11institutetext: Observatorio Astronómico Nacional (OAN), Alfonso XII, 3,
28014. Madrid. Spain
11email<EMAIL_ADDRESS>22institutetext: Centro de Astrobiología (CAB),
INTA-CSIC, Carretera de Ajalvir Km. 4, Torrejón de Ardoz, 28850, Madrid, Spain
33institutetext: Département d’Astrophysique (DAp), Commissariat à l’Énergie
Atomique et aux Énergies Alternatives (CEA), Orme des Merisiers, Bât. 709,
91191 Gif sur Yvette, Paris-Saclay, France 44institutetext: Institut de
Ciències de l’Espai (ICE, CSIC), Can Magrans s/n, E-08193, Bellaterra,
Barcelona, Spain 55institutetext: Institut d’Estudis Espacials de Catalunya
(IEEC), Barcelona, Spain 66institutetext: Center for Space and Habitability,
Universität Bern, Gesellschaftsstrasse 6, CH-3012 Bern, Switzerland
77institutetext: Max-Planck-Institut für extraterrestrische Physik, 85748
Garching, Germany

# Evolution of Chemistry in the envelope of Hot Corinos (ECHOS)

I. Extremely young sulphur chemistry in the isolated Class 0 object B 335

G. Esplugues 11 M. Rodríguez-Baras 11 D. San Andrés 22 D. Navarro-Almaida 33
A. Fuente 1122 P. Rivière-Marichalar 11 Á. Sánchez-Monge 4455 M. N.
Drozdovskaya 66 S. Spezzano 77 and P. Caselli 77

###### Abstract

Context. Within the project Evolution of Chemistry in the envelope of HOt
corinoS (ECHOS), we present a study of sulphur chemistry in the envelope of
the Class 0 source B 335 through observations in the spectral range $\lambda$
= 7, 3, and 2 mm.

Aims. Our goal is to characterise the sulphur chemistry in this isolated
protostellar source and compare it with other Class 0 objects to determine the
environmental and evolutionary effects on the sulphur chemistry in these young
sources.

Methods. We have modelled observations and computed column densities assuming
local thermodynamic equilibrium (LTE) and large velocity gradient (LVG)
approximation. We have also used the code Nautilus to study the time evolution
of sulphur species, as well as of several sulphur molecular ratios.

Results. We have detected 20 sulphur species in B 335 with a total gas-phase S
abundance similar to that found in the envelopes of other Class 0 objects, but
with significant differences in the abundances between sulphur carbon chains
and sulphur molecules containing oxygen and nitrogen. Our results highlight
the nature of B 335 as a source especially rich in sulphur carbon chains
unlike other Class 0 sources. The low presence or absence of some molecules,
such as SO and SO+, suggests a chemistry not particularly influenced by
shocks. We, however, detect a large presence of HCS+ that, together with the
low rotational temperatures obtained for all the S species ($<$15 K), reveals
the moderate or low density of the envelope of B 335. Model results also show
the large influence of the cosmic ray ionisation rate and density variations
on the abundances of some S species (e.g. SO, SO2, CCS, and CCCS) with
differences of up to $\sim$4 orders of magnitude. We also find that
observations are better reproduced by models with a sulphur depletion factor
of 10 with respect to the sulphur cosmic elemental abundance.

Conclusions. The comparison between our model and observational results for B
335 reveals an age of 104$<$$t$$<$105 yr, which highlights the particularly
early evolutionary stage of this source. B 335 presents a different chemistry
compared to other young protostars that have formed in dense molecular clouds,
which could be the result of accretion of surrounding material from the
diffuse cloud onto the protostellar envelope of B 335. In addition, the
theoretical analysis and comparison with observations of the SO2/C2S, SO/CS,
and HCS+/CS ratios within a sample of prestellar cores and Class 0 objects
show that they could be used as good chemical evolutionary indicators of the
prestellar to protostellar transition.

###### Key Words.:

survey-stars: formation - ISM: abundances - ISM: clouds - ISM: molecules -
Radio lines: ISM

##  1 Introduction

Hot corinos are regions that arise during the formation of solar-type
protostars. The progressive collapse of a prestellar core leads to the heating
of the infalling envelope of dust and gas to temperatures of hundreds of
Kelvin, while the densities increase up to $\sim$108-109 cm-3 in the inner
$\sim$100 au around the central protostar. These are also the scales at which
protoplanetary disks are expected to arise owing to the conservation of
angular momentum. As the temperatures increase, the water-rich ice mantles
sublimate, injecting molecules into the gas phase. Hot corinos are therefore
chemically rich regions in Solar-like young protostars (Ceccarelli 2004;
Ceccarelli et al. 2007b). In particular, these regions are relatively rich in
interstellar complex organic molecules (Herbst & van Dishoeck 2009). Studying,
therefore, the inventory and abundances of molecules in the earliest stages of
star formation, that is in hot corinos, is essential to probe the initial
conditions of planet and star formation processes. In spite of the detection
of various hot corinos in the last decades (e.g. Cazaux et al. 2003; Okoda et
al. 2023), just a few of them (such as IRAS 16293-2422, NGC 1333, and IRAS 4A
van Dishoeck et al. 1995; Ceccarelli et al. 2007a; Jaber et al. 2014; Caselli
& Ceccarelli 2012; Jørgensen et al. 2016) have been investigated in detail
until now. Many questions, therefore, still remain open about their nature and
molecular composition: for instance, chemical differences between the earliest
stages of star formation (Class 0 versus Class I objects), the role of the
chemical characteristics inherited from the parent cloud, as well as the
environmental effect on the chemical composition of hot corinos.

One way to understand the dynamics and evolution of the earliest stages of
star formation is through molecular depletion. At temperatures of roughly 10 K
and densities above 104 cm-3, several molecules, such as CO and CS, condense
out onto dust grain surfaces (e.g. Caselli et al. 1999; Crapsi et al. 2005),
and depletion increases with time (e.g. Bergin & Langer 1997; Aikawa et al.
2003). Therefore, depletion can be used as a clock, since evolved cores should
be more depleted of certain species than younger cores. Regarding depletion,
sulphur plays a fundamental role since, although sulphur is one of the most
abundant species in the Universe and plays a crucial role in biological
systems on Earth (e.g. Leustek 2002; Francioso et al. 2020), S-bearing
molecules are not as abundant as expected in the interstellar medium (ISM). In
particular, unlike the diffuse ISM and photon-dominated regions where the
observed gaseous sulphur accounts (e.g. Goicoechea et al. 2006; Howk et al.
2006) for its total solar abundance (S/H$\sim$1.5$\times$10-5; Asplund et al.
2009), sulphur is strongly depleted in more dense molecular gas, since the sum
of the detectable S-bearing molecules only accounts for a very small fraction
of the elemental S abundance (Tieftrunk et al. 1994). In fact, to reproduce
observations in hot corinos and hot cores, one needs to assume a significant
sulphur depletion of at least one order of magnitude lower than the solar
elemental sulphur abundance (e.g. Wakelam et al. 2004; Esplugues et al. 2014;
Crockett et al. 2014; Vastel et al. 2018; Bulut et al. 2021; Navarro-Almaida
et al. 2021; Esplugues et al. 2022; Hily-Blant et al. 2022; Fuente et al.
2023). Most of the sulphur seems to be locked on the icy grain mantles (e.g.
Millar & Herbst 1990; Ruffle et al. 1999; Vidal et al. 2017; Laas & Caselli
2019) in the form of organo-sulphur molecules, also present in the comet 67P
(Calmonte et al. 2016) and in meteoritic material (e.g. Naraoka et al. 2022;
Ruf et al. 2021). However, OCS and SO2 are the only S-bearing molecules
unambiguously detected in ice mantles to date (Geballe et al. 1985; Palumbo et
al. 1995; McClure et al. 2023), while H2S has not been detected (Yang et al.
2022; McClure et al. 2023). Theoretical models also suggest that sulphur could
be locked into pure allotropes of sulphur, especially S8 (Shingledecker et al.
2020). In any case, sulphur reservoirs in dense regions remain as an open
question, as well as the time at which sulphur depletion occurs.

Given the low number of discovered hot corinos and, therefore, the limited
knowledge about them, the project Evolution of Chemistry in the envelope of
HOt corinoS (ECHOS) aims to provide a complete inventory of the chemistry of
hot corinos (with a sample including IRAS16293-2422, NGC 1333 IRAS 4A, HH 212,
and B 335). ECHOS is carried out through homogeneous and systematic spectral
surveys between 30 and 200 GHz using the Yebes-40m and IRAM-30m telescopes. In
this paper, we focus on the analysis of B 335 and present a study of sulphur-
bearing molecules in this region. Observations and a description of the source
are presented in Sects. 2 and 3. In Sect. 4 we present the data and calculate
column densities and abundances using different methods, depending on the
number of detected transitions for each species, and also depending on the
availability of collisional coefficients. A discussion of the results
(including a comparison with other similar objects, as well as the use of a
chemical code to study the fractional abundance evolution of sulphur species)
is presented in Sect. 5. We finally summarise our conclusions in Sect. 6.

##  2 Observations

The observations were carried out with the Yebes-40m and IRAM-30m telescopes
pointing to the position with coordinates $\alpha$J2000.0 = 19h37m0.93s,
$\delta$J2000.0 = +07o34$\arcmin$09.9$\arcsec$. For both telescopes, data were
reduced and processed by using the CLASS and GREG packages provided within the
GILDAS software111http://www.iram.fr/IRAMFR/GILDAS, developed by the IRAM
institute.

###  2.1 Yebes-40m telescope

The observations from the Yebes-40m radiotelescope located in Yebes
(Guadalajara, Spain) were obtained using a receiver that consists of two cold
high electron mobility transistor amplifiers covering the 31.0-50.3 GHz Q-band
with horizontal and vertical polarisations. The backends are
2$\times$8$\times$2.5 GHz fast Fourier transform spectrometers with a spectral
resolution of 38.15 kHz, providing the whole coverage of the Q-band in both
polarisations. The observations were performed in the position-switching mode
with (-400$\arcsec$, 0$\arcsec$) as the reference position. The main beam
efficiency varies from 0.6 at 32 GHz to 0.43 at 50 GHz. Pointing corrections
were derived from nearby quasars and SiO masers, and errors remained within
2-3$\arcsec$.

