#  Koala: An Index for Quantifying Overlaps with Pre-training Corpora

Thuy-Trang Vu‡ Xuanli He† Gholamreza Haffari‡ Ehsan Shareghi‡
‡Department of Data Science & AI, Monash University
†Department of Computer Science, University College London
{trang.vu1, gholamreza.haffari<EMAIL_ADDRESS><EMAIL_ADDRESS>Corresponding author

###### Abstract

In very recent years more attention has been placed on probing the role of
pre-training data in Large Language Models (LLMs) downstream behaviour.
Despite the importance, there is no public tool that supports such analysis of
pre-training corpora at large scale. To help research in this space, we launch
Koala, a searchable index over large pre-training corpora using compressed
suffix arrays with highly efficient compression rate and search support. In
its first release we index the public proportion of OPT 175B pre-training
data. Koala provides a framework to do forensic analysis on the current and
future benchmarks as well as to assess the degree of memorization in the
output from the LLMs. Koala is available for public use at https://koala-
index.erc.monash.edu/

##  1 Introduction

Large Language Models (LLMs) have achieved state-of-the-art results in NLP and
on many benchmarks have reached the performance ceiling Chowdhery et al.
(2022). This evergrowing success has been facilitated by the algorithmic and
computational progress in scaling up model sizes Wei et al. (2022a); Chowdhery
et al. (2022); Zhang et al. (2022); Brown et al. (2020), integrating human
feedback Ouyang et al. (2022), adopting modes of instructional inference at
both zero- or few-shot settings Chen et al. (2022); Kojima et al. (2022); Wei
et al. (2022b); Nye et al. (2021), as well as the ability of feeding them
massive volumes of free text during pre-training.

Recent works exhibit various cases which highlight the sensitivity of
downstream behaviour of LLMs (and their smaller variants) to the frequency of
observed overlap between pre-training corpora and test set Carlini et al.
(2022); Tänzer et al. (2022); Razeghi et al. (2022); Magar and Schwartz
(2022); Lewis et al. (2020). In the generative setting, several issues such as
hallucination Dziri et al. (2022), undesired biases Kirk et al. (2021), or
toxicity Gehman et al. (2020) have been attributed partly or fully to the
characteristics of the pre-training data, while a parallel line of works have
emphasised on the positive role of filtering the pre-training data for safety
and factual grounding Thoppilan et al. (2022).

The above observations are not a comprehensive list but echo _the undeniable
role of pre-training data in how these models would function in practice_.
Understanding the limitations imposed by pre-training data would also lead to
more informed algorithmic and computational innovations Collier et al. (2022).
However, these forensic studies are done either at a small scale or by using
surrogate sources such as web search hit counts. To the best of our knowledge,
there is no existing work that offers a tool or service for supporting deeper
analyses in this space at large scale.

To help research in this direction, we launch the Koala project, a service
backed by lossless compressed suffix arrays (CSA) Navarro and Mäkinen (2007),
with efficient compression rate and query support. Koala contains a searchable
index over the public portion of the pre-training data111We plan to extend our
coverage of pre-training corpora. behind the OPT 175B Zhang et al. (2022)
model, after deduplication. The constructed index is intended to provide
overlap count statistics for text query (with $\infty$-gram length) files
provided by users. We foresee several areas of impact for Koala; (i) as a tool
to measure data leakage between existing benchmarks and pre-training corpora
of LLMs, (ii) and evaluate the degree of memorisation or creativity in
generative models’ output, (iii) and to support designing harder benchmarks by
reducing the overlap with pre-training corpora.

We present a brief overview of the Koala pipeline for pre-processing and
constructing the index. We also provide examples of the types of analyses that
could be done via Koala by looking at a few commonly used test benchmarks.

##  2 Pre-processing and Corpora Coverage

###  2.1 Pre-processing Steps

Our pre-processing pipeline includes three main steps: cleaning, deduplication
and tokenization. The cleaning step varies according to the pre-trained corpus
and is described in Section 2.2 where we provide the coverage of Koala. In
this section, we describe the deduplication and tokenization steps which are
shared across all pretrained corpora.

We use MinHashLSH (Rajaraman and Ullman, 2011, Chapter 3), a widely-adopted
duplicate detection method for large-scale dataset, in the deduplication step.
Documents are first converted into a set of unigram tokens (shingling) and
then hashed into a short signature, namely minhash, such that the similarity
among documents is preserved. MinHash is a hashing algorithm based on
permutation to generate random hashes to approximate the Jaccard similarity
(Broder, 1997; Cohen et al., 2001). We generate the minhashes with 100
permutations. Finally, the locality-sensitive hashes (LSH) of the minhash
values are calculated to detect the duplicated candidate pairs. We follow
Zhang et al. (2022) to remove those having Jaccard similarity scores above
0.95 threshold. Our deduplication implementation is based on the datasketch
library222https://github.com/ekzhu/datasketch. To scale the deduplication
process to the large corpus, we first perform deduplication in a small batch
and gradually merge the deduplicated batches.

The deduplicated corpus is then tokenized with moses (Koehn et al., 2007) to
normalize punctuation and remove non-printing characters. We do not apply any
casefolding.

###  2.2 Corpora Coverage

The latest version of koala at the time of writing this manuscript covers the
following corpora:333We plan to index more public pre-training corpora as they
become available.

BookCorpus

Zhu et al. (2015) obtained from Hugging
Face.444https://huggingface.co/datasets/bookcorpus

CCNewsv2

extracted English news published between 2016 and 09/2021 from CommonCrawl
(Nagel, 2016) using news-please (Hamborg et al., 2017).

ThePile

(Gao et al., 2021) includes a subset of The Pile: Pile-CC, USPTO Backgrounds,
Guthenberg Rae et al. (2020), OpenWebTexts Gokaslan and Cohen (2019),
OpenSubtitles Tiedemann (2016), Wikipedia (en), DM Mathematics Saxton et al.
(2019), HackerNews.

Pushshift Reddit

     555https://files.pushshift.io/reddit

We used langdetect666https://github.com/fedelopez77/langdetect to detect and
extract the English comments and submission posted from 2005 to 2019. We
followed pre-processing procedure in (Roller et al., 2021) to remove the post
from known non-English subreddits and
bot777https://github.com/eliassjogreen/Reddit-Bot-List, comments longer than
2048 characters or containing URL, or at depth larger than 7 in a thread.

For readers’ reference, the above collection covers the pre-training corpora
of OPT Zhang et al. (2022) with the exception of CC-Stories Trinh and Le
(2018) which is not publicly available at the time of writing this manuscript.
Table 1 reports the size of each corpus in raw and deduplicated version.

| Raw | Deduplication | CSA Indexing
---|---|---|---
| Size | Time | Size | Time | Size
Corpus | (GB) | (Min) | (GB) | (Min) | (GB)
HackerNews | 3.9 | 7,147.2 | 3.2 | 34.2 | 3.3
BookCorpus | 4.3 | 14,301.2 | 3.7 | 88.1 | 3.6
DM Mathematics | 7.8 | 7,881.6 | 1.7 | 32.5 | 3.7
OpenSubtitles | 13 | 19,920.1 | 4.9 | 58.1 | 4.8
Guthenberg | 10.9 | 23,893.0 | 9.7 | 139.0 | 9.5
Wikipedi | 17 | 31,124.4 | 14 | 160.4 | 13
USPTO | 22.9 | 41,866.8 | 22 | 206.8 | 16
OpenWebTexts | 62.8 | 115,088.2 | 54 | 885.8 | 47
CCNewsv2 | 150 | 292,724.7 | 94 | 818.3 | 80
Pile-CC | 227.1 | 416,186.8 | 123 | 1,965.2 | 106
Reddit | 420 | 617,906.5 | 345 | 4,821.2 | 358

Table 1: Statistics of corpora, deduplication step, and the index
construction. Indexing is done on a single CPU core of a 2.70 GHz Intel Xeon
Gold 6150, and requires $2.5\times$ of index size of RAM memory.

