A study of singly deuterated cyclopropenylidene c-C3HD in protostar IRAS 16293-2422

0.59 MB·

by  L. Majumdar

MNRAS000,000–000(2015) Preprint31January2017 CompiledusingMNRASLATEXstylefilev3.0
A study of singly deuterated cyclopropenylidene c-C HD
3
in protostar IRAS 16293-2422
L. Majumdar1,2(cid:63), P. Gratier1, I. Andron1, V. Wakelam1, E. Caux3,4
1Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, all´ee Geoffroy Saint-Hilaire, 33615 Pessac, France
2 Indian Centre For Space Physics, 43 Chalantika, Garia Station Road, Kolkata, 700084, India
3Universit´e de Toulouse, UPS-OMP, IRAP, Toulouse, France
4CNRS, IRAP, 9 Av. Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France
7
1
0 AcceptedXXX.ReceivedYYY;inoriginalformZZZ
2

n
ABSTRACT
a
J Cyclic-C3HD (c-C3HD) is a singly deuterated isotopologue of c-C3H2, which is one of
themostabundantandwidespreadmoleculesinourGalaxy.WeobservedIRAS16293-
0
2422inthe3mmbandwithasinglefrequencysetupusingtheEMIRheterodyne3mm
3
receiveroftheIRAM30mtelescope.Weobservedsevenlinesofc-C3HDandthreelines

] of c-C3H2. Observed abundances are compared with astrochemical simulations using
A the NAUTILUS gas-grain chemical model. Assuming that the size of the protostellar
G envelope is 3000 AU and same excitation temperatures for both c-C3H2 and c-C3HD,
we obtain a deuterium fraction of 14+4%.
. −3
h
p Key words: Astrochemistry, ISM: molecules, ISM: abundances, ISM: evolution,
- methods: statistical
o
r
t
s
a
[ 1 INTRODUCTION detectedrecentlybySpezzanoetal.(2013)towardthestar-

less cores TMC-1C and L1544. They measured the abun-
1 The cyclic form of C H , cyclopropenylidene (c-C H ), is
v one of the most abun3dan2t and widespread molecule3 in2 our dance of c-C3D2 with respect to the c-C3H2 and found it
2 tobe0.4%-0.8%inTMC-1Cand1.2%-2.1%inL1544.This
Galaxy (Matthews & Irvine 1985). It is also the first hy-
2 drocarbon ring molecule found in space. It has been de- clearly shows that the abundance of c-C3D2 is much lower
5 thanthatofc-C HDandthussupportstheideathatsingly
tected in different astronomical environments: from diffuse 3
8 deuteratedspeciesformsmoreeasilyintheISMascompared
0 gastocolddarkclouds,giantmolecularclouds,photodisso- to the multiply deuterated species (Brown & Millar (1989),
1. cuilaateio(nTrheagdiodneus,sceirtcualm.s1t9e8ll5a;rVenrtvielelokpeets,aal.nd19p8l7a;neCtoaxryenteabl-. Willacy&Millar(1998)).Thismakesc-C3HDabettercan-
0 didate to study the chemistry and the physical conditions
1987; Madden et al. 1989; Lucas & Liszt 2000).
7 of cold environments compared to c-C D . The main goal
c-C H showsstrongrotationaltransitionsinmillimetre 3 2
1 3 2 of the present paper is to report the detection of c-C HD
wave bands due to its large dipole moment and favourably 3
: inthelowmassprotostarIRAS16293-2422(hereafterIRAS
v small partition function, which make this molecule a useful
Xi probeofphysicalconditionswhereitisfound(seeBelletal. 1b6o2th93o)basenrdvasttiuodnyaldaenudtetrhiueomreftricaacltiponoianttisonofovfiecw-C.3H2 from
(1986) for the discussion). c-C H is then often used as a
r 3 2 This paper is structured as follows. In Section 2, we
a template to study deuteration along different sources since
give a detailed description of our observations along with
therotationaltransitionsofitsisotopicspeciesarealsovery
methodology for the analysis. In Section 3, we discuss the
intense.c-C H canexistinsingly(c-C HD)anddoubly(c-
3 2 3 chemical model, which includes our latest deuterium chem-
C D ) deuterated forms. c-C HD was first detected in the
3 2 3 ical network with associated spin chemistry and finally re-
dense molecular cloud TMC-1 by Bell et al. (1986). Gerin
sults are discussed in the last Section.