Table 1: Yebes 40 m and IRAM 30 m telescope efficiency data along the covered frequency range. Telescope | Frequency |  $\eta$MB | HPBW
---|---|---|---
| (GHz) |  | ($\arcsec$)
Yebes 40 m | 32.4 | 0.61 | 54.4
| 34.6 | 0.58 | 51.0
| 36.9 | 0.57 | 47.8
| 39.2 | 0.55 | 45.0
| 41.5 | 0.53 | 42.5
| 43.8 | 0.52 | 40.3
| 46.1 | 0.49 | 38.3
| 48.4 | 0.47 | 36.4
IRAM 30 m | 86 | 0.82 | 29.0
| 100 | 0.79 | 22.0
| 145 | 0.74 | 17.0
| 170 | 0.70 | 14.5

###  2.2 IRAM-30m telescope

The observations from the IRAM-30m radio telescope located in Pico Veleta
(Granada, Spain) cover the 73-118 GHz and 130-175 GHz spectral ranges. These
observations were carried out in one session in July 2021 with the Wobbler-
Switching mode ($\pm$120$\arcsec$), using the broad-band EMIR (E090 and E150)
receivers and the fast Fourier transform spectrometer in its 200 kHz of
spectral resolution. The intensity scale in antenna temperature
($T$${}^{\star}_{\mathrm{A}}$, which is corrected for atmospheric absorption
and for antenna ohmic and spillover losses) was calibrated using two absorbers
at different temperatures and the atmospheric transmission model (ATM;
Cernicharo et al. 1985; Pardo et al. 2001). Calibration uncertainties were
adopted to be 10$\%$.

To convert to main beam brightness temperature ($T$MB), we used the expression

$T_{\mathrm{MB}}=\left(F_{\mathrm{eff}}/B_{\mathrm{eff}}\right)\times{T^{\star}_{\mathrm{A}}}=\left(T^{\star}_{\mathrm{A}}/\eta_{\mathrm{MB}}\right),$
(1)

where $F$eff is the telescope forward efficiency and $B$eff is the main beam
efficiency222https://rt40m.oan.es/rayo/index.php,333http://www.iram.es/IRAMES/mainWiki/Iram30mEfficiencies.
See Table 1 for a summary of the telescope beam sizes depending on frequency.

##  3 The source

B 335 is an isolated dense globule associated with the embedded far-infrared
source IRAS 19347+0727 (Keene et al. 1980, 1983), located at a distance of
$\sim$100 pc (Olofsson & Olofsson 2009). The central source is a Class 0
source with a luminosity of 0.72 L⊙ (Evans et al. 2015), whose mass is
estimated to be 0.08 M⊙ (Yen et al. 2015). Complex organic molecules (COMs),
such as acetaldehyde (CH3CHO), methyl formate (HCOOCH3), and formamide
(NH2CHO), have been detected (Imai et al. 2016; Okoda et al. 2022) in the
vicinity of the protostar ($r$$\sim$10 au). It reveals that B 335 harbors a
hot corino (Cazaux et al. 2003; Herbst & van Dishoeck 2009), which warms up
the surrounding regions leading to the sublimation of grain mantles and
injecting complex organic molecules into the gas-phase (e.g. Ceccarelli 2004;
Caselli & Ceccarelli 2012). Emission of CCH and c-C3H2 has also been detected
around the protostar, which indicates the presence of carbon-chain molecules
in this source (Sakai et al. 2008; Sakai & Yamamoto 2013). This carbon-chain
molecules could suggest the presence of a so-called warm carbon-chain
chemistry (WCCC, Sakai et al. 2008), characterised by various carbon-chain
molecules being produced by reactions of CH4 (evaporated from grain mantles in
a lukewarm region) and where the formation of HCnN is slower than that of CnHm
molecules (Sakai et al. 2008, 2009; Oya et al. 2017).

Particularly interesting are the single-dish observations of CS and H2CO in B
335 (Zhou et al. 1993; Choi et al. 1995), since their optically thick lines
show asymmetric profiles. This implies the presence of infalling motions in
the envelope around B335. A more detailed analysis with C18O, SO, HCN, and
HCO+ ALMA observations (Evans et al. 2015; Yen et al. 2015; Evans et al. 2023)
confirms an infalling gas motion of the inner part of the protostellar core,
but rotation motion has not been detected at a spatial resolution of
0.3$\arcsec$ ($\sim$30 au). A rotation structure is only found at a scale of
about 10 au from CH3OH and HCOOH emission (Imai et al. 2019). Single-dish and
interferometric 12CO (1–0) and 13CO (1– 0) observations (e.g. Hirano et al.
1988, 1992; Stutz et al. 2008; Bjerkeli et al. 2019) show also the presence of
an east-west molecular outflow on $\sim$0.2 pc (Cabrit et al. 1988; Moriarty-
Schieven & Snell 1989) with an inclination between 3o-10o on the plane of the
sky and an outflow opening angle of 45o (Hirano et al. 1988, 1992; Stutz et
al. 2008; Yen et al. 2010). A dynamical analysis of the outflow molecular
structure (Yıldız et al. 2015) implies that dynamical timescales for the CO
emitting gas are of the order of 104 yr. This result, along with the absence
of a rotationally supported disk on scales greater than $\sim$10 au in size
(Evans et al. 2015; Yen et al. 2015), suggest that the B 335 system is a
particularly young source compared to other Class 0 objects, such as L 1527
which contains an embedded IRAS source and has a dynamical age of
2$\times$104-105 yr (Tamura et al. 1996; André et al. 2000; Agúndez et al.
2019). The detection of abundant CCS (see Sect. 4.3) and other carbon-chain
molecules in B 335 also confirms the early stage of this source since it is
generally recognised that CCS and other carbon-chain molecules are abundant in
the early stage of chemical evolution and become deficient at the advanced
stage (Sakai et al. 2008).

So far, B 335 is one of the few hot corinos identified in a Bok globule,
isolated from a large molecular cloud complex. This is therefore an ideal
source for the study of the earliest stages of star formation with a chemical
composition that could be regarded as a standard template for isolated
protostellar cores.

##  4 Data analysis and results

We have detected 81 emission lines from 21 different sulphur-bearing species
(including isotopologs) in B 335. In particular, we have detected three
transitions of CS, three of 13CS, three of C34S, three of C33S, nineteen of
CCS, three of CC34S, seven of CCCS, three of CCC34S, five of OCS, three of
HCS+, two of HC34S+, seven of SO, one of SO2, one of 34SO, one of H2S, one of
H234S, ten of H2CS, one of HSCN, one of HNCS, and six of NS (see Table
LABEL:table:line_parameters and Figs. 13-33 in Appendix). These transitions
span an energy range of $E_{\mathrm{up}}$=2.0-65.3 K.

###  4.1 Line profiles

All the lines are observed in emission. We first fitted the observed lines
with Gaussian profiles using the CLASS software to derive the radial velocity
(vLSR), the line width, and the intensity for each line. Results are given in
Table LABEL:table:line_parameters. We observed that most of the detected
molecules show narrow line profiles ($\Delta$v$\lesssim$1.5 km s-1) that can
be adjusted by a single velocity component.

It is well known that the gravitational collapse of a molecular cloud when a
new star is formed is accompanied by the development of highly supersonic
outflows (e.g. Bachiller & Pérez Gutiérrez 1997; Holdship et al. 2019). The
material ejected through these jets collides with the surrounding cloud,
compressing and heating the gas, which leads to a drastic alteration of the
chemistry as endothermic reactions become efficient and dust grains are
partially destroyed. Many observations have shown that several sulphur-bearing
species are enhanced in the shocked regions with respect to other areas of the
cloud (e.g. Pineau des Forets et al. 1993; Bachiller & Pérez Gutiérrez 1997;
Codella & Bachiller 1999; Wakelam et al. 2004, 2005; Esplugues et al. 2013).
However, the sulphur lines observed in B 335 present very narrow line widths
(Figs. 13-33), which is more consistent with the emission arising from the
ambient quiescent cloud. Only for H2S, formed through the hydrogenation of
sticked atomic sulphur on grains (Hatchell et al. 1998; Garrod et al. 2007;
Esplugues et al. 2014; Oba et al. 2019) and thought to be the main sulphur
reservoir in ices (Vidal et al. 2017; Navarro-Almaida et al. 2020), it is
necessary to also consider a wider component (with $\Delta$v=2.5 km s-1) to
fit its only detected line, since the line profile shows the presence of faint
wings. This could indicate that part of the H2S emission arises from the
outflow, however, the line width of this component is much smaller ($\sim$2.5
km s-1) than the ones observed for 12CO ($\sim$10-20 km s-1) in the outflow
(Yen et al. 2010). Therefore, the wider H2S emission may be likely related to
infall motions.

On the other hand, there are some species (CCS, CCCS, and H2CS) whose low
transition lines present a double peak emission. The peak with the lowest
intensity is located for all the cases at lower velocity (vLSR=7.39-8.1 km
s-1, blue peak) than for the more intense peak (vLSR=8.80-8.97 km s-1, red
peak). Line widths are slightly larger ($\Delta$v$\lesssim$0.83-1.63 km s-1)
in the blue peaks than in the red ones ($\Delta$v$\lesssim$0.55-0.83 km s-1).
The comparison of these profiles with those from the less abundant
isotopologues shows that these two-peak profiles are due to self-absorption
due to the large optical depths. All the detected lines present
0.005$<$$T_{\mathrm{MB}}$$<$1.5 K.

###  4.2 Rotational diagrams

Figure 1: Rotational diagrams of the detected sulphur-bearing molecules in B
335. Fitted values of the rotational temperature, $T$rot, column density, $N$,
and their respective uncertainties are also indicated for each molecule.

