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

The simplest complex organic molecule (COM), 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 hydrogenation of CO by H atoms on the dust grain surfaces in cold condition 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 non-thermal 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 the 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; van Gelder et al., 2020; Imai et al., 2022; Manigand et al., 2020; 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 the 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 the 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, b; Jørgensen et al., 2018; Taquet et al., 2019; Manigand et al., 2020; van Gelder et al., 2022; Drozdovskaya et al., 2022; Yamato et al., 2023), 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 understand 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 Senction 2. Some key information on the observation are 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.

B335 is a Bok globule (Keene et al., 1980), with which the Class 0 protostar IRAS 19347+0727 is associated. The bolometric temperature ($T_{\rm bol}$) is 37 K (Andre et al., 2000), while the bolometric luminosity ($L_{\rm bol})$ is 1.6 $L_{\odot}$ (Kang et al., 2021). The distance to B335 is reported to be 165 pc, based on the Gaia DR2 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; Bjerkeli et al., 2019; Imai et al., 2016, 2019, 2022; Okoda et al., 2022). A bipolar outflow extending along the east-to-west direction (P.A. $\sim$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 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 $M_{\odot}$ from imperceptible rotation motion in the C¹⁸O 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 ($\sim$0$\farcs$1). They derived the protostellar mass and the radius of the centrifugal barrier to be 0.03$-$0.1 $M_{\odot}$ and $<$8 au, respectively, assuming the infalling-rotating motion. Meanwhile, the velocity gradient seen in the CH₃OH and SO₂ lines are independently reported by Bjerkeli et al. (2019), where the results are consistent with a pure free fall or a Keplerian rotation with the protostellar mass of 0.08 $M_{\odot}$. They also estimated the disk/envelope mass from the dust continuum emission within 12 au to be 8 $\times$ 10^-4 $M_{\odot}$. 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 et al. (2023) imply 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 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 5 degree difference on the P.A. does not significantly affect any result.

Recently, CH₃OH and CH₂DOH were observed in B335 with Atacama Large Millimeter/submillimeter Array (ALMA) at a high resolution of 0.″03 ($\sim$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 were 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 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 on the line analysis (The details are described elsewhere: Yamamoto, 2017; Oyama et al., 2023, e.g.,). 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.

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 June 10, 12, 13, and 23 in 2019. 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 CHD₂OH (4${}_{1,2}-$4_0,1, o₁-e₀) line, based on the spectroscopic data by Coudert et al. (2021) and the database of CDMS (Endres et al., 2016). Since the maximum recoverable scale is 0$\farcs$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^-1, and the root-mean-square noise is 1.0 mJy beam^-1channel^-1. Further observation parameters (calibrators, primary beamwidth, and correlator setups etc.) are described elsewhere (Okoda et al., 2022).

The data reduction was performed with Common Astronomy Software Applications package (CASA) 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.

We here analyze the CH₃OH, CH₂DOH, CHD₂OH, and CH₃OD lines listed in Table 1 to study the deuterium fractionation of CH₃OH in the disk/envelope system. Figure 1 shows the moment 0 maps of the CH₃OH (18${}_{3,15}-$18_2,16, A), CH₂DOH (4${}_{2,2}-$4_1,3, e₀), CHD₂OH (4${}_{1,2}-$4_0,1, o₁-e₀), and CH₃OD (5${}_{1}-$4₀, E) lines with the synthesized beam size (0$\farcs$030$\times$0$\farcs$023: Table 1). They have a ring-shaped distribution around the protostar with the intensity depression at the continuum peak due to the high dust opacity. Similar images are also reported for the CH₃OH, CH₂DOH, and CH₃OD lines by Okoda et al. (2022), where the beam sizes are smoothed to be 0$\farcs$034 to perform the PCA.

Okoda et al. (2022) derived the column densities of CH₃OH and CH₂DOH with each aperture of 0$\farcs$03 for 9 positions along the midplane of the envelope (P.A. 0°) using the $S\mu^{2}$ values calculated from the line intensities listed in the database of JPL. A recent experimental measurement for some lines of CH₂DOH with SUMIRE (Spectrometer Using superconductor MIxer REceiver) by Oyama et al. (2023) found that the $S\mu^{2}$ values in the database of JPL significantly deviate from the measured values. The experimental $S\mu^{2}$ values for some lines of CHD₂OH are now available with SUMIRE very recently (Oyama et al. in prep). In the following, we first derive the column densities and abundances of CH₂DOH and CHD₂OH by using the newly available experimental $S\mu^{2}$ values (hereafter referred to as $S\mu^{2}_{\rm\ SUMIRE}$) listed in Table 1. We discuss the dependence of the gas temperature and the column densities on the $S\mu^{2}$ values later (Section 5).

