the
plasma tail. We estimate the comet aberration angles and solar wind speeds
from the position angles and the known geometry of observation. We will
introduce a new method to determine the aberration angles.

The paper is organized as follows: In section 2, the STEREO-A and SoHO data
are described. In section 3, measurements of the comet tails are described and
analyzed. The results are discussed in section 4, and a summary is given in
section 5.

##  2 Observations

Comet S3 was observed using two spacecraft: the Solar Terrestrial Relations
Observatory-A (STEREO-A) (Kaiser et al., 2008), and the Solar and Heliospheric
Observatory (SoHO) (Domingo et al., 1995). In chronological order, the comet
was first recorded by a wide field camera (HI-1), then by a narrow field
coronagraph (COR2), both onboard STEREO-A (Howard et al., 2008; Eyles et al.,
2009), then by a coronagraph (C3) which is a part of the Large Angle and
Spectrometric Coronagraph Experiment (LASCO) (Brueckner et al., 1995) onboard
SoHO. The observational times and instrument parameters are listed in Table
(1). The two STEREO-A cameras have similar spectral coverage with filter
bandwidths from 630 to 730 nm for HI-1 and from 650 to 750 nm for COR2, but
they have different fields of view and angular resolutions. The LASCO/C3
camera has a filter wheel containing five filters: a wide bandpass filter (400
to 835 nm), blue, orange, deep red, and infrared filters. The clear filter is
normally used for the observations, which is the case for the current study.

The comet observations lasted from 2020 mid-November to 2021 January. STEREO-A
is a sun-orbiting spacecraft drifting far from Earth while SoHO orbits the
Earth-Sun L1 Lagrangian point; as a result, the observing geometry at any time
differs between the two. For easy reference, Figure (1) shows a plan view of
the orbital path of S3, together with the terrestrial planets and the
STEREO-A, SoHO and, for reference, the Parker Solar Probe (PSP) spacecraft
during the observing period. Figure (2) shows the temporal variation of the
geometric parameters as S3 crossed HI-1 (solid curves), COR2 (dotted curves)
and C3 (solid curves at later time) cameras. S3 exited the COR2 field-of-view
almost exactly one day after perihelion.

The comet stayed in the wide angle HI-1 camera field for 24 days from UT 2020
November 13.0 to December 7.0. It then crossed the narrower field of view of
COR2 from UT December 6.5 to 13.7. Starting about 4.3 days later, it was
observed by LASCO/C3, from December 18.0 to 2021 January 3.0. The comet image
quality becomes too poor to obtain reliable measurements of the tail position
angles after 2021 January 1. Therefore, we use only the combined observational
data between 2020 mid-November and the end of December. S3 was not observed at
the same time from different vantage points and, therefore, a stereoscopic
view like that obtained by Cheng et al. (2020) with the twin STEREO spacecraft
is not available for this work.

We downloaded level-0 data from the STEREO-A site222https://stereo-
ssc.nascom.nasa.gov/data/ins_data/secchi/L0/a/img/ and further processed them
to level-1 using the standard IDL procedure, secchi_prep, in the SolarSoftWare
(SSW) package (Freeland & Handy, 1998). This step included flat-field and
stray light corrections. We applied a data reduction technique similar to that
described in Jewitt & Li (2010), with the purpose being to obtain “clean”
images free of stars and transient features such as coronal mass ejections.
This was achieved by subtracting a rolling median image of the corona from
individual images within the sequence. The comet was located in the STEREO-A
images using the World Coordinate System (WCS) provided in the STEREO-A FITS
headers (Thompson & Wei, 2010) combined with JPL Horizons comet ephemerides in
celestial coordinates. The examples of final processed images from HI-1 and
COR2 cameras are shown in Figure (3) in the top and middle panels.

We downloaded the C3/LASCO data from the LASCO level_0.5 data site
333https://umbra.nascom.nasa.gov/pub/lasco_level05/960430/c3/. To remove the
background coronal emission, a minimal image was obtained by adopting the
minimum values at each pixel from all images. The final images were obtained
by subtracting the minimal image from the original C3 images. While the
spacecraft attitude data is absent in the C3 FITS headers (Bill Thompson,
private communication), the comet was bright enough to be tracked by a
computer algorithm from image to image. An example of a processed image from
C3 is shown in Figure (3) on the bottom panel.

In Fig. (3), projected comet paths are overlaid on each image from three
different instruments for their respective observation periods. The comet
moves from right to left in all three instrument field-of-view.

##  3 Comet Tails

To enhance the signal to noise levels, we computed image medians using data
taken over time spans between 0.2 and 1.0 days (Tables 2, 3, and 4). All three
tables list the dates and times of the image medians, position angles of anti-
sun ($\theta_{-S}$) and anti-orbital-motion ($\theta_{-V}$) directions, of the
measured position angles of dust ($\theta_{dust}$) and plasma
($\theta_{plasma}$) tails. Although dust is not our primary interest, we
computed syndyne and synchrone dust models to compare with the data, assuming
a range of particle sizes and ejection dates. In these models, dust particles
are released at zero velocity and accelerated by the gravity of the Sun and by
radiation pressure. The particle size is described by a dimensionless
parameter, $\beta$, equal to the ratio of the acceleration induced by
radiation pressure to that owing to local solar gravity (Bohren & Huffman,
1983). To a first approximation, $\beta\sim a^{-1}$, where $a$ is the particle
radius in microns. These models not only reveal an estimate of the effective
particle sizes in the dust tail, they also serve the purpose of identifying
and separating dust from plasma tails in the plane of sky. The synchrone and
syndyne curves are superimposed on the comet image in figures (4), (5) and
(6). Synchrones were computed for ejection times 20, 40, 60, 80, and 100 days
prior to the date of observation (curves from bottom to top, in the figure).
Syndynes were computed for $\beta$ = 1, 0.3, 0.1, 0.03, 0.01 (curves from
bottom to top), corresponding to nominal particle radii 1, 3, 10, 30 and 100
$\mu$m, respectively.

###  3.1 Observations of Dust and Plasma Tails

HI-1: A total of 26 HI-1 median images were generated as listed in Table (2).
An example median image, from UT 2020 December 5, is shown in the top panel of
Figure (4). The STEREO-A images are aligned solar north up (Karl Battams,
private communication). Before combination into image medians, we rotated the
individual images to equatorial orientation (North up, East left) using the
telescope header roll angles. An animation of the median images (Figure 7)
shows a bright tail growing longer and brighter as the comet approaches
perihelion. The tail position angles are broadly consistent with the antisolar
($-S$) direction. Above the bright long tail, a faint tail branch is seen
having position angle closer to the negative heliocentric velocity (-V)
direction.