For each molecule, we have computed a representative rotational temperature
($T$rot) and a column density ($N$) by constructing a rotational diagram,
assuming a single rotational temperature for all energy levels (Goldsmith &
Langer 1999). Rotational diagrams represent a technique to analyse cloud
properties from molecular line emission assuming local thermodynamic
equilibrium (LTE). The standard relation for the rotational diagram analysis
is

$\mathrm{ln}(\frac{N_{\mathrm{u}}}{g_{\mathrm{u}}})=\mathrm{ln}N-\mathrm{ln}Z-\frac{E_{\mathrm{u}}}{kT_{\mathrm{rot}}},$
(2)

with $N$u/$g$u given by

$\frac{N_{\mathrm{u}}}{g_{\mathrm{u}}}=\frac{8k\pi}{hc^{3}}\times\frac{\nu^{2}_{\mathrm{ul}}}{A_{\mathrm{ul}}g_{\mathrm{u}}}\times{f}^{-1}\times\int
T_{\mathrm{MB}}d$v$,$ (3)

where $N$u is the column density of the upper level in the optically thin
limit, $N$ is the total column density, $g$u is the statistical weight of the
upper state of each level, $Z$ is the partition function evaluated at a
rotational temperature $T$rot, $E$u/k is the energy of the upper level of the
transition, $\nu$ul is the frequency of the $u$→$l$ transition, $\int$ $T$MB
dv is the velocity-integrated line intensity corrected from beam efficiency,
and $f$ is the beam filling factor. Assuming that the emission source has a 2D
Gaussian shape, $f$ is equal to
$f$bf=$\theta$${}^{2}_{\mathrm{s}}$/($\theta$${}^{2}_{\mathrm{s}}$ \+
$\theta$${}^{2}_{\mathrm{b}}$) being $\theta$b the HPBW of the telescope in
arcsec and $\theta$s the diameter of the Gaussian source in arcsec. In order
to derive the values of $f$ in each case, we have used the HPBW values listed
in Table 1, and we have assumed a source size of 10$\arcsec$ according to
interferometric maps of C17O emission in B 335 (Cabedo et al. 2021).

The resulting rotational diagrams are shown in Fig. 1, while the column
densities and rotational temperatures obtained are listed in Table
LABEL:table:results_from_RD. The uncertainties shown in Table
LABEL:table:results_from_RD indicate the uncertainty obtained in the least
squares fit of the rotational diagrams. These uncertainties include the 10$\%$
error in the observed line intensities due to calibration. The uncertainty
obtained in the determination of the line parameters with the Gaussian fitting
programme is included within the error bars at each point of the rotational
diagram. We did not applied the rotational diagram method to NS since its four
observed lines are close to the detection limit and/or blended with other
species, which would introduce a high uncertainty in the results. The analysis
of NS and others molecules with only one emission line detected (e.g. SO2) has
been done only with a LVG code (see next Section) instead.

The obtained rotational temperatures are $\lesssim$15 K. In the case of CCS,
the molecule with the largest number of detected transitions, we observe a
trend variation (Fig. 1) between the low and the high transition energies. In
particular, the transitions with $E$u¡40 K are well adjusted for a
$T$rot$\sim$5 K, while transitions with $E$u¿40 K are better adjusted for a
$T$rot$\sim$15 K. This suggests that CCS arises from different regions
characterised by distinct excitation temperatures. The rotational temperatures
for the rest of molecules with several detected transitions (e.g. C3S, OCS,
SO, H2CS) have 4.5$\lesssim$$T$rot$\lesssim$7.4 K. These low temperatures
together with their narrow line widths are consistent with emission arising
from a cold and extended part of the dense core. Gas density at these scales
is probably not too high as also indicated by the low $T$rot obtained for most
of the S-molecules. All this suggests that the gas is sub-thermally excited
with a moderate or low ($<$105 cm-3) density, in agreement with Frerking et
al. (1987). In addition, the low number of transitions detected for several
species (CS, 13CS, C34S, C33S, HCS+, and HC34S+) and the optically thick
emission of some transitions of CCS, CCCS, and H2CS, also indicate that the
rotational diagram method not suitable to derive column densities.

Table 2: Column densities ($N$), rotational temperatures, and abundances ($X$)
relative to H2 of the sulphur-bearing molecules detected in B 335.

Species |  $N$rot$\times$1013 |  $T$rot |  a$N$LVG$\times$1013 |  b$X$$\times$10-9
---|---|---|---|---
| (cm-2) | (K) | (cm-2) |
CS | 8$\pm$2 | 3.6$\pm$0.8 | 12.00 (34.2) | 11.0
13CS | 0.8$\pm$0.1 | 2.8$\pm$0.9 | 0.73 | 0.24
C34S | 2.1$\pm$0.8 | 2.7$\pm$0.7 | 1.40 | 0.45
C33S | 0.18$\pm$0.09 | 2.9$\pm$0.5 | 0.13 | 0.04
CCS | 5.4$\pm$0.8 | 5$\pm$0.5 | 4.40 | 1.42
| 0.19$\pm$0.06 | 15$\pm$1 |  |
CC34S | 0.27$\pm$0.01 | 6.4$\pm$0.3 | 0.90 | 0.29
CCCS | 1.8$\pm$0.4 | 7.4$\pm$0.8 | 0.65 | 0.02
CCC34S | 0.14$\pm$0.07 | 2.8$\pm$0.9 | 0.12 | 0.04
OCS | 3.8$\pm$0.5 | 7.0$\pm$0.8 | 2.00 | 0.65
HCS+ | 0.5$\pm$0.2 | 3.8$\pm$0.4 | 0.55 (1.5) | 0.05
HC34S+ | 0.08$\pm$0.02 | 6$\pm$1 | 0.06 | 0.01
SO | 1.8$\pm$0.6 | 7.2$\pm$0.1 | 6.10 | 1.97
34SO | - | - | 0.25 | 0.08
o-H2CS | 1.6$\pm$0.7 | 4.5$\pm$0.5 | 1.00 | 0.32
p-H2CS | 0.6$\pm$0.2 | 5.4$\pm$0.2 | 0.70 | 0.22
NS | - | - | 0.13 | 0.04
SO2 | - | - | 0.47 | 0.21
H2S | - | - | 6.50 | 2.10
H234S | - | - | 0.11 | 0.04
HSCN | - | - | 0.10 | 0.03
HNCS | - | - | 0.47 | 0.15
Total $N$ |  |  | 6.2$\times$1014 |
Total $X$ |  |  |  | 2.0$\times$10-8

Numbers in parentheses are obtained from its corresponding 34S isotopologue
considering 32S/34S=24.4 (Mauersberger et al. 2004).
a LVG calculations assuming $n$${}_{\mathrm{H_{2}}}$=5$\times$104 cm-3 and
$T$K=15 K (Shirley et al. 2011; Cabedo et al. 2021).
b Considering $N$${}_{\mathrm{H_{2}}}$=3.1$\times$1022 cm-2 (Cabedo et al.
2021).

###  4.3 Column densities and abundances

We have therefore calculated molecular column densities for the detected
S-species using a large velocity gradient (LVG) approximation. In particular,
we have derived them by fitting the emission line profiles using the LVG code
MADEX (Cernicharo 2012), which assumes that the radiative coupling between two
relatively close points is negligible, and the excitation problem is local.
The LVG models are based on the Goldreich & Kwan (1974) formalism. MADEX also
includes corrections for the beam dilution of each line, depending on the
different beam sizes at different frequencies. The final considered fit is the
one that reproduces more line profiles better from all the observed
transitions. To carry out the fits, we assume uniform physical conditions
(kinetic temperature, density, line width, radial velocity). In particular, we
have assumed a gas density of 5$\times$104 cm-3 according to results from
Sect. 4.2 and to results from Cabedo et al. (2023), who deduced a density of
$\sim$104 cm-3 for the outer regions of B 335 based on interferometric
observations. We have also assumed a source size of 10$\arcsec$ according to
interferometric maps (Cabedo et al. 2021), and a kinetic temperature of the
gas $T$K$\sim$15 K estimated by Shirley et al. (2011) from the formula for
dust temperature considering only central heating by the B 335 protostar, and
that dust and gas are coupled.

In the case of H2CS and H2S, we have used the code RADEX (van der Tak et al.
2007) since there are not available collisional rates in MADEX for these two
molecules. The results are shown in Table LABEL:table:results_from_RD. For
those species for which one transition is observed (34SO, SO2, H2S, H234S,
HSCN, and HNCS), we have derived their column densities using only the LVG
approximation and not the rotational diagram technique described in Section
4.2. For NS, since there are not available collisional rates, we have
considered LTE approximation.

Column densities derived using the rotational diagram technique and LVG
calculations agree within a factor $\lesssim$3\. Sources of uncertainty are
the low angular resolution of the used telescopes (with beam sizes between
$\sim$36$\arcsec$ and $\sim$54$\arcsec$ for the 40m-Yebes telescope, and
$\sim$14$\arcsec$ and $\sim$29$\arcsec$ for the 30m-IRAM telescope depending
on frequency), which implies that the emission from the inner region of the B
335 is blended with the outer envelope, the possible overlap with the emission
from other species (e.g. the case of H234S), the limited number of detected
transitions (one transition in many cases, such as for H2S, H234S, SO2, HSCN,
HNCS, and 34SO), the lack of collisional rates for some species (e.g. NS), and
the assumed source size derived from C17O interferometric observations. This
is one of the most important uncertainties due to the lack of interferometric
observations of S-species in B 335, since the emission from the different
S-molecules may arise from distinct regions with slightly different sizes
leading to a significant impact on the fits. In order to derive the
uncertainty associated with the LVG results, we have run the LVG code varying
the considered values for density, temperature, and source size. In
particular, we have run models with density 5$\times$104 cm-3 and
2.5$\times$104 cm-3 (variation of a factor 2), temperatures of 15 K and 12 K,
and source sizes of 10$\arcsec$ and 8 $\arcsec$ (reduction of 20$\%$). We
found variations in the S-column densities $\lesssim$10$\%$ between these two
$T$K which is comparable to the calibration errors, while the variations when
changing the density and the source size were $\lesssim$20$\%$ and
$\sim$30$\%$, respectively. Taking all this into account, we estimate the
uncertainties in the column densities derived with LVG approximation to be of
the order of $\sim$50$\%$.

