# Ethynyl around the H ii regions S255 and S257††thanks: This work is based on
observations carried out under the project 027-18 with the IRAM 30 m
Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN
(Spain).

Anna I. Buslaeva,1 Maria. S. Kirsanova,1 Anna F. Punanova2
1Institute of Astronomy, Russian Academy of Sciences, 119017, 48 Pyatnitskaya
Str., Moscow, Russia
2Institute of Natural Sciences and Mathematics, Ural Federal University, 19
Mira Str., 620075 Ekaterinburg, Russia
E-mail<EMAIL_ADDRESS>(MSK)

(Accepted January 29, 2021. Received July 5, 2020)

###### Abstract

We present the results of the ethynyl (C2H) emission line observations towards
the H ii regions S255 and S257 and the molecular cloud between them. Radial
profiles of line brightness, column density, and abundance of C2H are
obtained. We show that the radial profile of the ethynyl abundance is almost
flat towards the H ii regions and drops by a factor of two towards the
molecular cloud. At the same time, we find that the abundance of ethynyl is at
maximum towards the point sources in the molecular cloud – the stars with
emission lines or emitting in X-ray. The line profiles are consistent with the
assumption that both H ii regions have front and back neutral walls that move
relative to each other.

###### keywords:

astrochemistry – ISM: dust, extinction – ISM: molecules – ISM:
photodissociation region (PDR) – galaxies: star formation – radio lines: ISM

††pubyear: 2019††pagerange: Ethynyl around the H ii regions S255 and
S257††thanks: This work is based on observations carried out under the project
027-18 with the IRAM 30 m Telescope. IRAM is supported by INSU/CNRS (France),
MPG (Germany), and IGN (Spain).–Ethynyl around the H ii regions S255 and
S257††thanks: This work is based on observations carried out under the project
027-18 with the IRAM 30 m Telescope. IRAM is supported by INSU/CNRS (France),
MPG (Germany), and IGN (Spain).

##  1 Introduction

Over the past 80 years, more and more new molecules have been discovered in
the interstellar medium (Tielens, 2013). To date, more than 200 chemical
species have been found in the dense and diffuse molecular clouds, apart to
the atoms in different degrees of ionization in the H ii regions (see, for
example, the list of molecules at the website of the Cologne database for
molecular spectroscopy CDMS111https://cdms.astro.uni-
koeln.de/classic/molecules, Endres et al., 2016). Complex organic molecules,
such as methanol (CH3OH), ethylene-glycol ((CH2OH)2), and many others, are
formed by successive additions of individual atoms and radicals in the gas
phase and on the surfaces of dust grains (Tielens, 2013). It is important that
the so-called bottom-up chemistry requires reactions to occur on the surface
of interstellar dust grains, which often serve as the catalysts for reactions.
At the periphery of the H ii regions, in the photodissociation regions (PDR),
where physical and chemical processes are caused by the absorption of the
ultraviolet radiation with the energy below hydrogen ionization potential (UV,
from 4 to 13.6 eV), the opposite process, namely, destruction of long carbon
chains, so-called top-down chemistry occurs (Berné & Tielens, 2011; Berné et
al., 2015). It is important to note that the main species (molecules,
radicals) are different in the bottom-up and top-down chemistry (Tielens,
2013). While the initial stages of the bottom-up chemistry are fairly well
understood (e.g., the chain of methanol formation from a CO molecule on the
dust, Tielens & Hagen, 1982), the starting point of the top-down chemistry and
its main species are unknown, apart from the confirmed formation of fullerenes
(Zhen et al., 2014) as products of photodissociation of polycyclic aromatic
hydrocarbons (PAH). However, the top-down chemistry is known to be closely
related to the effect of UV radiation upon PAH, hydrocarbon grains, and long
carbon chains formed in the atmospheres of red giants (Pety et al., 2005;
Guzmán et al., 2015; van Dishoeck, 2018).

Destruction of PAHs under the action of UV radiation (Pavlyuchenkov et al.,
2013; Murga et al., 2019) can cause interesting features in the molecular
composition of the gas in PDRs. For instance, Pety et al. (2005) found high
abundance of small hydrocarbons C2H, c–C3H2, C4H towards the illuminated edge
of the Horsehead Nebula. The authors were unable to explain the formation of
hydrocarbons at $A_{\rm V}=0.1$ using PDR model and suggested formation of
small hydrocarbons as a result of the photo-destruction of PAHs. Later, Le Gal
et al. (2017) simulated formation of hydrocarbons in the Horsehead Nebula,
taking into account the presence of gas and dust in the PDR at the stage of a
dark cloud before the beginning of ultraviolet irradiation by the $\sigma$ Ori
star. They managed to explain the distribution of the molecular abundances
everywhere, except for the illuminated edge of the Horsehead. Guzmán et al.
(2015) reported an excess of the l-C3H+ ion abundance towards the illuminated
edge of the Horsehead as compared to the results of astrochemical modelling.

