# Refining Implicit Argument Annotation For UCCA

Ruixiang Cui and Daniel Hershcovich
Department of Computer Science
University of Copenhagen
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###### Abstract

Few resources represent implicit roles for natural language understanding, and
existing studies in NLP only make coarse distinctions between categories of
arguments omitted from linguistic form. In this paper, we design a typology
for fine-grained implicit argument annotation on top of Universal Conceptual
Cognitive Annotation’s foundational layer [Abend and Rappoport, 2013]. Our
design aligns with O’Gorman [O’Gorman, 2019]’s implicit role interpretation in
a linguistic and computational model. The proposed implicit argument
categorisation set consists of six types: Deictic, Generic, Genre-based, Type-
identifiable, Non-specific, and Iterated-set. We corroborate the theory by
reviewing and refining part of the UCCA EWT corpus and providing a new dataset
alongside comparative analysis with other schemes. It is anticipated that our
study will inspire tailored design of implicit role annotation in other
meaning representation frameworks, and stimulate research in relevant fields,
such as coreference resolution and question answering.

##  1 Introduction

Semantic representation frameworks have been a major medium to understanding
the nature of languages for NLP. Through these frameworks, researchers have
been exploring linguistic phenomena such as quantification [Pustejovsky et
al., 2019], coreference [Prange et al., 2019], and word sense [Schneider et
al., 2018]. However, most efforts were put into studying linguistic complexity
superficially, rather than the more latent, implicit omission of arguments in
an event. Distinct from gapping or ellipsis, such omission can not be
recovered directly, but require a higher level of understanding and inference
from the context. Traditional studies approach argument omission from
different aspects, namely syntactically, semantically, or pragmatically. The
interpretation of implicit roles varies to a great extent, from phonological
deleted role during production [Perlmutter, 1968, Mittwoch, 1971, Pérez-Leroux
et al., 2018] to timecourse reference omission from a psycholinguistic aspect
[Garrod and Terras, 2000]. However, few studies have explored the implicit
role phenomenon in NLP.

In this paper, we propose a fine-grained cross-linguistically applicable
implicit argument annotation typology as a refinement for Universal Conceptual
Cognitive Annotation [Abend and Rappoport, 2013, UCCA] categories, built on
O‘Gorman [O’Gorman, 2019]’s inventory of implicit role categorisation. The
typology follows UCCA’s design concept, focusing on the semantic notion of
Scene rather than linguistic form phenomena. The proposed implicit argument
set contains six categories: Deictic, Generic, Genre-based, Type-identifiable,
Non-specific, and Iterated-set. We refine the existing UCCA relation labels
and add information to them, while keeping all categories from the underlying
annotation.

Based on the proposed typology, we conduct a pilot annotation study, including
review and refinement of the UCCA EWT dataset,111The corpus will be released
upon publication of this paper. and subsequently make a comparative analysis
with the only other existing fine-grained implict role annotation scheme,
Fine-grained Annotations of Referential Interpretation Types [O’Gorman, 2019,
FiGref].

Our studies of implicit arguments can potentially enhance natural language
understanding. For example, when companies conduct satisfaction analyses
through web reviews, customers often express themselves colloquially in these
reviews. Examples include “Serves bad ice cream, Joe’s is better” and “Near a
nice district, bad service and expensive.” If these reviews are annotated with
Genre-based implicit arguments, referring to the conventional omission of
reviewees, algorithms can study which part of the reviews really refers to the
companies rather than other entities, and make better predictions, despite the
omission of subjects and non-standard language.

##  2 Universal Conceptual Cognitive Annotation

Participant | A | Linker | L
---|---|---|---
Center | C | Connector | N
Adverbial | D | Process | P
Elaborator | E | Quantifier | Q
Function | F | Relator | R
Ground | G | State | S
Parellel Scene | H | Time | T
Table 1: Legends of UCCA edge categories [Hershcovich et al., 2019a]

Universal Conceptual Cognitive Annotation is a semantic representation scheme
whose design concept comes from the Basic Linguistic Theory typological
framework [Dixon, 2010a, Dixon, 2010b, Dixon, 2012] and Cognitive Linguistics
literature [Croft and Cruse, 2004]. Abstracting away from syntactic forms, it
aims at representing the main semantic phenomena in text while maintaining a
low learning cost and rapid annotation by non-experts [Abend et al., 2017].
Already providing datasets in English, French, and German, UCCA has
demonstrated its cross-linguistic applicability in several languages and has
become a popular target framework in multiple parsing tasks [Hershcovich et
al., 2019b, Oepen et al., 2019].

UCCA presents the meaning of a sentence with a directed acyclic graph (DAG)
whose terminal nodes correspond either to surface lexical tokens or extra
units representing implicit arguments. Non-terminal nodes correspond to
semantic units that participate in some super-ordinate relation. Edges are
labeled with the role of a child node related to its parent node. The basic
notion in UCCA is Scene, describing a state, action, movement, or some other
relation that evolves in time. Each Scene involves one main relation (Process
or State), and one or more Participants, including locations, abstract
entities and sub-Scenes serving as arguments.

Furthermore, UCCA distinguishes primary edges, appearing explicitly in one
relation, from remote edges, allowing a Scene to indicate its arguments by
linking from another Scene. Primary edges form a tree while Remote edges allow
reentrancy, forming a DAG. In some cases, an entity of importance in the
interpretation of a Scene does not explicitly exist in the text. Hence, UCCA
introduces the notion of Implicit Units to represent such kind of entity.

IMP1AHaveDaFrealmechanicCAcheckPHbeforeLyouAleavePIMP2AHAD

Figure 1: Example of UCCA graph: Abbreviation of UCCA edge labels is explained
in Table 1. The dashed edge is Remote. An IMP represents an Implicit argument
denoting a null-instantiated core element in its corresponding Scene.

For instance, the sentence “Have a real mechanic check before you leave” in
Figure 1 contains two Scenes, evoked by “check” and “leave”. The individual
Scenes are annotated as follows:

  1. 1.

“(You)A haveD[aF realD mechanicC]A checkP IMP1A”

  2. 2.

“YouA leaveP IMP2A”

“A mechanic” is a Participant in the first Scene, while “You” is Participant
in both Scenes, as Remote constituting reentrancy in the first one (shown in
dashed line), but explicit in the latter super-ordinate relations. In the
first Scene, “Check” is the main Process used in the causative construction,
requiring three Participants. While “You” refers to the customer making a
request and “a real mechanic” is the service provider who should check
something, the object that needs to be “checked” is missing. Therefore, we
introduce an IMP A node to symbolize it. In the second Scene, “leave” is the
Process meaning someone moves away from a source location. Although we state
our little concern for non-core elements like location in this study in §3.2,
the case is different for the “leaving” Scene since the source location is
vital to the understanding of the departing action. For this reason, we add an
IMP A to represent the place that is being left.

In UCCA’s foundational layer, only limited cases of implicit arguments have
been annotated. The main focus is on omission licensed by certain grammatical
structures,222https://github.com/UniversalConceptualCognitiveAnnotation/docs/blob/master/guidelines.pdf
whose notion is similar to Constructional Null Instantiation in FrameNet
[Ruppenhofer et al., 2006]. Two typical examples of such constructions are
imperatives (forced omission of subjects) and passives (agent omission) in
English:

  1. 1.

Imperative: IMPA DoF n’tD botherP.

  2. 2.

Passive: [TheF doctorC]A hasF alreadyT beenF paidP IMPA.

Several other kinds of constructions are mentioned in UCCA foundation layer
guidelines, such as infinitive clause, gerund, and thank construction.

  1. 3.

Infinitive clause: IsF thereF [noE otherE VerizonC]A IMPA toF goP toR [aroundR
downtownC]A?

  2. 4.

Gerund: HowD addictingS IMPA goingP [toR Fitness UnlimitedC]A can${}_{F}D$
beF!”

  3. 5.

“Thank” construction: IMPA ThanksP, JohnA!

The annotation of implicit arguments in UCCA’s foundation layer is restricted
to certain linguistic constructions, which is coarse, language-specific,
incomplete, and unlike other distinctions in UCCA, is based on criteria of
form rather than meaning. We are faced with the challenge of maintaining
UCCA’s idiosyncrasy of differentiating Remote and Implicit while extending its
boundary to include a rather refined categorisation for implicit roles.

##  3 Implicit Roles In Meaning Representations

###  3.1 Background and Motivation

In UCCA’s design concept, FrameNet [Baker et al., 1998] was frequently
referred to due to its usage of Frames, similar to the context-independent
abstraction of UCCA’s Scenes, and their shared emphasis on semantic rather
than distributional consideration. FrameNet developed Fillmore [Fillmore,
1986]’s notion of null-instantiation into three types—Constructional Null
Instantiation (CNI), licensed by grammatical constructions, Definite Null
Instantiation (DNI), equivalent to core Frame Elements mentioned previously in
text or inferrable from the discourse, and Indefinite Null Instantiation
(INI), an element that is unknown and nowhere to be retrieved.

Nevertheless, this trichotomy treats unfavourably many cases where implicit
roles occur, such as Free Null Instantiation [Fillmore and Kay, 1993, FNI;]
and Identity of Sense Null Anaphora [Kay, 2006, ISNA;]. FNI is neither
restricted to definite nor indefinite null arguments, and ISNA is null
instantiation within noun phrases. Lyngfelt [Lyngfelt, 2012] even argues that
the unclear definition of FNI leads to much false categorisation—some FNIs are
unspecified, some are generic, and some should be considered DNI.