The total column density of the sulphur-bearing species observed in B 335 is
6.2$\times$1014 cm-2, with the highest contribution coming from CS (calculated
from C34S considering 32S/34S=24.4 since CS is optically thick, Mauersberger
et al. 2004), H2S, SO, and CCS. The lowest values are found for NS and HSCN.
We have also observed several isotopologues relative to 13C, 34S, and 33S. In
particular, from CS, we obtain 34S/33S=10.7 (which is slightly higher than the
solar abundance value 34S/33S=5.6-6.3, Anders & Grevesse 1989; Mauersberger et
al. 2004), and 12C/13C=46.8, which is similar to that found in dark clouds by
Cernicharo & Guelin (1987).

Figure 2: Comparison of fractional abundances of sulphur-bearing species
between three Class 0 objects B 335 (this work), L 483 (Agúndez et al. 2019),
and B1-b (Fuente et al. 2016).

Table LABEL:table:results_from_RD also shows the fractional abundances
relative to H2 (with $N$${}_{\mathrm{H_{2}}}$ obtained from Cabedo et al.
2021) of the sulphur molecules detected in the range $\lambda$ = 2, 3, and 7
mm. Considering the detected S-molecules, we have obtained a total molecular
sulphur abundance of 2.0$\times$10-8, which is alike to the one found in
similar sources, such as L 1544 (1.1$\times$10-8, Vastel et al. 2018), L 483
(9.1$\times$10-9, Agúndez et al. 2019), and B1-b (1.2$\times$10-8, Fuente et
al. 2016). The highest S-abundances are $>$10-9 (CS, H2S, CCS, and SO), with
also several relatively abundant ($>$10-10) species, such as OCS and H2CS. In
general, B 335 presents a great variety of S-bearing molecules, but less than
other similar sources. In particular, although the total sulphur abundance in
B 335 is similar to other sources, such as L 483, we detect a significant
lower number of sulphur molecules in B 335 than in L 483. We are also missing
some other S-species already reported towards L 483, including SO+, HCS, and
CH3SH, for which we have derived upper limits for their column densities of
$N$(SO+)$<$1.5$\times$1011 cm-2, $N$(HCS)$<$3$\times$1012 cm-2, and
$N$(CH3SH)$<$2$\times$1012 cm-2. To derive these upper limits, once the
physical parameters are fixed, we vary (for each species) the column density
until the model fit reaches the observed intensity peak of any of the observed
lines. We do not allow the model fit to be greater than any observed line.

##  5 discussion

###  5.1 Chemical comparison

Even though the total sulphur abundance in B 335 is similar to that from other
Class 0 sources, the abundances of some specific molecules significantly vary
among them. Figure 2 shows a comparison between abundances of different
sulphur species in three Class 0 sources, B 335, L 483, and B1-b. The first
thing that stands out is that sulphur carbon chains (CS, CCS, and CCCS) in B
335 are about one order of magnitude higher than the ones observed in L 483
and B1-b. Although high abundances of carbon-chain molecules have already been
found in other cold clouds, such as TMC1 (Agúndez & Wakelam 2013), it is not a
universal characteristic of this type of early regions, since many of them
present different degrees of carbon chain richness (e.g. Suzuki et al. 1992;
Hirota et al. 2009). This therefore highlights the nature of B 335 as a source
especially rich in sulphur carbon chains.

Unlike carbon chains, sulphur molecules containing oxygen in B 335 have a
similar (OCS) or even lower (SO and SO2) abundance by up to one order of
magnitude than those found in L 483 and B1-b (see also Fig. 3). These oxygen-
sulphur molecules are usually detected in cold dense regions with abundances
between 10-10-10-8, while in hot cores and hot corinos they are significantly
enhanced (e.g. Tercero et al. 2010; Esplugues et al. 2013). In particular, SO2
is a better tracer of warm gas than SO (Esplugues et al. 2013), while SO is a
well-known outflow tracer (e.g. Codella & Scappini 2003; Lee et al. 2010;
Tafalla et al. 2010). SO seems to be more enhanced than SO2 in shocks for
timescales $\sim$104 yr (e.g. Codella & Bachiller 1999; Viti et al. 2004;
Jiménez-Serra et al. 2005). The low SO abundance found in B 335 with respect
to the other two sources L 483 and B1-b suggests that its chemistry may not be
significantly affected by shocks associated with the bipolar outflow (e.g.
Hirano et al. 1988, 1992; Stutz et al. 2008; Bjerkeli et al. 2019).

Other sulphur molecules detected in B 335 with low abundances (Fig. 3) are
those containing nitrogen, that is NS and HSCN (4$\times$10-11 and
3$\times$10-11, respectively). HSCN, unlike HNCS which is the most stable
isomer, is metastable and only detected on Earth under specific conditions
(through UV-photolysis of HNCS (Wierzejewska & Mielke 2001) or through a low-
pressure discharge (Brünken et al. 2009)). In contrast, HSCN is more easily
observed in the interstellar medium. For instance, in Sgr B2 (where HSCN was
first time detected) the ratio HNCS/HSCN$\sim$3 (Halfen et al. 2009) and in
TMC1 this ratio is $\sim$1 (Adande et al. 2010), while in L 1544 Vastel et al.
(2018) only detect HSCN, but not HNCS. This shows the important role of non-
equilibrium chemistry in dense clouds. In B 335, we only detect one transition
of HNCS with a signal to noise ratio $\sigma$$\sim$3.1, so we have considered
its column density ($N_{\mathrm{HNCS}}$$\leq$4.7$\times$1012 cm-2) as an upper
limit. This leads to a ratio HNCS/HSCN$<$4.7 consistent with the one found in
Sgr B2.

Figure 3: Fractional abundance ($X$) ratios between B 335 and L 483, and B 335
and B1-b for all the detected sulphur-bearing species in B 335.

###  5.2 Sulphur ions

Apart from neutral sulphur species, we have also observed the presence of some
ions in B 335. Molecular ions are commonly observed in dense prestellar or
protostellar regions (e.g. Caselli et al. 1998; Hogerheijde et al. 1998;
Caselli et al. 2002; van der Tak et al. 2005). To a lesser extent, ions (such
as HCO+ and N2H+) have also been observed in protostellar shocks (e.g.
Bachiller & Pérez Gutiérrez 1997; Hogerheijde et al. 1998; Caselli et al.
2002; van der Tak et al. 2005). The presence of ions in shocked regions is a
balance between their enhancement by the sputtering of dust grain mantles,
which ejects molecules into the gas phase that undergo reactions forming ions,
and their destruction by electronic recombination (e.g. Neufeld & Dalgarno
1989; Viti et al. 2002). For this reason, those ions that usually decrease in
shocks (such as N2H+) may indicate the presence of a pre-shock chemistry
(Codella et al. 2013), while the ions that are enhanced by shock chemistry
will be effective tracers of shocked gas. This is the case of HOCO+ and SO+
(Podio et al. 2014) since their abundances are predicted to be very low in the
quiescent gas, but significantly enhanced in shocks following the release of
CO2 and S-species from dust grain mantles (Minh et al. 1991; Turner 1992,
1994; Deguchi et al. 2006).

Among the sulphur ions, in B 335 we do not detect SO+ (strong tracer of
shocked gas which forms from S+ and OH Neufeld & Dalgarno 1989), but we detect
HCS+ and HC34S+ with abundances of 4.7$\times$10-10 and 1.9$\times$10-11,
respectively. The value we have obtained for HCS+ is similar to the one
observed in the bow shock L 1157-B1 (Podio et al. 2014) and one order of
magnitude higher than the ones obtained by Agúndez et al. (2019) and Fuente et
al. (2016) in the Class 0 objects L 483 and B1-b, respectively, as also found
for CS. The abundances of HCS+ and CS are strongly related, since this ion
forms through the reaction of CS with HCO+, H${}^{+}_{3}$, H3O+ (Millar et al.
1985). In addition, large abundances of CS and HCS+ may also indicate that OCS
is one of the main sulphur carriers on dust grains upon sputtering from the
grain mantles according to previous theoretical (Podio et al. 2014) and
observational (Wakelam et al. 2005; Codella et al. 2005) results.

Regarding the ratio $R$=HCS+/CS, we obtain from observations a value of 0.043.
Thaddeus et al. (1981) determined an abundance ratio $R$$\sim$0.01-0.03 in ten
molecular sources located in Sgr B2 and Ori A, while Millar (1983) found that
$R$ could be as large as 0.1 in cold dark clouds. This result was also
verified by Irvine et al. (1983). A similar $R$ value to that from B 335 is
found as well in the pre-stellar core L 1544 (0.03, Vastel et al. 2018), while
in the protostellar sources L 483 and B1-b the HCS+/CS ratio is 0.017 and
0.008, respectively (Agúndez et al. 2019; Fuente et al. 2016). According to
Clary et al. (1985), rate coefficients for ion-CS reactions rapidly increase
at low temperatures suggesting that the sources B 335 and L 1544 are
characterised by lower temperatures than L 483 and B1-b, which can be due to
an earlier evolutionary stage of B 335 and L 1544 compared to L 483 and B1-b.

###  5.3 Time evolution of fractional abundances

Figures 4-7 show the evolution of several S-bearing species along 10 Myr for
different physical conditions of the cosmic-ray (CR) ionisation rate
($\zeta$${}_{\mathrm{H_{2}}}$), gas temperature ($T$g), hydrogen number
density ($n$H), and initial sulphur abundance ($S$${}^{+}_{\mathrm{init}}$).
Given that the CR ionisation rate is still uncertain and spreads over a range
of values (van der Tak & van Dishoeck (2000) determined as
$\zeta$${}_{\mathrm{H_{2}}}$$\sim$3$\times$10-17 s-1 in dense clouds, Indriolo
& McCall (2012) obtained a range (1.7-10.6)$\times$-16 s-1 in a sample of
diffuse clouds, and Neufeld & Wolfire (2017) derived a
$\zeta$${}_{\mathrm{H_{2}}}$ of the order of a few 10-16 s-1 in the Galactic
disk), we have considered two values for the cosmic ionisation rate
$\zeta$${}_{\mathrm{H_{2}}}$=1.3$\times$10-16 s-1 and 1.3$\times$10-17 s-1.
For the gas temperature and density, given the results obtained in Sects. 4.2
and 4.3, we have run models considering $T$g=7 K and 15 K, and
$n$H=2$\times$104 cm-3 and 2$\times$105 cm-3. For the case of the initial
sulphur abundance, we have considered the solar elemental sulphur fractional
abundance ($S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-5) and also one factor of
S depletion (1.5$\times$10-6) since to reproduce observations in hot corinos
one needs to assume a significant sulphur depletion of at least one order of
magnitude lower than the solar elemental sulphur abundance as previously
stated in Sect. 1.