##  3 Pipeline and Features of Koala

###  3.1 Data Structure of Koala

Our index construction is inspired by the language models of Shareghi et al.
(2015, 2016), which leverage compressed data structures for building language
models on large text corpora. In this subsection we provide a brief overview
of the data structures behind Koala.

$n$ |  $n$-grams list | Pile-CC | BookCorpus | CCNewsv2 | DM | Guthenberg | HackerNews | OpenSubtitles | OpenWebTexts | USPTO | Wikipedia | Reddit
---|---|---|---|---|---|---|---|---|---|---|---|---
1 | plastic | 959364 | 33845 | 580607 | 0 | 4964 | 14397 | 14114 | 329535 | 598625 | 39435 | 2650049
bags | 578401 | 29213 | 415672 | 0 | 17160 | 5405 | 21590 | 166685 | 111115 | 13708 | 1697726
floating | 303836 | 19752 | 162095 | 0 | 36242 | 10058 | 8165 | 120146 | 244489 | 21938 | 976575
in | 355723492 | 9260245 | 308475794 | 3347881 | 30592137 | 7135629 | 7831355 | 150523086 | 63002717 | 54190836 | 749899124
the | 1056004732 | 34886372 | 782874590 | 6519155 | 107380032 | 20809865 | 23296159 | 428544710 | 251429575 | 128120455 | 2128039302
ocean | 575919 | 30175 | 273507 | 0 | 65172 | 8467 | 23233 | 235331 | 23909 | 41516 | 1125595
1-13 2 | plastic bags | 39722 | 843 | 38094 | 0 | 0 | 588 | 367 | 19323 | 7544 | 1267 | 79539
bags floating | 77 | 4 | 57 | 0 | 0 | 2 | 2 | 25 | 0 | 5 | 275
floating in | 29619 | 3326 | 19189 | 0 | 3492 | 408 | 1397 | 12907 | 2913 | 1695 | 101880
in the | 91136626 | 2440752 | 81218136 | 52379 | 7948909 | 1572721 | 1925941 | 37928620 | 19087529 | 13710461 | 175900138
the ocean | 284689 | 18995 | 139332 | 0 | 33275 | 4066 | 14749 | 114465 | 11596 | 18558 | 667336
1-13 3 | plastic bags floating | 34 | 0 | 22 | 0 | 0 | 1 | 0 | 12 | 0 | 2 | 110
bags floating in | 27 | 0 | 34 | 0 | 0 | 0 | 0 | 8 | 0 | 3 | 101
floating in the | 14481 | 1621 | 10734 | 0 | 1791 | 141 | 725 | 6594 | 1760 | 897 | 43090
in the ocean | 44233 | 1573 | 28680 | 0 | 2025 | 1035 | 2513 | 21517 | 1588 | 2566 | 163343
1-13 4 | plastic bags floating in | 16 | 0 | 10 | 0 | 0 | 0 | 0 | 3 | 0 | 2 | 43
bags floating in the | 20 | 0 | 29 | 0 | 0 | 0 | 0 | 5 | 0 | 3 | 76
floating in the ocean | 580 | 19 | 413 | 0 | 7 | 10 | 16 | 372 | 24 | 42 | 2078
1-13 5 | plastic bags floating in the | 13 | 0 | 8 | 0 | 0 | 0 | 0 | 1 | 0 | 2 | 33
bags floating in the ocean | 4 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 0 | 2 | 9
1-13 6 | plastic bags floating in the ocean | 4 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 2 | 2

Table 2: The n-gram hit statistics per corpus for the correct answer (_plastic
bags floating in the ocean_) to the query _Which of these situations is an
example of pollutants?, choices : [ plastic bags floating in the ocean,
mallard ducks floating on a lake, cottonwood seeds floating in the air, cirrus
clouds floating in the sky]_. This is a sample from the OpenBookQA benchmark.

A Suffix Array (SA) Manber and Myers (1993) of a string $\mathcal{T}$ with
alphabet $\sigma$ is an array of its sorted suffixes. A cell in a suffix
array, denoted by $\text{SA}[i]$, stores a number indicating the staring
position of its corresponding suffix in $\mathcal{T}$. Using a suffix array,
searching for any sequence $\mathbf{u}$ in $\mathcal{T}$ translates into a
binary search to find the range that spans over all substrings that have
$\mathbf{u}$ as their prefix, and is
$\mathcal{O}(|\mathbf{u}|\log|\mathcal{T}|)$. Constructing SA takes
$4$-$8|\mathcal{T}|$ bytes in practice, making them impractical to use for
large data.

To support search on large collections, Compressed Suffix Array exploits the
compressibility of $\mathcal{T}$ while providing the same functionality of SA
in space equal to bzip2 compressed $\mathcal{T}$ in practice. We follow
Shareghi et al. (2016) and use the FM-Index Ferragina et al. (2008) that
utilises the text compressibility vi the Burrows-Wheeler transformation (BWT)
Burrows and Wheeler (1994) of the text. The BWT is defined as,
$\text{BWT}[i]=[\text{SA}[i]-1\ \text{mod}\ |\mathcal{T}|]$. Searching for a
sequence in BWT is done in reverse order and requires
$\mathcal{O}(|\mathbf{u}|\log|\sigma|)$. For more details on BWT and reverse
searching, refer to Navarro and Mäkinen (2007).

The CSA is at the core of Koala’s index and search backbone. We used the SDSL
library Gog et al. (2014) to implement our corpus indexer. We index each
corpus separately. Once a corpus is indexed, its constructed index sits on
disk and could be queried through the Koala web interface (introduced
shortly). Each query is launched into the indexed collection of corpora and
returns the hit counts of the query in the corresponding corpus.

Figure 1: Visualisations of $n$-gram overlap statistics for OpenBookQA and
PIQA test sets, Answer side. Top: OpenBookQA Answer Set ; Bottom: PIQA Answer
Set. Left: Average of Per Instance K-gram hit ratio (i.e., K-gram hit ratio =
1 means 100% of k-grams in one instance were a hit); Right: Average of Per
Instance K-gram hit length ratio (i.e., K-gram hit length ratio with respect
to the instance length = 1 means the k-gram was fully covered, 0.75 means it
was 3/4 covered, etc). PIQA test set size is 1838, OpenBookQA test set size is
500.

Table 1 reports the time and memory usage for construction of indexes.

Figure 2: Screenshots from different features of the Koala webpage. For the
latest version of the interface, please refer to the website.