UCCA’s foundational layer mainly focuses on CNI, that is, the current
annotated datasets only include grammatically licensed implicit arguments. So
far, only a few corpora for implicit role labelling have been proposed, such
as SemEval-2010 Task 10 [Ruppenhofer et al., 2009], Beyond NomBank [Gerber and
Chai, 2010, Gerber and Chai, 2012], and Multi-sentence AMR [O’Gorman et al.,
2018]. But none of them is based on a more comprehensive fine grained implicit
role characterisation theory aside from Fine-grained Annotations of
Referential Interpretation Type [O’Gorman, 2019], refined on three corpora
mentioned above for recoverability studies.

Although FiGref is not available to the public, O‘Gorman [O’Gorman, 2019] has
counterbalanced previous studies on implicit role description and synthesized
an inventory of eleven interpretation types for implicit roles. They are
distinguished by their referential behaviours, that is, Script-inferrable
pragmatic, Salient/recent, Deictic, Remembered Roles of Event Reference,
Implicit “Sloppy anaphora” and Bridging, Genre-based Default, Type-
identifiable, Generic (“People in General”), Cataphoric, Low-information, and
Iterated Events Implicit Roles.

Recoverable implicit roles fall into the category of Remote Participants in
UCCA, which typically calls for coreference resolution [Prange et al., 2019].
We discern eleven types of implicit roles from O‘Gorman [O’Gorman, 2019]’s
categories, recoverable or not, and extract those types where only true
Implicit arguments occur, that is, the argument cannot be explicitly recovered
from text, but inference and non-specificity are allowed as they are aligned
with the definition of implicit arguments of UCCA. In the following section,
we will analyze the implicit role types proposed by O‘Gorman [O’Gorman, 2019]
and argue the appropriateness of the set of categories we choose.

###  3.2 Forming UCCA Implicit Argument Typology

O’Gorman’s Catagorisation | Definite Implicit | Indefinite | Edge Cases | UCCA’s Typology
---|---|---|---|---
Salient/recent | ✓ |  |  | ✗
Remember Roles | ✓ |  |  | ✗
Script-inferrable | ✓ |  |  | ✗
Deictic | ✓ |  |  | Deictic
Cataphoric |  | ✓ |  | ✗
Low-information |  | ✓ |  | Non-specific
Iterated Events |  | ✓ |  | Iterated-set
Bridging |  |  | ✓ | ✗
Genre-based |  |  | ✓ | Genre-based
Generic |  |  | ✓ | Generic
Type-Identifiable |  |  | ✓ | Type-Identifiable
Table 2: O’Gorman’s categories and the set for UCCA’s implicit argument
typology.

For the sake of operability and consistency, we only focus on core arguments
in Scenes where these arguments are essential to the meaning of corresponding
predicates [Jackendoff, 1992, Jackendoff, 1997, Goldberg, 1992, Grimshaw,
1993]. Elements such as location, time, and manner are of little interest in
this study whilst they are able to appear as foundational units or Remote
Participant in UCCA.

As UCCA distinguishes Remote edges from Implicit units, it is natural to take
advantage of this property to account for argument recoverability. The
definition of implicit arguments in UCCA, particularly for its strong emphasis
on the inability of explicit recovering from text, is not strictly
corresponding with O‘Gorman [O’Gorman, 2019]’s.

Table 2 shows the comparison of O’Gorman’s categories and UCCA’s implicit
argument set. Among eleven types of implicit roles in his inventory, four are
definite implicit role constructions, viz. Salient/recent, Remember Roles,
Script-inferrable, and Deictic. Only the last one of four, Deictic, we would
consider a candidate category for UCCA’s Implicit arguments. Salient/recent
roles, which can be directly found in the recent prior discourse, is the
quintessential type of DNI, and they can be easily replaced by pronouns.
Remember Roles and Script-inferrable roles, however, require a cognitive and
reasoning process, as the referents can be understood through a common ground
in the text shared between the speaker and the addressee, or are reflecting a
different facet of the same or a subordinate event. Deictic roles, albeit
explicit reference to the speaker or addressee, is an extra-linguistic and can
not be annotated as Remote Participant, since we are unable to retrieve them
explicitly in the text. Therefore, we incorporate it in our set of Implicit
arguments categories.

Three roles out of O‘Gorman [O’Gorman, 2019]’s inventory are marked as clearly
indefinite arguments, namely Cataphoric, Low-information Arbitrary role, and
Iterated Events Implicit Roles. Cataphoric, which Bhatia et al. [Bhatia et
al., 2014] define as “pragmatically specific indefinite”, is the only type we
do not include in UCCA’s typology since it relies heavily on the
interpretation of the discourse whether it will be referred to again. We would
annotate it as Remote Participant if the role is mentioned in a later text, or
Non-specific type if not so as not to complicate the reasoning process.

The other four, Bridging implicit roles, Genre-based Default, Generic and Type
Identifiable, are regarded as edge cases by O‘Gorman [O’Gorman, 2019]. Once
again, we will only admit the latter three in our typology. As far as we are
concerned, bridging in ellipsis situations might not refer to the same
referent conceptually. Nonetheless, it can be clearly resolved in the text.
Therefore, it will be annotated as a Remote edge in UCCA.

We will focus on referents that do not appear anywhere in the text. Therefore,
we follow the philosophy of UCCA and propose six categories of implicit
argument, that is, Deictic, Generic, Genre-based, Type-identifiable, Non-
specific and Iterated-set. In the next section, we will present and exemplify
each one of them.

###  3.3 Categorisation Set for UCCA Implicit Arguments

####  3.3.1 Deictic

Deictic implicit arguments specifically refer to the speaker or the addressee
in a sentence. In example 1, the second-person subject is exhorted to take a
certain action, and such imperative construction allows the subject not to
appear in the text explicitly. Shown in example 2, Deictic can also occur with
certain interjections, where the subject as the speaker is habitually
implicit.

  1. (1)

JustD askP themA exactlyE whatC [youA wantS (what)A]E IMPDeictic.

  2. (2)

[Thank you]P guysG/A IMPDeictic.

It should be mentioned that only in certain languages is imperative likely to
induce implicit arguments. In Romance languages such as Spanish, deictic
information tends to be encoded morphologically due to person agreement
[Ingram, 1971].

####  3.3.2 Generic

Generic implicit arguments denote “people in general” [Lambrecht and Lemoine,
2005]. In example 3, the agent who “understands how this place has survived
the earthquake” is not explicitly mentioned in the text, but it can be
understood as it is the set of people in general. Example 4 can be construed
as a gerund construction. “I” recommend taking a certain action. While the
patient would not be specific, it conveys the message that “people in general”
should follow such advice.

  1. (3)

ItF ’sF impossibleD toF understandP [howC [[thisE placeC]A hasF survivedP
[theF earthquakeC]A]E]A IMPGeneric.

  2. (4)

IA wouldF recommendP [notD usingP [thisE companyC]A IMPGeneric]A.

####  3.3.3 Genre-based

Ruppenhofer and Michaelis [Ruppenhofer and Michaelis, 2010] found certain text
genres, namely instructional imperatives, labelese, diary style, match report,
and judgment-expressing quotative verbs, are closely linked with conventional
omission. UCCA EWT corpus is based on online reviews of businesses and
services by individuals. The review genre is so prominent acoss all dataset
that it forms a pattern where the reviewers do not bother to mention the
reviewees explicitly. In example 5 and 6, the review genre licenses the
omission of the deliverer of the action “deliver” and server of the action
“serve”, as they refer to the reviewees by default, because in both contexts
it is the restaurants that are being reviewed.

  1. (5)

DeliveryP isF [lightningE fastC]D IMPGenre-based IMPNon-specific!

  2. (6)

[GreatD serviceP IMPGenre-based IMPGeneric]H andL [awesomeS pricesA]H.

####  3.3.4 Type-identifiable

Some predicates allow omitting referents whose types are so predictable that
the listeners simply take it as “known” referents [O’Gorman, 2019]. In example
7, the vague referent of “eat” can be understood from an inherent
understanding of the listeners as “some kind of food“. In example 8, the thing
that “I drive” is not mentioned. Instead, it comes from common sense that the
referent should be a kind of vehicle. Whatever kind it is, the lack of
explicit mention barely affects the understanding of the text.

  1. (7)

ItA isF myA favouriteS [placeC [(my)A toF eatP IMPType-identifiable]E]A.

  2. (8)

IA ’llF driveP [anQ hourC]T [justE forR [theirS (volcano)A]E volcanoC]A
IMPType-identifiable.

####  3.3.5 Non-specific

Non-specific implicit arguments refer to the kind of referents that cannot be
inferred or understood at all. Such required information absent from the
context attributes to the low interpretability of the implicit arguments,
leaving them non-specific. As in example 9 and 10, it is impossible to infer
what is “delivered” or who “charged me“ neither from common knowledge nor
given context. Such kind of implicit arguments are commonly found in
nominalization and passive because there are high possibilities that not all
agents/patients are always mentioned despite the fact that they might be core
frame elements.

  1. (9)

ThereF isF noD deliveryP IMPGenre-based IMPNon-specific.

  2. (10)

IA donF ’tD thinkP [IA haveF everT beenF chargedP beforeT IMPNon-specific]A.

####  3.3.6 Iterated-set

Iterated-set implicit arguments refer to a heterogeneous set of entities when
the predicates are often an action that happens repeatedly, either iteratively
or generically [Goldberg, 2001]. For example, in sentence 11, the predicate
“wait” implies high repetition, and the set of patients of “what/who I am
waiting for” is so general that it does not hold any meaning beyond the
context. As in example 12, the action “ steal” designates a Scene where
anything could be stolen, but “I” do not and will never steal. Unlike §3.3.4
Type-identifiable referring to a specific type of referents, the set of
“things” in Iterated-set points to a vague set of entities to fill a role in a
more functional way.

