11institutetext: Niels Bohr Institute & Centre for Star and Planet Formation,
University of Copenhagen, Øster Voldgade 5-7, DK-1350 Copenhagen K, Denmark
22institutetext: Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux,
CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
33institutetext: Institut de Recherche en Astrophysique et Planétologie,
Université de Toulouse, UPS-OMP, CNRS, CNES, 9 av. du Colonel Roche, 31028
Toulouse Cedex 4, France 44institutetext: Leiden Observatory, Leiden
University, PO Box 9513, 2300 RA Leiden, The Netherlands 55institutetext:
Max–Planck Institute für extraterrestrische Physik (MPE), Giessenbachstrasse,
85748 Garching, Germany 66institutetext: National Astronomical Observatory of
Japan, Osawa 2–21–1, Mitaka, Tokyo 181–8588, Japan 77institutetext: Institute
of Astronomy and Astrophysics, Academia Sinica, No. 1, Sec. 4, Roosevelt Road,
Taipei 10617, Taiwan, R. O. C. 88institutetext: Department of Space, Earth and
Environment, Chalmers University of Technology, Onsala Space Observatory, 439
92 Onsala, Sweden

# ALMA observations of doubly deuterated water: Inheritance of water from the
prestellar environment

S. S. Jensen 11<EMAIL_ADDRESS>J. K. Jørgensen 11 L. E. Kristensen 11
A. Coutens 2233 E. F. van Dishoeck 4455 K. Furuya 66 D. Harsono 4477 M. V.
Persson 88

(Draft date: )

###### Abstract

Context. Establishing the origin of the water D/H ratio in the Solar System is
central to our understanding of the chemical trail of water during the star
and planet formation process. Recent modeling suggests that comparisons of the
D2O/HDO and HDO/H2O ratios are a powerful way to trace the chemical evolution
of water and, in particular, determine whether the D/H ratio is inherited from
the molecular cloud or established locally.

Aims. We seek to determine the D2O column density and derive the D2O/HDO
ratios in the warm region toward the low-mass Class 0 sources B335 and L483.
The results are compared with astrochemical models and previous observations
to determine their implications for the chemical evolution of water.

Methods. We present ALMA observations of the D2O $1_{1,0}$–$1_{0,1}$
transition at 316.8 GHz toward B335 and L483 at $\lesssim
0.\\!\\!^{\prime\prime}5$ ($\lesssim 100\leavevmode\nobreak\ $au) resolution,
probing the inner warm envelope gas. The column densities of D2O, HDO, and
H${}_{2}^{18}$O are determined by synthetic spectrum modeling and direct
Gaussian fitting, under the assumption of a single excitation temperature and
similar spatial extent for the three water isotopologs.

Results. D2O is detected toward both sources in the inner warm envelope. The
derived D2O/HDO ratio is $(1.0\pm 0.2)\times 10^{-2}$ for L483 and $(1.4\pm
0.1)\times 10^{-2}$ for B335. These values indicate that the D2O/HDO ratio is
higher than the HDO/H2O ratios by a factor of $\gtrsim 2$ toward both sources.

Conclusions. The high D2O/HDO ratios are a strong indication of chemical
inheritance of water from the prestellar phase down to the inner warm
envelope. This implies that the local cloud conditions in the prestellar
phase, such as temperatures and timescales, determine the water chemistry at
later stages and could provide a source of chemical differentiation in young
systems. In addition, the observed D2O/H2O ratios support an observed
dichotomy in the deuterium fractionation of water toward isolated and
clustered protostars, namely, a higher D/H ratio toward isolated sources.

###### Key Words.:

astrochemistry — stars: formation — ISM: abundances — submillimeter: stars —
ISM: individual objects: L483, B335

##  1 Introduction

Addressing when and how water is synthesized during the formation of stars and
planetary systems is essential to our understanding of the delivery of water,
and other volatiles, to young planets. Water is a requirement for life as we
know it and therefore central for the habitability of planets (e.g., Chyba &
Hand 2005). Additionally, water acts as a coolant in molecular gas and is a
major constituent of the solid mass reservoirs in protoplanetary disks (e.g.,
van Dishoeck et al. 2014; Karska et al. 2018).

Figure 1: Schematics of the predicted ice structure in the prestellar core
stage (left) and the observed water deuterium fractionation toward embedded
low-mass protostars (right). The outer layer of the ice mantle, which has high
water D/H ratio, may stem from nonthermal desorption in the cold envelope or
cold gas-phase formation. Meanwhile, the whole mantle is sublimated in the hot
corino, lowering the HDO/H2O ratio. The schematical structure is proposed by
Furuya et al. (2016). The figure is adopted from van Dishoeck et al. (2021)..