etal.(1987)measureda1:5ratio(i.e.20%)ofthe2 →1
1,2 0,1
lines of c-C HD to c-C H in TMC-1. According to Gerin
3 3 2
etal.(1987),thishighdegreeofdeuteriumfractionationin-
dicates that the emission comes from extremely cold dense 2 OBSERVATIONS AND DATA REDUCTION
cores (T = 4-7 K) and thus c-C HD samples the cold-
ROT 3 2.1 Observations
est part of the interstellar medium (ISM). c-C D was also
3 2
TheobservationswereobtainedattheIRAM30mtelescope
during the period August 18-23, 2015. Overall, the weather
(cid:63) E-mail:[email protected] conditionwaslikeanaveragesummer(amedianvalueof4-6
(cid:13)c 2015TheAuthors
2 Majumdar et al.
Figure 1. Here top three and bototom seven panels are for c-C3H2 and c-C3HD respectively. Red line: Observed lines attributed to
c-C3HD and c-C3H2. Black line: Distribution of modelled spectra following the posterior distribution of parameters shown in Figure 2
andFigure3.Thickline:medianofthedistribution.Darkgreyregion68%andrespectivelylightgreyregion95%confidenceintervals.
Dottedlinesare1,3,5σ noiselevels.
mmwatervapour).Weperformedourobservationsbyusing elevation. At the beginning of each observing run, the clos-
the EMIR heterodyne 3 mm receiver tuned at a frequency est planet Saturn was used for focus. Pointing was checked
of89.98GHzintheLowerInnersideband.Thisreceiverwas everyhourwithmostlygoodpointingcorrections(lessthan
followedbyaFourierTransformSpectrometerinits195kHz a third of the telescope beam size 30(cid:48)(cid:48)).
resolution mode. The observed spectrum was composed of
two regions: one from 84.4 GHz to 92.3 GHz and another
one from 101.6 GHz to 107.9 GHz. 2.2 Results
2.2.1 c-C HD and c-C H line properties
The observations were made towards the midway 3 3 2
point between sources A and B of IRAS 16293 at ThedatawerereducedandanalysedusingtheCLASSsoft-
α2000 =16h32m22.75s, δ2000 =−24◦28(cid:48)34.2(cid:48)(cid:48). The A and B warefromtheGILDAS1 package.WemadeGaussianfitsto
components,separatedby5.5(cid:48)(cid:48),arebothinsidethetelescope thedetectedlinesfollowingalocallow(0or1)orderpolyno-
beamofourobservationsatallfrequencies.Allobservations mial baseline subtraction. Table 1 shows the result of these
were performed using the wobbler switching mode with a
periodof 2seconds andathrowof 90(cid:48)(cid:48) ensuringmostlyflat
baselineseveninsummerconditionsandobservationsatlow 1 https://www.iram.fr/IRAMFR/GILDAS/
MNRAS000,000–000(2015)
Cyclic-C HD in IRAS 16293-2422 3
3
Table 1.Observedlinesandspectroscopicparametersforc-C3HDandc-C3H2
Species LinesRef. Integratedflux VLSR FWHM Observed Aij Eup Quantum
(Kkms−1) (kms−1) (kms−1) Frequency (s−1) (K) numbers
(MHz)
0.013±0.009 4.3±0.162 1.0±0.70 85643.318 1.43×10−5 26.6 43,2→42,3
0.028±0.003 4.3±0.064 1.3±0.12 102423.019 1.53×10−5 22.3 41,3→40,4
0.243±0.024 4.2±0.016 1.1±0.02 104187.126 3.96×10−5 10.8 30,3→21,2
c-C3HD Bogeyetal.(1987) 0.047±0.006 4.2±0.031 0.8±0.08 104799.707 7.29×10−6 10.9 31,3→21,2
0.032±0.005 4.5±0.086 1.4±0.19 106256.108 1.69×10−5 22.5 42,3→41,4
0.054±0.006 4.1±0.025 0.9±0.07 106811.09 7.87×10−6 10.8 30,3→20,2
0.280±0.028 4.1±0.005 0.8±0.01 107423.671 4.47×10−5 10.9 31,3→20,2
0.125±0.013 4.2±0.018 1.4±0.06 84727.688 1.04×10−5 16.14 32,2→31,3
c-C3H2 Thaddeusetal.(1985) 1.372±0.137 4.2±0.010 1.4±0.006 85338.894 2.32×10−5 6.45 21,2→10,1
0.173±0.017 4.3±0.028 1.9±0.05 85656.431 1.52×10−5 29.07 43,2→42,3
scopic catalog. The spectroscopic catalogs for c-C HD and
Table2.Priorsdistributionfunctionsfortheparametersusedin 3
thebayesianapproach. c-C3H2 wereretrievedfromtheCDMS(Mu¨lleretal.2005).