Interestingly, the Horsehead remains the only PDR where the abundance of small
hydrocarbons has not been explained by the existing astrochemical models. In
the Orion Bar PDR, close to the Orion nebula, high abundance of small
hydrocarbons was explained by high-temperature chemical reactions involving
excited hydrogen molecules (Agúndez et al., 2010; Cuadrado et al., 2015).
Also, no discrepancies were found between the observed abundances of C2H and
the results of the astrochemical modelling in the M8 PDR by Tiwari et al.
(2019). Murga et al. (2020) showed that an effective formation of C2H from
acetylene molecules (C2H2) occurs as a result of photo-destruction of PAHs in
the Orion Bar PDR, while in the Horsehead this process is practically
insignificant in comparison to the formation of C2H via gas-phase reactions
starting from ionised carbon C+. Experimental data on the efficiency of
acetylene formation as a result of the photo-destruction of PAHs are
contradictory. Some authors find that the products of PAH photo-destruction
are C and H atoms, as well as H2 molecules (see, e.g., Jochims et al., 1994;
Zhen et al., 2015; Joblin et al., 2019).

In the infrared images obtained by space telescopes, H ii regions look like
ring nebulae – projections of spherical shells or ring structures onto the
plane of the sky (Deharveng et al., 2005; Deharveng et al., 2010). Despite
several thousand infrared nebulae have been catalogued to date, there are no
more than ten well-studied PDRs around H ii regions (Churchwell et al., 2006;
Simpson et al., 2012). There is a lack of statistical data on the features of
the size distribution of PAH particles and on the abundance of hydrocarbons in
PDRs. Moreover, the profiles of the molecular abundances, obtained from the
ionization source deep into the molecular cloud, are required for comparison
with the results of theoretical modelling.

The aim of the present study is to obtain the radial profile of the C2H
abundances in the H ii regions Sh2-255 and Sh2-257 (hereafter S255 and S257,
see Sharpless, 1959) in the complex S254-S258 (Chavarría et al., 2008). Entire
complex is located at $\approx 1.78$ kpc from the Sun (Russeil et al., 2007).
A molecular cloud is compressed between these two H ii regions, as found by
Bieging et al. (2009); Ojha et al. (2011), see Fig. 1. Spectral types of
ionizing stars of these H ii regions are B0V (LS 19 star in S255, Moffat et
al., 1979) and B0.5V (HD 253327 in S257 Ojha et al., 2011). The sizes of both
H ii regions are about 1.3 pc. The neighbourhoods of S255 and S257 are active
star-forming regions as was shown by Chavarría et al. (2008); Zinchenko et al.
(2012); Chavarría et al. (2014); Zinchenko et al. (2020).

The details of our observations are presented in Sect. 2, and the Herschel Hi-
GAL data used in the work are described in Sect. 3. The spectral data analysis
is described in Sect. 4, the results on the ethynil column density and
abundance are presented in Sec. 5. We discuss the ethynil abundance profiles
and the environmental context in Sect. 6 and give conclusions in Sect. 7.

Figure 1: Optical image of the H ii regions S255 and S257 from the DSS survey
in the filter POSS2 Red. The observed positions are shown by empty circles
whose sizes correspond to the telescope beam at the frequency 87 GHz (28″).
Ionizing stars of the H ii regions are shown by red stars. IR-sources S255
IRS1 and S255 IRS3 are shown by white diamonds.

##  2 Observations

In order to obtain the C2H abundance profile in the S255 and S257 H ii
regions, we made observations in several selected positions along the straight
lines connecting the S255 IRS1 infrared source, which is located in the
molecular cloud between the H ii regions (J2000 $\alpha$=06h12m54s,
$\delta$=17∘59′23′′), and the ionizing stars of each of the H ii regions: LS
19 (J2000 $\alpha$=06h13m04.2s, $\delta$=17∘58′41.5′′) and HD 253327 (J2000
$\alpha$=06h12m44.2s, $\delta$=17∘59′14.3′′), see Fig.1. Observations were
done on 19–21 August 2018 with the IRAM 30 m telescope using the EMIR 090
receiver and the FTS 50 spectrograph in the full power mode. We made sure that
the OFF-position (J2000 $\alpha$=06h12m54.0s, $\delta$=18∘09′23.0′′) was free
of the C2H(1–0) emission down to the rms of 25 mK ($T_{\rm mb}$) using the
frequency switching mode. The beam size at the frequency of 87.4 GHz was 28″,
observations were carried out position-by-position with the step of 14″.
Spectral resolution was 50 kHz, that at the frequency of 87.4 GHz corresponds
to 0.17 km s-1. Observations were carried out under acceptable weather
conditions, the amount of precipitable water vapour pwv =7–13 mm. The noise
temperature of the system was at the level of 100 K. The intensity scale was
converted to the main beam temperature ($T_{\rm mb}$) units taking into
account the antenna efficiency $F_{\rm eff}=0.95$, $B_{\rm
eff}=0.81$222http://www.iram.es/IRAMES/mainWiki/Iram30mEfficiencies. The
signal integration time at each point was 7.7 min, which made it possible to
achieve the sensitivity of 0.05 K in units of $T_{\rm mb}$. The processing and
analysis of spectra (taking into account the antenna efficiency, subtraction
of the baseline, approximation of the lines by the Gaussian profiles) were
done using the CLASS/ GILDAS package333Continuum and Line Analysis Single-Dish
Software http://www.iram.fr/IRAMFR/GILDAS.