###  3.2 $n$-gram Overlap Statistics of Koala

Given a text query, Koala can provide its count statistics in several
pretraining corpora by querying the indexes. An example of the raw count
output for the phrase _plastic bags floating in the ocean_ is shown in Table
2. Meaningful insights can be derived from these raw statistics. Figure 1
illustrates two high-level statistics built on top of the $n$-gram counts for
two question answering benchmark test sets, PIQA (Bisk et al., 2020) and
OpenBookQA (Mihaylov et al., 2018), highlighting the amount of leakage or
overlap that exists between these test sets and the entire pre-training data
collection indexed in Koala. We first introduce how these statistics are
calculated per instance, noting that Figure 1 is reporting them as an average
across all instances in each test set. The high-level statistics are defined
as follows:

_Per Instance $k$-gram hit ratio_

measures $\frac{M^{k,t}_{x}}{N^{k}_{x}}$, where $N^{k}_{x}$ is the set of all
$k$-grams of instance $x$, and ${M^{k,t}_{x}}$ is the subset of $N^{k}_{x}$
containing only the $k$-grams with frequency above the pre-set thresholds $t$
(e.g., $\geq$ 1, $\geq$ 10, $\geq$ 100, $\geq$ 1k, $\geq$ 10k, $\geq$100k,
$\geq$1M).

_Per Instance $k$-gram hit length ratio_

measures $\frac{M^{l,t}_{x}}{N^{l}_{x}}$, where $N^{l}_{x}$ is the set of all
substrings of instance $x$ that fall within the length bin $l$ (e.g.,
$l=[0.75,100]$ means all substrings whose lengths are 3/4 of the length of $x$
or more), and $M_{x}^{l,t}$ is the subset of $N^{l}_{x}$, containing only the
substrings with frequency above the pre-set thresholds $t$ (e.g., $\geq$ 1,
$\geq$ 10, $\geq$ 100, $\geq$ 1k, $\geq$ 10k, $\geq$100k, $\geq$1M). We
considered 4 length bins: [0,0.25), [0.25,0.50), [0.5,0.75), and [0.75,1].

While a deep dive into exploring the dependence between data overlap, model
size, and model performance requires a separate work, here we unpack some
highlights from the figures:

#### Highlights from Figure 1 (Left Panel):

The top-left panel highlights that for OpenBookQA above 75% of the unigrams
and bigrams of test set occur at least once ($\geq$ 1) in the pretraining
data, while this drops to below 50% with a higher threshold ($\geq$ 1k). We
observe that above 25% of trigrams occur at least $100$ times in the
pretraining data. Looking at the bottom-left panel for PIQA, we see a much
stronger indication of data overlap. For instance we observe above 55% of
bigrams occur at least $100$ times in the pre-training data. Comparing the two
dataset at the extreme frequency threshold of $\geq$ 1M, we observe that above
50% of PIQA unigrams occur at least 1M times in the pretraining data, while
this is roughly 30% for OpenBookQA.

#### Highlights from Figure 1 (Right Panel):

The average answer length in PIQA and OpenBookQA test sets are 101, and 20,
respectively. This means that [0.25,0.5) length bin covers sequences of
roughly 25-50 tokens for PIQA, while this is roughly 5-10 tokens for
OpenBookQA. We now turn to the highlights from the right panel of Figure 1.
For OpenBookQA (top-right) we observe from the red bars that above 25% of test
instances (roughly 125 cases out of 500 test instances in OpenBookQA) are
almost [75%,100%] covered in the pre-training data for at least 100 times
($\geq$ 100). This corresponds to matches of length 15-20 words. Looking at
PIQA (Bottom-Right), although the coverage with respect to the full length is
not as apparent as OpenBookQA, matches in each corresponding length bin of
PIQA are roughly 4$\times$ longer than OpenBookQA. For instance, about 5% of
test instances of PIQA (roughly 90 cases out of 1838 test instances in PIQA)
have a matching substring of 25-50 words which occur at least $1k$ times in
the pretraining data (see yellow bar for $\geq$ 1000).

The performance ceiling obtained by GPT-3 and OPT models for these two
benchmarks (reported numbers in Appendix A of Zhang et al. (2022)) indicate
the largest variant of both models achieve roughly 80% accuracy for PIQA, and
above 57% accuracy on OpenBookQA. Our highlighted findings suggests a positive
correlation between the amount of data overlap we highlighted and the task
performance ceiling by the LLMs trained on the same pre-training corpora. As a
future direction of analysis, it would be interesting to leverage Koala to
analyse the interdependence of the amount of data overlap, model size, and
task performance. Our preliminary analyses suggest that the connection between
model size and capacity to memorise is not trivial, and varies from task to
task.

###  3.3 Interface of Koala

In this section, we give an overview of the interface of Koala. Figure 2
demonstrates some of Koala’s features. In addition to reporting the raw
counts, Koala provides an interface to upload an $n$-gram file and to
visualize different hit ratio statistics (§3.2). The $n$-gram file is a plain
text file where each line is an $n$-gram whose overlap statistics will be
computed. Figure 2(a) shows the output from this feature. We also provide the
interactive version of the ratio plots (e.g., Figure 1) for 3 question
answering benchmarks: HellaSwag (Zellers et al., 2019), PIQA (Bisk et al.,
2020) and OpenBookQA (Mihaylov et al., 2018).888We plan to expand the coverage
of benchmarks.

In the first release, we limit the live demo queries to $n$-gram files below
2MB and report only on the BookCorpus pretraining corpus. For larger files and
more comprehensive statistics, we provide a form for users to submit the data
and queue the computation. An example of the form is shown in Figure 2(c). We
plan to extend the live demo to the entire pretraining corpora in the near
future.

Another use case of the overlap statistics is to provide a measure of the
memorization vs. creativity for generative LLMs, i.e. how much of the
generated text overlaps with the pretraining corpora. Koala implements a tool
to verify the novelty of an output of generative LLM given a prompt. Figure
2(b) shows an example of this feature which provides the count statistics of
the $n$-grams in the generated text and highlight the overlap $n$-grams.

##  4 Conclusion and Future Work

We presented Koala, a web-based service powered by a compressed data structure
backbone that facilitates efficient search over large collections of texts.
Koala is a tool for comprehensive overlap analysis with potential use-cases
including but not limited to assessing leakage of test benchmarks, measuring
the degree of memorization in generative LLMs outputs. Additionally, Koala not
only provides a public tool for forensic analysis of these phenomena it could
also help benchmark designers towards constructing more challenging testbeds
for LLMs. We will continue to grow our coverage of the existing pre-training
corpora.

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11institutetext: Institut de Recherche en Astrophysique et Planétologie
(IRAP), Université de Toulouse, UT3-PS, CNRS, CNES, 9 av. du Colonel Roche,
31028 Toulouse Cedex 4, France
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>22institutetext: Konkoly Observatory, Research Centre for Astronomy and Earth
Sciences, Eötvös Loránd Research Network (ELKH), Konkoly-Thege Miklós út
15-17, 1121 Budapest, Hungary 33institutetext: CSFK, MTA Centre of Excellence,
Budapest, Konkoly Thege Miklós út 15-17., H-1121, Hungary 44institutetext:
Centre for Star and Planet Formation, Niels Bohr Institute & Natural History
Museum of Denmark, University of Copenhagen, Øster Voldgade 5-7, DK-1350
Copenhagen K, Denmark 55institutetext: Max-Planck-Institut für Astronomie,
Königstuhl 17, D-69117 Heidelberg, Germany 66institutetext: Eötvös Loránd
University, Department of Astronomy, Pázmány Péter sétány 1/A, 1117 Budapest,
Hungary 77institutetext: Institute of Astronomy, Department of Physics,
National Tsing Hua University, Hsinchu, Taiwan

# A high HDO/H2O ratio in the Class I protostar L1551 IRS5††thanks: This work
is based on observations carried out under project numbers W18AO and S16AE
with the IRAM NOEMA Interferometer. IRAM is supported by INSU/CNRS (France),
MPG (Germany), and IGN (Spain).