Both synchrone and syndyne trajectories have position angles
$\theta_{PA}>270\arcdeg$ showing that the faint and short upper component in
the HI-1 image is the dust tail with characteristic dust particle sizes $\sim
10\mu$m. The lower and brighter long tail is the plasma tail.

COR2 Seventeen median-combined images were generated from COR2 data, as
summarized in Table (3). The left column of Figure (5) displays four selected
images, while the middle and right columns show overplotted synchrone and
syndyne models. In all images, except for the one from UT 2020 December 10,
two tails can be clearly seen, separated from each other. The syndyne dust
models fit better to the thick tail profiles compared to the synchrones,
suggesting that the dust particles are distributed over a range of sizes,
which is consistent with the HI-1 data. Notably, the tail observed around
position angle $270\arcdeg$ is identified as the dust tail, while the second
tail with variable position angles is attributed to the plasma tail. One
remarkable finding from the COR2 image sequence is that, while the position
angle of the dust tail remains stable near $\theta_{PA}=270\arcdeg$, the
plasma tail (indicated by orange arrows in Figure 5) exhibits unprecedented
and rapid swings around the antisolar direction. This tail swing is
prominently captured in the animation shown in Figure (8) and discussed in
Section 4.

On December 10, the two tails of the comet appear merged, making it difficult
to distinguish one from the other. This merging of the tails lasted from UT
12/10 02:00 to 12/12 11:15. During this time, the plasma tail is completely
invisible at UT 12/10 23:29 and 12/11 06:45. The position angles of the plasma
tail at these times are omitted from Table (3). There are several reasons why
the plasma tail may be obscured from observers, while we do recognize that the
dust tail is located at $\theta_{PA}\approx 270^{\circ}$. The small phase
angles (see Table (3)) and the alignment of the tail with the sun-comet line
may contribute to the plasma tail’s obscurity. The strong background emission
from the solar corona also plays a role in masking the plasma tail.

LASCO/C3: The telescope roll angles are not stored in the LASCO FITS headers
and therefore, in order to align the C3 images with the celestial north, we
measured the angles using the positions of known stars in the C3 images. In
total, 25 background suppressed median images (see Table (4)) were generated
from LASCO/C3 data. An example is shown in the top panel of Figure (6). The
synchrone (second panel) and syndyne (third panel) models in Figure (6) reveal
the wide large dust tail around the position angle $270\arcdeg$. At smaller
particle sizes of about $<30\mu$m, syndynes fit to the dust tail better than
synchrones, but the synchrone with longer ejection times (e.g. 100 days) seems
to match better to the dust tail. Meanwhile, the plasma tail, indicated by an
orange arrow, is well separated from the dust tail.

###  3.2 Tail Properties

Tail Widths: Tail width measurements support the identification of the dust
and plasma tails. At each position along the tail we measured the Full Width
at Half Maximum (FWHM, $w$) defined as the perpendicular width at half the
maximum surface brightness. Figure (9) shows $w$ as a function of distance
from the nucleus, with errors estimated by comparing with Gaussian profiles.
The nucleus FWHM is about 5 pixels for COR2 and 3 pixels for HI-1 and C3,
reflecting the different point-spread functions of the instruments. The HI-1
and C3 cameras provide greater sensitivity to low surface brightness emission
against the sky background. We obtain a composite dust tail image with
LASCO/C3 images, and a composite plasma tail image with HI-1 images. They are
embedded in Figure (9). As expected from the dynamics of dust, a linear fit
shows that the dust tail is strongly flared, with width $w=(0.24\pm
0.02)r+(1.68\pm 0.24)\times 10^{5}$ [km], where $r$ is the distance from the
nucleus in km. By comparison, the width of the plasma tail varies only
slightly with increasing distance from nucleus, consistent with a magnetically
confined structure. The fit to the plasma tail yielded $w=(0.01\pm
0.01)r+(2.42\pm 0.14)\times 10^{5}$ [km].

Tail Lengths: The tails fade progressively to invisibility with increasing
distance from the nucleus allowing only lower limits to the lengths to be
placed. A rough estimate of the length was obtained using the DS9
display444http://ds9.si.edu/doc/ref/how.html with the histogram equalization
function on the best tail image. This technique increases global contrast of
images which have limited range of values. The longest dust tail is found in
C3 camera images at 6.5 Mkm. The plasma tail length is given by the HI-1
camera at 10.0 Mkm. The COR2 images are less sensitive to low surface
brightness emission and reveal the dust and plasma tails only to $\sim$0.7
Mkm.

Tail Position Angles: The position angles of the dust and plasma tails
($\theta_{dust}$, $\theta_{plasma}$) are crucial quantities to this study,
especially $\theta_{plasma}$. We tried different methods to measure the tail
directions, including Gaussian fits to the tail profiles made perpendicular to
their axes. In the end, the tail position angles were determined manually by
fitting a straight line to data points along the axes with uncertainties
determined from multiple measurements. The position angles of the tails were
measured counterclockwise from the celestial north (see images shown as
examples in Figures (4, 5, and 6)). Figure (10) shows the position angles as
functions of time, with three panels to represent the observations from wide-
field camera HI-1 (top), narrow-field camera COR2 (middle) and LASCO/C3
(bottom). Blue and orange circles distinguish the position angles of the dust
and plasma tails. The solid blue and red curves represent the position angles
of -V and -S viewed from each telescope. The measured position angles and
their uncertainties are also listed in Tables (2, 3 and 4).

##  4 Discussion

The discussion will be focused on the plasma tail. Position angles of the tail
are used to infer the solar wind speed, and other conditions.

###  4.1 Determination of the Plasma Tail Aberration Angle

The comet aberration angle is measured in the comet orbital plane (Figure 11).
At the comet position, C, a number of quantities are plotted with respect to
the Sun: the cometary velocity V (and the anti-motion-velocity -V); anti-Sun
direction -S. The comet and its plasma tail are represented by a brown tail-
like image. It extends to the opposite direction of V forming an aberration
angle $\varepsilon$ with respect to the -S direction (sun-comet line). The
tail intercepts with another anti-sun direction -Sp marking the sun-comet line
at an earlier time. As the comet moves along its orbit, its progression can be
measured with the comet true anomaly which is the angle in the orbit plane
from the perihelion direction to the comet, measured positively in the
direction of motion. At the time of observation ($t$), the comet true anomaly
is $\nu$. But the comet plasma tail tilts backward opposite of the motion
direction, corresponding to the true anomaly $\nu_{p}$ at an earlier time
($t_{p}$). As a result, $t-t_{p}>0$, and $\Delta\nu=\nu-\nu_{p}>0$. Under
assumption that the cometary tails lie in the orbital plane, we have a
triangle of the sun-comet-intercept point of the comet tail with sun-comet
line in the -Sp direction. In this triangle, r is the heliocentric distance of
the comet; L is the length of the comet tail. The comet aberration angle is
simply calculated as $\varepsilon=\Delta\nu+\eta$. We note that this relation
is independent of the tail length, L, regardless how $\eta$ and $\Delta\nu$
change in quantity. Taking $\eta\rightarrow 0$, we can reasonably put
$\varepsilon\sim\Delta\nu$.