Figure 4: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

Figure 5: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

Figure 6: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

Figure 7: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

We have obtained these models using the Nautilus time-dependent chemical code
(Ruaud et al. 2016). Nautilus is a three-phase model in which gas, surface icy
mantle, bulk icy mantle, and their interactions are considered. Nautilus
solves the kinetic equations for both the gas phase species and the surface
species of interstellar dust grains and computes the evolution with time of
chemical abundances for a given physical structure. The chemical network is
based on the KInetic Database for Astrochemistry
(KIDA444http://kida.obs.u-bordeaux1.fr/). The used version here is detailed in
Wakelam et al. (2021). In particular, this Nautilus version considers gas-
phase processes including neutral-neutral and ion-neutral reactions, direct
cosmic ray ionisation or dissociation, ionisation or dissociation by UV
photons, ionisation or dissociation produced by photons induced by cosmic-ray
interactions with the medium (Prasad & Tarafdar 1983), and electronic
recombinations. For species on the surfaces, there is a distinction between
species in the most external layers (surface species) and species below these
layers (mantle species). The species are adsorbed on the surface and become
the mantle during the construction of the ices. Similarly, when the species
desorb, only the species from the surface can desorb, but surface species are
gradually replaced by the mantle species. Regarding surface reactions, the
model includes thermal desorption, photo-desorption, chemical desorption, and
cosmic-ray heating. See Wakelam et al. (2021) for extensive details about the
surface parameters considered in each surface reaction. In all models, we have
adopted the initial abundances shown in Table LABEL:table:abundances_Nautilus
and a visual extinction $A$V=15 mag555Derived from results in Table
LABEL:table:results_from_RD and the expression  $N_{i}=X_{i}\times A_{V}\times
1.6\times 10^{21},$ (4) where $N$i is the column density of the species $i$,
$X$i its abundance, $A$V the visual extinction, and 1.6$\times$1021 the
hydrogen column density at 1 mag of extinction (Bohlin et al. 1978)..

Table 3: Abundances with respect to total hydrogen nuclei considered in the
chemical code Nautilus.

Species | Abundance | Reference
---|---|---
He | 9.0$\times$10-2 | (1)
O | 2.4$\times$10-4 | (2)
Si+ | 8.0$\times$10-9 | (3)
Fe+ | 3.0$\times$10-9 | (3)
S+ | 1.5$\times$10-5, 1.5$\times$10-6 | (1)
Na+ | 2.0$\times$10-9 | (3)
Mg+ | 7.0$\times$10-9 | (3)
P+ | 2.0$\times$10-10 | (3)
Cl+ | 1.0$\times$10-9 | (3)
F+ | 6.7$\times$10-9 | (4)
N | 6.2$\times$10-5 | (5)
C+ | 1.7$\times$10-4 | (5)
666 References: (1) Taken from Asplund et al. (2009) and Wakelam & Herbst
(2008). (2) Taken from Hincelin et al. (2011). (3) Taken from Graedel et al.
(1982). (4) Taken from Neufeld et al. (2005). (5) Taken from Jenkins (2009).

In general, we observe that the abundances of all the species considered in
Figs. 4-7 increase with time up to $t$$\sim$5$\times$105 yr, moment at which
the abundances of various species decrease abruptly. This is the case of CS,
SO, and SO2, whose abundances decrease by about 2-4 orders of magnitude
between $t$$\sim$5$\times$105 yr and $t$$\sim$5$\times$106 yr since they react
with other species to form more complex molecules. In particular, for
$t$$>$105 yr, CS SO, and SO2 are mainly destroyed by reacting with
H${}^{+}_{\mathrm{3}}$ and forming HCS+, HSO+, and HSO${}^{+}_{\mathrm{2}}$,
respectively. For the abundances of the rest of sulphur species, this decrease
after reaching the maximum value is lower and not greater than two orders of
magnitude. From these figures, we also deduce the formation time scales of
S-species. In particular, we have observed that CS is one of the molecules
reaching first its maximum abundance value in all the models at
$t$$\sim$5$\times$104 yr, followed by HCS+ with its maximum abundance reached
at $t$$\sim$105 yr. Other molecules, such as H2CS, can be considered as late
molecules, since their maximum abundance values are found when the chemical
evolution exceeds one million years.

Regarding the influence of the physical conditions (cosmic-ray ionisation
rate, temperature, density, and initial sulphur abundance) on the
S-abundances, the parameter with the highest impact is the hydrogen nuclei
number density, $n$H, since varying $n$H by one order of magnitude leads to
abundance variations of up to three orders of magnitude for CS, CCS, OCS,
HCS+, SO, and SO2 given a specific evolutionary time (see Fig. 6). In general
terms, we observe in Fig. 6 that the chemical evolution of each considered
species is accelerated when the density increases since collisions are more
frequent than in a low density regime. This results in the abundance peak of
the species being reached at earlier times for larger densities, although the
chemical behaviour along time is roughly maintained. In particular, for
$t$$\sim$104 yr, we obtain that SO2 is mainly formed by the reaction O+SO for
$n$H=2$\times$104 and 2$\times$105 cm-3, while for $t$$\sim$105 yr (when the
SO2 peak is reached) this molecule mainly forms by the reaction O+SO for
$n$H=2$\times$104 cm-3 and by OH+SO for $n$H=2$\times$105 cm-3. The most
responsible species of destroying SO2 for both densities is C for $t$$\sim$104
yr, and H${}^{+}_{\mathrm{3}}$ for $t$$\geq$105 yr. Regarding CS, for
$t$$\sim$104 yr, it is mainly formed by the reaction HCS++e- for the low
density value, while CS is mainly formed through the reaction between atomic S
and C4 for $n$H=2$\times$105 cm-3. For $t$$\sim$105 yr (when the CS abundance
decreases for any model), CS is mainly destroyed by its reaction with
H${}^{+}_{\mathrm{3}}$ and with HCO+.

Another parameter with a big impact on S-abundances is the cosmic-ray
ionisation rate, $\zeta$, since the variation from $\zeta$=1.3$\times$10-17 to
1.3$\times$10-16 s-1 changes by about two orders of magnitude the abundances
of all the sulphur species considered in the sample (Fig. 4). For the case of
carbon-chains (CCS, C3S), we observe that the larger $\zeta$, the larger the
S-abundances for $t$$\lesssim$105 yr. Similar results are found for the
species SO, SO2, NS, H2CS, and OCS. For $t$$\sim$104 yr, we find that CCS is
mainly formed by C+HCS for the low $\zeta$ model, while it is mainly formed
through HC3S++e- in a more efficient way for a model with larger $\zeta$
(1.3$\times$10-16 s-1). In the case of SO (one of the most affected molecules
by $\zeta$ between 104$\lesssim$$t$$\lesssim$106 yr), it is mostly formed by
the reaction O+HS in a model with low $\zeta$, while the reaction between S+OH
becomes more important to form SO2 when increasing $\zeta$ by one order of
magnitude.

On the other hand, changing the temperature (from $T$gas=7 K to 15 K) and
especially the initial sulphur abundance (from
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-5 to 1.5$\times$10-6) in the models
leads to abundance variations smaller than two orders of magnitude for
$t$$>$104 yr. In particular, we have found that an increase of the
$S$${}^{+}_{\mathrm{init}}$ value by one order of magnitude also enhances the
S-abundances by one order of magnitude during the entire duration of core
evolution.

For the particular case of HCS+ and CS, the main physical parameters
significantly influencing their abundances are the density (the lower density,
the higher the HCS+ and CS abundances for $t$$>$104 yr) and the cosmic-ray
ionisation rate (the higher the $\zeta$, the higher the HCS+ and CS abundances
for $t$$>$5$\times$105 yr). By contrast, other physical parameters, such as
the gas temperature, barely affect the HCS+ and CS abundances for $t$$<$106
yr.

Figure 8: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

Figure 9: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

Figure 10: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

Figure 11: Evolution of fractional abundances of CS, CCS, C3S, OCS, SO, SO2,
HCS+, H2CS, and NS as a function of time for an initial sulphur abundance
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, a hydrogen number density
$n$H=2$\times$104 cm-3, $T$gas=7 K, and two values of CR ionisation rate
$\zeta$=1.3$\times$10-17 s-1 (solid line) and $\zeta$=1.3$\times$10-16 s-1
(dashed line).

