11institutetext:  Instituto de Física Fundamental, CSIC, C/ Serrano 123,
E-28006 Madrid, Spain
11email<EMAIL_ADDRESS>22institutetext: LERMA, Observatoire de
Paris, PSL Research University, CNRS, Sorbonne Université, F-92190, Meudon,
France

# First detection of doubly deuterated methyl acetylene
(CHD2CCH and CH2DCCD)††thanks: Based on observations carried out with the IRAM
30m Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN
(Spain).

M. Agúndez 11 E. Roueff 22 C. Cabezas 11 J. Cernicharo 11 N. Marcelino 11

(Received; accepted)

We report the first detection in space of the two doubly deuterated
isotopologues of methyl acetylene. The species CHD2CCH and CH2DCCD were
identified in the dense core L483 through nine and eight, respectively,
rotational lines in the 72-116 GHz range using the IRAM 30m telescope. The
astronomical frequencies observed here were combined with laboratory
frequencies from the literature measured in the 29-47 GHz range to derive more
accurate spectroscopic parameters for the two isotopologues. We derive beam-
averaged column densities of (2.7 $\pm$ 0.5) $\times$ 1012 cm-2 for CHD2CCH
and (2.2 $\pm$ 0.4) $\times$ 1012 cm-2 for CH2DCCD, which translate to
abundance ratios CH3CCH/CHD2CCH = 34 $\pm$ 10 and CH3CCH/CH2DCCD = 42 $\pm$
13\. The doubly deuterated isotopologues of methyl acetylene are only a few
times less abundant than the singly deuterated ones, concretely around 2.4
times less abundant than CH3CCD. The abundances of the different deuterated
isotopologues with respect to CH3CCH are reasonably accounted for by a gas-
phase chemical model in which deuteration occurs from the precursor ions
C3H6D+ and C3H5D+, when the ortho-to-para ratio of molecular hydrogen is
sufficiently low. This points to gas-phase chemical reactions, rather than
grain-surface processes, as responsible for the formation and deuterium
fractionation of CH3CCH in L483. The abundance ratios CH2DCCH/CH3CCD = 3.0
$\pm$ 0.9 and CHD2CCH/CH2DCCD = 1.25 $\pm$ 0.37 observed in L483 are
consistent with the statistically expected values of three and one,
respectively, with the slight overabundance of CHD2CCH compared to CH2DCCD
being well explained by the chemical model.

###### Key Words.:

astrochemistry – line: identification – molecular processes – ISM: molecules –
radio lines: ISM

##  1 Introduction

Deuterium fractionation is an extraordinary tool to study the early stages of
star formation, in particular, the pre-stellar core phase, where the cold
temperatures and high CO depletion offer optimal conditions to enrich
molecules in deuterium, and the protostellar Class 0 phase, where the gas
displays some of the largest levels of deuteration observed as a consequence
of the inheritance of gas and ice molecules enriched in deuterium during the
pre-stellar core phase (Ceccarelli et al., 2014). The cosmic D/H ratio is
$1.5\times 10^{-5}$ (Linsky, 2003), but deuterium fractionation is so
efficient in these environments that deuterated molecules can reach abundances
as high as 30-40 % relative to the parent hydrogenated species, as occurs for
HDCS (Marcelino et al., 2005) and CH2DOH (Parise et al., 2006). Moreover, for
abundant molecules containing more than one hydrogen atom, multiply deuterated
forms have been observed with abundance enhancements of many orders of
magnitude over the statistically expected value.

Molecules with two deuterium atoms observed to date comprise D2CO (Turner,
1990; Ceccarelli et al., 1998), NHD2 (Roueff et al., 2000), CHD2OH (Parise et
al., 2002), D2S (Vastel et al., 2003), D2H+ (Vastel et al., 2004; Parise et
al., 2011), D2CS (Marcelino et al., 2005), D2O (Butner et al., 2007), $c$-C3D2
(Spezzano et al., 2013), CHD2CN (Calcutt et al., 2018), HCOOCHD2 (Manigand et
al., 2019), and ND2 (Melosso et al., 2020; Bacmann et al., 2020). Even a
couple of triply deuterated molecules have been detected: ND3 (Lis et al.,
2002; van der Tak et al., 2002; Roueff et al., 2005) and CD3OH (Parise et al.,
2004). Multiply deuterated molecules have abundances relative to the
hydrogenated species ranging from $5\times 10^{-5}$, in the case of D2O for
hot corino conditions (Butner et al., 2007), to values of the order of 10 % in
cold dark cloud environments, which may become comparable to those of the
corresponding singly deuterated species, as occurs for D2CS (Marcelino et al.,
2005; Vastel et al., 2018; Agúndez et al., 2019) and D2CO (Parise et al.,
2006). It is remarkable that in the case of the ion H${}_{3}^{+}$, whose
deuterated species drive most of the deuterium fractionation in the gas phase,
the doubly deuterated form (first detected unambiguously by Parise et al.
2011) has an abundance similar to that of the singly deuterated species.
Moreover, chemical models predict that the different deuterated species H2D+,
D2H+, and D${}_{3}^{+}$ become occasionally more abundant than H${}_{3}^{+}$
itself for some time intervals and specific physical conditions (Roberts et
al., 2004; Sipilä et al., 2017).

Multiply deuterated molecules allow to put constraints on the deuteration
mechanism, either in the gas phase or in the surface of dust grains, and by
extension on the formation process of the precursor hydrogenated molecule. If
deuterium fractionation occurs in the gas phase, the resulting abundance
ratios between singly, doubly, and even triply deuterated forms of a given
molecule vary depending on the abundances of H2D+, D2H+, and D${}_{3}^{+}$ and
the efficiency of the reactions of deuteron transfer from these ions, which in
turn depend on parameters like the gas kinetic temperature, the level of CO
depletion, and the ortho-to-para ratio of H2 (Roberts et al., 2004; Roueff et
al., 2005; Flower et al., 2006). If deuteration occurs on grains surfaces, the
relative abundances of the different deuterated forms of a molecule are
expected to follow a statistical pattern as they should basically depend on
the relative arrival rates on grains of D and H atoms from the gas phase and
thus on the abundance ratio between atomic D and H in the gas phase (Brown &
Millar, 1989).