##  3 Additional data

We used the data on the hydrogen column density along the line of sight
($N_{\rm H_{2}}$) and the dust temperature ($T_{\rm dust}$), obtained as a
result of processing the Herschel data in the Hi-GAL project (Molinari et al.,
2010) in order to determine the abundance of C2H. The processing algorithm was
presented by Marsh et al. (2015) and was applied to the objects from the Hi-
GAL survey by Marsh et al. (2017). The data were taken from the open
sources444http://www.astro.cardiff.ac.uk/research/ViaLactea/. Angular
resolution of the $N_{\rm H_{2}}$ and $T_{\rm dust}$ maps was 12″.

##  4 Analysis

To estimate the C2H column density ($N_{\rm C_{2}H}$, cm-2), we checked that
the ratio between the hyperfine components brightness temperatures is
consistent with optically thin emission. The ratio of the components at
87328.624 MHz to 87316.925 MHz was in the range of 0.48–0.52 (close to the
theoretical 0.50) in the observed positions. We also tried to analyse the
intensity ratio of the multiplet using the CLASS hfs procedure (that assumes
that the widths of all lines in the multiplet are equal). The approximation
did not converge due to the asymmetric line profiles (see below).

To measure $N_{\rm C_{2}H}$, we applied an LTE approximation in the optically
thin case (Eq. 1). Also, we used the Rayleigh-Jeans relation
$h\nu~{}\ll~{}kT$, which is valid in observations at 3 mm. The background
radiation temperature ($T_{\rm bg}=2.73$ K) was not taken into account, since
its value is negligible. Thus, the column density is determined as follows
(see, e.g., Mangum & Shirley, 2015):

$N_{\rm C_{2}H}={8\pi\nu_{\rm ul}^{2}{\rm{k}}\over A_{\rm
ul}{\rm{h}}c^{3}}\frac{Q}{g_{\rm u}}\frac{1}{f}\exp{\left({E_{\rm u}\over
kT_{\rm ex}}\right)}W_{\rm C_{2}H},$ (1)

where $\nu_{\rm ul}$ is the average weighted frequency of transition u $\to$ l
(Hz), that is computed taking into account the line strength of each hyperfine
component (see Table 1), $A_{\rm ul}$ is the Einstein coefficient for
spontaneous emission (s-1), $g_{\rm u}$ is the statistical weight of the
level, $Q$ is the rotational partition function, $E_{\rm u}$ is the the energy
of the upper level (ergs), k is the Boltzmann constant (ergs K-1), h is the
Planck constant (ergs s), c is the speed of light (cm s-1), $T_{\rm ex}$ is
the excitation temperature (K), $W_{\rm C_{2}H}$ is the integrated intensity
of the spectral line (K km s-1), $f$ is the filling factor of the telescope
beam.

The Einstein coefficient for entire transition $A_{\rm ul}$ is, in general
form, given by the formula:

$A_{\rm ul}={64\pi^{4}\over 3{\rm hc^{3}}}\nu^{3}_{\rm ul}{S_{\rm ul}\over
g_{\rm u}}\mu^{2},$ (2)

where the strength of the transition $S_{\rm ul}=1$ in our case because we
compute column density using the integrated intensity of the entire multiplet;
$\mu=7.7\times 10^{-19}$ CGS units (0.77 D) is the dipole moment of the
molecule.