To determine $\Delta\nu$, we use the relation between the true anomaly ($\nu$)
and the position angle of the anti-Sun direction (-S) projected to the
observer’s plane of sky ($\theta_{-S}$). The relation
$\nu(t)=f(\theta_{-S}(t))$ is established by the quantities “Tru_Anom” and
“PsAng” in the JPL HORIZONS’ “Observer Table”. The observed position angle of
the plasma tail ($\theta_{plasma}$) often differs from -S direction
($\theta_{-S}$) (see Figure (10)), which results in a different true anomaly
from a different time $\nu_{p}=f(\theta_{plasma})$ on the orbital plane.
Figure (12) demonstrates the comet true anomalies $\nu$ (light blue circles)
at the observing times and the true anomalies $\nu_{p}$ (grey circles)
corresponding to the observed tail position angles at different times. Both
$\nu$ and $\nu_{p}$ fall along the $\nu(t)=f(\theta_{-S}(t))$ function curve
(black solid curve). On the top panel with HI-1, five grey data points are off
the function curve. The aberration angles cannot be resolved for these data
points. This underscores the limitation of the technique. As a result, these
five data points are left with $\varepsilon$ listed in Table (2). They also
appear above the dotted horizontal line on the top panel (HI-1) of the Figure
(10).

Figure (13) shows the aberration angles ($\varepsilon$) derived from observed
position angles of the plasma tail ($\theta_{plasma}$) as function of time.
Those errors in the observed position angles (see Figure (10)) are adapted for
the errors of the observed aberration angles, $\Delta\varepsilon$. The
aberration angles also are found in the column $\varepsilon$ in Tables (2, 3
and 4). For those data points with $\varepsilon\sim\Delta\nu=\nu-\nu_{p}>0$,
the indication is that the tail tilts away from the comet motion; For those
data points where $\varepsilon<0$, the tail is tilted forward in the same
direction as the orbital motion (V).

###  4.2 Solar Wind Velocity Inferred from Plasma Tail Position Angles

From the equation (1), the solar wind radial velocity can be inferred to

$w_{r}=\frac{v_{t}}{\tan\varepsilon}+v_{r}$ (2)

The errors are estimated from:

$\Delta
w_{r}=\left|-\frac{v_{t}}{\sin^{2}\varepsilon}\right|\Delta\varepsilon$ (3)

where $\Delta\varepsilon$ is in radians. Units for $w_{r}$, $v_{t}$ and
$\Delta w_{r}$ are km/s.

The cometary radial velocity $v_{r}$ and the absolute velocity $v$ are known
quantities provided by JPL HORIZONS. The tangential component is
$v_{t}=\pm\sqrt{v^{2}-v_{r}^{2}}$, where $v_{t}>0$ as it points at the comet
motion direction. The inferred solar wind velocities and their error bars are
shown in Figure (14) as functions of heliocentric distance (top), longitude
(middle) and latitude (bottom). They are found in “$w_{r}$” columns of Tables
(2, 3 and 4). The data points with $\varepsilon<0$ are not presented with the
values of $w_{r}$ because such aberrations are probably caused by other
phenomena rather than the radial solar wind, as we will discuss in the
following sections. Some data points have very large uncertainties of the
solar wind velocity. These data points are often coincident with the
aberration angle $\varepsilon\lesssim 2\arcdeg$. This is specially evident
with observations of HI-1 (see Table 2).

Figure (14) consists of two sets of plots, with the left side showing the
solar wind radial velocities as a function of heliocentric distance,
longitude, and latitude as comet C/2020 S3 (Erasmus) moves inbound towards the
Sun. The right side, on the other hand, shows the same quantities but as the
comet moves outbound away from the Sun. Comet S3 appears to be in the slow
solar wind velocity domain during observations, with wind speeds approximately
doubling as the comet travels inbound compared to its outbound journey.

To verify the solar wind environment around comet S3, we compare the solar
wind measurements with large-scale, physics-based space weather prediction
models known as WSA-Enlil Solar Wind Prediction models: Wang-Sheeley-Arge
(WSA)-Enlil Solar Wind Prediction. These models are generated at The Space
Weather Prediction Center (SWPC)555https://www.swpc.noaa.gov/productswsa-
enlil-solar-wind-prediction, which provides advance warning of solar wind
structures and Earth-directed coronal mass ejections (CMEs).

We downloaded the models generated by SWPC for the time period from mid-
November to the end of December 2020. We examine models of the solar wind
velocity structures in the ecliptic plane, looking down from above the solar
north. The positions of Earth, STEREO-A, and STEREO-B are also given in the
simulations, allowing for a comparison between the model results and the
actual observations made by STEREO-A and SoHO. The models predict solar wind
velocities $<$550 km/s during the HI-1 observations; $<$400 km/s during the
COR2 observations; and $<$300 km/s during the C3 observations. The models have
the minimum velocity 200 km/s, while the observed solar wind velocities are
often $<$200 km/s around the S3 on the comet’s journey both inbound and
outbounds (Fig. 14). One possibility is that the solar wind mass loading due
to pick up of cometary ions may decelerate the solar wind (Omidi & Winske,
1987). The evidence is that the solar wind velocities are $<$ 100 km/s as S3
near the perihelion ($<$0.455 au) with the exception of observations taken in
the COR2 visibility window.