Table 1: Observed line parameters of CHD2CCH and CH2DCCD in L483.

Transition | Frequency | $\Delta v$ |  $T_{A}^{*}$ peak | $\int T_{A}^{*}dv$
---|---|---|---|---
| (MHz) |  (km s-1) | (mK) |  (mK km s-1)
CHD2CCH
51,5-41,4 | 76643.616 | 0.47(6) | 12.9 | 6.5(6)
50,5-40,4 | 76979.250 | 0.37(4) | 33.0 | 13.1(11)
51,4-41,3 | 77317.279 | 0.42(5) | 21.5 | 9.7(11)
61,6-51,5 | 91971.307 | 0.29(4) | 17.4 | 5.3(8)
60,6-50,5 | 92372.787 | 0.27(2) | 31.0 | 8.9(7)
61,5-51,4 | 92779.672 | 0.30(6) | 17.4 | 5.6(9)
71,7-61,6 | 107298.386 | 0.30(6) | 13.7 | 4.4(7)
70,7-60,6 | 107765.046 | 0.29(3) | 28.3 | 8.7(9)
71,6-61,5 | 108241.467 | 0.39(7) | 15.5 | 6.5(9)
CH2DCCD
51,5-41,4 | 73589.402 | 0.31(5) | 12.5 | 4.2(7)
50,5-40,4 | 73861.275 | 0.35(5) | 24.8 | 9.1(13)
51,4-41,3 | 74133.292 | 0.36(10) | 11.4 | 4.4(11)
61,6-51,5 | 88306.511 | 0.42(9) | 12.0 | 5.4(9)
61,5-51,4 | 88959.161 | 0.36(8) | 15.3 | 5.9(9)
71,7-61,6 | 103023.214 | 0.35(6) | 11.4 | 4.2(6)
70,7-60,6 | 103402.198 | 0.34(3) | 23.6 | 8.5(6)
71,6-61,5 | 103784.607 | 0.41(9) | 8.9 | 3.9(6)

Numbers in parentheses are 1$\sigma$ uncertainties in units of the last
digits. Line parameters were derived from a Gaussian fit to the line profile.
Observed frequencies are obtained adopting $V_{\rm LSR}$ = 5.30 km s-1
(Agúndez et al., 2019) and have an uncertainty of 20 kHz for all the lines.
$\Delta v$ is the full width at half maximum.

For molecules with various hydrogen atoms among which some of them are
equivalent, the relative abundances of the different deuterated variants can
also give clues on the formation of the molecule. For example, for methanol
(CH3OH) deuteration on the methyl group is three times more probable than on
the hydroxyl group, but observed CH2DOH/CH3OD ratios differ significantly from
the statistical value of three, with values well above or below depending on
the source (Parise et al., 2006; Ratajczak et al., 2011; Agúndez et al.,
2019). The case of methyl acetylene (CH3CCH) is also interesting as, similarly
to methanol, it contains a methyl group with three equivalent H atoms and one
non-equivalent H atom in the terminal CCH group. The two singly deuterated
forms of CH3CCH, CH2DCCH and CH3CCD, were first detected in the interstellar
medium by Gerin et al. (1992) and Markwick et al. (2005), respectively. Using
the ARO 12m telescope, Markwick et al. (2005) reported CH2DCCH/CH3CCD ratios
in the range 1.20-2.04 along the TMC-1 ridge, significantly different from the
statistical value of three, although in L483 the observed ratio is consistent
with the statistical value (Agúndez et al., 2019).

Here we report the first identification in space of the two forms of doubly
deuterated methyl acetylene: CHD2CCH and CH2DCCD. These species were detected
toward the dense core L483 using the IRAM 30m telescope. The observation of
the two singly and two doubly deuterated forms of methyl acetylene stimulated
us to build a gas-phase chemical model, including multiply deuterated species,
to investigate the mechanisms of deuteration of CH3CCH in L483.

##  2 Observations

The target of the observations, L483, is a dark cloud core located in the
Aquila Rift star-forming region, which hosts an embedded infrared source, IRAS
18148$-$0440, classified as a Class 0 object. The observations were carried
out with the IRAM 30m telescope in the frame of a $\lambda$ 3 mm line survey
covering the 80-116 GHz range (Agúndez et al., 2019). Additional observations
in the 72-80 GHz range were taken with the IRAM 30m telescope in December
2018. During this observing run, weather conditions were good, with 4-5 mm of
precipitable water vapor.

We describe briefly the observations. For more details we refer to Agúndez et
al. (2019). We used the EMIR receiver E090 connected to a fast Fourier
transform spectrometer providing a spectral resolution of 50 kHz. All
observations were carried out using the frequency-switching technique, with a
frequency throw of 7.2 MHz. Intensities are expressed in terms of $T_{A}^{*}$,
the antenna temperature corrected for atmospheric absorption and for antenna
ohmic and spillover losses. The uncertainty in $T_{A}^{*}$ is estimated to be
10 %. The antenna temperature $T_{A}^{*}$ can be converted to main beam
brightness temperature $T_{\rm mb}$ by dividing by $B_{\rm eff}$/$F_{\rm
eff}$, where $B_{\rm eff}$ = 0.871 $\exp{[-(\nu{\rm(GHz)}/359)^{2}]}$ and
$F_{\rm eff}$ = 0.95111http://www.iram.es/IRAMES/mainWiki/Iram30mEfficiencies.
Pointing errors were typically 2-3′′ and the half power beam width of the IRAM
30m telescope ranges between 34′′ at 72 GHz and 21′′ at 116 GHz. All data were
reduced using the program CLASS of the GILDAS software
package222http://www.iram.fr/IRAMFR/GILDAS.

