# Understanding Physical Breakdowns in Virtual Reality

Wen-Jie Tseng  LTCI, INFRES, Telecom Paris, IP ParisPalaiseauFrance wen-
<EMAIL_ADDRESS>
(2023)

###### Abstract.

Virtual Reality (VR) moves away from well-controlled laboratory environments
into public and personal spaces. As users are visually disconnected from the
physical environment, interacting in an uncontrolled space frequently leads to
collisions and raises safety concerns. In my thesis, I investigate this
phenomenon which I define as _the physical breakdown in VR_. The goal is to
understand the reasons for physical breakdowns, provide solutions, and explore
future mechanisms that could perpetuate safety risks. First, I explored the
reasons for physical breakdowns by investigating how people interact with the
current VR safety mechanism (e.g., Oculus Guardian). Results show one reason
for breaking out of the safety boundary is when interacting with large motions
(e.g., swinging arms), the user does not have enough time to react although
they see the safety boundary. I proposed a solution, FingerMapper, that maps
small-scale finger motions onto virtual arms and hands to enable whole-body
virtual arm motions in VR to avoid physical breakdowns. To demonstrate future
safety risks, I explored the malicious use of perceptual manipulations (e.g.,
redirection techniques) in VR, which could deliberately create physical
breakdowns without users noticing. Results indicate further open challenges
about the cognitive process of how users comprehend their physical environment
when they are blindfolded in VR.

Physical Breakdown; Safety Boundary; Break-Out; Virtual-Physical Perceptual
Manipulation

††journalyear: 2023††copyright: rightsretained††conference: Extended Abstracts
of the 2023 CHI Conference on Human Factors in Computing Systems; April 23–28,
2023; Hamburg, Germany††booktitle: Extended Abstracts of the 2023 CHI
Conference on Human Factors in Computing Systems (CHI EA ’23), April 23–28,
2023, Hamburg, Germany††doi: 10.1145/3544549.3577064††isbn:
978-1-4503-9422-2/23/04††ccs: Human-centered computing Virtual reality††ccs:
Human-centered computing Empirical studies in HCI

##  1\. Introduction

Virtual Reality (VR) becomes more available in public and personal spaces,
eliciting new contexts, like social interaction (Gugenheimer et al., 2017),
in-vehicle (McGill et al., 2017), and confined space (Tseng et al., 2021; Li
et al., 2021). These contexts all share one common dilemma — users are
visually disconnected from the physical environment. Perhaps this outcome
might originate from pursuing a higher presence and better immersive
experience. However, imagine using VR in an uncertain environment (e.g.,
home). Accidents could happen and did happen. Prominent examples would be
colliding, hitting, and falling over, identified in people’s everyday VR usage
(Dao et al., 2021). I define these accidents as _the physical breakdown in VR_
— an abrupt disruption of the VR experience caused by a collision with the
physical environment.

Physical breakdowns become relevant because VR is available in uncontrolled
environments. They deviate the VR user’s attention from the virtual
environment to the real world and lead to safety concerns that people may get
hurt when it occurs. Although current VR Head-Mounted Displays (HMDs) provide
safety mechanisms (e.g., Oculus Guardian) to avoid these accidents, they still
cannot cover all types of physical breakdowns in VR. There is a lack of
knowledge about the process of physical breakdowns in VR and how future
technologies should mitigate them.

My thesis investigates the reasons for physical breakdowns, how they could
happen, and how to mitigate them by exploring solutions and future safety
mechanisms. I position physical breakdowns into the attentional model for
synthetic environment (Draper et al., 1998) by adding physical breakdowns as
an outcome of actions (Figure 1). The model interprets how people elicit a
sense of presence in VR. A VR user perceives and processes all the sensory
information from the virtual and physical environments. Presence is a
psychological state arising from the commitment of attentional resources to
the virtual environment. The VR user then makes an action to interact in VR
(e.g., interaction or locomotion). These actions lead to several outcomes,
like continuing or exiting VR. I explore physical breakdowns in VR within this
structure and present the following research questions.

  * •

RQ1: How and why physical breakdowns happen with the current HMD-based VR
technology?

  * •

RQ2: What harm and risks come with the physical breakdown, and how to mitigate
them?

  * •

RQ3: What are the behavior and cognitive process behind the physical breakdown
phenomena?

---

Figure 1. My research explores physical breakdowns in VR within a structure
adapted from the attentional model for synthetic environment (Draper et al.,
1998), in which I position my research projects (sky-blue) and future
directions (pink).

Figure 1 shows my thesis structure adapted from the attentional model for
synthetic environments. A human user perceives the perceptual input from the
virtual and physical environment and then performs actions. I position
physical breakdowns in VR as an outcome of the VR user’s action within the
structure. My current research progress focuses on actions. For example, I
investigate why VR users break out of the safety boundary and develop
solutions (FingerMapper) to reduce the required interaction space to avoid
physical breakdown. I also explore how future physical breakdowns could be
exploited by malicious actors using perceptual manipulations. Future research
aims to understand the behavioral process of the human user when a physical
breakdown happens, to inform the future safety mechanisms in VR.

To address RQ1, I started by investigating empirical evidence of physical
breakdown by observing how users perceive and interact with the safety
boundary in their everyday VR usage through an online survey and a lab study.
Results indicate VR users break out of the safety boundary for accidental and
intentional reasons. One accidental reason was that participants could not
stop themselves while performing large gestures, although they saw the safety
boundary. Therefore, I developed a solution, FingerMapper, which maps small-
scale finger motions onto virtual arms and hands to enable whole-body virtual
movements when using VR in confined spaces. This technique mitigates
collisions with the physical environment by reducing the interaction space,
contributing to RQ2. FingerMapper shows that the virtual and physical
movements do not need to keep a one-to-one mapping. Perceptual manipulations
in VR (e.g., redirection techniques) leverage this discrepancy to direct the
user’s actions. I explored how malicious actors could exploit perceptual
manipulations to provoke physical breakdowns through a speculative design
workshop. By analyzing scenarios created by our participants, I identified two
main risks (puppetry and mismatching) and proposed suggestions and mitigations
for current practitioners and the research committee (RQ2). Finally, all
research projects point to open challenges in RQ3. For example, when
identifying actions and reasons when interacting with safety boundaries, I
found participants sometimes rely on their understanding of the physical
environment when deciding whether to break out. My thesis aims to understand
the psychological process of physical breakdowns with empirical studies and
inform future mechanisms that mitigate risks and safety concerns.

#### Research Situation

I am in the third year of my PhD at Telecom Paris, France. In 2023, I will
transition to the Department of Computer Science, TU Darmstadt, Germany, to
continue my PhD. I plan to hand in my thesis in approximately 2.5 years. By
participating in the Doctoral Consortium, I hope to get valuable feedback on
my research direction and approach.

##  2\. Background and Key Related Work

#### Virtual Reality and Presence

VR technologies immerse users by providing multi-sensory input (e.g., visual,
audio, haptic) and motion tracking, enabling 3D interaction inside a simulated
environment. A user feels a psychological state of “being there” inside a
computer-mediated environment (Witmer and Singer, 1998; Slater et al., 1994)
called the sense of presence. However, a VR user may be distracted by stimuli
from the physical environment (e.g., break in presence (Slater and Steed,
2000)). This phenomenon can be explained using the attentional model (Draper
et al., 1998) where participants’ attention resources shift from the virtual
content to the physical environment. These findings indicate we are not always
present inside the virtual environment. Instead, multiple transitions happen
within the virtual/physical environments and perceptual/conceptual tasks. The
physical breakdown is an abrupt transition in the context of presence.
Studying the physical breakdown in VR improves the user’s safety and opens
opportunities to explore the behavior process behind these transitions.