In the previous section, we use the experimental value, $S\mu^{2}_{\rm\ SUMIRE}$, for the derivation of the column density of CH₂DOH and CHD₂OH. 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 CH₂DOH ($S\mu^{2}_{\rm\ SUMIRE}$ vs. $S\mu^{2}_{\rm\ JPL}$) and CHD₂OH ($S\mu^{2}_{\rm\ SUMIRE}$vs. $S\mu^{2}_{\rm\ CDMS}$) lines. In Table 1, column 4 represents the $S\mu^{2}$ values calculated from the line intensity in the database of JPL (hereafter referred to as $S\mu^{2}_{\rm JPL}$) for the CH₂DOH lines and those taken from the database of CDMS (hereafter referred to as $S\mu^{2}_{\rm CDMS}$) for the CHD₂OH lines.

The differences between $S\mu^{2}_{\rm JPL}$ and $S\mu^{2}$_SUMIRE are conspicuous for CH₂DOH: $S\mu^{2}$_SUMIRE is 0.6-0.8 times smaller than $S\mu^{2}$_JPL. The temperature and the column density toward the offset of -0$\farcs$03 from the continuum peak are derived with $S\mu^{2}$_JPL to be 162${}^{+12}_{-8}$ K and 2.5${}^{+0.8}_{-0.4}\times$10¹⁸ cm^-2, respectively. When we use $S\mu^{2}$_SUMIRE, they are derived to be 161${}^{+8}_{-6}$ K and 3.6${}^{+1.1}_{-0.6}\times$10¹⁸ cm^-2, 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 CH₂DOH derived with $S\mu^{2}_{\rm JPL}$ is also 1.4-1.6 times smaller than those derived with $S\mu^{2}_{\rm\ SUMIRE}$, as shown in Table 2, resulting in the range of the column densities and the ratios as: $N$(CH₂DOH)=[0.41-3.5]$\times$10¹⁸ cm^-2, $[$CH₂DOH$]$/$[$CH₃OH$]$=[0.07-0.26], and $[$CH₂DOH$]$/$[$CH₃OD$]$=[3.5-9.7]. Note that some of the CH₂DOH column densities are different from those reported by Okoda et al. (2022) beyond the errors and the effect of the $S\mu^{2}$ difference, particularly at the continuum peak position. This is because the circle area with the diameter of 0$\farcs$03 was employed for their derivation.

On the other hand, a difference between $S\mu^{2}$_CDMS and $S\mu^{2}$_SUMIRE for the CHD₂OH lines is relatively small (Table 1). The $S\mu^{2}$_SUMIRE values are about 1.2 times larger than the $S\mu^{2}$_CDMS values at most for the observed lines. In this case, the upper limits to the column densities at the offset of -0$\farcs$03 are similar to each other: they are $<$0.77$\times$10¹⁸ cm^-2 and $<$0.68$\times$10¹⁸ cm^-2 with the $S\mu^{2}$_CDMS and $S\mu^{2}$_SUMIRE values, respectively, where we assume the CH₃OH temperature of 186$\pm$15 K. Therefore, a choice of the $S\mu^{2}$_CDMS and $S\mu^{2}$_SUMIRE values does not cause serious differences on the abundance ratios in our observation (Table 3). The $[$CHD₂OH$]$/$[$CH₂DOH$]$ ratio is mostly affected by the difference on the $S\mu^{2}$ value of CH₂DOH. Using the $S\mu^{2}_{\rm\ JPL}$ value for CH₂DOH and the $S\mu^{2}_{\rm\ CDMS}$ value for CHD₂OH, we obtain [0.20-0.46] (Table 3).

It should be noted that an effect of $S\mu^{2}$ values on the column densities depend on which lines are used for the derivation. In other words, different lines have different differences between the S$\mu^{2}_{\rm JPL}$ and $S\mu^{2}$_SUMIRE values or between the S$\mu^{2}_{\rm CDMS}$ and $S\mu^{2}$_SUMIRE values. Therefore, an effect of the $S\mu^{2}$ values on the column densities in any other observations would be different from those reported here. Thus, we need a special care for a comparison of column densities and their ratios with those in other sources reported previously.

