# Contextualizing Argument Quality Assessment with Relevant Knowledge

Darshan Deshpande Zhivar Sourati Filip Ilievski Fred Morstatter
Information Sciences Institute, University of Southern California
{darshang, souratih, ilievski<EMAIL_ADDRESS>
###### Abstract

Automatic assessment of the quality of arguments has been recognized as a
challenging task with significant implications for misinformation and targeted
speech. While real-world arguments are tightly anchored in context, existing
efforts to judge argument quality analyze arguments in isolation, ultimately
failing to accurately assess arguments. We propose SPARK: a novel method for
scoring argument quality based on contextualization via relevant knowledge. We
devise four augmentations that leverage large language models to provide
feedback, infer hidden assumptions, supply a similar-quality argument, or a
counter-argument. We use a dual-encoder Transformer architecture to enable the
original argument and its augmentation to be considered jointly. Our
experiments in both in-domain and zero-shot setups show that SPARK
consistently outperforms baselines across multiple metrics. We make our code
available to encourage further work on argument assessment.

##  1 Introduction

Reliable analysis of arguments in natural language holds the promise to
support applications such as automated grading Ludwig et al. (2021), and
tackling misinformation and targeted speech Alhindi, Tariq (2023).
Computational argument analysis has been relatively popular through tasks like
argument extraction Chakrabarty et al. (2019), evidence mining Rinott et al.
(2015), relation assignment Trautmann et al. (2020), writing support Stab and
Gurevych (2014b) and claim generation Bilu and Slonim (2016). A particularly
challenging task is argument quality assessment Fromm et al. (2022), which
addresses the cogency, effectiveness, and reasonableness of an argument
Wachsmuth et al. (2017b) given a topic. For instance, on the topic of whether
cell phones are distracting, one may argue that cell phones are distracting
and dangerous while driving (Figure 1). Assessing quality of the argument
involves analyzing the objective evidence, relevant assumptions and structural
soundness, making the overall task difficult.

Figure 1: Overview of SPARK.

Research on argument quality assessment has focused on extracting textual
patterns using various learning frameworks and content features Lauscher et
al. (2022). Yet, it has been widely recognized that contextualizing arguments
with implicit knowledge from external documents Marro et al. (2022) or visual
data Hasan et al. (2021) can be informative for models. Claim revisions help
models learn by contrasting data Skitalinskaya et al. (2021) while generating
explicit conclusions can help the assessment of the persuasiveness of an
argument Gurcke et al. (2021). We note that prior work has focused on
individual enrichment strategies, however, they have not explored enrichments
as a system of necessary contextual information.

In this work, we investigate the following research question: Does augmenting
arguments with contextually relevant background knowledge enhance model
judgments of argument quality? We devise SPARK: a novel framework for
contextualizing arguments based on additional evidence with two innovations.
First, it includes augmentation strategies that employ a large language model
(LLM), GPT 3.5 OpenAI (2022), to contextualize an argument with elements
prominent in argumentation literature Nickerson (2020); Mulyati et al. (2023);
Harvey (2009): feedback, assumptions, arguments with a similar quality, and
counter-arguments. Second, we process the original argument and its
augmentations separately by using a dual-encoder language modeling
architecture with a multi-head cross-attention layer that dynamically weights
all augmentations for a novel example. We experiment with in-domain and out-
of-domain corpora to show the effectiveness of the SPARK’s augmentation
strategies and architecture. We make our code available to facilitate future
work on contextualizing argumentation with external
knowledge.111https://github.com/usc-isi-i2/forecast-argument

##  2 Background

###  2.1 Task Formulation

Following prior work Gretz et al. (2020); Lauscher et al. (2020), we formalize
argumentation quality assessment as a regression task predicting the quality
of an argument in natural language. The task input consists of a topic and
argument. For the output, we evaluate three quality indicators: 1) cogency,
which determines if the premise of the argument is relevant and sufficient
with respect to the conclusion, 2) effectiveness, which measures the
persuasive power of the argument with respect to aspects such as arrangement,
clarity, and appropriateness, and 3) reasonableness, which determines the
sufficiency of the argument to resolve the debate’s issue Wachsmuth et al.
(2017a), following Lauscher et al. (2020). We assume that the overall quality
of an argument can be approximated by averaging these three metrics Gretz et
al. (2020).

###  2.2 Connection to Prior Studies

The introduction of benchmarks for argument quality Stab and Gurevych (2014a);
Gretz et al. (2020) has inspired a variety of methods based on logistic
regression Ghosh et al. (2016), fully connected and recurrent neural networks
Habernal and Gurevych (2016), and lately, fine-tuned Transformer models Toledo
et al. (2019). Lauscher et al. (2022) study the categories of knowledge needed
for argumentation and observe that argument assessment research so far has
focused on linguistic, task-specific, and argument-specific knowledge.This
reiterates Hulpus et al. (2019) that contextualizing an argument with implicit
knowledge is essential to understand its quality. Durmus and Cardie (2018)
incorporate users’ prior beliefs as predictors of argument persuasiveness, El
Baff et al. (2020) train classifiers for different audience groups, and Al
Khatib et al. (2020) utilize historical behavior to predict persuasion. Marro
et al. (2022) augment an argument with documents that support or refute it,
whereas Hasan et al. (2021) augment the textual elements of arguments with
visual features. Most similar to SPARK, Skitalinskaya et al. (2021) leverage
revisions on the same claims, while Gurcke et al. (2021) generate conclusions
to assess argument sufficiency. Nevertheless, annotating datasets with
conclusions and revisions for these methods is a costly and time-consuming
process. Inspired by prior work, SPARK is a framework that supports four novel
augmentation strategies based on argument analysis.

##  3 SPARK

Augmentation Strategies: We devise four augmentation techniques to
contextualize argumentative tasks. We generate the augmentations with a LLM,
GPT 3.5 OpenAI (2022), and provide the complete prompts in the appendix.

Feedback:  Constructive feedback, formalized as writing comments and
suggestions, helps to understand the organization of text and induces domain
knowledge Mulyati et al. (2023). We hypothesize that identification of the
strengths and weaknesses of arguments can help computational methods rank
arguments more effectively. In the example in Figure 1, the feedback addresses
appeal to emotion, lack of evidence, and generalization. We prompt the LLM in
a zero-shot setting, by instructing it to provide feedback for a topic-
argument pair.

Assumptions:  Arguments are often biased by unstated assumptions Nickerson
(2020). Analysis of assumptions in arguments may help identify hidden biases
which may not be explicit. We expect that making assumptions explicit helps
determine the persuasiveness and relevance of the argument. As observed in
Figure 1, a key assumption is that people do not take driving seriously, which
is key in assessing the argument’s quality. We use an LLM in a zero-shot
setting, instructing it to extract assumptions that underlie the argument.

Similar-quality instance: Prior work leveraging claim revisions Skitalinskaya
et al. (2021) posits that comparing arguments with those of similar-quality
leads to more robust argument assessment. We expect that it is beneficial to
retrieve arguments with a similar quality at training time as additional
evidence helps the model to learn better. We enhance the arguments by
introducing a synthetic argument derived from the given argument and that
exhibits similar reasonableness, cogency, and effectiveness. We prompt an LLM
to create an argument in a few-shot setting, by providing it the original
argument together with example arguments with quality scores (1-5). As we do
not have access to argument scores during inference, we provide the model with
a similar-quality argument with a probability of $\gamma=0.5$ during training,
which acts as a masking probability. This allows the model to work when a
similar quality argument is lacking.

Counter-arguments: Counter-arguments provide objections, alternatives, and
possible doubts of a skeptical reader Harvey (2009). As counter-arguments
allow the model to contrast two dissimilar arguments and evaluate their
strengths and weaknesses, we expect them to be effective in assessing the
quality of the arguments. The counter-argument in Figure 1 counters the
original argument by making a firm claim that alternative activities (e.g.,
eating) lead to distractions and solely blaming phones is unfair. We ask the
LLM to provide a counter-argument for a topic and an argument in a zero-shot
setting.