#### Physical Breakdowns as Potential Harm and Risks in VR

A breakdown represents the moment of an abrupt disruption of an experience
(Bødker, 1995). Dao and colleagues (Dao et al., 2021) applied the breakdown
concept to explore VR fails (e.g., overreacting, colliding, hitting) and their
causes by analyzing YouTube videos. Here, I extend their work and define “the
physical breakdown in VR” as an abrupt disruption of the VR experience caused
by a collision with the physical environment. Physical breakdowns are a subset
of VR fails, which could potentially induce harm to the user. In some cases,
they may lead to exiting a VR experience (Knibbe et al., 2018).

The safety boundary (e.g., Oculus Guardian, Vive Chaperone) can prevent
accidents in VR by displaying 2D grids based on the user’s proximity. Recent
research explored multiple sensory feedback to notify the VR user (George et
al., 2020; Faltaous et al., 2020). Nevertheless, the physical environment is
usually unknown and uncontrolled at home. Blending the virtual content with
the physical surroundings can keep the presence in VR and prevent collision
(Hartmann et al., 2019). Still, blending techniques are not as prevalent as
safety boundaries. Instead of building new artifacts, I study the VR user’s
behavior while interacting with safety boundaries to understand the behavior
process before physical breakdowns happen and inform future safety mechanisms.

VR technologies are highly persuasive for benefits (e.g., training) as well as
malicious purposes because of the realism (Slater et al., 2020). Interaction
techniques in VR leverage the visual limits of the user (e.g., humans are
visually dominant when combining several sources of sensory information
(Posner et al., 1976; van Beers et al., 2002)) to hack human perception.
Examples like redirection techniques (Razzaque et al., 2002; Azmandian et al.,
2016; Sun et al., 2018) and pseudo haptic illusions (Lecuyer et al., 2000;
Rietzler et al., 2018), can direct the user’s action to overcome limitations
in current VR systems (e.g., limited tracked space, lack of haptic feedback).
I define them as _Virtual-Physical Perceptual Manipulation_ (VPPM) referring
to Extended Reality (XR) driven exploits that _alter the human multi-sensory
perception of our physical actions and reactions to nudge the user’s physical
movements_ (e.g., the position of body and hands). While VPPMs had positive
intents, malicious actors can also exploit VPPMs to provoke physical
breakdowns and even harm the VR user. Casey et al. identified the _human
joystick attack_ directing an immersed user’s physical movement to a location
without the user’s knowledge (Casey et al., 2019). My thesis broadly explores
how malicious actors could impose VPPMs to manipulate the user’s body movement
and provoke future physical breakdowns using a speculative design workshop.

##  3\. Dissertation Status

###  3.1. Breaking Out of the Safety Boundary in VR

In this project, I investigated physical breakdowns in the everyday usage of
VR to address RQ1. Instead of observing physical breakdowns directly, I chose
the moment when VR users break out of the Safety Boundary (SB). Break-outs
happen during interaction with SBs, and they are one step before a physical
breakdown could happen (e.g., colliding with objects in the environment). I
explored how VR users interact with SBs and the reasons for break-outs in VR
(RQ1 and RQ3) using an online survey (n=64) and a lab study (n=12) with a
mixed-method approach.

---

Figure 2. Despite having the safety boundary, VR users may still break out
accidentally or intentionally (the red circle), leading to safety concerns
(e.g., collision). I implemented an apparatus (FruitSlicer) to replicate the
break-out experience.

Figure 2 shows a VR user who broke out of the safety boundary while playing a
VR game. Although there is a safety boundary, VR users still break out of it
for accidental or intentional reasons.

The online survey collected data about attitudes towards the SB, behavior
while interacting with SBs, and reasons for breaking out. The results show
participants perceived SBs as positive and helpful, keeping them safe and
alert during a VR experience. However, half of them (52%) still broke out
while using VR, indicating SBs still cannot prevent participants from break-
outs every time. By analyzing open-ended questions using a thematic analysis
(Braun and Clarke, 2006), I identified four physical behaviors (retreat, stop,
adapt, and ignore in Figure 1) that VR users did when seeing SBs. Further, I
categorized multiple reasons for breaking out into two main classes of break-
outs: intentional (57%) and accidental (43%). To understand intentional break-
outs, I implemented FruitSlicer (Figure 2), a VR application that can provoke
breaking out of SB, allowing us to observe participants’ reactions and
interview them afterward about their reasons. The lab study exposed
participants to break-out experiences with multiple obstacles in a mock-up
living room (Figure 2). The analysis of the semi-structured interview revealed
three interaction strategies. Cage indicates participants tend to break out
with arms instead of the body. Confine means participants stay inside the SB
and avoid break-outs. Lastly, participants sometimes touched the obstacles,
obtaining more spatial information about the physical environment (update),
and dared to break out intentionally because they assumed it would be safe.

Through the two studies, I observed that intentional break-outs are usually
associated with the participant’s understanding of the virtual and physical
environment. I interpret this observation with the Spatial Mental Model (SMM)
(Lee and Tversky, 2005; Franklin et al., 1992) that VR user forms the spatial
relation inside a small or well-known environment, and they recall their SMM
when they decide whether to break out of the SB (RQ3). This finding point to
new open challenges in the user’s behavior and cognitive process while
interacting with VR and being aware of the physical environment
simultaneously.

---

Figure 3. FingerMapper leverages less physically demanding finger motions,
enabling whole-body virtual arm movements in confined spaces (e.g., the
passenger seat of a car) with fewer collisions while preserving presence and
enjoyment.

Figure 3 illustrates FingerMapper, a technique that maps small and less
physically demanding motions of fingers onto the virtual arm. FingerMapper
enables whole-body virtual arm interaction in confined spaces to avoid
physical breakdowns in the mobile VR context, providing a higher perceived
safety.

###  3.2. FingerMapper [CHI EA ’21]

I found some participants broke out of safety boundaries because they had
large movements. Although whole-body movements enhance the presence and
enjoyment of VR experiences, using large gestures is often uncomfortable and
impossible in confined spaces (e.g., public transport). This context may lead
to collisions and break the VR experience.

I developed a solution to address RQ2, FingerMapper (Figure 3), through a
user-centered design approach. FingerMapper maps small-scale finger motions
onto virtual arms and hands to enable whole-body virtual movements in VR.
Since the user has fewer physical movements, this technique can also reduce
collisions. In a first target selection study (n=13) comparing FingerMapper to
hand tracking and ray-casting, I found that FingerMapper can significantly
reduce physical motions and fatigue while having a similar degree of
precision. In a consecutive study (n=13), I compared FingerMapper to hand
tracking inside a confined space (car). The results showed participants had
significantly higher perceived safety and fewer collisions with FingerMapper
while preserving a similar degree of presence and enjoyment as hand tracking.
Finally, I present three applications demonstrating how FingerMapper could be
applied for locomotion and interaction for VR in confined spaces. The results
point out that in a different context (e.g., confined spaces), perceived
safety should also be considered as other metrics like presence.

###  3.3. Exploring Future Physical Breakdowns by Exploiting Perceptual
Manipulations in VR [CHI ’22]

---

Figure 4. (a) Participants created scenarios in the speculative design
workshop to speculate on the malicious use of VPPMs. The left shows the
puppetry attack that directs a user to fall over the stairs. The right
illustrates the mismatching attack in that the VR user punches a virtual
zombie overlay on a bystander. (b) Physical harm was identified in all
collected scenarios, from mild pain or discomfort to extreme cases like death.