A. Andreu 11 A. Coutens 11 F. Cruz-Sáenz de Miera 112233 N. Houry 11 J. K.
Jørgensen 44 A. Kóspál 22335566 D. Harsono 77

(Received xxx; accepted xxx)

###### Abstract

Context.  Water is a very abundant molecule in star-forming regions. Its
deuterium fractionation provides an important tool for understanding its
formation and evolution during the star and planet formation processes. While
the HDO/H2O abundance ratio has been determined toward several young Class 0
protostars and comets, the number of studies toward Class I protostars is
limited.

Aims. Our aim is to study the water deuteration toward the Class I
protostellar binary L1551 IRS5 and to investigate the effect of evolutionary
stage and environment on variations in the water D/H ratio.

Methods. Observations were carried out toward L1551 IRS5 using the NOrthern
Extended Millimeter Array (NOEMA) interferometer. The HDO 31,2–22,1 transition
at 225.9 GHz and the H${}_{2}^{18}$O 31,3–22,0 transition at 203.4 GHz were
covered with a spatial resolution of 0.5$\arcsec\times$ 0.8$\arcsec$, while
the HDO 42,2–42,3 transition at 143.7 GHz was observed with a resolution of
2.0$\arcsec$ $\times$ 2.5$\arcsec$. We constrained the water D/H ratio using
both local thermodynamic equilibrium (LTE) and non-LTE models.

Results. The three transitions are detected. The line profiles display two
peaks, one at $\sim$6 km s-1 and one at $\sim$9 km s-1. We derive an HDO/H2O
ratio of (2.1 $\pm$ 0.8) $\times$ 10-3 for the redshifted component and a
lower limit of $>$ 0.3 $\times$ 10-3 for the blueshifted component. This lower
limit is due to the blending of the blueshifted H${}_{2}^{18}$O component with
redshifted CH3OCH3 emission.

Conclusions. The HDO/H2O ratio in L1551 IRS5 is similar to the values in Class
0 isolated sources and in the disk of the Class I protostar V883 Ori, while it
is significantly higher than in the previously studied clustered Class 0
sources and the comets. This result suggests that the chemistry of protostars
that belong to molecular clouds with relatively low source densities, such as
L1551, share more similarities with the isolated sources than the protostars
of very dense clusters. If the HDO/H2O ratios in Class 0 protostars with few
sources around are comparable to those found to date in isolated Class 0
objects, it would mean that there is little water reprocessing from the Class
0 to Class I protostellar stage.

###### Key Words.:

astrochemistry – stars: formation – stars: protostars – ISM: molecules – ISM:
individual objects (L1551 IRS5)

##  1 Introduction

Water is one of the most abundant molecules in the interstellar medium. Its
role is significant in the star formation process as it cools down the warm
regions and boosts the gravitational collapse. It has been detected in
multiple environments, such as protostars (e.g., van Dishoeck et al., 2021),
protoplanetary disks (e.g., Hogerheijde et al., 2011), comets (e.g., Mumma et
al., 1986; Davies et al., 1997), and asteroids (e.g., Rivkin & Emery, 2010).
Deuteration is extremely sensitive to density and temperature conditions
(Ceccarelli et al., 2014), and higher D/H ratios are expected in particular
when water forms in cold and dense conditions (e.g., Coutens et al., 2012;
Jensen et al., 2019). The comparison of the D/H abundance ratio of the
terrestrial oceans (Vienna Standard Mean Ocean Water (VSMOW) $\sim$ 1.557
$\times$ 10-4, de Laeter et al. 2003) with comets and asteroids (a few 10-4)
suggests that these primitive objects could have delivered part of the water
found on Earth (e.g., Hartogh et al., 2011; Altwegg et al., 2015; Trigo-
Rodríguez et al., 2019). Chemical models of water deuteration in
protoplanetary disks also show that the fractionation is not efficient enough
to reproduce the terrestrial water D/H ratio without considering an
inheritance from the parental molecular cloud (Cleeves et al., 2014). Studying
the water deuteration in protostars can consequently help understand the
origin of water in disks and planets (Furuya et al., 2016).

During the last decade the water deuterium fractionation ratio111The D/H ratio
of water is equal to 1/2 $\times$ HDO/H2O due to statistics. has been measured
in the warm inner regions of several Class 0 protostars, thanks to
interferometric observations with the Atacama Large Millimeter/submillimeter
Array (ALMA), the Submillimeter Array, and the Plateau de Bure Interferometer
(Jørgensen & van Dishoeck, 2010; Taquet et al., 2013; Coutens et al., 2014,
and references thereafter). In the clustered sources (IRAS 16293$-$2422,
NGC1333 IRAS2A, IRAS4A$-$NW, and IRAS4B) the HDO/H2O ratio was found to range
between 6 $\times$ 10-4 and 19 $\times$ 10-4 (Persson et al., 2013, 2014).
However, for the isolated sources (L483, B335, and BHR71$-$IRS1) Jensen et al.
(2019) found a HDO/H2O ratio of (1.7 - 2.2) $\times$ 10-3, which is a factor
of $\sim$2–4 higher than for the clustered sources. This difference was
proposed to be the consequence of different durations or temperatures in the
prestellar phase (Jensen et al., 2021).

To reconstruct the full history of water during the star formation process and
bridge the gap between the Class 0 protostellar stage and the formation of
planets, comets, and asteroids, studies of more evolved protostars are needed.
Even if the detection of water is usually difficult in such sources (Harsono
et al., 2020), there are a few Class I objects in which water can be detected,
for example after a strong increase in the accretion rate from the disk onto
the protostar (e.g., FUor or EXor sources, Audard et al., 2014; Fischer et
al., 2022). Such an event leads to a luminosity burst that warms up the disk
and the envelope in which the icy grain mantles can sublimate (Cieza et al.,
2016). However, the studies were limited to only two sources. A first study by
Codella et al. (2016) showed the detection of HDO toward the EXor-like source
SVS13-A with the IRAM 30 m telescope. The presence of high-energy transitions
suggests that they come from the warm inner regions even though emission from
large-scale shocks cannot be excluded. From the nondetection of the
H${}_{2}^{18}$O transition at 203.4 GHz, they estimated a lower limit of the
HDO/H2O ratio of $\gtrsim$ 10-3. More recently, a HDO/H2O ratio of (2.26 $\pm$
0.63) $\times$ 10-3 was obtained with ALMA in the disk of the FUor protostar
V883 Ori (Tobin et al., 2023). The similarity of the water deuteration in
isolated Class 0 protostars supports the inheritance of water from the
envelope to the disk.