Water is among the most abundant molecules in the interstellar medium and has
been observed at all major stages of star and planet formation. In prestellar
cores, water is a major constituent of the thick ice caps with
$X_{\mathrm{ice}}\sim 10^{-4}$ with respect to H2 (e.g., Whittet et al. 1996;
Bergin & Snell 2002; Boogert et al. 2015). In the inner warm envelope toward
Class 0 sources, water ice is thermally desorbed, and the derived gas-phase
water abundance reaches $X_{\mathrm{gas}}\sim 10^{-7}$–$10^{-4}$ (e.g.,
Ceccarelli et al. 2000; Persson et al. 2016). In outflows, water is sputtered
off the grains or synthesized directly in the gas phase, and the abundances
can reach $X_{\mathrm{gas}}\sim 10^{-6}$–$10^{-4}$ (e.g., Kristensen et al.
2017). Meanwhile, a recent search for water toward nearby Class I sources
shows that gas-phase water abundances are low in young
disks($X_{\mathrm{gas}}\lesssim 10^{-6}$), indicating that most of the water
remains locked in ice at this stage (Harsono et al. 2020). These observations
provide vital constraints on the chemical evolution of water and reveal that
water is formed as ice at high abundance in molecular clouds and prestellar
cores (van Dishoeck et al. 2021). This is confirmed by models of the chemical
evolution during star formation (e.g., Taquet et al. 2013b; Furuya et al.
2016; Coutens et al. 2020). However, a central question remains as to what
extent is water in protoplanetary disk inherited from the prestellar cloud or
synthesized locally in the disk (e.g., Visser et al. 2009; Cleeves et al.
2014). If prestellar inheritance is the dominant source of water in the
protoplanetary disk, then the water chemistry is set by the conditions in the
local cloud environment (e.g., the temperature, radiation field, and
duration). This could promote some chemical differentiation in planetary
systems. Conversely, if local processing in the disk is significant, then
local conditions in the disk may strongly influence the chemistry of water and
other volatiles.

By studying the deuterium fractionation of water, we can determine how the
physical conditions affect the water chemistry and track the chemical
evolution during star and planet formation (e.g., Ceccarelli et al. 2014).
Deuterium fractionation occurs as a consequence of several chemical processes
that depend sensitively on the temperature, density, visual extinction, and
ionization sources (Caselli et al. 2012). At low temperatures ($\lesssim
50\leavevmode\nobreak\ $K), the prominent pathway is the gas-phase exchange
reaction H${}_{3}^{+}$ \+ HD $\rightleftharpoons$ H2D+ \+ H2 \+ $\Delta E$,
where $\Delta E$ depends on the spin state of the involved reactants. This
forward reaction is endothermic, and the backward reaction is inhibited at low
temperatures, thereby leading to an enrichment of H2D+ relative to
H${}_{3}^{+}$. H2D+ (and D2H+, D${}_{3}^{+}$) dissociatively recombines with
free electrons to form atomic D, thus increasing the local atomic D/H ratio in
the gas phase and ultimately on dust grain surfaces where water and other
molecules are formed through hydrogenation (Tielens 1983; Roberts et al.
2003). Detections of gas phase H2D+ confirm that this enrichment is occurring
in the gas phase in prestellar cores (Caselli et al. 2003; Vastel et al.
2004).

Observations of HDO and H${}_{2}^{18}$O toward Class 0 source show that the
degree of deuterium fractionation varies on different spatial scales (e.g.,
Persson et al. 2014). Single-dish observations, some of which may arise in the
cold extended envelope, reveal high D/H ratios of water; HDO/H2O ratios range
from 10-3 to 10-2 (Stark et al. 2004; Parise et al. 2005; Coutens et al.
2012). Meanwhile, interferometric observations targeting the inner warm region
have found much lower water deuteration; in these observations HDO/H2O ratios
range from $10^{-4}-10^{-3}$ (Jørgensen & van Dishoeck 2010; Taquet et al.
2013a; Persson et al. 2014; Jensen et al. 2019). The first detection of
interstellar D2O was presented by Butner et al. (2007), who derived a D2O/HDO
ratio of 1.7$\times 10^{-3}$ toward IRAS16293–2422 based on single-dish
observations. In a later work, Coutens et al. (2012) found a higher D2O/HDO
ratio of $\sim$0.06 toward the same source using _Herschel_ HIFI data.
Interferometric detections of D2O on inner envelope scales prior to this work
are limited to Coutens et al. (2014), who found a high D2O/HDO ratio of $\sim
1\%$ and D2O/H2O $\sim$ 2$\times$10-5 toward NGC1333 IRAS 2A. The current
observational understanding is outlined in Fig. 1.

The observed difference in D/H ratios on different spatial scales can be
understood as a result of the chronological evolution of water chemistry
during star formation (Dartois et al. 2003; Taquet et al. 2013b; Furuya et al.
2016). Before cloud collapse, water ice is formed in the molecular cloud with
a lower deuterium fraction, as a result of higher temperatures and moderate
extinction in this phase ($T\sim 20$ K, $A_{\mathrm{v}}\lesssim 5$ mag).
Later, as the cloud core cools and contracts, the extinction increases and CO
is depleted (e.g., Caselli et al. 1999). During this phase, the deuterium
fractionation becomes highly efficient, and a second generation of highly
deuterated water ice is formed. This chronology leads to two distinct
components in the interstellar ice: the bulk ice mantle consists of a water-
rich ice with lower D/H ratio, and the surface consists of a mix of highly
deuterated water, CO, and complex organics (see Fig. 1). This scenario can
explain the observed deuterium fractionations: on larger spatial scales, the
bulk water reservoir remains in the solid phase, and the observed gas phase
primarily consists of water with a high D/H ratio. This gas-phase water is
either photo-desorbed from the ice surface layers or formed directly in the
gas phase at low temperature and high extinction, that is, with a high D/H
ratio (Taquet et al. 2013b; Furuya et al. 2016). Meanwhile, in the inner warm
gas, where the ice is entirely sublimated, the gas-phase HDO/H2O ratio of
water is lowered, since the ice reservoir with a lower D/H ratio is released
from the dust grains. The similarity between D2O/HDO ratios on larger and
smaller scales support this scenario; the abundance of deuterated water
isotopologs is low in the bulk water ice, and consequently the ratio is
largely unaffected by the sublimation of the bulk water ice.