All the observed frequencies along with their Einstein co-
Parameter Distribution efficients, upper level energies and the associated quantum
numbers are listed in Table 1. Here, we have chosen to fix
log10N(cm−2) Uniform(8,22) the source size to 25(cid:48)(cid:48) (∼ 3000 AU, typical size of the pro-
log10Tex (K) Uniform(log103,log10200) tostellar envelope by Caux et al. (2011)) since the range of
V(kms−1) Uniform(2.8,4.8)
frequencies is small. The likelihood function assumes that
∆V(kms−1) Uniform(0.25,10)
the errors are normally distributed with a noise term con-
log σ (K) Uniform(−3,1)
10 add
sisting of a sum in quadrature of the observed per channel
Notes: Uniform(min-value, max-value) is a uniform distribu- uncertainty and an additional noise term left as a free pa-
tion with values going from minimum value to maximum rameter of the model. The priors are chosen to be uniform
value.
and non informative over the range of variation as defined
in Table 2.
fits for the 7 observed lines of c-C HD and 3 observed lines
3 The sampling of the posterior distribution function
of c-C H . In Table 1, uncertainties on integrated flux are
3 2 is carried out using the Python implementation EMCEE2
the Gaussian fit uncertainties (with an added 10% calibra-
(Foreman-Mackey et al. 2013) of the Affine Invariant En-
tionerror),uncertaintiesonVLSRarethequadraticsumof
semble Monte Carlo Markov Chain approach (Goodman &
the gaussian fit statistical uncertainties and the frequency
Weare 2010). Sixty walkers are initialised in a small 6 di-
uncertainties from the spectroscopic catalog, uncertainties
mensional sphere in the center of the parameter space. The
on FWHM are the gaussian fit uncertainties only. All the
chainsareevolvedforaburn-insequenceof3000stepsafter
observedlinesaresinglecomponentfeatureswiththemean
whichtheconvergenceischeckedbyexaminingaplotofthe
LSR velocity of ∼ 4.2 km/s and the mean FWHM of ∼ 1
running mean of each parameter.
km/s. Caux et al. (2011) identified four types of kinemat-
Figure1showsthecomparisonofobservedspectraand
ical behaviours for different species based on the different
modelledspectra.Figures2and3showthe1Dand2Dhis-
FWHM and VLSR distributions. We found that c-C HD
3 tograms of the posterior probability distribution function
and c-C H belong to the type I (i.e. FWHM≤2.5 km/s,
3 2 for c-C HD and c-C H respectively. In both cases, all pa-
VLSR∼4km/s,Eup∼0-50K),whichcorrespondstospecies 3 3 2
rametersarewelldefined.Table3summarisestheonepoint
abundant in the cold envelope of IRAS 16293.
statistics for the marginalised posterior distributions of pa-
rameters.TheuncertaintiesreportedinTable3are1σsym-
2.2.2 Radiative transfer modelling for c-C HD and metricerrorbars.Thereisaboutafactor2differenceinline
3
c-C3H2 widthbetweenc-C3HDandc-C3H2 (showninTable3),this
cannot arise from opacity effects as all the lines are opti-
Majumdar et al. (2016b) used a bayesian model to recover callythinexceptc-C H lineat85.338GHz.Onepossibility
3 2
the distribution of parameters which best agree with the is that c-C H comes both from the central hotter region
3 2
observedlineintensitiesforCH3SHinthesamesource.Here, and the outer envelope while c-C3HD only comes from the
weusethesamemodelwiththeexceptionthatnotonlythe outercoldenvelope.Thisisfurtherstrengthenbythechem-
integrated intensities but also the full modelled spectra are icalmodellingwhichshowssuchapatterninFigure4.Thus,
compared to the observed ones. deuterium fraction we obtain in Section 2.3 is a lower limit
We use the local thermal equilibrium (LTE) radiative in the external envelope.
