Cyanopolyyne Chemistry around Massive Young Stellar Objects
Kotomi Taniguchi Eric Herbst Paola Caselli Alec Paulive Dominique M. Maffucci Masao Saito



















































Kotomi Taniguchi
kt8pm@virginia.edu

0000-0003-4402-6475]Kotomi Taniguchi
Virginia Initiative on Cosmic Origins Fellow
Department of Astronomy, University of Virginia, Charlottesville, VA 22904, USA
Department of Chemistry, University of Virginia, Charlottesville, VA 22903, USA

0000-0002-4649-2536]Eric Herbst
Department of Astronomy, University of Virginia, Charlottesville, VA 22904, USA
Department of Chemistry, University of Virginia, Charlottesville, VA 22903, USA

0000-0003-1481-7911]Paola Caselli
Max-Planck-Institute for Extraterrestrial Physics (MPE), Giessenbachstr, 1, D-85748 Garching, Germany

0000-0002-6001-8048]Alec Paulive
Department of Chemistry, University of Virginia, Charlottesville, VA 22903, USA

0000-0002-4483-1733]Dominique M. Maffucci
Department of Chemistry, University of Virginia, Charlottesville, VA 22903, USA

0000-0003-0769-8627]Masao Saito
National Astronomical Observatory of Japan (NAOJ), Osawa, Mitaka, Tokyo 181-8588, Japan
Department of Astronomical Science, School of Physical Science, SOKENDAI (The Graduate University for Advanced Studies), Osawa, Mitaka, Tokyo 181-8588, Japan















Recent radio astronomical observations have revealed that HC_5N, the second shortest cyanopolyyne (HC_2n+1N), is abundant around some massive young stellar objects (MYSOs), which is not predicted by classical carbon-chain chemistry.  
For example, the observed HC_5N abundance toward the G28.28-0.36 MYSO is higher than that in L1527, which is one of the warm carbon chain chemistry (WCCC) sources, by more than one order of magnitude <cit.>.
In this paper, we present chemical simulations of hot-core models with a warm-up period using the astrochemical code Nautilus.
We find that the cyanopolyynes are formed initially  in the gas phase and accreted onto the bulk and surface of granular ice mantles during the lukewarm phase, which occurs at 25 < T < 100 K.
In slow warm-up period models,  the peak  abundances occur as the cyanopolyynes desorb from dust grains after the temperature rises above 100 K.
The lower limits of the abundances of HC_5N, CH_3CCH, and CH_3OH observed in the G28.28-0.36 MYSO can be reproduced in our hot-core models, after their desorption from dust grains.
Moreover, previous observations  suggested chemical diversity in envelopes around different MYSOs.  
We discuss possible interpretations of relationships between stages of the star-formation process and such chemical diversity, such as the different warm-up timescales.   
This timescale depends not only on the mass of central stars but also on the relationship between the size of warm regions and their infall velocity.
























§ INTRODUCTION
 

Knowledge of the chemical composition allows us to use molecules as powerful diagnostic tools of the physical conditions and dynamical evolution of star-forming regions <cit.>.
Recent improvements in efficiencies of radio telescopes enable the achievement of  high sensitivities with high angular resolution within reasonable observing times.
Owing to such developments, we can detect molecules with abundances significantly lower than previously detected species <cit.>, including isotopologues <cit.>.
The discovery of these molecules in various evolutionary stages raises new challenges in the fields of chemical network simulation and laboratory experiment.

Unsaturated carbon-chain species, such as C_2nH, CCS, and the cyanopolyynes (HC_2n+1N), are unique molecules in the interstellar medium.
For a long time, they have been thought to be abundant in young starless cores and decrease in abundance in later stages of low-mass star formation <cit.>.
The precursors of carbon-chain molecules in starless cores are mainly ionic carbon (C^+) and atomic carbon (C).
Carbon-chain molecules are mainly formed via gas-phase ion-molecule reactions and neutral-neutral reactions, the reaction rate coefficients of which can be large even at low temperatures such as T ≃ 10 K.

In contrast to the above classical picture,  low-mass protostellar cores rich in carbon-chain species have been found in sources such as L1527 in Taurus <cit.> and IRAS15398–3359 in Lupus <cit.>. On the other hand,
 saturated complex organic molecules (COMs) have been found to be abundant around protostars <cit.> in  so-called hot cores and hot corinos in high- and low-mass star-forming regions, respectively.
Therefore, the discovery of such low-mass protostellar cores   rich in carbon-chain species was surprising initially. 
The chemistry that produces these species was named “warm carbon chain chemistry” <cit.>.
In WCCC, the formation of carbon-chain molecules starts with the desorption of CH_4 from dust grains at a temperature of ∼25 K.
The reaction between CH_4 and C^+ and subsequent gas-phase reactions then lead to the formation of carbon chains <cit.>.
The different timescale of prestellar collapse was proposed as an origin of the difference between WCCC and hot corino chemistry <cit.>; the short and long starless core phases lead to WCCC and hot corino sources, respectively.
On the other hand, <cit.> suggested that different illumination by the interstellar radiation field around dense cloud cores could produce such chemical differentiation, based on their observations toward the L1544 prestellar core.
Hence, the origin of the chemical diversity found in low-mass star-forming regions is still controversial.

