<figure><img src="image_1.png" /></figure>

# CH₃OH and Its Deuterated Species in the Disk/Envelope System of the Low-mass Protostellar Source B335

Yuki Okoda¹, Nami Sakai¹, Yoshimasa Watanabe⁴, Ana López-Sepulcre⁵,⁶, Takahiro Oyama¹, Shaoshan Zeng¹, and Satoshi Yamamoto⁷,⁸

¹ RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan; yuki.okoda@riken.jp

² Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

³ Department of Physics, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

⁴ Materials Science and Engineering, College of Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548, Japan

⁵ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France

⁶ Institut de Radioastronomie Millimétrique, 38406 Saint-Martin d'Hères, France

⁷ The Graduate University for Advanced Studies SOKENDAI, Shonan Village, Hayama, Kanagawa 240-0193, Japan

⁸ Research Center for the Early Universe, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Received 2023 November 1; revised 2024 May 12; accepted 2024 May 16; published 2024 July 12

## Abstract

Deuterium fractionation in the closest vicinity of a protostar is important in understanding its potential heritage to a planetary system. Here, we have detected the spectral line emission of CH₃OH and its three deuterated species, CH₂DOH, CHD₂OH, and CH₃OD, toward the low-mass protostellar source B335 at a resolution of 0.03 (5 au) with Atacama Large Millimeter/submillimeter Array. They have a ring distribution within the radius of 24 au with the intensity depression at the continuum peak. We derive the column densities and abundance ratios of the above species at six positions in the disk/envelope system as well as the continuum peak. The D/H ratio of CH₃OH is ~[0.03–0.13], which is derived by correcting the statistical weight of 3 for CH₂DOH. The [CHD₂OH]/[CH₂DOH] ratio is derived to be higher ([0.14–0.29]). On the other hand, the [CH₂DOH]/[CH₃OD] ratio ([4.9–15]) is higher than the statistical ratio of 3 and is comparable to those reported for other low-mass sources. We study the physical structure on a few astronomical unit scales in B335 by analyzing the CH₃OH (18$_{,}$15 – 18$_{,}$16, A) and HCOOH (12$_{,}$12 – 11$_{,}$11) line emission. Velocity structures of these lines are reasonably explained as the infalling-rotating motion. The protostellar mass and the upper limit to the centrifugal barrier are thus derived to be 0.03–0.07 M☉ and <7 au, respectively, showing that B335 harbors a young protostar with a tiny disk structure. Such youth of the protostar may be related to the relatively high [CH₂DOH]/[CH₃OH] ratio.

*Unified Astronomy Thesaurus concepts: Young stellar objects (1834); Star formation (1569); Protostars (1302); Interstellar molecules (849); Astrochemistry (75)*

## 1. Introduction

The simplest complex organic molecule, methanol (CH₃OH), is widely observed toward protostellar sources to explore their chemical and physical structures. In star-forming clouds, it is thought to be formed through the hydrogenation of CO by H atoms on the dust grain surfaces in cold conditions during the prestellar phase (e.g., Watanabe & Kouchi 2002; Geppert et al. 2005; Fuchs et al. 2009). In this phase, desorption of CH₃OH into the gas phase is limited to nonthermal processes such as surplus energy release of grain surface reactions (e.g., Garrod et al. 2007; Garrod & Widicus Weaver 2013). During the growth of the protostar, CH₃OH is released into the gas phase in the inner envelope mainly through thermal desorption by protostellar heating. Therefore, the CH₃OH emission is used as a tracer of hot core/corino around the protostar (e.g., Herbst & van Dishoeck 2009; Caselli & Ceccarelli 2012; Oya et al. 2016; Manigand et al. 2020; van Gelder et al. 2020; Imai et al. 2022; Ceccarelli et al. 2023; Okoda et al. 2023). The CH₃OH emission is also observed in the outflow-shocked regions through sputtering and heating

processes (e.g., Bachiller & Pérez Gutiérrez 1997; Codella et al. 2020; Okoda et al. 2021).

Recent high-angular-resolution observations reveal the detailed distribution of the CH₃OH emission. For instance, Oya et al. (2016) reported that the CH₃OH emission in the low-mass protostellar source, IRAS 16293-2422 A, is enhanced in a ring-like structure of the innermost part of the infalling-rotating envelope, which corresponds to the transition zone between the envelope and the disk structure. Accretion shock and/or the geometrical effect favorable for protostar heating is proposed as the origin of enhancement (Oya & Yamamoto 2020). Accretion shock is also suggested for the enhancement of the CH₃OH emission in some sources such as B335 (Okoda et al. 2022) and [BHB2007] 11 (Vastel et al. 2022). In short, studies on CH₃OH emission provide us with important information connecting the chemical and physical structures of protostellar sources.

The deuterated species of CH₃OH such as CH₂DOH, CHD₂OH, CD₃OH, and CH₃OD have also been detected in various protostellar sources. Generally, the D/H ratio of molecules (deuterium fractionation) reflects their formation processes as well as physical conditions and evolutionary stages. In fact, it has extensively been studied with observations of various deuterated species of not only CH₃OH but also other molecules over the various regions, such as starless cores (e.g., Bizzocchi et al. 2014; Ambrose et al. 2021), both low-mass and high-mass protostars (e.g., Bianchi et al. 2017a, 2017b; Jørgensen et al. 2018; Taquet et al. 2019; Manigand et al.

<figure><img src="image_2.png" /></figure>

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
2020; Drozdovskaya et al. 2022; van Gelder et al. 2022; Yamato et al. 2024), and comets (e.g., Drozdovskaya et al. 2021; Müller et al. 2022). In these studies, the D/H ratios toward low-mass protostars are found to reach up to 10%.

In particular, the deuterium fractionation of CH3OH in various protostellar sources would be a key to understanding their physical and chemical evolution. Nevertheless, there still remain controversial issues on the CH3OH deuteration. For instance, previous observations suggested a systematic trend of the [CH2DOH]/[CH3OD] ratio between low-mass and high-mass protostellar sources. The ratio in low-mass protostellar sources tends to be higher than the statistical ratio of 3 (e.g., Bizzocchi et al. 2014; Jørgensen et al. 2018), whereas it is much lower than 3 in high-mass protostellar sources (e.g., Charnley et al. 1997; Belloche et al. 2016; Bøgelund et al. 2018; Wilkins & Blake 2022). Thus, more observational efforts for CH3OH and its deuterated spices are awaited to understand the physical meaning of the ratio.

This paper is organized as follows. Our target is introduced in Section 2. Some key information on the observation is described in Section 3. In Section 4, we derive and discuss the column densities and the abundances of deuterated CH3OH in the disk/envelope system. We show the effect of $S\mu^2$ on the column densities in Section 5. The distributions and velocity maps of the disk/envelope system are shown in Section 6. Using the infalling-rotating-envelope (IRE) model reported by Oya et al. (2022), we explore kinematics in the disk/envelope system in Section 7. In Section 8, we discuss the abundance ratios with those in other sources. We summarize the main results in Section 9.

## 2. Target: B335

B335 is a Bok globule (Keene et al. 1980), with which the Class 0 protostar IRAS 19347+0727 is associated. The bolometric temperature ($T_{bol}$) is 37 K (Andre et al. 2000), while the bolometric luminosity ($L_{bol}$) is 1.6 $L_⊙$ (Kang et al. 2021). The distance to B335 is reported to be 165 pc, based on the Gaia Data Release 2 parallax data (Watson 2020). In this paper, we employ this distance not only for our results but also for those in the previous works. We adjusted the physical parameter values of the previous works for the new distance (165 pc), since the studies before 2020 employed the distance to B335 of 100 pc, except for Yen et al. (2015) who employed 150 pc.

Extensive observations toward this isolated protostellar source have been carried out to develop star formation studies in terms of both physical and chemical structures (e.g., Hirano et al. 1988; Evans et al. 2015; Yen et al. 2015; Imai et al. 2016; Bjerkeli et al. 2019; Imai et al. 2019, 2022; Okoda et al. 2022). A bipolar outflow extending along the east-to-west direction (P.A. ~90°) was found (e.g., Hirano et al. 1988, 1992; Stutz et al. 2008; Bjerkeli et al. 2019; Cabedo et al. 2021), which is almost in parallel to the plane of the sky. Dedicated works have been reported on the physical properties of the disk/ envelope system and the protostellar mass (Evans et al. 2015; Yen et al. 2015; Bjerkeli et al. 2019; Imai et al. 2019). The protostellar mass was estimated to be 0.06 $M_⊙$ from imperceptible rotation motion in the C$^{18}$O line on the assumption of the infalling-rotating motion by Yen et al. (2015). Imai et al. (2019) clearly revealed a rotation motion around the protostar in the methanol (CH3OH) and formic acid (HCOOH) lines with a higher-resolution observation

(~0′′1). They derived the protostellar mass and the radius of the centrifugal barrier to be 0.03–0.1 $M_⊙$ and <8 au, respectively, assuming the infalling-rotating motion. Meanwhile, the velocity gradient seen in the CH3OH and SO2 lines is independently reported by Bjerkeli et al. (2019), where the results are consistent with a pure freefall or a Keplerian rotation with the protostellar mass of 0.08 $M_⊙$. They also estimated the disk/envelope mass from the dust continuum emission within 12 au to be $8 \times 10^{-4} M_⊙$. In B335, a Keplerian disk is still veiled, although recent observations have found it around other young sources even in the Class 0/I stages (e.g., Ohashi et al. 2014; Aso et al. 2015; Okoda et al. 2018; Oya 2020). Bjerkeli (2023) implies that the disk structure just started to form in B335, based on the continuum observation.

The disk/envelope direction is close to the south-to-north axis. We employ the position angle (P.A.) of 5° for the disk/ envelope direction in this paper (Figure 3(a)), based on the recent works observing a foot of the outflow with the Atacama Large Millimeter/submillimeter Array (ALMA; P.A. 95°: Bjerkeli et al. 2019; Cabedo et al. 2021). Bjerkeli et al. (2019, 2023) suggested the disk/envelope axis to be P.A. 5°, and Cabedo et al. (2021) reported it to be P.A. 2°. On the other hand, Oya et al. (2022) and Okoda et al. (2022) employed P.A. 0° to just take a consistent approach with Imai et al. (2019). However, only a 5° difference in the P.A. does not significantly affect any result.

Recently, CH3OH and CH2DOH were observed in B335 with ALMA at a high resolution of 0′′03 (~5 au at $d = 165$ pc) by Okoda et al. (2022). In their study, the temperature structure in the disk/envelope system was the main focus by using CH3OH, CH2DOH, HCOOH, and NH2CHO line emission. The chemical differentiation among molecular distribution was also studied, based on the principal component analysis (PCA). They found that the CH3OH and deuterated CH3OH species (CH2DOH, CHD2OH, and CH3OD) have a ring-shaped and extended distribution. Their velocity structures most likely trace the disk/envelope system, while HCOOH, HNCO, and NH2CHO have a more compact distribution. Although the column densities of CH3OH and CH2DOH were derived simultaneously in the derivation of the temperature to show its variation along the major axis of the disk/envelope system, they were not discussed in terms of the D/H ratio. Since the intrinsic line intensities, $S\mu^2$ ($S$ is the line strength and $\mu$ the dipole moment responsible for the transition: e.g., Yamamoto 2017), of CH2DOH in the database of JPL (Pickett et al. 1998) was recognized to be inaccurate for their observed transitions in B335, the analysis and discussion of the CH3OH deuteration including CHD2OH and CH3OD were left for a separate publication.