  1. (11)

IA neverT waitP [inR theF waitingE roomC]A [[moreC [thanR twoC]C]Q minutesC]T
IMPIterated-set.

  2. (12)

IA donF ’tD stealP IMPIterated-set.

###  3.4 Inherent Ambiguity and “Continuum” of Coreness

####  3.4.1 Category Priority

There are a few cases when it is difficult to choose between two categories.
Since UCCA does not aspire to annotate all possible interpretations [Abend and
Rappoport, 2013], the annotator should make a best guess and choose one
option. The first one is between Deictic and Generic, shown in example 13. The
second one is between Genre-based and Non-specific, as in example 14. To keep
the annotation consistent and maintain as much information as possible, we
always choose Deictic over Generic, and Genre-based over Non-specific if
available.

  1. (13)

[TheF experienceC]A [withR everyQ departmentC]A hasF beenF greatD IMPDeictic.

  2. (14)

IA willF definitelyD referP [[myA friendsA/S]C andN [(my)A familyA/S]C]A
IMPGenre-Based.

####  3.4.2 Nominalization As Occupation

It is a judgment call whether the patient of Process instantiated by a
profession should be annotated at all. Even so it remains debatable which
category such kind of implicit argument belongs to. In the current version of
corpus, we will always annotate it as Type-identifiable. As in example 15, the
patients of whom has been taught is unclear but neither require clarification.
The Scene of teacher/teaching is annotated with a Type-identifiable implicit
argument denoting a type of people recieving education.

  1. (15)

TheyA areF [veryE goodC]D teachersA/P IMPType-identifiable.

##  4 Refined Implicit Corpus

In furtherance of investigating the characteristics of UCCA’s implicit
arguments, we piloted a study to review and refine part of English Web
Treebank333https://catalog.ldc.upenn.edu/LDC2012T13 annotated with the UCCA
foundational
layer.444https://github.com/UniversalConceptualCognitiveAnnotation/UCCA_English-
EWT 200 passages were randomly selected for experiment from the total 723
passages comprising the UCCA EWT dataset.

Abend et al. [Abend et al., 2017] developed an open-source web-based
annotation system, UCCAApp, which supports fast annotation for linguistic
representations. We use this system for carrying out the annotation. The
effectiveness and efficiency in annotating UCCA have been proven by several
studies [Shalev et al., 2019, Prange et al., 2019]. Our annotation process is
divided into two stages. Firstly, we create passage-level review tasks to
check the existing annotation whether they contain implicit arguments, and add
missing arguments if necessary. Secondly, we split passages into sentences,
create tasks with refinement layer and then annotate with corresponding fine-
grained implicit categories. Since all the annotation works were undertaken by
one single annotator, the dataset preferably serves as a demonstration of
concept, and thus further measurement of inter-annotator agreement would be
desired to establish a more sound dataset.

###  4.1 Reviewing Orignial EWT UCCA Dataset

The original implicit argument annotation in EWT UCCA corpus is restricted
only to put concern on constructional null instantiations, and when a unit
lacks a Center or a Process/State, which is out of the scope of this study. We
only regard implicit argument whose category is Participant in UCCA as valid
implicit in this research. Therefore, it is necessary to check and refine the
dataset. Considering the original corpus was annotated on passage-level,
whereas our new dataset will be done on sentence-level, Remote edges across
sentences will be treated by adding a new Implicit node under its origin
Scene.

| # Passages | # Passages | # Sentences | # Sentences | # Implicit
---|---|---|---|---|---
|  | w/ Implicit |  | w/ Implicit | (Valid)
Original | 200 (out of 723) | 103 | 306 | 111 | 153 (98)
Refined | 200 | 116 | 339 | 221 | 413 (348)
Table 3: Statistics of the UCCA EWT dataset sampled passages before and after
reviewing. Implicit (Valid) denotes implcit argument whose role is Participant
in UCCA. Figure 2: Statistics of pilot UCCA implicit dataset

Table 3 shows the statistics before and after reviewing according to the new
UCCA Implicit Argument Typology. It can be seen that in the refined dataset,
116 out of 200 passages contain implicit arguments, 13 more passages than the
original dataset, in which only 103 passages contain implicit arguments.
Yielding an increase of 255%, the review process added 250 more valid implicit
arguments in the corpus.

###  4.2 Statistics

Tokenized and split according to the Universal Dependencies English Web
Treebank [Silveira et al., 2014, Hershcovich et al., 2019a], this pilot corpus
consists of 3702 tokens, 1411 nodes, and 4759 edges over 339 sentences. In
total, 348 valid implicit arguments are found and annotated on 221 sentences.
Figure 2 demonstrates each implicit argument category with its corresponding
number in the pilot refined implicit corpus, and illustrates the percentage of
each implicit category in the dataset. One can see that Genre-based and Non-
specific are the two most frequent categories, both of which have more than 80
instances in the dataset, making up approximately 52% combined. They are
followed by Generic and Deictic, and each occupies about 18%. Type-
identifiable comes penultimate with 33 instances, while Iterated-set is the
least frequent type, which merely has nine instances, accounting for 2.59% of
the whole corpus.

###  4.3 Comparisons to FiGref Annotation

| Type-Identifiable | Deictic | Generic | Non-specific | Genre-based | Iterated-set | Script-inferrable | Other | Invalid
---|---|---|---|---|---|---|---|---|---
Ours | 9.48% | 17.52% | 18.10% | 26.72% | 25.57% | 2.59% | \ | \ | \
FiGref | 7% | 5% | 10% | 4% | \ | \ | 9% | 12% | 53%

Table 4: Relative frequency of annotated implicit types in UCCA’s refinement
layer and FiGref’s annoation for non-recoverable roles in Multi-sentence AMR.
The first four types are shared by both annotation corpora. The following two
are exclusive to UCCA’s refinement layer. The last three are additonally
introduced into FiGref’s set of interpretation types.

FiGref is annotated over Multi-sentence AMR training data [O’Gorman et al.,
2018], SemEval-2010 Task 10 training data, and Beyond NomBank. It contains 856
implicit roles classified into 14 types, which includes all 11 proposed
interpretation types except Genre-based, and four more kinds of invalid roles
to account for those implicit roles of low importance or deal with tricky
occasions. However, FiGref has a relatively low Cohen’s $\kappa$ score [Cohen,
1960] of 55.2 due to its ambiguity and excessive annotation complexity.

Comparatively, we do not annotate genuinely invalid implicit role in the
implicit argument refinement layer for UCCA since we consider it is not a core
element of the event Scene. As UCCA differs Implicit units from Remote edges,
it naturally reduces the annotation complexity as we only need to annotate
essential and unrecoverable implicit arguments within the set of six types we
propose in §3.3.

Owing to the distinct annotation design and lack of statistics provided by
FiGref, it is difficult to perform a comparative quantitative study between
UCCA’s implicit refinement layer and FiGref. However, we are able to look into
the relative frequency of annotated implicit types in UCCA and FiGref’s
annotation for non-recoverable roles in Multi-sentence AMR shown in Table 4.
The distribution distinction can be possibly explained by the different
domains of the corpora and their annotation methodology. We keep Genre-based
type to account for the particular “review” genre in EWT dataset. Among the
three types FiGref has introduced, We can see that invalid roles dominate the
FiGref annotation with 53%. This is because a large amount of non-important
interpretations of null-instantiation are taken into account in FiGref,
whereas the implicit refinement annotation designed for UCCA is limited to
essential important implicit arguments so as to lower annotation complexity
and ambiguity.

##  5 Conclusion

We proposed a novel typology for different implicit arguments in UCCA, which
allows annotation with a relatively low cognitive load. Then we reviewed part
of the existing UCCA English Web Treebank dataset and piloted annotation of
our guidelines with a refinement layer of fine-grained implicit arguments. Our
work provides an example for conducting linguistic analyses of implicit role
interpretation and helping implicit role resolution for natural language
understanding, especially in genre-specific context, e.g., social media and
customer reviews. While the pilot design is promising, future work is needed
to validate the annotation quality, expand the corpus and extend it to
multiple languages. Ideally, a parser that can emit implicit nodes dynamically
should be developed to further the studies of implicit roles.

## Acknowledgements

We would like to thank Omri Abend and Dotan Dvir for their helpful feedback.

## References

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# Recover of acoustic-gravity wave properties revealed from measurements of
VLF radio wave amplitudes

A. K. Fedorenko  E. I. Kryuchkov  O. K. Cheremnykh  A. D. Voitsekhovska  Yu.
O. Klymenko<EMAIL_ADDRESS>aSpace Research Institute National Academy of
Sciences of Ukraine and State Space Agency of Ukraine, prosp. Akad. Glushkova
40, build. 4/1, 03187 MSP Kyiv-187, Ukraine

###### Abstract

A simple method has been proposed to determine acoustic-gravity wave (AGW)
properties at mesosphere heights from measurements of VLF radio signals. For
relatively short paths (less than $\sim$ 2000 km long), simple relations are
obtained for estimation of AGW neutral density fluctuation from measurements
of amplitudes of radio signals. In the wave-hop approximation, we relate the
fluctuations in radio signal reflection height with AGW-induced vertical
displacement of an elementary volume of atmospheric gas. Using these
relations, we can recover some properties of AGWs at mesosphere heights.