###  5.4 Comparison with observations

We now compare the different models considered in the previous section with
observational results to derive the current evolutionary stage of B335.
Figures 34-37 show the ratio between the abundances obtained from the models
($X$model) and from the observations ($X$obs) for several sulphur-bearing
species. In particular, we have considered those S-species for which we
observe more than one emission line and those that are not close to the limit
of detection. The results are shown for five specific evolution times
($t$=104, 5$\times$104, 105, 5$\times$105, and 106 yr). In order to find the
cases with the closest values between the theoretical and observational
results, we have considered for each model the largest number of S-species for
which -0.5$\leq$log($X$model/$X$obs)$\leq$0.5 in order to only consider
discrepancies between model and observational results smaller than a factor of
$\sim$3\. Results show that the evolutionary stages that better reproduce the
observed abundances of the largest number of S-species in B 335 are those
between $t$=104-105 yr. This result obtained from a chemical approach agrees
with the results obtained from Evans et al. (2015) who derived an age of
$\sim$5$\times$104 yr for B 335 through a dynamical perspective, by applying
an inside-out collapse model that is compared with ALMA observations.
Altogether this reveals, therefore, the particularly early evolutionary stage
of B 335, which is comparable to the ages of pre-stellar condensations (e.g.
Caselli & Ceccarelli 2012). As B 335 is an isolated globule, this may be due
to the fact that the condensation has formed from very little dense gas
($\sim$103 cm-3) without a dense pre-phase between the formation of the
globule and the beginning of the collapse. This gives B 335 a different
chemistry compared to other young protostars that have form in dense molecular
clouds, such as L 483 and B1-b. Another plausible scenario is that material
from the diffuse cloud surrounding B 335 may currently be accreting onto the
protostellar envelope, thus rejuvinating its chemistry. This accretion has
been found (e.g. Pineda et al. 2020) in another Class 0 source embedded in the
Perseus Molecular Cloud Complex. Interferometric observations are requested to
distinguish between both scenarios.

From Figs. 34-37, we have also deduced that chemical models with values of
$n$H=2$\times$104 cm-3, $T$g=15 K,
$S$${}^{+}_{\mathrm{init}}$=1.5$\times$10-6, and $\zeta$=1.3$\times$10-17 s-1
best reproduce the observations of the largest number of S-species for
$t$=104-105 yr. This value of $\zeta$ agrees with results from Cabedo et al.
(2023) who found a cosmic-ray ionisation rate $\lesssim$10-16 s-1 in the outer
regions of B 335, especially for an envelope radii$>$500 au. A sulphur
depletion factor of 10 with respect to the sulphur cosmic elemental abundance
is also consistent with results from Fuente et al. (2023) in low-mass star-
forming regions, such as Taurus and Perseus.

###  5.5 Sulphur chemical ratios

We have considered several sulphur-bearing molecular ratios and have also
analysed their evolution with time. Model results obtained with the Nautilus
code are shown in Figures 8-11. We have also changed some of the physical
conditions (cosmic-ray ionisation rate, temperature, density, and initial
sulphur abundance) in order to study their impact on the evolution of these
ratios. We first notice that while there are some ratios, such as HCS+/CS,
that present small variations of up 1 order of magnitude between $t$=104-106
yr, there are other ratios that significantly change with time. In particular,
the SO2/C2S, SO/CS, SO2/CS, NS/CS, H2S/CS, and H2CS/CS ratios show variations
of up to $\sim$5 orders of magnitude in that time range (104-106 yr). The
physical parameter affecting sulphur ratios the most is the density, leading
to differences of up to $\sim$4-5 orders of magnitude especially between
5$\times$104 and 106 yr. The cosmic-ray ionisation rate is the next physical
parameter with the greatest effect on the sulphur ratios with differences of
about one order of magnitude in their values. In particular, the SO2/CS,
SO/CS, SO2/C2S, and C2S/CS ratios are among those mostly influenced by
$\zeta$, while the SO/SO2 ratio is one of the least affected. The SO/SO2 ratio
is, however, more sensitive to the density variation. We also observe a large
density impact on the NS/CS ratio, finding that the higher the density, the
larger the NS/CS for $t$$\sim$105-106 yr, with NS being mostly formed during
that time range through the neutral-neutral reaction N+HS and, to a lesser
extent, through the dissociative recombination of HNS+. On the other hand,
varying the gas temperature from 7 to 15 K (Fig. 9) mostly affects the H2S/SO
ratio between 104 and 106 yr, and the SO/CS, SO2/CS, and H2S/CS ratios at late
times ($t$$\gtrsim$106 yr). Regarding the only ion detected in B 335, its
HCS+/CS ratio slightly increases when the initial sulphur abundance is
decreased, and also when the cosmic-ray ionisation rate or the density
increase.

The use of molecular ratios as indicators of chemical evolution of young
stellar sources has been previously approached from both observational and
theoretical perspectives (e.g. Pineau des Forets et al. 1993; Charnley 1997;
Hatchell et al. 1998; Codella & Bachiller 1999; Gibb et al. 2000; Boogert et
al. 2000; Wakelam et al. 2004). Our models (Figs. 4-7) show that SO and SO2
constantly increase with time reaching both their peaks at
$t$$\gtrsim$5$\times$105 yr, which prevents the use of their ratio as a
chemical clock. Nevertheless, Figures 8-11 show that there are other sulphur
ratios that could be used as evolutionary tracers since they maintain a
constant trend over time. This is for instance the case of the SO2/C2S and
SO/CS ratios, whose values constantly increase during the first
$\sim$2$\times$105 yr. In order to compare these theoretical results with
observations, we have considered a sample of sources that includes starless
cores (TMC1 and L 1544 considered as starless and prestellar cores,
respectively, see for example Crapsi et al. 2005; Schnee et al. 2007; Lefloch
et al. 2018; Agúndez et al. 2019; Cernicharo et al. 2021) and Class 0 objects
(B 335, L 483, and B1-b). Observational results are shown in Fig. 12, where we
have indeed found a clear trend where the SO2/C2S and SO/CS ratios increase
with the age of the objects, suggesting that these sulphur ratios could be
used as chemical clocks. We have also included in Fig. 12 observational
results for the HCS+/CS ratio. In this case, we have obtained a negative trend
in which the value of HCS+/CS decreases with the age of the objects.

Comparing the observational HCS+/CS, SO2/C2S, and CO/CS ratios for B 335 with
the theoretical results (Figs. 8-11), we observe that, for the temperature and
density values used in Sect. 4.3 to derive observational results, the three
ratios would be reproduced at 5$\times$104$\lesssim$$t$$\lesssim$105 yr when
considering a high cosmic-ray ionisation rate ($\zeta$=1.3$\times$10-16 s-1)
and a S depletion of at least a factor 10 with respect to the solar elemental
sulphur abundance. This depletion is also found by many authors (e.g. Wakelam
et al. 2004; Crockett et al. 2014; Vastel et al. 2018; Bulut et al. 2021;
Navarro-Almaida et al. 2021; Esplugues et al. 2022; Hily-Blant et al. 2022;
Fuente et al. 2023) in other star-forming regions.

Figure 12: Observational sulphur molecular ratios of potentially good chemical
evolution tracers of the prestellar to protostellar transition for different
objects (TMC1, L 1544, B 335, L 483, and B1-b). Data for TMC1 were taken from
Marcelino et al. (2007), Cernicharo (2012), Cernicharo et al. (2021), and
Rodríguez-Baras et al. (2021). Data for L 1544 were taken from Vastel et al.
(2018). L 483 and B1-b data were gathered from Agúndez et al. (2019) and
Fuente et al. (2016), respectively.

##  6 Summary and conclusions

We have carried out a comprehensive observational and theoretical study of
sulphur in the Class 0 object B 335. This source is an isolated dense Bok
globule located at a distance of $\sim$100 pc. We have detected 20 different
sulphur-bearing species (including isotopologues) using Yebes 40m and IRAM 30m
telescope observations. In order to derive column densities, we have applied
the method of rotational diagrams. For this purpose, we have also used non-LTE
radiative transfer codes given the low number of transitions detected for some
species and the optically thick emission of some lines. Our results show low
rotational temperatures ($\lesssim$15 K), suggesting that the gas is sub-
thermally excited, and thus revealing a relatively low ($<$105 cm-3) gas
density. These low temperatures, the narrow line widths, and the relatively
low density are also consistent with emission arising from a cold and extended
region, suggesting that the detected S-emission does not trace the hot corino,
but its cold envelope.

From the column densities of all the observed sulphur species, we have derived
a total molecular sulphur abundance of 2.0$\times$10-8, which is similar to
that found in the envelopes of other Class 0 objects. Nevertheless, we have
also found that the abundances of some specific S-molecules vary significantly
across the sample of Class 0 objects (B 335, L 483, and B1-b) considered in
this paper. In particular, we have derived high abundances of sulphur carbon-
chain molecules in B 335 compared to those found in other Class 0 objects, and
also compared with those abundances of S-molecules containing oxygen or
nitrogen. This points out the nature of B 335 as a source especially rich in
sulphur carbon chains, which could be due to the fact that B 335 is an
isolated source compared to other young protostars that have formed in dense
molecular clouds, such as L 483 and B1-b, or to accretion of material from the
diffuse cloud surrounding B 335 onto the protostellar envelope, thus
rejuvenating its chemistry. The comparison between envelopes of different
Class 0 objects has also allowed to deduce a low SO abundance in B 335 with
respect to L 483 and B1-b. SO is a well-known outflow tracer, which is thought
to be enhanced in shocks. Its low abundance in B 335 together with the non-
detection of other shock tracers, such SO+, suggests that its chemistry in B
335 is not particularly influenced by shocks.

In this work, we have also used the time-dependent chemical code Nautilus to
study the time evolution of fractional S-abundances, as well as the influence
of several physical and chemical parameters (cosmic-ray ionisation rate,
density, gas temperature, and initial sulphur abundance) on these abundances.
The comparison between chemical model results and observations shows that the
evolutionary stages that better reproduce the observed abundances of the
largest number of S-species in B 335 correspond to $t$=104-105 yr, in
agreement with previous age estimations obtained by applying theoretical
methods with the use of a dynamical model. The results from Nautilus have also
revealed that the physical parameters with the highest influence on the
S-abundances are the density and the cosmic-ray ionisation rate whose
variations by one order of magnitude lead to abundance variations of several
orders of magnitude for different sulphur-bearing species such as SO, SO2, CS,
and CCCS. We have also used Nautilus to explore the behaviour of different
S-molecular ratios with time, finding that there are some sulphur ratios that
could be used as chemical evolution tracers since they maintain a constant
trend over time. A comparison of the observational results of S-ratios in a
sample of objects (including starless and prestellar cores, and Class 0
objects) characterised by different evolutionary stages confirms a clear trend
where the SO2/C2S and SO/CS ratios increase with the age of the objects, while
HCS+/CS decreases with the evolutionary stage. We, therefore, conclude that
these S-ratios could be used as good chemical evolutionary indicators tracing
the prestellar to protostellar transition.