Here we report the interferometric determination of the HDO/H2O ratio in
another Class I source, L1551 IRS5 (Chen et al., 1995). This protostellar
binary, located in the Taurus molecular cloud (d $\sim$ 155 pc, Zucker et al.
2019), is classified as a FUor-like object by Connelley & Reipurth (2018)
based on its near-infrared spectra (Mundt et al., 1985; Carr et al., 1987).
The detection of complex organic molecules in its inner regions suggests high-
temperature conditions that would be sufficient to thermally desorb the
molecules frozen on grains, similarly to hot corinos (Bianchi et al., 2020,
Cruz-Sáenz de Miera, in prep.).

Table 1: Detected HDO and H${}_{2}^{18}$O transitions toward the L1551 IRS5 source. Molecule | Transition | Frequency | $E_{\rm up}$ | $A_{\rm ij}$ | $g_{\rm up}$ | Beam size | PA | rms | $d\varv$ | Project
---|---|---|---|---|---|---|---|---|---|---
|  | [MHz] | [K] | [s-1] |  | [$\arcsec$ $\times$ $\arcsec$] | [°] | [mJy beam-1] | [km s-1] |
HDO | 31,2 \- 22,1 | 225896.72 | 168 | 1.3 $\times$ 10-5 | 7 | 0.76 $\times$ 0.51 | 21.7 | 4.2 | 0.5 | W18AO
H${}_{2}^{18}$O | 31,3 \- 22,0 | 203407.52 | 204 | 4.8 $\times$ 10-6 | 7 | 0.83 $\times$ 0.57 | 24.0 | 3.7 | 0.5 | W18AO
HDO | 42,2 \- 42,3 | 143727.21 | 319 | 2.8 $\times$ 10-6 | 9 | 2.51 $\times$ 2.05 | 37.1 | 2.1 | 4.0 | S16AE

##  2 Observations

Observations of two HDO transitions and one H${}_{2}^{18}$O transition were
carried out toward L1551 IRS5 with the Northern Extended Millimeter Array
(NOEMA) through the projects W18AO and S16AE (see Table 1). The HDO 31,2–22,1
and H${}_{2}^{18}$O 31,3–22,0 transitions at 225.9 GHz and 203.4 GHz,
respectively, were observed simultaneously in the A configuration on 15 and 17
February 2019 and in the C configuration on 27 February 2019. High spectral
resolution windows with channel spacing of 62.5 kHz (i.e., 0.08 – 0.09 km s-1)
were used to cover the two transitions. We resampled the data with a
resolution $d\varv$ of 0.5 km s-1 to increase the signal-to-noise ratio. The
HDO 42,2–42,3 transition at 143.7 GHz was covered with a poor resolution of
1.95 MHz (i.e., 4 km s-1) in other NOEMA observations carried out on 25 August
and 31 August 2016 in the D configuration. All the data were calibrated and
imaged using the CLIC and MAPPING packages of the
GILDAS222http://www.iram.fr/IRAMFR/GILDAS/ software. The list of calibrators
for each observation is in Table 3. The continuum was subtracted before the
Fourier transform was applied to the line data. The data were imaged with the
natural weighting mode. The synthesized beam sizes and rms obtained for each
transition are listed in Table 1. The two components, N and S, of L1551 IRS5
are not fully resolved in our observations as they are only separated by
0.36$\arcsec$ (i.e., $\sim$56 AU, Cruz-Sáenz de Miera et al. 2019).

##  3 Results

Figure 1:  Comparison of the spectra of the water isotopolog transitions. The
green, blue, red, and orange solid lines represent the spectra extracted at
the position S, M, N, and O, respectively. The dotted lines show velocities of
6.0 km s-1 (blue) and 9.5 km s-1 (red). Considering the synthetic beam sizes
and the separation of the N and S components, the extracted spectra are not
entirely independent from each other. For the HDO line at 143.7 GHz, the
spatial resolution is too low to distinguish O from N and M from S. The x-axis
scale is larger for this transition.

In a first step, we visualized the datacubes of the HDO and H${}_{2}^{18}$O
lines with the Aladin333https://aladin.u-strasbg.fr/AladinDesktop/ and
CASSIS444CASSIS (http://cassis.irap.omp.eu/) has been developed by IRAP-
UPS/CNRS. softwares (Bonnarel et al., 2000; Glorian et al., 2021). We
extracted the spectra at the positions of the northern source ($\alpha_{\rm
J2000}$=04h31m34$\aas@@fstack{s}$161, $\delta_{\rm
J2000}$=+18$\degr$08$\arcmin$04.72$\arcsec$) and the southern source
($\alpha_{\rm J2000}$=04h31m34$\aas@@fstack{s}$165, $\delta_{\rm
J2000}$=+18$\degr$08$\arcmin$04.359$\arcsec$, Takakuwa et al. 2020). To study
variations in the line intensities with the position, the spectra were also
extracted for a position between the two sources, at an equal distance from
them ($\alpha_{\rm J2000}$=04h31m34$\aas@@fstack{s}$163, $\delta_{\rm
J2000}$=+18$\degr$08$\arcmin$04.550$\arcsec$), that we call M. Because of the
asymmetry in emission maps with respect to M, we include a position at a
similar distance from N in the opposite direction ($\alpha_{\rm
J2000}$=04h31${}^{\rm m}34\aas@@fstack{s}$159, $\delta_{\rm
J2000}$=+18$\degr$08$\arcmin$04.890$\arcsec$) called O. A comparison of these
spectra is shown in Figure 1, and their locations are indicated in Figure 2.

Two velocity components are seen in the line profiles at 203.4 and 225.9 GHz,
similarly to Bianchi et al. (2020) and Mercimek et al. (2022) for complex
organic molecules. The component at $\sim$9 km s-1 is brighter at the N and O
positions than at the M and S positions. The HDO component at $\sim$6 km s-1
is slightly brighter at the M position than the N and S positions, while it is
less bright at the O position. The high-velocity peak corresponds to the N
source or farther to the north, in agreement with Bianchi et al. (2020). The
HDO component at 6 km s-1 seems to arise closer to the M position than the S
position based on the comparison of the observed line intensities. The double
peak created by these two velocity components could then possibly indicate
rotation from a disk surrounding the N source. For the HDO line at 143.7 GHz,
the spatial resolution is too low ($\sim$2.0-2.5$\arcsec$) compared to the
binary separation (0.36$\arcsec$) to observe spectral differences at the four
positions (see Fig. 1). The two velocity components are not observed because
of the low spectral resolution of the data (4 km s-1).

We used the CASSIS software to check possible blending with other molecules at
velocities of both 6 km s-1 and 9 km s-1. The spectroscopic data come from the
CDMS and JPL databases (Pickett et al., 1998; Müller et al., 2005). No
blending is observed for the component at $\sim$ 9 km s-1 either for HDO or
H${}_{2}^{18}$O. However, the H${}_{2}^{18}$O component at $\sim$ 6 km s-1 is
blended with a CH3OCH3 33,1,1 \- 22,1,1 line emitted at $\sim$ 9 km s-1. A
faint line of CH3OCHO 66,0 \- 55,0 (emission at 9 km s-1) is observed in the
wing of the HDO transition at 225.9 GHz. The HDO line at 143.7 GHz does not
seem to be affected by blending.