Figure 4a shows the results of the speculative design workshop. Participants
were asked to create scenarios, where malicious actors exploit perceptual
manipulations in VR to provoke physical harm to the user. I identified the
puppetry attack, which directs the user’s body action to provoke physical
harm, and the mismatching attack, which makes the user misinterpret their
virtual and physical information. Figure 4b shows the severity of the physical
harm collected in the workshop. The harm varies from little pain and
discomfort (e.g., eyestrain, cramp) to extreme harm (e.g., drowning, getting
driven over).

VR interaction does not have to stay in a one-to-one mapping (e.g.,
FingerMapper). Figure 1 shows VR users perceive sensory information from the
virtual and physical environments, and the perceptual input is dominated by
the visual content in VR. Human-Computer Interaction (HCI) and VR research
leverages this discrepancy to create VPPMs, effecting changes in the user’s
physical movements, becoming able to (perceptibly and imperceptibly) nudge
their physical actions to enhance interactivity in VR. This project (Tseng et
al., 2022) explores the risks of how malicious actors could provoke future
physical breakdowns could be by exploiting VPPMs to manipulate a VR user’s
body motions (RQ1) and how to mitigate them (RQ2).

I chose speculative design workshop (Auger, 2013; Markussen and Knutz, 2013)
to explore the future physical breakdowns and risks posed by the malicious use
of VPPMs. The goal was to critique current practices and reflect on future
technologies and their ethical implications. Through a thematic analysis
(Braun and Clarke, 2006), I analyzed 19 scenarios (Figure 4a) created by eight
VR and design experts, identifying two main risks and characterizing harm
(Figure 4b). The puppetry attacks control the physical actions of different
body parts of an immersed user. The mismatching attacks are manipulations in
which the adversary exploits a difference in information between a virtual
object and its physical counterpart to elicit misinterpretation for the VR
user. Two sample applications were implemented to show how existing VPPMs
could be trivially subverted to create the potential for physical
harm.Finally, I proposed mitigations and preventative recommendations against
the malicious use of VPPMs. Unlike software leaks, one cannot patch a human
perception hack easily. My goal was to raise awareness that the current way we
apply and publish VPPMs can lead to malicious exploits of our perceptual
vulnerabilities.

##  4\. Future Work and Open Challenges

In my future research, RQ3 is going to be the main focus. I plan to conduct
experiments to understand the VR user’s behavior and cognitive process of the
physical breakdown phenomenon. One ongoing project is about the intentional
break-outs and the concept of the Spatial Mental Model (SMM) — a mental model
that allows us to remember the spatial relation inside a small or well-known
environment (Franklin et al., 1992; Lee and Tversky, 2005). Users can form an
SMM of their physical environment (e.g., their home) and recall it despite
only seeing the virtual environment while using VR.

When an intentional break-outs happens, I assume the VR user might use their
SMM of the physical and virtual environment to determine their interaction.
Future research should focus on establishing this link even further to
understand how these two constructs are related and what the user relies more
on when breaking out. The goal would be identifying this process with SMM
exists (i.e., the VR user not only using their perceptual information but
their SMM in the physical environment to interact). Next, I want to observe
the relationship between the user’s SMM and other VR metrics (e.g., presence
and enjoyment). An example could be a higher presence may lead to an imprecise
SMM. My future research should create hypotheses around this direction and
test them.

Physical breakdowns also represent a risk when using VR/XR. Future work could
quantify physical breakdowns (or actions) and develop algorithms to predict
the user’s behavior. This approach can be a part of future safety mechanisms.
I co-organized a workshop (Gugenheimer et al., 2022) focusing on the
intersection of safety, security, and privacy in XR. Hacking human perception
in VR (e.g., FruitSlicer or VPPMs) is also a potential risk in XR. I also plan
to explore the countermeasure against manipulating human users with XR
technology.

Most HCI and VR research inherit the concept of enhancing the VR experience
(e.g., presence, immersion, and enjoyment) in a controlled environment.
However, the context of everyday VR usage is uncertain and uncontrolled. Users
may encounter multiple attentional transitions in one VR experience, switching
between different realities and activities. One insight gained from my current
progress is that applications should not only optimize for the user experience
in VR. Instead, new metrics (e.g., safety) should be considered and enhanced
in a different context. My future research aims to understand the cognitive
process of how a user comprehends and interacts with the physical environment
while being in VR. By investigating physical breakdowns in VR, I anticipate my
thesis can contribute to the knowledge of VR users’ behavior and cognitive
process, further providing insights into future VR safety mechanisms.

###### Acknowledgements.

I am grateful to my supervisors, Jan Gugenheimer, Samuel Huron, Eric
Lecolinet, and my colleagues for their valuable feedback on my research. This
work was conducted within INFRES and SES at Telecom Paris, IP Paris, LTCI,
Institut Mines-Télécom, and the University of Glasgow. This work was supported
by the Investments for the Future Program (PIA), CONTINUUM (ANR-21-ESRE-0030),
and the INTERPLAY project (ANR-21-CE33-0022), funded by French National
Research Agency (ANR).

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2008) as Zahnle et al. (2016), the different condensation behavior should be
due to a warmer upper stratosphere in Zahnle et al. (2016). Zahnle et al.
(2016) indeed noted that S8 would condense if the temperature were just a few
degrees lower.

Figure 31: The computed abundance profiles of 51 Eri b, assuming solar (left
panels) and 10 times solar (right panels) metallicity. The top row presents
the main species, with equilibrium profiles shown in dotted lines. The middle
row shows the main sulfur species and the bottom has S2/S8 vapor (solid),
S2/S8 condensate particles (dashed-dotted), and the saturation mixing ratios
of S2/S8 (dotted). The particles are plotted in the ratio of the number
density of particles to the total number density of gas molecules and
multiplied by 1010.

Figure 32: The abundances of several main species that show differences from
models including sulfur kinetics (solid) and without sulfur kinetics (dashed)
for 51 Eri b.

####  4.4.3 Effects of Super-Solar Metallicity

The left and right columns of Figure 31 compare the results of solar and 10
times solar metallicity. The model with 10 times solar metallicity has
slightly hotter troposphere (Figure 30) which favored CO over CH4. Although
the equilibrium abundance of CH4 in the stratosphere is increased in the 10
$\times$ solar metallicity model, CH4 is in fact decreased with a lower CH4/CO
ratio at the quench level. In the end, the 10 $\times$ solar metallicity model
shows higher CO, CO2, H2O and lower CH4 abundances, which in turn reduces
other hydrocarbons as well. The mixing ratio of CO2 exceeds CH4 for 10
$\times$ solar metallicity and can reach $\sim$ 0.1$\%$ in the upper
atmosphere. The production of O2 also raises with metallicity following the
increase of water.

####  4.4.4 Effects of Sulfur

Compared to HD 189733b and GJ 436b, H2S can only remain stable against
hydrogen abstraction (30) at higher pressure about 0.05 bar. The reverse rate
of (30) significantly drops in the cooler stratosphere of 51 Eri b and
prohibits the reformation of H2S. The active SH radical produced by H2S leads
to a rich variety of sulfur species, as illustrated in the middle row of
Figure 31. Compared to Zahnle et al. (2016), our model exhibits a more
oxidized upper stratosphere due to stronger UV irradiaion from the closer
orbit in our setting (11.1 AU compared to 13.2 AU). Nonetheless, both models
predict efficient polymerization forming great abundance of S8. Since S8 is
the end pool of sulfur chain reactions, we find the condensation of S8 does
not affect other sulfur species. Elemental S is still the leading sulfur
species above the S8 condensing layers until being oxidized into SO and SO2 in
the upper stratosphere.