Figure 2: Dual BERT Encoder Architecture.

SPARK’s Dual Encoder Architecture: To enable the model to encode the original
argument in contrast with the additional evidence, we propose a dual encoder
(Figure 2) as an improvement to the Gillick et al. (2018) architecture. The
first encoder embeds the topic and argument, whereas the second encoder embeds
the augmentations into a fixed dimensional space. We use a multi-head cross-
attention layer Vaswani et al. (2017) to adjust the model’s focus on each
augmentation with respect to the argument and the topic. We pass the attention
outputs to a mean pooler, whose output is fed into three separate regressor
heads, one per quality metric. In addition to the ability of this model to
encode the original input and the further evidence separately, it affords the
additional benefit of handling twice as many tokens in the input sequence
compared to a single Transformer encoder.

Table 1: Performance of Dual-BERT model with augmentations applied in comparison to the baseline models. The performance of the model achieving the best scores per metric is boldfaced and the second best score is underlined. Model | Augmentation | GAQ Corpus (in-domain) | IBM-Rank-30K (ZS)
---|---|---|---
|  | Cogency | Effectiveness | Reasonableness | WA
|  | $\sigma$ | $\rho$ | $\sigma$ | $\rho$ | $\sigma$ | $\rho$ | $\sigma$ | $\rho$
BERT | - | 0.3480 | 0.3268 | 0.2804 | 0.2821 | 0.3285 | 0.3356 | 0.1989 | 0.1751
XLNet | - | 0.1790 | 0.1673 | 0.2008 | 0.1930 | 0.1778 | 0.1847 | 0.1989 | 0.1816
BERT | DPR | 0.3215 | 0.3182 | 0.2728 | 0.2763 | 0.2821 | 0.3012 | 0.0706 | 0.0774
XLNet | DPR | 0.2459 | 0.1778 | 0.2259 | 0.2271 | 0.2024 | 0.2160 | 0.1201 | 0.1254
Dual BERT | DPR | 0.3536 | 0.3525 | 0.3227 | 0.3224 | 0.3396 | 0.3497 | 0.1571 | 0.1408
BERT | Our-All | 0.3418 | 0.3340 | 0.2863 | 0.3047 | 0.3459 | 0.3664 | 0.1510 | 0.1374
XLNet | Our-All | 0.2675 | 0.1930 | 0.2450 | 0.2060 | 0.2142 | 0.2046 | 0.1318 | 0.1352
Dual BERT | Our-All | 0.4242 | 0.4371 | 0.4513 | 0.4762 | 0.4135 | 0.4362 | 0.2238 | 0.2293
Dual BERT | Feedback | 0.4184 | 0.4187 | 0.3925 | 0.4037 | 0.4174 | 0.4318 | 0.2742 | 0.2854
Dual BERT | Assumptions | 0.3699 | 0.3704 | 0.3881 | 0.3946 | 0.3681 | 0.3806 | 0.1728 | 0.1769
Dual BERT | Similar quality argument | 0.4059 | 0.4038 | 0.4150 | 0.4252 | 0.3545 | 0.3775 | 0.2629 | 0.2037
Dual BERT | Counter-argument | 0.4030 | 0.4092 | 0.4048 | 0.4143 | 0.3989 | 0.4171 | 0.2086 | 0.2044

##  4 Experiments

###  4.1 Baselines

Encoder models: We use bert-base-uncased Devlin et al. (2019) as a baseline
encoding model. To prove that disjoint embeddings work better for our task, we
compare our dual BERT with a standard BERT model. To compare the efficacy of
the dual BERT architecture over models that can handle longer token sequences
than 512 tokens, we include XLNet Yang et al. (2019).

Alternative augmentation strategies: We test each augmentation in combination
and individually. To test the effect of augmentations, we compare against
ablated baselines without augmentations. Finally, we compare against Wikipedia
paragraph augmentations extracted using the state-of-the-art method of dense
passage retrieval (DPR) Karpukhin et al. (2020).

###  4.2 Datasets and Evaluation

We use the GAQCorpus Lauscher et al. (2020) as our training dataset for its
diversity of domains and quality metrics. The GAQCorpus includes three
domains: reviews, QA, and debates, and uses three quality metrics: cogency,
effectiveness, and reasonableness. Additionally, we use the IBM-Rank-30K Gretz
et al. (2020) dataset to perform zero-shot experiments by averaging the three
metric scores (denoted as WA), similar to Lauscher et al. (2020). This is
because there is a high correlation between the weighted average metric used
by the IBM-30K and those metrics used by GAQCorpus, as observed by Lauscher et
al. (2020). We use the Pearson ($\rho$) and Spearman ($\sigma$) coefficients
between the predictions and ground truth to assess our models.

###  4.3 Results

We investigate whether augmentation strategies help language models assess the
quality of arguments more accurately (Q1); how different augmentation
strategies compare to each other (Q2); and how the proposed method and
baselines generalize to novel benchmarks (Q3).

Effect of augmentation on in-domain performance (Q1) Table 1 shows that the
overall best-performing combination uses Dual BERT with all four augmentations
combined, which improves the Spearman correlation over the baseline BERT by
0.08-0.17 across the three metrics. The improvement is the largest for
effectiveness, where the Spearman correlation increases from 0.28 to 0.45 (61%
relative increase). We also note a significant increase in the correlation for
the baseline models. Both single BERT encoder and XLNet see a performance
increase consistently across all metrics when using our augmentations. DPR, in
contrast, improves XLNet’s performance but not BERT’s. We believe that this is
due to the token limit of BERT, which does not hold for XLNet.

Comparison of augmentation variants (Q2) We experiment with using one
augmentation strategy at a time and compare these results against the method
that uses all augmentations jointly. We note that leveraging the argument
feedback is most effective for predicting argument cogency and reasonableness,
which is intuitive, given that the feedback exposes weak points and
argumentation flaws that directly relate to these two metrics as observed in
Table 2. On the other hand, considering arguments with a similar-quality
instance is optimal for predicting the effectiveness of the argument. We
credit the few-shot setup for the impact of similar-quality instances on
effectiveness. We believe that illustrating how the argument structure,
arrangement, and wording vary with variations in the output scores is
advantageous to the effectiveness metric, which aligns with the definition
provided in 2.1. We explore the impact of different effectiveness scores on
the LLM-generated output in the appendix.

Results on out-of-domain task (Q3) SPARK outperforms all baselines in the
zero-shot setting on the IBM-Rank-30K dataset even more convincingly. Here,
the best performance is obtained by the feedback-augmented Dual BERT model.
This model even outperforms the Dual BERT with all augmentations. This
suggests that feedback augmentation is more relevant across domains as the
IBM-Rank-30K and GAQCorpus have different sources of data. Meanwhile,
augmentation with DPR is consistently harmful, as is the augmentation with our
method with the single-encoder methods. These results emphasize the
effectiveness of combining dual encoding with complementary augmentation
strategies and show that merely adding more data may not yield strong
generalization.

##  5 Conclusions

In this paper, we aid quality estimation models by contextualizing the
argument content by providing feedback, inferring assumptions, and providing
arguments with similar quality or counter-arguments. To effectively contrast
the information between the argument and the additional evidence, we provide
them separately within a Dual BERT-based architecture. Our experiments reveal
that the best performance is obtained with all augmentations together,
weighted with an attention mechanism, revealing that they bring complementary
insights. The performance of SPARK with Dual BERT is significantly higher
compared to single BERT or XLNet, which is capable of handling extended
sequence lengths. SPARK also outperforms the baselines and alternative
augmentations in a zero-shot setting. We note that feedback augmentation
performs best on both in- and out-of-domain settings, whereas including an
argument with a similar quality argument is especially helpful for estimating
argument effectiveness. In the future, we will extend SPARK by augmentations
based on factual knowledge and study the relation between augmentation
strategies, models, and argument quality metrics.