###### keywords:

acoustic-gravity wave, ionospheric disturbance, VLF radio wave

##  1 Introduction

Acoustic-gravity waves (AGWs) efficiently transfer the energy and the momentum
between different atmospheric heights (Hines, 1960; Roy et al., 2019;
Cheremnykh et al., 2019). AGWs can also be sources of atmospheric convection
and turbulence redistributing the energy of disturbances between different
scales (from several thousand kilometers to hundreds of meters). These waves
are registered by various satellite and ground-based techniques in the form of
periodic ionosphere parameters fluctuations with periods of $\sim$ 5 min up to
several hours. According to direct satellite measurements, these disturbances
are systematically observed at altitudes of F2 ionosphere region with relative
amplitude of several percent (Johnson et al., 1995; Innis, Conde, 2002;
Fedorenko, Kryuchkov, 2011; Fedorenko et al., 2015). To study the lower
ionosphere, mainly remote methods are used, including a network of ground-
based VLF radio stations. Using this method to study the AGWs it is important
to relate the observed fluctuations in the amplitudes of VLF radio signals
with actual characteristics of the wave disturbances in a neutral atmosphere.

The reflection of VLF radio waves from the upper wall of the Earth-ionosphere
waveguide occurs in the daytime at altitudes of $\sim$ 70–74 km (ionosphere
D-region) and in the nighttime at altitudes of $\sim$ 85–90 km (lower E-region
of ionosphere) (Wait, Spies, 1964; Bezrodny et al., 1988). The interaction of
VLF radio waves with the ionosphere is determined primarily by the
concentration of electrons, its altitude gradient, and the frequency of
electron collisions with neutral particles at the reflection heights. The
waveguide geometry and the reflection coefficients are also changed in the
presence of the disturbances. It leads to fluctuations of amplitudes and
phases in receiving VLF radio signals (Bezrodny et al., 1988). Thus, there is
a hypothetical possibility to restore the properties of atmospheric
disturbances at the heights of VLF radio wave reflection by measuring their
amplitudes. The existing worldwide network of VLF radio stations makes it
possible to systematically study the distribution of AGW activity in the lower
ionosphere and the mesosphere on a global scale.

Two main approaches are commonly used for a theoretical study of VLF radio
wave propagation in the Earth-ionosphere waveguide: the mode theory and the
wave-hop theory (Berry, 1964; Yoshida et al., 2008). In the mode theory, the
waveguide properties are studied over entire path from the transmitter to the
receiver. Here the special software has been developed allowing us to
calculate the value and the gradient of the electron concentration depending
on the path geometry as well as geo- and heliophysical conditions (Ferguson,
1998). This method is effectively used to study the ionosphere based on the
response of VLF radio signals on solar flares (Kolarski, Grubor, 2015). In the
wave-hop theory, the amplitude of the radio signal at the receiving point can
be considered as a superposition of ground wave with several ionospheric ones
which are reflected from the ionosphere (Berry, 1964; Ferguson, 1998; Yoshida
et al., 2008).

The AGWs are the local perturbations of the atmosphere with a typical scale –
mainly from tens to hundreds of kilometers. These waves are observed by
various methods at different altitudes of the atmosphere and the ionosphere.
The amplitudes of AGW-induced fluctuations of VLF radio waves depend on the
AGW spectral characteristics, the radio path length, the ionosphere condition
direction of the wave propagation, etc. Therefore, it is important to localize
the disturbance relative to the path. In this regard, for the study of AGWs,
it is advisable to choose relatively short paths (up to $\sim$ 2000 km) for
which the wave-hop approximation is valid.

In this paper, we show how some properties of AGWs at mesosphere heights can
be recover by using VLF radio signal measurements. The relations connecting
the fluctuation of the radio wave amplitudes with AGW neutral density
fluctuations are obtained. Using these relations, it is possible to determine
the properties of AGW at the heights of the mesosphere.

##  2 AGW fluctuations of atmospheric parameters

AGWs are observed as periodic changes of atmospheric parameters. It is mostly
considered in AGW theory the relative fluctuations of atmospheric gas
concentration $\Delta N_{n}/N_{n}$, of temperature $\Delta T_{n}/T_{n}$, and
of pressure $\Delta p/p$. These AGW fluctuations are connected by so-called
polarization relations (Hines, 1960).

The density AGW fluctuations are related to the displacement of the elementary
gas volume by the following relation (Makhlouf et al., 1990):

$\frac{\Delta\rho}{\bar{\rho}}=\left(\frac{\gamma-1}{\gamma}\right)\frac{\Delta
z_{n}}{H}+\frac{V_{x}U_{x}}{c_{s}^{2}}.$ (1)

Here $\bar{\rho}$ is the undisturbed density, $\Delta z_{n}$ is the vertical
displacement of a volume element, $H=kT_{n}/mg$ is the atmosphere scale
height, $\gamma$ is the ratio of specific heats, $U_{x}=\omega/k_{x}$ is the
AGW horizontal phase velocity, $\omega$ is the frequency, $k_{x}$ is the
horizontal component of wave vector, $V_{x}$ is the horizontal particle
velocity, and $c_{s}$ is the sound speed.

All atmospheric gases are intensively mixed below the turbopause ($\sim$100
km) and, therefore, one can get $\Delta\rho/\bar{\rho}=\Delta
N_{n}/\bar{N}_{n}$, where $\bar{N}_{n}$ is the undisturbed neutral particle
concentration. For simplification, we consider AGWs with periods $T>T_{B}$
($T_{B}$ is Brunt-Väisälä period) and relatively small horizontal phase
velocities $V_{x}<<c_{s}$. In this case one can neglect the second term in the
right side of Eq. (1). We have to also take into account that the temperature
in the upper mesosphere decreases with average vertical gradient of $\sim$3∘
K/km. The latter can be accounted for by using the additional term which is
similar to the non-isothermal frequency of Brunt-Väisälä (Fedorenko,
Kryuchkov, 2014). Under such assumptions, Eq. (1) is rewritten as:

$\frac{\Delta
N_{n}}{N_{n}}\approx\left(\frac{\gamma-1}{\gamma}+\frac{dH}{dz}\right)\frac{\Delta
z_{n}}{H}.$ (2)

Here $dH/dz=\left(H/T_{n}\right)\left(dT_{n}/dz\right)$.

Eq. (2) relates the fluctuation of the atmospheric gas concentration with the
vertical displacement of the volume during an AGW propagation. The physical
sense of the equation can be understood from the following considerations.
When the wave propagates, the area of adiabatic gas compression moves down
until the pressure inside the volume becomes equal approximately the pressure
of background atmosphere. However, the gas density inside the volume remains
lower than the background density. At first view, this leads to a paradoxical
result. Namely, the areas of the adiabatic compression are observed at each
altitude level in the form of concentration minima $\left(\Delta
N_{n}/N_{n}\right)_{\min}$. But the region of adiabatic gas expansion moves
upwards and the density inside the volume remains higher than the background
density. Such regions are observed as concentration maxima $\left(\Delta
N_{n}/N_{n}\right)_{\max}$ (Dudis, Reber, 1976; Fedorenko, Kryuchkov, 2014).

Due to the high density of the neutral gas in the ionosphere D-region,
different chemical reactions involving charged particles occur so quickly that
the electron transport can be neglected at the time scales of AGWs (tens of
minutes). One can assume that chemical equilibrium is achieved in the regions
of AGW density fluctuations. The velocities of chemical reactions determining
the production and the loss of electrons are also changed periodically.
Therefore, the AGW neutral density fluctuation will apparent in the form of
periodic modulation of electron concentration with the wave period. As a
result, AGW propagation at heights of VLF radio wave reflection is accompanied
by the periodic fluctuations of the amplitudes and the phases of the signals
received (Nina, Cadez̆, 2013; Rozhnoi et al., 2014).

##  3 Relation of AGW fluctuations with reflection height of VLF signals

In the wave-hop approximation, it has been found that AGW-induced fluctuations
of the VLF radio wave amplitudes are related to the change of the reflection
height by approximate expression (Fedorenko et al., 2019):

$\frac{\Delta A}{\bar{A}}\approx K\Delta h.$ (3)

Here $\bar{A}$ is the average undisturbed value of radio wave amplitude,
$\Delta A$ is the amplitude disturbance, and $K$ is some function that depends
on the path length, the signal frequency, the time of the day, and the
conditions in the ionosphere. This function has to be calculated for each
radio path separately.

The AGW-induced changes in $\Delta h$ are close in magnitude on different
paths and the daily conditions. Periodic fluctuations of the reflection height
belong on average to interval of $\Delta h\approx 0.2-0.4km$ (Fedorenko et
al., 2019). When AGW propagates in the atmosphere, the vertical displacement
$\Delta z_{n}$ of the neutral gas volume can also be from hundreds of meters
to several kilometers. Therefore, it is important to relate the $\Delta h$
fluctuations in the reflection height of the VLF radio signals with the AGW
properties in the neutral atmosphere.

Let us make some simplifying assumptions. We assume that the volume of the
atmospheric gas moves so slowly under AGW propagation that there is enough
time for photochemical equilibrium to establish in the volume. The
concentration of molecular ions and ion-clusters with which electrons
recombine depend primarily on the neutral particle concentration. Therefore,
we can assume approximately that the equilibrium density of electrons is
determined by the AGW density fluctuation of the neutral particles. We also
neglect the influence of AGW temperature fluctuations on value of $\Delta h$.

Further, we suppose that the VLF wave in the absence of disturbances is
reflected at some effective altitude level $h$ corresponding to the
equilibrium concentration of neutral particles $N_{n0}\left(h\right)$.
Hereinafter, the equilibrium concentration will be indicated by subscript ”0”.
A periodic modulation of the neutral density occurs at level $h$ due to the
propagation of AGWs. The concentration of the neutral particles equals
$N_{n\max}\left(h\right)=N_{n0}\left(h\right)+\Delta N_{n}\left(h\right)$ in
the regions of maximums. Here $\Delta N_{n}\left(h\right)$ is the AGW-induced
variation of concentration. It is related to the vertical displacement of the
volume described by Eq. (2) in (Makhlouf et al., 1990). These regions
correspond to upward movement of atmospheric gas volume (see Section 2). The
regions of density minima $N_{n\min}\left(h\right)=N_{n0}\left(h\right)-\Delta
N_{n}\left(h\right)$ correspond to the volume which is moving down.