Observational studies of carbon-chain molecules in high-mass star-forming regions tend to be less detailed  than those of low-mass star-forming regions.
Nevertheless, cyanopolyynes have been detected in some famous high-mass star-forming regions such as Sgr B2 <cit.> and the Orion region, Orion KL <cit.> and OMC-2 FIR4 <cit.>.
Survey observations of HC_3N and HC_5N have been conducted toward high-mass starless cores (HMSCs) and high-mass protostellar objects (HMPOs) using the Nobeyama 45-m radio telescope <cit.>.
This group detected HC_3N in almost all of the target sources and detected HC_5N in  half of the HMPOs.
Indeed, HC_3N seems to be ubiquitous around HMPOs.
<cit.> found that HC_5N is abundant in envelopes around three massive young stellar objects (MYSOs) associated with the 6.7 GHz methanol masers using the Green Bank 100-m and Nobeyama 45-m telescopes.
The HC_5N abundance in G28.28-0.36, which is one of the target MYSOs, is higher than that in the Class 0 protostar L1527 by a factor of 20.
In addition, <cit.> suggested chemical diversity around MYSOs as a reason for the varying cyanopolyyne abundances; organic-poor MYSOs are surrounded by a cyanopolyyne-rich lukewarm envelope, while organic-rich MYSOs, namely hot cores, are surrounded by a CH_3OH-rich lukewarm envelope.

In this paper, we report an investigation of  the cyanopolyyne chemistry using  hot-core models with a warm-up period, motivated by the particularly high abundance of HC_5N in the G28.28-0.36 MYSO.
Cyanopolyynes are relatively stable species compared with other carbon-chain species and can survive in high temperature regions <cit.>.
In fact, the vibrationally excited lines of HC_3N and the extremely high-J rotational lines of HC_5N have been detected in Sgr B2(N) and Orion KL <cit.>.
In addition, HC_3N and HC_5N were detected in a candidate position of the molecular outflow around  G28.28-0.36  <cit.>.
Therefore, there is a large possibility that cyanopolyynes exist in hot core regions, where the temperature is higher than in WCCC sources, and where formation mechanisms of cyanopolyynes may differ in the two types of regions.
Furthermore, the formation paths of cyanopolyynes  have been thought to consist of possible steps in the synthesis of prebiotic molecules <cit.>, so it is also important to reveal their formation paths for science related to the origins of life.

In Section <ref>, we describe our models, with results found in Section <ref>.
We compare models, and the model results with the observational results around MYSOs <cit.> in Sections <ref> and <ref>, respectively. 
Effects of the cosmic-ray ionization rate on the HC_5N abundance are investigated in Section <ref>.
The chemistry of cyanopolyynes is compared with that of other carbon-chain species during the warm-up period in Section <ref>.
Possible origins of the chemical diversity around MYSOs are discussed in Section <ref>. 
Finally, our conclusions are presented in Section <ref>.



§ MODELS
 

In this study, we used the gas-grain Nautilus code <cit.> supplemented by preliminary reactions involving irradiation <cit.> to model the free-fall collapse and warm-up periods of hot core evolution <cit.>.
We ran both the three-phase model, in which the chemistry of the grain surface and the bulk ice are distinguished, and the two-phase model, in which the grain surface and bulk ice are not distinguished <cit.>.
The cosmic-ray ionization rate was assumed to be 1.3 × 10^-17 s^-1.
The ratio between diffusion energy and binding energy was set at 0.5 <cit.>.
The binding energies of major species and key species in the following sections are summarized in Appendix <ref>.
The competitive mechanism was used for surface reactions with chemical activation energy <cit.>.
Table <ref> lists the initial elemental abundances with respect to total hydrogen.
These elemental abundances correspond to the low-metal abundances, which are typically used for modeling the chemistry of dark clouds.
We assume that all of hydrogen is in the form of  H_2 at the initial stage.
There are 7646 gas-phase reactions and 498 gas-phase species,  mainly taken from the Kinetic Database for Astrochemistry (KIDA)[http://kida.obs.u-bordeaux1.fr]. 
We also included data taken from <cit.> and <cit.>.
<cit.> proposed the new formation reactions forming methyl formate and dimethyl ether.
<cit.> studied a new scheme for the synthesis of glycolaldehyde, acetic acid, and formic acid.
There are 5323 grain-surface reactions and 431 grain-surface species including suprathermal species <cit.>.
The surface reactions come mainly from <cit.>, with additional data taken from <cit.> and <cit.>.
The reactions between CH_3OH and CH_2^∗ <cit.> and between CH_3CO and CH_3 including suprathermal species <cit.> are included.
The self-shielding effects of H_2 <cit.>, CO <cit.>, and N_2 <cit.> are included.  