A consequence of the above scenario for water formation is that the D/H ratio
of water could depend on the physical conditions in the molecular cloud and
prestellar core prior to and during the protostellar collapse. Lower
temperatures or a longer duration of the deeply embedded phase would increase
the D/H ratio observed in the inner warm region. Conversely, a faster collapse
or warmer gas temperature could lower the D/H ratio in the inner warm region.
This would imply a relation between the bulk water D/H ratio and the dynamics
of the formation environment. Isolated protostars may collapse more slowly
than clustered counterparts because the stability of the cloud is determined
solely by the internal cloud structure (Ward-Thompson et al. 2007; Enoch et
al. 2008). Moreover, the temperature in clustered regions could be higher
owing to, for instance, more external radiation or shock heating (Krumholz
2014; Hocuk et al. 2017). Either of these scenarios would enhance the D/H
ratio toward isolated protostars in contrast to clustered protostars, in which
external factors can influence the physical conditions. Such a differentiation
was recently suggested based on ALMA observations of HDO and H${}_{2}^{18}$O
in the warm inner envelope toward three isolated protostars (Jensen et al.
2019). If the enhanced HDO/H2O ratio is a consequence of environmental
effects, then the same might also apply to D2O.

In this work, we present the first ALMA detections of D2O in the inner warm
region toward the isolated low-mass Class 0 protostars B335 and L483. We
combine the D2O detections with previous detections of HDO and H${}_{2}^{18}$O
toward the sources to derive D2O/HDO, D2O/H2O and HDO/H2O ratios consistently.
This work aims to constrain the chemical evolution of water between the
molecular cloud and the inner warm envelope toward Class 0 sources.
Furthermore, accurate determination of the D/H ratio in the warm envelope
allow for comparison between the deuterium fractionation in protoplanetary
disk and warm envelopes toward Class 0 sources, thereby establishing a
possible link between these regimes.

The paper is organized as follows. In Section 2, the observations and data
reduction are presented. The data analysis is presented in Section 3, and the
results are discussed in Section 4. Throughout the paper we refer to NGC1333
IRAS 2A as IRAS 2A. We denote HDO/H2O as fD1 and D2O/HDO as fD2, and use both
terms interchangeably. Furthermore, we refer to the inner warm gas component,
where $r\lesssim 100$ au and $T\gtrsim 100$ K, as the warm envelope.

##  2 Observations

Table 1: Observation log. Source | Date | Phase calibrator | Bandpass calibrator | Max. baseline (m) | nantennas |  $v_{\mathrm{LSR}}$(km/s)
---|---|---|---|---|---|---
L483 | 2019 October 29 | J1743$-$0350 | J1924$-$2914 | 697 | 42 | 4.5
B335 | 2019 October 8 | J1938$+$0448 | J1924$-$2914 | 784 | 42 | 8.3
Figure 2: Continuum emission at 301.7 GHz toward L483 and B335. The map shows
emission above 1$\sigma_{\mathrm{rms}}$ with white contours at
5$\sigma_{\mathrm{rms}}$, 10$\sigma_{\mathrm{rms}}$, and
30$\sigma_{\mathrm{rms}}$. Linear scales are indicated in the lower right
corner, assuming a distance of 100 pc to B335 and 200 pc to L483 (see Jensen
et al. 2019, and references therein). The gray arrows indicate the direction
of outflows that may be perturbing the dust distribution. The synthesized beam
size is shown in the lower left corner.

Figure 3: Moment 0 maps of the D2O and CH3OD emission, excluding channels
where the emission is blended. Maps show emission above $3\sigma$, where
$\sigma=\sigma_{\mathrm{rms}}\times N_{\mathrm{channels}}^{0.5}\times d\varv$;
$d\varv$ is the channel width and $N$ is the number of collapsed channels. The
black cross indicates the continuum peak position.

The low-mass protostars B335 and L483 were observed with ALMA during Cycle 7
(PI: Sigurd S. Jensen, projectid: 2019.1.00720.S). Information on the
observation dates and calibration sources can be found in Table 1. In the
present analysis, we also utilize additional spectral windows from the data
presented in Jensen et al. (2019) toward both sources; this latter work gives
a detailed description of those observations.

The spectral setup targeted the D2O $1_{1,0}$–$1_{0,1}$ transition at 316.8119
GHz in the ALMA band 7. The imaged spectral windows contain 1920 channels with
a width of 122 kHz (0.11 km s-1). The observed phase centers are
$\alpha_{\mathrm{J2000}}:$ 19:37:00.89, $\delta_{\mathrm{J2000}}:$ +07:34:09.5
for B335, and $\alpha_{\mathrm{J2000}}:$ 18:17:29.91,
$\delta_{\mathrm{J2000}}:$ -04:39:39.6 for L483. The source velocities applied
to the spectral tunings are listed in Table 1.

Each dataset was pipeline-calibrated using casa 5.6 (McMullin et al. 2007).
Subsequent phase self-calibration was attempted for each dataset with casa
5.6. For B335, self-calibration was successful with an improved signal-to-
noise ratio (S/N) of $\sim 25\%$; however, for L483, no improvement in S/N
level was achieved, and therefore the ALMA pipeline product was preferred.