##  3 Results

###  3.1 Detection of CHD2CCH and CH2DCCD in L483

Figure 1: Observed lines of CHD2CCH in L483 in the 72-116 GHz range. The
systemic velocity of L483 (5.30 km s-1) is indicated by a vertical dotted blue
line. Green lines are Gaussian fits to each line profile. Frequencies and line
parameters are given in Table 1. Figure 2: Observed lines of CH2DCCD in L483
in the 72-116 GHz range. The systemic velocity of L483 (5.30 km s-1) is
indicated by a vertical dotted blue line. Green lines are Gaussian fits to
each line profile. Frequencies and line parameters are given in Table 1. The
$6_{0,6}$-$5_{0,5}$ line is not detected because it overlaps with the strong
HCN $J=1$-0 line.

In the data of L483 covering the 72-116 GHz frequency range there are several
lines which could not be assigned to any known molecule after inspection of
the CDMS333https://cdms.astro.uni-koeln.de/ (Müller et al., 2005) and
JPL444https://spec.jpl.nasa.gov/ (Pickett et al., 1998) catalogues. Several of
these unidentified lines could be grouped in sets of three lines with harmonic
relations 5/6/7, with rotational constants around either 7700 MHz or 7400 MHz.
These values are close to the rotational constants $B$ or $(B+C)/2$ of the
isotopologues of methyl acetylene. For example, for CH3CCD the rotational
constant $B$ is 7788 MHz and for CH2DCCH the value of $(B+C)/2$ is 8091 MHz
(Le Guennec et al., 1993). A closer inspection of the private catalogue of J.
Cernicharo generated from the MADEX
code555https://nanocosmos.iff.csic.es/?page_id=1619 (Cernicharo, 2012)
revealed that the observed frequencies of these sets of harmonically related
lines differ by 0.9-2.7 MHz and 0.2-1.7 MHz from the frequencies predicted for
rotational transitions of CHD2CCH and CH2DCCD, respectively. The rotational
spectrum of these two molecules has been measured in the laboratory in the
frequency range 29-47 GHz with uncertainties of 0.1 MHz in the frequencies
(Thomas et al., 1955). Using these data, the frequencies predicted for the
72-116 GHz range have errors of a few MHz, and this is the reason why some of
the unidentified lines seen in the 80-116 GHz range were not properly assigned
to CHD2CCH and CH2DCCD by Agúndez et al. (2019). In fact, the identification
of these two molecules reduces drastically the number of lines pending of
identification in the $\lambda$ 3 mm line survey of L483 (see Table A.2 of
Agúndez et al. 2019). The parameters derived for the lines assigned to the two
doubly deuterated isotopologues of methyl acetylene are given in Table 1 and
the observed line profiles are shown in Fig. 1 for CHD2CCH and in Fig. 2 for
CH2DCCD. We note that the line at 91971.307 MHz, assigned to the 61,6-51,5
transition of CHD2CCH, was incorrectly assigned to the transition 53-43 $F$ =
6-5 of CH3CN by Agúndez et al. (2019).

The astronomical frequencies observed in the 72-116 GHz range (see Table 1)
and the laboratory frequencies measured in the 29-47 GHz range (Thomas et al.,
1955) were used to derive more accurate spectroscopic parameters for CHD2CCH
and CH2DCCD (see Table 2). These constants improve considerable over those
reported by Thomas et al. (1955) and allow to predict the rotational spectrum
of the two molecules with an accuracy better than 0.1 MHz up to 200 GHz. Since
the lines of doubly deuterated CH3CCH are relatively bright in L483, it would
not be surprising to detect the triply deuterated species CHD2CCD, which
should be three times more abundant than CD3CCH. However, the rotational
spectrum has only been measured in the 28-43 GHz range with a modest accuracy
(Thomas et al., 1955), which may translate to frequency errors of a few MHz
for lines lying above 72 GHz. It would therefore be interesting to measure the
rotational spectrum of triply deuterated CH3CCH at millimeter wavelengths.

Table 2: Spectroscopic parameters of CHD2CCH and CH2DCCD.

Parameter |  CHD2CCH |  CH2DCCD
---|---|---
$A_{0}$ (MHz) ……………………. | 95746(533) | 119688.0(170)
$B_{0}$ (MHz) ……………………. | 7765.71927(255) | 7440.77759(341)
$C_{0}$ (MHz) ……………………. | 7630.99013(254) | 7332.00345(340)
$\Delta_{J}$ (kHz) …………………….. | 2.3807(270) | 2.0759(347)
$\Delta_{JK}$ (kHz) …………………… | 123.83(224) | 118.93(295)
$N$ a …………………………….. | 16 | 17
rms (kHz) b …………………. | 52 | 80

Numbers in parentheses are 1$\sigma$ uncertainties in units of the last
digits.
a Number of lines included in the fit. For CHD2CCH, $J_{\rm max}$ = 7, $K_{\rm
max}$ = 2, and $\nu_{\rm max}$ = 108.241 GHz, and for CH2DCCD, $J_{\rm max}$ =
7, $K_{\rm max}$ = 2, and $\nu_{\rm max}$ = 103.784 GHz. b Root mean square of
the fit.

###  3.2 Observed column densities

We derived beam-averaged column densities for methyl acetylene and its singly
and doubly deuterated isotopologues in L483 assuming local thermodynamic
equilibrium. Values for CH3CCH and the two singly deuterated forms were
already reported by Agúndez et al. (2019). Here we have revised some of these
values including new lines observed in the 72-80 GHz range and using new
values for the electric dipole moments.

Table 3: Column densities and ratios for CH3CCH and its singly and doubly
deuterated species in L483.

