CH_3OH and Its Deuterated Species in the Disk/Envelope System of the Low-Mass Protostellar Source B335

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 6 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 au scale in B335 by analyzing the CH3OH (183,15-182,16, A) and HCOOH (120,12-110,11) line emission. Velocity structures of these lines are reasonably explained as the infalling-rotating motion. The protostellar mass and the upper limit to centrifugal barrier are thus derived to be 0.03-0.07 M_{\odot} 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.


INTRODUCTION
The simplest complex organic molecule (COM), methanol (CH 3 OH), 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 CH 3 OH 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, CH 3 OH is released into the gas phase in the inner envelope mainly through the thermal desorption by protostellar heating.Therefore, the CH 3 OH 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 CH 3 OH emission is also observed in the outflow shocked regions through sputtering and heat-ing 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 CH 3 OH emission.For instance, Oya et al. (2016) reported that the CH 3 OH 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 CH 3 OH emission in some sources such as B335 (Okoda et al. 2022) and [BHB2007] 11 (Vastel et al. 2022).In short, studies on the CH 3 OH emission provide us with important information connecting the chemical and physical structures of protostellar sources.
The deuterated species of CH 3 OH such as CH 2 DOH, CHD 2 OH, CD 3 OH, and CH 3 OD 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 CH 3 OH 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 highmass 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 CH 3 OH in various protostellar sources would be a key to understand their physical and chemical evolution.Nevertheless, there still remain controversial issues on the CH 3 OH deuteration.
For instance, previous observations suggested a systematic trend of the [CH 2 DOH]/[CH 3 OD] ratio between low-mass and highmass 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 CH 3 OH 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 CH 3 OH in the disk/envelope system.We show the effect of Sµ 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.

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 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 starformation 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. 2016Imai et al. , 2019Imai et al. , 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. 1988Hirano et al. , 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 ⊙ 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 (CH 3 OH) 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.Mean-while, the velocity gradient seen in the CH 3 OH and SO 2 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 ⊙ .They also estimated the disk/envelope mass from the dust continuum emission within 12 au to be 8 × 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 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. (2019Bjerkeli et al. ( , 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, CH 3 OH and CH 2 DOH were observed in B335 with Atacama Large Millimeter/submillimeter Array (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 CH 3 OH, CH 2 DOH, HCOOH and NH 2 CHO line emission.The chemical differentiation among molecular distribution were also studied, based on the principal component analysis (PCA).They found that the CH 3 OH and deuterated CH 3 OH species (CH 2 DOH, CHD 2 OH, and CH 3 OD) have a ringshaped and extended distribution.Their velocity structures most likely trace the disk/envelope system, while HCOOH, HNCO, and NH 2 CHO have a more compact distribution.Although the column densities of CH 3 OH and CH 2 DOH 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, Sµ 2 (S is the line strength and µ the dipole moment responsible for the transition: e.g., Yamamoto 2017), of CH 2 DOH 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 CH 3 OH deuteration including CHD 2 OH and CH 3 OD were left for a separate publication.
The Sµ 2 value is directly related to the individual line intensity and is an important parameter on the line analysis (The details are described elsewhere: e.g., Yamamoto 2017;Oyama et al. 2023).Since the Sµ 2 values of CH 2 DOH were recently measured with the laboratory experiment (Oyama et al. 2023) and those of CHD 2 OH 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 CH 3 OH deuteration and the velocity structure of the disk/envelope system within a few 10 au scale.