Substituting Eq. 2 into Eq. 1, we obtain the following equation to estimate
the column density:

$N_{\rm C_{2}H}={3{\rm k}\over 8\pi^{3}\nu_{\rm
ul}\mu^{2}}\frac{Q}{f}\exp{\left({E_{\rm u}\over kT_{\rm ex}}\right)}W_{\rm
C_{2}H}.$ (3)

Table 1: Parameters of the C2H(1–0) hyperfine structure taken from CDMS. Transition | Frequency | $E_{\rm u}/{\rm k}$ | $g_{\rm u}$ | $S_{\rm ul}$
---|---|---|---|---
| [MHz] | [K] |  |
13/2,1 – 01/2,1 | 87284.156 | 4.2 | 3 | 0.17
13/2,2 – 01/2,1 | 87316.925 | 4.2 | 5 | 1.66
13/2,1 – 01/2,0 | 87328.624 | 4.2 | 3 | 0.83
11/2,1 – 01/2,1 | 87402.004 | 4.2 | 3 | 0.83
11/2,0 – 01/2,1 | 87407.165 | 4.2 | 1 | 0.33
11/2,1 – 01/2,0 | 87446.512 | 4.2 | 3 | 0.17

All the parameters in Eq. 3, excluding the product $Q\exp{({E_{\rm u}/({\rm
k}T_{\rm ex})})}W_{\rm C_{2}H}$, only depend on the transition type and the
structure of a molecule. The value of $Q$ depends on the excitation
temperature $T_{\rm ex}$, while $W_{\rm C_{2}H}$ is determined from
observations. For each observed position we computed $Q$ from the adopted
value of $T_{\rm ex}$, using an expression for linear molecules:

$Q=\frac{{\rm{k}}~{}T_{\rm ex}}{{\rm{h}}~{}B_{0}}+{1\over 3},$ (4)

where $B_{0}~{}=~{}43674.534~{}\times~{}10^{6}$ s-1 is the rotational constant
for the molecule.

We used the dust temperature $T_{\rm dust}$ as the excitation temperature
$T_{\rm ex}$. To do this, in the dust temperature map we selected the regions
with a diameter of 28″ (our beam size), centered at the positions of our
observations (see Fig. 1) and averaged the $T_{\rm dust}$ value over our beam
size. The standard deviations from the mean value was used as the uncertainty
of the $T_{\rm dust}$ and $N_{\rm H_{2}}$ values. Below we discuss a possible
inconsistency between the dust temperature and the excitation temperature for
the C2H(1–0) transition.

Molecular abundance ($x_{\rm C_{2}H}$) was determined relative to the column
density of the hydrogen nuclei (Eq. 5):

$x_{\rm C_{2}H}={N_{\rm C_{2}H}\over 2N_{\rm H_{2}}}.$ (5)

The values of integrated intensity $W_{\rm C_{2}H}$ were determined as an
integral of the brightness temperature $T_{\rm mb}$ over velocity of the
emission spectra using CLASS.

##  5 Results

The hyperfine components of the ethynyl $J=1-0$ transition were detected at
all observed positions. The spectrum of the entire hyperfine structure at
position 10 is shown in Fig. 2, while the four brightest components at all
positions are shown in Fig. 3. The brightest lines were found at positions
8–12, towards the molecular cloud. The hyperfine components (at frequencies
$\nu=87284.156$ MHz and $\nu=87446.512$ MHz) are poorly detected towards the
ionizing star LS 19 (position 1). Towards HD 253327 (position 18), only the
brightest components of the hyperfine structure were detected. The parameters
of the ethynyl emission lines are listed in Table 2. The line profiles are
asymmetric, they differ from the Gaussian shape by a higher intensity on the
red side (see, for example, the spectra at positions 2–4 and 13, close to the
ionizing stars). The flattened line profiles are also observed (for instance,
positions 3 and 14). The line profiles of the hyperfine components can be
different at the same position. The line profiles are symmetric at the central
positions 8–12. The line widths towards the ionizing stars ($\Delta v=3.5\pm
0.17$ km s-1 at position 1; $\Delta v=5.12\pm 0.71$ km s-1 at position 18) are
1.5–2 times higher than the widths towards the molecular cloud ($\Delta
v=2.37\pm 0.17$ km s-1 at position 10). The velocity of the line peak towards
the molecular cloud ($v=7.31$ km s-1) corresponds to the dip of the double-
peaked line towards the ionizing stars (for example, at positions 2, 3, 5, 14,
17, and 18, peaks at the velocities $\approx 5.5$ and 8.2 km s-1). The
distance between the peaks at the positions with the double-peaked line is
approximately 1–1.5 km s-1. Such a difference in velocities corresponds to the
characteristic expansion rate of the spherically-symmetric H ii regions (see,
e.g., Kirsanova et al., 2009; Kirsanova et al., 2019). All this indicates the
presence of several kinematic components along the line of sight near the
ionizing stars. Apparently, we observe the front and back molecular walls of
the H ii regions, which contribute to the formation of a blended components
with close velocities. Examples of position – velocity diagrams for expanding
envelopes around star-forming complexes with several H ii regions can be found
in works by Lozinskaya et al. (2003); Pokhrel et al. (2020). Despite the
quantitative difference between the characteristic expansion rates of star-
forming complexes and H ii regions around single stars, the qualitative
picture is similar (see also Kirsanova et al., 2020b).