Species |  $\mu$ (D) a |  $N_{\rm lines}$ e |  $E_{\rm up}$ (K) f |  $T_{\rm rot}$ (K) |  $N$ (cm-2) h |  |  Column density ratio i
---|---|---|---|---|---|---|---
CH3CCH |  0.7839 b | 8 | 11.5 - 82.3 |  10.2 g | $9.10\times 10^{13}$ |  |  |
CH2DCCH |  0.7850 c | 15 | 11.6 - 43.6 | $10.2\pm 0.7$ | $(1.76\pm 0.34)\times 10^{13}$ |  |  CH3CCH / CH2DCCH | $5.2\pm 1.6$
CH3CCD |  0.7698 d | 6 | 10.5 - 20.9 |  10.2 g | $5.79\times 10^{12}$ |  |  CH3CCH / CH3CCD | $15.7\pm 4.7$
CHD2CCH |  0.7870 c | 9 | 11.1 - 25.0 |  10.2 g | $2.69\times 10^{12}$ |  |  CH3CCH / CHD2CCH | $33.8\pm 10.1$
CH2DCCD |  0.7711 c | 8 | 10.6 - 25.3 |  10.2 g | $2.16\times 10^{12}$ |  |  CH3CCH / CH2DCCD | $42.1\pm 12.6$

a Dipole moments along the principal axis $a$. b Experimental value from
Burrell et al. (1980). c Calculated value (this work). d Experimental value
from Muenter & Laurie (1966) corrected for a more accurate dipole moment of
the reference OCS than used by these authors (see text). e Number of lines
observed. f Range of upper level energies of the lines observed. g Rotational
temperature has been fixed to the value derived for CH2DCCH. h Errors in the
column densities are estimated to be 20 %. i Errors in the column density
ratios are estimated to be 30 %.

The dipole moment of CH3CCH was experimentally measured by Burrell et al.
(1980) to be 0.7839 D. For CH3CCD, the dipole moment was measured by Muenter &
Laurie (1966). Here we adopt the value measured by these latter authors
corrected by using a more accurate value of the dipole moment of OCS, which is
used as reference (see Burrell et al. 1980). The dipole moment of CH3CCD turns
out to be only $\sim 2\leavevmode\nobreak\ \%$ lower than that of CH3CCH (see
Table 3). For CH2DCCH, CHD2CCH, and CH2DCCD, all of which are asymmetric
rotors, dipole moments are not known, and we thus evaluated them using quantum
chemical calculations. Since for these species the dipole moment is only due
to vibrational effects connected to isotopic substitution, anharmonic force
field calculations were required. All the calculations were done using the
orbital-dependent functional (dubbed B2PLYP) (Grimme, 2006) with the Becke-
Johnson D3(BJ) damping function (Risthaus & Grimme, 2013) and the Dunning’s
basis set cc-pVTZ (Dunning, 1989). In order to obtain more reliable values we
also calculated the dipole moments for CH3CCH, CD3CCH, CH3CCD and CD3CCD,
whose dipole moments are experimentally known (Muenter & Laurie, 1966; Burrell
et al., 1980). In this manner, we obtained an experimental/theoretical ratio
that was used to correct the theoretical values for CH2DCCH, CHD2CCH, and
CH2DCCD. The calculated dipole moments along the principal axis $a$, which is
the relevant parameter since the observed lines are of $a$-type, are given in
Table 3. It is found that they differ only slightly, up to $\sim
2\leavevmode\nobreak\ \%$, from that of CH3CCH.

For CH3CCD we now include two new lines, the 50-40 and 51-41, observed in the
72-80 GHz range. For CH3CCH, we observed lines with $K=0,1,2,3$, and thus the
column density includes these four $K$ ladders, although the $K=0$ and $K=1$
levels account for most of the column density (92 %). For CH3CCD only $K=0$
and $K=1$ lines were observed. Among all isotopologues of methyl acetylene,
CH2DCCH has the most precise determination of the rotational temperature, 10.2
$\pm$ 0.7 K, due to the higher number of lines observed and the wider range of
upper level energies involved. We therefore adopted this value for all other
isotopologues when deriving column densities. We note that if the rotational
temperature is not fixed, the values obtained are consistent with the
rotational temperature of 10.2 K adopted. For example, for CHD2CCH we obtain a
rotational temperature of 9.3 $\pm$ 1.3 K while for CH2DCCD we get 11.4 $\pm$
2.0 K. The rotational partition function was computed by summation including
energy levels up to $J$ = 100. For guidance, in Table 4 we give rotational
partition functions for CHD2CCH and CH2DCCD at different temperatures. The
column densities derived in L483 for CH3CCH and its singly and doubly
deuterated forms are given in Table 3. Deuterium ratios for various molecules
in L483 have been discussed by Agúndez et al. (2019). Regarding doubly
deuterated methyl acetylene, the two forms show a deuterium enrichment
comparable to H2CO and H2CS, which show the largest levels of deuteration in
L483 (H2CO/D2CO = 31.3 and H2CS/D2CS = 21.7; Agúndez et al. 2019), and are
significantly more enriched in deuterium than CH3OH and $c$-C3H2, for which
CH3OH/CHD2OH = 357 and $c$-C3H2/$c$-C3D2 = 103 (Agúndez et al., 2019).

Table 4: Rotational partition functions for CHD2CCH and CH2DCCD.

Temperature (K) |  $Q_{rot}$ a
---|---
|  CHD2CCH |  CH2DCCD
300.0 | 11646.9629 | 10855.0235
225.0 | 7563.8563 | 7049.8187
150.0 | 4117.1979 | 3837.5133
75.00 | 1456.4144 | 1357.4949
37.50 | 515.6773 | 480.6346
18.75 | 182.8944 | 170.4479
9.375 | 65.0786 | 60.6361
5.000 | 25.6362 | 23.8844
2.725 | 10.5863 | 9.9782

a Computed including energy levels up to $J$ = 100.