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 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 CHD 2 OH (4 1,2 −4 0,1 , o 1 -e 0 ) 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 0.544-0.691km s −1 , and the root-mean-square noise is 1.0 mJy beam −1 channel −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.  1 to study the deuterium fractionation of CH 3 OH in the disk/envelope system.Figure 1 shows the moment 0 maps of the CH 3 OH (18 3,15 −18 2,16 , A), CH 2 DOH (4 2,2 −4 1,3 , e 0 ), CHD 2 OH (4 1,2 −4 0,1 , o 1 -e 0 ), and CH 3 OD (5 1 −4 0 , 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 3 OH, CH 2 DOH, and CH 3 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 3 OH and CH 2 DOH with each aperture of 0. ′′ 03 for 9 positions along the midplane of the envelope (P.A. 0 • ) using the Sµ 2 values calculated from the line intensities listed in the database of JPL.A recent experimental measurement for some lines of CH 2 DOH with SUMIRE (Spectrometer Using superconductor MIxer REceiver) by Oyama et al. (2023) found that the Sµ 2 values in the database of JPL significantly deviate from the measured values.The experimental Sµ 2 values for some lines of CHD 2 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 2 DOH and CHD 2 OH by using the newly available experimental Sµ 2 values (hereafter referred to as Sµ 2 SUMIRE ) listed in Table 1.We discuss the dependence of the gas temperature and the column densities on the Sµ 2 values later (Section 5).

Column Densities
We derive the column densities of CH 3 OH and deuterated CH 3 OH species towards 7 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, we focus on the disk/envelope system within 20 au in radius from the protostar.The LTE analysis is justified, since the H 2 density for that area is roughly estimated to be higher than 10 8 cm −3 , based on its apparent size and the H 2 column density of 5.66×10 23 cm −2 reported by Imai et al. (2016).In addition, the CH 3 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 χ 2 analysis.The offset in Table 2 means the distance from the protostar along the midplane of the disk/envelope system from the southwestern to north-eastern direction (P.A. 5 • ), where the offset of 0. ′′ 1 (∼17 au) is almost close to the edge of the distributions of CH 3 OH and its deuterated species.Examples of the line parameters of CH 3 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 2 OH are close to one another and there is only one line of CH 3 OD in our set up, we cannot determine the temperature independently for these two species.Therefore, in the calculation of the column densities of CHD 2 OH and CH 3 OD, we assume the CH 3 OH temperature obtained for each position, considering the coexisitng nature of CH 3 OH and its isotopologues (See Figure 1).In addition, the temperature of CH 3 OH is better determined than that of CH 2 DOH due to the higher signal to noise ratio.For CH 3 OD, we employ the Sµ 2 value calculated by Anderson et al. (1988).
At the continuum peak, the observed column densities of CH 3 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 2 DOH (>5.2×10 18 cm −2 ), while those of CHD 2 OH and CH 3 OD are derived to be 1.1 +0.4  −0.2 × 10 18 cm −2 and 2.0 +0.5 −0.3 × 10 18 cm −2 , respectively.Therefore, we mainly focus on the column densities at the six positions in the envelope.Among three deuterated species, CH 2 DOH shows the highest column density at all positions, which is in the range of [0.61-4.7]×10 18cm −2 .The column densities of CHD 2 OH and CH 3 OD are in the range of [0.11-0.67]×10 18cm −2 and [0.05-0.47]×10 18cm −2 , 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 χ 2 analysis for CH 3 OH and CH 2 DOH, where 1σ uncertainty is presented as the error for each parameter.For CHD 2 OH and CH 3 OD, we estimate the errors of their column densities, based on the assumed temperature range of ±15 K from the CH 3 OH temperature.

Abundances
Using these derived column densities (Table 2), we derive the five abundance ratios: 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 the large uncertainties or just the lower and upper limits due to high dust opacity.The  [4.9-15] and [0.14-0.29],respectively (See also Table 3).We discuss the and [CH 2 DOH]/[CH 3 OD] ratios in Section 8.Although the column densities and the abundances are roughly constant over the disk/envelope system, the temperatures of CH 3 OH and CH 2 DOH decrease as an increasing distance from the protostar position.
The dust optical depths (τ dust ) are summarized in Appendix C. Note that the τ dust values obtained in the analyses of the CH 3 OH and CH 2 DOH lines are slightly different for some positions due to the different temperature.If we employ the CH 3 OH temperature for the calculation of CH 2 DOH, its column density is (0.44-2.8)×10 18 cm −2 in the disk/envelope system, and the lower limits to the abundance ratios are higher than those when the CH 2 DOH temperature is employed.In short, the different treatments of the CH 2 DOH temperature do not seriously affect the trend as discussed in Section 8.  3).
It should be noted that an effect of Sµ 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 Sµ 2 JPL and Sµ 2 SUMIRE values or between the Sµ 2 CDMS and Sµ 2 SUMIRE values.Therefore, an effect of the Sµ 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.