The equilibrium abundance of H2S scales with metallicity, which leads to more
production of S8 vapor as metallicity increased. The 10 times solar
metallicity model has slightly warmer temperature which allows higher
saturation pressure of sulfur as well. In the end, both the gas and
condensates of S2 and S8 increase with metallicity.

The effects of coupling to sulfur on other species are highlighted in Figure
32. The most remarkable feature is the enhanced oxygen abundances in the upper
atmosphere with sulfur. In the absence of sulfur, atomic O can be released
from H2O with the aid of CO2:

$\displaystyle\begin{aligned} \ce{H2O&->[h\nu]OH+H}\\\ \ce{CO+OH&->CO2+H}\\\
\ce{CO2&->[h\nu]CO+O}\\\ \vglue 5.0pt\cr\hline\cr\vglue
5.0pt\cr\mbox{net}:\ce{H2O&->[2h\nu]2H+O}.\end{aligned}$ (33)

While sulfur is present, SO and SO2 dissociate more than CO2 around
Ly-$\alpha$ and provide a faster channel to liberate O from H2O:

$\displaystyle\begin{aligned} \ce{H2O&->[h\nu]OH+H}\\\ \ce{SO+OH&->SO2+H}\\\
\ce{SO2&->[h\nu]SO+O}\\\ \vglue 5.0pt\cr\hline\cr\vglue
5.0pt\cr\mbox{net}:\ce{H2O&->[2h\nu]2H+O}.\end{aligned}$ (34)

or

$\displaystyle\begin{aligned} \ce{H2O&->[h\nu]OH+H}\\\ \ce{S+OH&->SO+H}\\\
\ce{SO&->[h\nu]S+O}\\\ \vglue 5.0pt\cr\hline\cr\vglue
5.0pt\cr\mbox{net}:\ce{H2O&->[2h\nu]2H+O}.\end{aligned}$ (35)

The excess atomic O readily reacts with OH to form O2. This enhanced oxidized
region along with NS accelerates the oxidization of NH3, via the same pathway
(32) but more pronounced than that on GJ 436b. On the other hand, CH4 is
unaffected because the intermediates HCS and CS are deficient in the colder
stratosphere of 51 Eri b. Lastly, the coupling to H2S also helps atomic H
recycle back to H2 faster, as seen on GJ 436b.

Figure 33: The low-pressure limit rate coefficient of S + CO -¿[M] OCS
estimated in this work (37), compared to those in the literature. Figure 34:
Main sulfur species from our nominal model with solar metallicity (solid)
compared to those adopting the faster rate of (36) from Zahnle et al. (2016)
(dashed).

####  4.4.5 sensitivity to OCS recombination

The fate of elemental S after being released from H2S is critical in sulfur
kinetics. Several reactions potentially control whether S proceeds to chain
formation into larger polysulfur (S_x), forming OCS, or being oxidized to SO,
SO2. To address the effects of kinetics uncertainties, Zahnle et al. (2016)
explore the sensitivity to H2S recombination and Sx polymerization. The
authors found a faster H2S recombination counteracts the destruction of H2S
and reduces the production of S8, while their results are not sensitive to the
polymerizing rates of forming S4 and S8 within the tested ranges. We have
tested the polymerization rates for GJ 436b and confirmed its general
insensitivity to S8 formation. For 51 Eri b, we recognize that the
recombination of OCS

$\ce{S+CO->[\textrm{M}]OCS}$ (36)

could be important in determining the oxidizing rate of sulfur. The rate
coefficient of Reaction (36) has in fact not been measured. Only the reverse
step of (36), the dissociation of OCS, has available data at high
temperatures. Recently, Ranjan et al. (2020) has also identified this reaction
to modestly alter the CO abundance in a CO2-N2 atmosphere and advocate
laboratory investigation. Here, we will explain how the rate coefficient of
Reaction (36) is estimated in our nominal model and then explore the
sensitivity to the uncertainty for 51 Eri b.

Reaction (36) is a spin-forbidden reaction and usually many orders of
magnitude slower than a typical three-body reaction. Since the measured high-
temperature dissociation reaction has a high activation energy, extrapolating
the dissociation reaction (the reversal of (36)) to low temperatures will
result in unrealistically rates. Instead, we estimate the activation energy
from the well-studied analogous reaction, O + CO -¿[M] CO2. The pre-
exponential factor is then determined by matching the reverse of dissociation
reaction at 2000 K from Oya et al. (1994). The low-pressure limit rate of (36)
we estimate is

$k_{\textrm{0}}=4.47\times 10^{-34}\textrm{exp}(-1510/T).$ (37)

We compare the rate coefficient (37) with those assumed in Zahnle et al.
(2016) and Venus literature (Zhang et al., 2012; Krasnopolsky, 2013) in Figure
33. The reaction rates show diverse values especially toward lower
temperatures, the relevant temperature range for the stratosphere of 51 Eri b.
Albeit the rate discrepancy in each model, the rate constants in Zhang et al.
(2012), Krasnopolsky (2013) and this work exhibit consistent temperature
dependence from 1000 K to 200 K, whereas that in Zahnle et al. (2016) has
suprisingly almost no temperature dependence. Since rate constant of (36) from
Zahnle et al. (2016) is the most different from the literature and yields
fastest OCS forming rate, we will use the rate from Zahnle et al. (2016) as
the upper limit to test the sensitivity.

We run our nominal model with solar metallicity but adopt the rate constant of
(36) from Zahnle et al. (2016). The effects of faster OCS recombination are
illustrated in Figure 34. With the OCS recombination rate from Zahnle et al.
(2016), OCS mixing ratio is significantly increased above 0.1 bar. S8 is
slightly reduced but remains the major sulfur carrier between 10-2 and 10-4
bar, consistent with the model results in Zahnle et al. (2016). The abundance
of S and S2 are subsequently affected by more ample OCS photodissociation but
that of S8 remains the same as set by condensation. Given these differences,
we reiterate further investigation to pin down the reaction rate of OCS
recombination.

Figure 35: Synthetic emission spectra of 51 Eri b produced from equilibrium
abundances, disequilibrium abundances, and with S8 condensate layer. Data
points show GPI observations from Macintosh et al. (2015) and SPHERE
observations from Samland et al. (2017). Figure 36: A Schematic diagram
illustrating the main pathways for sulfur kinetics in an H2-dominated
atmosphere. The dashed line represents the transition from the lower region
where sulfur is predominantly locked in H2S to the upper region where H2S is
subject to dissociation. Rectangles indicate stable species whereas ellipses
indicate active radical or intermediate species.

####  4.4.6 Emission Spectra

Figure 35 demonstrates the effects of disequilibrium chemistry and S8 clouds
on the planetary emission spectra. For both metallicities, quenched CH4 and
H2O have lower abundances than equilibrium, leading to higher emission in the
H and J bands from the deeper region. The 10 times solar metallicity further
reduces CH4 and prompts the flux at 1.6 - 1.8 $\mu$m. We assume 1 $\mu$m
particle size for S8 condensates, which scatter strongly and reduce the
emission in this wavelength range. However, using the higher effective
temperature and metallicity from Samland et al. (2017), our models generate
emission that are too high in the H and J bands and fail to reproduce the
observed spectra. We conclude that either $T_{\textrm{eff}}$ is lower than
that determined by Samland et al. (2017) and/or additional cloud layers (e.g.
Moses et al., 2016) is required to match the lower observed emission.