transfer code implemented in the GILDAS-Weeds package
(Maretetal.2011)tomodeltheemissionofc-C HDandc-
3
C H .Theinputparametersinthisradiativetransfermodel
3 2
arethespeciescolumndensity,thelinewidth,theexcitation
temperature,thesourcesizealongwithanaccuratespectro- 2 https://github.com/dfm/emcee
MNRAS000,000–000(2015)
4 Majumdar et al.
logN [cm−2] = 13.42+00..0011
−
logT [K] = 0.95+0.03
ex 0.03
−
0
0
1.
]K 95
[Tex 0.0
g 9
lo 0.
5
8
0.
V [kms−1] = 4.23+00..0011
−
5
7
2
4.
1]ms− 4.250
[Vk 4.225
0
0
2
4.
0.15 log∆V [kms−1] = 0.11−+00..0011
] 12
1− 0.
ms
[∆Vk 0.09
g
o
l 6
0
0.
σ [mK] = 12.00+1.45
add 1.18
−
8
1
]K 5
m 1
[σadd 12
9
0.000 0.025 0.050 0.85 0.90 0.95 1.00 4.200 4.225 4.250 4.275 0.06 0.09 0.12 0.15 9 12 15 18
logN [cm−2+]1.34e1 logTex [K] V [kms−1] log∆V [kms−1] σadd [mK]
Figure 2. 1Dand2Dhistogramsoftheposteriordistributionofparametersforc-C3H2.Contourscontainrespectively68and95%of
samples.Thequoteduncertaintiesarestatisticalonly,withoutthe10%calibrationerror.
2.3 Observational constraint on deuterium (hν/K)1/[ehν/KT −1] is the radiation temperature and τ
fraction for c-C H is the opacity. For the optically thin conditions, we can as-
3 2
sume that τ ∝N. Under this assumption, T ∝[J(T )−
The observed main beam temperature T , for a beam of mb ex
mb J(T )]N.
size θ of a gaussian source of size θ is CMB
t s Underopticallythinconditions,wecanassumethatthe
T =η[J(T )−J(T )][1−e−τ] excitation properties of the two isotopologues are going to
mb ex CMB
θ2 (1) be similar which is confirmed by the fact that we find sim-
= s [J(T )−J(T )][1−e−τ], ilar values for the excitation temperatures when doing the
θ2+θ2 ex CMB
s t independent analysis. We need more lines, therefore more
where, η is the beam dilution factor which is identical sensitive observations to see whether temperatures are in
for two molecules since we fix the source size, J(T) = fact different. The choice to use the same temperature has
MNRAS000,000–000(2015)
Cyclic-C HD in IRAS 16293-2422 5
3
logN [cm−2] = 12.83+00..0046
−
logT [K] = 0.80+0.05
ex 0.05
−
9
0.
]K
[Tex 0.8
g
o
l
7
0.
V [kms−1] = 4.13+00..0011
−
6
1
4.
1]ms− 4.14
[Vk 4.12
0
1
4.
log∆V [kms−1] = −0.09−+00..0022
6
0
0.
]
1kms− 0.09
[∆V 12
g 0.
o
l
5
1
0. σ [mK] = 5.43+0.49
add 0.45
8 −
7
]K
m 6
[σadd 5
4
12.80 12.88 12.96 13.04 0.7 0.8 0.9 4.10 4.12 4.14 4.16 0.15 0.12 0.09 0.06 4 5 6 7 8
logN [cm−2] logTex [K] V [kms−1] log∆V [kms−1] σadd [mK]
Figure 3. 1Dand2Dhistogramsoftheposteriordistributionofparametersforc-C3HD.Contourscontainrespectively68and95%of
samples.Thequoteduncertaintiesarestatisticalonly,withoutthe10%calibrationerror.
alsobeenmadeinthepastfortheLTEmodelingofisotopo- at T = 2.73 K], we derive a column density of N(c-
CMB
logues (See for instance Caselli et al. (2002); Daniel et al. C H )=N = 1.78N = 4.7 × 1013cm−2. Thus, we ob-
3 2 2 1
(2013)). tain a deuteration fraction N(c-C HD)/N(c-C H )=6.7×
3 3 2
Now we can represent the column density (N ) of c- 1012/4.7×1013 =14%.