The recombination losses of electrons increase in the regions of the neutral
concentration maxima. Therefore, the electron concentration at level $h$
becomes insufficient to provide a reflection. The VLF wave may not be
reflected at level $h$ but it can be happened at some level $h_{1}=h+\Delta h$
where the same concentrations of the neutral particles and the electrons are
achieved as at the unperturbed level. The recombination losses of electrons
are less in the regions of concentration minima. In this case, the VLF wave
should be reflected at level $h_{2}=h-\Delta h$ where the concentration of the
neutral particles is also established as for the unperturbed level.

In view of the foregoing, the condition for the reflection of VLF radio waves
in the neutral concentration maxima can be written as

$N_{n0}\left(h_{1}\right)+\Delta
N_{n}\left(h_{1}\right)=N_{n0}\left(h\right).$ (4)

The equilibrium concentration at level $h_{1}$ is:

$\begin{array}[]{cc}N_{n0}\left(h_{1}\right)=N_{n0}\left(h\right)e^{-\frac{\Delta
h}{H}\left(1+\frac{dH}{dz}\right)}\approx\\\
N_{n0}\left(h\right)\left[1-\frac{\Delta
h}{H}\left(1+\frac{dH}{dz}\right)\right].\end{array}$ (5)

From Eqs. (4) and (5) we can obtain the following expression for relative
fluctuations of neutral particle concentration:

$\frac{\Delta N_{n}\left(h_{1}\right)}{N_{n0}\left(h_{1}\right)}=\frac{\Delta
h}{H}\left(1+\frac{dH}{dz}\right).$ (6)

The condition for the reflection of VLF radio waves in the neutral
concentration minima has the form

$N_{n0}\left(h_{2}\right)-\Delta
N_{n}\left(h_{2}\right)=N_{n0}\left(h\right).$ (7)

Given expression

$\begin{array}[]{cc}N_{n0}\left(h\right)=N_{n0}\left(h_{2}\right)e^{-\frac{\Delta
h}{H}\left(1+\frac{dH}{dz}\right)}\approx\\\
N_{n0}\left(h_{2}\right)\left[1-\frac{\Delta
h}{H}\left(1+\frac{dH}{dz}\right)\right]\end{array}$

for relative concentration fluctuations in the regions of the minima we obtain

$\frac{\Delta N_{n}\left(h_{2}\right)}{N_{n0}\left(h_{2}\right)}=\frac{\Delta
h}{H}\left(1+\frac{dH}{dz}\right).$ (8)

Equations (6) and (8) are identical. They relate the AGW amplitude at the
reflection height radio waves with shift of $\Delta h$.

From Eqs. (3), (6), and (8) it follows some useful relation between relative
fluctuation of neutral density at reflection height and the fluctuation in
amplitudes of radio waves $\Delta A/\bar{A}$:

$\frac{\Delta N_{n}}{N_{n0}}=\alpha\frac{\Delta A}{\bar{A}}.$ (9)

Here, ”transfer” coefficient $\alpha=\left(1+dH/dz\right)/(HK)$ determines by
atmosphere parameters $H$ and $dH/dz$ and by function $K$ mostly depending on
the path length and the VLF wave frequency (Fedorenko et al., 2019).

From Eq. (2) one can obtain the expression for vertical displacement of the
neutral gas volume:

$\Delta z_{n}=\frac{\gamma\left(1+dH/dz\right)}{\gamma-1+\gamma dH/dz}\Delta
h.$ (10)

We have $dH/dz\approx-0.08$ for typical day reflection heights of VLF radio
waves (below the mesopause). Reflection of radio waves at night occurs near
the mesopause ($dH/dz\approx 0$) or slightly higher ($dH/dz\approx 0.1$). We
get $\left(\Delta N_{n}/N_{n}\right)_{day}\approx 3\%$ at daily values of
$\Delta h=200m$ and $\left(\Delta N_{n}/N_{n}\right)_{night}\approx 5\%$ for
$\Delta h=300m$ at night. Taking into account the temperature dependence on
the altitude we get that $\left(\Delta z_{n}/\Delta h\right)_{day}\approx 4.5$
and $\left(\Delta z_{n}/\Delta h\right)_{night}\approx 2.9-3.5$ depending on
the gradient value of $dH/dz$ at the reflection height. Therefore, we obtain
approximately that $\Delta z_{n}$= 0.6–1.2 km at typical AGW-induced shifts of
radio wave reflection level $\Delta h=200-400m$.

For comparison with our results, let us estimate the values of $\Delta z_{n}$
based on the data of AGW observations at the mesosphere heights. The work
(Mitchell, Howells, 1998) presents the results of AGW observations at
altitudes near the mesopause according to EISCAT radar measurements. Following
these investigations, AGWs dominate near the mesopause altitudes with periods
of 30–40 min and the amplitudes of vertical velocity of 2.5 m/s. To estimate
the vertical displacement of the gas volume we use relation
$V_{z}=i\omega\Delta z_{n}$ and obtain $\Delta z_{n}=710-950m$ for AGWs with
properties observed. It is in good agreement with our estimates given above.
Such AGWs would create fluctuations of reflection level $\Delta h=200-270m$
when observed its using the VLF radio waves.

##  4 Conclusions

It is proposed a simple method which allows us to calculate approximately the
fluctuations of the neutral atmosphere caused by AGW propagation from the
measurements of the radio signal amplitudes over relatively short paths (less
than $\sim$ 2000 km long).

The relations between the AGW amplitudes and the amplitudes of the VLF radio
waves are obtained in the wave-hop approximation. Approximate relations (9)
and (10) can be used to determine the fluctuations of the AGW neutral density
and the vertical displacement of the gas volume from the measurements of VLF
radio waves amplitudes. Thus, we can determine the basic properties of AGW at
the heights of the mesosphere.

Note that any information about the properties of the ionospheric plasma has
not been used. We directly relate the variations in the effective reflection
height with the vertical displacements of the gas volume and the neutral
density fluctuations.

The study was supported by grant 2020.02/0015 ”Theoretical and experimental
studies of global perturbations of natural and artificial origin in the Earth-
atmosphere-system” of National Research Foundation of Ukraine.

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# Neutrinos from the Brightest Gamma-Ray Burst?

Kohta Murase11affiliation: Department of Physics; Department of Astronomy &
Astrophysics; Center for Multimessenger Astrophysics, Institute for
Gravitation and the Cosmos, The Pennsylvania State University, University
Park, PA 16802, USA 22affiliation: School of Natural Sciences, Institute for
Advanced Study, Princeton, NJ 08540, USA 33affiliation: Center for
Gravitational Physics and Quantum Information, Yukawa Institute for
Theoretical Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan Mainak
Mukhopadhyay11affiliation: Department of Physics; Department of Astronomy &
Astrophysics; Center for Multimessenger Astrophysics, Institute for
Gravitation and the Cosmos, The Pennsylvania State University, University
Park, PA 16802, USA Ali Kheirandish44affiliation: Department of Physics &
Astronomy; Nevada Center for Astrophysics, University of Nevada, Las Vegas,
NV, 89154 Shigeo S. Kimura55affiliation: Frontier Research Institute for
Interdisciplinary Sciences; Astronomical Institute, Graduate School of
Science, Tohoku University, Sendai 980-8578, Japan Ke Fang66affiliation:
Department of Physics & Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA

###### Abstract

We discuss implications that can be obtained by searches for neutrinos from
the brightest gamma-ray burst, GRB 221009A. We derive constraints on GRB model
parameters such as the cosmic-ray loading factor and dissipation radius,
taking into account both neutrino spectra and effective areas. The results are
strong enough to constrain proton acceleration near the photosphere, and we
find that the single burst limits are comparable to those from stacking
analysis. Quasithermal neutrinos from subphotospheres and ultrahigh-energy
neutrinos from external shocks are not yet constrained. We show that GeV-TeV
neutrinos originating from neutron collisions are detectable, and urge
dedicated analysis on these neutrinos with DeepCore and IceCube as well as
ORCA and KM3NeT.

##  1 Introduction

Gamma-ray bursts (GRBs) are the most powerful explosive phenomena in the
Universe, which have been extensively discussed as ultrahigh-energy (UHE)
cosmic-ray (CR) accelerators (Waxman, 1995; Vietri, 1995). Accompanied high-
energy neutrinos have been searched for, but no detection has been reported so
far (Abbasi et al., 2012; Aartsen et al., 2017a; Albert et al., 2020).
Canonical high-luminosity GRBs cannot make a major contribution to the all-sky
neutrino flux measured in IceCube, and optimistic cases have been ruled out.
The hypothesis that UHE CRs come from GRBs has not yet been excluded, and
various possibilities of high-energy CR and neutrino production in GRBs have
been investigated (see reviews Mészáros, 2015; Kimura, 2022, and references
therein).