DISTRIBUTIONS AND VELOCITY MAPS OF THE DISK/ENVELOPE SYSTEM
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 CH 3 OH (12 6,7 −13 5,8 , E, E u =360 K) and HCOOH (12 0,12 −11 0,11 , E u =83 K) lines at a resolution of 0. ′′ 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 CH 3 OH (18 3,15 −18 2,16 , A, E 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 CH 3 OH is the same as Figure 1(a).We choose this line of CH 3 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 3 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 1 maps of CH 3 OH 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 CH 3 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 et al. 2023).Hence, the observed velocity structure has a gradient along the different direction from the suggested disk/envelope system, particularly for the CH 3 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 0 maps of CH 3 OH and HCOOH show a ring-shaped distribution in spite of the almost edgeon configuration suggested by Bjerkeli et al. (2019) and Evans et al. (2023).The CH 3 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 3 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 3 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 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. ′′ 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 CH 3 OH 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.

KINEMATICS OF THE DISK/ENVELOPE
SYSTEM WITH FERIA In this section, we analyze the CH 3 OH 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 χ 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 CH 3 OH 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.
7.1.CH 3 OH (18 3,15 −18 2,16 , A) Based on the distributions in the moment 0 and 1 maps (Figure 3(a)) and the analyses presented by Imai et al. (2019), the CH 3 OH emission is expected to trace an infalling-rotating envelope (IRE).To explore the velocity structure of the CH 3 OH (18 3,15 −18 2,16 , 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 CH 3 OH emission, which is assumed to be equal to r CB .R out indicates the outer radius of IRE (R out ) traced by the CH 3 OH 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 from 70 • to 90 • for i.The position angles (P.A.) of the disk/envelope is set to be 5 • (Bjerkeli et al. 2019(Bjerkeli et al. , 2023;;Cabedo et al. 2021).We compare the model with the observation on the cube data to calculate the reduced χ 2 value.Then, we obtain the best-fit parameters at the reduced χ 2 values of 0.88, where M star , r CB (= R in ), and i are 0.07M ⊙ , 3 au, and 70 • , respectively.Imai et al. (2019) reported M star of 0.03-0.1 M ⊙ and r CB <8 au.With the same data, Oya et al. (2022) obtained the best-fit parameters of M star =0.03 M ⊙ and r CB =2 au through the χ 2 tests (the reduced χ 2 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 star =0.07 M ⊙ and R in =2 au at a reduced χ 2 value of 0.78.Bjerkeli et al. (2019) independently derived M star to be 0.08 M ⊙ from the analysis of the PV diagrams of CH 3 OH and SO 2 at a similar resolution to our observation, assuming a Keplerian rotation.Thus, the small M star and r CB 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 CH 3 OH in colors, where the cutting width of 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 of 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.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 1 map (Figure 3(b)) looks similar to the infalling-rotating motion (Oya et al. 2022).Nevertheless, we examine the following two cases to explore its velocity structure by using the model on the cube data.One is the case that HCOOH traces an infallingrotating 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 the radius of 10 au (=R out =r CB ) is traced by HCOOH, where the gas infalling on the above and below disk mid-plane toward the protostar is traced by CH 3 OH.The two cases are schematically shown in Figures 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.

Case 1: Infalling-rotating envelope (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 χ 2 test for HCOOH on the cube data.The best-fit value of M star is 0.04 M ⊙ , where the reduced χ 2 value is 0.81.The other best-fit parameters are: r CB (= R in )=7 au, and i =90 • .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 bestfit 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 ⊙ and 90 • , respectively, where the reduced χ 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 the 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 χ 2 analysis on the data cube yields the best-fit parameters as: M star =0.03 M ⊙ , r CB (= R in ) =6 au, and i =90 • , where the reduced χ 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.