Imaging was performed with the tclean algorithm with a robust parameter of
0.5. Toward each source, a continuum image at 302 GHz was created and compared
with previous ALMA observations toward the sources. The intensities and
morphologies of the continuum images are consistent with previous
interferometric observations of the sources (e.g., Imai et al. 2016; Oya et
al. 2017; Jacobsen et al. 2019; Imai et al. 2019). The final continuum images
are shown in Fig. 2. The synthesized beam size in spectral window centered on
the D2O transition are $0.\\!\\!^{\prime\prime}38\times
0.\\!\\!^{\prime\prime}37$ and $0.\\!\\!^{\prime\prime}56\times
0.\\!\\!^{\prime\prime}46$ for B335 and L483, respectively.

Continuum subtraction for each spectral window was performed using the sigma-
clipping method with the statcont code presented in detail in Sánchez-Monge et
al. (2018). We preferred to use this method because both sources display rich
hot corino emission, which made continuum subtraction through the uvcontsub
routine in casa challenging (see, e.g., Jørgensen et al. 2016). For the line
analysis, we extracted the spectrum from a single pixel toward the continuum
peak position for each source.

The emission lines presented in this work are identified using data from the
Jet Propulsion Laboratory (JPL, Pickett et al. 1998) and the Cologne Database
for Molecular Spectroscopy (CDMS, Müller et al. 2001). The spectroscopic data
used to identify D2O, HDO, H${}_{2}^{18}$O are from Brünken et al. (2007),
Messer et al. (1984), and de Lucia et al. (1972), respectively. Furthermore,
spectroscopic data for CH3OCH3, and CH3OD are from Endres et al. (2009) and
Anderson et al. (1993), respectively. For CH3OD, the exact partition function
is unknown, and the current analysis relies on a partition function scaled
from the CH${}_{3}^{18}$OH partition function, similar to Jørgensen et al.
(2018). All querying was done through the Splatalogue
interface111https://splatalogue.online. Throughout this work, the H2O column
density is estimated from H${}_{2}^{18}$O by adopting a 16O/18O ratio of 560
(Wilson & Rood 1994).

##  3 Results

The D2O lines were detected toward both sources as part of a broad emission
feature. The emission feature was identified as D2O blended with two CH3OD
transitions and, potentially, one CH3OCH3 transition. This identification is
consistent with the observed feature toward IRAS 2A (Coutens et al. 2014). As
the line is heavily blended, estimation of the column density is challenging,
and two complimentary methods were employed. The spatial extent of the D2O and
CH3OD emission is confined to the inner envelope, as shown in Fig. 3.

Figure 4: Overview of the two methods used to determine the column density of
D2O toward B335. _Left_) Synthetic spectrum model for the emission feature
toward B335 for an assumed source size of 0$.\\!\\!^{\prime\prime}$2\. The
estimated optical depth $\tau$ for D2O is shown in the upper left corner. The
synthetic spectrum includes components from D2O, CH3OD, and CH3OCH3. _Right_)
Least-squares fit to the emission profile. The best fit includes three
Gaussian components, one identified as D2O, one identified as CH3OD at
316.7651 GHz, and a third component that may be either CH3OD at 316.7916 GHz
or CH3OCH3 at 316.7904 GHz, or a convolution of both. Figure 5: Overview of
the two methods used to determine the column density of D2O toward L483.
_Left_) Synthetic spectrum model for the emission feature toward L483 for an
assumed source size of 0$.\\!\\!^{\prime\prime}$2\. All molecules are fitted
with double Gaussians. The estimated optical depth $\tau$ for both D2O
profiles are shown in the upper left corner. The synthetic spectrum includes
components from D2O, CH3OD, and CH3OCH3. _Right_) Least-squares fit to the
emission profile. The best fit includes three components, one identified as
D2O, one identified as CH3OD at 316.7651 GHz, and a third component that may
be either CH3OD at 316.7916 GHz or CH3OCH3 at 316.7904 GHz, or a convolution
of both.

###  3.1 Synthetic spectrum modeling

The first method for the estimation of the D2O column density relies on a
synthetic spectrum of the sources. Combining the ALMA data from Jensen et al.
(2019) with those presented in this work, spectral coverage extends to several
spectral windows in ALMA bands 5, 6, and 7. For B335, two unblended
transitions of CH3OD and four unblended transitions of CH3OCH3 were
identified. For L483, three unblended transitions of CH3OD and three unblended
transitions of CH3OCH3 were identified. This allowed for accurate modeling of
the blended emission feature around the D2O line (i.e., the combined emission
from D2O, CH3OD, and CH3OCH3). The best fit was determined by $\chi^{2}$
minimization of the data around emission lines. Blended lines and transitions
with high optical thickness were manually excluded from the $\chi^{2}$
estimation. The synthetic spectrum was calculated following the methodology
presented in Möller et al. (2017) with the addition of an optical depth
correction from Goldsmith & Langer (1999). Toward B335, the observed spectrum
was best reproduced by a synthetic model with $N$(D2O) = $3.5\times 10^{15}$
cm-2, $N$(CH3OD) = $2.5\times 10^{17}$ cm-2, and $N$(CH3OCH3) = $1.3\times
10^{17}$ cm-2. For the water isotopologs, the synthetic spectrum model yields
HDO/H2O $=(6.3\pm 1.5)\times 10^{-3}$ and D2O/HDO $=(1.4\pm 0.1)\times
10^{-2}$ for B335.