Table 2: The parameters of the C2H(1–0) multiplet. The parameters marked by an asterisk (*) are determined using the hfs method, which considers them to be equivalent to a single Gaussian with different levels of relative intensity. The peak intensity $T_{\rm peak}$ was measured for the brightest component at the frequency $\nu=87316.925$ MHz using the gauss method. Position |  $v^{*}$, |  $\Delta v^{*}$, |  $T_{\rm peak}$, |  $W_{\rm C_{2}H}$,
---|---|---|---|---
| [km s-1] | [km s-1] | [K] | [K km s-1]
1 | 7.59 $\pm$ 0.17 | 3.43 $\pm$ 0.17 | 0.33 $\pm$ 0.02 | 2.98 $\pm$ 0.36
2 | 8.24 $\pm$ 0.17 | 3.08 $\pm$ 0.17 | 0.36 $\pm$ 0.03 | 3.45 $\pm$ 0.39
3 | 8.24 $\pm$ 0.17 | 2.90 $\pm$ 0.17 | 0.42 $\pm$ 0.03 | 3.32 $\pm$ 0.38
4 | 8.06 $\pm$ 0.17 | 2.63 $\pm$ 0.17 | 0.50 $\pm$ 0.03 | 3.47 $\pm$ 0.33
5 | 7.59 $\pm$ 0.17 | 3.07 $\pm$ 0.17 | 0.62 $\pm$ 0.04 | 4.89 $\pm$ 0.50
6 | 7.28 $\pm$ 0.17 | 2.73 $\pm$ 0.17 | 0.81 $\pm$ 0.04 | 5.68 $\pm$ 0.51
7 | 7.30 $\pm$ 0.17 | 2.09 $\pm$ 0.74 | 1.49 $\pm$ 0.03 | 8.18 $\pm$ 0.65
8 | 7.47 $\pm$ 0.17 | 2.12 $\pm$ 0.17 | 2.63 $\pm$ 0.06 | 15.09 $\pm$ 1.16
9 | 7.45 $\pm$ 0.17 | 2.19 $\pm$ 0.17 | 3.29 $\pm$ 0.06 | 19.80 $\pm$ 0.99
10 | 7.31 $\pm$ 0.17 | 2.37 $\pm$ 0.17 | 3.66 $\pm$ 0.11 | 24.46 $\pm$ 1.85
11 | 7.32 $\pm$ 0.17 | 2.33 $\pm$ 0.17 | 3.86 $\pm$ 0.08 | 25.23 $\pm$ 1.81
12 | 7.46 $\pm$ 0.17 | 2.41 $\pm$ 0.17 | 2.45 $\pm$ 0.07 | 16.95 $\pm$ 1.26
13 | 7.55 $\pm$ 0.17 | 3.02 $\pm$ 0.17 | 0.77 $\pm$ 0.04 | 6.09 $\pm$ 0.52
14 | 7.21 $\pm$ 0.17 | 3.47 $\pm$ 0.17 | 0.33 $\pm$ 0.02 | 2.82 $\pm$ 0.37
15 | 7.25 $\pm$ 0.17 | 3.33 $\pm$ 0.19 | 0.21 $\pm$ 0.02 | 2.16 $\pm$ 0.32
16 | 7.14 $\pm$ 0.17 | 3.77 $\pm$ 0.34 | 0.16 $\pm$ 0.01 | 1.49 $\pm$ 0.43
17 | 6.52 $\pm$ 0.23 | 4.27 $\pm$ 0.58 | 0.10 $\pm$ 0.01 | 1.43 $\pm$ 0.43
18 | 6.50 $\pm$ 0.29 | 5.12 $\pm$ 0.71 | 0.07 $\pm$ 0.01 | 1.02 $\pm$ 0.30
19 | 6.57 $\pm$ 0.50 | 4.12 $\pm$ 1.01 | 0.06 $\pm$ 0.01 | 0.24 $\pm$ 0.25
20 | 5.93 $\pm$ 0.31 | 4.11 $\pm$ 0.72 | 0.06 $\pm$ 0.02 | 0.44 $\pm$ 0.22
Figure 2: Emission spectrum of the C2H(1–0) transition at the position 10.
Figure 3: The brightest hyperfine components of the C2H(1–0) transition. The
position numbers correspond to Fig. 1.