The $S\mu^2$ value is directly related to the individual line intensity and is an important parameter in the line analysis (the details are described elsewhere, e.g., Yamamoto 2017; Oyama et al. 2023). Since the $S\mu^2$ values of CH2DOH were recently measured with the laboratory experiment (Oyama et al. 2023) and those of CHD2OH with the theoretical calculation (Coudert et al. 2021, See also Drozdovskaya et al. 2022), reliable derivations of their column densities are now possible by making use of them. In this paper, we study the CH3OH deuteration and the velocity structure of the disk/envelope system within a few 10 au scale.
<table><caption>**Table 1**

Analyzed Molecular Lines<sup>a</sup></caption><thead><tr><th>Molecule</th><th>Transition</th><th>Frequency (GHz)</th><th>S<sub>μ</sub><sup>2</sup> <sup>b</sup><br>(D<sup>2</sup>)</th><th>S<sub>μ</sub><sup>2</sup> SUMIRE <sup>c</sup><br>(D<sup>2</sup>)</th><th>log<sub>10</sub> A<sup>d</sup></th><th>log<sub>10</sub> A<sub>SUMIRE</sub><sup>e</sup></th><th>E<sub>u</sub> k<sup>-1</sup><br>(K)</th><th>Synthesized Beam Size</th></tr></thead><tbody><tr><td>CH<sub>3</sub>OH</td><td>18<sub>3,15</sub> – 18<sub>2,16</sub>, A</td><td>247.610918</td><td>17.358</td><td>...</td><td>-4.081</td><td>...</td><td>446.6</td><td>0"033×0"027 (P.A. –2°6)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>21<sub>3,18</sub> – 21<sub>2,19</sub>, A</td><td>245.223019</td><td>20.623</td><td>...</td><td>-4.084</td><td>...</td><td>585.8</td><td>0"033×0"028 (P.A. –6°9)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>12<sub>6,7</sub> – 13<sub>5,8</sub>, E</td><td>261.704409</td><td>2.131</td><td>...</td><td>-4.75</td><td>...</td><td>359.8</td><td>0"032×0"026 (P.A. 4°6)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>17<sub>3,14</sub> – 17<sub>2,15</sub>, A</td><td>248.282424</td><td>16.315</td><td>...</td><td>-4.081</td><td>...</td><td>404.8</td><td>0"032×0"026 (P.A. –9°4)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>4<sub>2,2</sub> – 5<sub>1,5</sub>, A</td><td>247.228587</td><td>1.086</td><td>...</td><td>-4.673</td><td>...</td><td>60.9</td><td>0"033×0"027 (P.A. –5°1)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>2<sub>1,1</sub> – 1<sub>0,1</sub>, E</td><td>261.805675</td><td>1.334</td><td>...</td><td>-4.254</td><td>...</td><td>28.0</td><td>0"032×0"026 (P.A. 4°3)</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>10<sub>2,8</sub> – 10<sub>1,9</sub>, o<sub>1</sub></td><td>244.9888456</td><td>3.439</td><td>2.22</td><td>-4.552</td><td>-4.74</td><td>153.3</td><td>0"033×0"028 (P.A. –7°4)</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>4<sub>2,2</sub> – 4<sub>1,3</sub>, e<sub>0</sub></td><td>244.8411349</td><td>2.540</td><td>1.80</td><td>-4.317</td><td>-4.47</td><td>37.6</td><td>0"033×0"028 (P.A. –7°5)</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>5<sub>2,4</sub> – 5<sub>1,5</sub>, e<sub>0</sub></td><td>261.6873662</td><td>4.006</td><td>3.01</td><td>-4.119</td><td>-4.24</td><td>48.3</td><td>0"032×0"026 (P.A. 4°6)</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>3<sub>2,1</sub> – 3<sub>1,2</sub>, e<sub>0</sub></td><td>247.6257463</td><td>2.360</td><td>1.68</td><td>-4.225</td><td>-4.37</td><td>29.0</td><td>0"033×0"027 (P.A. –2°6)</td></tr><tr><td>CHD<sub>2</sub>OH<sup>f</sup></td><td>6<sub>1,1</sub> – 5<sub>1,1</sub>, o<sub>1</sub></td><td>246.1432950</td><td>4.821</td><td>5.22</td><td>-4.191</td><td>-4.16</td><td>52.9</td><td>0"033×0"027 (P.A. –4°4)</td></tr><tr><td>CHD<sub>2</sub>OH<sup>f</sup></td><td>6<sub>1,2</sub> – 5<sub>1,2</sub>, e<sub>0</sub></td><td>246.2530390</td><td>4.759</td><td>5.36</td><td>-4.196</td><td>-4.14</td><td>44.6</td><td>0"033×0"027 (P.A. –4°4)</td></tr><tr><td>CHD<sub>2</sub>OH<sup>f</sup></td><td>4<sub>1,2</sub> – 4<sub>0,1</sub>, o<sub>1</sub>-e<sub>0</sub></td><td>247.2524160</td><td>5.655</td><td>6.86</td><td>-3.956</td><td>-3.87</td><td>31.8</td><td>0"032×0"027 (P.A. –7°7)</td></tr><tr><td>CH<sub>3</sub>OD</td><td>5<sub>1</sub> – 4<sub>0</sub>, E</td><td>245.142988</td><td>3.8</td><td>...</td><td>-4.8</td><td>...</td><td>37.3</td><td>0"033×0"028 (P.A. –6°9)</td></tr><tr><td>HCOOH</td><td>12<sub>0,12</sub> – 11<sub>0,11</sub></td><td>262.1034810</td><td>24.157</td><td>...</td><td>-3.694</td><td>...</td><td>82.8</td><td>0"032×0"026 (P.A. 4°4)</td></tr></tbody></table>

**Notes.**

<sup>a</sup> Line parameters are taken from CDMS (Endres et al. 2016) and JPL (Pickett et al. 1998) except for CH<sub>3</sub>OD. The parameters for CH<sub>3</sub>OD are taken from Anderson et al. (1988) and Duan et al. (2003).

<sup>b</sup> Taken from CDMS for CH<sub>3</sub>OH and CHD<sub>2</sub>OH and calculated from the intensity listed in JPL for CH<sub>2</sub>DOH. For CH<sub>3</sub>OD, we employ the data reported by Anderson et al. (1988).

<sup>c</sup> Taken from Oyama et al. (2023) for CH<sub>2</sub>DOH. Provided by T. Oyama for CHD<sub>2</sub>OH. These values are the experimental data. The uncertainty is 10% for the S<sub>μ</sub><sup>2</sup> SUMIRE value.

<sup>d</sup> Einstein coefficients calculated from S<sub>μ</sub><sup>2</sup><sub>JPL</sub> or S<sub>μ</sub><sup>2</sup><sub>CDMS</sub>.

<sup>e</sup> Einstein coefficients calculated from S<sub>μ</sub><sup>2</sup><sub>SUMIRE</sub>.

<sup>f</sup> The quantum numbers follow the definition of CDMS.

**3. Observation**

Single-point ALMA observations toward B335 were carried out with the Band 6 receiver in the four execution blocks of the Cycle 6 operation on 2019 June 10, 12, 13, and 23. The molecular lines analyzed in this paper are summarized in Table 1. The line at 247.2524160 GHz is newly identified in this paper as the CHD<sub>2</sub>OH (4<sub>1,2</sub>–4<sub>0,1</sub>, o<sub>1</sub>-e<sub>0</sub>) line, based on the spectroscopic data by Coudert et al. (2021) and the database of CDMS (Endres et al. 2016). Since the maximum recoverable scale is 0"3 for these observations, we here focus on the small-scale structure around the protostar. The synthesized beam size for each line is summarized in Table 1. The spectral resolution is 0.544–0.691 km s<sup>-1</sup>, and the rms noise is 1.0 mJy beam<sup>-1</sup>channel<sup>-1</sup>. Further observation parameters (calibrators, primary beamwidth, correlator setups, etc.) are described elsewhere (Okoda et al. 2022).

The data reduction was performed with the Common Astronomy Software Applications package 5.8.0 (McMullin et al. 2007) as well as a modified version of the ALMA calibration pipeline. We combined four visibility data in the uv plane after phase self-calibration using each continuum data and the application of their solution to the spectral line data.

**4. Deuterated CH<sub>3</sub>OH Species in the Disk/Envelope System**

We here analyze the CH<sub>3</sub>OH, CH<sub>2</sub>DOH, CHD<sub>2</sub>OH, and CH<sub>3</sub>OD lines listed in Table 1 to study the deuterium fractionation of CH<sub>3</sub>OH in the disk/envelope system. Figure 1 shows the moment zero maps of the CH<sub>3</sub>OH (18<sub>3,15</sub> – 18<sub>2,16</sub>, A), CH<sub>2</sub>DOH (4<sub>2,2</sub> – 4<sub>1,3</sub>, e<sub>0</sub>), CHD<sub>2</sub>OH (4<sub>1,2</sub> – 4<sub>0,1</sub>, o<sub>1</sub>-e<sub>0</sub>), and CH<sub>3</sub>OD (5<sub>1</sub>–4<sub>0</sub>, E) lines with the synthesized beam size (0"030×0"023: Table 1). They have a ring-shaped distribution around the protostar with the intensity depression at the

continuum peak due to the high dust opacity. Similar images are also reported for the CH<sub>3</sub>OH, CH<sub>2</sub>DOH, and CH<sub>3</sub>OD lines by Okoda et al. (2022), where the beam sizes are smoothed to be 0"034 to perform the PCA.

Okoda et al. (2022) derived the column densities of CH<sub>3</sub>OH and CH<sub>2</sub>DOH with each aperture of 0"03 for 9 positions along the midplane of the envelope (P.A. 0°) using the S<sub>μ</sub><sup>2</sup> values calculated from the line intensities listed in the database of JPL. A recent experimental measurement for some lines of CH<sub>2</sub>DOH with SUMIRE (Spectrometer Using superconductor Mixer Receiver) by Oyama et al. (2023) found that the S<sub>μ</sub><sup>2</sup> values in the database of JPL significantly deviate from the measured values. The experimental S<sub>μ</sub><sup>2</sup> values for some lines of CHD<sub>2</sub>OH are now available with SUMIRE very recently (Oyama et al. in prep). In the following, we first derive the column densities and abundances of CH<sub>2</sub>DOH and CHD<sub>2</sub>OH by using the newly available experimental S<sub>μ</sub><sup>2</sup> values (hereafter referred to as S<sub>μ</sub><sup>2</sup><sub>SUMIRE</sub>) listed in Table 1. We discuss the dependence of the gas temperature and the column densities on the S<sub>μ</sub><sup>2</sup> values later (Section 5).

**4.1. Column Densities**

We derive the column densities of CH<sub>3</sub>OH and deuterated CH<sub>3</sub>OH species toward seven rectangle areas (0"03×0"05) along the disk/envelope direction (P.A. 5°) including the continuum peak position, as shown in Figure 1(a). The rectangle shape is here employed to obtain the spectra with the high signal-to-noise ratio as much as possible for the disk/ envelope system with the apparently thick disk height. For our derivation, we use the same equations as those reported by Okoda et al. (2022), assuming the local thermodynamic equilibrium (LTE) condition (Appendix A). In this analysis,
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Moment zero maps of the CH<sub>3</sub>OH (18<sub>3,15</sub> – 18<sub>2,16</sub>, A, E<sub>u</sub> = 447 K), CH<sub>2</sub>DOH (4<sub>2,2</sub> – 4<sub>1,3</sub>, e<sub>0</sub>, E<sub>u</sub> = 38 K), CHD<sub>2</sub>OH (4<sub>1,2</sub> – 4<sub>0,1</sub>, o<sub>1</sub>e<sub>0</sub>, E<sub>u</sub> = 32 K), and CH<sub>3</sub>OD (5<sub>1,40</sub>, E, E<sub>u</sub> = 37 K) emission. The integrated velocity range is from –0.2 km s<sup>–1</sup> to 14.5 km s<sup>–1</sup>. The systemic velocity is 8.34 km s<sup>–1</sup> (Yen et al. 2015). Contour levels are every 3σ from 3σ, where σ is 1.5 mJy beam<sup>–1</sup>, 3.0 mJy beam<sup>–1</sup>, 3.0 mJy beam<sup>–1</sup>, and 2.0 mJy beam<sup>–1</sup>, respectively. The spectra are obtained within each rectangle area (0″03×0″05) to calculate the temperature and the column density. The numbers represent the offsets from the continuum peak (0″′0). The white cross mark shows the continuum peak position (α<sub>2000</sub>, δ<sub>2000</sub>) = (19<sup>h</sup>37″00″90<sub>−</sub>7″34′09″49). The red ellipse in each map represents the beam size. The red and blue arrows in panel (a) show the directions of the red- and blueshifted outflow.</figcaption></figure>

we focus on the disk/envelope system within 20 au in radius from the protostar. The LTE analysis is justified, since the H<sub>2</sub> density for that area is roughly estimated to be higher than 10<sup>8</sup> cm<sup>-3</sup>, based on its apparent size and the H<sub>2</sub> column density of 5.66 × 10<sup>23</sup> cm<sup>-2</sup> reported by Imai et al. (2016). In addition, the CH<sub>3</sub>OH emission in our observation selectively traces the warm/hot region because of the maximum recoverable scale of 0″′3. In the derivation, the optical depths of molecular lines and dust emission are considered by assuming that the gas and dust are well mixed and the gas temperature is equal to the dust temperature. Since the dust continuum emission is intense, we take its effect into the analysis approximately (Appendix A).