Integrated emission maps of the HDO 225.9 GHz and H${}_{2}^{18}$O 203.4 GHz
lines are shown in Figure 2. The water emission is compact (less than 70 AU in
diameter), as also seen for complex organic molecules (Bianchi et al., 2020).
As expected, the HDO component at 9 km s-1 (in red) peaks close to the N
position, while the one at 6 km s-1 (in blue) peaks closer to the M position.
A similar distribution is seen for the H${}_{2}^{18}$O component at 9 km s-1.
However, the one at 6 km s-1 peaks closer to the N position. This can be
explained by the blending with the CH3OCH3 line, which is emitted at a
velocity of 9 km s-1. It consequently means that the CH3OCH3 emission
contributes significantly to the flux observed at 6 km s-1. The HDO and H218O
emission sizes were estimated with circular Gaussian fitting of the lines in
the ($u$,$\varv$)-plane. We found approximate source sizes of 0.35$\arcsec$
and 0.45$\arcsec$ for the components at 6 and 9 km s-1, respectively (see
Table 8).

Figure 2:  Integrated emission maps of the HDO line at 225.9 GHz (top) and the
H${}_{2}^{18}$O line at 203.4 GHz (bottom). The blue and red contours
correspond to the integrated flux between 4.5 and 7.5 km s-1 and 7.5 and 12 km
s-1, respectively. The levels of contours start at 3$\sigma$ with a step of
3$\sigma$ for all except for the HDO contours in red (7.5–12 km s-1) which are
spaced by 5$\sigma$. Dust continuum is indicated in grayscale. The beam sizes
are shown in the bottom left corner.

To determine the water deuteration for the two velocity components, we used
the HDO 225.9 GHz and H${}_{2}^{18}$O 203.4 GHz lines. We focused our analysis
on the spectra extracted at the position of the N source for the component at
9 km s-1 and the spectra extracted at the position M (between N and S) for the
component at 6 km s-1. The line fluxes of the two components were collected by
fitting the HDO and H${}_{2}^{18}$O lines with double Gaussian profiles with
the Levenberg-Marquardt fitter (see Figure 4). The results of the fits are
presented in Table 7. Adding a third Gaussian for the CH3OCHO peak does not
affect the HDO flux within the uncertainties. The Gaussian fluxes also do not
differ if we fix the same FWHM and $\varv_{\rm LSR}$ for the HDO and
H${}_{2}^{18}$O lines. Based on the Gaussian fits, we calculated the column
densities of each isotopolog assuming local thermodynamic equilibrium (LTE),
following the formalism of Goldsmith et al. (1999) and Mangum & Shirley
(2015). Then we derived the HDO/H2O ratios assuming a 16O/18O ratio equal to
560 (Wilson & Rood, 1994). We considered a range of excitation temperatures,
$T_{\rm ex}$, between 100 and 300 K, which are characteristic of hot corinos
(e.g., Jørgensen et al., 2018). Source sizes of 0.35$\arcsec$ and
0.45$\arcsec$ were assumed for M and N, respectively. The lines are optically
thin ($\tau$ $\leq$ 0.23 for HDO and $\tau$ $\leq$ 0.15 for H${}_{2}^{18}$O)
in both cases. Figure 6 shows the variation in the HDO/H2O ratio as a function
of the excitation temperature. The extreme values found for the HDO/H2O ratio
are listed in Table 5. The ratio varies between (1.6$\pm$0.6) $\times$ 10-3
and (2.1$\pm$0.8) $\times$ 10-3 for the component at 9 km s-1. Only a lower
limit of $>$0.3 $\times$ 10-3 can be derived for the component at 6 km s-1
given the blending of the H${}_{2}^{18}$O line with CH3OCH3. Using a different
size does not significantly affect the HDO/H2O ratio (see Appendix B.1). Non-
LTE analysis also leads to similar results (see Appendix B.2).

As the fluxes of the two components at 6 and 9 km s-1 are not disentangled in
the HDO observation at 143.7 GHz, we could not use it to derive the HDO/H2O
ratios. However, it can help us constrain the excitation temperatures of HDO.
The analysis described in Appendix B.3 shows that a model with an excitation
temperature for N equal to or lower than 220 K cannot reproduce the flux of
the 143.7 GHz line within 20%. The HDO/H2O ratio derived for $T_{\rm ex}$ =
300 K should consequently be considered more reliable than the value obtained
for $T_{\rm ex}$ = 100 K.

Table 2: Column densities and HDO/H2O ratio in L1551 IRS5 for different
excitation temperatures.

| Component 9 km s-1, position N | Component 6 km s-1, position M
---|---|---
|  $T_{\rm ex}$ = 100 K |  $T_{\rm ex}$ = 300 K |  $T_{\rm ex}$ = 100 K |  $T_{\rm ex}$ = 300 K
Column density [cm-2]
HDO | (7.5 $\pm$ 0.7) $\times$ 1015 | (1.3 $\pm$ 0.2) $\times$ 1016 | (4.8 $\pm$ 0.1) $\times$ 1015 | (8.0 $\pm$ 1.7) $\times$ 1015
H${}_{2}^{18}$O | (8.4 $\pm$ 2.5) $\times$ 1015 | (1.1 $\pm$ 0.3) $\times$ 1016 |  $<$ (1.6 $\pm$ 0.3) $\times$ 1016 |  $<$ (2.1 $\pm$ 0.4) $\times$ 1016
Isotopic ratio
HDO/H2O | (1.6 $\pm$ 0.6) $\times$ 10-3 | (2.1 $\pm$ 0.8) $\times$ 10-3 |  $>$ (0.5 $\pm$ 0.2) $\times$ 10-3 |  $>$ (0.7 $\pm$ 0.3) $\times$ 10-3

555 The source sizes are assumed to be 0.35$\arcsec$ and 0.45$\arcsec$ for M
and N, respectively. The error bars are based on the Gaussian fit
uncertainties.

##  4 Discussion

Figure 3: Comparison of HDO/H2O ratios in comets and protostars. The values
and references can be found in Table 6. The equivalent D/H ratio is indicated
on the right axis. For L1551 IRS5 N ($\varv_{\rm LSR}$ $\sim$ 9 km s-1), the
ratio is plotted for an excitation temperature of 300 K.

Figure 3 shows a comparison of the HDO/H2O ratio of L1551 IRS5 with the values
previously found in protostars and comets. For the component at 9 km s-1, the
HDO/H2O ratio is similar to those measured in isolated Class 0 protostars
(Jensen et al., 2019) and in the disk of the Class I V883 Ori (Tobin et al.,
2023), and significantly higher than the previously studied clustered sources.
At 6 km s-1, the lower limit does not provide sufficient constraints to
discriminate between the two categories.

Water observed in the warm inner regions of protostellar objects results from
the thermal desorption of the icy grain mantles. Deuteration takes place early
in the star formation process when the temperature is low and the density is
relatively high. As a result, the gas phase HDO/H2O ratio observed in the warm
regions of Class 0 objects should reflect those of the icy grain mantles.
Consequently, the observed deuterium fractionation ratio at the Class I stage
should either be similar to the Class 0 stage or decrease if water is
partially reprocessed in the hot corino. In the latter case the deuteration
process would not be efficient enough to increase or maintain the overall
deuteration level. From the HDO/H2O ratio found in the high-velocity component
of L1551 IRS5 we can conclude that the HDO/H2O ratio does not decrease and is
still quite high, similarly to what is found for V883 Ori (Tobin et al., 2023)
and SVS13-A (Codella et al., 2016).