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 the radius of 10 au.With this situation in mind, we prepare the models with a Keplerian rotion 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 0.02-0.08M ⊙ , 1-6 au, and 70-90 • , respectively, as summarized in Table 4.We obtain the best-fit parameters of M star =0.05 M ⊙ , R in =5 au, and i =90 • with the reduced χ 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.The reduced χ 2 value in the 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 on the HCOOH emission suggests that we need a higher-angular resolution and/or other molecular lines specifically tracing a more compact distribution to find a Keplerian disk.

DEUTERATION AND PHYSICAL ENVIRONMENT
Based on our analysis in Section 7, the CH 3 OH 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 ∼ 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 CB ).Considering these results, we here discuss the abundance ratios

[CH 2 DOH]/[CH 3 OH]
The [CH 2 DOH]/[CH 3 OH] 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. 2020van Gelder et al. , 2022)).van Gelder et al. (2022) discussed the D/H ratio of [CH 2 DOH]/[CH 3 OH] among large samples including low-mass and intermediate sources as well as high-mass sources, where the lines of CH 3 OH isotopologues, 13 CH 3 OH and CH 3 18 OH, as well as normal CH 3 OH lines are used.Since most of the samples of low-mass protostars in their paper have the ratio much lower than 0.1, its average in low-mass protostars was reported to be [CH 2 DOH]/[CH 3 OH]∼0.06(D/H∼0.02).It is higher than the ratios in highmass protostars.The [CH 2 DOH]/[CH 3 OH] 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 CH 3 OH.The optical depths of the CH 3 OH lines are derived to be relatively high, as summarized in Appendix D. The D/H ratio of CH 3 OH could thus be consistent with those of the previous reports.Anyway, further comfirmation of the D/H ratio by optically thin isotopologues is awaited: a few 13 CH 3 OH lines are in the observed spectral windows, but none of them provide further constraints on the column density.
Note that the Sµ 2 JPL values are used for CH 2 DOH in the previous studies.Even if we employed the Sµ 2 JPL 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 [CH 2 DOH]/[CH 3 OH] does not change even for this case (Table 3).

[CHD 2 OH]/[CH 2 DOH]
The [CHD 2 OH]/[CH 2 DOH] ratio (D/H ratio) of [0.14-0.29] in B335 is comparable to those in the lowmass 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±0.02and 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 CHD 2 OH and CH 2 DOH 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 CHD 2 OH and CH 2 DOH is reported to be higher than that from CH 2 DOH and CH 3 OH in 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 CH 3 OH is comparable to the lower range of the [CHD 2 OH]/[CH 2 DOH] ratio.There may be the effect of the underestimated CH 3 OH column density due to the high optical depth in our observation.Since the actual CH 3 OH column density could become higher, the [CH 2 DOH]/[CH 3 OH] ratio would be lower, resulting in the values in the range of D/H ratio from CHD 2 OH and CH 2 DOH higher than that from CH 2 DOH and CH 3 OH.