The best-fit temperatures and column densities are summarized in Table 2, where the errors are evaluated by the χ² analysis. The offset in Table 2 means the distance from the protostar along the midplane of the disk/envelope system from the southwestern to the northeastern direction (P.A. 5°), where the offset of 0″′1 (~17 au) is almost close to the edge of the

distributions of CH<sub>3</sub>OH and its deuterated species. Examples of the line parameters of CH<sub>3</sub>OH at the offset of –0″′03 used for the analysis are shown in Appendix B. As the upper-state energies of the observed lines of CHD<sub>2</sub>OH are close to one another and there is only one line of CH<sub>3</sub>OD in our setup, we cannot determine the temperature independently for these two species. Therefore, in the calculation of the column densities of CHD<sub>2</sub>OH and CH<sub>3</sub>OD, we assume the CH<sub>3</sub>OH temperature obtained for each position, considering the coexisting nature of CH<sub>3</sub>OH and its isotopologues (see Figure 1). In addition, the temperature of CH<sub>3</sub>OH is better determined than that of CH<sub>2</sub>DOH due to the higher signal-to-noise ratio. For CH<sub>3</sub>OD, we employ the Sμ² value calculated by Anderson et al. (1988).

At the continuum peak, the observed column densities of CH<sub>3</sub>OH and its isotopologues are seriously affected by the high optical depth of dust continuum emission, as revealed by the central dip of the images in Figure 1. Only a lower limit can be derived for the column density of CH<sub>2</sub>DOH
<table><caption>**Table 2**
Temperatures and Column Densities in the Disk/Envelope System</caption><thead><tr><th rowspan="2">Molecules</th><th rowspan="2">Offsets<sup>a</sup></th><th colspan="2"><i>S</i><sub>JPL</sub><sup>2</sup> or <i>S</i><sub>CDMS</sub><sup>c</sup></th><th colspan="2"><i>S</i><sub>SUMIRE</sub><sup>2</sup></th></tr><tr><th><i>T</i> (K)</th><th><i>N</i> (10<sup>18</sup> cm<sup>-2</sup>)</th><th><i>T</i> (K)</th><th><i>N</i> (10<sup>18</sup> cm<sup>-2</sup>)</th></tr></thead><tbody><tr><td rowspan="6">CH<sub>3</sub>OH<sup>b</sup></td><td>0.1</td><td>107<sup>+2</sup><sub>-2</sub></td><td>4.4<sup>+0.5</sup><sub>-0.5</sub></td><td>...</td><td>...</td></tr><tr><td>0.06</td><td>142<sup>+3</sup><sub>-4</sub></td><td>9.0<sup>+3.0</sup><sub>-1.7</sub></td><td>...</td><td>...</td></tr><tr><td>0.03</td><td>164<sup>+6</sup><sub>-6</sub></td><td>&gt;9.6</td><td>...</td><td>...</td></tr><tr><td>0<sup>d</sup></td><td>217<sup>+2</sup><sub>-2</sub></td><td>11<sup>+5</sup><sub>-2</sub></td><td>...</td><td>...</td></tr><tr><td>-0.03</td><td>186<sup>+2</sup><sub>-2</sub></td><td>13<sup>+4</sup><sub>-3</sub></td><td>...</td><td>...</td></tr><tr><td>-0.06</td><td>146<sup>+4</sup><sub>-3</sub></td><td>8.0<sup>+1.7</sup><sub>-1.3</sub></td><td>...</td><td>...</td></tr><tr><td>-0.1</td><td>124<sup>+5</sup><sub>-5</sub></td><td>3.7<sup>+1.1</sup><sub>-0.8</sub></td><td>...</td><td>...</td></tr><tr><td rowspan="6">CH<sub>2</sub>DOH<sup>b</sup></td><td>0.1</td><td>72<sup>+3</sup><sub>-1</sub></td><td>0.47<sup>+0.06</sup><sub>-0.06</sub></td><td>72<sup>+2</sup><sub>-2</sub></td><td>0.74<sup>+0.10</sup><sub>-0.10</sub></td></tr><tr><td>0.06</td><td>119<sup>+12</sup><sub>-8</sub></td><td>0.85<sup>+0.09</sup><sub>-0.06</sub></td><td>118<sup>+8</sup><sub>-8</sub></td><td>1.2<sup>+0.2</sup><sub>-0.1</sub></td></tr><tr><td>0.03</td><td>143<sup>+3</sup><sub>-3</sub></td><td>2.6<sup>+0.9</sup><sub>-0.4</sub></td><td>143<sup>+3</sup><sub>-3</sub></td><td>3.8<sup>+0.9</sup><sub>-0.6</sub></td></tr><tr><td>0<sup>d</sup></td><td>188<sup>+8</sup><sub>-6</sub></td><td>&gt;3.5</td><td>188<sup>+8</sup><sub>-4</sub></td><td>&gt;5.2</td></tr><tr><td>-0.03</td><td>162<sup>+12</sup><sub>-8</sub></td><td>2.5<sup>+0.8</sup><sub>-0.4</sub></td><td>161<sup>+8</sup><sub>-6</sub></td><td>3.6<sup>+1.1</sup><sub>-0.6</sub></td></tr><tr><td>-0.06</td><td>135<sup>+30</sup><sub>-16</sub></td><td>1.00<sup>+0.20</sup><sub>-0.11</sub></td><td>132<sup>+22</sup><sub>-12</sub></td><td>1.5<sup>+0.3</sup><sub>-0.2</sub></td></tr><tr><td>-0.1</td><td>106<sup>+36</sup><sub>-14</sub></td><td>0.52<sup>+0.26</sup><sub>-0.10</sub></td><td>104<sup>+26</sup><sub>-12</sub></td><td>0.79<sup>+0.41</sup><sub>-0.18</sub></td></tr><tr><td rowspan="6">CHD<sub>2</sub>OH<sup>c</sup></td><td>0.1</td><td>107<sup>+15</sup><sub>-15</sub></td><td>0.15<sup>+0.02</sup><sub>-0.02</sub></td><td>107<sup>+15</sup><sub>-15</sub></td><td>0.13<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>0.06</td><td>142<sup>+15</sup><sub>-15</sub></td><td>0.35<sup>+0.04</sup><sub>-0.03</sub></td><td>142<sup>+15</sup><sub>-15</sub></td><td>0.31<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>0.03</td><td>164<sup>+15</sup><sub>-15</sub></td><td>0.71<sup>+0.05</sup><sub>-0.01</sub></td><td>164<sup>+15</sup><sub>-15</sub></td><td>0.629<sup>+0.042</sup><sub>-0.002</sub></td></tr><tr><td>0<sup>d</sup></td><td>217<sup>+15</sup><sub>-15</sub></td><td>1.2<sup>+0.6</sup><sub>-0.2</sub></td><td>217<sup>+15</sup><sub>-15</sub></td><td>1.1<sup>+0.4</sup><sub>-0.2</sub></td></tr><tr><td>-0.03</td><td>186<sup>+15</sup><sub>-15</sub></td><td>&lt;0.77</td><td>186<sup>+15</sup><sub>-15</sub></td><td>&lt;0.68</td></tr><tr><td>-0.06</td><td>146<sup>+15</sup><sub>-15</sub></td><td>0.35<sup>+0.03</sup><sub>-0.02</sub></td><td>146<sup>+15</sup><sub>-15</sub></td><td>0.31<sup>+0.03</sup><sub>-0.02</sub></td></tr><tr><td>-0.1</td><td>124<sup>+15</sup><sub>-15</sub></td><td>0.20<sup>+0.02</sup><sub>-0.01</sub></td><td>124<sup>+15</sup><sub>-15</sub></td><td>0.17<sup>+0.02</sup><sub>-0.01</sub></td></tr><tr><td rowspan="6">CH<sub>3</sub>OD<sup>c</sup></td><td>0.1</td><td>107<sup>+15</sup><sub>-15</sub></td><td>0.06<sup>+0.01</sup><sub>-0.01</sub></td><td>...</td><td>...</td></tr><tr><td>0.06</td><td>142<sup>+15</sup><sub>-15</sub></td><td>0.22<sup>+0.02</sup><sub>-0.03</sub></td><td>...</td><td>...</td></tr><tr><td>0.03</td><td>164<sup>+15</sup><sub>-15</sub></td><td>&lt;0.34</td><td>...</td><td>...</td></tr><tr><td>0<sup>d</sup></td><td>217<sup>+15</sup><sub>-15</sub></td><td>2.0<sup>+0.5</sup><sub>-0.3</sub></td><td>...</td><td>...</td></tr><tr><td>-0.03</td><td>186<sup>+15</sup><sub>-15</sub></td><td>0.45<sup>+0.02</sup><sub>-0.01</sub></td><td>...</td><td>...</td></tr><tr><td>-0.06</td><td>146<sup>+15</sup><sub>-15</sub></td><td>0.19<sup>+0.02</sup><sub>-0.02</sub></td><td>...</td><td>...</td></tr><tr><td>-0.1</td><td>124<sup>+15</sup><sub>-15</sub></td><td>0.11<sup>+0.01</sup><sub>-0.01</sub></td><td>...</td><td>...</td></tr></tbody></table>

**Notes.**

<sup>a</sup> Offsets from the continuum peak position along the envelope (P.A. 5°).

<sup>b</sup> The errors are estimated by using the $\chi^2$ analysis.

<sup>c</sup> These temperatures are assumed to be that of CH<sub>3</sub>OH. For the error estimation of CHD<sub>2</sub>OH and CH<sub>3</sub>OD, we assume the temperature error of ±15 K. These values are derived from the spectra for the rectangle area (0′′03×0′′05) shown in Figure 1(a).

<sup>d</sup> At the continuum peak, the observed column densities are seriously affected by the high optical depth of dust continuum emission, and hence, we focus on the values at the six positions in the envelope in this paper.

<sup>e</sup> For CH<sub>2</sub>DOH and CHD<sub>2</sub>OH, the column densities are calculated with the $S\mu^2_{JPL}$ and $S\mu^2_{CDMS}$ values, respectively.

(>5.2 × 10<sup>18</sup> cm<sup>-2</sup>), while those of CHD<sub>2</sub>OH and CH<sub>3</sub>OD are derived to be 1.1<sup>+0.4</sup><sub>-0.2</sub> × 10<sup>18</sup> cm<sup>-2</sup> and 2.0<sup>+0.5</sup><sub>-0.3</sub> × 10<sup>18</sup> cm<sup>-2</sup>, respectively. Therefore, we mainly focus on the column densities at the six positions in the envelope. Among three deuterated species, CH<sub>2</sub>DOH shows the highest column density at all positions, which is in the range of [0.61–4.7] × 10<sup>18</sup> cm<sup>-2</sup>. The column densities of CHD<sub>2</sub>OH and CH<sub>3</sub>OD are in the range of [0.11–0.67] × 10<sup>18</sup> cm<sup>-2</sup> and [0.05–0.47] × 10<sup>18</sup> cm<sup>-2</sup>, respectively. Within the radius of 0′′1, the column densities of all species seem to decrease as an increasing offset. The errors are estimated by using the $\chi^2$ analysis for CH<sub>3</sub>OH and CH<sub>2</sub>DOH, where 1σ uncertainty is presented as the error for each parameter. For CHD<sub>2</sub>OH and

CH<sub>3</sub>OD, we estimate the errors of their column densities, based on the assumed temperature range of ±15 K from the CH<sub>3</sub>OH temperature.

## 4.2. Abundances

Using these derived column densities (Table 2), we derive the five abundance ratios: [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH], [CHD<sub>2</sub>OH]/[CH<sub>3</sub>OH], [CH<sub>3</sub>OD]/[CH<sub>3</sub>OH], [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OD], and [CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH] (Figure 2 and Table 3). As seen in Figure 2, the abundance ratios do not reveal any systematic variation. Rather, they are roughly constant over the envelope (see also Table 3). At the continuum peak, all of the ratios have large uncertainties or just the lower and upper limits due to high dust opacity. The [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH], [CHD<sub>2</sub>OH]/[CH<sub>3</sub>OH], and [CH<sub>3</sub>OD]/[CH<sub>3</sub>OH] ratios in the envelope are in the range of [0.09–0.38], [0.02–0.06], and [0.011–0.06], respectively (Figures 2(a), (b), and (c)). In Figures 2(d) and (e), the [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH] and [CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH] ratios are in the range of [4.9–15] and [0.14–0.29], respectively (see also Table 3). We discuss the [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH], [CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH], and [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OD] ratios in Section 8. Although the column densities and the abundances are roughly constant over the disk/ envelope system, the temperatures of CH<sub>3</sub>OH and CH<sub>2</sub>DOH decrease with increasing distance from the protostar position.