A second conclusion is that the chemistry of L1551 IRS5 appears to be closer
to isolated sources than to clustered sources. The similarity with isolated
sources can be surprising at first sight, as L1551 IRS5 is part of the Taurus
molecular cloud. However, it is located in the LDN 1551 group in the southern
part of the cloud (e.g., Roccatagliata et al., 2020). This group shows a lower
density of sources than other regions in Taurus (Gomez et al., 1993). The
spatial density of sources in the Taurus molecular cloud is also much lower
(only a few tens in $\sim$1 pc3, Gomez et al. 1993) than in Ophiuchus, which
contains IRAS 16293-2422, and the NGC1333 cloud in Perseus (a few 102–103,
Bontemps et al. 2001; Jørgensen et al. 2006). As explained in Jensen et al.
(2021), the higher water deuteration in isolated sources would be due to
either a lower temperature or a longer prestellar phase compared to clustered
sources. The environment around L1551 IRS5 could be colder than around
IRAS16293 and the NGC1333 sources. The dense cores could also have more time
to evolve before their collapse if L1551 IRS5 is on the edge of the cloud and
if it is surrounded by fewer sources. As a consequence, the water deuteration
in L1551 IRS5 would be closer to the Class 0 isolated sources. A similar
explanation was proposed for the Class I protostar V883 Ori, which belongs to
the Orion molecular cloud, but is in a relatively isolated area (Tobin et al.,
2023). The lower values found in comets and in the protostars IRAS 16293-2422,
NGC1333 IRAS2A, IRAS4A, and IRAS4B suggest that our Solar System formed in a
relatively dense clustered area. The similarity of the HDO/H2O ratio between
the binary L1551 IRS5 and the singly Class I object V883 Ori also seems to
indicate that the binarity does not influence the water deuteration.

In conclusion, this study highlights the importance of carrying out water
deuteration measurements toward more sources, at different evolutionary
stages, and in different environments in order to better understand the water
formation and evolution during the formation process of solar-type stars.
Investigations of the D2O/HDO ratio in Class I protostars would also be useful
to check the similarity with Class 0 sources.

###### Acknowledgements.

The authors thank the IRAM staff, especially Jan Martin Winters and Jérémie
Boissier for their help with the data reduction. This study is part of a
project that has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
under Grant agreement No. 949278 (Chemtrip) and Grant agreement No. 716155
(SACCRED). This work made use of Astropy:666http://www.astropy.org a
community-developed core Python package and an ecosystem of tools and
resources for astronomy (Astropy Collaboration et al., 2013, 2018, 2022).

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##  Appendix A Additional tables and figures on observations

Table 3: List of calibrators. Project | Date | Configuration | Phase calibrators | Bandpass calibrator | Flux scale calibrator
---|---|---|---|---|---
W18AO | 15 February 2019 | A | 0507+179, 0446+112 | 3C84 | LkH$\alpha$ 101
W18AO | 17 February 2019 | A | 0507+179, 0446+112 | 3C84 | LkH$\alpha$ 101, 2013+370
W18AO | 27 February 2019 | C | 0507+179, 0446+112 | 3C84 | LkH$\alpha$ 101
S16AE | 25 August 2016 | D | 0507+179, 0354+231 | 3C454.3 | MWC349
S16AE | 31 August 2016 | D | 0507+179, 0354+231 | 3C454.3 | LkH$\alpha$ 101
Table 4: Gaussian fitting parameters and fluxes of the water isotopolog lines.

Molecule | Rest frequency [MHz] |  $\varv_{\rm LSR}$ [km s-1] | Peak intensity [K] | FWHM [km s-1] | Flux [K.km s-1]
---|---|---|---|---|---
North source position (N)
HDO | 225896.72 | 9.11 $\pm$ 0.06 | 5.22 $\pm$ 0.19 | 2.78 $\pm$ 0.15 | 15.46 $\pm$ 1.41
|  | 5.71 $\pm$ 0.09 | 2.90 $\pm$ 0.23 | 1.96 $\pm$ 0.28 | 6.06 $\pm$ 1.34
H${}_{2}^{18}$O | 203407.52 | 9.71 $\pm$ 0.15 | 1.61 $\pm$ 0.21 | 2.25 $\pm$ 0.38 | 3.85 $\pm$ 1.16
|  | 5.44 $\pm$ 0.14 | 2.22 $\pm$ 0.21 | 2.71 $\pm$ 0.48 | 6.39 $\pm$ 1.73
Middle position (M)
HDO | 225896.72 | 5.73 $\pm$ 0.10 | 3.20 $\pm$ 0.25 | 2.01 $\pm$ 0.26 | 6.87 $\pm$ 1.43
|  | 9.15 $\pm$ 0.09 | 4.06 $\pm$ 0.21 | 2.89 $\pm$ 0.23 | 12.48 $\pm$ 1.67
H${}_{2}^{18}$O | 203407.52 | 5.46 $\pm$ 0.09 | 2.06 $\pm$ 0.17 | 2.31 $\pm$ 0.26 | 5.07 $\pm$ 0.98
|  | 9.54 $\pm$ 0.16 | 1.18 $\pm$ 0.17 | 2.29 $\pm$ 0.43 | 2.87 $\pm$ 0.96
N and M positions(a)
HDO | 143727.21 |  |  |  | 1.07 $\pm$ 0.30

777(a) The two components at 6 and 9 km s-1 cannot be distinguished because of
the poor spectral resolution of the data (1.95 MHz). The total integrated flux
is consequently only given for this transition. A similar flux is obtained for
the N and M positions because of the low spatial resolution of the data
(2.5$\arcsec$ $\times$ 2.1$\arcsec$).

Figure 4: Gaussian line fits using the CASSIS software. The upper panel shows
the spectra of the HDO transition at 225.9 GHz, while the lower panel is for
the H${}_{2}^{18}$O transition at 203.4 GHz. The left plots are for the M
position with the fit of the component at 6 km s-1 (blue), while the right
plots are for the N position with the fit of the component at 9 km s-1 (red).
The dotted lines indicate the central velocity of the respective Gaussian. The
green line shows the corresponding double-Gaussian profiles (see Table 7).

Table 3 lists the calibrators used for the different observations. Gaussian
fitting was performed on the spectra to extract the fluxes of the HDO and
H218O lines (see Figure 4). A summary of the fit results is presented in Table
7. We also performed circular Gaussian fitting of the emission lines in the
($u$,$\varv$)-plane to estimate the size of the sources. The results of the
fits are summarized in Table 8.

Table 5: Results from the circular Gaussian fits performed in the
($u$,$\varv$)-plane.

Transition | R.A. | Dec | FWHP [$\arcsec$]
---|---|---|---
HDO 225 GHz | 04h31m34$\aas@@fstack{s}$158 (0.007) | +18$\degr$08$\arcmin$04.75 (0.01) | 0.45 (0.02)
6.7 - 12 km s-1 |  |  |
H${}_{2}^{18}$O 203 GHz | 04h31m34$\aas@@fstack{s}$155 (0.044) | +18$\degr$08$\arcmin$04.80 (0.05) | 0.45 (0.11)
6.7 - 11 km s-1 |  |  |
HDO 225 GHz | 04h31m34$\aas@@fstack{s}$162 (0.014) | +18$\degr$08$\arcmin$04.60 (0.02) | 0.35 (0.04)
3 - 7.3 km s-1 |  |  |
888The uncertainties are indicated in parentheses.