It is of fundamental importance for 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 CH₃OH (12${}_{6,7}-$13_5,8, E, $E_{\rm u}=$360 K) and HCOOH (12${}_{0,12}-$11_0,11, $E_{\rm u}=$83 K) lines at a resolution of 0$\farcs$1. Since the resolution of our data is higher by a factor of 3-4, we re-investigate the kinematic structure of the disk/envelope system with these molecular species.

The upper panels of Figure 3 show the moment 0 maps of CH₃OH (18${}_{3,15}-$18_2,16, A, $E_{\rm u}=$447 K) and HCOOH (12${}_{0,12}-$11_0,11), respectively. The velocity range for the integration is from -0.2 km s^-1 to 14.5 km s^-1, where the systemic velocity is 8.34 km s^-1(Yen et al., 2015). The moment 0 map of CH₃OH is the same as Figure 1(a). We choose this line of CH₃OH 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 CH₃OH 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 1 maps of CH₃OH and HCOOH, respectively, where the velocity range is from 1.6 km s^-1 to 13.3 km s^-1. The velocity gradient can be seen in the both of the moment 1 maps. The velocity gradient in the map of CH₃OH 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 et al., 2023). Hence, the observed velocity structure has a gradient along the different direction from the suggested disk/envelope system, particularly for the CH₃OH 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 0 maps of CH₃OH 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 CH₃OH distribution is more extended in height of the disk/envelope system than the HCOOH distribution as well as in radius. Part of the CH₃OH 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 CH₃OH emission and provide us with a better estimate of the disk height. Therefore, the apparent scale height of the disk/envelope system is roughly be 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$\farcs$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 (Imai et al., 2019). Its distribution covers the area where both of 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 the protostellar heating.

In this section, we analyze the CH₃OH and HCOOH data to determine the protostellar mass ($M_{\rm star}$), the centrifugal barrier ($r_{\rm CB}$), and the inclination ($i$) of the disk/envelope system, the inner radius ($R_{\rm in}$) 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 $R_{\rm in}$ 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 3$\sigma$ noise level; 1.5 mJy beam^-1 and 1.8 mJy beam^-1 for CH₃OH and HCOOH. For the models, we set a 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.

Based on our analysis in Section 7, the CH₃OH emission traces an infalling-rotating motion within 24 au in radius. The free-fall time is very short, which is roughly estimated to be only $\sim$ 10 yr, where the infall velocity of 5 km s^-1 is assumed at the radius of 10 au. Even if the dynamical time scale 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 the radius of $<$7 au ($r_{\rm CB}$). Considering these results, we here discuss the abundance ratios $[$CH₂DOH$]$/$[$CH₃OH$]$, $[$CHD₂OH$]$/$[$CH₂DOH$]$, and $[$CH₂DOH$]$/$[$CH₃OD$]$ in B335 and compare them with those in other sources reported previously.

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$\farcs$03$\sim$5 au) with ALMA. Main results are summarized below.

1. We analyze 4 lines of CH₂DOH, 3 lines of CHD₂OH, and 1 line of CH₃OD as well as 6 lines of CH₃OH in Band 6 originally observed by Okoda et al. (2022). The CHD₂OH (4${}_{1,2}-$4_0,1, 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$]$/$[$CH₃OH$]$, $[$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 ($\sim 10^{4}$ 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 ($S\mu^{2}_{\rm\ JPL}$or $S\mu^{2}_{\rm CDMS}$) and the experimental $S\mu^{2}$ values by Oyama et al. (2023) ($S\mu^{2}_{\rm\ SUMIRE}$) are different. Since $S\mu^{2}_{\rm\ SUMIRE}$ for the CH₂DOH lines that we use is 0.6-0.8 times smaller than $S\mu^{2}_{\rm\ JPL}$, its column density derived with $S\mu^{2}_{\rm\ SUMIRE}$ is about 1.5 times larger than that with $S\mu^{2}_{\rm\ JPL}$. On the other hand, the difference is smaller for CHD₂OH, which does not make 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 $M_{\rm star}$, $r_{\rm CB}$($=R_{\rm in}$), and $i$ are 0.07$M_{\odot}$, 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 $M_{\rm star}$ 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$\sim$0.02) and prestellar sources (D/H$\sim$0.034$\pm$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 a 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: 107-217K 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.