##  4 Chemical model

To our knowledge, detailed studies of multiple deuteration have been
essentially focused on simple hydrides, like H2O, NH2, and NH3 (Sipilä et al.,
2015; Furuya et al., 2015; Roueff et al., 2005; Hily-Blant et al., 2018;
Bacmann et al., 2020), and molecules containing a single carbon atom, like
H2CO, H2CS, and CH3OH (Marcelino et al., 2005; Parise et al., 2006; Taquet et
al., 2012). Multiple deuteration proceeds essentially in the gas phase through
successive reactions of HD with H${}_{3}^{+}$, H2D+, and D2H+, and with
CH${}_{3}^{+}$, CH2D+, and CHD${}_{2}^{+}$, as introduced by Roberts et al.
(2004). Additional deuterium exchange reactions with HD suggested to be
considered for carbon chain molecules involve C2H${}_{2}^{+}$ and C2HD+
(Turner, 2001). We further introduce exchange reactions of C3H+ with HD and
D2, which have been studied by Savić & Gerlich (2005); Savić et al. (2005) as
displayed in Table 5. We estimate the endothermicity for the reverse reactions
from the values reported for the cyclic and the linear isomers of C3H and C3D
(Etim et al., 2020).

We consider here a pure gas-phase chemical network including species
containing up to three deuterium atoms, extending our previous study on the
recent detection of HDCCN in TMC-1 (Cabezas et al., 2021). As an example, let
us mention that, in order to comply with the present observational challenges,
we introduced the various isomers of deuterated methyl acetylene CH2DCCH,
CH3CCD, CHD2CCH, CH2DCCD, CD3CCH, and CHD2CCD. The final chemical network
comprises 394 species linked through more than 14,000 reactions. When no
experimental information is available, we assume that the total rate
coefficient of reactions involving deuterium atoms is identical to that with
hydrogenated compounds. The derivation of branching ratios is principally
based on statistical considerations.

Table 5: Reactions involving C3H+ and C3D+.

Reaction |  $\alpha$ (cm3s-1) |  $\gamma$ (K) | Ref.
---|---|---|---
C3H+ \+ HD $\rightleftarrows$ C3D+ \+ H2 | $5.6\times 10^{-11}$ | 500 - 375 | (1)
C3H+ \+ D2 $\rightleftarrows$ C3D+ \+ HD | $3.0\times 10^{-13}$ | 420 - 320 | (1)
C${}_{3}^{+}$ \+ H2 $\rightarrow$ C3H+ \+ H | $1.7\times 10^{-9}$ |  | (1)
C${}_{3}^{+}$ \+ HD $\rightarrow$ C3D+ \+ H | $9.3\times 10^{-10}$ |  | (1)
C${}_{3}^{+}$ \+ HD $\rightarrow$ C3H+ \+ D | $7.6\times 10^{-10}$ |  | (1)
C${}_{3}^{+}$ \+ D2 $\rightarrow$ C3D+ \+ D | $1.3\times 10^{-9}$ |  | (1)
C3H+ \+ H2 $\rightarrow$ c-C3H${}_{2}^{+}$ \+ H | $1.0\times 10^{-12}$ |  | (2)
C3H+ \+ HD $\rightarrow$ c-C3HD+ \+ H | $4.6\times 10^{-10}$ |  | (1)
C3H+ \+ HD $\rightarrow$ c-C3H${}_{2}^{+}$ \+ D | $3.0\times 10^{-12}$ |  | (1)
C3H+ \+ D2 $\rightarrow$ c-C3HD+ \+ D | $1.0\times 10^{-11}$ |  | (1)
C3H+ \+ D2 $\rightarrow$ c-C3D${}_{2}^{+}$ \+ H | $2.7\times 10^{-11}$ |  | (1)
C3D+ \+ H2 $\rightarrow$ c-C3HD+ \+ H | $1.0\times 10^{-12}$ |  | (3)
C3D+ \+ HD $\rightarrow$ c-C3HD+ \+ H | $1.0\times 10^{-10}$ |  | (1)
C3D+ \+ HD $\rightarrow$ c-C3D${}_{2}^{+}$ \+ H | $8.3\times 10^{-11}$ |  | (1)
C3D+ \+ D2 $\rightarrow$ c-C3D${}_{2}^{+}$ \+ D | $1.7\times 10^{-10}$ |  | (1)

The rate coefficient, $\alpha$, corresponds to the value reported at 10 K or
15 K in reference (1). The first two displayed reactions correspond to
deuterium exchange and $\gamma$ stands for the estimated endothermicity (see
text) of the reverse reaction.
References: (1) Savić & Gerlich (2005); (2) Loison et al. (2017); (3) assumed.

Table 6: Reactions involving ortho H2.

Reaction |  $\alpha$ (cm3s-1) | $\beta$ |  $\gamma$ (K) | Ref.
---|---|---|---|---
$o$-H2 \+ H2D+ $\rightarrow$ HD + H${}_{3}^{+}$ | $9.4\times 10^{-11}$ |  $-$0.79 | 56.0 | (1)
$o$-H2 \+ D2H+ $\rightarrow$ HD + H2D+ | $3.3\times 10^{-10}$ |  $-$0.55 | 23.1 | (1)
$o$-H2 \+ D2H+ $\rightarrow$ D2 \+ H${}_{3}^{+}$ | $3.5\times 10^{-11}$ |  $-$0.82 | 181.7 | (1)
$o$-H2 \+ D${}_{3}^{+}$ $\rightarrow$ HD + D2H+ | $9.2\times 10^{-10}$ |  $-$0.59 | 68.8 | (1)
$o$-H2 \+ D${}_{3}^{+}$ $\rightarrow$ D2 \+ H2D+ | $1.5\times 10^{-10}$ |  $-$0.85 | 174.4 | (1)
$o$-H2 \+ N+ $\rightarrow$ NH+ \+ H | $4.2\times 10^{-10}$ |  $-$0.15 | 44.1 | (2)

Reaction rate coefficient is given by
$k(T)=\alpha\,(\frac{T}{300\,K})^{\beta}\,\exp{(-\gamma/T)}$.
References: (1) Hily-Blant et al. (2018); (2) Dislaire et al. (2012).