###  4.5 Sulfur Mechanism

Figure 36 summerizes the important pathways for sulfur species in the
irradiated H2-dominated atmospheres we explored in this section. H2S is the
dominant molecule, which is thermochemically stable for a wide range of
temperatures in the lower atmosphere followed by OCS. The photochemistry of
sulfur is initiated from SH and S produced by H2S dissociation, leading to
multiple channels including chain formation and oxidization depending on the
atmospheric condition. Sulfur chain formation is highly temperature sensitive
where S2 is favored about 600 - 800 K and S8 can only form below $\sim$ 500 K
(e.g. the stratosphere of 51 Eri b). When OH is sufficiently produced by H2O
photolysis, S will most likely be oxidized into SO and SO2 in the upper
atmosphere. S also participates in accelerating CH4 and NH3 destruction via
the coupling to CH2 or NH2, as seen in our HD 189733b and GJ 436b models.

Figure 37: The column number densities (molecules cm-2) above 1 mbar of haze
precursors for the simulated atmospheres in Section 4, including sulfur (left)
and without sulfur (right). Some molecule abundances are negligible and not
shown for WASP-33b. For GJ 436b, the models with T${}_{\textrm{int}}$ = 400 K
and weak/strong vertical mixing are used.

###  4.6 Trends of Photochemical Hazy Precursors

Figure 37 summarizes the column densities of haze precursors above 1 mbar for
the simulated atmospheres in Section 4. Across the various irradiated
H2-atmospheres we explored, we find HCN consistently to be the most prevailing
precursor. This is not surprising as HCN is a robust photochemical product of
CH4 and NH3 and also recently been detected on HD 209458b (Giacobbe et al.,
2021). Nonetheless, it does not necessarily imply HCN will lead to complex
nitriles formation, since HCN is not the limiting factor as we discussed in
Section 2.8. A more careful assessment at high temperatures is required before
extrapolating the haze-forming mechanism below 200 K on Titan. We observe a
general increasing trend with decreasing temperature for the more indicative
nitrile precursors HC3N but opposite for CH3CN. The same trend is seen for the
hydrocarbon precursors C4H2 and C6H6.

Only HCN and C2H2 can reach appreciable levels on WASP-33b, even as
photochemical hazes are not expected on WASP-33b. For GJ 436b, most of the
precursors are not too sensitive to eddy diffusion. For 51 Eri b, almost all
precursors are reduced with increasing metallicity, except for CS2 since it
contains no H. In fact, CS2 is most favored on HD 189733b, which suggests
sulfur-containing hazes in the hot Jupiter condition as carbon and sulfur can
couple closely. In addition to sulfur condensates, 51 Eri b might also be
covered by nitrile-type hazes according to the precursor distribution.

##  5 Discussion

###  5.1 High-Temperature UV Cross Sections

We have implemented layer-by-layer UV cross sections according to the
temperature at each atmospheric level in VULCAN. Due to the sparsely available
data, we did not perform systematic study in this work. Nonetheless, we have
gained some insights through the case studies in Section 4.

We found the effects of temperature dependence for H2O is mostly negligible in
a H2-dominated atmosphere. However, this is solely based on the limited
wavelength-range measurements we assembled. For the high-temperature ($T>$
1000 K) cross sections, only wavelengths longer than about 190 nm are included
(Figure 38). The high-temperature cross sections in the FUV could have larger
effects.

We confirm the analysis in Venot et al. (2013) that although the CO2 abundance
is not directly influenced by the temperature dependence of CO2 photolysis,
the shielding effects can impact other species. As CO2 absorb more strongly
with increasing temperature, the UV photosphere is lifted to lower pressure.
The production of radicals, such as H and OH, is reduced and subsequently
alters other species. However, we also find that the shielding effects of CO2
are completely shadowed when sulfur species are included (e.g. see the right
panel of Figure 18). The temperature dependence of CO2 photolysis should be
more amplified in CO2-dominated atmospheres.

###  5.2 Implication of Ionization

Ions are not included in this work. We are working on including ionchemistry
in the next update of VULCAN. Photoionization is known to be critical in
initiating the haze formation (Wong et al., 2003; Krasnopolsky, 2009; Plessis
et al., 2012; Lavvas et al., 2013). Even thermoionization can be important for
ultra hot Jupiters. In our study about WASP-33b, atomic Ti and V in the upper
atmosphere are expected to be partly ionized and contribute to free electrons.
Since Ti has an ionization threshold of 180 nm, compared to about 240 nm for
Na, the effects of photoionization on Ti and V should be similar and probably
smaller than those on the alkali atoms, as investigated in Lavvas & Koskinen
(2017). An important outcome of photoionization is that the increased
electrons can lead to more hydrogen anions (H-) than predicted by thermal
equilibrium, which are found to be important opacity sources in some hot
Jupiters atmospheres (Lewis et al., 2020). In terms of sulfur chemistry,
several sulfur species have relatively lower-energy threshold of ionization
and can be subject to photoionization. For example, atomic S starts to ionize
from Lyman-$\alpha$. Since S is likely the dominant sulfur species in the hot
Jupiter’s stratosphere (Section 4.2.2), S can be photoionized and ramify into
various organic molecules through ion-exchange reactions.

###  5.3 More Intriguing Questions about Sulfur

In Section 4, we find the coupling to sulfur chemistry impacts the core C-H-
N-O kinetics in several ways for H2-dominated atmospheres. The coupling
effects essentially depend on if the sulfur-containing intermediates are
active, which is not well-understood in general as it can vary with
atmospheric conditions such as temperature and bulk compositions. Gersen et
al. (2017) find that CH3S and CH3SH provide more efficient pathways for
methane oxidization in the combustion (oxidizing) environment. He et al.
(2020) also observe the photochemical formation of CH3S and CH3SH in a
CO2-rich gas mixture in the experiments. Although we have included reactions
involving CH3S and CH3SH in our sulfur mechanism, they are not identified to
be important in the pathway analysis for all of the H2-atmospheres we
investigated. The chemical role of CH3SH is worth further study in the broad
context of biologically produced sulfur.

The temperature profiles are fixed without considering the radiative feedback
in this whole work. The radiative effects might be more prominent in the
presence of sulfur, such as the absorption of SH and S2 in the optical and
NUV. 51 Eri b or other directly imaged planets with a relatively cold
stratosphere ($\lesssim$ 500 K) and under sufficient UV irradiation sit in the
sweet spot for testing the radiative feedback on sulfur condensates.

##  6 Summary

In this paper, we present a thorough theoretical framework of the updated
photochemical code VULCAN. We validate our models for the atmospheres of hot
Jupiters, Jupiter, and modern Earth and carry out comparative study on
representative cases of extrasolar giant planets: WASP-33b, HD 189733b, GJ
436b, and 51 Eridani b. The highlights of our results are:

  * $\bullet$

We have carefully validated the model of HD 189733b. The updated methanol
scheme in Venot et al. (2020) is found to bring the quenching behavor of
methane close to Moses et al. (2011) and VULCAN. We pointed out the
photochemical source plays a non trivial part in the model differences between
Moses et al. (2011), Venot et al. (2012), and VULCAN.

  * $\bullet$

We demonstrate advection transport in the downdraft can qualitatively explain
the deep ammonia distribution in Jupiter, which can not be explained by eddy
diffusion alone.