The dust optical depths ($\tau_{dust}$) are summarized in Appendix C. Note that the $\tau_{dust}$ values obtained in the analyses of the CH<sub>3</sub>OH and CH<sub>2</sub>DOH lines are slightly different for some positions due to the different temperatures. If we employ the CH<sub>3</sub>OH temperature for the calculation of CH<sub>2</sub>DOH, its column density is (0.44–2.8) × 10<sup>18</sup> cm<sup>-2</sup> in the disk/ envelope system, and the lower limits to the abundance ratios are higher than those when the CH<sub>2</sub>DOH temperature is employed. In short, the different treatments of the CH<sub>2</sub>DOH temperature do not seriously affect the trend as discussed in Section 8.

## 5. An Effect of $S\mu^2$ on the Column Densities

In the previous section, we use the experimental value, $S\mu^2_{SUMIRE}$, for the derivation of the column density of CH<sub>2</sub>DOH and CHD<sub>2</sub>OH. Since the derived column density and rotation temperature depend on the $S\mu^2$ values used, we here note the effects on the results for the different $S\mu^2$ values for the CH<sub>2</sub>DOH ($S\mu^2_{SUMIRE}$ versus $S\mu^2_{JPL}$) and CHD<sub>2</sub>OH ($S\mu^2_{SUMIRE}$ versus $S\mu^2_{CDMS}$) lines. In Table 1, column four represents the $S\mu^2$ values calculated from the line intensity in the database of JPL (hereafter referred to as $S\mu^2_{JPL}$) for the CH<sub>2</sub>DOH lines and those taken from the database of CDMS (hereafter referred to as $S\mu^2_{CDMS}$) for the CHD<sub>2</sub>OH lines.

The differences between $S\mu^2_{JPL}$ and $S\mu^2_{SUMIRE}$ are conspicuous for CH<sub>2</sub>DOH: $S\mu^2_{SUMIRE}$ is 0.6–0.8 times smaller than $S\mu^2_{JPL}$. The temperature and the column density toward the offset of −0′′03 from the continuum peak are derived with $S\mu^2_{JPL}$ to be 162<sup>+12</sup><sub>-8</sub> K and 2.5<sup>+0.8</sup><sub>-0.4</sub> × 10<sup>18</sup> cm<sup>-2</sup>, respectively. When we use $S\mu^2_{SUMIRE}$, they are derived to be 161<sup>+8</sup><sub>-6</sub> K and 3.6<sup>+1.1</sup><sub>-0.6</sub> × 10<sup>18</sup> cm<sup>-2</sup>, respectively. The former column density is about 1.4 times smaller than the latter column density, while the temperatures are almost the same as each other. At the other positions, the column densities of CH<sub>2</sub>DOH derived with $S\mu^2_{JPL}$ is also 1.4–1.6 times smaller than those derived with $S\mu^2_{SUMIRE}$, as shown in Table 2, resulting in the range of the column densities and the ratios as: $N(CH_2DOH) = [0.41-0.8]$.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (a)–(e) Abundance ratios along the envelope (P.A. 5°). Column densities of CH<sub>2</sub>DOH and CHD<sub>2</sub>OH derived from Sμ<sup>2</sup><sub>SUMIRE</sub> are employed here. At the continuum peak, the observed column densities are seriously affected by the high optical depth of dust continuum emission, and hence, we focus on the abundances at the six positions in the envelope in this paper. The left and right arrows show the upper and lower limits of the abundance ratios, respectively. (a) The red vertical line represents the average in low-mass protostars (0.06) reported by van Gelder et al. (2022). (b) The ratio in the low-mass protostellar source IRAS 16293-2422 B (3.9) is shown in the orange vertical line for comparison (Jørgensen et al. 2018). Green and gray areas indicate the ratios in high-mass sources NGC 6334 I (0.1–0.5; Bøgelund et al. 2018) and Orion KL (0.9–1.5; Peng et al. 2012; Neill et al. 2013), respectively.</figcaption></figure>

3.5] × 10<sup>18</sup> cm<sup>-2</sup>, [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH] = [0.07–0.26], and [CH<sub>2</sub>DOH]/[CH<sub>3</sub>OD] = [3.5–9.7]. Note that some of the CH<sub>2</sub>DOH column densities are different from those reported by Okoda et al. (2022) beyond the errors and the effect of the Sμ<sup>2</sup> difference, particularly at the continuum peak position. This is because the circle area with a diameter of 0.03 was employed for their derivation.

On the other hand, the difference between Sμ<sup>2</sup><sub>CDMS</sub> and Sμ<sup>2</sup><sub>SUMIRE</sub> for the CHD<sub>2</sub>OH lines is relatively small (Table 1). The Sμ<sup>2</sup><sub>SUMIRE</sub> values are about 1.2 times larger than the Sμ<sup>2</sup><sub>CDMS</sub> values at most for the observed lines. In this case, the upper limits to the column densities at the offset of -0.03 are similar to each other: they are <0.77 × 10<sup>18</sup> cm<sup>-2</sup> and <0.68 × 10<sup>18</sup> cm<sup>-2</sup> with the Sμ<sup>2</sup><sub>CDMS</sub> and Sμ<sup>2</sup><sub>SUMIRE</sub> values, respectively, where we assume the CH<sub>3</sub>OH temperature of 186 ± 15 K. Therefore, a choice of the Sμ<sup>2</sup><sub>CDMS</sub> and Sμ<sup>2</sup><sub>SUMIRE</sub>

values does not cause serious differences on the abundance ratios in our observation (Table 3). The [CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH] ratio is mostly affected by the difference in the Sμ<sup>2</sup> value of CH<sub>2</sub>DOH. Using the Sμ<sup>2</sup><sub>JPL</sub> value for CH<sub>2</sub>DOH and the Sμ<sup>2</sup><sub>CDMS</sub> value for CHD<sub>2</sub>OH, we obtain [0.20–0.46] (Table 3).

It should be noted that the effect of Sμ² values on the column densities depends on which lines are used for the derivation. In other words, different lines have different differences between the Sμ²<sub>JPL</sub> and Sμ²<sub>SUMIRE</sub> values or between the Sμ²<sub>CDMS</sub> and Sμ²<sub>SUMIRE</sub> values. Therefore, an effect of the Sμ² values on the column densities in any other observations would be different from those reported here. Thus, we need special care for a comparison of column densities and their ratios with those in other sources reported previously.
<table><caption>**Table 3**
Abundance Ratios in the Disk/Envelope System</caption><thead><tr><th>Sμ<sup>2</sup><sub>JPL</sub> or Sμ<sup>2</sup><sub>CDMS</sub><sup>a</sup></th><th>Offset<sup>b</sup></th><th>[CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH]</th><th>[CHD<sub>2</sub>OH]/[CH<sub>3</sub>OH]</th><th>[CH<sub>3</sub>OD]/[CH<sub>3</sub>OH]</th><th>[CH<sub>2</sub>DOH]/[CH<sub>3</sub>OD]</th><th>[CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH]</th></tr></thead><tbody><tr><td></td><td>0.1</td><td>0.11<sup>+0.02</sup><sub>-0.02</sub></td><td>0.03<sup>+0.01</sup><sub>-0.01</sub></td><td>0.014<sup>+0.005</sup><sub>-0.003</sub></td><td>7.8<sup>+1.9</sup><sub>-1.5</sub></td><td>0.32<sup>+0.06</sup><sub>-0.06</sub></td></tr><tr><td></td><td>0.06</td><td>0.09<sup>+0.02</sup><sub>-0.02</sub></td><td>0.04<sup>+0.01</sup><sub>-0.01</sub></td><td>0.024<sup>+0.008</sup><sub>-0.007</sub></td><td>3.9<sup>+0.7</sup><sub>-0.4</sub></td><td>0.41<sup>+0.05</sup><sub>-0.05</sub></td></tr><tr><td></td><td>0.03</td><td>&lt;0.27</td><td>&lt;0.07</td><td>&lt;0.04</td><td>&gt;7.7</td><td>0.27<sup>+0.04</sup><sub>-0.07</sub></td></tr><tr><td></td><td>0<sup>e</sup></td><td>&gt;0.32</td><td>0.11<sup>+0.06</sup><sub>-0.04</sub></td><td>0.18<sup>+0.06</sup><sub>-0.06</sub></td><td>&gt;1.8</td><td>&lt;0.34</td></tr><tr><td></td><td>-0.03</td><td>0.19<sup>+0.07</sup><sub>-0.05</sub></td><td>&lt;0.06</td><td>0.04<sup>+0.02</sup><sub>-0.01</sub></td><td>5.6<sup>+1.8</sup><sub>-0.9</sub></td><td>&lt;0.31</td></tr><tr><td></td><td>-0.06</td><td>0.12<sup>+0.03</sup><sub>-0.03</sub></td><td>0.04<sup>+0.01</sup><sub>-0.01</sub></td><td>0.024<sup>+0.008</sup><sub>-0.005</sub></td><td>5.3<sup>+1.2</sup><sub>-0.8</sub></td><td>0.35<sup>+0.05</sup><sub>-0.06</sub></td></tr><tr><td></td><td>-0.1</td><td>0.14<sup>+0.07</sup><sub>-0.04</sub></td><td>0.05<sup>+0.01</sup><sub>-0.01</sub></td><td>0.03<sup>+0.01</sup><sub>-0.01</sub></td><td>4.7<sup>+2.4</sup><sub>-1.0</sub></td><td>0.38<sup>+0.07</sup><sub>-0.13</sub></td></tr></tbody><thead><tr><th>Sμ<sup>2</sup><sub>SUMIRE</sub></th><th>Offset<sup>b,d</sup></th><th>[CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH]</th><th>[CHD<sub>2</sub>OH]/[CH<sub>3</sub>OH]</th><th>[CH<sub>3</sub>OD]/[CH<sub>3</sub>OH]</th><th>[CH<sub>2</sub>DOH]/[CH<sub>3</sub>OD]</th><th>[CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH]</th></tr></thead><tbody><tr><td></td><td>0.1</td><td>0.17<sup>+0.03</sup><sub>-0.03</sub></td><td>0.03<sup>+0.01</sup><sub>-0.01</sub></td><td>...</td><td>12<sup>+3</sup><sub>-2</sub></td><td>0.18<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td></td><td>0.06</td><td>0.13<sup>+0.03</sup><sub>-0.04</sub></td><td>0.03<sup>+0.01</sup><sub>-0.01</sub></td><td>...</td><td>5.5<sup>+1.3</sup><sub>-0.6</sub></td><td>0.26<sup>+0.03</sup><sub>-0.04</sub></td></tr><tr><td></td><td>0.03</td><td>&lt;0.40</td><td>&lt;0.07</td><td>...</td><td>&gt;11</td><td>0.17<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td></td><td>0<sup>e</sup></td><td>&gt;0.47</td><td>0.10<sup>+0.04</sup><sub>-0.04</sub></td><td>...</td><td>&gt;2.6</td><td>&lt;0.21</td></tr><tr><td></td><td>-0.03</td><td>0.28<sup>+0.1</sup><sub>-0.08</sub></td><td>&lt;0.05</td><td>...</td><td>8.0<sup>+2.5</sup><sub>-1.4</sub></td><td>&lt;0.19</td></tr><tr><td></td><td>-0.06</td><td>0.19<sup>+0.05</sup><sub>-0.04</sub></td><td>0.04<sup>+0.01</sup><sub>-0.01</sub></td><td>...</td><td>7.9<sup>+1.3</sup><sub>-1.3</sub></td><td>0.21<sup>+0.03</sup><sub>-0.04</sub></td></tr><tr><td></td><td>-0.1</td><td>0.21<sup>+0.12</sup><sub>-0.07</sub></td><td>0.05<sup>+0.01</sup><sub>-0.01</sub></td><td>...</td><td>7.2<sup>+3.8</sup><sub>-1.7</sub></td><td>0.22<sup>+0.05</sup><sub>-0.07</sub></td></tr></tbody></table>

**Notes.**

<sup>a</sup> For CH<sub>2</sub>DOH and CHD<sub>2</sub>OH, the abundances are derived by using the column densities calculated with the Sμ<sup>2</sup><sub>JPL</sub> and Sμ<sup>2</sup><sub>CDMS</sub> values, respectively.

<sup>b</sup> Offsets from the continuum peak position along the envelope (P.A. 5°).

<sup>c</sup> For CH<sub>2</sub>DOH and CHD<sub>2</sub>OH, the abundances are derived by using the column densities calculated with the Sμ<sup>2</sup><sub>SUMIRE</sub> value.

<sup>d</sup> The abundance ratios are plotted in Figure 2.

<sup>e</sup> At the continuum peak, the observed column densities are seriously affected by the high optical depth of dust continuum emission, and hence, we focus on the abundances at the six positions in the envelope in this paper.