###  4.3 Plasma Tail Influenced by Non-Radial Solar Wind Flow

On the top panel of Figure (13), some data points have $\varepsilon<0$,
meaning that the tails tilt forward in the cometary motion direction opposite
to the non-radial flows carried by the solar rotation (Weber & Davis, 1967).
This implies the presence of the azimuthal solar wind flow against Archimedes
spiral which is about a few km/s according to an analytical models by Tasnim &
Cairns (2016). The equation (1) can be slightly modified by replacing $v_{t}$
with $v_{t}+w_{nonr}$. Then the non-radial velocity component can be estimated
with $\varepsilon$:

$w_{nonr}=\tan\varepsilon(w_{r}-v_{r})-v_{t}$ (4)

where $v_{t}$ and $v_{r}$ are the cometary tangential and radial components of
the orbital velocity; $w_{r}$ is the solar wind radial velocity; $\varepsilon$
is simply the angle of the plasma tail with respect to the solar radial
direction in negative values. The azimuthal component of the solar wind due to
Archimedes spiral is omitted in this estimation. Therefore, the equation (4)
gives the lower limit of the non-radial solar wind component in the cometary
motion direction. Given an average $w_{r}=183.6$ km s-1 during the HI-1
observations, we obtain the average non-radial velocity $\sim-$66.8 km s-1 in
the same period of time. The negative value represents the non-radial velocity
direction against the co-rotating direction. The individual inferred
$w_{nonr}$ corresponding to each data point are listed in the last column of
Table (2).

Several causes can result in non-radial solar wind flows. A survey of non-
radial flows during nearly five years of observation reveals that the average
non-radial flow speed is $\sim 30$ km s-1. Furthermore, about half of the non-
radial flow events are associated with interplanetary coronal mass ejections
(ICMEs) with average speeds exceeding 100 km/s (Owens & Cargill, 2004). The
cause of non-radial flow by a CME is the diversion of flow in the sheath
region behind an ICME shock front due to the compression of the shockwave
(Gosling et al., 1987). Another possible cause of non-radial flow is in the
co-rotating interaction regions (CIRs) which can play a role in deflecting the
fast and slow solar wind flows azimuthally in opposite directions (Gosling &
Pizzo, 1999). In the absence of the detectable ICMEs, we investigate whether
CIRs are responsible for the observed non-radial flows during the time period
under study (DOY318.6 to 329.6, as shown in the top panel of Figure 14). Enlil
models are examined for clues regarding the presence of corotating streams.
The models show that the corotating streams swept through the path of the S3
with velocities ranging from 200 to 550 km/s. However, without careful
examination of the comet’s path overlapping with the corotating regions, it is
challenging to determine with certainty whether the non-radial flows are
caused by CIRs, although this remains a possibility.

###  4.4 Plasma Tail and ICME

The most noteworthy feature in our data is a rapid change in the plasma tail
position angles occurring as soon as the comet enters the COR2 FOV. The plasma
tail position angles swing like a pendulum by an amount that is very large
compared to the uncertainties of measurement (see the first 5 data points in
the middle panel of Figure 10). The tail position angle began at
$\theta_{plasma}\sim 180\arcdeg$ in the first two data points, then decreased
to $\sim 150\arcdeg$ and then abruptly swung near the anti-solar direction
($\sim 210\arcdeg$). Despite the dramatic change in position angles in the
observer’s frame, the tail angles with respect to the Sun-comet line show a
more modest variation. The average $-\varepsilon\sim-12.7\arcdeg\pm
3.5\arcdeg$ in the comet orbital plane (see middle panel of Figure (13)) among
the first four data points (a time period $\sim 25.5$ hours). The tail angle
then swings back over the next $\sim$8.5 hours to near the sun-comet line
($0\arcdeg$) as it is shown with the 5th data point in the figure, and
thereafter to $\sim$+15°. The abnormal tail orientation lasted at least $\sim
34$ hours.

We searched for evidence to support the conjecture that the plasma tail of S3
might have been deflected by a coronal mass ejection. While there are no in-
situ observations to confirm an ICME interaction with comet S3, we do indeed
find a Halo CME which occurred on UT 2020 December 7.68 from the NASA SoHO
LASCO CME catalog666https://cdaw.gsfc.nasa.gov/CME_list. Using the
Helioview777https://www.jhelioviewer.org tool, we identify the likely source
of the CME as active region NOAA 12786. This active region had rotated to the
far side of the Sun from STEREO-A at the time of the comet observation (c.f.
Figure 2), meaning that the Halo CME travelled directly toward the comet,
which was also on the far side of the Sun from STEREO-A. Given the 0.418 au
heliocentric distance of S3 and an estimated speed of 1407 [km
s-1]888https://cdaw.gsfc.nasa.gov/CME_list/UNIVERSAL_ver1/2020_12/univ2020_12.html,
the travel time for the CME front to reach the comet is $\sim$12.4 hours,
corresponding to arrival on UT December 8.2 (DOY 343.2). This arrival time
approximately matches the tail wagging motion detected in COR2 data (Figure
10). Furthermore, the 34 hour time scale of the tail disturbance is comparable
to the $\sim$30 hour average ICME crossing time (Wu & Lepping, 2011). In the
last column of Table (3), we listed the non-radial wind velocity estimated
with $\varepsilon<0$ using the equation (4). The average non-radial velocity
is $>100$ km s-1 quite consistent with the non-radial velocities caused by
CMEs found in the survey by Owens & Cargill (2004). While it is possible that
the CME and the tail disturbance are only coincidentally related, we note that
comparable CMEs are comparatively rare; only two such events occurred in the
entire month of December. In this interpretation, the absence of tail wagging
in the earlier HI-1 and later C3 observations occurs simply because no other
ICME impacts S3 during those times. After passing an ICME, the tail angle
should naturally return close to the solar wind radial direction, as observed
in Figure (10) in the middle panel. We conclude that the plasma tail swing in
COR2 is plausibly attributed to interaction with an ICME.

##  5 SUMMARY

We present near-perihelion observations of long-period comet C/2020 S3
(Erasmus) from the STEREO-A and SoHO spacecraft. The STEREO-A camera HI-1 and
the coronagraph COR2 captured the comet from $\sim$ 0.836 au to perihelion at
0.398 au. About 4.3 days later, the comet was imaged by the LASCO/C3
coronagraph over the outbound heliocentric distance range $\sim$0.427 to 0.658
au. The comet moved from heliocentric latitude $-20\arcdeg$ to $20\arcdeg$ and
longitude 119$\arcdeg$ to 285$\arcdeg$ during our observations. In order to
understand the comet plasma tail motions in the observer’s plane of sky, a
simple technique is developed to obtain the comet aberration angles
($\varepsilon$) from the observed position angles of the plasma tail. We
summarize the observations and conclusions below:

  * •

We detected a large and transient excursion in the position angle of the
plasma tail on UT 2020 December 8, from $180^{\circ}$ to $150\arcdeg$ then
back to $210\arcdeg$, lasting about 34 hours. The excursion cannot be caused
by changes in the speed of the solar wind. However, the excursion is
coincident with the passage of an interplanetary coronal mass ejection (ICME).
We find that NOAA 12786 launched a halo CME with a direction and time
consistent with the observed deflection of the comet tail.