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##  Appendix A Appendix

Table 2: Augmentation examples for the topic Do cell phones cause a distraction to people? with argument: If you mean do they cause a distraction when driving the answer is a resounding YES!!! That includes bluetooth or speaker. Nothing makes me more angry when people don’t take driving as seriously as they should. It is a major killer and if you don’t follow the rules and focus you are putting other people in danger. Feedback |  \- The argument takes a clear position that cell phones cause distraction while driving.
\- The writer expresses strong emotions regarding the topic, which may
influence the persuasiveness of the argument.
\- The argument does not provide any evidence or supporting details beyond the
writer’s personal experience and emotions.
\- The argument does not address whether cell phones cause distractions in
other contexts beyond driving.
---|---
Assumptions |  \- Cell phones cause a distraction when driving.
\- Bluetooth or speaker use of cell phones can also be a distraction while
driving.
\- People don’t take driving as seriously as they should.
Similar quality argument |  Yes, cell phones can be a major distraction to people. People are constantly checking their phones for notifications, messages, and other tasks that can take away from what they should be focusing on. This can lead to people not paying attention in class, not being productive at work, and not being present in conversations. Cell phones are an amazing invention, but they can also be a major distraction.
Counter-Argument |  While it is true that distracted driving can be a major problem, it is unfair to blame cell phones as the sole cause of distraction. Many other factors can also contribute to distracted driving, such as eating, applying makeup, or even talking with passengers. Furthermore, cell phones can also be used in a responsible manner while driving, such as with the use of hands-free devices or by pulling over to take a call. Therefore, instead of demonizing cell phones, we should focus on educating drivers on safe driving practices and the dangers of distracted driving in general.

###  A.1 GPT 3.5 Prompt Templates

Feedback
The feedback on writing is sampled by considering both the topic and the
argument related to the topic. To ensure brevity, we output the feedback in
bullet point format. We follow the format below for sampling the feedback from
the LLM:

Give concise writing feedback for the following argument in context with the
topic, preferably in bullet points:
Topic: topic
Argument: argument.

Assumptions
Similar to feedback, assumptions are sampled in bullet point format to ensure
brevity. Additionally, to constrain the hallucinations of the LLM, we restrict
it to output "No assumptions" for the cases where it does not find assumptions
or biases. We use the below prompt to sample this assumptions list:

Summarize the assumptions, if any, in the following argument in a bullet
format otherwise return "No assumptions"
Topic: topic
Argument: argument.

Similar quality argument
To sample a similar quality argument, we use the following template:

Cogency Score: cogency score
Effectiveness Score: effectiveness score
Reasonableness Score: reasonableness score
Topic: topic

We use ten samples in the few shot setting with two each from every integer
ranking from 1-5 on the ranking scale for each metric. Finally, we prompt the
LLM to generate the argument with respect to the cogency, effectiveness and
robustness scores.

Counter-argument
The counter-argument is generated using the given argument and topic, and the
following template:

Give a counter-argument for the following argument with respect to the Topic:
topic
Argument: argument

Effectiveness Score |  Generated similar quality argument to: Do you equate legality with morality?
---|---
1.0 |  Yes, I think that if the law says something is wrong, then it is wrong. People should follow the law and not do anything illegal.
2.0 |  No, I do not think that legality necessarily equates to morality. Laws can often be outdated, biased, or simply not reflective of what is right and wrong. For example, slavery used to be legal in many countries, yet it was obviously immoral. So legality and morality do not always align.
3.0 |  No, I do not equate legality with morality. Just because something is legal does not make it moral, and just because something is illegal does not make it immoral. Laws are made by people and can be changed, while morality is often determined by an individual’s personal values and beliefs. Therefore, legality should not be used as a measure of morality.
4.0 |  No, I do not equate legality with morality. I believe that there are laws that should be followed in order to maintain the peace and order of a society, but there are also moral standards that must be adhered to for the same purpose. For example, it may be legal in some places to drive over the speed limit, but it is still morally wrong to do so.
5.0 |  I do not necessarily equate legality with morality. Legality is based on laws, which can be changed to reflect the morality of a society. Morality, in contrast, is based on principles and values that don’t necessarily have to be enforced by law. For example, while it may be legal to drive over the speed limit, it is not necessarily moral to do so.
Table 3: Similar quality examples.

###  A.2 Augmentation examples

Table 2 shows augmentation examples for one topic-argument pair. The topic
questions if cell phones distract people and the argument agrees with it in
context to distracted driving due to cell phones.

Feedback:  The feedback discusses how the argument takes a clear position but
appears overly emotional while answering, which may influence the
persuasiveness of the argument. Additionally, the feedback regarding lack of
evidence other than personal experience and the lack of discussion on phones
causing a distraction beyond driving aim to help improve understanding while
ensuring that the model pays careful attention to the topic in context.

Assumptions: The LLM lists several important assumptions in the proposed
argument with respect to the topic. The first is the base assumption of the
author’s perspective, which is that cell phones cause distraction during
driving. The LLM extracts the sentence " people don’t take driving as
seriously as they should" and labels it as an assumption because this is a
faulty generalization to apply a general rule to all people, which is, in this
case, people not taking driving seriously.

Similar quality argument:  The generated similar quality argument tries to
replicate the structural pattern of the given argument. The similar quality
instance contains open-ended, long-winded sentences such as "Cell phones are
an amazing invention, but they can also be a major distraction" which reduce
the score of the argument, similar to the original argument. We also see that
the LLM understands the ranking progression in a few shot setting and similar
to the original argument, the similar quality argument also focuses solely on
driving based cell phone distractions.

Counter argument: We notice that the LLM recognizes that the original argument
only discusses distracted driving and so it only produces a counter argument
of the stance that distracted driving is not the only cause for distraction.
The response discusses the safe use of cell phones such as hands free, etc and
advocates educating drivers on the effects of cell phone based distracted
driving.

###  A.3 Impact of effectiveness score on GPT 3.5 outputs for similar quality
argument

Table 3 discusses the impact of effectiveness score on the generated similar
quality argument. As can be seen in Table 3, the generated argument with an
effectiveness score of 1.0 oversimplifies the relationship between legality
and morality and treats related laws as fixed. Comparatively, the argument
with an effectiveness score of 2.0 provides an example of slavery which
enhances the effectiveness of the argument. Despite the addition of this
example, the second argument lacks elaboration on why the example is immoral
and fails to provide relevant evidence. The argument generated, given an
effectiveness score of 3.0, recognizes that the law is not the sole arbiter of
morality and that laws are subject to change. It does not only highlight the
potential flaws in legal systems but also addresses the distinction between
personal values and the law. However, this argument oversimplifies morality by
implying that personal values and beliefs solely determine morality and lacks
supporting evidence for the statement: just because something is legal does
not make it moral, and just because something is illegal does not make it
immoral.. The argument generated with an effectiveness score of 4.0 considers
the coexistence of legal and moral standards. The addition of a specific
example in this argument adds concreteness and strengthens its persuasiveness.
However, the argument can be further strengthened by acknowledging a broader
range of situations where legality and morality may diverge. Finally, the
argument ranked with the highest effectiveness score emphasizes the
independence of morality from legal enforcement, which makes it even more
persuasive. The contrasting comparison adds clarity to the flow of the
argument and hence makes it better than all previously generated arguments.