**6. Distributions and Velocity Maps of the Disk/Envelope System**

It is of fundamental importance for the characterization of this source to verify the protostellar mass and the presence/absence of the disk structure, which may relate to the evolutionary stage of the protostar. As mentioned in Section 2, various efforts toward this direction have been reported. In particular, Imai et al. (2019) studied velocity structures of the disk/ envelope system with the CH<sub>3</sub>OH (12<sub>6,7</sub> – 13<sub>5,8</sub>, E, E<sub>u</sub> = 360 K) and HCOOH (12<sub>0,12</sub> – 11<sub>0,11</sub>, E<sub>u</sub> = 83 K) lines at a resolution of 0"/1. Since the resolution of our data is higher by a factor of 3–4, we reinvestigate the kinematic structure of the disk/ envelope system with these molecular species.

The upper panels of Figure 3 show the moment zero maps of CH<sub>3</sub>OH (18<sub>3,15</sub> – 18<sub>2,16</sub>, A, E<sub>u</sub> = 447 K) and HCOOH (12<sub>0,12</sub> – 11<sub>0,11</sub>), respectively. The velocity range for the integration is from –0.2 km s<sup>–1</sup> to 14.5 km s<sup>–1</sup>, where the systemic velocity is 8.34 km s<sup>–1</sup> (Yen et al. 2015). The moment zero map of CH<sub>3</sub>OH is the same as that in Figure 1(a). We choose this line of CH<sub>3</sub>OH for the kinematic analysis in the next section because of the relatively high signal-to-noise ratio. In addition, we can avoid the contamination from the outflow as much as possible with the line, since it has the relatively high upper-state energy among the CH<sub>3</sub>OH lines in our observation. In the upper panel of Figure 3(b), the HCOOH line shows a more compact distribution, which would selectively trace the velocity structure of the inner disk/ envelope system. To study the inner structure, we also explore the velocity structure of the HCOOH emission in this paper.

The lower panels of Figure 3 show the moment one maps of CH<sub>3</sub>OH and HCOOH, respectively, where the velocity range is from 1.6 km s<sup>–1</sup> to 13.3 km s<sup>–1</sup>. The velocity gradient can be seen in both of the moment one maps. The velocity gradient in

the map of CH<sub>3</sub>OH is almost along the west-to-east axis, whereas that of HCOOH is rather close to the south-to-north axis. The outflow and disk/ envelope directions are suggested to be nearly along the west-to-east (P.A. 95°) and south-to-north axes (P.A. 5°), respectively (e.g., Bjerkeli 2023). Hence, the observed velocity structure has a gradient along the different directions from the suggested disk/ envelope system, particularly for the CH<sub>3</sub>OH line. As Imai et al. (2019) and Oya et al. (2022) pointed out, this can occur for the contribution of the infalling-rotating motion, which will be discussed later (Section 7.1).

The moment zero maps of CH<sub>3</sub>OH and HCOOH show a ring-shaped distribution in spite of the almost edge-on configuration suggested by Bjerkeli et al. (2019) and Evans et al. (2023). The CH<sub>3</sub>OH distribution is more extended in height of the disk/ envelope system than the HCOOH distribution as well as in radius. Part of the CH<sub>3</sub>OH emission can be caused by the interaction with the outflow as shown in the lower panel of Figure 3(b) in addition to the infalling-motion effect above and below the midplane of the disk/ envelope system. Such a stratified molecular distribution was also reported in the other low-mass source: HH212 by Lee et al. (2022). The HCOOH emission would be less affected by the outflow interaction than the CH<sub>3</sub>OH emission and provide us with a better estimate of the disk height. Therefore, the apparent scale height of the disk/ envelope system is roughly estimated to be about 20 au based on the HCOOH maps for the analysis in the next section (Figure 3(b)).

Moreover, in B335, the SiO emission was reported to have an extended distribution along the east-to-west axis near the protostar (< 0"/1) by Bjerkeli et al. (2019). SiO is well known as a shock tracer (e.g., Mikami et al. 1992; Bachiller & Pérez Gutiérrez 1997), and could trace the launching point of the outflow or the accretion shock of infalling material
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a), (b) Moment zero and one maps of the CH₃OH (18₃,15 – 18₂,16, A) and HCOOH (12₀,12 – 11₀,11) emission in the upper and lower panels, respectively. The moment zero map of CH₃OH is the same as Figure 1(a), where the black dotted circle indicates the area covered by the SiO emission with previous work, as mentioned in Section 6. Contour levels for HCOOH are every 3σ from 3σ, where σ is 1.8 mJy beam⁻¹. For the moment zero and one maps, the integrated velocity range is from −0.2 km s⁻¹ to 14.5 km s⁻¹ and from 1.6 km s⁻¹ to 13.3 km s⁻¹, respectively. The systemic velocity is 8.34 km s⁻¹ (Yen et al. 2015). The gray dotted arrows in the moment one map of CH₃OH show the directions of the PV diagrams of Figures 4, 6, and 7. The white cross marks represent the continuum peak (α₂₀₀, δ₂₀₀) = (19h37m00s90, +7°34'09.49). The red ellipses represent the beam size.</figcaption></figure>

(Imai et al. 2019). Its distribution covers the area where both the CH₃OH and HCOOH line intensities are enhanced around the west of the protostar, as shown in the dotted black circle of Figure 3(a). In terms of the detection of SiO, the intensity enhancement would be caused by a shock on the surface area of the disk/envelope system rather than protostellar heating.

## 7. Kinematics of the Disk/Envelope System with FERIA

In this section, we analyze the CH₃OH and HCOOH data to determine the protostellar mass ($M_{star}$), the centrifugal barrier ($r_{CB}$), and the inclination (i) of the disk/envelope system, the inner radius ($R_{in}$) with the aid of a general-purpose computer code FERIA (Flat Envelope model with Rotation and Infall under Angular momentum conservation) developed by Oya et al. (2022). The physical meaning of $R_{in}$ depends on the model, and hence, we will specify it for each case later. We perform the $\chi^2$ test to obtain the best-fit model parameters on the molecular-line data cube, where the intensities are higher than 3σ noise level; 1.5 mJy beam⁻¹ and 1.8 mJy beam⁻¹ for

CH₃OH and HCOOH. For the models, we set the height of the disk/envelope system to be 20 au based on the apparent height in the map of HCOOH, as mentioned in Section 6.

### 7.1. CH₃OH (18₃,15 – 18₂,16, A)

Based on the distributions in the moment zero and one maps (Figure 3(a)) and the analyses presented by Imai et al. (2019), the CH₃OH emission is expected to trace an IRE. To explore the velocity structure of the CH₃OH (18₃,15 – 18₂,16, A) emission, we prepare the IRE models by taking $M_{star}$, $r_{CB}$, and i as the free parameters. $R_{in}$ here represents the inner radius of IRE ($R_{in}$) traced by the CH₃OH emission, which is assumed to be equal to $r_{CB}$. $R_{out}$ indicates the outer radius of IRE ($R_{out}$) traced by the CH₃OH emission, which is fixed to be 24 au according to the observed emission. The parameter ranges are summarized in Table 4.

The disk/envelope system was suggested to be the almost edge-on configuration (0° for face-on: e.g., Bjerkeli et al. 2019; Imai et al. 2019; Evans et al. 2023), and hence, we set the range
<figure><img src="image_6.png" /><figcaption>**Figure 4.** PV diagrams of CH₃OH (18<sub>3,15</sub> – 18<sub>2,16</sub>, A) in colors and the best-fit model obtained by the χ² analysis for the IRE model with FERIA in contours. The best-fit parameters for the IRE model are the protostellar mass of 0.07M<sub>☉</sub>, the outer radius of 24 au, the inner radius and the centrifugal barrier of 3 au, and the inclination of 70° (90° for edge-on), where the reduced χ² value is 0.88. Dotted horizontal lines show the systemic velocity of 8.34 km s⁻¹ (Yen et al. 2015), and dotted vertical lines show the protostar position.</figcaption></figure>

<table><caption>**Table 4**
Free Parameters in the Reduced χ² Test on the Cube Data</caption><thead><tr><th>Model</th><th>Molecule</th><th>M<sub>star</sub><br>(M<sub>☉</sub>)</th><th>r<sub>CB</sub><br>(au)</th><th>i<br>(deg)</th><th>R<sub>in</sub><br>(au)</th><th>R<sub>out</sub><br>(au)</th><th>Reduced<br>χ<sup>2</sup> Values</th></tr></thead><tbody><tr><td rowspan="2">IRE<br>(Best-fit)</td><td rowspan="2">CH<sub>3</sub>OH</td><td>0.02–0.08</td><td>2–9</td><td>70–90</td><td rowspan="2">r<sub>CB</sub></td><td rowspan="2">24</td><td rowspan="2">0.88</td></tr><tr><td>0.07</td><td>3</td><td>70</td></tr><tr><td rowspan="2">IRE<br>(Best-fit)</td><td rowspan="2">HCOOH</td><td>0.02–0.08</td><td>2–9</td><td>70–90</td><td rowspan="2">r<sub>CB</sub></td><td rowspan="2">10</td><td rowspan="2">0.81</td></tr><tr><td>0.04</td><td>7</td><td>90</td></tr><tr><td rowspan="2">Combined<br>(Best-fit)</td><td rowspan="2">HCOOH</td><td>0.02–0.08</td><td>2–9</td><td>70–90</td><td rowspan="2">1</td><td rowspan="2">10</td><td rowspan="2">0.82</td></tr><tr><td>0.03</td><td>6</td><td>90</td></tr><tr><td rowspan="2">Kepler<br>(Best-fit)</td><td rowspan="2">HCOOH</td><td>0.02–0.08</td><td>10</td><td>70–90</td><td>1–6</td><td rowspan="2">r<sub>CB</sub></td><td rowspan="2">0.82</td></tr><tr><td>0.05</td><td></td><td>90</td><td>5</td></tr></tbody></table>

**Notes.** In the FERIA code, the heights of the envelope and disk are set to be 20 au. The fittings are applied for the cube data of CH₃OH and HCOOH with the intensities higher than 3σ noise level; 1.5 mJy beam⁻¹ and 1.8 mJy beam⁻¹, respectively.

from 70° to 90° for *i*. The position angles (P.A.) of the disk/envelope are set to be 5° (Bjerkeli et al. 2019; Cabedo et al. 2021; Bjerkeli 2023). We compare the model with the observation on the cube data to calculate the reduced χ² value. Then, we obtain the best-fit parameters at the reduced χ² values of 0.88, where M<sub>star</sub>, r<sub>CB</sub>(= R<sub>in</sub>), and *i* are 0.07M<sub>☉</sub>, 3 au, and 70°, respectively.

Imai et al. (2019) reported M<sub>star</sub> of 0.03–0.1 M<sub>☉</sub> and r<sub>CB</sub> < 8 au. With the same data, Oya et al. (2022) obtained the best-fit parameters of M<sub>star</sub> = 0.03 M<sub>☉</sub> and r<sub>CB</sub> = 2 au through the χ² tests (the reduced χ² value = 0.77) for the infalling-rotating model. They also analyzed the observed data with a Keplerian model, resulting in the best-fit parameters of M<sub>star</sub> = 0.07 M<sub>☉</sub> and R<sub>in</sub> = 2 au at a reduced χ² value of 0.78. Bjerkeli et al. (2019) independently derived M<sub>star</sub> to be 0.08 M<sub>☉</sub> from the analysis of the position–velocity (PV)

diagrams of CH₃OH and SO₂ at a similar resolution to our observation, assuming a Keplerian rotation. Thus, the small M<sub>star</sub> and r<sub>CB</sub> values obtained in this study are consistent with those reported in the previous works.