##  Appendix B Exploration of the physical parameters and the LTE assumption

###  B.1 Impact of source size and excitation temperature on HDO/H2O ratio

To investigate the impact of source size and excitation temperature on the
HDO/H2O ratio derived for the component at 9 km s-1, we calculated the column
densities needed to reproduce the fluxes of the HDO line at 225.9 GHz and the
H218O line at 203.4 GHz for a wide range of excitation temperatures (100–300
K) and sizes (0.10–0.75$\arcsec$). The results of this method, which assumes
LTE and optically thin lines, are presented in Figure 5. The derived HDO/H2O
ratio is not very sensitive to the excitation temperature and size as it
ranges between 1.5 $\times$ 10-3 and 2.2 $\times$ 10-3. An analogous study
done by Jørgensen & van Dishoeck (2010) led to similar conclusions.

Figure 6 shows how the HDO/H2O ratios of both components vary as a function of
the excitation temperature when using the source sizes derived with circular
Gaussian fitting of the lines in the ($u$,$\varv$)-plane.

Figure 5: HDO/H2O ratios ($\times$ 10-3) obtained for the component at 9 km
s-1 (N) of L1551 IRS5 as a function of different excitation temperatures and
sizes assuming optically thin LTE emission.

Figure 6: Evolution of HDO/H2O ratio as a function of excitation temperature
assuming source sizes of 0.35$\arcsec$ and 0.45$\arcsec$ for the M and N
positions, respectively. The solid red line represents the ratio found for N
(component at 9 km s-1), while the blue dashed line is for M (6 km s-1). The
arrows indicate lower limits.

###  B.2 Non-LTE modeling

The LTE assumption has been tested and approved for the same transitions in
other hot corinos (Persson et al. 2014; Coutens et al. 2014). We carried out a
similar test for L1551 IRS5 using the non-LTE radiative transfer code RADEX
(van der Tak et al. 2007) with the Large Velocity Gradient (LVG) expanding
sphere method. We varied the temperature between 100 and 300 K, similarly to
the LTE analysis. For the H2 density, we considered a range from 107 to 1011
cm-3. With a non-LTE analysis of three HDO lines, Coutens et al. (2014)
derived a H2 density higher than 108 cm-3 in the warm inner regions of the
low-mass protostar NGC1333 IRAS2A. The results are shown in Figure 7. The
HDO/H2O ratio derived with RADEX, (1.3 - 1.8) $\times$ 10-3 is in agreement
with the LTE values within the uncertainties.

Figure 7: HDO/H2O ratio ($\times$ 10-3) obtained for the component at 9 km s-1
(N) of L1551 IRS5 with the non-LTE radiative transfer code RADEX as a function
of the kinetic temperature and the H2 density.

###  B.3 Modeling of the HDO line at 143.7 GHz and constraints on the
excitation temperatures

The spectral resolution of the HDO transition at 143.7 GHz does not allow us
to distinguish between the fluxes coming from the component at 6 km s-1 and
the one at 9 km s-1. However, we can use the total flux to constrain the
excitation temperatures for the two components. Assuming the source sizes
obtained with the fits in the ($u$,$\varv$)-plane, we calculated the column
densities of HDO needed to reproduce the two components at 225.9 GHz for
various excitation temperatures. Then we predicted the expected flux at 143.7
GHz at 6 and 9 km s-1, and summed the two fluxes before comparing them to the
observed flux (see Table 7). Figure 8 shows that a good agreement ($<$ 20%) is
only found if the excitation temperature for the component at 9 km s-1 is
$\gtrsim$ 240 K. The excitation temperature is not constrained for the
component at 6 km s-1.

Figure 8: Percentage errors between the predicted and observed fluxes of the
HDO line at 143.7 GHz as a function of excitation temperature for positions M
and N. Source sizes of 0.35$\arcsec$ and 0.45$\arcsec$ are assumed for the M
and N positions, respectively.

##  Appendix C Previous results on water deuteration

Table 6 summarizes the HDO/H2O ratios determined in comets and protostars.

Table 6: Water deuterium fractionation ratios determined in comets and
protostars.

Source name | HDO/H2O | Ref.
---|---|---
| ($\times$ 10-4) |
Oort Cloud Comets
1/P Halley | 4.2 $\pm$ 0.6 | (1)
C/1996 B2 Hyatuake | 5.8 $\pm$ 2.0 | (2)
C/1995 O1 Hale-Bopp | 6.6 $\pm$ 1.6 | (3)
C/2007 B3 Lulin | ¡ 11.2 | (4)
8P/Tuttle | 8.2 $\pm$ 2.9 | (5)
C/2009 P1 Garradd | 4.1 $\pm$ 0.4 | (6)
C/2002 T7 LINEAR | 5.0 $\pm$ 1.4 | (7)
153P Ikeya-Zhang | ¡ (5.6 $\pm$ 0.6) | (8)
C/2012 F6 Lemmon | 13.0 $\pm$ 3.2 | (9)
CC/2014 Q2 Lovejoy | 2.8 $\pm$ 0.8 | (9)
Jupiter Family Comets
45P/Honda-Mrkos-Pajdus̆áková | ¡ 4.0 | (10)
103P Hartley 2 | 3.2 $\pm$ 0.5 | (11)
67/P Churyumov-Gerasimenko | 10.6 $\pm$ 1.4 | (12)
46P/Wirtanen | 3.2 $\pm$ 1.3 | (13)
Clustered Class 0 protostars
NGC1333 IRAS 4A-NW | 5.4 $\pm$ 1.5 | (14)
NGC1333 IRAS 2A | 7.4 $\pm$ 2.1 | (14)
NGC1333 IRAS 4B | 5.9 $\pm$ 2.6 | (14)
IRAS 16293-2422 | 9.2 $\pm$ 2.6 | (15)
Isolated Class 0 protostars
BHR71-IRS1 | 18 $\pm$ 4 | (16)
B335 | 17 $\pm$ 3 | (16)
L483 | 22 $\pm$ 4 | (16)
Class I protostars
V883 Ori | 23 $\pm$ 6 | (17)
L1551 IRS5 – $N,\varv_{\rm LSR}$ $\sim$ 9 km s-1 | 21 $\pm$ 8 | (18)
L1551 IRS5 – M, $\varv_{\rm LSR}$ $\sim$ 6 km s-1 |  $>$ (5 $\pm$ 2) | (18)
999This table is an updated version of Table A1 from Jensen et al. (2019). A
factor 2 error on the conversion of the D/H ratio onto the HDO/H2O ratio has
been corrected for the comets C/2012 F6 Lemmon and CC/2014 Q2 Lovejoy (Biver
et al. 2016).

(1) Brown et al. (2012); (2) Bockelée-Morvan et al. (1998); (3) Meier et al.
(1998); (4) Gibb et al. (2012); (5) Villanueva et al. (2009); (6) Bockelée-
Morvan et al. (2012); (7) Hutsemékers et al. (2008); (8) Biver et al. (2006);
(9) Biver et al. (2016); (10) Lis et al. (2013); (11) Hartogh et al. (2011);
(12) Altwegg et al. (2015); (13) Lis et al. (2019); (14) Persson et al.
(2014); (15) Persson et al. (2013); (16) Jensen et al. (2019); (17) Tobin et
al. (2023); (18) This work.