2
C H at the excitation temperature (6.3 K) of c-C HD as:
3 2 3
N =N [J(T )−J(T )]/[J(T )−J(T )] (2)
2 1 ex1 CMB ex2 CMB If we define the error on column densities of c-C H
3 2
Where, N is the column density of c-C H at 8.9 andc-C HDbyerrN anderrN1,statisticalerroroncolumn
1 3 2 3 2
K. At frequency 85 GHz, J(T ) = 7.02 for T of 8.9 densitiesofc-C H andc-C HDbyerrstatN anderrstatN
ex1 ex1 3 2 3 2 1
K; J(T ) = 4.46 for T of 6.3 K [J(T ) = 1.17 andrelativecalibrationerrorbyerrcal(10%inbothcases),
ex2 ex2 CMB
MNRAS000,000–000(2015)
6 Majumdar et al.
Figure4.AbundancewithrespecttoH2forc-C3H2andc-C3HDpredictedbyourmodelasafunctionofradius.sc-C3H2andsc-C3HD
representsthec-C3H2 andc-C3HDonthesurfaceofgrains.
Thus, error on the deuterium fraction can be written
Table 3. Point estimates of the posterior distribution function
correspondingtothemedianandonesigmauncertainty. as N(c-C3HD)/N(c-C3H2)=14+−43%. Bell et al. (1988) also
measureddeuteriumfractionationofc-C H intheorderof
3 2
Parameter c-C3HD c-C3H2 5 to 15% in TMC-1.
log N(cm−2) 12.83±0.05 13.42±0.01
10
log10Tex (K) 0.80±0.05 0.95±0.03
log ∆V(kms−1) -0.09±0.02 0.11±0.01
10 3 1D MODELLING OF THE PROTOSTELLAR
log [X]a −11.3±0.05 −10.7±0.01
10 ENVELOPE
Notes:a [X]=N(X)/N(H2)and b valuewith95%confidence.
Herequoteduncertaintiesarestatisticalonly,withoutthe 3.1 The NAUTILUS chemical model with
10%calibrationerror. deuteration
To model the chemistry of c-C HD and c-C H in IRAS
3 3 2
then we can write:
16293, we used the same approach as Majumdar et al.
errN (cid:114) errstatN (2016b). For our simulation, we have used the 2 phase ver-
2 = ( 2)2+(errcal)2
N2 N2 (3) sion of the NAUTILUS gas-grain chemical model (Majumdar
(cid:112) et al. 2016b; Ruaud et al. 2015; Wakelam et al. 2015) with
= 0.022+0.12 =0.10
deuteration and spin chemistry (Majumdar et al. submit-
ted).NAUTILUSallowsthecomputationofthechemicalcom-
(cid:114)
errN1 = (errstatN1)2+(errcal)2 position as a function of time in the gas-phase and at the
N1 N1 (4) surfaceofinterstellargrains.Alltheequationsandthechem-
(cid:112) ical processes included in the model are described in detail
= 0.12+0.12 =0.14
in Ruaud et al. (2015). In the current model, several types
For N(c-C3HD)/N(c-C3H2)=R, then of chemical reactions are considered in the gas phase by
following the kida.uva.2014 chemical network of Wakelam
R =N(c-C HD) /N(c-C H )
max 3 max 3 2 min et al. (2015) with the recent extension to deuteration and
=6.7×(1+0.14)×1012/4.7×(1−0.1)×1013 (5) spin chemistry of Majumdar et al. (2016a). In the 2 phase
=18% version of NAUTILUS, there is no differentiation between the
species in the mantle and at the surface. NAUTILUS consid-
ers interaction between gas and grains via four major pro-
R =N(c-C HD) /N(c-C H )
min 3 min 3 2 max cesses : physisorption of gas phase species onto grain sur-
=6.7×(1−0.14)×1012/4.7×(1+0.1)×1013 (6) faces,diffusionoftheaccretedspecies,reactionatthegrain
=11% surface, and finally by evaporation to the gas phase. Our
MNRAS000,000–000(2015)
Cyclic-C HD in IRAS 16293-2422 7
3
modelalsoconsidersdifferenttypesofevaporationprocesses knownas‘protostellarcore’.Inthemodel,theinitialprestel-
such as thermal evaporation, evaporation induced by cos- larcoreevolvestotheprotostellarcorein2.5×105yr.When
micrays(followingHasegawa&Herbst1993),andchemical protostarisformed,themodelfurtherfollowstheevolution
desorption as suggested by Garrod et al. (2007). We adopt for 9.3×104 yr, during which the protostar grows by mass
thesimilarinitialelementalabundancesreportedinHincelin accretion from the envelope.