[CH
The [CH 2 DOH]/[CH 3 OD] ratio in B335 is found to be as high as [4.9-15] (Table 3).The similar values were found in other low-mass sources (e.g., Parise et al. 2004Parise et al. , 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 highmass 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 [CH 2 DOH]/[CH 3 OD] ratio.
Even if the Sµ 2 SUMIRE values for CH 2 DOH were used for the calculation in the previously reported [CH 2 DOH]/[CH 3 OD] ratios, the trend would still be significant for most cases.For the strong lines of CH 2 DOH, except for some c-type transitions or extremely high excitation ones, the differences of Sµ 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 [CH 2 DOH]/[CH 3 OD] ratios more than an order of magnitude only by the different Sµ 2 values used in each study.
For CH 3 OH, the methyl group has three equivalent H atoms, while the hydroxy group only one H atom.If the hydrogenation of CO randomly occurs without isotope effect, the [CH 2 DOH]/[CH 3 OD] 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 CH 3 group can be enhanced through abstraction of H by the D atom and 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 are high in cold conditions.This mechanism would make the [CH 2 DOH]/[CH 3 OD] ratio higher than the statistical ratio of 3.Such a high abundance ratio was also sug-gested with chemical models by Kulterer et al. (2022).According to their studies, CH 3 OD is formed at a warmup stage, although CH 2 DOH could be inherited from prestellar stage to protostellar stage.
The chemical pathway for CH 3 OD is still controversial, where 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;Wilkins & Blake 2022;Kulterer et al. 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 [CH 2 DOH]/[CH 3 OD] ratios in high-mass source (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. (2012Taquet et al. ( , 2013Taquet et al. ( , 2014)).The models follow deuteration of CH 3 OH in cold dense cores (10-40 K), resulting in the 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 [CH 2 DOH]/[CH 3 OD] ratios in low-mass and high-mass protostellar sources, respectively, considering the pathway exchanging between water and CH 3 OH 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 toward the high-mass star forming region Orion KL.According to their observation, the column density of CH 3 OD 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 of the gas-phase CH 3 OD column density due to the D-H exchange between water and CH 3 OH on ices.In fact, the similar increase of the CH 3 OD 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 [CH 2 DOH]/[CH 3 OD] ratio in Orion KL is caused by the increase of the CH 3 OD column density at the temperature (∼100-200 K), while understandings of the D-H exchange to produce CH 3 OD at a temperature higher than ∼ 200 K is controversial.
If the high temperature were the only key factor for increasing CH 3 OD (i.e, low [CH 2 DOH]/[CH 3 OD] ratio), the [CH 2 DOH]/[CH 3 OD] 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 CH 3 OH).However, this simple thought contradicts our observational result.Therefore, the ratio may also depend on the physical environment at the prestellar core phase.The time scale that the D-H exchange reaches steady state in Orion KL is suggested to be <10 3 yr (Faure et al. 2015).The free-fall and dynamical time scales in B335 on a few 10 au scale seems to be shorter than the chemical reaction timescale.Alternatively, there might be an effect by 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 [CH 2 DOH]/[CH 3 OD] and physical environment.

SUMMARY
We study the CH 3 OH 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.Main results are summarized below.
1. We analyze 4 lines of CH 2 DOH, 3 lines of CHD 2 OH, and 1 line of CH 3 OD as well as 6 lines of CH 3 OH in Band 6 originally observed by Okoda et al. (2022).The CHD 2 OH (4 1,2 −4 0,1 , o 1 -e 0 ) line emission is newly identified in this paper, which was previously unidentified by Okoda et al. (2022).These molecular lines are ringshaped and extended within 24 au in radius around the protostar.JPL .On the other hand, the difference is smaller for CHD 2 OH, which does not make a large effect on our column density derivations.

The five abundance ratios ([CH
4. With the aid of the infalling-rotating-envelope model FERIA, we find that the CH 3 OH (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.

The [CH
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).CH 2 DOH 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.

In B335, the [CHD
. This feature follows the trend among the other low-mass protostars.([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 (CH 3 OH: 107-217K and CH 2 DOH: 72-188 K) in B335, the [CH 2 DOH]/[CH 3 OD] ratio is still high.This fact means that the ratio would not only depend on the temperature but on current and past physical environments.(Yen et al. 2015).Contour levels are every 3σ from 3σ, where σ is 1.5 mJy beam −1 , 3.0 mJy beam −1 , 3.0 mJy beam −1 , and 2.0 mJy beam −1 , 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 show the continuum peak position (α2000, δ2000) = (19 h 37 m 00 s .90,+7 • 34 ′ 09."49).The red ellipse in each map represents the beam size.The red and blue arrows in the panel (a) show the directions of the red-and blue-shifted outflow.SUMIRE 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) Red vertical line represents the average in low-mass protostars (0.06) reported by van Gelder et al. (2022). (d) 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.