The values of $T_{\rm ex}$ are listed in Table 3 and shown in Fig. 4a. The
excitation temperature reaches its maximum of $T_{\rm ex}=(28.6\pm 2.7)$ K at
the central position 10 (towards S255 IRS1 in the molecular cloud) and then
decreases at most by 5 K towards the ionizing stars. $N_{\rm H_{2}}$ reaches
its maximum towards S255 IRS1. Radial profile of $N_{\rm H_{2}}$ is shown in
Fig. 4b. It is similar to that of $T_{\rm ex}$ with a maximum at the position
10 and a gradual decrease towards both ionizing stars. The fact that $N_{\rm
H_{2}}$ does not decrease to zero at the positions 1 and 18 indicates the
presence of neutral gas towards the ionizing stars. This is consistent with
the assumption about the front and back walls of the H ii regions.

The column densities and the abundances of ethynyl are presented in Table 3
and shown in the lower panels in Fig. 4. The radial profile of $N_{\rm
C_{2}H}$ has the same shape as that of $N_{\rm H_{2}}$. The maximum column
density $N_{\rm C_{2}H}=11.78\pm 0.91\times 10^{14}$ cm-2 is reached at the
position 10. At the positions 1 and 18, the column density of ethynyl
decreases by an order of magnitude in S255 and 25 times in S257.

Having determined the value of $N_{\rm C_{2}H}$ under the LTE assumption, we
tested how close are the LTE and non-LTE estimates. For that purpose, we used
the RADEX package, which allows estimating the brightness of the emission
lines in the non-LTE model for given parameters of the medium: temperature,
density, line width, and column density of molecules (van der Tak et al.,
2007). We adopted the dust temperature as the kinetic temperature, the
observed line widths and our LTE-based estimates for $N_{\rm C_{2}H}$. Since
we have no information on the gas density in the molecular cloud, we estimated
the brightness of the theoretical spectra for several density values, namely
102, 103, and 104 cm-3. For the central positions, we achieved the agreement
of the observed brightness with the LTE and non-LTE models within 10% of the
intensities for the density of 104 cm-3. This value of density is reasonable
for molecular clouds. For the directions to the ionizing stars, the
theoretical non-LTE values of the brightness temperatures calculated for the
densities of 102-103 cm-3 (reasonable values of the density when moving from
molecular cloud to a star) are significantly (up to an order of magnitude)
lower than the observed. The calculated excitation temperatures are lower than
the adopted kinetic temperatures in those directions. To obtain the observed
line brightness, we would need to increase $N_{\rm C_{2}H}$ by an order of
magnitude. On the other hand, in the non-LTE simulation with the density of
104 cm-3, brightness of hyperfine components is reproduced within 10% towards
the ionizing stars also, which might be related to the presence of the dense
front and back molecular walls of the H ii regions. The $T_{\rm ex}$ values,
obtained in the non-LTE case, are of 4-6 K. Therefore, the ethynyl lines are
excited in sub-thermal regime. As the $N_{\rm C_{2}H}$ weakly depend on
excitation temperature at 3 mm, varying $T_{\rm ex}$ from 4-6 K to 25 K, we
obtain the results that differ within a factor of 2. To diminish the range of
parameters in the non-LTE modelling, it is necessary to carry out additional
observations of ethynyl lines corresponding to other transitions.

The ethynyl abundances at the positions 1-8 (towards the LS 19 star and
around, in S255) and 13–18 (HD 253327 and around, in S257) are higher in
comparison with the values at the positions 9-12. For example, towards the
molecular cloud, at the position 10, the abundance is $x_{\rm C_{2}H}=5.83\pm
5.07\times 10^{-9}$, while towards the ionizing stars (positions 1 and 18)
$x_{\rm C_{2}H}=13.91\pm 2.47\times 10^{-9}$ and $x_{\rm C_{2}H}=9.60\pm
2.83\times 10^{-9}$. A significant uncertainty in determination of the ethynyl
abundance towards the molecular cloud (for example, $x_{\rm C_{2}H}=10.18\pm
13.81\times 10^{-9}$ at the position 11) is due to the fact that at the
positions over which the value of $N_{\rm H_{2}}$ is averaged, there are
several bright spots in the $N_{\rm H_{2}}$ map. For this reason, the standard
deviation at the positions 8-11 is higher than at other positions. Therefore,
these uncertainties are formal values, and the real uncertainties are
determined by the brightness of the ethynyl lines. Nevertheless, we clearly
see the factor of 2 decrease in the $x_{\rm C_{2}H}$ values towards the
molecular cloud in comparison with rather flat areas of the radial profile
towards the H ii regions. The flat parts of the abundance profile suggest that
the H ii regions are surrounded by quasi-spherical molecular shells in which
ethynyl is distributed almost uniformly.