  * $\bullet$

The implementation of surface boundary conditions and condensation in an
oxygen-rich atmosphere is validated in the present-day Earth model. A general
oxidation timescale analysis is provided for assessing the chemical lifetime
of biosignature gases.

  * $\bullet$

The atmosphere of WASP-33b is not affected by vertical quenching but consisted
of an upper photolytic region and a thermochemical equilibrium region below.
For GJ 436b, we find NH3 insensitive to vertical mixing and the sulfur species
governed by photolysis and mixing in the upper stratosphere are independent of
the deep thermal structure, which can be complementary to the CH4/CO metric
for breaking degeneracies. The quenched CO always predominates over CH4 on 51
Eri b and sulfur aerosols (chiefly S8) condense out in the stratosphere.

  * $\bullet$

We find the coupling to sulfur chemistry impact C-H-N-O kinetics. Sulfur can
provide catalytic paths to destroy CH4 and NH3 and generally lower the
hydrocarbon abundances. H2S makes H recycled back to H2 faster on the cooler
GJ 436b and 51 Eri b. The dissociation of SO and SO2 also make the upper
atmosphere of 51 Eri b more oxidizing.

  * $\bullet$

We suggest including several photochemical haze precursors such as C6H6 and
HC3N, which are more indicative than the commonly considered HCN and C2H2. We
observe a general increasing trend with decreasing temperature for C4H2, C6H6,
and HC3N but opposite for CH3CN.

## Model availability

The results in this work are produced by version 2.0 of VULCAN
(https://github.com/exoclime/VULCAN/releases/tag/v2.0). In addition to the
public code, the configuration files used for the models in Section 3 are
available on https://github.com/exoclime/VULCAN and the main model output in
Section 3 and Section 4 can be found in the supplementary material.

Software: Python; Numpy (van der Walt et al., 2011); Scipy (Oliphant, 2007);
Matplotlib (Hunter, 2007)

S.-M.T gratefully thanks M. Zhang for customizing PLATON to read non-
equilibrium compositions. S.-M.T also thanks O. Venot and J. Moses for sharing
the output of HD189733b for model comparison, C. Li for providing the
retrieved ammonia results from Juno measurements, L.M. Lara for fruitful
discussions about setting up photochemistry, P. Rimmer for the compiled
observational data of Jupiter, and N. Wogan for pointing out a typo in
Equation (14) in an earlier version of this paper. S.-M.T acknowledges support
from PlanetS National Center of Competence in Research (NCCR) and University
of Oxford. M.M. acknowledges support from NASA under the XRP grant No.
18-2XRP18_2-0076. E.K.L. acknowledges support from the University of Oxford
and CSH Bern through the Bernoulli fellowship. K.H. acknowledges support from
the PlanetS National Center of Competence in Research (NCCR) of the Swiss
National Science Foundation and the European Research Council Consolidator
Grant EXOKLEIN (No. 771620). This work was supported by the European Research
Council Advanced Grant EXOCONDENSE (#740963; PI: R.T. Pierrehumbert).

##  Appendix A Molecular diffusion and thermal diffusion factor

For H2-based atmospheres, we take

$D_{\ce{H2}-\ce{CH4}}=2.2965\times 10^{17}T^{0.765}/N$ (A1)

from Marrero & Mason (1972) as the reference and scale the molecular diffusion
coefficient of H2 with other species according to Equation (3). The thermal
diffusion factor for H and He are approximately $\alpha_{\ce{H}}$ $\approx$
-0.1 and $\alpha_{\ce{He}}$ $\approx$ 0.145 (Moses et al., 2000). We assume
$\alpha_{i}$ = -0.25 for the rest of species based on rigid sphere
approximation (Banks & Kockarts, 1973).

For N2-based atmospheres, we take

$D_{\ce{N2}-\ce{CH4}}=7.34\times 10^{16}T^{0.75}/N$ (A2)

from Banks & Kockarts (1973) as the reference and scale the molecular
diffusion coefficient of N2 with other species according to Equation (3). The
thermal diffusion factor of Ar is $\alpha_{\ce{Ar}}$ $\approx$ 0.17 and
$\alpha_{i}$ = -0.25 for the rest species.

For CO2-based atmospheres, we take

$D_{\ce{CO2}-\ce{H2}}=7.51\times 10^{16}T^{0.759}/N$ (A3)

from Banks & Kockarts (1973) as the reference and scale the molecular
diffusion coefficient of CO2 with other species according to Equation (3). The
thermal diffusion factor of Ar is $\alpha_{\ce{Ar}}$ $\approx$ 0.17 and
$\alpha_{i}$ = -0.25 for the rest species.

Figure 38: Photoabsortion cross sections of H2O, CO2, and NH3 across various
temperatures, with Ref. denoting the cross sections measured at room
temperature. The measured cross sections of H2O at 423 K (dot) and 573 K
(cross) are noisy beyond 216 nm and we use linear fit for conservative
estimate. The references of the cross sections are described in Section 2.5.

##  Appendix B Resolution Errors of Photolysis Rates

Table 4: Errors from Low Spectral Resolution Bin (nm) | Stellar Flux (in $\%$) |  $\Delta$ J${}_{\ce{H2}}$ 282828$\Delta$ J = $|$J - J0$|$ / J0 where J0 is the reference photolysis rate calculated with constant 0.1 nm resolution |  $\Delta$ J${}_{\ce{H2O}}$
---|---|---|---
0.2 | 0 | 0.0004 | 0.003
0.5 | 0.08 | 0.18 | 1.13
1 | 0.08 | 0.44 | 0.87
10 | 2.65 | 0.22 | 0.87

Equation (11) is numerically computed in the form of finite sum. The
wavelength grid in the code needs to properly resolve the line structures in
the stellar flux and cross sections. This is especially important in the XUV
where there are more fine structures from the band transition (Rimmer &
Helling, 2016).

We demonstrate the errors of computing Equation (11) with the GJ 436b model in
Section 4.3. The effects are emphasized with its host M-star showing more
emission lines. Figure 39 shows the stellar flux overplotted with the UV cross
sections of H2 and H2O. The stellar flux is adopted from the MUSCLES survey
with a constant 0.1 nm resolution and the UV cross sections from the Lieden
database have the same resolution of 0.1 nm. Therefore, we consider constant
resolution of 0.1 nm as the reference for this test. The resolution for
computing Equation (11) is varied from 0.2 nm to 10 nm, where the trapezoidal
rule is applied for the integral. The errors with respect to summing-up the
total stellar flux and the resultant photolysis rate of H2 and H2O at the top
of atmosphere (10-8 bar) are summerized in Table 4. Starting from the bin size
of 0.5 nm, which is five times the native resolution of the flux and cross
section data, the errors become comparable to the absolute value of the
photolysis rate. The errors do not behave linearly with the bin size since the
overestimate from the peak can offset the underestimate from the trough. The
test shows the importance of using matching spectral resolution to attain
accurate photolysis rates.