For L483, the synthetic spectrum modeling yields column densities of $N$(D2O)
= $1.1\times 10^{15}$ cm-2, $N$(CH3OD) = $1.7\times 10^{17}$ cm-2, and
$N$(CH3OCH3) = $7.9\times 10^{16}$ cm-2. The D/H ratios toward this source are
then HDO/H2O $=(4.0\pm 0.5)\times 10^{-3}$ and D2O/HDO $=(1.0\pm 0.2)\times
10^{-2}$. The synthetic spectra are presented in the left panels of Figs. 4
and 5. For L483, the best-fit spectral model shows some deviation from the
observed profile, however, the D2O column density is robust: changing the
parameters of the CH3OD and CH3OCH3 components has little impact on the D2O
abundance. We note that for L483, many emission lines are double-peaked
Gaussians (see, e.g., Oya et al. 2017; Jacobsen et al. 2019). The parameters
for the best-fit synthetic spectrum are presented in Table 2, for B335 and
L483. The full spectral models for both sources are shown in Appendix A.

###  3.2 Least-squares fitting

In the second, complimentary method, the line profiles were fitted using the
least-squares method with the scipy routine curve_fit. Toward B335, the fit
was allowed to include up to four Gaussian line profiles, one for each
potential transition in the blended emission feature. Bounds on the fits were
estimated from the HDO data, and other non-blended emission lines in the
dataset. The best fit does not include a fourth component, corresponding to
either the CH3OCH3 line at 316.7904 GHz or the CH3OD transition at 316.7916
GHz (i.e., only three Gaussian profiles were included in the final fit). The
exclusion of a fourth component has limited impact on the Gaussian profile for
D2O. The resulting fit is shown the right panel of Fig. 4. The column density
is estimated from the fitted line profile by assuming local thermodynamic
equilibrium (LTE) (Mangum & Shirley 2015). We adopted an excitation
temperature of 220 K, which is derived from the synthetic spectrum; this
method results in a D2O column density of $4.0\times 10^{15}$ cm-2. The HDO
transitions presented in Jensen et al. (2019) give a HDO column density of
$1.9\times 10^{17}$ cm-2 at the same excitation temperature, when a beam
filling factor is applied for a source size of $0.\\!\\!^{\prime\prime}2$.
This method then results in a D2O/HDO ratio of $(2.1\pm 0.6)\times 10^{-2}$.
Evidently, the D2O/HDO ratios toward B335 are somewhat higher when using the
Gaussian fits, however both methods yield high D2O/HDO ratios $\gtrsim
10^{-2}$. We note that the HDO column density is different from that presented
in Jensen et al. (2019) because a higher excitation temperature of 220 K and a
smaller source size are used in this work. Furthermore, the synthetic model
includes an optical depth correction and identifies a slight blending of the
H${}_{2}^{18}$O line, increasing the HDO/H2O ratio. Because of this, we
consider the column densities presented in this work as more accurate.
However, this does not impact the results and discussions of the relative
HDO/H2O abundances in Jensen et al. (2019), in which identical excitation
temperatures were used for all sources. The differences in the reported
HDO/H2O ratios in this work and in Jensen et al. (2019) illustrate the
dependence on the methodology and assumptions, however, the observed dichotomy
between isolated and clustered protostars reported in that paper is robust. To
remove the observed dichotomy requires consistently adopting lower excitation
temperatures for the isolated sources, independent of the luminosity of the
respective sources.

In the case of L483, the emission lines are generally double-peaked Gaussian
profiles (Jensen et al. 2019). These features are more challenging to fit when
strongly blended and attempts to fit double-peaked Gaussians to all four
potential emission lines did not produce good results. Instead, single
Gaussians were fitted to each transition, which provided reasonable fits (as
shown in the right panel of Fig. 5). The fitted Gaussian profiles result in
$N$(D2O) = $1.7\times 10^{15}$ cm-2, which, combined with $N$(HDO) =
$1.2\times 10^{17}$ cm-2, yield D2O/HDO $=(1.4\pm 0.4)\times 10^{-2}$. Again,
this method returns a higher D2O/HDO than the synthetic spectrum model. For
L483, an excitation temperature of 165 K was used, which was derived from the
synthetic spectrum model. Overall, both methods agree, given the inherent flux
density uncertainty of ALMA ($\sim 10\%$) and the uncertainties in the fitting
($\sim 10\%$).

Both methods assume that water emission from the warm envelope is in LTE.
Previous studies of water isotopologs with interferometers have assessed the
validity of this approach. Persson et al. (2014) compare the optically thin
LTE approximation to radiative transfer models for two Class 0 sources and
find agreement between the two methods. Coutens et al. (2014) compare non-LTE
radex calculations and LTE calculations for the same HDO transitions presented
in this work and found that the LTE approach is valid for these transitions.
Generally, the LTE approach is suitable for water emission in the inner
envelope, where the densities are similar or higher than the critical
densities for the targeted transitions.