etal.(2011)withadeuteriumandfluorineelementalabun-
dancerelativetohydrogenof1.6×10−5 (Linskyetal.2006)
and6.68×10−9 (Neufeldetal.2005)respectively.Herethe
4 MODELLING RESULTS AND DISCUSSIONS
species are assumed to be initially in an atomic form as in
diffusecloudsexceptforhydrogenanddeuterium,whichare Here, we present the predicted abundances of c-C HD and
3
initially in H2 and HD forms respectively. For our standard c-C3H2 in the protostellar envelope using the physical and
model,wehaveusedaC/Oratioof0.7andanortho-to-para chemicalmodelspreviouslydescribed,andcomparewithour
H2 ratio of 3. observations. Figure 4 shows the computed abundances of
Inourcurrentmodel,allthevariablesrelativetoH2has c-C3HD and c-C3H2, in the gas-phase and at the surface
been modified in terms of nuclear spin states ortho-H2 and of the grains in the protostellar envelope as a function of
para-H2. Since, it has been known from long time that H2, radii, at the end of the simulations, i.e. for a protostellar
D2, H3+, H2D+, D2H+ and D3+ along with their spin iso- age of 9.3×104 yr. We considered abundances at 9.3×104
mersarethemainspeciesthatdictatedeuteriumfractiona- yrsincethephysicalstructureoftheenvelopeatthisageis
tionatlowtemperature(seeCeccarellietal.2014).Detailed similartotheoneconstrainedintheenvelopeofIRAS16293
description and benchmarking of our deuterated network by Crimier et al. (2010) from multi-wavelength dust and
withspinchemistryispresentedinMajumdaretal.(2016a). molecular observations (see Wakelam et al. (2014) for the
This network is available on the KIDA3 website. Our net- discussion).
workforsurfacereactionsandgas-graininteractionsisbased Abundanceprofilesofc-C HDandc-C H predictedby
3 3 2
ontheonefromGarrodetal.(2007)withaddeddeuteration our model can be divided into three regions. First region is
and spin chemistry from Majumdar et al. (2016a). defined by radii larger than 200 AU and temperatures be-
low 50 K. In this region, the gas phase abundance of both
c-C HD and c-C H decrease toward the centre of the en-
3 3 2
3.2 1D physical structure
velope due to high depletion because of density increase. In
To follow the deuterium fractionation of c-C H in IRAS the outer part of the envelope (radii greater than 2000 AU
3 2
16293, we have used the same 1D physical structure as in and temperatures below 30 K), gas phase c-C3HD forms
Aikawaetal.(2008);Wakelametal.(2014);Majumdaretal. mainly by the dissociative recombination of c-C3H2D+. c-
(2016b). This physical structure was based on the nongray C3H2D+isproducedmainlyfromthedeuterontransferfrom
radiation hydrodynamic model by Masunaga & Inutsuka para-H2D+ and DCO+ to c-C3H2. c-C3H2D+ is also partly
(2000) to follow the core evolution from pre-stellar core to produced by c-C3H2 + H2DO+ and para-H2 + C3D+ reac-
protostellarcore.Itstartsfromahydrostaticprestellarcore tions.Sointhecoldouterenvelope,deuterationofc-C3HDis
with central density n(H2) ∼3×104 cm−3. The core is ex- mainlycontrolledbypara-H2D+andDCO+.Intheseregion,
tendeduptor=4×104 AUwithatotalmassof3.852M(cid:12), c-C3H2 also mainly forms from the dissociative recombina-
which exceeds the critical mass for gravitational instability. tionreactionof c-C3H3+. From 2000AUto 200AU (where
Initial temperature for the core is around 7 K at the center temperaturestartedtoincreasefrom30Kto50K),c-C3HD
andaround8Kattheouteredge.Here,cosmicrayheating, mainlyformsfromtheneutral-neutralreactionCH+C2HD
cosmic background radiation, and ambient stellar radiation → H + c-C3HD whereas c-C3H2 mainly forms from the H
balancethecoolingcausedbydustthermalemission.Inthe + CH2CCH → para-H2 + c-C3H2 reaction.