Figure 2 .
Figure 2. (a-e) Abundance ratios along the envelope (P.A. 5 • ).Column densities of CH2DOH and CHD2OH derived from Sµ 2SUMIRE 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) Red vertical line represents the average in low-mass protostars (0.06) reported byvan Gelder et al. (2022).(d)  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.

Figure 3 .
Figure 3. (a,b) Moment 0 and 1 maps of theCH3OH (183,16, A)  andHCOOH (120,11)  emission in the upper and lower panels, respectively.The moment 0 map of CH3OH is the same as Figure1(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 0 and 1 maps, the integrated velocity range are 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 1 map of CH3OH show the directions of the PV diagrams of Figures4, 6, and 7.The white cross marks represent the continuum peak (α2000, δ2000) = (19 h 37 m 00 s .90,+7 • 34 ′ 09."49).The red ellipses represent the beam size.

Figure 4 .Figure 5 .
Figure 4. PV diagrams of CH3OH (183,15−182,16, A) in colors and the best-fit model obtained by the χ 2 analysis for infalling-rotating envelope (IRE) model with FERIA in contours.The best-fit parameters for the IRE model are the protostellar mass of 0.07M⊙, 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 χ 2 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.

Figure 6 .Figure B. 1 .
Figure 6.PV diagrams of HCOOH (120,11)  in colors and the best-fit model obtained by the χ 2 analysis for the infallingrotating envelope (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⊙, 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 χ 2 value is 0.81.Those for the combined model are the protostellar mass of 0.03M⊙, 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 χ 2 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.
Okoda et al. (2022)he derivation of the column density of CH 2 DOH and CHD 2 OH.Since the derived column density and rotation temperature depend on the Sµ 2 values used, we here note the effects on the results for the different Sµ 2 values for the CH 2 DOH (Sµ 2 In Table1, column 4 represents the Sµ 2 values calculated from the line intensity in the database of JPL (hereafter referred to as Sµ 2 JPL ) for the CH 2 DOH lines and those taken from the database of CDMS (hereafter referred to as Sµ 2 CDMS ) for the CHD 2 OH lines.×1018−2,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 CH 2 DOH derived with Sµ 2 JPL is also 1.4-1.6 times smaller than those derived with Sµ 2 SUMIRE , as shown in Table 2, resulting in the range of the column densities and the ratios as: N (CH 2 DOH)=[0.41-3.5]×1018−2,[CH 2 DOH]/[CH 3 OH]=[0.07-0.26],and[CH 2 DOH]/[CH 3 OD]=[3.5-9.7].Note that some of the CH 2 DOH column densities are different from those reported byOkoda et al. (2022)beyond the errors and the effect of the Sµ 2 difference, particularly at the continuum peak position.This is because the circle area with the diameter of 0. ′′ 03 was employed for their derivation.On the other hand, a difference between Sµ 2 CDMS and Sµ 2 SUMIRE for the CHD 2 OH lines is relatively small (Table1).The Sµ 2 SUMIRE values are about 1.2 times larger than the Sµ 2 CDMS 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 <0.77×1018 cm −2 and <0.68×10 18 cm −2 with the Sµ 2 CDMS and Sµ 2 SUMIRE values, respectively, where we assume the CH 3 OH temperature of 186±15 K. Therefore, a choice of the Sµ 2 CDMS and Sµ 2 SUMIRE values does not cause serious differences on the abundance ratios in our observation (Table 3).The [CHD 2 OH]/[CH 2 DOH] ratio is mostly affected by the difference on the Sµ 2 value of CH 2 DOH.Using the Sµ 2 JPL value for CH 2 DOH and the Sµ 2 CDMS value for CHD 2 OH, we obtain [0.20-0.46](Table 5. AN EFFECT OF Sµ 2 ON THE COLUMN DENSITIESIn the previous section, we use the experimental value, and [CHD 2 OH]/[CH 2 DOH]) 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 (∼ 10 4 yr).3.We examine the effect of Sµ 2 values on the calculation for column densities and temperatures of CH 2 DOH and CHD 2 OH, because the calculated Sµ 2 values (Sµ 2