  * •

We detected a long duration ($\gtrsim$11 days) wagging of the plasma tail
about the Sun-comet line caused by non-radial flows. The Enlil solar wind
models show that the corotating streams swept through the path of the comet
with velocities ranging from 200 to 550 km/s. However, careful examination of
the comet’s path overlapping with the corotating regions is needed to
determine with certainty whether the non-radial flows are caused by CIRs,
although this remains a possibility.

  * •

Wind speeds inferred from the position angles range from $\sim$73.9 to
$\sim$573.5 km s-1, showing that comet S3 was in the slow solar wind region.
This is confirmed by Enlil models during the observation period. The average
(median) solar wind radial velocities are 205.5 (182.3) km s-1 as the comet
moves in space. The velocities show a very rough increase with decreasing
heliocentric latitude in the STEREO-A observations. On the other hand, they
tend to increase slightly with increasing heliocentric latitude in LASCO/C3.

  * •

The average (median) plasma tail aberration angles are $20.3\arcdeg$
($16.3\arcdeg$) with minimum and maximum values $\varepsilon=1.2\arcdeg$ and
$\varepsilon=46.8\arcdeg$, respectively.

  * •

The technique to obtain the comet aberrations relies on accurate measurements
of position angles of the plasma tail in the equatorial frame. Therefore,
knowledge of the telescope roll angles between spacecraft image frames and the
celestial coordinates is crucial. The technique is valid under the assumption
that the comet tails lie in the orbital plane. The inferred solar wind radial
velocity becomes unreliable when $\varepsilon<2^{\circ}$.

  * •

The dust tail is spatially distinguished from the plasma tail in the COR2 and
LASCO/C3 cameras, but only marginally resolved in HI-1 data. Comparison with
synchrone and syndyne dust models indicates that the dust tail is dominated by
particles with $\beta\sim 0.1$ corresponding to characteristic sizes of order
10 $\mu$m.

We thank Drs. Yingdong Jia, John Raymond, Pedro Lacerda, Masateru Ishiguro and
Bin Yang for reading the manuscript and providing comments. We would like to
express our gratitude to the anonymous referee whose critical comments urged
us to re-examine the observational data. We are grateful to Dr. William
Thompson for prompt help with world coordinate system questions, and general
data reduction. Dr. Bernhard Fleck was also very kind to help with our
inquiries. Dr. Karl Battams advised us regarding LASCO/C3 image rotations.

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Table 1: Instrument Parameters

Instrument | Field of View | Pixel Size | Bandpass [nm]
---|---|---|---
HI-1/STEREO-A | 4°-24°(15-90 R☉)aaThe wide field camera is aimed at an angle 14° off the solar limb from the principal axis of the instrument. | 71.9″ | 630-730
COR2/STEREO-A | 0.5°-3.8° (2-15 R☉)bbPosition angle of the anti-Sun direction, degree, by HORIZONS | 14.7″ | 650-750
C3/SoHO | 1°-8°(3.7-30 R☉)ccPosition angle of the negative heliocentric velocity, degree, by HORIZONS | 56.0″ | 400-835ddThe filter wheel contains blue (420-520 nm), orange (540-640 nm), deep red (730-835 nm), infrared (860-1050 nm) and broadband clear (400-850 nm) filters. A narrow band Hα (2 nm) filter is mounted in a wheel holding three polarizers. However, the clear filter is normally used for the observations, which is the case for the current study.
b,cb,cfootnotemark:

Both instruments are coronagraphs. The angles quoted are the inner and outer
edges of the field of view, measured from Sun center.

Table 2: Measurements From HI-1 Date | DaysaaNumber of days used to make median images |  $\theta_{-S}$bbPosition angle of the anti-Sun direction, degree, by HORIZONS |  $\theta_{-V}$ccPosition angle of the negative heliocentric velocity, degree, by HORIZONS |  $\theta_{dust}$ ddPosition angle of the dust tail and its uncertainty, degree. |  $\theta_{plasma}$eePosition angle of the plasma tail and its uncertainty, degree. |  $\varepsilon$ffAberration angle. |  $w_{r}$ggInferred solar wind radial velocity from equation (2). Unit: km s-1 |  $w_{nonr}$hhNon-radial solar wind velocity from Equation (4) assuming $w_{r}=183.6$ in average. Unit: km s-1. The nagative values represent the $w_{nonr}$ has in the opposite of the aberration.
---|---|---|---|---|---|---|---|---
2020-11-13 14:29 | 1.0 | 268.3 | 281.6 | $\cdots$ | 268.2$\pm 1.7$ | -8.2 | $\cdots$ | -63.5
2020-11-14 19:15 | 1.0 | 268.4 | 281.6 | $\cdots$ | 268.7$\pm 3.0$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-11-16 00:14 | 1.0 | 268.4 | 281.5 | $\cdots$ | 268.0$\pm 1.3$ | -7.1 | $\cdots$ | -61.0
2020-11-17 05:00 | 1.0 | 268.3 | 281.4 | $\cdots$ | 267.0$\pm 3.3$ | -13.4 | $\cdots$ | -86.8
2020-11-18 09:45 | 1.0 | 268.3 | 281.3 | $\cdots$ | 267.1$\pm 1.2$ | -11.0 | $\cdots$ | -78.4
2020-11-19 14:29 | 1.0 | 268.1 | 281.2 | $\cdots$ | 267.2$\pm 2.6$ | -8.1 | $\cdots$ | -68.3
2020-11-20 19:15 | 1.0 | 267.9 | 281.1 | $\cdots$ | 269.3$\pm 1.0$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-11-22 00:14 | 1.0 | 267.7 | 280.9 | $\cdots$ | 267.3$\pm 1.8$ | -3.3 | $\cdots$ | -52.6
2020-11-23 00:30 | 0.7 | 267.4 | 280.7 | $\cdots$ | 269.5$\pm 3.4$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-11-23 19:44 | 0.7 | 267.2 | 280.5 | $\cdots$ | 265.7$\pm 1.7$ | -8.2 | $\cdots$ | -73.3
2020-11-24 14:45 | 0.7 | 266.9 | 280.3 | $\cdots$ | 266.6$\pm 1.9$ | -2.0 | $\cdots$ | -50.8
2020-11-25 09:59 | 0.7 | 266.6 | 280.1 | $\cdots$ | 269.5$\pm 1.6$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-11-26 05:15 | 0.7 | 266.2 | 279.9 | $\cdots$ | 268.1$\pm 2.5$ | 13.0 | 164.2$\pm 38.7$ | $\cdots$
2020-11-27 00:30 | 0.7 | 265.8 | 279.7 | $\cdots$ | 267.9$\pm 1.8$ | 13.3 | 165.6$\pm 28.8$ | $\cdots$
2020-11-27 19:44 | 0.7 | 265.3 | 279.5 | $\cdots$ | 269.8$\pm 1.6$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-11-28 14:45 | 0.7 | 264.8 | 279.2 | $\cdots$ | 266.7$\pm 2.5$ | 9.5 | 262.0$\pm 80.4$ | $\cdots$
2020-11-29 09:59 | 0.7 | 264.1 | 278.9 | $\cdots$ | 268.3$\pm 1.3$ | 25.9 | 73.9$\pm 6.0$ | $\cdots$
2020-11-30 05:15 | 0.7 | 263.4 | 278.6 | 265.3$\pm$4.3 | 263.1$\pm 2.4$ | -1.0 | $\cdots$ | -54.9
2020-12-01 00:30 | 0.7 | 262.6 | 278.3 | 267.6$\pm$1.7 | 263.0$\pm 1.4$ | 1.2 | $\cdots$ | $\cdots$
2020-12-01 19:44 | 0.7 | 261.6 | 277.9 | $\cdots$ | 264.0$\pm 1.0$ | 7.7 | 374.8$\pm 56.7$ | $\cdots$
2020-12-02 14:45 | 0.7 | 260.5 | 277.6 | 266.9$\pm$1.3 | 263.5$\pm 1.3$ | 8.9 | 325.9$\pm 54.7$ | $\cdots$
2020-12-03 09:59 | 0.7 | 259.2 | 277.2 | $\cdots$ | 264.4$\pm 1.5$ | 15.3 | 182.1$\pm 21.9$ | $\cdots$
2020-12-04 05:15 | 0.7 | 257.6 | 276.8 | $\cdots$ | 266.0$\pm 1.0$ | 25.3 | 99.8$\pm 4.7$ | $\cdots$
2020-12-05 00:30 | 0.7 | 255.6 | 276.4 | $\cdots$ | 265.0$\pm 1.4$ | 24.1 | 111.2$\pm 9.1$ | $\cdots$
2020-12-05 19:44 | 0.7 | 253.1 | 275.9 | 268.7$\pm$2.3 | 263.1$\pm 1.1$ | 20.9 | 138.7$\pm 9.3$ | $\cdots$
2020-12-06 14:45 | 0.7 | 249.9 | 275.5 | $\cdots$ | 262.9$\pm 2.6$ | 23.9 | 121.1$\pm 17.2$ | $\cdots$