On October 9, 2022, an extraordinarily bright burst, GRB 221009A was reported.
This burst was reported by Swift-BAT as an unknown-type transient (Dichiara et
al., 2022), and it had triggered Fermi-GBM about one hour before the BAT
trigger time (Veres et al., 2022). The burst showed an initial pulse of $\sim
10$ s, followed by the main burst beginning at $\sim 180$ s after the GBM
trigger time. The preliminary estimate of the gamma-ray energy fluence
reported by Konus-Wind is $\sim 5\times{10}^{-2}~{}\rm erg~{}cm^{-2}$
(Frederiks et al., 2022). Afterglow emission has been observed at different
wavelengths, and optical follow-up observations revealed that the redshift of
this GRB is $z=0.15$ (de Ugarte Postigo et al., 2022), which suggests that the
isotropic-equivalent gamma-ray energy is ${\mathcal{E}}_{\gamma}^{\rm iso}\sim
3\times 10^{54}$ erg. The detection of high-energy gamma-rays at $\sim
200-600$ s after the GBM trigger time was reported by Fermi-LAT. The highest-
energy photon of 99 GeV was detected by LAT at 240 s after the trigger
(Pillera et al., 2022). The Large High Altitude Air Shower Observatory
observed more than 5000 very-high-energy photons in the TeV range, and even
$\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}10$ TeV photons were detected (Huang et
al., 2022).

In this work, we demonstrate how observations of neutrinos from the brightest
GRB can be used for learning about models of GRB neutrino emission. We focus
on neutrinos emitted during the prompt phase, and consider not only nonthermal
neutrinos accompanied by CR acceleration but also quasithermal neutrinos
produced by inelastic collisions with neutrons. We use $Q_{x}/Q=10^{x}$ in CGS
units and assume cosmological parameters with $\Omega_{m}=0.3$,
$\Omega_{\Lambda}=0.7$ and $h=0.7$.

##  2 Nonthermal Emission

###  2.1 Gamma-ray constraints

The detection of high-energy gamma-rays can be used for placing a lower limit
on the bulk Lorentz factor $\Gamma$ (e.g., Lithwick & Sari, 2001) and/or the
dissipation radius $r_{\rm diss}$ (e.g., Murase & Ioka, 2008; Gupta & Zhang,
2008; Zhang & Pe’er, 2009). The detection of a $\sim 100$ GeV photon at $\sim
240$ s after the trigger (Pillera et al., 2022) suggests that the emission
region has to be trasparent to $\gamma\gamma\rightarrow e^{+}e^{-}$. The two-
photon annihilation optical depth for a gamma-ray with energy
$\varepsilon_{\gamma}$ is

$\tau_{\gamma\gamma}\simeq
150\frac{\eta_{\gamma\gamma,-1}L_{\gamma,52.5}}{r_{\rm
diss,14}\Gamma_{2.5}^{2}\varepsilon_{\rm
MeV}^{b}}\left\\{\begin{array}[]{rl}{(\varepsilon_{\gamma}/\varepsilon_{\gamma}^{b})}^{\beta-1}&\mbox{($\varepsilon_{\gamma}<\varepsilon_{\gamma}^{b}$)}\\\
{(\varepsilon_{\gamma}/\varepsilon_{\gamma}^{b})}^{\alpha-1}&\mbox{($\varepsilon_{\gamma}^{b}<\varepsilon_{\gamma}$)}\end{array}\right.,$
(1)

where $\eta_{\gamma\gamma}\sim 0.1$ is a spectrum-dependent coefficient
(Svensson, 1987), $L_{\gamma}$ is the isotropic-equivalent gamma-ray
luminosity during the main brightest episode, where we take $10^{52.5}~{}{\rm
erg}~{}{\rm s}^{-1}$ in the Konus-Wind band, $\varepsilon^{b}\equiv 1~{}{\rm
MeV}~{}\varepsilon_{\rm MeV}^{b}$ is the photon break energy in the GRB frame,
$\alpha$ and $\beta$ are low- and high-energy photon indices, respectively.
The typical energy of high-energy gamma-rays interacting with target photons
at a break energy is
$E_{\gamma}^{b}=\varepsilon_{\gamma}^{b}/(1+z)\approx\Gamma^{2}m_{e}^{2}c^{4}/\varepsilon^{b}/(1+z)\simeq
23~{}{\rm GeV}~{}\Gamma_{2.5}^{2}{(\varepsilon_{\rm MeV}^{b})}^{-1}$ for GRB
221009A.

Requiring $\tau_{\gamma\gamma}(E_{\gamma}=100~{}\rm GeV)<1$, with
$\varepsilon^{b}\sim 1~{}{\rm MeV}$, $\alpha\sim 1.0$ and $\beta\sim 2.6$
(Frederiks et al., 2022), the dissipation radius can be constrained as

$r_{\rm diss}\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}1.5\times{10}^{16}~{}{\rm
cm}~{}L_{\gamma,52.5}\Gamma_{2.5}^{-2}\left\\{\begin{array}[]{rl}1&\mbox{($\Gamma\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}700$)}\\\
{(5\Gamma_{2.5}^{-2})}^{1.6}&\mbox{($\Gamma\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}700$)}\end{array}\right..$ (2)

We also obtain $\Gamma\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}800~{}{(L_{\gamma,53}{\delta
t}_{-2}^{-1})}^{5/36}$ with $r_{\rm diss}\approx 2\Gamma^{2}c\delta t/(1+z)$
that is expected in the internal shock scenario (where $\delta t$ is the
variability time scale), although this constraint can be relaxed in multi-zone
models (Aoi et al., 2010). High-energy gamma-rays with
$\varepsilon_{\gamma}\gg 1$ GeV are unlikely to be produced near the
photosphere, as has been argued for some of the past bright GRBs (e.g., Zhang
& Pe’er, 2009).

###  2.2 Neutrino constraints

Figure 1:  (Left): Constraints on $\Gamma$ as a function of $r_{\rm diss}$ for
different values of the CR loading factor $\xi_{\rm cr}$. The region below
$r_{\rm ph}$ is not considered for nonthermal neutrino production. (Middle):
Constraints on $\xi_{\rm cr}$ as a function of $r_{\rm diss}$ for a given
Lorentz factor of $\Gamma=10^{2.5}$, where color scale represents the number
of signal events ${\mathcal{N}}_{\rm sig}$. (Right): Constraints on $\xi_{\rm
cr}$ as a function of $\Gamma$, where the internal shock model is assumed with
$\delta t=0.01$ s. The IceCube stacking limit at $90\%$ C.L. (Aartsen et al.,
2017a) for this model is also shown.

If the high-energy CRs are accelerated during the prompt phase, they should
interact with GRB photons via the photomeson production process (Waxman &
Bahcall, 1997), leading to a flux of high-energy neutrinos via decay processes
like $\pi^{+}\to\mu^{+}\nu_{\mu}\to\nu_{\mu}\bar{\nu}_{\mu}\nu_{e}e^{+}$. The
effective $p\gamma$ optical depth is (e.g., Waxman & Bahcall, 1997; Murase et
al., 2006)

$f_{p\gamma}\simeq 0.15\frac{\eta_{p\gamma}L_{\gamma,52.5}}{r_{\rm
diss,14}\Gamma_{2.5}^{2}\varepsilon_{\rm
MeV}^{b}}\left\\{\begin{array}[]{lr}{(\varepsilon_{p}/\varepsilon_{p}^{b})}^{\beta-1}&\mbox{($\varepsilon_{p}<\varepsilon_{p}^{b}$)}\\\
{(\varepsilon_{p}/\varepsilon_{p}^{b})}^{\alpha-1}&\mbox{($\varepsilon_{p}^{b}<\varepsilon_{p}$)}\end{array}\right.,$
(3)

where $\varepsilon_{p}^{b}\approx
0.5\bar{\varepsilon}_{\Delta}m_{p}c^{2}\Gamma^{2}/\varepsilon^{b}$ is the
proton break energy in the GRB frame, and $\bar{\varepsilon}_{\Delta}\sim 0.3$
GeV. Here $\eta_{p\gamma}$ is a correction factor that is $\sim(2-3)$ for
$\alpha\sim 1$ due to the effects of multipion production and high
inelasticity (Murase & Nagataki, 2006). The resulting typical neutrino energy
is $E_{\nu}^{b}\approx 0.05\varepsilon_{p}^{b}/(1+z)\sim 0.6~{}{\rm
PeV}~{}\Gamma_{2.5}^{2}{(\varepsilon_{\rm MeV}^{b})}^{-1}$.

By introducing the CR loading factor $\xi_{\rm cr}\equiv{\mathcal{E}}_{\rm
cr}^{\rm iso}/{\mathcal{E}}_{\gamma}^{\rm iso}$ (Murase & Nagataki, 2006), the
neutrino fluence

$\displaystyle E_{\nu}^{2}\phi_{\nu_{\mu}}$ $\displaystyle\approx$
$\displaystyle\frac{1}{8}\frac{(1+z)}{4\pi d_{L}^{2}}{\rm
min}[1,f_{p\gamma}]\xi_{\rm cr}\frac{{\mathcal{E}}_{\gamma}^{\rm
iso}}{\mathcal{R}_{\rm cr}}$ (4) $\displaystyle\sim$ $\displaystyle
4\times{10}^{-3}~{}{\rm erg}~{}{\rm cm}^{-2}~{}{\rm
min}[1,f_{p\gamma}]\xi_{\rm cr,1}{\mathcal{E}}_{\gamma,54.5}^{\rm
iso}{\mathcal{R}_{\rm cr,1.2}^{-1}},\,\,\,\,\,\,$

where $1/8$ comes from the facts that the $\pi^{\pm}/\pi^{0}$ ratio is $\sim
1$ in $p\gamma$ interactions due to the contribution from direct production
and each flavor of neutrinos after the mixing carries $\sim 1/4$ of the pion
energy in the decay chain. Also, ${\mathcal{R}}_{\rm cr}$ is a spectrum
dependent factor that converts the bolometric CR energy to the differential CR
energy, which is ${\mathcal{R}}_{\rm cr}\sim 15-20$ for a CR spectral index of
$s_{\rm cr}=2.0$ depending on the CR maximum energy.