###### Acknowledgements.

We thank the Spanish MICINN for funding support from PID2019-106235GB-I00.
This project has been carried out with observations from the 30-m radio
telescope of the Institut de radioastronomie millimétrique (IRAM) and from the
40-m radio telescope of the National Geographic Institute of Spain (IGN) at
Yebes Observatory. Yebes Observatory thanks the ERC for funding support under
grant ERC-2013-Syg-610256-NANOCOSMOS. A.F. is grateful to the European
Research Council (ERC) for funding under the Advanced Grant project SUL4LIFE,
grant agreement No101096293. D.N.A. acknowledges funding support from
Fundación Ramón Areces through their international postdoc grant program.
Á.S.M. acknowledges support from the RyC2021-032892-I grant funded by
MCIN/AEI/10.13039/501100011033 and by the European Union ’Next
GenerationEU’/PRTR, as well as the program Unidad de Excelencia María de
Maeztu CEX2020-001058-M. M.N.D. acknowledges the support by the Swiss National
Science Foundation (SNSF) Ambizione grant no. 180079, the Center for Space and
Habitability (CSH) Fellowship, and the IAU Gruber Foundation Fellowship. We
also thank the anonymous referee for valuable comments that improved the
manuscript.

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##  Appendix A Tables and figures

Table 4: Line parameters of sulphur-bearing molecules detected in B 335. Species | Transition | Frequency | vLSR |  $\Delta$v |  $T$MB |  $\int$$T$MB dv
---|---|---|---|---|---|---
|  | (MHz) | (km s-1) | (km s-1) | (K) | (K km s-1)
CS | 1-0 | 48990.98 | 8.27$\pm$0.07 | 1.20$\pm$0.08 | 1.29$\pm$0.50 | 1.64$\pm$0.03
| 2-1 | 97980.95 | 8.25$\pm$0.08 | 1.41$\pm$0.05 | 1.13$\pm$0.32 | 1.70$\pm$0.07
| 3-2 | 146969.02 | 8.01$\pm$0.06 | 1.05$\pm$0.03 | 1.50$\pm$0.17 | 1.68$\pm$0.04
13CS | 1-0 | 46247.56 | 8.31$\pm$0.08 | 0.81$\pm$0.02 | 0.15$\pm$0.03 | 0.128$\pm$0.002
| 2-1 | 92494.27 | 8.34$\pm$0.04 | 1.34$\pm$0.07 | 0.06$\pm$0.01 | 0.095$\pm$0.007
| 3-2 | 138739.26 | 8.24$\pm$0.06 | 0.99$\pm$0.07 | 0.06$\pm$0.01 | 0.066$\pm$0.008
C34S | 1-0 | 48206.97 | 8.43$\pm$0.02 | 0.97$\pm$0.06 | 0.39$\pm$0.05 | 0.403$\pm$0.004
| 2-1 | 96412.95 | 8.31$\pm$0.07 | 1.27$\pm$0.09 | 0.21$\pm$0.05 | 0.279$\pm$0.006
| 3-2 | 144617.10 | 8.28$\pm$0.07 | 0.84$\pm$0.08 | 0.18$\pm$0.06 | 0.165$\pm$0.005
C33S | 1-0 | 48585.88 | 8.17$\pm$0.05 | 0.80$\pm$0.08 | 0.04$\pm$0.01 | 0.041$\pm$0.004
| 2-1 | 97172.06 | 9.07$\pm$0.04 | 0.86$\pm$0.05 | 0.02$\pm$0.01 | 0.020$\pm$0.006
| 3-2 | 145755.62 | 8.21$\pm$0.07 | 0.80$\pm$0.06 | 0.02$\pm$0.01 | 0.020$\pm$0.007
CCS | 23-12 | 33751.37 | 8.80$\pm$0.03 | 0.83$\pm$0.04 | 0.34$\pm$0.05 | 0.306$\pm$0.001
|  |  | 7.39$\pm$0.03 | 1.10$\pm$0.05 | 0.15$\pm$0.02 | 0.185$\pm$0.001
| 33-22 | 38866.42 | 8.29$\pm$0.05 | 0.77$\pm$0.04 | 0.11$\pm$0.02 | 0.087$\pm$0.001
| 43-32 | 43981.02 | 8.39$\pm$0.08 | 0.55$\pm$0.08 | 0.16$\pm$0.03 | 0.095$\pm$0.001
| 34-23 | 45379.03 | 8.35$\pm$0.02 | 0.67$\pm$0.06 | 0.85$\pm$0.07 | 0.606$\pm$0.001
| 66-55 | 77731.71 | 8.13$\pm$0.04 | 1.24$\pm$0.07 | 0.08$\pm$0.02 | 0.100$\pm$0.010
| 67-56 | 81505.17 | 8.05$\pm$0.01 | 1.52$\pm$0.07 | 0.22$\pm$0.03 | 0.357$\pm$0.006
| 76\- 65 | 86181.39 | 8.18$\pm$0.07 | 0.78$\pm$0.05 | 0.10$\pm$0.04 | 0.084$\pm$0.004
| 77\- 66 | 90686.38 | 8.47$\pm$0.07 | 0.77$\pm$0.09 | 0.06$\pm$0.01 | 0.051$\pm$0.006
| 78\- 67 | 93870.09 | 9.14$\pm$0.06 | 1.35$\pm$0.04 | 0.19$\pm$0.02 | 0.274$\pm$0.005
| 87\- 76 | 99866.52 | 8.54$\pm$0.03 | 0.75$\pm$0.03 | 0.08$\pm$0.02 | 0.061$\pm$0.007
| 88\- 77 | 103640.75 | 8.42$\pm$0.05 | 0.76$\pm$0.04 | 0.05$\pm$0.01 | 0.044$\pm$0.004
| 89\- 78 | 106347.72 | 7.99$\pm$0.09 | 1.10$\pm$0.05 | 0.12$\pm$0.04 | 0.140$\pm$0.004
| 98\- 87 | 113410.18 | 8.63$\pm$0.04 | 0.93$\pm$0.07 | 0.04$\pm$0.01 | 0.040$\pm$0.006
| 1011-910 | 131551.96 | 8.38$\pm$0.03 | 0.72$\pm$0.04 | 0.05$\pm$0.01 | 0.038$\pm$0.007
| 1110-109 | 140180.74 | 8.60$\pm$0.04 | 1.10$\pm$0.08 | 0.03$\pm$0.01 | 0.033$\pm$0.007
| 1111-1010 | 142501.69 | 8.55$\pm$0.06 | 0.95$\pm$0.04 | 0.03$\pm$0.01 | 0.027$\pm$0.006
| 1112-1011 | 144244.82 | 8.35$\pm$0.05 | 0.92$\pm$0.07 | 0.05$\pm$0.01 | 0.040$\pm$0.020
| 1314-1213 | 169753.46 | 8.14$\pm$0.07 | 0.84$\pm$0.08 | 0.03$\pm$0.01 | 0.027$\pm$0.005
| 1313-1212 | 168406.79 | 8.38$\pm$0.05 | 0.62$\pm$0.08 | 0.03$\pm$0.01 | 0.017$\pm$0.004
CC34S | 23-12 | 33111.83 | 8.97$\pm$0.05 | 0.55$\pm$0.06 | 0.010$\pm$0.001 | 0.070$\pm$0.003
|  |  | 8.10$\pm$0.02 | 1.63$\pm$0.05 | 0.008$\pm$0.001 | 0.013$\pm$0.003
| 43-32 | 42918.18 | 8.37$\pm$0.04 | 0.60$\pm$0.05 | 0.008$\pm$0.001 | 0.030$\pm$0.002
| 34-23 | 44497.59 | 8.23$\pm$0.01 | 0.60$\pm$0.07 | 0.05$\pm$0.01 | 0.005$\pm$0.001
CCCS | 6-5 | 34684.36 | 8.78$\pm$0.03 | 0.66$\pm$0.08 | 0.12$\pm$0.02 | 0.090$\pm$0.001
|  |  | 7.54$\pm$0.05 | 0.83$\pm$0.09 | 0.06$\pm$0.01 | 0.053$\pm$0.001
| 7-6 | 40465.01 | 8.32$\pm$0.04 | 0.60$\pm$0.05 | 0.24$\pm$0.04 | 0.158$\pm$0.001
| 8-7 | 46245.62 | 8.34$\pm$0.02 | 0.77$\pm$0.05 | 0.20$\pm$0.05 | 0.170$\pm$0.012
| 13-12 | 75147.92 | 8.60$\pm$0.02 | 1.20$\pm$0.06 | 0.04$\pm$0.01 | 0.063$\pm$0.012
| 14-13 | 80928.18 | 7.82$\pm$0.09 | 1.66$\pm$0.09 | 0.03$\pm$0.01 | 0.060$\pm$0.007
| 15-14 | 86708.37 | 8.30$\pm$0.06 | 0.90$\pm$0.03 | 0.07$\pm$0.01 | 0.071$\pm$0.005
| 16-15 | 92488.49 | 8.57$\pm$0.05 | 1.01$\pm$0.08 | 0.02$\pm$0.01 | 0.027$\pm$0.009
CCC34S | 6-5 | 33844.24 | 8.77$\pm$0.04 | 0.84$\pm$0.05 | 0.005$\pm$0.001 | 0.005$\pm$0.001
| 7-6 | 39484.87 | 8.36$\pm$0.03 | 0.55$\pm$0.05 | 0.012$\pm$0.03 | 0.007$\pm$0.001
| 8-7 | 45125.47 | 8.33$\pm$0.04 | 0.41$\pm$0.07 | 0.009$\pm$0.003 | 0.004$\pm$0.001
OCS | 3-2 | 36488.81 | 8.45$\pm$0.06 | 0.94$\pm$0.06 | 0.015$\pm$0.002 | 0.015$\pm$0.005
| 4-3 | 48651.60 | 8.11$\pm$0.07 | 1.10$\pm$0.08 | 0.023$\pm$0.002 | 0.027$\pm$0.001
| 7-6 | 85139.10 | 8.50$\pm$0.03 | 0.90$\pm$0.06 | 0.033$\pm$0.003 | 0.031$\pm$0.012
| 8-7 | 97301.20 | 8.40$\pm$0.04 | 1.45$\pm$0.09 | 0.017$\pm$0.002 | 0.026$\pm$0.012
| 9-8 | 109463.06 | 8.62$\pm$0.03 | 1.09$\pm$0.05 | 0.020$\pm$0.002 | 0.024$\pm$0.007
HCS+ | 1-0 | 42674.19 | 8.34$\pm$0.05 | 0.56$\pm$0.05 | 0.10$\pm$0.02 | 0.061$\pm$0.001
| 2-1 | 85347.87 | 8.25$\pm$0.03 | 0.75$\pm$0.07 | 0.11$\pm$0.04 | 0.089$\pm$0.004
| 4-3 | 170691.64 | 8.27$\pm$0.06 | 0.56$\pm$0.04 | 0.05$\pm$0.01 | 0.035$\pm$0.004
HC34S+ | 1-0 | 41983.06 | 8.43$\pm$0.07 | 0.60$\pm$0.04 | 0.006$\pm$0.001 | 0.004$\pm$0.001
| 4-3 | 167927.26 | 8.90$\pm$0.08 | 0.75$\pm$0.08 | 0.023$\pm$0.01 | 0.018$\pm$0.006
SO | 23-22 | 36202.04 | 8.77$\pm$0.09 | 0.51$\pm$0.05 | 0.005$\pm$0.001 | 0.003$\pm$0.001
| 22-11 | 86093.98 | 8.55$\pm$0.06 | 0.86$\pm$0.04 | 0.04$\pm$0.01 | 0.045$\pm$0.007
| 32-21 | 99299.90 | 8.35$\pm$0.07 | 0.91$\pm$0.07 | 0.56$\pm$0.04 | 0.550$\pm$0.006
| 23-12 | 109252.21 | 8.39$\pm$0.02 | 1.08$\pm$0.08 | 0.05$\pm$0.01 | 0.057$\pm$0.005
| 43-32 | 138178.68 | 8.32$\pm$0.02 | 0.81$\pm$0.06 | 0.37$\pm$0.02 | 0.318$\pm$0.006
| 34-23 | 158971.85 | 8.65$\pm$0.01 | 0.88$\pm$0.05 | 0.07$\pm$0.01 | 0.066$\pm$0.012
| 44-33 | 172181.40 | 8.38$\pm$0.05 | 1.00$\pm$0.08 | 0.06$\pm$0.01 | 0.071$\pm$0.009
34SO | 23-12 | 97715.40 | 8.24$\pm$0.04 | 1.20$\pm$0.09 | 0.02$\pm$0.01 | 0.023$\pm$0.006
SO2 | 31,3-20,2 | 104029.41 | 8.63$\pm$0.03 | 1.15$\pm$0.07 | 0.02$\pm$0.01 | 0.028$\pm$0.005
H2S | 11,0-10,1 | 168762.76 | 8.10$\pm$0.04 | 1.00$\pm$0.06 | 0.17$\pm$0.04 | 0.184$\pm$0.009
|  |  | 8.30$\pm$0.03 | 2.50$\pm$0.10 | 0.11$\pm$0.03 | 0.290$\pm$0.008
H234S | 11,0-10,1 | 167910.51 | 8.20$\pm$0.02 | 1.00$\pm$0.08 | 0.05$\pm$0.01 | 0.049$\pm$0.004
o-H2CS | 10,1-00,0 | 34351.45 | 8.84$\pm$0.01 | 0.76$\pm$0.05 | 0.09$\pm$0.01 | 0.069$\pm$0.001
|  |  | 7.62$\pm$0.08 | 0.86$\pm$0.05 | 0.05$\pm$0.01 | 0.0423$\pm$0.001
| 30,3-20,2 | 103040.54 | 8.31$\pm$0.01 | 0.85$\pm$0.06 | 0.17$\pm$0.04 | 0.151$\pm$0.003
| 40,4-30,3 | 137371.29 | 8.52$\pm$0.02 | 0.81$\pm$0.03 | 0.11$\pm$0.04 | 0.095$\pm$0.007
| 50,5-40,4 | 171687.90 | 8.01$\pm$0.01 | 0.92$\pm$0.07 | 0.09$\pm$0.01 | 0.089$\pm$0.006
p-H2CS | 31,3-21,2 | 101477.88 | 8.31$\pm$0.02 | 0.97$\pm$0.08 | 0.18$\pm$0.05 | 0.181$\pm$0.008
| 31,2-21,1 | 104617.11 | 8.48$\pm$0.03 | 0.68$\pm$0.08 | 0.23$\pm$0.07 | 0.171$\pm$0.003
| 41,4-31,3 | 135298.36 | 8.50$\pm$0.06 | 0.75$\pm$0.05 | 0.14$\pm$0.04 | 0.115$\pm$0.007
| 41,3-31,2 | 139483.69 | 8.38$\pm$0.04 | 0.60$\pm$0.07 | 0.13$\pm$0.04 | 0.080$\pm$0.005
| 51,5-41,4 | 169114.16 | 8.41$\pm$0.03 | 0.76$\pm$0.04 | 0.09$\pm$0.01 | 0.075$\pm$0.004
| 51,4-41,3 | 174345.22 | 8.35$\pm$0.05 | 0.72$\pm$0.04 | 0.07$\pm$0.01 | 0.055$\pm$0.006
HSCN | 40,4-30,3 | 45877.81 | 8.05$\pm$0.07 | 0.55$\pm$0.04 | 0.014$\pm$0.001 | 0.008$\pm$0.002
HNCS | 30,3-20,2 | 35187.11 | 8.40$\pm$0.06 | 0.60$\pm$0.05 | 0.005$\pm$0.001 | 0.003$\pm$0.001
NS |  $J$=5/2-3/2, $\Omega$=1/2, $F$=5/2-3/2, $l$=$e$ | 115156.81 | 8.40$\pm$0.03 | 1.50$\pm$0.08 | 0.06$\pm$0.01 | 0.10$\pm$0.02
|  $J$=5/2-3/2, $\Omega$=1/2, $F$=3/2-3/2, $l$=$f$ | 115524.60 | 8.75$\pm$0.05 | 0.95$\pm$0.06 | 0.08$\pm$0.01 | 0.08$\pm$0.02
|  $J$=5/2-3/2, $\Omega$=1/2, $F$=7/2-5/2, $l$=$f$ | 115556.25 | 7.95$\pm$0.06 | 0.90$\pm$0.06 | 0.06$\pm$0.01 | 0.05$\pm$0.02
|  $J$=7/2-5/2, $\Omega$=1/2, $F$=9/2-7/2, $l$=$e$ | 161297.24 | 8.26$\pm$0.01 | 0.73$\pm$0.05 | 0.03$\pm$0.01 | 0.020$\pm$0.004
|  $J$=7/2-5/2, $\Omega$=1/2, $F$=7/2-5/2, $l$=$e$ | 161298.41 | 8.62$\pm$0.01 | 0.70$\pm$0.06 | 0.02$\pm$0.01 | 0.016$\pm$0.004
|  $J$=7/2-5/2, $\Omega$=1/2, $F$=9/2-7/2, $l$=$f$ | 161697.25 | 7.95$\pm$0.03 | 0.65$\pm$0.07 | 0.02$\pm$0.01 | 0.014$\pm$0.004
Table 4: continued.