Figure 4: The profiles of the physical parameters: a) dust temperature adopted as the $T_{\rm ex}$ value, b) the H2 column density, c) the column density of C2H; d) the abundance of ethynyl. Table 3: The column densities and abundances of ethynyl in S255 and S257. Position |  $T_{\rm ex}$, |  $N_{\rm H_{2}}$, |  $N_{\rm C_{2}H}$, |  $x_{\rm C_{2}H}$,
---|---|---|---|---
| [K] |  $10^{20}$ [cm-2] |  $10^{14}$ [cm-2] | $10^{-9}$
1 | 25.3 $\pm$ 0.3 | 47.6 $\pm$ 6.2 | 1.33 $\pm$ 0.16 | 13.9 $\pm$ 2.5
2 | 25.3 $\pm$ 0.2 | 55.3 $\pm$ 3.6 | 1.53 $\pm$ 0.17 | 13.9 $\pm$ 1.8
3 | 25.0 $\pm$ 0.2 | 56.1 $\pm$ 7.6 | 1.47 $\pm$ 0.17 | 13.1 $\pm$ 2.3
4 | 24.8 $\pm$ 0.1 | 56.7 $\pm$ 17.4 | 1.52 $\pm$ 0.14 | 13.4 $\pm$ 4.3
5 | 24.8 $\pm$ 0.2 | 72.9 $\pm$ 31.2 | 2.15 $\pm$ 0.22 | 14.7 $\pm$ 6.5
6 | 24.9 $\pm$ 0.2 | 93.5 $\pm$ 44.7 | 2.50 $\pm$ 0.22 | 13.4 $\pm$ 6.5
7 | 24.9 $\pm$ 0.7 | 162.2 $\pm$ 71.2 | 3.60 $\pm$ 0.29 | 11.1 $\pm$ 4.9
8 | 23.9 $\pm$ 1.3 | 436.6 $\pm$ 365.2 | 6.48 $\pm$ 0.50 | 7.4 $\pm$ 6.2
9 | 25.7 $\pm$ 3.5 | 780.9 $\pm$ 483.2 | 8.89 $\pm$ 0.49 | 5.7 $\pm$ 3.5
10 | 28.6 $\pm$ 2.7 | 1011.0 $\pm$ 877.0 | 11.78 $\pm$ 0.91 | 5.8 $\pm$ 5.1
11 | 25.9 $\pm$ 2.1 | 559.3 $\pm$ 758.1 | 11.38 $\pm$ 0.83 | 10.2 $\pm$ 13.8
12 | 25.2 $\pm$ 0.6 | 159.9 $\pm$ 65.1 | 7.52 $\pm$ 0.56 | 23.5 $\pm$ 9.7
13 | 25.5 $\pm$ 0.4 | 75.7 $\pm$ 27.7 | 2.72 $\pm$ 0.23 | 18.0 $\pm$ 6.8
14 | 25.5 $\pm$ 0.6 | 48.5 $\pm$ 10.5 | 1.26 $\pm$ 0.17 | 13.09 $\pm$ 3.3
15 | 25.1 $\pm$ 0.4 | 38.0 $\pm$ 6.0 | 0.96 $\pm$ 0.14 | 12.6 $\pm$ 2.7
16 | 24.6 $\pm$ 0.2 | 30.6 $\pm$ 2.4 | 0.65 $\pm$ 0.19 | 10.6 $\pm$ 3.2
17 | 24.1 $\pm$ 0.4 | 25.5 $\pm$ 3.0 | 0.62 $\pm$ 0.19 | 12.1 $\pm$ 3.9
18 | 23.8 $\pm$ 0.2 | 22.8 $\pm$ 0.6 | 0.44 $\pm$ 0.13 | 9.6 $\pm$ 2.8
19 | 23.8 $\pm$ 0.3 | 24.0 $\pm$ 1.4 | 0.10 $\pm$ 0.11 | 2.1 $\pm$ 2.2
20 | 23.4 $\pm$ 0.5 | 26.6 $\pm$ 1.7 | 0.19 $\pm$ 0.09 | 3.5 $\pm$ 1.8