model, core stays at its hydrostatic structure for 1×106 yr Between 200 and 100 AU, the gas phase abundance of
to set up the initial molecular conditions for the collapse bothc-C3HDandc-C3H2 increasesrapidlyduetothecom-
stage. After 1×106 yr, the core starts to contract and the pleteevaporationofc-C3HDandc-C3H2fromthegrainsur-
contractionisalmostisothermalaslongasthecoolingiseffi- face. Inside the inner 60 AU, the gas phase abundance of
cient.Eventuallythecompressionalheatingoverwhelmsthe c-C3HD decreases rapidly due to slow deuteration process,
cooling,whichcausesrisingintemperatureinthecentralre- i.e.unavailabilityofanyformsofH2D+totransferdeuteron.
gion.Contractionthendeceleratedduetoincreaseinthegas Butinthisregion,c-C3H2 canstillsurvivewithaveryhigh
pressure which eventually makes the first hydrostatic core, abundance (∼ 10−9) due to its efficient production via the
known the ‘first core’ at the center. When the core center reactions H + CH2CCH → ortho-H2 + c-C3H2 and H +
reachesveryhighdensity(107 cm−3)andhightemperature CH2CCH → para-H2 + c-C3H2.
(2000 K), the hydrostatic core becomes unstable due to H In Table 4, we give our modelled abundances and frac-
2
dissociationandstartstocollapseagain.Thiscollapseisre- tionation ratios at 3000 AU, 4000 AU and 7000 AU. The
ferredasthe‘secondcollapse’.Withinashortperiodoftime, variationofpredicteddeuteriumfractionationbetween3000
the dissociation degree approaches unity at the center due AU and 4000 AU is very small whereas we observe a large
torapidincreaseofcentraldensity.Thenthesecondcollapse variation at 7000 AU (i.e. in the outer part of the envelope
ceases, and the second hydrostatic core, i.e., the protostar, where the temperature is below 30 K). In the outer part
isformedandtheinfallingenvelopearoundthisprotostaris of the envelope, H3+ reacts with HD, the major reservoir
of D-atoms and D-atom is transferred from HD to H D+
2
(ortho/para). As a result, H D+ becomes very abundant in
2
3 http://kida.obs.u-bordeaux1.fr/ theouterpartandservesasaprimaryspeciestowardsdeu-
MNRAS000,000–000(2015)
8 Majumdar et al.
Table 4.Modeledandobservedfractionationsforc-C3H2.
Radius 3000AU 4000AU 7000AU Observedvalues
(at3000AU)
log10[c−C3HD]a -10.15 -10.07 -9.50 -11.3
log10[c−C3H2]a -8.37 -8.35 -8.33 -10.45c
[c−C3HD/c−C3H2]b 1.7% 2% 7% 14%
Notes:a [X]=N(X)/N(H2)
Notes:b Deuteriumfractionofc-C3H2
Notes:c Abundanceofc-C3H2 byconsideringthesameexcitationtemperatureofc-C3HD(seeSection2.3)
terium fractionation. Besides that, other abundant neutrals gramme PCMI for funding of their research. We would like
and important destruction partners of H + isotopologues, to thank the anonymous referee for constructive comments
3
suchasOandCO,depletefromthegasphase(forexample that helped to improve the manuscript.
becauseofthefreezeoutontodustgrainsincoldanddense
regions). As a consequence, in the outer part, the main for-
mation reaction of c-C HD via c-C H D+ + e− becomes
3 3 2
very fast due to efficient deuteron transfer between para-
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