Table 3: Measurements From COR2 Date | DaysaaNumber of days used to make median images |  $\alpha$bbS3 Phase Angle |  $\theta_{-S}$ccPosition angle of the anti-Sun direction, degree. |  $\theta_{-V}$ddPosition angle of the negative velocity, degree. |  $\theta_{Dust}$eePosition angle of the dust tail, degree. |  $\theta_{Plasma}$ffPosition angle of the plasma tail, degree. |  $\varepsilon$ggAberration angle. |  $w_{r}$hhInferred solar wind radial velocity with measured plasma tail position angles from the equation (2). Unit: km s-1 |  $w_{nonr}$iiNon-radial solar wind velocity, km s-1. The nagative values represent the $w_{nonr}$ has in the opposite of the aberration.
---|---|---|---|---|---|---|---|---|---
2020-12-08 09:30 | 0.3 | 9.14 | 237.6 | 274.4 | 265.0$\pm$1.0 | 182.0$\pm 1.5$ | -13.0 | $\cdots$ | -109.7
2020-12-08 18:00 | 0.3 | 8.31 | 233.6 | 274.2 | 264.5$\pm$.71 | 180.7$\pm 7.6$ | -11.4 | $\cdots$ | -104.1
2020-12-09 02:29 | 0.3 | 7.52 | 228.6 | 274.0 | 264.8$\pm$2.0 | 150.8$\pm 2.6$ | -14.4 | $\cdots$ | -114.8
2020-12-09 11:00 | 0.3 | 6.77 | 222.4 | 273.8 | 261.1$\pm$1.6 | 155.6$\pm 9.0$ | -11.6 | $\cdots$ | -105.2
2020-12-09 19:15 | 0.3 | 6.12 | 215.0 | 273.6 | 260.6$\pm$3.9 | 210.3$\pm 5.8$ | -1.0 | $\cdots$ | -68.9
2020-12-10 02:00 | 0.2 | 5.68 | 207.7 | 273.4 | 262.2$\pm$3.9 | 235.6$\pm 6.3$ | 7.9 | 465.7$\pm 388.5$ | $\cdots$
2020-12-10 09:14 | 0.2 | 5.30 | 198.6 | 273.2 | 262.0$\pm$5.5 | 247.0$\pm 1.8$ | 16.4 | 215.4$\pm 26.7$ | $\cdots$
2020-12-10 16:15 | 0.2 | 5.08 | 188.7 | 273.0 | 264.5$\pm$2.0 | 233.1$\pm 9.4$ | 10.0 | 367.4$\pm 358.0$ | $\cdots$
2020-12-10 23:29 | 0.2 | 5.01 | 177.7 | 272.8 | 264.7$\pm$2.2 | $\cdots$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-12-11 06:45 | 0.2 | 5.13 | 166.8 | 272.6 | 259.1$\pm$4.5 | $\cdots$ |  $\cdots$ | $\cdots$ | $\cdots$
2020-12-11 14:00 | 0.2 | 5.41 | 156.7 | 272.4 | 253.8$\pm$1.8 | 231.9$\pm 3.8$ | 14.5 | 253.8$\pm 69.6$ | $\cdots$
2020-12-11 21:14 | 0.2 | 5.84 | 147.6 | 272.2 | 254.2$\pm$10. | 226.1$\pm 3.3$ | 14.2 | 260.1$\pm 63.6$ | $\cdots$
2020-12-12 04:15 | 0.2 | 6.37 | 140.2 | 272.0 | 260.0$\pm$5.4 | 219.0$\pm 8.9$ | 13.8 | 268.2$\pm 181.6$ | $\cdots$
2020-12-12 11:29 | 0.2 | 7.01 | 133.8 | 271.8 | 261.0$\pm$2.2 | 208.0$\pm 9.7$ | 13.2 | 284.5$\pm 218.9$ | $\cdots$
2020-12-12 18:59 | 0.3 | 7.75 | 128.2 | 271.6 | 256.8$\pm$4.1 | 156.4$\pm 2.1$ | 6.6 | 573.4$\pm 188.7$ | $\cdots$
2020-12-13 03:30 | 0.3 | 8.64 | 123.1 | 271.4 | 255.8$\pm$3.1 | 159.8$\pm 2.6$ | 9.2 | 413.7$\pm 119.0$ | $\cdots$
2020-12-13 12:00 | 0.3 | 9.59 | 118.9 | 271.2 | 257.8$\pm$3.7 | 157.4$\pm 1.6$ | 10.7 | 353.9$\pm 54.3$ | $\cdots$