Figure 4 shows the PV diagrams of the best-fit model in contours compared with those of CH₃OH in colors, where the cutting width is 7 au for PVs. Directions of the PV diagrams are shown as the arrows in Figure 3(a). The model can almost reproduce the major features of the observation, although some emission is veiled by the dust continuum at the continuum peak (offset of 0.′′0). In addition, the redshifted component is weaker than the blueshifted one in Figure 4. This may be due to the self-absorption in the infalling gas (i.e., inverse P-Cygni profile). An increase in the velocity around the offsets of 0.′′1–0.′′2, as seen in the panels of P.A. 95° and 65°, is likely a contribution of an outflow interaction.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Schematic illustration of the disk/envelope system of B335. The HCOOH and CH₃OH emitting region areas are enclosed by colors and by solid and dashed lines, respectively. (a) Inner envelope traced by the HCOOH emission and overall envelope traced by the CH₃OH emission. (b) A stratified molecular distribution is considered. A possible Keplerian disk is traced by the HCOOH emission and the infalling gas envelope is traced by the CH₃OH emission motion.</figcaption></figure>

## 7.2. HCOOH (12$_{0,12}$ − 11$_{0,11}$)

We obtain $r_{CB}$ of 3 au in the analysis for the CH$_3$OH line. This means that if there were a rotationally supported disk inside the infalling-rotating envelope traced by CH$_3$OH, its radius would be 3 au. This size cannot fully be resolved by the resolution of our data (~5 au). Since the HCOOH emission has a distribution of 10 au in radius that is larger than the obtained $r_{CB}$, it seems to overlap with part of the CH$_3$OH distribution. As well, the moment one map (Figure 3(b)) looks similar to the infalling-rotating motion (Oya et al. 2022). Nevertheless, we examine the following two cases to explore the velocity structure by using the model on the cube data. One is the case that HCOOH traces an infalling-rotating motion with $R_{out}$ of 10 au in the inner part of the disk/envelope system. In this case, there could be a very small rotationally supported disk within $R_{in}$ ($r_{CB}$). Another case is that a Keplerian disk with a radius of 10 au($= R_{out} = r_{CB}$) is traced by HCOOH, where the gas infalling on the above and below disk midplane toward the protostar is traced by CH$_3$OH. The two cases are schematically shown in Figure 5. In the following cases of Sections 7.2.1 and 7.2.2, $R_{out}$ and $R_{in}$ refer to the outer and inner radii of the structure traced by the HCOOH emission, respectively.

### 7.2.1. Case 1: IRE

We here consider the IRE model with $R_{out}$ of 10 au as well as the combined model. In the combined model, the IRE model and the Keplerian rotation model are considered simultaneously, where the Keplerian disk is assumed to exist inward of the centrifugal barrier of the IRE (i.e., for $r_{Kepler} < r_{CB}$). At first, we prepare the IRE models using $M_{star}$, $r_{CB}(=R_{in})$, and $i$ summarized in Table 4, and perform a reduced $\chi^2$ test for HCOOH on the cube data. The best-fit value of $M_{star}$ is 0.04 $M_{\odot}$, where the reduced $\chi^2$ value is 0.81. The other best-fit parameters are: $r_{CB}(=R_{in}) = 7$ au, and $i = 90^{\circ}$. These parameters are slightly different from those in the CH$_3$OH analysis (Section 7.1). $r_{CB}$ of 7 au is within the range reported by Imai et al. (2019). The larger value of $r_{CB}$ than that obtained by the CH$_3$OH analysis ($r_{CB} = 3$ au) may be caused by the weaker intensities near the continuum peak. In Figure 6, PV diagrams

of the best-fit IRE (upper) and Combined (below) models are overlaid on those of the HCOOH emission. Most of the observed features are reproduced by the IRE model. If we set $r_{CB}(=R_{in})$ to be 3 au obtained in the CH$_3$OH analysis, the best-fit parameters of $M_{star}$ and $i$ are 0.03 $M_{\odot}$ and 90$^{\circ}$, respectively, where the reduced $\chi^2$ value is 0.84.

For the combined models, we fix the inner radius ($R_{in}$) of the Keplerian part to be 1 au to reduce the number of free parameters. The outer radius ($R_{out}$) and the ranges for the other parameters ($M_{star}$, $r_{CB}$, and $i$) are the same as those of the IRE model. The $\chi^2$ analysis on the data cube yields the best-fit parameters as: $M_{star} = 0.03 M_{\odot}$, $r_{CB}(=R_{in}) = 6$ au, and $i = 90^{\circ}$, where the reduced $\chi^2$ value is 0.82. Then, we cannot confirm the disk structure in this observation, because of the insufficient resolution and the relatively weak emission of the central part due to the dust opacity effect.

### 7.2.2. Case 2: Keplerian Rotation

The stratified molecular distributions mentioned above being considered, the disk structure could be embedded in the infalling gas traced by the CH$_3$OH emission. An infalling-rotating motion on the surface of the disk/envelope system near the protostar would be traced by CH$_3$OH (Figure 5(b)). In this case, HCOOH might trace a Keplerian disk with a radius of 10 au. With this situation in mind, we prepare the models with a Keplerian motion in the FERIA code. The size of the disk, $R_{out}$, is fixed to be 10 au, and the free parameters are $M_{star}$, $R_{in}$, and $i$, which are varied in the ranges of 0.02–0.08 $M_{\odot}$, 1–6 au, and 70–90$^{\circ}$, respectively, as summarized in Table 4. We obtain the best-fit parameters of $M_{star} = 0.05 M_{\odot}$, $R_{in} = 5$ au, and $i = 90^{\circ}$ with the reduced $\chi^2$ value of 0.82. $i$ suggests a completely edge-on disk, while $M_{star}$ is similar to that in the CH$_3$OH analysis based on the IRE model. Figure 7 shows PV diagrams of the best-fit Keplerian models overlaid on those of the HCOOH emission. The reduced $\chi^2$ value in Case 2 is similar to that in Case 1.

In short, our observation is not able to determine which of Case 1 and Case 2 is more appropriate for the HCOOH distribution. Nevertheless, we can conclude that B335 has a very small protostellar mass and a disk structure smaller than the HCOOH emission. Our analysis of the HCOOH emission
<figure><img src="image_8.png" /><figcaption>**Figure 6.** PV diagrams of HCOOH (12<sub>0.12</sub> − 11<sub>0.11</sub>) in colors and the best-fit model obtained by the χ² analysis for the IRE model (upper) and the combined model (lower) with FERIA in contours. The parameters for the IRE model are the protostellar mass of 0.04M<sub>☉</sub>, the outer radius of 10 au, the inner radius and the centrifugal barrier of 7 au, and the inclination of 90° (90° for edge-on), where the reduced χ² value is 0.81. Those for the combined model are the protostellar mass of 0.03M<sub>☉</sub>, the outer radius of 10 au, the inner radius and the centrifugal barrier of 6 au, and the inclination of 90° (90° for edge-on), where the reduced χ² value is 0.82. Dotted horizontal lines show the systemic velocity of 8.34 km s<sup>-1</sup> (Yen et al. 2015), and dotted vertical lines show the protostar position.</figcaption></figure>

suggests that we need a higher-angular resolution and/or other
molecular lines specifically tracing a more compact distribution
to find a Keplerian disk.

8. Deuteration and Physical Environment

Based on our analysis in Section 7, the CH3OH emission traces
an infalling-rotating motion within 24 au in radius. The freefall

time is very short, which is roughly estimated to be only ~10 yr,
where the infall velocity of 5 km s⁻¹ is assumed at the radius of
10 au. Even if the dynamical timescale is estimated by the Kepler
time, it is about 100 yr. As a result, there would not be enough
time to change the isotopic ratios in the inner envelope by gas-
phase chemical reactions. Furthermore, our analysis with FERIA
implies a tiny disk structure with a radius of <7 au (r<sub>CB</sub>).
Considering these results, we here discuss the abundance
<figure><img src="image_9.png" /><figcaption>**Figure 7.** PV diagrams of HCOOH (12$_{0.12}$ − 11$_{0.11}$) in colors and the best-fit model obtained by the χ² analysis for the Keplerian disk model with FERIA in contours. The parameters for the model are the protostellar mass of 0.05M$_{⊙}$, the inner radius of 5 au, the outer radius of 10 au, and the inclination of 90° (90° for edge-on), where the reduced χ² value is 0.82. Dotted horizontal lines show the systemic velocity of 8.34 km s⁻¹ (Yen et al. 2015), and dotted vertical lines show the protostar position.</figcaption></figure>

ratios [CH₂DOH]/[CH₃OH], [CHD₂OH]/[CH₂DOH], and
[CH₂DOH]/[CH₃OD] in B335 and compare them with those
in other sources reported previously.

8.1. [CH₂DOH]/[CH₃OH]

The [CH₂DOH]/[CH₃OH] ratio can be converted to the D/H ratio by dividing by 3 because there are three equivalent H atoms of the methyl group for the D substitution. The D/H ratio was reported to be up to 0.1 toward low-mass protostars (e.g., Taquet et al. 2019; van Gelder et al. 2020, 2022). van Gelder et al. (2022) discussed the D/H ratio of [CH₂DOH]/[CH₃OH] among large samples including low-mass and intermediate sources as well as high-mass sources, where the lines of CH₃OH isotopologues, ¹³CH₃OH and CH₃¹⁸OH, as well as normal CH₃OH lines are used. Since most of the samples of low-mass protostars in their paper have a ratio much lower than 0.1, its average in low-mass protostars was reported to be [CH₂DOH]/[CH₃OH]~0.06 (D/H~0.02). It is higher than the ratios in high-mass protostars. The [CH₂DOH]/[CH₃OH] ratio in B335 is [0.09–0.38] (D/H~[0.03–0.13]), which tends to be relatively high even among other low-mass protostars and low-mass prestellar cores (D/H~0.034 ± 0.019; van Gelder et al. 2022). This result may be related to the young evolutionary stage of the B335 protostar. Since not enough time would have passed to decrease the D/H ratio to its equilibrium ratio at the current temperature in B335, the D/H ratio in the prestellar stage may be converted to some extent. Nevertheless, the derived D/H ratio could be due to underestimating the column density of CH₃OH. The optical depths of the CH₃OH lines are derived to be relatively high, as summarized in Appendix D. The D/H ratio of CH₃OH could thus be consistent with those of the previous reports. Anyway,

further confirmation of the D/H ratio by optically thin
isotopologues is awaited: a few ¹³CH₃OH lines are in the
observed spectral windows, but none of them provide further
constraints on the column density.

Note that the $S\mu_{JPL}^2$ values are used for CH₂DOH in the previous studies. Even if we employed the $S\mu_{JPL}^2$ values in our calculation, the D/H ratio in B335 would be smaller only by a factor of ~1.5. Therefore, the above trend on [CH₂DOH]/[CH₃OH] does not change even for this case (Table 3).

8.2. [CHD₂OH]/[CH₂DOH]

The [CHD₂OH]/[CH₂DOH] ratio (D/H ratio) of
[0.14–0.29] in B335 is comparable to those in the low-mass
protostellar sources IRAS 16293–2422 Source A (0.20 ± 0.07)
and B (0.25 ± 0.09; Drozdovskaya et al. 2022). For the low-
mass protostellar sources, B1-c and Serpens S68N, van Gelder
et al. (2022) derived the ratios 0.13 ± 0.02 and 0.12 ± 0.05,
respectively, on the assumption of the temperature of 150 K.
They are slightly lower than or comparable to our result. On the
other hand, our result in B335 is lower than the ratios in the
other low-mass protostellar sources, NGC1333 IRAS 2A
(0.70 ± 0.26), IRAS 4A (0.56 ± 0.22; Taquet et al. 2019),
and HOPS373SW (0.75; Lee et al. 2023). Recently, the
CHD₂OH and CH₂DOH lines were detected in the prestellar
sources as well, the ratios being 0.8 ± 0.4 in H-MM1 and
0.5 ± 0.3 in L694-2 (Lin et al. 2023). Furthermore, the D/H
ratio from CHD₂OH and CH₂DOH is reported to be higher
than that from CH₂DOH and CH₃OH in the above protostellar
and prestellar sources (Appendix E). Our results in B335
follow this trend even in the close vicinity of protostar
(<24 au). Note that the upper range of the D/H ratio of
CH₃OH is comparable to the lower range of the [CHD₂OH]/
[CH₂DOH] ratio. There may be an effect of the underestimated CH₃OH column density due to the high optical depth in our observation. Since the actual CH₃OH column density could be higher, the [CH₂DOH]/[CH₃OH] ratio would be lower, resulting in the values in the range of D/H ratio from CHD₂OH and CH₂DOH higher than that from CH₂DOH and CH₃OH.

## 8.3. [CH₂DOH]/[CH₃OD]

The [CH₂DOH]/[CH₃OD] ratio in B335 is found to be as high as [4.9–15] (Table 3). Similar values were found in other low-mass sources (e.g., Parise et al. 2004, 2006; Bizzocchi et al. 2014; Jørgensen et al. 2018). In the low-mass Class 0 protostellar source, IRAS 16293-2422 Source B, the ratio is derived to be 3.9 at the position shifted from the continuum peak as one beam to avoid the dust opacity effects with ALMA (Jørgensen et al. 2018). Bizzocchi et al. (2014) reported its lower limit of 10 in the external layers of the prestellar core L1544. On the other hand, the ratios in some high-mass star-forming regions are lower than 1.0 (e.g., Jacq et al. 1993; Ratajczak et al. 2011; Belloche et al. 2016; Bøgelund et al. 2018; Wilkins & Blake 2022). Thus, it is recognized that there is a systematic trend between low-mass and high-mass protostars. The physical environment would thus be one of the important effects on the [CH₂DOH]/[CH₃OD] ratio.