Figure 39: The stellar UV flux of GJ 436 and cross sections of H2 and H2O, showing the native resolution 0.1 nm adopted in the model. Table 5: List of forward reactions (backward reactions with even indexes are reversed numerically with thermodynamic data) and rate coefficients (cm3 s-1 for bimolecular reactions and s-1 for k0) of titanium and vanadium species. $E_{a}$ est. means the activation energy is estimated by the enthalpy difference as described in Section 2.7. Reaction | Rate Coefficient | Reference
---|---|---
TiO + O -¿ Ti + O2 | 5.42 $\times 10^{-13}$ $\exp(-20794/T)$ |  $E_{a}$ est. with $A$292929The pre-exponential factor. from matching NIST 1994LIA/MIT (at room temperature)
TiO + N -¿ Ti + NO | 4.76 $\times 10^{-12}$ $\exp(-4772/T)$ |  $E_{a}$ est. with $A$ from matching NIST1993CLE/HON (at room temperature)
TiO + N2 -¿ Ti + N2O | 5.9 $\times 10^{-12}$ $\exp(-62193/T)$ |  $E_{a}$ est. with $A$ from matching NIST 1994LIA/MIT (at room temperature)
TiO + H -¿ Ti + OH | 2.0 $\times 10^{-10}$ $\exp(-28418/T)$ |  $E_{a}$ est. with $A$ based on FeO + H -¿ Fe + OH from Rumminger et al. (1999)
TiO + H2 -¿ Ti + H2O | 2.0 $\times 10^{-11}$ $\exp(-21270/T)$ |  $E_{a}$ est. with $A$ based on FeO + H2 -¿ Fe + OH from Decin et al. (2018)
Ti + CO2 -¿ TiO + CO | 7.01 $\times 10^{-11}$ $\exp(-1790/T)$ | NIST 1993CAM/MCC7942-7946
TiO2 + H -¿ TiO + OH | $1.0\times 10^{-10}\exp(-19500/T)$ |  $E_{a}$ est. with $A$ based on FeO2 + H -¿ FeO + OH from Rumminger et al. (1999)
TiO2 + O -¿ TiO + O2 | $1.0\times 10^{-10}\exp(-11877/T)$ |  $E_{a}$ est.
TiO2 + CO -¿ TiO + CO2 | $1.0\times 10^{-10}\exp(-9160/T)$ |  $E_{a}$ est. with $A$ based on FeO2 + O -¿ FeO + O2 from Rumminger et al. (1999)
TiH + H -¿ Ti + H2 | 8.3 $\times 10^{-11}$ | Est. from FeH + H -¿ Fe + H2 (Rumminger et al., 1999)
TiH + O -¿ Ti + OH | 1.66 $\times 10^{-10}$ | Est. from FeH + O -¿ Fe + OH (Rumminger et al., 1999)
TiH + CH3 -¿ Ti + CH4 | 1.0 $\times 10^{-10}$ | Est. from FeH + CH3 -¿ Fe + CH4 (Rumminger et al., 1999)
TiC + H -¿ Ti + CH | $1.0\times 10^{-10}\exp(-20109/T)$ |  $E_{a}$ est.
Ti + CO -¿ TiC + O | $8.0\times 10^{-10}\exp(-68842/T)$ |  $E_{a}$ est.
Ti + CN -¿ TiC + N | $5.0\times 10^{-10}\exp(-29543/T)$ |  $E_{a}$ est.
Ti + NO -¿ TiN + O | $5.0\times 10^{-11}\exp(-19706/T)$ |  $E_{a}$ est. with $A$ from matching Campbell & McClean (1993)
TiN + H -¿ Ti + NH | $10^{-10}\exp(-15655/T)$ |  $E_{a}$ est.
VO + O -¿ V + O2 |  $6.19\times 10^{-12}$ $\exp(-14763/T)$ |  $E_{a}$ est. with $A$ from matching NIST 1990RIT/WEI (at room temperature)
V + N2O -¿ VO + N2 |  $4.7\times 10^{-11}$ $\exp(-1299/T)$ | NIST 2000CAM/KOL
VO + H -¿ V + OH |  $1.66\times 10^{-10}$ $\exp(-22386/T)$ |  $E_{a}$ est. with $A$ based on FeO + H -¿ Fe + OH from Rumminger et al. (1999)
VO + H2 -¿ V + H2O |  $1.0\times 10^{-11}$ $\exp(-15239/T)$ |  $E_{a}$ est. with $A$ based on FeO + H2 -¿ Fe + H2O from Decin et al. (2018)
TiO2 -¿[M] Ti + O2 |  $k_{0}$ = $1.38\times T^{-1.8}$ $\exp(-94079/T)$ $k_{\infty}$ = $2\times 10^{17}$ $T^{-0.91}$ $\exp(-94079/T)$ |  $E_{a}$ est. $A$ based on FeO2 -¿[M] Fe + O2 from Rumminger et al. (1999)
TiO -¿[M] Ti + O |  $k_{0}$ = $1.38\times T^{-1.8}$ $\exp(-82202/T)$ $k_{\infty}$ = $2\times 10^{17}$ $T^{-0.91}$ $\exp(-76171/T)$ |  $E_{a}$ est. $A$ based on FeO -¿[M] Fe + O from Rumminger et al. (1999)
VO -¿[M] V + O |  $k_{0}$ = $1.38\times T^{-1.8}$ $\exp(-76171/T)$ $k_{\infty}$ = $2\times 10^{17}$ $T^{-0.91}$ $\exp(-76171/T)$ |  $E_{a}$ est. $A$ based on FeO -¿[M] Fe + O from Rumminger et al. (1999)