Table 4: Measurements From LASCO/C3 Date | DaysaaNumber of days used to make median images |  $\theta_{-S}$bbPosition angle of the anti-Sun direction, degree. |  $\theta_{-V}$ccPosition angle of the negative velocity, degree. |  $\theta_{Dust}$ddPosition angle of the dust tail, degree. |  $\theta_{Plasma}$eePosition angle of the plasma tail, degree. |  $\varepsilon$ffAberration angle.  |  $w_{r}$ggInferred solar wind radial velocity with measured plasma tail position angles from the equation (2). Unit: km s-1
---|---|---|---|---|---|---|---
2020-12-18 23:45 | 0.4 | 292.9 | 252.5 | 263.1$\pm$1.3 | 273.5$\pm 2.6$ | 39.7 | 91.9$\pm 6.9$
2020-12-19 10:30 | 0.4 | 295.3 | 252.4 | 262.9$\pm$2.3 | 275.9$\pm 2.5$ | 30.8 | 120.4$\pm 10.3$
2020-12-19 21:14 | 0.4 | 297.9 | 252.2 | 263.0$\pm$1.4 | 274.0$\pm 1.7$ | 41.2 | 88.5$\pm 4.1$
2020-12-20 08:15 | 0.4 | 300.8 | 252.0 | 265.2$\pm$3.4 | 274.6$\pm 2.8$ | 40.0 | 91.6$\pm 7.2$
2020-12-20 18:59 | 0.4 | 303.9 | 251.9 | 263.3$\pm$2.6 | 275.8$\pm 4.1$ | 37.3 | 98.7$\pm 11.6$
2020-12-21 05:45 | 0.4 | 307.1 | 251.7 | 266.4$\pm$2.2 | 274.0$\pm 2.3$ | 46.8 | 76.9$\pm 4.4$
2020-12-21 16:30 | 0.4 | 310.6 | 251.6 | 267.2$\pm$2.3 | 274.6$\pm 4.8$ | 45.6 | 79.2$\pm 9.4$
2020-12-22 03:14 | 0.4 | 314.2 | 251.4 | 267.1$\pm$2.1 | 281.4$\pm 3.5$ | 28.2 | 129.0$\pm 15.7$
2020-12-22 14:15 | 0.4 | 318.0 | 251.2 | 267.5$\pm$1.1 | 289.3$\pm 4.7$ | 18.8 | 187.2$\pm 43.7$
2020-12-23 00:59 | 0.4 | 321.9 | 251.1 | 266.3$\pm$1.9 | 283.3$\pm 4.0$ | 28.4 | 126.5$\pm 16.9$
2020-12-23 11:45 | 0.4 | 325.8 | 250.9 | 268.9$\pm$3.0 | 281.0$\pm 4.5$ | 34.0 | 106.0$\pm 13.5$
2020-12-23 22:30 | 0.4 | 329.7 | 250.8 | 266.6$\pm$2.9 | 282.5$\pm.61$ | 32.9 | 109.0$\pm 1.9$
2020-12-24 09:14 | 0.4 | 333.6 | 250.6 | 267.1$\pm$1.5 | 286.5$\pm 5.6$ | 28.7 | 123.1$\pm 22.4$
2020-12-24 20:15 | 0.4 | 337.5 | 250.5 | 268.3$\pm$3.4 | 299.0$\pm 2.8$ | 18.4 | 182.5$\pm 25.6$
2020-12-25 06:59 | 0.4 | 341.1 | 250.3 | 267.9$\pm$2.7 | 293.0$\pm 6.3$ | 24.7 | 138.8$\pm 32.0$
2020-12-25 17:45 | 0.4 | 344.6 | 250.2 | 268.4$\pm$.98 | 296.1$\pm 7.9$ | 23.6 | 143.8$\pm 43.6$
2020-12-26 04:30 | 0.4 | 348.0 | 250.0 | 267.8$\pm$2.8 | 292.8$\pm 5.8$ | 27.7 | 123.4$\pm 23.5$
2020-12-26 15:14 | 0.4 | 351.1 | 249.9 | 268.5$\pm$2.6 | 322.2$\pm 5.2$ | 11.8 | 262.1$\pm 105.4$
2020-12-27 02:15 | 0.4 | 354.1 | 249.8 | 269.6$\pm$1.6 | 315.3$\pm 3.3$ | 16.3 | 194.7$\pm 35.4$
2020-12-27 12:59 | 0.4 | 356.8 | 249.6 | 269.5$\pm$3.0 | 323.9$\pm 3.1$ | 13.8 | 223.8$\pm 45.4$
2020-12-27 23:45 | 0.4 | 359.3 | 249.5 | 269.3$\pm$3.7 | 331.7$\pm 6.9$ | 11.8 | 254.5$\pm 135.3$
2020-12-28 10:30 | 0.4 | 361.6 | 249.4 | 269.7$\pm$3.7 | 337.8$\pm 2.2$ | 10.6 | 278.0$\pm 52.9$
2020-12-28 21:14 | 0.4 | 363.7 | 249.2 | 272.1$\pm$5.1 | 335.6$\pm 5.0$ | 12.6 | 234.1$\pm 84.0$
2020-12-29 08:15 | 0.4 | 365.7 | 249.1 | 271.5$\pm$3.9 | 343.7$\pm 1.7$ | 10.5 | 271.8$\pm 41.7$
2020-12-29 18:59 | 0.4 | 367.5 | 249.0 | 272.3$\pm$1.5 | 343.0$\pm 1.8$ | 11.9 | 240.5$\pm 33.2$