Even if the $S\mu^2_{SUMIRE}$ values for CH₂DOH were used for the calculation in the previously reported [CH₂DOH]/[CH₃OD] ratios, the trend would still be significant for most cases. For the strong lines of CH₂DOH, except for some c-type transitions or extremely high excitation ones, the differences in $S\mu^2$ between the JPL database and the experiment are within a factor of a few. It is therefore hard to explain the reported difference of the [CH₂DOH]/[CH₃OD] ratios more than an order of magnitude only by the different $S\mu^2$ values used in each study.

For CH₃OH, the methyl group has three equivalent H atoms, while the hydroxy group has only one H atom. If the hydrogenation of CO randomly occurs without isotope effect, the [CH₂DOH]/[CH₃OD] ratio should be 3. This is so-called the statistical ratio, which is predicted by conventional gas-grain chemical models (e.g., Charnley et al. 1997; Osamura et al. 2004). However, it is known that the deuterium fractionation of the CH₃ group can be enhanced through the abstraction of H by the D atom and the subsequent addition of D on the grain surface (Hidaka et al. 2009). This additional process occurs efficiently if the atomic D/H ratio on dust grains is high in cold conditions. This mechanism would make the [CH₂DOH]/[CH₃OD] ratio higher than the statistical ratio of 3. Such a high abundance ratio was also suggested with chemical models by Kulterer et al. (2022). According to their studies, CH₃OD is formed at a warm-up stage, although CH₂DOH could be inherited from the prestellar stage to the protostellar stage.

The chemical pathway for CH₃OD is still controversial, and many studies have been done by the chemical models (e.g., Charnley et al. 1997; Rodgers & Charnley 2002; Osamura et al. 2004; Taquet et al. 2014; Kulterer et al. 2022; Wilkins & Blake 2022) and the laboratory experiments (e.g., Nagaoka et al. 2005; Ratajczak et al. 2009). Bøgelund et al. (2018) and Taquet et al. (2019) compared the [CH₂DOH]/[CH₃OD] ratios in high-mass sources (NGC 6334 I: 0.1-0.5) and low-mass sources (IRAS 2A: 0.8-3.6 and IRAS 4A: 1.2-5.3) with the

chemical models presented by Taquet et al. (2012, 2013, 2014). The models follow the deuteration of CH₃OH in cold dense cores (10–40 K), resulting in a ratio close to or a little higher than 3. Hence, the observed trend for the high-mass protostellar source, NGC6334I, is not reproduced. On the other hand, Faure et al. (2015) reported a model that can reproduce the observational trend of the high and low [CH₂DOH]/[CH₃OD] ratios in low-mass and high-mass protostellar sources, respectively, considering the pathway exchanging between water and CH₃OH in icy mantles of dust grains. Kulterer et al. (2022) also pointed out the same mechanism.

Recently, Wilkins & Blake (2022) discussed rapid D–H exchange in methanol-containing ices depending on the temperature, based on its chemical model and the observation of the high-mass star-forming region Orion KL. According to their observation, the column density of CH₃OD starts to rise steeply at ~110 K and keeps increasing until before ~185 K. This result is consistent with their chemical model representing the rapid variation in the gas-phase CH₃OD column density due to the D–H exchange between water and CH₃OH on ices. In fact, the similar increase in the CH₃OD column density as increasing temperature up to around 200 K is also supported experimentally (Souda et al. 2003; Kawanowa et al. 2004). Wilkins & Blake (2022) suggested that the low [CH₂DOH]/[CH₃OD] ratio in Orion KL is caused by the increase in the CH₃OD column density at the temperature (~100–200 K), while understanding the D–H exchange to produce CH₃OD at a temperature higher than ~200 K is controversial.

If the high temperature were the only key factor for increasing CH₃OD (i.e., low [CH₂DOH]/[CH₃OD] ratio), the [CH₂DOH]/[CH₃OD] ratio in the inner envelope of B335 should be as low as in high-mass star-forming regions because of the high-temperature condition (107–217 K for CH₃OH). However, this simple thought contradicts our observational result. Therefore, the ratio may also depend on the physical environment at the prestellar core phase. The timescale that the D–H exchange reaches a steady state in Orion KL is suggested to be <10³ yr (Faure et al. 2015). The freefall and dynamical timescales in B335 on a few 10 au scale seems to be shorter than the chemical reaction timescale. Alternatively, there might be an effect of high cosmic rays in the envelope of B335, where the cosmic-ray ionization rate is reported to be 10⁻¹⁶–10⁻¹⁴ s⁻¹ by Cabedo et al. (2021). This rate is higher than usually assumed in chemical models (10⁻¹⁷ s⁻¹; Yamamoto 2017). Apparently, we need more observations of other protostellar sources in various physical environments to clarify the link between [CH₂DOH]/[CH₃OD] and the physical environment.

## 9. Summary

We study the CH₃OH and its deuterated species in terms of the abundance ratios and kinematics of the disk/envelope system in the low-mass protostellar source B335 at a high resolution (0.′′03~5 au) with ALMA. The main results are summarized below.

1. We analyze four lines of CH₂DOH, three lines of CHD₂OH, and one line of CH₃OD as well as six lines of CH₃OH in Band 6 originally observed by Okoda et al. (2022). The CHD₂OH (4₁,₂ – 4₀,₁, o₁-e₀) line emission is newly identified in this paper, which was previously unidentified by Okoda et al. (2022). These molecular lines are ring-shaped and extended within 24 au in radius around the protostar.
2. The five abundance ratios ([CH₂DOH]/[CH₂OH], [CHD₂OH]/[CH₃OH], [CH₃OD]/[CH₃OH], [CH₂DOH]/[CH₃OD], and [CHD₂OH]/[CH₂DOH]) are almost constant over the envelope. This likely originates from the short dynamical timescale (10–100 yr) in the inner envelope compared to the chemical timescale (~10⁴ yr).

3. We examine the effect of $S\mu^2$ values on the calculation for column densities and temperatures of CH₂DOH and CHD₂OH, because the calculated $S\mu^2$ values ($S\mu^2_{JPL}$ or $S\mu^2_{CDMS}$) and the experimental $S\mu^2$ values by Oyama et al. (2023; $S\mu^2_{SUMIRE}$) are different. Since $S\mu^2_{SUMIRE}$ for the CH₂DOH lines that we use is 0.6–0.8 times smaller than $S\mu^2_{JPL}$, its column density derived with is about 1.5 times larger than that with $S\mu^2_{JPL}$. On the other hand, the difference is smaller for CHD₂OH, which does not have a large effect on our column density derivations.

4. With the aid of the infalling-rotating-envelope model FERIA, we find that the CH₃OH (18$_{3,15}$–18$_{2,16}$, A) emission traces an infalling-rotating envelope with $M_{star}$, $r_{CB} (=R_{in})$, and $i$ are 0.07M$_{⊙}$, 3 au, and 70°, respectively. Additionally, we study the HCOOH (12$_{0,12}$–11$_{0,11}$) line with the IRE model and the Keplerian model to examine the existence of the disk structure. The disk structure is not definitively found, and these analyses just suggest a tiny disk structure smaller than 7 au in radius. The low $M_{star}$ and the very small disk structure imply a very young protostellar stage of this source.

5. The [CH₂DOH]/[CH₃OH] ratio in B335 ([0.09–0.38]) is relatively high among other low-mass protostellar (D/H~0.02) and prestellar sources (D/H~0.034 ± 0.019; van Gelder et al. 2022). CH₂DOH produced on dust grains at the prestellar phase seems to remain in the gas phase after desorption. This result may be related to the youth of the B335 protostar, where fresh gas is being supplied from the outer cold envelope. Further confirmation using optically thin isotopologue lines is necessary.

6. In B335, the [CHD₂OH]/[CH₂DOH] ratio ([0.14–0.29]) is higher than the D/H ratio of CH₃OH ([CH₂DOH]/[CH₃OH]/3 = [0.03–0.13]). This feature follows the trend among the other low-mass protostars.

7. The [CH₂DOH]/[CH₃OD] ratio in B335 ([4.9–15]) is higher than the statistical weight of 3. This result further supports the systematic trend between low-mass and high-mass sources in previous studies. Even under the high-temperature condition (CH₃OH: 107–217 K and CH₂DOH: 72–188 K) in B335, the [CH₂DOH]/[CH₃OD] ratio is still high. This fact means that the ratio would not only depend on the temperature but on current and past physical environments.

## Acknowledgments

This paper makes use of the following ALMA data set: ADS/JAO.ALMA# 2018.1.01311.S (PI: Muneaki Imai). ALMA is a partnership of the ESO (representing its member states), the NSF (USA), and NINS (Japan), together with the NRC (Canada) and the NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by the ESO, the AUI/NRAO, and the NAOJ. The authors thank the ALMA staff for their excellent support. This project is supported by a Grant-in-Aid from Japan Society for the Promotion of Science (KAKENHI: Nos.

19H05069, 19K14753, 20H05845, 20H05645 and 22K20390). Y. Okoda thanks RIKEN Special Postdoctoral Researcher Program (Fellowships) for financial support.

## Appendix A
Equations for the LTE Calculation

The column densities of CH₃OH, CH₂DOH, CHD₂OH, and CH₃OD in the envelope direction are derived under the LTE assumption from the observed intensities and the velocity widths (Table B1). The following formulation is taken from Okoda et al. (2022). Since the dust emission is bright in B335, we explicitly consider the effect of the optical depth of the dust emission ($\tau_{dust}$) as well as that of the line emission ($\tau_{line}$). For simplicity, we assume the condition that gas and dust are well mixed and the gas temperature is equal to the dust temperature. In this case, the observed brightness temperature ($T_{obs}$) is represented as follows:

$$T_{\text{obs}} = \frac{c^2}{2\nu^2 k_{\text{B}}} [B_{\nu}(T) + \exp \{-(\tau_{\text{line}} + \tau_{\text{dust}})\} \{B_{\nu}(T_{\text{cb}}) - B_{\nu}(T)\} - I_{\text{dust}}], \quad (\text{A1})$$

where $B_{\nu}(T)$ and $B_{\nu}(T_{cb})$ are the Planck function for the source temperature at $T$ and the cosmic microwave background temperature $T_{cb}$, respectively, and $I_{dust}$ is the intensity of the dust continuum emission. $\tau_{line}$ represents the optical depth of the molecular line, which can be written under the assumption of LTE as:

$$\tau_{\text{line}} = \frac{8\pi^3 S \mu^2}{3h\Delta\nu U(T)} \left\{ \exp\left(\frac{h\nu}{k_{\text{B}}T}\right) - 1 \right\} \exp\left(-\frac{E_u}{k_{\text{B}}T}\right) N, \quad (\text{A2})$$

where $S$ is the line strength, $\mu$ the dipole moment responsible for the transition, $h$ the Planck constant, $\Delta\nu$ the full width at half maximum, $U(T)$ the partition function of the molecule at the source temperature $T$. $\nu$ the frequency, $E_u$ the upper-state energy, and $N$ the column density. The $S\mu^2$ values depend on the transitions (Table 1). We employ the experimental values ($S\mu^2_{SUMIRE}$) for the lines of CH₂DOH and CHD₂OH in Section 4.1. On the other hand, $\tau_{dust}$ is given as:

$$\tau_{\text{dust}} \sim -\ln \left\{ \frac{B_{\nu}(T) - I_{\text{dust}}}{B_{\nu}(T)} \right\}, \quad (\text{A3})$$

assuming that $B_{\nu}(T) \gg B_{\nu}(T_{cb})$. The derived $\tau_{dust}$ values are summarized in Table C1. Further details are presented by Okoda et al. (2022).