# Molecular Gas within the Milky Way’s Nuclear Wind

Frances H. Cashman Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA  Andrew J. Fox AURA for ESA, Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Blair D. Savage
Department of Astronomy, University of Wisconsin-Madison, 475 North Charter
Street, Madison, WI 53706, USA  Bart P. Wakker Department of Astronomy,
University of Wisconsin-Madison, 475 North Charter Street, Madison, WI 53706,
USA  Dhanesh Krishnarao NSF Astronomy & Astrophysics Postdoctoral Fellow,
Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA
Department of Physics, Colorado College, 14 East Cache La Poudre Street,
Colorado Springs, CO 80903, USA  Space Telescope Science Institute, 3700 San
Martin Drive, Baltimore, MD 21218, USA  Robert A. Benjamin Department of
Physics, University of Wisconsin-Whitewater, 800 West Main Street, Whitewater,
WI 53190, USA  Philipp Richter Institut für Physik und Astronomie, Universität
Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, D-14476, Potsdam, Germany
Trisha Ashley Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA  Edward B. Jenkins Department of Astrophysical
Sciences, Princeton University, Princeton, NJ 08544-1001, USA  Felix J.
Lockman Green Bank Observatory, P.O. Box 2, Rt. 28/92, Green Bank, WV 24944,
USA  Rongmon Bordoloi Department of Physics, North Carolina State University,
421 Riddick Hall, Raleigh, NC 27695-8202, USA  Tae-Sun Kim  Department of
Astronomy, University of Wisconsin-Madison, 475 North Charter Street, Madison,
WI 53706, USA

(Received November 10, 2021; Revised November 21, 2021; Accepted November 22,
2021)

###### Abstract

We report the first direct detection of molecular hydrogen associated with the
Galactic nuclear wind. The Far-Ultraviolet Spectroscopic Explorer spectrum of
LS 4825, a B1 Ib–II star at $l,b$ = 1.67°,$-$6.63° lying $d$ =
9.9${}^{+1.4}_{-0.8}$ kpc from the Sun, $\sim$1 kpc below the Galactic plane
near the Galactic Center, shows two high-velocity H2 components at
$v_{\mathrm{LSR}}$ = $-79$ and $-108$ km s-1. In contrast, the FUSE spectrum
of the nearby ($\sim$0.6° away) foreground star HD 167402 at
$d$=4.9${}^{+0.8}_{-0.7}$ kpc reveals no H2 absorption at these velocities.
Over 60 lines of H2 from rotational levels $J$ = 0 to 5 are identified in the
high-velocity clouds. For the $v_{\mathrm{LSR}}$ = $-79$ km s-1 cloud we
measure total log $N$(H2) $\geq$ 16.75 cm-2, molecular fraction
$f_{\mathrm{H_{2}}}$ $\geq$ 0.8%, and $T_{01}$ $\geq$ 97 and $T_{25}$ $\leq$
439 K for the ground- and excited-state rotational excitation temperatures. At
$v_{\mathrm{LSR}}$ = $-108$ km s-1, we measure log $N$(H2) = 16.13 $\pm$ 0.10
cm-2, $f_{\mathrm{H_{2}}}$ $\geq$ 0.5%, and $T_{01}$ = 77${}^{+34}_{-18}$ and
$T_{25}$ = 1092${}^{+149}_{-117}$ K, for which the excited-state ortho- to
para-H2 is 1.0${}^{+0.3}_{-0.1}$, much less than the equilibrium value of 3
expected for gas at this temperature. This non-equilibrium ratio suggests that
the $-108$ km s-1 cloud has been recently excited and has not yet had time to
equilibrate. As the LS 4825 sight line passes close by a tilted section of the
Galactic disk, we propose that we are probing a boundary region where the
nuclear wind is removing gas from the disk.

Galactic Center (565) — Galactic winds (572) — Molecular gas (1073) —
Ultraviolet astronomy (1736)

††journal: ApJL††facilities: FUSE, GBT, HST (STIS)††software: linetools
(Prochaska et al., 2017)

##  1 Introduction

The Galactic Center (GC) is host to the Milky Way’s (MW) nuclear wind, powered
by the supermassive black hole Sagittarius A∗ and surrounding regions of
intense star formation. Evidence for the nuclear activity comes from multiple
sources, the most notable being the Fermi (Su et al., 2010; Ackermann et al.,
2014) and eROSITA Bubbles (Bland-Hawthorn & Cohen, 2003; Predehl et al.,
2020), giant gamma- and X-ray lobes extending $\sim$10 kpc above and below the
Galactic plane (see Figure 1), which outline the present boundaries of the
wind (see also Sofue & Kataoka, 2021). Additional evidence is provided by an H
I outflow, seen in the form of several hundred hydrogen 21 cm clouds (McClure-
Griffiths et al., 2013; Di Teodoro et al., 2018; Lockman et al., 2020)
detected at low latitude within the Fermi Bubbles. Finally, ultraviolet (UV)
absorption-line studies reveal high-velocity absorption in low-ionization
(e.g. C I, O I, S II) and high-ionization (e.g. C IV, Si IV) species in sight
lines through the Fermi Bubbles. These UV absorbers trace outflowing gas that
spans an extremely large range in physical conditions (Keeney et al., 2006;
Zech et al., 2008; Fox et al., 2015; Bordoloi et al., 2017; Savage et al.,
2017; Karim et al., 2018; Ashley et al., 2020). Nuclear outflow is also
detected in H$\alpha$ emission (see Krishnarao et al. 2020a).

Together these observations suggest that a multiphase nuclear outflow exists,
with neutral, warm-ionized, and highly ionized components. But until now, very
little information on _molecular_ gas in the nuclear outflow has existed, with
the only information being from two CO emission-line clouds reported by Di
Teodoro et al. (2020), and no detection in near-IR H2 emission lines (Fox et
al., 2021). ALMA observations toward J1744-3116 show millimeter-wave molecular
absorption (HCO+, HCN, CS) at velocities arising inside the Galactic bulge
near the GC (Liszt & Gerin, 2018).

High-velocity molecular gas is rarely detected _anywhere_ in the Galactic
halo, not just the GC. The only UV absorption-line detections of H2 in high-
velocity clouds (HVCs) are by Richter et al. (1999, 2001), Sembach et al.
(2001), and Wakker (2006), with low molecular fractions $f$(H2)$\sim
10^{-6}-10^{-2}$.

In this paper, we present the first detection of H2 associated with the MW
nuclear wind from analysis of archival spectra of two closely spaced low-
latitude stars, LS 4825 and HD 167402, observed by the Far-Ultraviolet
Spectroscopic Explorer (FUSE; Moos et al., 2000). At low latitudes close to
the GC, tracing the nuclear outflow is complicated by irregularities in the
shape of the Galactic disk (Liszt & Burton, 1980; Krishnarao et al., 2020b),
which make the disk/wind separation nontrivial. The sight lines lie in close
proximity to a warped portion of the Galactic disk, indicating that we may be
probing an interface between the disk and the nuclear wind.

Figure 1: (Left) Edge-on depiction of the Galaxy, with the positions of LS
4825 and HD 167402 marked at their Gaia EDR3 distances of 9.9 and 4.9 kpc,
respectively, from the Sun. The purple symmetric lobes show the Fermi Bubbles
(image adapted from NASA’s Goddard Space Flight Center). The blue edges of the
lobes show X-ray emission from ROSAT (Bland-Hawthorn & Cohen, 2003). The inset
panels show the absorption profiles of H2 $J$ = 3 1053.9 Å, one of over 60
lines of H2 detected in the FUSE spectra. The vertical line at 0 km s-1 marks
absorption associated with the MW. The strong absorption shaded in orange near
$-100$ km s-1 in the background spectrum of LS 4825 is not present in the
foreground spectrum of HD 167402, thus bracketing the absorbing region to
$4.9<d<9.9$ kpc. (Right) 21 cm H I emission map from the GASS survey showing
the H I column density at the Galactic tangent points (red scale) from Lockman
& McClure-Griffiths (2016) and at velocities anomalous to circular rotation
which track the tilt of the disk near the Galactic Center (green scale: left
half from $-110$ to $-70$ km s-1, right half from $+70$ to $+110$ km s-1). The
black squares denote the gamma-ray boundaries of the Fermi bubbles from Su et
al. (2010). The foreground FUSE sight line toward HD 167402 at $d$ = 4.9 kpc
is marked with a blue circle and the background sight line toward LS 4825 at
$d$ = 9.9 kpc is marked with a magenta triangle.