Non-detection of neutrinos from GRB 221009A was reported by IceCube-
Collaboration (2022), which gives $E_{\nu}^{2}\phi_{\nu_{\mu}}\leq 3.9\times
10^{-2}~{}{\rm GeV}~{}{\rm cm}^{-2}$ at 90% C.L. for an $E_{\nu}^{-2}$
spectrum. This naively infers

${\rm min}[\xi_{\rm cr,-1},f_{p\gamma,-2}\xi_{\rm cr,1}]\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}2.$ (5)

However, this constraint is optimistic and it should not be used in general
cases. Since GRB neutrino spectra are not described by a single power law, it
is significantly relaxed when $E_{\nu}^{b}$ is higher than $10-100$ TeV, the
regime in which IceCube is the most sensitive (Abbasi et al., 2021a).

Because the dissipation radius of prompt emission is not well-known and under
debate, it is often more useful to treat $r_{\rm diss}$ as an uncertain
parameter (Murase et al., 2008; Zhang & Kumar, 2013). In Figure 1 left and
middle, we present constraints in the $r_{\rm diss}-\Gamma$ plane (see also
Gao et al., 2013, for GRB 130427A) and $r_{\rm diss}-\xi_{\rm cr}$ plane,
respectively. The neutrino spectra are calculated using the prescription in He
et al. (2012) and Kimura et al. (2017), assuming $\xi_{B}=1$ for magnetic
fields (Murase & Nagataki, 2006). We adopt $\varepsilon^{b}=1.2~{}{\rm MeV}$,
$\alpha=1.1$ and $\beta=2.6$ (Frederiks et al., 2022), which is sufficient for
the purpose of this work to demonstrate the constraints and to encourage
further searches with detailed information on time-dependent spectra. We use
the point source effective area111In general the GFU effective area (Aartsen
et al., 2017b) should be used for real time follow-ups. But the publicly
available data do not have a sufficiently fine binning in the zenith angle.
(Abbasi et al., 2021b) at declination, $\delta\approx 19.8^{\circ}$. The
convolution of the neutrino flux and the effective area over a relevant energy
range ($200~{}{\rm GeV}\leq E_{\nu}\leq 10^{9}~{}{\rm GeV}$) gives the number
of signal events, ${\mathcal{N}}_{\rm sig}$. Our limit for an $E_{\nu}^{-2}$
spectrum also agrees with the IceCube limit (IceCube-Collaboration, 2022).

Remarkably, we obtain strong constraints on particle acceleration near the
photosphere at $r_{\rm ph}\simeq 3.8\times{10}^{12}~{}{\rm
cm}~{}\zeta_{e}L_{p,53}\Gamma_{2.5}^{-3}$ in the limit that the coasting
occurs under $r_{\rm ph}$. Here $L_{p}$ is the proton luminosity and
$\zeta_{e}$ is the number ratio of electrons and positrons to protons. From
Figure 1 left and middle, we obtain $\xi_{\rm cr}\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}1$ for
$\Gamma\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}300$, which excludes the benchmark case of
the baryonic photospheric scenario ($\xi_{\rm cr}=1$ and $\zeta_{e}=1$),
although the limits can be relaxed with larger values of $\Gamma$. Note that
these constraints on the baryonic photospheric scenario are largely
insensitive to uncertainty in $L_{\gamma}$ because of $f_{p\gamma}\sim
20(L_{\gamma,52.5}/L_{p,53})(\Gamma_{2.5}/\varepsilon_{\rm
MeV}^{b})\tau_{T}\gg 1$ near the photosphere (Murase, 2008), where $\tau_{T}$
is the Thomson optical depth. Our results are conservative in the sense that
we do not include $pp$ collisions that are relevant in the TeV range (Murase,
2008; Wang & Dai, 2009).

On the other hand, IceCube’s non-detection is consistent with outer-zone
(i.e., large $r_{\rm diss}$) models. For example, we obtain
$(2-20)\times{10}^{14}$ cm for $\Gamma\sim 300$ and $\xi_{\rm cr}\sim 10-100$.
Such parameter space is favored by the scenario where UHE CRs are nuclei
rather than protons (see Figure 8 of Murase et al., 2008) and some of the
magnetic reconnection models (e.g., Zhang & Kumar, 2013; Pitik et al., 2021).
This also rules out the neutron escape scenario for UHE CRs (Ahlers et al.,
2011). We also note that low efficiencies of the photomeson production process
are also consistent with the detection of a $\sim 100$ GeV photon. From Eqs.
(2) and (3) we obtain

$f_{p\gamma}\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}3\times{10}^{-3}~{}\eta_{p\gamma,0.5}\left\\{\begin{array}[]{lr}1&\mbox{($\Gamma\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}700$)}\\\
{(\Gamma_{2.5}^{2}/5)}^{1.6}&\mbox{($\Gamma\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}700$)}\end{array}\right..$ (6)

This limit does not depend on $L_{\gamma}$ and $r_{\rm diss}$, and it is
applicable to all proton energies given $\alpha\sim 1$. Although Eq. (6) is
robust as long as neutrinos and gamma-rays are co-produced, it is worthwhile
to note that their emission regions may be different. For example, in the
photospheric scenario, sub-TeV gamma-rays are unlikely to escape and hence
should come from large dissipation radii, e.g., at the external reverse shock.

Prompt GRB neutrinos have been best studied in the context of the internal
shock scenario, and the UHE CR hypothesis requires $\xi_{\rm cr}\sim 10-100$
(Murase et al., 2008; Biehl et al., 2018). The constraints with the assumption
of $r_{\rm diss}\approx 2\Gamma^{2}c\delta t/(1+z)$ are presented in Figure 1
right, where we find $\xi_{\rm cr}\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}3$ for $\Gamma=300$. Interestingly, this
limit is comparable to the IceCube stacking limit (Aartsen et al., 2017a). Our
results are useful because the stacking limit is subject to systematic
uncertainties coming from the aggregation of many bursts. One single burst
provides complementary constraints, and support that canonical high-luminosity
GRBs contribute less than $\sim 1$% of the all-sky neutrino flux.

##  3 Quasithermal Emission

Subphotospheric neutrino production at $\tau_{\rm T}\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}1$ is efficient if
CRs exist. However, CR acceleration at radiation-mediated shocks is
inefficient, and the detection of nonthermal neutrinos from deep
subphotospheres is unlikely for canonical high-luminosity GRBs (Murase & Ioka,
2013). However, high-energy neutrinos can still be produced without relying on
CR acceleration. Neutrons can provide neutrinos through inelastic collisions
between bulk flows or neutron diffusion (Mészáros & Rees, 2000), without
involving collisionless shocks or magnetic reconnections. Such “quasithermal”
neutrinos are naturally produced during neutron decoupling (Bahcall &
Mészáros, 2000) and/or by internal collisions between neutron-loaded outflows
(Murase et al., 2013; Bartos et al., 2013; Zegarelli et al., 2022).

Figure 2: Left: Energy fluences of quasithermal $\nu_{\mu}$ from GRB 221009A
for both collision and decoupling scenarios, where $\xi_{N}=5$ and
${\mathcal{E}}_{\gamma}^{\rm iso}=10^{54.5}$ erg are used. Right: Expected
number of signal events, ${\mathcal{N}}_{\rm sig}$, in DeepCore+IceCube as a
function of $\xi_{N}$ and $\Gamma$. The solid and dashed lines show the
parameter set that lead to doublet and triplet events, respectively.

###  3.1 Neutrinos from neutron decoupling

Recent studies have shown that a GRB jet is collimated during its propagation
inside a star (e.g., Bromberg et al., 2011; Mizuta & Ioka, 2013; Hamidani &
Ioka, 2020; Gottlieb et al., 2022). The jet material becomes hot and the post-
collimation density is so high that $\tau_{\rm T}\gg\tau_{np}\gg 1$, in which
protons and neutrons are coupled. After the breakout, the hot jet material may
expand with $\Gamma(r)\approx\Gamma_{*}(r/R_{*})$ like a fireball, where
$\Gamma_{*}\approx 1/\theta_{j}=10~{}\theta_{j,-1}^{-1}$ is the Lorentz factor
at the breakout. By equating the $np$ collision time $t_{np}\approx
1/(n^{\prime}_{p}\sigma_{np}c)$ (where $\sigma_{np}\approx
3\times{10}^{-26}~{}{\rm cm}^{2}$ is the approximate $np$ cross section) and
the expansion time $t_{\rm dyn}\approx r/(\Gamma c)$, the decoupling radius is
estimated to be $r_{\rm dec}\approx 8.7\times{10}^{11}~{}{\rm
cm}~{}L_{p,53}^{1/3}R_{*}^{2/3}\Gamma_{*}^{-2/3}\Gamma_{\rm max,2.9}^{-1/3}$
(where $\Gamma_{\rm max}$ is the maximum Lorentz factor), at which the Lorentz
factor becomes

$\Gamma_{n,\rm dec}\approx
65~{}L_{p,53}^{1/3}R_{*,11}^{-1/3}\Gamma_{*,1}^{1/3}\Gamma_{\rm
max,2.9}^{-1/3},$ (7)

where a numerical factor of $3/4$ is taken into account. Note that the
decoupling during the acceleration occurs if $\Gamma_{\rm max}$ is larger than
the critical value,

$\Gamma_{np}\approx{\left(\frac{\sigma_{np}L_{p}\Gamma_{*}}{4\pi
m_{p}c^{3}R_{*}}\right)}^{1/4}.$ (8)

Radiative acceleration is fast and the flow is accelerated relativistically,
in which inelastic $np$ collisions occur during the neutron decoupling
(Bahcall & Mészáros, 2000). The $np$ optical depth is around unity at the
decoupling radius by definition, and the energy of quasithermal neutrinos is

$E_{\nu}^{\rm qt}\approx 0.1\Gamma_{n,\rm dec}m_{p}c^{2}/(1+z),$ (9)

which predicts $\sim 1-10$ GeV neutrinos.