## Appendix B
Gaussian Fitting

Using the method described in Appendix A, we perform the analysis on the observed intensities for each molecule at each position. The observed intensities and the velocity widths are obtained by Gaussian fitting. Figure B1 shows examples of the fitting results at the offset of -0.003, whose values are summarized in Table B1. In Figure B1, orange lines and black lines represent the fitting and the observation, respectively.
<figure><img src="image_10.png" /><figcaption>**Figure B1.** Examples of the spectra used for derivation of the column density and the temperature. The spectra are obtained within the rectangle in Figure 1 at the offset of −0.02′′03. The Gaussian fitting spectrum in the orange solid line is overlaid with the observed spectrum in black. The systemic velocity is 8.34 km s⁻¹ (Yen et al. 2015), as shown in gray dotted lines. *Lines I, II, III and IV are disturbed lines: CH₂DOH (5₂,₄ – 5₁,₅, e₀), t-HCOOH (11₃,₈ – 10₃,₇), CH₃CHO (13₀,₁₃ – 12₀,₁₂, A), and CH₃OH (18₃,₁₅ – 18₂,₁₆, A), respectively.</figcaption></figure>
<table><caption>Table B1
Examples of the Results of the Gaussian Best-fit Model at the Offset of −0.0′′03</caption><thead><tr><th>Line</th><th>Transition</th><th>Frequency<br>(GHz)</th><th>δν<br>(km s<sup>-1</sup>)<sup>a</sup></th><th>I<sub>peak</sub><br>(K)<sup>b</sup></th><th>V<sub>sys</sub><br>(km s<sup>-1</sup>)<sup>c</sup></th></tr></thead><tbody><tr><td>CH<sub>3</sub>OH</td><td>18<sub>3,15</sub> – 18<sub>2,16</sub>, A</td><td>247.610918</td><td>5.92 ± 0.33</td><td>106.99 ± 5.10</td><td>6.36 ± 0.14</td></tr><tr><td>CH<sub>3</sub>OH</td><td>21<sub>3,18</sub> – 21<sub>2,19</sub>, A</td><td>245.223019</td><td>5.86 ± 0.23</td><td>109.73 ± 3.76</td><td>6.54 ± 0.10</td></tr><tr><td>CH<sub>3</sub>OH</td><td>12<sub>6,7</sub> – 13<sub>5,8</sub>, E</td><td>261.704409</td><td>4.96 ± 0.45</td><td>89.71 ± 7.05</td><td>6.74 ± 0.19</td></tr><tr><td>CH<sub>3</sub>OH</td><td>17<sub>3,14</sub> – 17<sub>2,15</sub>, A</td><td>248.282424</td><td>6.10 ± 0.76</td><td>112.8 ± 12.04</td><td>6.46 ± 0.32</td></tr><tr><td>CH<sub>3</sub>OH</td><td>4<sub>2,2</sub> – 5<sub>1,5</sub>, A</td><td>247.228587</td><td>5.20 ± 0.41</td><td>107.49 ± 7.37</td><td>6.10 ± 0.17</td></tr><tr><td>CH<sub>3</sub>OH</td><td>2<sub>1,1</sub> – 1<sub>0,1</sub>, E</td><td>261.805675</td><td>4.84 ± 0.54</td><td>94.14 ± 9.15</td><td>5.92 ± 0.23</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>10<sub>2,8</sub> – 10<sub>1,9</sub>, o<sub>1</sub></td><td>244.9888456</td><td>4.59 ± 0.29</td><td>58.33 ± 3.16</td><td>6.57 ± 0.12</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>4<sub>2,2</sub> – 4<sub>1,3</sub>, e<sub>0</sub></td><td>244.8411349</td><td>5.27 ± 0.60</td><td>77.77 ± 7.64</td><td>7.18 ± 0.25</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>5<sub>2,4</sub> – 5<sub>1,5</sub>, e<sub>0</sub></td><td>261.6873662</td><td>4.45 ± 0.48</td><td>79.01 ± 7.38</td><td>6.63 ± 0.20</td></tr><tr><td>CH<sub>2</sub>DOH</td><td>3<sub>2,1</sub> – 3<sub>1,2</sub>, e<sub>0</sub></td><td>247.6257463</td><td>5.38 ± 0.76</td><td>64.61 ± 7.89</td><td>6.61 ± 0.32</td></tr><tr><td>CHD<sub>2</sub>OH</td><td>6<sub>1,1</sub> – 5<sub>1,1</sub>, o<sub>1</sub></td><td>246.1432950</td><td>3.66 ± 0.52</td><td>52.04 ± 6.44</td><td>6.87 ± 0.22</td></tr><tr><td>CHD<sub>2</sub>OH</td><td>6<sub>1,2</sub> – 5<sub>1,2</sub>, e<sub>0</sub></td><td>246.2530390</td><td>3.59 ± 0.47</td><td>44.48 ± 5.07</td><td>6.43 ± 0.20</td></tr><tr><td>CHD<sub>2</sub>OH</td><td>4<sub>1,2</sub> – 4<sub>0,1</sub>, o<sub>1</sub>–e<sub>0</sub></td><td>247.2524160</td><td>7.01 ± 0.45</td><td>70.58 ± 3.82</td><td>6.48 ± 0.19</td></tr><tr><td>CH<sub>3</sub>OD</td><td>5<sub>1</sub> – 4<sub>0</sub>, E</td><td>245.142988</td><td>5.38 ± 0.69</td><td>41.6 ± 4.63</td><td>7.84 ± 0.29</td></tr></tbody></table>

### Notes.

a Line width of the spectrum.

b Peak intensity of the spectrum.

c Velocity at the peak intensity of the spectrum.

## Appendix C
### Dust Optical Depth

Here, we summarize the dust optical depths derived in the analysis in Table C1. They are evaluated by using Equation (A3).

<table><caption>Table C1
Optical Depth and Brightness Temperature of Dust</caption><thead><tr><th>Position</th><th>CH<sub>3</sub>OH</th><th>CH<sub>2</sub>DOH</th><th>CHD<sub>2</sub>OH</th><th>CH<sub>3</sub>OD</th><th>T<sub>dust</sub><br>(K)<sup>a</sup></th></tr></thead><tbody><tr><td>0.1</td><td>0.04<sup>+0.03</sup><sub>-0.02</sub></td><td>0.07<sup>+0.04</sup><sub>-0.05</sub></td><td>0.04<sup>+0.03</sup><sub>-0.02</sub></td><td>0.04<sup>+0.03</sup><sub>-0.02</sub></td><td>4.2</td></tr><tr><td>0.06</td><td>0.12<sup>+0.02</sup><sub>-0.02</sub></td><td>0.15<sup>+0.02</sup><sub>-0.04</sub></td><td>0.12<sup>+0.03</sup><sub>-0.02</sub></td><td>0.12<sup>+0.03</sup><sub>-0.02</sub></td><td>15.4</td></tr><tr><td>0.03</td><td>0.63<sup>+0.05</sup><sub>-0.04</sub></td><td>0.78<sup>+0.04</sup><sub>-0.05</sub></td><td>0.63<sup>+0.10</sup><sub>-0.08</sub></td><td>0.63<sup>+0.10</sup><sub>-0.08</sub></td><td>74.0</td></tr><tr><td>0</td><td>1.01<sup>+0.10</sup><sub>-0.03</sub></td><td>1.4<sup>+0.1</sup><sub>-0.1</sub></td><td>1.0<sup>+0.2</sup><sub>-0.1</sub></td><td>1.0<sup>+0.2</sup><sub>-0.1</sub></td><td>136.9</td></tr><tr><td>-0.03</td><td>0.52<sup>+0.03</sup><sub>-0.03</sub></td><td>0.64<sup>+0.05</sup><sub>-0.08</sub></td><td>0.52<sup>+0.07</sup><sub>-0.06</sub></td><td>0.52<sup>+0.07</sup><sub>-0.06</sub></td><td>73.0</td></tr><tr><td>-0.06</td><td>0.11<sup>+0.02</sup><sub>-0.02</sub></td><td>0.12<sup>+0.03</sup><sub>-0.03</sub></td><td>0.11<sup>+0.03</sup><sub>-0.02</sub></td><td>0.11<sup>+0.03</sup><sub>-0.02</sub></td><td>14.7</td></tr><tr><td>-0.1</td><td>0.04<sup>+0.02</sup><sub>-0.03</sub></td><td>0.04<sup>+0.03</sup><sub>-0.03</sub></td><td>0.04<sup>+0.02</sup><sub>-0.03</sub></td><td>0.04<sup>+0.02</sup><sub>-0.03</sub></td><td>4.2</td></tr></tbody></table>

### Notes.

a The averaged brightness temperature of dust continuum emission within each rectangle area is shown in Figure 1(a). The noise level of T<sub>dust</sub> (K) is 2.6 K for a rectangle area (0.0′′03 × 0.0′′05).

## Appendix D
### Optical Depths of CH<sub>3</sub>OH Lines

Here, we summarize the optical depths of the CH<sub>3</sub>OH lines derived in the analysis in Table D1. They are evaluated by using Equation (A2).
<table><caption>**Table D1**
Optical Depths of the CH<sub>3</sub>OH Lines</caption><thead><tr><th>Position</th><th>0"<sup>1</sup></th><th>0"<sup>06</sup></th><th>0"<sup>03</sup></th><th>0"</th><th>-0"<sup>03</sup></th><th>-0"<sup>06</sup></th><th>-0"<sup>1</sup></th></tr></thead><tbody><tr><td>18<sub>3,15</sub> - 18<sub>2,16</sub>, A</td><td>12.646</td><td>11.566</td><td>12.161</td><td>6.725</td><td>7.382</td><td>7.898</td><td>8.963</td></tr><tr><td>21<sub>3,18</sub> - 21<sub>2,19</sub>, A</td><td>6.841</td><td>6.504</td><td>6.814</td><td>3.097</td><td>4.415</td><td>5.099</td><td>5.005</td></tr><tr><td>12<sub>6,7</sub> - 13<sub>5,8</sub>, E</td><td>0.783</td><td>1.899</td><td>2.834</td><td>1.739</td><td>1.924</td><td>1.734</td><td>1.061</td></tr><tr><td>17<sub>3,14</sub> - 17<sub>2,15</sub>, A</td><td>3.932</td><td>8.621</td><td>12.446</td><td>6.294</td><td>8.898</td><td>6.938</td><td>5.165</td></tr><tr><td>4<sub>2,2</sub> - 5<sub>1,5</sub>, A</td><td>2.942</td><td>7.341</td><td>10.819</td><td>5.207</td><td>7.767</td><td>6.176</td><td>3.934</td></tr><tr><td>2<sub>1,1</sub> - 1<sub>0,1</sub>, E</td><td>1.162</td><td>3.121</td><td>5.213</td><td>3.377</td><td>4.360</td><td>2.895</td><td>1.576</td></tr></tbody></table>

## Appendix E
D/H ratios in B335 and Other Sources

The D/H ratios discussed in Section 8.2 are summarized in Table E1. We select the seven low-mass protostellar sources and the low-mass prestellar sources (H-MM1 and L694-2) as samples for comparison. The values of B335 are derived in this paper.

<table><caption>**Table E1**
Abundances</caption><thead><tr><th>Source</th><th>[CHD<sub>2</sub>OH]/[CH<sub>2</sub>DOH]</th><th>[CH<sub>2</sub>DOH]/[CH<sub>3</sub>OH]/3</th><th>References<sup>c</sup></th></tr></thead><tbody><tr><td>B335</td><td>0.14–0.29<sup>b</sup></td><td>0.03–0.13<sup>b</sup></td><td>This work</td></tr><tr><td>IRAS 16293–2422 A</td><td>0.20 ± 0.07</td><td>0.028 ± 0.012</td><td>1</td></tr><tr><td>IRAS 16293–2422 B</td><td>0.25 ± 0.09</td><td>0.024 ± 0.009</td><td>1</td></tr><tr><td>B1-c</td><td>0.13 ± 0.02</td><td>0.028 ± 0.09</td><td>2</td></tr><tr><td>Serpens S68N</td><td>0.12 ± 0.05</td><td>0.014 ± 0.006</td><td>2</td></tr><tr><td>NGC1333 IRAS 2A</td><td>0.70 ± 0.26</td><td>0.019 ± 0.01</td><td>3</td></tr><tr><td>NGC1333 IRAS 4A</td><td>0.56 ± 0.22</td><td>0.014 ± 0.008</td><td>3</td></tr><tr><td>HOPS373SW</td><td>0.75</td><td>0.131</td><td>4</td></tr><tr><td>H-MM1<sup>a</sup></td><td>0.8 ± 0.4</td><td>0.06 ± 0.02</td><td>5</td></tr><tr><td>L694-2<sup>a</sup></td><td>0.5 ± 0.3</td><td>0.03 ± 0.02</td><td>5</td></tr></tbody></table>

**Notes.**

<sup>a</sup> Low-mass prestellar core.

<sup>b</sup> These values are derived with the experimental value ($\mu_{\text{SUMIRE}}^2$).

<sup>c</sup> 1: Drozdovskaya et al. (2022). 2: van Gelder et al. (2022). 3: Taquet et al. (2019). 4: Lee et al. (2023). 5: Lin et al. (2023).

## ORCID iDs

Yuki Okoda https://orcid.org/0000-0003-3655-5270

Nami Sakai https://orcid.org/0000-0002-3297-4497

Yoshimasa Watanabe https://orcid.org/0000-0002-9668-3592

Ana López-Sepulcre https://orcid.org/0000-0002-6729-3640

Takahiro Oyama https://orcid.org/0000-0002-2301-7951

Shaoshan Zeng https://orcid.org/0000-0003-3721-374X

Satoshi Yamamoto https://orcid.org/0000-0002-9865-0970

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