##  2 H2 Data and Measurements

LS 4825 is a B1 Ib–II blue supergiant with extinction $E(B-V)$ = 0.24 (Savage
et al. 2017, hereafter S17) located at $l,b$ = 1.67°,$-$6.63°. HD 167402, a B0
Ib supergiant with $E(B-V)$ = 0.23 (Shull & Danforth, 2019), lies $\sim$0.6°
away at a maximum projected distance of $\sim$50 pc, at $l,b$ =
2.26°,$-$6.39°. Ryans et al. (1997) measured a spectroscopic distance of
21$\pm$5 kpc for LS 4825, though recent Gaia EDR3 astrometry measurements
(Bailer-Jones et al., 2021) place LS 4825 at a much closer distance of
9.9${}^{+1.4}_{-0.8}$ kpc. HD 167402 has multiple estimates of its
spectrophotometric distance, with S17 reporting 7.0$\pm$1.7 kpc and Shull &
Danforth (2019) finding 7.6 kpc (see also Shull et al. 2021). Gaia EDR3
reports $d$ = 4.9${}^{+0.8}_{-0.7}$ kpc for HD 167402. We adopt the Gaia
distances in our analysis. Through comparative analysis of the foreground HD
167402 and background LS 4825 sight lines, we isolate absorption from the
interval $5\lesssim d\lesssim 10$ kpc assuming that the ISM coherence length
is larger than the projected separation.

FUSE observations of LS 4825 and HD 167402 were performed on 2000 August 29
under program ID P101 (PI: K. Sembach). The raw spectra were obtained from the
FUSE archive, and the CalFUSE pipeline (v3.2.1, Dixon & Kruk 2009) was used to
extract the spectra. The SiC channels ($\lambda<1000$ Å) show complex,
overlapping absorption and low signal-to-noise (S/N) ratios and were not used
for the analysis. Instead we focus on the spectra from the LiF1 and LiF2
channels, which have S/N$\sim$9$-$13 per resolution element and a velocity
resolution of 20 km s-1 (FWHM). The data were binned by three pixels for the
fitting analysis. A detailed explanation of the refinements to the CalFUSE
data reduction procedures can be found in Wakker et al. (2003) and Wakker
(2006).

The FUSE spectrum of LS 4825 shows high-velocity H2 absorption in over 60
distinct lines from the rotational levels $J$ = 0, 1, 2, 3, 4, and 5 (see
Figure 2). Two components are seen at $v_{\mathrm{LSR}}$ = $-79.4\pm 1.5$ and
$-107.6\pm 1.3$ km s-1. Both components have high deviation velocities
(Wakker, 1991), thus we label both as HVCs even though the $-79$ km s-1
component is below the commonly used HVC threshold of $|v|=90$ km s-1. The
spectrum of LS 4825 is complex due to its spectral type (B1 Ib$-$II), and the
stellar continuum placement was guided by reference to the behavior of the
FUSE spectrum of the comparison star HD 58510 (FUSE program ID P102; PI: K.
Sembach). HD 58510 has the identical spectral type (S17) and tracks the
continuum of LS 4825 closely, with similar zero-velocity H2 absorption but
without the high-velocity H2 absorption. The continua were normalized in local
regions of interest using linetools (Prochaska et al., 2017).

We used the VPFIT (v12.2, Carswell & Webb 2014) Voigt-profile fitting software
to simultaneously fit the individual HVC components for the $J$ = 4 and 5
transitions, as these transitions are unsaturated. Since the two HVC
components in the lower-$J$ levels ($J<4$) show significant blending, we
assume the velocity centroid and $b$-value derived from $J$=4 and 5 (see Table
1) apply to the $J<4$ levels. There is some evidence that $b$-values of
interstellar H2 may vary as a function of $J$ (Spitzer & Morton, 1976; Jenkins
& Peimbert, 1997), but because of saturation we are unable to determine
whether this is the case in our dataset. Jensen et al. (2010) performed a
study on a sample of 22 Galactic sight lines to determine the effects of
assuming a uniform $b$-value for $J$ $\geq$ 2 versus independent measurements
and overall found log $N$(H2) differences $<$ 0.07 dex for the excited states.
We quantify the effect this may have on our $J<4$ column densities (including
$J$ = 0 and 1) by lowering $b$ by 3 km s-1, as any larger reduction in $b$
results in fits that overfit the profile. For weak unsaturated transitions we
find that log $N$(H2) at $-79$ and $-108$ km s-1 increases by at most 0.04
dex.

We denote the resulting total column density for a component of a given
$J$-level as a lower limit if the profile of the _weakest_ (lowest $f$-value)
transition in the set of simultaneously fit lines reaches zero flux. H2 lines
blended with ISM metal lines were excluded from fitting, as were lines blended
with other H2 lines and those in regions of geocoronal emission. All lines of
a single $J$-level were visually inspected in velocity space to verify that
when progressing from weakest to strongest lines the absorption behaved as
expected, and to check for the presence of damping wings on the HVC H2
components. Following continuum reconstruction using the reference star and
the adoption of a two-component fit, we find no evidence for HVC damping
wings. This is also consistent with the very small differential extinction
between the foreground and background sight lines using $E(B-V)$ values
reported in S17 and Shull & Danforth (2019), $\Delta E(B-V)$ = 0.01, because
this indicates a similar total dust column and therefore similar total
hydrogen column in the two directions.

We employed a slightly different procedure to fit the HVC ground state $J$ =
0, 1 components due to overlapping with strong Milky Way (MW) foreground H2
absorption. For these lines we fit a Voigt profile to the MW H2 component with
fixed $b$=5.5 km s-1 and adjusted its column density interactively until the
profile best fit the damping wings for all selected lines of the given
$J$-level. The choice of $b$=5.5 km s-1 was motivated by published high-
resolution (FWHM = 6.6 km s-1) STIS observations of C I toward LS 4825 (S17),
where $b_{\mathrm{CI}}$=5.4 km s-1 at $T$ $\sim$100 K indicates that the gas
is almost fully turbulent. The velocity, $b$-value, and column density of the
MW foreground component were then held fixed, and the column density for the
HVC components was then determined as described above for the excited
$J$-levels. The resulting Voigt profile fits to the H2 lines are shown in
Figure 3 and the resulting velocities, $b$-values, and column densities are
shown in Table 1.

Figure 2:  FUSE spectra of LS 4825 (background star; black) and HD 167402
(foreground star; red) showing five vibrational H2 bands, each of which has
rotational substructure. The LS 4825 spectrum has been multiplied by the
average flux ratio of the two stars in the corresponding region to facilitate
the comparison. Absorption associated with MW for $J$-levels 0, 1, 2, 3, 4,
and 5 are marked in the panels with blue, purple, pink, orange, green, and
yellow vertical lines, respectively. The shaded bands mark the region of the
HVCs in the background spectrum. The bottom two side-by-side panels show
separate radial velocity plots of the normalized data for the $J$ = 4 1044 Å
transition to illustrate the difference between the background and foreground
spectra, where the vertical line at 0 km s-1 marks absorption associated with
the MW, and the 1$\sigma$ error in the normalized flux is shown in blue. The
HD 167402 (foreground) spectrum only shows H2 absorption associated with the
MW near 0 km s-1. The LS 4825 (background) spectrum shows additional strong
multi-component H2 absorption centered near $-100$ km s-1. Figure 3: Velocity
profiles of H2 absorption lines and H I emission toward LS 4825. Panel 1: LS
4825 21 cm GBT spectrum from S17. Panel 2: refit to the MW foreground-
subtracted spectrum with log $N_{\mathrm{HI}}$ = 19.14$\pm$0.16 at $-86$ km
s-1 and $\leq$ 18.77 at $-108$ km s-1. Panel 3: closely aligned H2 from this
work with C I from S17. Panels 4–8: a sample of H2 absorption lines for
rotational levels $J$ = 0–5. The normalized flux is shown in black, the
continuum level is in red, and the 1$\sigma$ error in the normalized flux is
in blue. The vertical line at 0 km s-1 marks the region associated with the
MW. The solid orange and magenta curves are Voigt profile fits to the H2
absorption features for the MW and the HVCs, respectively. In all panels, the
two vertical dashed magenta lines indicate the velocities of the HVC
components. Figure 4: Boltzmann excitation plot for the two high-velocity H2
components toward LS 4825. The H2 column density in each rotation level
$N_{J}$ divided by the level’s statistical weight $g_{J}$ is plotted as a
function of excitation energy ($E_{J}$) for each cloud, for $J$=0–5. The HVCs
at $-79$ and $-108$ km s-1 are indicated with gold circles and blue squares,
respectively. For the cloud at $-79$ km s-1, we adopt a two-slope solution to
describe the relative population of the ground-state ($J$=0,1) and excited-
state levels ($J$=2–5), as indicated in the legend. For the cloud at $-108$ km
s-1, we also consider a model in which the ortho-to-para ratio (OPR) of the
excited-state levels is 1 instead of 3, which would shift log $N_{J}$/$g_{J}$
for $J$=3,5 upward to the positions indicated by the light blue squares and
for which the light blue dashed line is a better fit to the distribution of
points.  Table 1: HVC Molecular Absorption-Line Measurements