However, for deuterated methyl acetylene we consider that the external CH and
CCH (or CD and CCD) groups are much more mobile than the methyl group. Then,
we assume that for reactions involving the ejection of CH and CCH (or CD and
CCD), only the terminal group is implied in the reaction. As an example:

$\displaystyle\rm C^{+}+CH_{2}DCCH$ $\displaystyle\rightarrow\rm
C_{3}H_{2}D^{+}+CH$ (1a) $\displaystyle\rm C^{+}+CH_{2}DCCH$
$\displaystyle\rightarrow\rm C_{2}H_{2}D^{+}+C_{2}H$ (1b) $\displaystyle\rm
C^{+}+CH_{3}CCD$ $\displaystyle\rightarrow\rm C_{3}H_{3}^{+}+CD$ (2a)
$\displaystyle\rm C^{+}+CH_{3}CCD$ $\displaystyle\rightarrow\rm
C_{3}H_{3}^{+}+C_{2}D$ (2b)

For reactions of dissociative recombination, we consider that atomic hydrogen
is ejected twice more efficiently than deuterium, as found in some experiments
(e.g., Jensen et al. 1999). We include the findings of Savić & Gerlich (2005)
and Savić et al. (2005), who showed that the rate coefficients of reactions of
C3H+ with HD and D2 are different from those with H2. We also report in Table
5 the corresponding rate coefficients used in our network. Let us point out
that these values are still subject to some uncertainties as discussed in
Savić & Gerlich (2005) and Savić et al. (2005).

As in our previous studies of isotopic fractionation (Roueff et al., 2015), we
do not solve the full para/ortho chemistry of hydrogen compounds but rather
introduce the ortho-to-para ratio of H2, OPR, as a free parameter. This factor
impacts the reverse reactions of the deuteron exchanges of HD with
H${}_{3}^{+}$, H2D+, and D2H+ and the reaction N+ \+ H2 (Dislaire et al.,
2012), as shown in Table 6, where $n$($o$-H2) = $\frac{{\small OPR}}{1+{\small
OPR}}n({\rm{H_{2}}}$). The exponential terms, $\gamma$, were obtained by
subtracting the energy of the $J=1$ level of $o$-H2, 170.5 K, from the
endothermicity of the reaction with reactants and products in their ground
states. We did not introduce the similar reactions CH3-nD${}_{n}^{+}$
($n=0,1,2,3$) + $o$-H2, C2H2-nD${}_{n}^{+}$ ($n=0,1,2$) + $o$-H2, and C3D+ \+
$o$-H2 since the corresponding endothermicities are much larger (Roueff et
al., 2013; Nyman and Yu, 2019) and the reactions do not take place in the
present low temperature, $\sim$ 10 K, conditions.

Table 7: H/D ratios of C-containing molecules observed in L483 and steady-
state values calculated with our gas-phase chemical model a.

Molecular ratio | L483 | Model 1 | Model 2 | Model 3
---|---|---|---|---
OPR H2 …………………. |  |  10-3 |  10-4 |  10-4
$\zeta$ (10-17 s-1) d ………….. |  | 1.3 | 1.3 | 0.5
CH3CCH / CH2DCCH |  5.2 c | 10.1 | 7.6 | 6.3
CH3CCH / CH3CCD |  15.7 c | 27.3 | 20.4 | 17.1
CH3CCH/ CHD2CCH |  33.8 c | 91.1 | 56.0 | 38.0
CH3CCH / CH2DCCD |  42.1 c | 131.5 | 78.4 | 54.5
$c$-C3H / $c$-C3D |  22.7 d | 18.2 | 15.4 | 12.8
$c$-C3H2 / $c$-C3HD |  9.8 d | 13.4 | 13.1 | 11.1
$c$-C3H2 / $c$-C3D2 |  103 d | 173 | 130 | 95.5
$l$-C3H2 / $l$-C3HD |  13.2 d | 7.0 | 6.5 | 5.4
C4H / C4D |  52.6 d | 13.0 | 9.7 | 8.9
HC3N / DC3N |  35.7 d | 14.1 | 10.8 | 9.0
CH3CN / CH2DCN |  7.6 d | 18.2 | 15.4 | 13.8

a See text for the assumed physical conditions. We adopted the elemental
abundance ratios O/H = $8\times 10^{-6}$, D/H = $1.5\times 10^{-5}$, C/O =
0.5, and C/N = 4. b Cosmic-ray ionization rate of H2. c Observed values in
this work (see Table 3). d Observed values from Agúndez et al. (2019).

Table 7 displays the deuterium ratios of various carbon-containing molecules
observed in L483, including present methyl acetylene detections, and three
steady-state model results corresponding to the physical conditions, $n$(H2) =
$3\times 10^{4}$ cm-3 and $T$ = 10 K, prevailing in L483 (Agúndez et al.,
2019). Model 1 represents a fiducial model with OPR = 10-3 and
$\zeta=1.3\times 10^{-17}s^{-1}$, which corresponds to typical values for dark
clouds. We notice that this choice overestimates the H/D ratio of methyl
acetylene by about a factor of two, a feature that we already noticed in our
previous study of TMC-1 (Cabezas et al., 2021). Decreasing the ortho-to-para
ratio of H2 by a factor of ten, as done in model 2, allows to decrease
reasonably the H/D ratios of the various C-containing molecules. This trend is
further strengthened in model 3, where the cosmic-ray ionization rate is
reduced down to $5\times 10^{-18}$ s-1, which results in H/D ratios for singly
and doubly deuterated methyl acetylene close to the observed values.