Table 6: Full List of Photolysis Reactions in VULCAN Photolysis |  Reaction |  Threshold (nm) |  Temp. Dependence (K) |  Reference
Cross Sections / Quantum Yields ($\lambda$ in nm)
---|---|---|---|---
H2O |  -¿ H + OH |  207 |  300, 423, 573, 1230, 1540, 1630, 1820, 2010, 2360 |  a, b, e / d, Stief et al. (1975); Slanger & Black (1982)
|  -¿ H2 + O(^1D) |  |  |
|  -¿ O + H + H |  |  |
CH4 |  -¿ CH3 + H |  145 |  — |  a / d ($\lambda$ $<$ 97.7), Gans et al. (2011) ($\lambda$ $\geq$ 118.2)
|  -¿ ^1CH2 + H2 |  |  |
|  -¿ ^1CH2 + H + H |  |  |
|  -¿ CH + H2 + H |  |  |
CH3 |  -¿ CH + H2 |  220 |  — |  a / Lavvas et al. (2008); Kassner & Stuhl (1994)
|  -¿ CH2 + H |  |  |
CH2 |  -¿ CH + H |  275 |  — |  a / a
CO |  -¿ C + O |  166 |  — |  a, b/ a
H2 |  -¿ H + H |  120 |  — |  a / a
C2H2 |  -¿ C2H + H |  217 |  — |  a / a, Okabe (1983)
CO2 |  -¿ CO + O |  202 |  150, 170, 195, 230, 300, 420, 500, 585, 700, 800, 1160 |  a, Venot et al. (2018) , e / b
|  -¿ CO + O(^1D) |  |  |
C2H4 |  -¿ C2H2 + H2 |  195 |  — |  a / Lavvas et al. (2008) and the references in
|  -¿ C2H2 + H + H |  |  |
|  -¿ C2H3 + H |  |  |
C2H6 |  -¿ C2H4 + H2 |  165 |  — |  a / b, Lias et al. (1970) (104 $<$ $\lambda$ $<$ 105)
|  -¿ C2H4 + H + H |  |  |
|  -¿ C2H2 + H2 + H2 |  |  |
|  -¿ CH4 + ^1CH2 |  |  |
|  -¿ CH3 + CH3 |  |  |
C4H2 |  -¿ C2H2 + C2 |  197 |  — |  a / Lavvas et al. (2008)
C6H6 |  -¿ C6H5 + H |  206 |  — |  a / Est. from Kislov et al. (2004)
|  -¿ C3H3 + C3H3 |  |  |
OH |  -¿ O + H |  265 |  — |  a / a, b ($\lambda$ $<$ 91)
HCO |  -¿ H + CO |  656 |  — |  a / a
H2CO |  -¿ H2 + CO |  360 |  — |  a / b ($\lambda$ $<$ 250), d
|  -¿ H + HCO |  |  |
CH3OH |  -¿ CH3 + OH |  220 |  — |  a / b, Hagege et al. (1968)
|  -¿ H2CO + H2 |  |  |
|  -¿ CH3O + H |  |  |
CH3CHO |  -¿ CH4 + CO |  350 |  — |  a / b
|  -¿ CH3 + HCO |  |  |
N2 |  -¿ N + N |  150 |  — |  a ($\lambda$ $<$ 100), c ($\lambda$ $>$ 120) / a
NH3 |  -¿ NH2 + H |  226 |  175, 300, 562 |  a / b
|  -¿ NH + H + H |  |  |
HCN |  -¿ H + CN |  179 |  — |  a / Nuth & Glicker (1982)
NO |  -¿ N + O |  202 |  |  a / a
NO2 |  -¿ NO + O |  398 |  |  b, Voigt et al. (2002) / b, d
NO3 |  -¿ NO2 + O |  703 |  — |  b / b, Sander et al. (2015)
|  -¿ NO + O2 |  |  |
N2O |  -¿ NO + O(^1D) |  340 |  300, 714, 833, 1000, 1250, 1667, 2000 |  a,c (Zuev & Starikovskii, 1990)) / b
HNO2 |  -¿ NO + OH |  591 |  — |  b / b
HNO3 |  -¿ NO2 + OH |  598 |  — |  b / b
N2O5 |  -¿ NO3 + NO2 |  500 |  — |  b / b (from here)
|  -¿ NO3 + NO + O |  |  |
N2H4 |  -¿ N2H3 + H |  291 |  — |  c (BiehlStuhl(1991) and Vaghjiani(1993) 296K 191-291n) / Lavvas et al. (2008)
O2 |  -¿ O + O |  240 |  200, 250, 300, 873, 1073 |  a / b,d
|  -¿ O + O(^1D) |  |  |
O3 |  -¿ O2 + O |  900 |  — |  a / Matsumi(2002)
|  -¿ O2 + O(^1D) |  |  |
HO2 |  -¿ O + OH |  275 |  — |  a / a
H2O2 |  -¿ OH + OH |  350 |  — |  a / a
HNCO |  -¿ NH + CO |  354 |  — |  b / b
|  -¿ H + NCO |  |  |
SH |  -¿ S + H |  345 |  300, 500, 750, 1000, 1250, 1500, 1750, 2000, 2250, 2500, 3000 |  a, Gorman et al. (2019) for $\lambda$ $\geq$ 314 nm / a
H2S |  -¿ SH + H |  238 |  423, 573, 773 |  a, e / a
SO |  -¿ S + O |  235 |  — |  a / a
SO2 |  -¿ SO + O |  220 |  — |  a / a
|  -¿ S + O2 |  |  — |  a / a
S2 |  -¿ S + S |  283 |  — |  a / a
S4 |  -¿ S + S |  575 |  — |  a / a
OCS |  -¿ CO + S |  280 |  — |  a / a
CS |  -¿ C + S |  160 |  — |  a / a
CS2 |  -¿ CS + S |  278 |  300, 423, 573, 773 |  a / a
CH3SH |  -¿ CH3S + H |  310 |  — |  a / b
|  -¿ CH3 + SH |  |  |

a: Leiden Observatory
database303030http://home.strw.leidenuniv.nl/~ewine/photo (Heays et al., 2017)
b: PHIDRATES database313131http://phidrates.space.swri.edu (Huebner et al.,
1992) c: MPI-Mainz UV/VIS Spectral Atlas
323232http://satellite.mpic.de/spectral_atlas/index.html (Keller-Rudek et al.,
2013)) d: Sander et al. (2015) e: ExoMol database
333333http://www.exomol.com/data/data-types/xsec_VUV

##  Appendix C The Choice of Zenith Angle

A global or hemispheric average 1-D photochemical model requires specifying an
effective zenith angle ($\overline{\theta}$) of the stellar beam to represent
the planetary-mean actinic flux. The zenith angle of 48∘ – 60∘ has been used
for the hemispheric average in various photochemical models (e.g. Moses et al.
(2011); Hu et al. (2012)). For instance, a common choice in radiative transfer
calculation is to take the flux-weighted cosine of the zenith angle (Cronin,
2014):

$\overline{\mu_{\textrm{I}}}=\frac{\int_{0}^{2\pi}\int_{0}^{1}\mu F_{0}\mu
d\mu d\phi}{\int_{0}^{2\pi}\int_{0}^{1}F_{0}\mu d\mu d\phi}$ (C1)

where $\phi$ is the azimuth angle and $F_{0}$ is the stellar flux at the top
of atmosphere. Equation (C1) yields $\overline{\mu_{\textrm{I}}}$ = 2/3 or
$\overline{\theta_{\textrm{I}}}\approx$ 48∘. For photochemistry calculation,
actinic-flux-weighted cosine should be considered and Equation (C1) becomes

$\overline{\mu_{\textrm{II}}}=\frac{\int_{0}^{1}\mu
J_{0}d\mu}{\int_{0}^{1}J_{0}d\mu}$ (C2)

where $J_{0}$ is the actinic flux at the top of atmosphere (i.e. total
intensity) and the azimuth term is dropped. Equation (C2) now yields
$\overline{\mu_{\textrm{II}}}$ = 1/2 or $\overline{\theta_{\textrm{II}}}$ =
60∘.

Hu et al. (2012) discuss this choice of mean zenith angle by further
considering the optical depth of the level where the hemispheric average of
the attenuated actinic flux is evaluated, e.g., the authors find a mean zenith
angle of 57∘ and 48∘ correspond to optical depth 0.1 and 1, respectively. We
will revisit the discussion of Hu et al. (2012) but with a different approach
here.

Instead of taking the average of $\mu$, we consider an effective zenith angle
such that the resulting mean actinic flux matches the hemispheric-mean actinic
flux, viz.

$\displaystyle J_{0}\,\textrm{exp}(-\frac{\tau}{\overline{\mu}})$
$\displaystyle=\frac{\int_{0}^{1}J_{0}\,\textrm{exp}(-\frac{\tau}{\mu})d\mu}{\int_{0}^{1}d\mu}$
(C3) $\displaystyle=J_{0}\int_{0}^{1}\textrm{exp}(-\frac{\tau}{\mu})d\mu.$

Equation (C3) can be evaluated numerically at the given optical depth, as
illustrated in Figure 40. We find that optical depth unity (i.e. where UV
photons are mostly utilized for photochemistry) corresponds to
$\overline{\theta}$ $\approx$ 58∘. Note that the evaluation in Hu et al.
(2012) is similar to Equation (C3) but weighted by $\mu$ within the integral,
which is effectively the mean stellar flux instead of the actinic flux.
Evaluating Equation (C3) at $\tau=1$, we find $\overline{\theta}$ $\approx$
58∘ for a dayside-average model. For a terminator-average model, the
denominator in Equation (C3) is integrated from -1 to 1 and we have
$\overline{\theta}$ $\approx$ 67∘.

Figure 40: Dayside mean zenith angle for photochemical calculation as a
function of optical depth from Equation (C3). Figure 41: Comparisons of
selective rate constants of Reaction (19): CO + OH -¿ CO2 + H with wide
temperature ranges available on NIST.

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