Figure 1: Plan view of the orbital paths of comet S3, the Planets, STEREO-A,
SoHO and Parker Solar Probe (PSP) in the heliocentric cartesian coordinate
during the observing period, from mid-November to end-December 2020. All
objects orbit counterclockwise. The comet trajectory is plotted as blue,
orange and purple arcs corresponding to the observations with HI-1, COR2 and
LASCO/C3 cameras, respectively. Tick marks “X” are plotted every 5 days on the
S3 path starting with DOY 318. Three terrestrial planets are represented by
brown color. The spacecraft are plotted with dotted pink curves.  Figure 2:
Observational geometry as a function of time. The S3 observations are made
with HI-1 wide field camera (solid lines) and COR2 coronagraph (dotted lines)
on STEREO-A. After DOY 350, S3 is detected by LASCO/C3 coronagraph on SoHO
(solid lines). Perihelion is at UT 2020 December 12.67, indicated by a
vertical line. Heliocentric distance, phase angle and elongation are
represented by red, green and purple colors, respectively. Calendar dates are
indicated along the top axis.  Figure 3: Full coronal images from the wide-
field camera HI-1 (top), the narrow-field camera COR2 (middle) both on
STEREO-A, and the LASCO/C3 coronagraph (bottom) on SoHO. The projected comet
paths are plotted with solid white curves. The comet positions at the times of
images are circled on each image.

Figure 4: An example image taken with the HI-1 wide field camera. Top: the
median image from UT 2020 December 05. The anti-Sun ($-S$) and anti-orbital
($-V$) directions are indicated by solid and dashed arrows. The bright long
tail is the plasma tail. A faint tail above the plasma tail is the dust tail.
The middle and bottom panels are the modeled synchrones and syndynes
overlapping the image. Synchrones were computed for ejection times 20, 40, 60,
80, and 100 days prior to the date of observation (curves from bottom to top,
in the figure). Syndynes were computed for $\beta$ = 1, 0.3, 0.1, 0.03, 0.01
(curves from bottom to top), corresponding to nominal particle radii 1, 3, 10,
30 and 100 $\mu$m, respectively. Celestial north is up, east is to the left.
The region shown is 3.2°$\times$1.2° (160$\times$60 pixels).

Figure 5: Left Column: Examples of median COR2 images showing the rapidly
changing position angle of the plasma tail (indicated by orange arrows). The
anti-Sun ($-S$) and anti-orbital velocity ($-V$) directions are indicated by
solid and dotted arrows. Middle and Right columns: The superimposed loci of
synchrones and syndynes computed with same parameters as in Fig. (4).
Celestial north is up and east to the left. The region shown is
$\sim$0.6°$\times$0.5° (150$\times$120 pixels).

Figure 6: Top: an example of the median image of LASCO/C3. -V (dotted arrow)
and -S (solid arrow) represent anti-motion and anti-Sun directions at the
location of the comet. The plasma tail is indicated by an orange arrow. Middle
and bottom: the computed synchrone and syndyne models superimposed on the
comet image to simulate the dust tails. The solid white curves are the modeled
synchrones and syndynes calculated with the same parameters as those in
Figures (4). North is up, east to the left and the region shown is
$\sim$1.9°$\times$1.6° (120$\times$100 pixels).

Figure 7: S3 in the HI-1 camera. This is one frame from the animated series
shown in the electronic edition. The bright tail is plasma. The faint,
approximately horizontal structure above the plasma tail is dust. Image size
is 3.2°$\times$1.2°(160$\times$60 pixels). Figure 8: COR2 camera image shown
raw (upper) and contoured (lower). The plasma tail points to the south, the
dust tail to the west, in this image. An animation including this image is
available in the electronic edition. Image size is
0.6°$\times$0.5°(150$\times$120 pixels). Figure 9: Full width at Half Maximum
(FWHM) of the comet tails as function of distance from nucleus. The error bars
are the 3$\sigma$ uncertainties of the tail width computed from the Gaussian
fits. The coma positions are marked with vertical dotted lines for each
camera. The embedded images are composites of HI-1 and LASCO/C3 images from
which the widths are measured (dust widths are from LASCO/C3 and plasma widths
are from HI-1). Scale bars on the images are 1 Mkm at the comet.

Figure 10: Time dependence of the position angle of the dust (blue) and plasma
(orange) tails from HI-1 (top), COR2 (middle) and C3 (bottom). Position angle
uncertainties on some points are comparable to the size of the symbols used to
plot the data. Red and blue solid curves are the anti-Sun ($-S$) and anti-
orbital-motion ($-V$) directions, respectively. The time of perihelion is
marked with a vertical dotted line on the COR2 (middle) panel. The data points
are presented in Tables (2, 3 and 4). Note that five orange data points are
above the horizontal dotted line on top panel. The comet aberration angles
cannot be resolved on these data points using the current technique. The
calendar dates are shown on the top horizontal axis.  Figure 11: Comet orbit
(green arc) viewed from above. r: comet heliocentric distance; V: comet
orbital velocity; -S: antisolar direction; -Sp: the antisolar direction
corresponding to the comet aberration; $\varepsilon$: aberration angle;
$\Delta\nu=\nu-\nu_{p}$ ($\nu$: true anomaly at the observing time; $\nu_{p}$:
true anomaly at the time associated with the observed tail position angle); L:
the plasma tail length; and $\eta$: the angle between -Sp and the plasma tail
axis. The relation $\varepsilon=\eta+\Delta\nu$ is independent of tail length.
Taking $\eta\rightarrow 0$, $\varepsilon\sim\Delta\nu$. Figure 12: The comet
true anomaly ($\nu$) as function of anti-solar position angle ($\theta$).
Functions are plotted as solid black curves provided by HORIZONS in all three
panels. Light blue circles represent comet true anomalies ($\nu$) at the times
of observations. Grey circles represent the comet true anomalies ($\nu_{p}$)
inferred from the tail position angles ($\theta_{plasma}$). Three panels
correspond to HI-1, COR2 and C3 instruments. Note the five grey data points
are not on the black curve on top panel with HI-1. The true anomalies cannot
be solved for these data points.  Figure 13: The comet plasma tail aberration
angles as function of time (bottom horizontal axis) and the heliocentric
distance (top horizontal axis) on the comet orbital plane. Three panels are
the measurements from three instruments, HI-1 (top), COR2 (middle) and C3
(bottom). Red horizontal lines show the sun-comet line,
$\varepsilon=0\arcdeg$.

Figure 14: Inferred solar wind radial velocities as functions of heliocentric
distance (top), longitude (middle), and latitude (bottom). Three plots on the
left represent the solar wind velocities as S3 moves inbound. Those on the
right represent the solar wind as S3 moves outbound. Symbols distinguish
measurements made with HI-1 (blue squares), COR2 (orange circles), and
LASCO/C3 (purple diamonds).