Table 2: Overview of the column densities for D2O, HDO, and H${}_{2}^{18}$O derived with the best-fit synthetic spectrum model ($N_{\mathrm{model}}$) and with the fitted Gaussian profiles ($N_{\mathrm{fit}}$). The reported full width at half maximum (FWHM) and $v_{\mathrm{LSR}}$ are for the synthetic spectrum model. A source size of 0$.\\!\\!^{\prime\prime}$2 is assumed for both sources for all molecules. Molecule |  $N_{\mathrm{model}}$ (cm-2) |  $N_{\mathrm{fit}}$ (cm-2) | FWHM (km/s) |  $v_{\mathrm{LSR}}$ (km/s) |  $T_{\mathrm{ex}}$ (K)
---|---|---|---|---|---
L483
D2O | $1.1\times 10^{15}$ | $1.7\times 10^{15}$ | (4.5, 5.2) | (1.75, 7.65) | 165
HDO | $1.1\times 10^{17}$ | $1.2\times 10^{17}$ | (4.9, 5.7) | (1.75, 7.65) | 165
H${}_{2}^{18}$O | $5.1\times 10^{16}$ | $5.9\times 10^{16}$ | (6.2, 7.1) | (1.75, 7.65) | 165
B335
D2O | $3.5\times 10^{15}$ | $4.0\times 10^{15}$ | 4.25 | 7.6 | 220
HDO | $2.5\times 10^{17}$ | $1.9\times 10^{17}$ | 4.0 | 7.9 | 220
H${}_{2}^{18}$O | $6.3\times 10^{16}$ | $7.1\times 10^{16}$ | 5.65 | 7.9 | 220

##  4 Discussion

The observed sources show high abundances of doubly deuterated water, D2O,
with D2O/HDO $\gtrsim$ $10^{-2}$ and D2O/HDO ¿ HDO/H2O for both sources. The
derived fD2/fD1 ratios for L483 and B335 are $\sim$2.5 and $\sim$2,
respectively. This is similar to the previous determination of D2O/HDO in the
warm envelope toward IRAS 2A presented in Coutens et al. (2014), who reported
D2O/HDO $\gtrsim$ $10^{-2}$ and fD2/f${}_{\mathrm{D1}}\gtrsim 7$. Table 3
presents an overview of the HDO/H2O and D2O/HDO ratios toward low-mass Class 0
sources, limited to data which are determined with interferometric
observations of the warm envelope. The high D2O abundances reported in this
work has several implications for the inheritance of water and the tentative
correlation between protostellar environment and D/H ratio in water, which is
discussed below.

Table 3: Overview of the D/H ratios of water in the warm region ($\lesssim
100\leavevmode\nobreak\ $au, $T\gtrsim 100$ K) toward Class 0 protostars. For
L483 and B335, the reported values are derived from the synthetic spectrum
model.

Object | HDO/H2O ($\times 10^{-4}$) | D2O/HDO ($\times 10^{-2}$) | fD2/fD1 | Reference
---|---|---|---|---
Clustered protostars
NGC1333 IRAS 2A | $7.4\pm 2.1$ | … | … | 1
– | $17\pm 8$ | $1.2\pm 0.5$ | $7\pm 4$ | 2
NGC1333 IRAS 4A-NW | $5.4\pm 1.5$ | … | … | 1,3
NGC1333 IRAS 4B | $5.9\pm 2.6$ | … | … | 1
IRAS 16293–2422 | $9.2\pm 2.6$ | … | … | 1
Isolated protostars
BHR71–IRS1 | $18\pm 4$ | … | … | 3
B335 | $17\pm 3$ | … | … | 3
– | $63\pm 15$ | $1.4\pm 0.1$ | $2.2\pm 0.5$ | 4
L483 | $22\pm 4$ | … | … | 3
– | $40\pm 5$ | $1.0\pm 0.2$ | $2.5\pm 0.3$ | 4
222The table only include interferometric observations of the inner warm
region toward low-mass Class 0 protostars.

(1) Persson et al. (2014); (2) Coutens et al. (2014); (3) Jensen et al.
(2019); (4) This work.

###  4.1 Inheritance of water D/H ratio

The D/H ratio of water is an essential tool for determining the chemical
evolution of water during star and planet formation. Deuterium fractionation
of water can proceed through multiple pathways during the evolutionary stages
of star and planet formation with varying efficiency (e.g., Caselli et al.
2012; van Dishoeck et al. 2014). In a recent work, Furuya et al. (2017)
studied the evolution of the water D/H ratio during the star formation process
from cloud to disk for hundreds of tracer particles in a 2D axisymmetric
model, including both the protostellar collapse and the protoplanetary disk
phases. These authors showed that water formation with HDO/H2O ratios in the
range $10^{-4}$–$10^{-3}$ can occur both through prestellar inheritance and in
situ water formation in the cold midplane of the protoplanetary disk. Hence,
distinguishing between inheritance and in situ formation based solely on the
HDO/H2O ratio is challenging. Meanwhile, models suggest that the formation of
D2O is inefficient in protoplanetary disks when compared to the prestellar
core phase. Therefore, Furuya et al. (2017) suggest that the ratio of fD2/fD1
is a more robust tracer of chemical inheritance for water. Quantitatively, the
model of Furuya et al. (2017) shows that a fD2/fD1 ratio around $\sim 10$ is
formed in the prestellar phase, while a much lower ratio of
fD2/f${}_{\mathrm{D1}}\sim 0.1$ is found for water formed within the
protoplanetary disk.

For L483 and B335, the observed fD2/fD1 ratios are $\gtrsim$2\. Prior to this
work, fD2/fD1 was determined in the hot corino toward IRAS 2A, where the ratio
is $\gtrsim 7$. The observed ratios, fD2/f${}_{\mathrm{D1}}>1$, suggest that
water in the warm envelope is predominantly inherited from the prestellar
phase and has not undergone reprocessing during accretion from the cloud to
the warm envelope toward these sources.