Species | $\lambda_{\mathrm{rest}}$ | $f^{a}$ | log $N$(H2)${}_{v=-79}^{b}$ | log $N$(H2)${}_{v=-108}^{c}$
---|---|---|---|---
$\nu_{u}$–$\nu_{l}$, R/P($J_{l}$) | (Å) |  | ($N$ in cm-2) | ($N$ in cm-2)
H2 $J=0$ |  |  | 16.01 $\pm$ 0.25 | 15.63 $\pm$ 0.27
$0-0$, R(0) | 1108.1273 | 1.66 $\times$ 10-3 |  |
$1-0$, R(0) | 1092.1952 | 5.78 $\times$ 10-3 |  |
$2-0$, R(0) | 1077.1387 | 1.17 $\times$ 10-2 |  |
H2 $J=1$ |  |  |  $>$ 16.20 | 15.62 $\pm$ 0.12
$1-0$, P(1) | 1094.0519 | 1.97 $\times$ 10-3 |  |
$2-0$, P(1) | 1078.9255 | 3.92 $\times$ 10-3 |  |
$4-0$, P(1) | 1051.0325 | 7.60 $\times$ 10-3 |  |
H2 $J=2$ |  |  |  $>$ 16.15 | 15.28 $\pm$ 0.08
$2-0$, P(2) | 1081.2660 | 4.70 $\times$ 10-3 |  |
$3-0$, P(2) | 1066.9007 | 7.09 $\times$ 10-3 |  |
$4-0$, P(2) | 1053.2843 | 9.02 $\times$ 10-3 |  |
H2 $J=3$ |  |  |  $>$ 16.13 | 15.15 $\pm$ 0.11
$3-0$, P(3) | 1070.1409 | 7.54 $\times$ 10-3 |  |
$3-0$, R(3) | 1067.4786 | 1.00 $\times$ 10-2 |  |
$5-0$, P(3) | 1043.5032 | 1.08 $\times$ 10-2 |  |
$4-0$, R(3) | 1053.9761 | 1.34 $\times$ 10-2 |  |
H2 $J=4$ |  |  | 15.08 $\pm$ 0.05 | 14.99 $\pm$ 0.06
$3-0$, P(4) | 1074.3130 | 7.74 $\times$ 10-3 |  |
$5-0$, P(4) | 1047.5519 | 1.10 $\times$ 10-2 |  |
$4-0$, R(4) | 1057.3807 | 1.29 $\times$ 10-2 |  |
$5-0$, R(4) | 1044.5433 | 1.55 $\times$ 10-2 |  |
H2 $J=5$ |  |  | 14.95 $\pm$ 0.05 | 14.81 $\pm$ 0.06
$3-0$, R(5) | 1075.2441 | 9.28 $\times$ 10-3 |  |
$5-0$, P(5) | 1052.4970 | 1.11 $\times$ 10-2 |  |
Total log $N$(H2) |  |  |  $>$ 16.75 | 16.13 $\pm$ 0.10
H I (S17)d | 21 cm | … | 19.43 $\pm$ 0.15 | 18.28 $\pm$ 0.15
H I (this work)e | 21 cm | … | 19.14 $\pm$ 0.16 |  $<$ 18.77
$f_{\mathrm{H_{2}}}$ (S17)f |  |  |  $>$ 0.41% | 1.40 $\pm$ 0.26%
$f_{\mathrm{H_{2}}}$ (this work)g |  |  |  $>$ 0.81% |  $>$ 0.46%

a The wavelengths and oscillator strengths used by VPFIT are calculated from
Bailly et al. (2010).
b The $b$-value from VPFIT for this component is 14.9$\pm$1.7 km s-1.
c The $b$-value from VPFIT for this component is 11.7$\pm$1.5 km s-1.
d S17 determine log $N_{\mathrm{HI}}$ = 19.43$\pm$0.01 and 18.28$\pm$0.02 for
the $-79$ and $-108$ km s-1 components in the 21 cm data from the Green Bank
Telescope (GBT, program ID: 14B-299). The log $N_{\mathrm{HI}}$ errors include
a beam smearing error of $\pm$0.15 since we are combining the GBT data (9′.1
beam) with the FUSE UV measurements (infinitesimal beam) to derive
$f_{\mathrm{H_{2}}}$.
e Revised estimate of log $N_{\mathrm{HI}}$ from a refit to the GBT LS 4825
spectrum in S17 where the MW foreground H2 absorption of HD 167402 has been
subtracted. The log $N_{\mathrm{HI}}$ error for the $v$ = $-79$ km s-1
component includes a beam smearing error of $\pm$0.15.
f The molecular fraction, $f_{\mathrm{H_{2}}}$ = 2$N$(H2)/[$N$(H I) +
2$N$(H2)], based on log $N_{\mathrm{HI}}$ from S17.
g Estimate of the molecular fractions derived from the revised multi-component
refit to the 21 cm H I GBT spectrum in S17.

##  3 Results

Our most significant result is the discovery of the presence of the high-
velocity H2 absorption in two components in the spectrum of the background
star LS 4825, centered at $-$79 and $-$108 km s-1. This remains true
irrespective of our detailed findings on column densities and rotational
excitations discussed below. The high-velocity H2 components are not seen in
the spectrum of the foreground star HD 167402, indicating that the H2 detected
at $-79$ and $-108$ km s-1 in the background star LS 4825 can be bracketed to
the range $5\lesssim d\lesssim 10$ kpc, which corresponds to a $z$-distance of
$-0.6$ to $-1.2$ kpc below the GC. The H2 is therefore potentially associated
with the southern Fermi Bubble, a region exposed to the Galactic nuclear wind.

The absence of high-velocity absorption toward HD 167402 was also seen in the
STIS E140M and E230M UV spectrum by S17, who reported multiphase gas at high
velocities only in the LS 4825 spectrum. Low-ion absorption is seen over the
range $-290$ to 94 km s-1. Of particular significance is C I absorption
detected at $v_{\mathrm{LSR}}$ = $-114.2$, $-100.8$, and $-77.7$ km s-1 in the
STIS spectrum (S17) because C I acts as a tracer for H2 (Ge et al., 1997,
2001). The combination of our results from H2 detected at similar velocities
with those from S17 allows us to construct a more complete picture of the
composition, properties, and environment of these cold clouds in the dynamic
environment near the GC.

###  3.1 The H2 HVC at $-$79 km s-1

By summing over the rotational levels from $J$=0 to 5, we derive a total H2
column density in the $-$79 km s-1 component of log $N$(H2) $>$ 16.75 cm-2.
This is a lower limit due to saturation in multiple $J$-levels. S17 report H I
21 cm emission at negative velocities of $-105$, $-89$, and $-70$ km s-1 using
a Green Bank Telescope (GBT) spectrum and conclude that the $-70$ km s-1
component with log $N_{\mathrm{HI}}$ = 19.43 $\pm$ 0.01 is most likely
associated with the absorption system near $-78$ km s-1. Combining this H I
measurement with our measurement of log $N$(H2) we derive a molecular fraction
of $f_{\mathrm{H_{2}}}$ = 2$N$(H2)/[$N$(H I) + 2$N$(H2)] $\geq$ 4.1 $\times$
10-3, or $\geq$0.41% (see Table 1). We conducted a refit to the LS 4825 GBT
spectrum, in which we subtracted the zero-velocity component of the foreground
HD 167402 spectrum. This results in two components at $-85.8$ and $-62.3$ km
s-1 with log $N_{\mathrm{HI}}$ = 19.14$\pm$0.16 and 19.07$\pm$0.16 cm-2,
respectively. We associate the H I emission near $-86$ km s-1 with the H2
absorption at $-79$ km s-1 and find $f_{\mathrm{H_{2}}}$ $\geq$ 0.81%. Either
limit is consistent with the upper end of $f_{\mathrm{H_{2}}}$=
$10^{-2}-10^{-6}$ measured in Galactic HVCs from absorption-line studies
(Richter et al. 2001; Sembach et al. 2001; Wakker 2006), but is not as high as
$f_{\mathrm{H_{2}}}$ $\sim$0.3–0.6 from emission-line CO detections seen in Di
Teodoro et al. (2020).