The neutrino energy fluence is estimated to be

$\displaystyle E_{\nu}^{2}\phi_{\nu_{\mu}}$ $\displaystyle\approx$
$\displaystyle\frac{1}{12}\frac{(1+z)}{4\pi
d_{L}^{2}}\zeta_{n}\left(\frac{\Gamma_{n,\rm
dec}}{\Gamma}\right)\xi_{N}{\mathcal{E}}_{\gamma}^{\rm iso}$ (10)
$\displaystyle\sim$ $\displaystyle 0.01~{}{\rm erg}~{}{\rm
cm}^{-2}~{}\zeta_{n}(\Gamma_{n,\rm
dec}/0.2\Gamma)\xi_{N,1}{\mathcal{E}}_{\gamma,54.5}^{\rm iso},\,\,\,\,\,\,\,$

where an inelasticity of $\sim 0.5$ is taken into account, $\zeta_{n}$ is the
number ratio of neutrons to protons, $\xi_{N}{\mathcal{E}}_{\gamma}^{\rm iso}$
is the kinetic energy of the proton outflow with $\Gamma\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}\Gamma_{n,\rm dec}$
and $\xi_{N}$ is the nucleon loading factor.

In Figure 2 left, we show neutrino fluences in the neutron “decoupling” model
with $\zeta_{n}=1$. We set $\Gamma_{n,\rm dec}$ from Eq. (7) assuming
$\Gamma=\Gamma_{\rm max}$. The spectra of neutrinos from $np$ collisions are
calculated with Geant4 following Murase et al. (2013).

###  3.2 Neutrinos from colliding neutron-loaded flows

If the neutron decoupling occurs before $\Gamma\approx\Gamma_{\rm max}$ is
achieved, the neutron flow will be caught up by the proton flow, leading to
$pn$ collisions (Beloborodov, 2010; Mészáros & Rees, 2011). Alternatively, if
the coasting occurs earlier than the decoupling, the dissipation of neutrons
via internal collisions between the compound flows may happen. Such collisions
are expected around $r_{\rm dec}\ll r_{\rm ph}$, where the $pn$ optical depth
is $\tau_{pn}\approx 1~{}(\Gamma/\Gamma_{n,\rm
dec})(\zeta_{n}/\zeta_{e})\tau_{T}$. The typical energy of neutrinos is given
by (Murase et al., 2013)

$E_{\nu}^{\rm qt}\approx 0.1\Gamma\Gamma_{\rm rel}^{\prime}m_{p}c^{2}/(1+z),$
(11)

where $\Gamma_{\rm rel}^{\prime}\sim 2$ is the relative Lorentz factor of the
interacting flow and $\sim 30\mbox{--}300$ GeV neutrinos are expected for
$\Gamma\sim{10}^{2}\mbox{--}{10}^{3}$.

The neutrino energy fluence is

$\displaystyle E_{\nu}^{2}\phi_{\nu_{\mu}}$ $\displaystyle\approx$
$\displaystyle\frac{1}{12}\frac{(1+z)}{4\pi
d_{L}^{2}}\tau_{pn}\xi_{N}{\mathcal{E}}_{\gamma}^{\rm iso}$ (12)
$\displaystyle\sim$ $\displaystyle 0.03~{}{\rm erg}~{}{\rm
cm}^{-2}~{}\tau_{pn}\xi_{N,1}{\mathcal{E}}_{\gamma,54.5}^{\rm iso}$

where the normalization is set by $\xi_{N}{\mathcal{E}}_{\gamma}^{\rm iso}$ as
the kinetic energy of the interacting flow. It has been suggested that
dissipation induced by internal collisions between neutron-loaded flows may be
relevant for subphotospheric dissipation (Beloborodov, 2010; Mészáros & Rees,
2011), in which $E_{\nu}^{2}\phi_{\nu}\sim E_{\gamma}^{2}\phi_{\gamma}$ and
$\xi_{N}\sim 3-30$ can be considered as fiducial values.

In Figure 2 left, we show neutrino fluences in the “collision” model for
$\Gamma=300$ and $\Gamma=800$, where $\tau_{pn}=1$ is assumed.

###  3.3 Implications

We calculate the number of signal events using the latest all-flavor effective
areas for GRECO selection (Abbasi et al., 2022) and through-going muon
neutrinos Abbasi et al. (2021b) in IceCube. The values of ${\mathcal{N}}_{\rm
sig}$ for different models are shown in Figure 2 left. Although the decoupling
model is difficult to test with IceCube and other detectors such as KM3Net and
Baikal-GVD, we find that the collision model is promising. A few events of
$\sim 100$ GeV neutrinos can be detected for $\xi_{N}\sim 10$ especially if
the Lorentz factor is sufficiently large (e.g., $\Gamma\sim 800$). These
results are encouraging and we urge dedicated searches for GeV–TeV neutrinos
for GRB 221009A with the existing IceCube data.

In Figure 2 right, we also show the sensitivity to $\xi_{N}$ as a function of
$\Gamma$ for double and triplet detections of signal neutrinos from GRB
221009A. Although the expected signal can dominate if angular uncertainty is
not far from the kinematic angle (Murase et al., 2013), the actual
detectability depends on the atmospheric background rate, so dedicated
analyses at sub-TeV energies are necessary. A search time window ($\Delta T$)
will also need to be carefully considered. The burst duration may vary
depending on energy bands (e.g., Zhang et al., 2014), and the engine duration
is uncertain. Neutrino emission may be dominated by the main episode that
lasts for $\Delta T\sim 100$ s, and luminosity-weighted searches could also be
helpful in more general.

Note that in both the decoupling and collision models, neutrinos and gamma-
rays are mainly produced deep inside the photosphere, from which gamma-rays
with $\varepsilon_{\gamma}\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$>$}}}\Gamma m_{e}c^{2}$ cannot escape (e.g.,
Murase & Ioka, 2008). Residual neutrons would eventually decay after $\sim
880/\Gamma_{n,\rm dec}$ s in the observer frame, but the resulting electron
antineutrino energy is $\sim 0.48~{}\Gamma_{n,\rm dec}$ MeV, which is
difficult to detect with IceCube-like detectors. Electrons may lose their
energies via synchrotron and inverse-Compton emission but their signatures may
easily be overwhelmed by other components.

##  4 Summary and Discussion

We considered how observations of neutrinos from the brightest GRB can be used
for constraining GRB model parameters, including the CR baryon loading factor
that is a critical parameter for the production of high-energy neutrinos and
UHE CRs. We showed that the IceCube non-detection of TeV-PeV neutrinos from
GRB 221009A leads to intriguing constraints on the parameter space of $r_{\rm
diss}$, $\Gamma$, and $\xi_{\rm cr}$, which are comparable to those from the
stacking analysis that is subject to systematics from many GRBs with different
properties. We found that CR acceleration near the photosphere is likely to be
subdominant and obtained $\xi_{\rm cr}\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}1$ for
$\Gamma\mathrel{\hbox{\hbox to0.0pt{\hbox{\lower
4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}300$. We also pointed out that the non-
detection of high-energy nonthermal neutrinos is not surprising in light of
the gamma-ray constraint. This is consistent with outer-zone models (e.g.,
Murase et al., 2008; Zhang & Kumar, 2013). However, neutrinos and gamma-rays
may come from different dissipation regions, and further investigation with
multi-zone models (Bustamante et al., 2017; Rudolph et al., 2020) might be
relevant.

Quasithermal neutrinos, which are naturally expected if neutrons are loaded
into GRB outflows, are not yet constrained. We found that in the collision
model the detection of GeV-TeV neutrinos is possible with IceCube’s low- and
high-energy channels, or reasonable constraints on $\xi_{N}$ can be obtained.
Even higher-energy neutrinos may be produced via the neutron-proton-converter
acceleration mechanism (Kashiyama et al., 2013), and we encourage dedicated
searches by considering appropriate time windows focusing on the bright
episodes of prompt emission.

Finally, we note that UHE CRs could be accelerated by external shocks during
the early afterglow phase (Waxman & Bahcall, 2000; Murase, 2007; Razzaque,
2013), in which PeV-EeV neutrinos are expected and the predicted fluxes have
not been reached by the current IceCube. Future UHE neutrino detectors
(Ackermann et al., 2022) such as IceCube-Gen2, Trinity, and GRAND will be
required to test those afterglow models.

We thank Francis Halzen and Kazumi Kashiyama for discussions. The work of K.M.
and M.M. is supported by the NSF Grant No. AST-2108466. K.M. also acknowledges
support from the NSF Grants No. AST-1908689, No. AST-2108467, and KAKENHI No.
20H01901 and No. 20H05852. M.M. also acknowledges support from the Institute
for Gravitation and the Cosmos (IGC) Postdoctoral Fellowship. A.K.
acknowledges support from Nevada Center for Astrophysics. S.S.K. acknowledges
support by the Tohoku Initiative for Fostering Global Researchers for
Interdisciplinary Sciences (TI-FRIS) of MEXTs Strategic Professional
Development Program for Young Researchers. While we were finalizing the
manuscript, the related work (Ai & Gao, 2022) came out. The approaches are
different, and we impose constraints on GRB parameters based on projecting
expected events with model spectra, instead of the reported single power-law
upper limit. Our study also includes calculations of nonthermal as well as
quasithermal neutrinos.

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