While a more detailed study is highly desirable, we can make some comments.
The abundance ratio between the two singly deuterated forms of methyl
acetylene, CH2DCCH/CH3CCD, is close to three according to the observations and
this fact is reproduced by the models. This feature results directly from the
statistical considerations for the insertion of deuterium in the CH3 group and
in the terminal CCH group. For example, in the dissociative recombination of
C3H6D+ and C3H5D+, which are the principal formation routes of deuterated
methyl acetylene, we explicitly account for this statistical factor in the
reaction rate coefficients. The doubly deuterated forms, on the other hand,
are assumed to be produced in equal amounts from the dissociative
recombinations of C3H5D${}_{2}^{+}$ and C3H4D${}_{2}^{+}$, following
statistical arguments as well. The difference between the abundances of
CH2DCCD and CHD2CCH results then from the destruction rates, for which we
assume that the possible ejection of H or D occurs from the terminal CCH or
CCD group. As an example, CH2DCCD + H${}_{3}^{+}$ $\rightarrow$ C3H2D+ \+ H2
\+ HD whereas CHD2CCH + H${}_{3}^{+}$ $\rightarrow$ C3HD2+ \+ H2 \+ H2. Then,
CHD2CCH is more easily recycled in a doubly deuterated form and its abundance
is somewhat larger than that of CH2DCCD, as derived from the observations. A
low ortho-to-para ratio of H2 favors significantly the deuterium enhancement
of methyl acetylene, which reflects the role of deuteron transfer in ion-
molecule reactions. We note that the range 10-3 \- 10-4 is within the OPR H2
values derived for typical conditions of dark clouds (Le Bourlot, 1991; Furuya
et al., 2015). In a similar way, lowering the cosmic-ray ionization rate leads
to a decrease in the ionization fraction, which enhances the abundance of
molecular ions and decrease the H/D ratio of the various molecular species.

We plan to further investigate the dependence of deuterium fractionation on
various parameters in a dedicated study but these first results show that the
gas-phase ion-molecule schema can explain the formation of methyl acetylene
and its singly and doubly deuterated substitutes. Moreover, if deuteration
occurs on grain surfaces and deuterated ratios are governed by the D/H ratio
in the gas phase, then it would hold that CH2DCCD/CH3CCD = 3 $\times$
CH3CCD/CH3CCH. That is, CH2DCCD/CH3CCD should be 0.19, while the observed
value is 0.37, meaning that doubly deuterated species are twice more abundant
than expected if deuteration occurs on grain surfaces following a statistical
scheme. This fact further strengthens the gas-phase origin of deuteration for
methyl acetylene. It is interesting to note that our models also predict the
deuteration of allene (CH2CCH2) at similar levels than methyl acetylene.
However, the dipole moment of the fully hydrogenated form of allene is zero
and that resulting from deuterium inclusion is probably too small to permit
the detection of any deuterium isotopologue.

##  5 Conclusions

We have presented the first detection in space of the two doubly deuterated
isotopologues of methyl acetylene, CHD2CCH and CH2DCCD, toward the dark cloud
core L483. The frequencies predicted for these two species from laboratory
data have significant errors when compared with those derived from
astronomical observations. We have therefore derived new spectroscopic
parameters for the two deuterium isotopologues which have the accuracy needed
to observe these species in cold interstellar clouds showing narrow lines. We
derive abundance ratios of CH3CCH/CHD2CCH = $34\pm 10$ and CH3CCH/CH2DCCD =
$42\pm 13$. Doubly deuterated methyl acetylene is found to be only a few times
less abundant than the singly deuterated forms. We have constructed a gas-
phase chemical model including multiply deuterated molecules, which is able to
reproduce the abundance ratios of the different deuterated isotopologues with
respect to CH3CCH observed in L483. In particular, the fact that CHD2CCH is
slightly more abundant than CH2DCCD is well accounted for by the chemical
model. This favors a scenario in which deuteration of methyl acetylene occurs
in the gas phase, rather than on the surface of dust grains.

###### Acknowledgements.

We acknowledge funding support from Spanish MICIU through grants
AYA2016-75066-C2-1-P, PID2019-106110GB-I00, and PID2019-107115GB-C21 and from
the European Research Council (ERC Grant 610256: NANOCOSMOS). M.A. also
acknowledges funding support from the Ramón y Cajal programme of Spanish MICIU
(grant RyC-2014-16277). C.C. thanks Prof. Cristina Puzzarini (Universitá di
Bologna) for her advices and comments about the quantum chemical calculations.