We determine limits on the excitation temperatures in the high-velocity
molecular gas by fitting a theoretical Boltzmann distribution to the observed
population of rotational levels, since our measurements of log $N$(H2) for $J$
= 1, 2, 3 are lower limits. For the $-79$ km s-1 component, the rotational
ground states $J$ = 0 and 1 are fit by a slope equivalent to a Boltzmann
temperature $T_{01}$ $\geq$ 97 K, whereas the excited rotational levels $J$ =
2$-$5 fit on a slope equivalent to $T_{25}$ $\leq$ 439 K (see Figure 4). The
adopted two-slope solution may suggest a core-envelope structure, with
$T_{01}$ reflecting the temperature in the cooler, shielded interior of the
cloud and the $T_{25}$ region tracing warmer gas heated by processes such as
UV pumping, H2 formation pumping, and shock excitation (Richter et al., 2001).
However, these processes could occur within a fairly homogeneous region.

S17 measure a near solar metallicity [S/H] = 0.02 $\pm$ 0.16 in the $-$78 km
s-1 HVC ([S/H] = 0.31 $\pm$ 0.17 using the H I measurement from the
foreground-subtracted GBT spectrum), and also report a subsolar Fe/S ratio,
finding [Fe II/S II] = $-1.05\pm 0.05$, which suggests that Fe in the cloud is
locked up in dust grains.

###  3.2 The H2 HVC at $-$108 km s-1

We report log $N$(H2)= 16.13 $\pm$ 0.10 cm-2 for the $-108$ km s-1 component,
0.6 dex lower than the H2 column at $-79$ km s-1. From the MW foreground-
subtracted GBT spectrum of LS 4825 we determine a 3$\sigma$ upper limit of log
$N_{\mathrm{HI}}$ $\leq$ 18.77 at $-107.6$ km s-1, which is $\sim$0.5 dex
higher than S17, who measure log $N_{\mathrm{HI}}$ = 18.28 $\pm$ 0.02 at
$-104.9$ km s-1. Combining the H I and H2 columns results in
$f_{\mathrm{H_{2}}}$ $\geq$ 0.46%, which is also consistent with the upper end
of $f_{\mathrm{H_{2}}}$ for HVCs in absorption-line studies (see section 3.1).
The metallicity [S/H] $\geq$ 0.87 is supersolar; and S17 measure [Fe II/S II]
= $-0.99\pm 0.09$ for this component, concluding that it is as equally dusty
as the $-79$ km s-1 component.

A two-slope solution for the Boltzmann distribution fit to the rotational
level populations yields $T_{01}$ = 77${}^{+34}_{-18}$ K and $T_{25}$ =
732${}^{+64}_{-55}$ K, as determined from the dark blue lines in Figure 4, but
is not a good fit for the $J\geq 2$ excited states. However, the up-and-down
distribution of the excited states, in which the para states $J$=2,4 lie
systematically above the ortho states $J$=3,5 may indicate an ortho-to-para
ratio (OPR) that deviates from the canonical (equilibrium) value of 3 for
warm, rotationally excited H2 gas (as included in the statistical weight,
$g_{J}$, where $g_{J}$(para)=2$J$+1 and $g_{J}$(ortho)=3(2$J$+1)). If we
adjust the OPR for $J\geq 2$ to a value of 1 (${}^{+0.3}_{-0.1}$) instead of
3, the data points for $J$=3,5 (in light blue) are shifted higher such that
all $J\geq 2$ levels fit on a straight line, with a slope that yields $T_{{\rm
exc}}$ = 1092${}^{+149}_{-117}$ K (see Figure 4). This suggests that the OPR
is out of equilibrium and is further discussed in Section 4. An OPR=1 provides
a good fit to the data for the excited states of the $-108$ km s-1 component,
however, we acknowledge that unresolved components with potentially varying
$b$-values could impact the measurements of the excited state column
densities. These fits represent what is currently capable given the resolution
of the data.

##  4 Discussion

The H2 components detected in the FUSE spectrum of LS 4825 ($d$ =
9.9${}^{+1.4}_{-0.8}$ kpc) at $-79$ and $-108$ km s-1 are not seen in the
spectrum of the foreground star HD 167402 ($d$ = 4.9${}^{+0.8}_{-0.7}$ kpc)
and therefore trace gas located between the two stars and most likely within
the southern Fermi Bubble (see Figure 1). Our results represent the first
detection of high-velocity H2 in the extended Galactic Center environment. We
measure total log $N$(H2) $>$ 16.75 and 16.13$\pm$0.10 cm-2 at $-79$ and
$-108$ km s-1 respectively, velocities which cannot be explained by circular
rotation. We determine respective H2 fractions $f_{\mathrm{H_{2}}}$ $\geq$
0.8% and $f_{\mathrm{H_{2}}}$ $\geq$ 0.5%. The low ground-state temperatures
we derive for the H2 absorption at $-79$ and $-108$ km s-1 of
$T_{0,1}\approx$97 and 77 K confirm that these are indeed cold clouds. The H2
detection augments the metal-line analysis from S17, who reported high-
velocity neutral, low-ion, and high-ion absorption toward LS 4825 but not HD
167402.

A natural interpretation of these results, as suggested by S17, is that the
multiphase high-velocity absorbers toward LS 4825 trace a nuclear wind. This
is supported by the very strong high-ion absorption seen along the line of
sight (S17) and the abundant multi-wavelength evidence for a wind in this
region (Bland-Hawthorn & Cohen, 2003; Su et al., 2010; Predehl et al., 2020;
Di Teodoro et al., 2018; Lockman et al., 2020). In this interpretation, only a
small component of the outflow velocity is projected along our line of sight;
deprojecting the velocity onto a vertically or radially oriented outflow
implies a high outflow velocity ($\sim$800–1000 km s-1), similar to the
velocity inferred from other UV HVCs in the Fermi Bubbles (Fox et al., 2015;
Bordoloi et al., 2017).

However, multiple structures house molecular and neutral gas in the GC. The
Galactic disk near the GC is warped, tilted at $\sim$22° (Liszt & Burton,
1980) with a portion protruding to $b\sim-5$° between $l$=0–10° (as shown in
Figure 1). Recent H$\alpha$ studies at the anomalous velocities that track the
tilt of the Galactic disk in this region from Krishnarao et al. (2020b)
predict asymmetric absorption profiles with peak absorption near $-100$ km
s-1, just as we observe. Even closer to the GC lies the Central Molecular Zone
inside $R_{G}\sim$0.5 kpc. The right panel of Figure 1 shows that the sight
lines lie in close proximity to the edge of the disk and could be probing the
boundary where the nuclear wind is passing by the disk since the HVCs and the
disk have similar velocities in this inner region. Irrespective of whether the
clouds are entrained in an escaping wind, we see strong evidence of disk-like
properties for the molecular components from their high metallicities,
including an above-solar [S/H] = 0.31$\pm$0.17 at $-79$ km s-1 and a
supersolar [S/H] $\geq$ 0.87 near $-108$ km s-1, as well as high dust
depletion levels, with [Fe II/S II] $\sim-1$ (S17).