Recently, Jensen et al. (2021) studied the D/H ratio of water during the
formation of several low-mass protostars in a dynamic 3D magnetohydrodynamics
simulation of a molecular cloud region. For each protostar, thousands of
tracer particles recorded the physical evolution during the accretion process
from the large-scale environment down to the warm envelope. The temperature
structure of the envelopes was calculated using the Monte Carlo radiative
transfer code radmc-3d (Dullemond et al. 2012). Subsequently, the chemical
evolution along each particle trajectory was modeled to determine the gas-
phase fD2 and fD1 ratios in the warm envelope. These authors find that fD2/fD1
depends on the choice of initial conditions in the prestellar cloud (e.g., the
duration and temperature of this phase). A similar conclusion is presented in
Taquet et al. (2013b), in which the authors study the formation of deuterated
water for a broad range of initial conditions in the prestellar phase. These
results suggest that the lower fD2/fD1 ratios may stem from different
prestellar conditions, which was not included in the study by Furuya et al.
(2017). By studying a range of initial conditions, Jensen et al. (2021) show
that the D/H ratio of water in the warm envelope is determined by the
conditions in the prestellar phase and is not sensitive to variations during
the protostellar collapse itself, in other words, suggestive of chemical
inheritance of water from the prestellar stages. A high degree of inheritance
for water is also suggested by Cleeves et al. (2014), who show that the D/H
ratio of water synthesized in situ in protoplanetary disks is low, and find
that a high degree of inheritance is necessary to explain the D/H ratios of
comets in the Solar System with low ionization rates.

With the high observed D2O/HDO ratios in the warm envelope, the case for a
high degree of inheritance from the prestellar core stage down to the warm
envelope ($\lesssim 100\leavevmode\nobreak\ $au) appears strong. The physical
and chemical link between the warm envelope and the formation of
protoplanetary disks and planets is unclear (e.g., Harsono et al. 2020).
Recently, the evidence for early planet formation is growing with a number of
detections of planetary signatures in young systems (e.g., Keppler et al.
2018; Teague et al. 2018; Harsono et al. 2018; Pinte et al. 2020; Alves et al.
2020). Furthermore, advances in planet formation theory suggest that planet
formation may be a fast process and can occur early (e.g., Johansen &
Lambrechts 2017). If planet formation starts early, the chemical inheritance
observed in these Class 0 sources may directly impact the chemistry at the
onset of planet formation. Currently, the D/H ratio of water in bona fide
protoplanetary disks is unknown. An alternative tracer for the chemistry
during planet formation is the study of the chemical composition of comets,
including the D/H ratio (e.g., Mumma & Charnley 2011; Bockelée-Morvan et al.
2015). Comets are planetesimals in the outer solar nebula that record the
pristine ice composition in the Solar System during planet formation.
Tentative evidence for a chemical link between the warm envelope and
protoplanetary disks is emerging. Altwegg et al. (2017) determine the D/H
ratios of water in the coma of comet 67P/Churyumov-Gerasimenko (hereafter
comet 67P) with the ROSINA instrument. They found D2O/HDO $=(1.8\pm 0.9)\times
10^{-2}$ and HDO/H2O $=(1.05\pm 0.14)\times 10^{-3}$, corresponding to
fD2/f${}_{\mathrm{D1}}\sim 17$, which is incompatible with in situ D2O
formation in the protoplanetary disk (Furuya et al. 2017). This suggests a
high degree of inheritance, and furthermore the measured D2O/HDO ratio is
similar to the ratios observed in warm envelopes. Overall, current estimates
of the D/H ratios of water in comets and warm envelopes could indicate a
similar chemical evolution for the cold icy component that constitute comets
such as comet 67P, and the material that enters the warm envelope, where ice
is sublimated off the dust grains. A chemical link between the warm envelope
and cometary bodies is also supported by the apparent correlation between
complex organic molecules (COMs) in the hot corino of IRAS16293–2422 and comet
67P, which may indicate a link between the chemical inventory in cold icy
planetesimals and hot corinos (Drozdovskaya et al. 2019). Similarly, a recent
study by Bianchi et al. (2019) also finds a correlation between the abundances
of COMs in protostars and comets. The authors compared the inventory of COMs
for a larger sample of Class 0 and Class I sources to cometary values in the
literature and find good agreement between the abundances of COMs in Class 0
sources and comets, while the Class I sources showed more variation.

###  4.2 Environmental impact on the D/H ratio

The D2O/HDO ratios toward B335 and L483 are on the order of $10^{-2}$, similar
to the lower limit derived in Coutens et al. (2014) toward IRAS 2A. Following
the definitions of Jensen et al. (2019), B335 and L483 are isolated protostars
(i.e., not associated with any cloud complexes) while IRAS 2A is located in
NGC1333. Given the higher HDO/H2O ratios in the isolated sources, these
results appear to follow the same trend between water deuterium fractionation
and protostellar environment. The isolated protostars show higher D/H ratios
in HDO and similar D2O/HDO ratios, that is, the overall D/H ratio is higher
than in clustered counterparts. Another way to illustrate this is to look at
the D2O/H2O ratio. For L483, B335, and IRAS 2A, the D2O/H2O is $9\times
10^{-5}$, $4\times 10^{-5}$, and $2\times 10^{-5}$, respectively. Hence, the
D2O/H2O ratios toward the isolated protostars are a factor $\gtrsim 2$ higher
than the clustered source observed so far. The D2O abundances therefore
corroborate a higher D/H ratio of water toward isolated protostars, similar to
the trend observed in HDO. However, the sample size remains too small to draw
definite conclusions and should be further expanded.