Figure 13: Observed lines of CS in B 335 (black) with rms$>$3$\sigma$. The red
dashed line indicates the systemic velocity of the source vLSR=8.3 km s-1.
Figure 14: Observed lines of 13CS in B 335 (black) with rms$>$3$\sigma$. The
red dashed line indicates the systemic velocity of the source vLSR=8.3 km s-1.
Figure 15: Observed lines of C34S in B 335 (black) with rms$>$3$\sigma$. The
red dashed line indicates the systemic velocity of the source vLSR=8.3 km s-1.
Figure 16: Observed lines of C33S in B 335 (black) with rms$>$3$\sigma$. The
red dashed line indicates the systemic velocity of the source vLSR=8.3 km s-1.
Figure 17: Observed lines of CCS in B 335 with rms$>$3$\sigma$. The red dashed
line indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 18:
Observed lines of CC34S in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 19:
Observed lines of CCCS in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 20:
Observed lines of CCC34S in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 21:
Observed lines of OCS in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 22:
Observed lines of HCS+ in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 23:
Observed lines of HC34S+ in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 24:
Observed lines of SO in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 25:
Observed lines of 34SO in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 26:
Observed lines of o-H2CS in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 27:
Observed lines of p-H2CS in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 28:
Observed lines of NS in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 29:
Observed line of SO2 in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 30:
Observed line of H2S in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 31:
Observed line of H234S in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 32:
Observed line of HSCN in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1. Figure 33:
Observed line of HNCS in B 335 with rms$>$3$\sigma$. The red dashed line
indicates the systemic velocity of the source vLSR=8.3 km s-1.

Figure 34: Ratios between the abundances obtained from the models, $X$model,
and the observations, $X$obs, for different sulphur species at specific
evolution times ($t$=104, 5$\times$104, 105, 5$\times$105, and 106 yr), when
varying the cosmic-ray rate ($\zeta$).

Figure 35: Ratios between the abundances obtained from the models, $X$model,
and the observations, $X$obs, for different sulphur species at specific
evolution times ($t$=104, 5$\times$104, 105, 5$\times$105, and 106 yr), when
varying the gas temperature.

Figure 36: Ratios between the abundances obtained from the models, $X$model,
and the observations, $X$obs, for different sulphur species at specific
evolution times ($t$=104, 5$\times$104, 105, 5$\times$105, and 106 yr), when
varying the hydrogen number density ($n$H).

Figure 37: Ratios between the abundances obtained from the models, $X$model,
and the observations, $X$obs, for different sulphur species at specific
evolution times ($t$=104, 5$\times$104, 105, 5$\times$105, and 106 yr), when
varying the initial sulphur abundance ($S$${}^{+}_{\mathrm{init}}$).