Both the wind interpretation and the warped-disk interpretation are allowed by
the data. However, the two are not mutually exclusive. We propose a hybrid
model in which the high-velocity H2 clouds probe a boundary region where the
nuclear wind is passing by the disk and accelerating fragments of gas into the
halo. This is supported by the sight line’s close proximity to the disk (both
spatially and kinematically), as well as unusual OPRs and thermal pressures
(S17), as we explain below.

Warm, rotationally excited H2 gas in thermal equilibrium is expected to have
an OPR=3, as the excited gas has been warm for long enough to reach
equilibrium between the (odd) ortho and (even) para states. As seen in Figure
4, an OPR=3 is a good description of the distribution of excited-state levels
for the cloud at $-79$ km s-1. However, as described in Section 3, an OPR=3
fails to describe the excited $J$ levels for the $-108$ km s-1 cloud, which
instead is much better fit by OPR=1. This deviation from the canonical
(equilibrium) value suggests that the observed $J$=2–5 levels at $-108$ km s-1
were only recently pumped into high $J$ states (and also to higher $T$) from
the ground states ($J$=0 and 1), where OPR$\lesssim$1 is expected (Flower &
Watt, 1984). The OPR equilibrates very slowly (Neufeld et al., 1998), so in
this explanation the excited-state gas has not had enough time to adjust to
the new environment to reach equilibrium between the ortho and para states,
and so preserves a ”memory” of the thermal state of gas in a previous epoch.
We note that an enhanced radiation field within the Fermi Bubbles is
_predicted_ in the models of Bland-Hawthorn et al. (2019), who find an
ionizing radiation field of log $\varphi$ = 6.5 photons cm-2 s-1 at $\sim$1
kpc below the GC, and potentially higher in the event of a recent Seyfert
flare. The unusual H2 excitation properties we observe are consistent with
this.

In the hybrid scenario, the two H2 clouds $\sim$1 kpc below the GC undergo
different histories. Both clouds formed much earlier in a quiescent disk
environment at $T<100$ K and were swept and/or broken up within the nuclear
wind. In this new environment, the outer skin of the clouds was rotationally
excited by photons and/or collisions with an ambient medium. Whereas the $-79$
km s-1 cloud has equilibrated to this environment with $T_{\rm exc}\approx$492
K for OPR=3, the $-108$ km s-1 cloud has not, as evidenced by $T_{\rm
exc}$=1092 K with an OPR=1 that still reflects the physical conditions of the
H2 gas from its prior environment.

Further support for a wind or hybrid model is provided by the high thermal
pressure in the HVCs. From observations of $N$(C I), $N$(C I∗), and $N$(C
I∗∗), S17 derive thermal pressures $P/k$ at $-78$, $-101$, and $-114$ km s-1
of $\sim$104.1, $10^{3.8}$, and $10^{5}$ cm-3 K, respectively. The pressures
reported at $-78$ and $-114$ are $\sim$3.2 and 25 times higher than the mean
$P/k=10^{3.6\pm 0.2}$ cm-3 K reported in the diffuse ISM in the Galactic disk
(Jenkins & Tripp, 2011), which suggests that the clouds may have been
compressed, perhaps by an outflowing hot wind. The pressure at $-101$ km s-1,
however, is similar to the mean ISM cloud pressure. Since we measure an H2
velocity centroid in the lower resolution FUSE spectrum at $-108$ km s-1, we
are unable to make a confirmed association with either of the STIS components
at $-101$ and $-114$ km s-1, but acknowledge that the range of pressures
observed near this velocity are consistent with a hybrid disk-wind environment
along this line of sight.

If the clouds are indeed being actively swept out of the disk, perhaps in a
biconical outflow from the GC (see Fox et al. 2015; Bordoloi et al. 2017),
then questions arise on how the cold gas became entrained and will survive in
this complex and energetic environment. HVCs are thought to have a finite
lifetime against disruptive instabilities as they interact with a surrounding
medium (Heitsch & Putman, 2009; Armillotta et al., 2017). However, recent
theoretical studies have explored the survival of cold gas in hot galactic
winds (e.g. Gronke & Oh 2020; Sparre et al. 2020). They indicate that a cold
gas cloud entrains hot gas via cooling-induced pressure gradients, thereby
acquiring the mass and momentum of the hot gas. Inclusion of a magnetic field,
and in particular, a turbulent magnetic wind, can suppress the cloud-
destroying Kelvin-Helmholtz instabilities, allowing the clouds to survive.
These models show that clouds with $N_{\mathrm{H}}$ $<$ 1018 cm-2 are not
predicted to survive due to erosion, whereas those with $N_{\mathrm{H}}$ $>$
1018 cm-2 are expected to survive and even grow.

The results of these models offer a plausible explanation for how the low
column density H2 components may survive, as comoving within clouds with
$N_{\mathrm{H}}$ $>$ 1018 cm-2 could possibly shield the H2 bearing
structures, ensuring their survival. If entrained in a wind, the existence of
these high-velocity molecular clouds in the dynamic and multiphase GC
environment will help to inform continuing research on models of cloud
acceleration and survival. However, further detections of molecular gas at
more locations within the nuclear wind are needed to test these theories.

##  5 Summary

We have detected two high-velocity molecular hydrogen clouds in the FUSE
spectrum of the massive star LS 4825. The sight line passes $\sim$1 kpc below
the GC near the boundary of the Galactic disk, a region where the nuclear wind
is thought to blow gas out into the southern Fermi Bubble. The clouds are not
seen in the spectrum of the foreground star HD 167402, lying $\sim$0.6° away,
confirming they are associated with the GC. We measure total log $N$(H2) $>$
16.75 and 16.13$\pm$0.10 cm-2 at $-79$ and $-108$ km s-1 respectively,
velocities which cannot be explained by circular rotation. We determine
respective H2 fractions $f_{\mathrm{H_{2}}}$ $\geq$ 0.8% and
$f_{\mathrm{H_{2}}}$ $\geq$ 0.5%. For the $-79$ km s-1 cloud we adopt a two-
component Boltzmann distribution to explain the rotational level populations,
with $T_{01}$ $\geq$ 97 K and $T_{25}$ $\leq$ 439 K. For the $-108$ km s-1
cloud, a two-component Boltzmann distribution yields $T_{01}$ =
77${}^{+34}_{-18}$ and $T_{25}$ = 732${}^{+64}_{-55}$ K, but is not a good fit
for the excited states given the canonical OPR=3. Instead we find that if
OPR=1, the excited states lie on a straight line corresponding to $T_{25}$ =
1092${}^{+149}_{-117}$ K.

We considered two possible origins for the high-velocity H2 components: a wind
interpretation which traces the projection of an outflow velocity along our
line of sight, and a warped-disk interpretation in which the clouds are
associated with the tilted portion of the Galactic disk. We conclude that the
best explanation for the data is a hybrid model in which the H2 clouds probe a
boundary region where the nuclear wind is passing by the disk and accelerating
fragments of gas into the halo.

We thank Enrico Di Teodoro for valuable conversations on the LS 4825 sight
line and Stephen McCandliss for helpful conversations about molecular
absorption lines. We gratefully acknowledge support from the NASA Astrophysics
Data Analysis Program (ADAP) under grant 80NSSC20K0435, 3D Structure of the
ISM toward the Galactic Center. The FUSE data were obtained under program
P101. FUSE was operated for NASA by the Department of Physics and Astronomy at
the Johns Hopkins University. The Green Bank Telescope data were obtained
under Program GBT14B-299, and the observatory is a facility of the National
Science Foundation, operated under a cooperative agreement by Associated
Universities, Inc. D.K. is supported by an NSF Astronomy and Astrophysics
Postdoctoral Fellowship under award AST-2102490. Some of the data presented in
this paper were obtained from the Mikulski Archive for Space Telescopes (MAST)
at the Space Telescope Science Institute. The specific observations analyzed
can be accessed via https://doi.org/10.17909/t9-axmr-t152 (catalog
10.17909/t9-axmr-t152). , VPFIT (Carswell & Webb, 2014)

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