##  6 Discussion

For the efficient formation of ethynyl, it is necessary to have C+ ion and
molecular hydrogen H2 (see Dalgarno & Black, 1976; Sternberg & Dalgarno, 1995;
Sakai & Yamamoto, 2013) in the gas-phase; these conditions are met in PDRs. In
molecular clouds, carbon is bounded mainly in CO molecules due to the
shielding of stellar UV radiation by dust and H2 molecules. Therefore, the
$x_{\rm C_{2}H}$ value decreases in the molecular cloud at the positions 7-13
due to the conversion of carbon into CO. Approximately equal abundances of
ethynyl towards the H ii regions indicates that the chemical evolution of the
surrounding PDRs proceeds in a similar way. This is not surprising, since
these H ii regions have similar sizes and they are ionised by stars of similar
spectral types. We note that several point sources are visible in the optical
(e.g., Fig. 1) and IR images (e.g., 2MASS) at the positions 12-13. In
particular, the position 12 contains an emission-line star S255 1, with
observed H$\alpha$ line (Alvarez & Hoare, 2005, bright spots are also visible
in our Fig. 1) and a Herbig-Haro object S255 H2 1 (Miralles et al., 1997).
Nearby X-ray source CXOU J061250.6+175909, a young low-mass star in the
S255-IR cluster, is located there (Mucciarelli et al., 2011). It is quite
possible that the ionizing radiation in the vicinity of these point sources
leads to a local increase of the ethynyl abundance due to the ionization of
carbon-containing molecules with the release of the C+ ion, which takes part
in the chemical chains of the ethynyl formation. There are no specific
features in the radial profiles of the ethynyl abundances towards the
ionization front (positions 6 and 16 for S255 and S257, respectively). The
values of $T_{\rm dust}\approx 23-25$ K at these positions correspond to the
UV field with $G_{0}=50-100$ in units of the Habing field (see, for example
Kirsanova et al., 2020a). The values of $G_{0}$ in S255–S257 are close to that
found in the Horsehead PDR, therefore it is necessary to make additional
observations of other ethynyl transitions in order to obtain accurate radial
profiles of the abundances and to compare ethynyl abundances at the ionised
edge of the Horsehead PDR and in the vicinity of the ionization front in
S255–S257.

Zinchenko et al. (2020) observed the C2H (4–3) lines towards S255 IRS1 with
ALMA and estimated the ethynyl column density there. Despite the difference in
the spatial resolution, the estimates agree within a factor of 5 (our estimate
is lower), indicating that ethynyl is present in the dense molecular cloud.

The values of the $N_{\rm C_{2}H}$ in the vicinity of the ionizing stars are
similar to those found in the Horsehead, IC 63 (Teyssier et al., 2004), and M
8 (Tiwari et al., 2019). Moving closer to the gas column density peak in the
molecular cloud, we find higher values of $N_{\rm C_{2}H}$ similar to the
values observed in the Orion Bar PDR (Cuadrado et al., 2015) and some other
molecular clouds (see, e.g., Pirogov et al., 2016; Bouvier et al., 2020). The
maximum observed values of $N_{\rm C_{2}H}$ at the positions 10 and 11 are
comparable with the values found in OMC-1 (Ungerechts et al., 1997, see also
Fig. 10 in Bouvier et al. (2020)). The abundances of ethynyl in S255–257 are
similar to the value observed in the Orion Bar PDR. Namely, according to the
estimates made by Cuadrado et al. (2015), the abundance of $(0.7-2.7)\times
10^{-8}$ in an object with the radiation field $G_{0}\approx 10^{4}-10^{5}$
can be explained using the high-temperature chemical reactions with excited
molecular hydrogen. In S255–257, a comparable abundance of ethynyl is observed
at by two orders of magnitude lower $G_{0}$. Thus, the PDRs in S255–S257 are
interesting for astrochemical modelling.

##  7 Conclusions

We summarise our main results below:

  1. 1.

We present observations of the C2H molecule in the H ii regions S255 and S257
at twenty positions along the straight lines connecting the IR source S255
IRS1, located in the molecular cloud, with the ionizing stars in each of the
regions, LS 19 and HD 253327.

  2. 2.

The brightest emission of ethynyl is observed towards the molecular cloud
(brightness temperature $\approx 4$ K), the weakest one – towards the ionizing
stars ($<0.5$ K). The largest line widths are found towards the ionizing stars
($\approx 3-5$ km s-1), while the smallest ones are found towards the
molecular cloud in between the H ii regions ($\approx 2$ km s-1). The spectral
line profiles indicate that several kinematic components exist in the
molecular envelopes of the H ii regions. The components are resolved on the
line of sight towards the ionizing stars. The components can be the front and
back walls of the H ii regions.

  3. 3.

We determine the column densities and the abundances of ethynyl at all twenty
studied positions. The maximum value of the column density $\approx 12\times
10^{14}$ cm–2 is found towards the centre of the molecular cloud; it decreases
closer to the ionizing stars in both directions. The minimum abundances, on
the contrary, are found towards the molecular cloud ($6\times 10^{-9}$), while
towards the ionizing stars the abundances are about two times higher. The
maximum ethynyl abundance of $2\times 10^{-8}$ is found towards the point
sources in the molecular cloud, namely, emission-line stars or X-ray sources.

## Acknowledgements

We are grateful to L. E. Pirogov, S. V. Kalenskii for valuable advice on the
observational data processing, to D. A. Semenov for the discussion on the
chemistry of ethynyl, and to the anonymous referee for valuable comments.

This study was supported by Russian Foundation for Basic research (contract
No. 20-02-00643 A). A. F. Punanova is a member of the Max-Planck-Gesellschaft
partner group in the Ural Federal University. A. F. Punanova is supported by
the Russian Ministry of Science and Higher Education via state assignment
FEUZ-2020-0038.

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