Jensen et al. (2019) propose that the observed trend in D/H ratios could
originate from either higher temperatures or stronger irradiation in star-
forming clusters, or a difference in the collapse timescale between isolated
cores, which is subject to limited external perturbations, and clustered
sources for which several mechanisms may perturb the dynamics of the cores,
such as jets and outflows from nearby stars. Clustered star-forming regions
may also be intrinsically more turbulent; that is, the probability of multiple
star formation events may correlate with the turbulence in the region (e.g.,
Ward-Thompson et al. 2007; Krumholz 2014).

The physicochemical 3D models of water deuteration presented in Jensen et al.
(2021) find that variations in the temperature or duration of the prestellar
phase can induce the observed dichotomy in water D/H ratios. Higher
temperatures during both the prestellar core phase and protostellar collapse
lead to lower D/H ratios of water. Similarly, a shorter embedded phase (i.e.,
a shorter prestellar core duration) leads to a lower D/H ratio, which is
consistent with the hypothesis that clustered sources collapse on shorter
timescales. Both effects can drive the differences in D/H ratios between
clustered and isolated low-mass protostars. Meanwhile, variations in
irradiation appear unlikely to directly drive the dichotomy in observed D/H
water ratios in the warm envelope toward low-mass protostars. The study by
Jensen et al. (2021) demonstrates a link between the chemistry in the
prestellar stages and gas-phase water D/H ratio in the warm envelope, which is
corroborated by the observed D/H ratios of water from this region toward Class
0 sources. This link motivates further study, both observationally and
theoretically, to determine whether other molecules exhibit a similar link
between conditions in the environment and the chemistry in the warm envelope
region toward young embedded protostars.

##  5 Summary and outlook

This work presents the first ALMA observations of D2O in the warm envelope
toward low-mass protostars. We determine HDO/H2O and D2O/HDO ratios by
combining the column densities of D2O with HDO and H${}_{2}^{18}$O data. These
ratios provide new insights into the chemical evolution of water during the
star formation process.

  * •

Both L483 and B335 have D2O/HDO ratios $\gtrsim 10^{-2}$. When combined with
previous ALMA estimates of the HDO/H2O ratios, the [D2O/HDO]/[HDO/H2O] ratios
are derived to be $\sim$2.5 and $\sim$2, respectively. D/H ratios of this
magnitude are strong evidence of chemical inheritance from the prestellar core
stage. Chemical models suggest that a D2O/HDO ratio of this magnitude can only
form during the cold phase prior to star formation.

  * •

Both sources are isolated and show enhanced D2O/H2O ratios compared to a
clustered counterpart by a factor of $\gtrsim 2$. The high D2O/H2O ratios
strengthen the evidence for a correlation between the D/H ratio of water and
the protostellar environment, as suggested in Jensen et al. (2019). This is
consistent with a high degree of inheritance from the prestellar phases and
provides a mechanism for chemical diversity in the envelopes surrounding
embedded protostars (e.g., through a longer duration or colder temperatures in
the prestellar phase).

  * •

The observed D2O/HDO ratios in hot corinos are similar to the value measured
in Comet 67P of $\sim 10^{-2}$, providing tentative evidence of a common
chemical evolution of the water that sublimates in the warm envelope and water
incorporated in comets and icy planetesimals that are the building blocks of
planets in the Solar System.

These observations highlight the power of the deuterium fractionation as a
tracer for the chemical trail during star formation. More observations of the
D/H ratios of water at different stages of star and planet formation will
provide further constraints on the amount of inheritance between the
evolutionary stages and establish the impact of the local environment on the
chemical evolution. The relation between the local cloud environment and
isotope fractionation should be explored further by studying, for example,
nitrogen or carbon fractionation, toward both isolated and clustered sources
at various evolutionary stages.

###### Acknowledgements.

The authors thank the referee for useful comments that helped improve the
manuscript. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2017.1.00693.S, ADS/JAO.ALMA#2019.1.00720.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. The group of JKJ
acknowledges support from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant
agreement No 646908) through ERC Consolidator Grant ”S4F”. AC acknowledges
financial support from the Agence Nationale de la Recherche (grant
ANR-19-ERC7-0001-01). This paper makes use of matplotlib (Hunter 2007) and
scipy (Virtanen et al. 2020).

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##  Appendix A Full synthetic models

The complete synthetic spectrum models for H${}_{2}^{18}$O, HDO , D2O, CH3OD,
CH3OCH3 are shown in the Figs. 6 and 7.

Figure 6: Overview of the complete synthetic spectrum model for emission lines
toward B335 for an assumed source size of 0$.\\!\\!^{\prime\prime}$2\. The
full model includes H${}_{2}^{18}$O, HDO , D2O, CH3OD, and CH3OCH3. Figure 7:
Overview of the complete synthetic spectrum model for emission lines toward
L483 for an assumed source size of 0$.\\!\\!^{\prime\prime}$2\. The full model
includes H${}_{2}^{18}$O, HDO , D2O, CH3OD, and CH3OCH3.