## References

  * Agúndez et al. (2019) Agúndez, M., Marcelino, N., Cernicharo, J. et al. 2019, A&A, 625, A147
  * Bacmann et al. (2020) Bacmann, A., Faure, A., Hily-Blant, P., et al. 2020, MNRAS, 499, 1795
  * Brown & Millar (1989) Brown, P. D. & Millar, T. J. 1989, MNRAS, 1989, 240, 25
  * Burrell et al. (1980) Burrell, P. M., Bjarnov, E., & Schwendeman, R. H. 1980, J. Mol. Spectr., 82, 193
  * Butner et al. (2007) Butner, H. M., Charnley, S. B., Ceccarelli, C., et al. 2007, ApJ, 659, L137
  * Cabezas et al. (2021) Cabezas, C., Endo, Y., Roueff, E., et al. 2021, A&A, 646, L1
  * Calcutt et al. (2018) Calcutt, H., Jørgensen, J. K., Müller, H. S. P., et al. 2018, A&A, 616, A90
  * Ceccarelli et al. (1998) Ceccarelli, C., Castets, A., Loinard, L., et al. 1998, A&A, 338, L43
  * Ceccarelli et al. (2014) Ceccarelli, C., Caselli, P., Bockelée-Morvan, D., et al. 2014, Protostars and Planets VI, 859
  * Cernicharo (2012) Cernicharo, J. 2012, in European Conference on Laboratory Astrophysics, eds. C. Stehlé, C. Joblin, & L. d’Hendecourt, EAS Publication Series, 58, 251
  * Dislaire et al. (2012) Dislaire, V, Hily-Blant, P., Maret, S., et al. 2012, A&A, 537, A20
  * Dunning (1989) Dunning Jr., T. H. 1989, J. Chem. Phys., 90, 1007
  * Etim et al. (2020) Etim, E. E., Akpan, N. I., Adelagun, R. A. O., et al. 2020, Indian J. Phys., doi: 10.1007/s12648-020-01747-x
  * Flower et al. (2006) Flower, D. R., Pineau des Forêts, & Walmsley, C. M 2006, A&A, 449, 621
  * Furuya et al. (2015) Furuya K., Aikawa, Y., Hincelin, U., et al. 2015, A&A, 584, A124
  * Gerin et al. (1992) Gerin, M., Combes, F., Wlodarczak, G., et al. 1992, A&A, 253, L29
  * Grimme (2006) Grimme, S. 2006, J. Chem. Phys., 124, 034108
  * Hily-Blant et al. (2018) Hily-Blant, P., Faure, A., Rist, C., et al. 2018, MNRAS, 477, 4454
  * Jensen et al. (1999) Jensen, M. J., Bilodeau, R. C., Heber, O., et al. 1999, Phys. Rev. A, 60, 2970
  * Le Bourlot (1991) Le Bourlot, J. 1991, A&A, 242, 235
  * Le Guennec et al. (1993) Le Guennec, M., Demaison, J., Wlodarczak, G., & Marsden, C. J. 1993, J. Mol. Spectr., 160, 471
  * Linsky (2003) Linsky, J. L. 2003, Space Sci. Rev., 106, 49
  * Lis et al. (2002) Lis, D. C., Roueff, E., Gerin, M., et al. 2002, ApJ, 571, L55
  * Loison et al. (2017) Loison J.-C., Agúndez, M., Wakelam V., et al. 2017, MNRAS, 470, 4075
  * Manigand et al. (2019) Manigand, S., Calcutt, H., Jørgensen, J. K., et al. 2019, A&A, 623, A69
  * Marcelino et al. (2005) Marcelino, N., Cernicharo, J., Roueff, E., et al. 2005, ApJ, 620, 308
  * Markwick et al. (2005) Markwick, A. J., Charnley, S. B., Butner, H. M., & Millar, T. J. 2005, ApJ, 627, L117
  * Melosso et al. (2020) Melosso, M., Bizzocchi, L., Sipilä, O., et al. 2020, A&A, 641, A153
  * Muenter & Laurie (1966) Muenter, J. S. & Laurie, V. W. 1966, J. Chem. Phys., 45, 855
  * Müller et al. (2005) Müller, H. S. P., Schlöder, F., Stutzki, J., & Winnewisser, G. 2005, J. Mol. Struct., 742, 215
  * Nyman and Yu (2019) Nyman, G. & Yu, H.-G. 2019, AIP Advances 9, 095017
  * Parise et al. (2002) Parise, B., Ceccarelli, C., Tielens, A. G. G. M., et al. 2002, A&A, 393, L49
  * Parise et al. (2004) Parise, B., Castets, A., Herbst, E., et al. 2004, A&A, 416, 159
  * Parise et al. (2006) Parise, B., Ceccarelli, C., Tielens, A. G. G. M., et al. 2006, A&A, 453, 949
  * Parise et al. (2011) Parise, B., Belloche, A., Du, F., et al. 2011, A&A, 526, A31
  * Pickett et al. (1998) Pickett, H. M., Poynter, R. L., Cohen, E. A., et al. 1998, J. Quant. Spectr. Rad. Transfer, 60, 883
  * Ratajczak et al. (2011) Ratajczak, A., Taquet, V., Kahane, C., et al. 2011, A&A, 528, L13
  * Risthaus & Grimme (2013) Risthaus, T. & Grimme, S. 2013, J. Chem. Theory Comput., 9, 1580
  * Roberts et al. (2004) Roberts, H., Herbst, E., & Millar, T. J. 2004, A&A, 424, 905
  * Roueff et al. (2000) Roueff, E., Tiné, S., Coudert, L. H., et al. 2000, A&A, 354, L63
  * Roueff et al. (2005) Roueff, E., Lis, D. C., van der Tak, F. F. S., et al. 2005, A&A, 438, 585
  * Roueff et al. (2013) Roueff, E., Gerin, M., Lis, D. C., et al. 2013, J. Phys. Chem. A, 117, 9959
  * Roueff et al. (2015) Roueff, E., Loison, J.-C., & Hickson, K. M. 2015, A&A, 576, A99
  * Savić & Gerlich (2005) Savić, I. & Gerlich, D. 2005, PCCP, 7, 1026
  * Savić et al. (2005) Savić, I., Schlemmer, S. & Gerlich, D. 2005, ApJ, 621, 1163
  * Sipilä et al. (2015) Sipilä, O., Harju, J., Caselli, P., & Schlemmer, S. 2015, A&A, 581, A122
  * Sipilä et al. (2017) Sipilä, O., Harju, J., & Caselli, P. 2017, A&A, 607, A26
  * Spezzano et al. (2013) Spezzano, S., Brünken, S., Schilke, P., et al. 2013, ApJ, 769, L19
  * Taquet et al. (2012) Taquet, V., Ceccarelli, C., & Kahane, C. 2012, ApJ, 748, L3
  * Thomas et al. (1955) Thomas, L. F., Sherrard, E. I., & Sheridan, J. 1955, Trans. Faraday Soc., 51, 619
  * Turner (1990) Turner, B. E. 1990, ApJ, 362, L29
  * Turner (2001) Turner, B. E. 2001, ApJS, 136, 579
  * van der Tak et al. (2002) van der Tak, F. F. S., Schilke, P., Müller, H. S. P., et al. 2002, A&A, 388, L53
  * Vastel et al. (2003) Vastel, C., Phillips, T. G., Ceccarelli, C., & Pearson, J. 2003, ApJ, 593, L97
  * Vastel et al. (2004) Vastel, C., Phillips, T. G. & Yoshida, H. 2004, ApJ, 606, L127
  * Vastel et al. (2018) Vastel, C., Quénard, D., Le Gal, R., et al. 2018, MNRAS, 478, 5514