In addition to the self-shielding effects, Nautilus allows for variation of different parameters through switches. 
Included switches are as follows: enhancement of H_2 grain formation (off); enabling of photodesorption of ices (on); inclusion of cosmic-ray diffusion (on)[The effect of cosmic ray impacts which cause a stochastic heating of the dust particles allowing for surface radicals to diffuse quickly and react to form more complex species <cit.>.] ; inclusion of Eley-Rideal mechanism (off); enabling of radiolysis (off).
In our reaction network, reactions between cyanopolyynes and radicals on dust surface, which lead to destruction of cyanopolyynes, are not included. 
Since few of these processes have been studied to the best of our knowledge, and since theoretical treatments are not readily available, we did not try to add such reactions to our network. 
As shown in the following sections, cyanopolyynes in the gas-phase are destroyed mainly by atomic and molecular ions, which are not included in dust surface and ice mantles: all dust-surface and ice-mantle species are neutral.
One neutral species, which can destroy the cyanopolyynes, is neutral atomic carbon, but its abundance on dust surfaces is rather low due to rapid hydrogenation reactions even at low temperatures.


cc

Initial elemental abundances with respect to total Hydrogen 
0pt

Element      Abundance

H_2     0.5 

He     0.09 

C^+     7.3 × 10^-5 

N     2.14 × 10^-5 

O     1.76 × 10^-4 

F     1.8 × 10^-8 

Si^+     8 × 10^-9 

S^+     8 × 10^-8 

Fe^+     3 × 10^-9 

Na^+     2 × 10^-9 

Mg^+     7 × 10^-9 

Cl^+     1 × 10^-7 

P^+     2 × 10^-10 

Taken from the AL model in <cit.>.
	


We adopted the physical evolution of the two-stage hot-core model described by <cit.>.
The first stage corresponds to the free-fall collapse period.
The initial gas density is n_H = 10^4 cm^-3 and increases to 10^7 cm^-3 during the free-fall collapse, which lasts for ∼ 5 × 10^5 yr, while the visual extinction (A_V) increases from 5 mag to over 500 mag according to the increase in n_H.
The temperature is kept constant at 10 K <cit.>.

The second stage is the warm-up period, during which the
 temperature rises from 10 K to 200 K according to the following formula <cit.>: 

    T = T_0 + (T_max - T_0) ( Δ t/t_h)^n,

where T_0, T_max, t_h, and n are the initial temperature (10 K), the maximum temperature (200 K), the heating timescale, and the order of the heating, respectively.
We chose n=2, following <cit.>.
Three heating timescales were adopted: 5 × 10^4 yr (Fast), 2 × 10^5 yr (Medium), and 1 × 10^6 yr (Slow), approximating high-mass, intermediate-mass, and low-mass star-formation, respectively <cit.>.
The dust temperature is assumed to be equal to the gas temperature.
Figure <ref> shows the time variation of temperature, H_2 density, and visual extinction.  
After the final temperature of 200 K is reached, the system remains at this temperature, at which chemistry can still occur.  
In practice, several dynamical changes such as the molecular outflow and disk formation occur, but our models do not include the effects from these phenomena.
Table <ref> summarizes the models utilized. 
 
 
cccc

Summary of models 
0pt

Model     t_ha     phase

M1     Fast     3 phase 

M2     Medium     3 phase 

M3     Slow     3 phase 

M4     Fast     2 phase 

M5     Medium     2 phase 

M6     Slow     2 phase 


aFast, Medium, Slow correspond to 5 × 10^4, 2 × 10^5, and 1 × 10^6 yr, respectively.
	








§ RESULTS
 



 §.§ Cyanopolyyne Chemistry during the Free-Fall Collapse Period
 





Figure <ref> shows the abundances of HC_3N, HC_5N, and HC_7N in the gas phase during the free-fall collapse period.
The abundances of HC_3N and HC_5N at time scales of 5 × 10^3 – 4 × 10^5 yr agree with the abundances observed in high-mass starless cores <cit.>.
High-mass starless cores typically have gas densities of order 10^4 cm^-3 at fractions of a parsec <cit.>. 
Therefore, the results during the free-fall collapse period seem to be reasonable.

During the free-fall collapse stage, the following reaction significantly contributes to the formation of HC_3N;

    N + C_4H→HC_3N + C.

After an interval of 6 × 10^3 yr, HC_3N is also formed significantly by the dissociative recombination reaction

    HC_3NH^+ + e^-→HC_3N + H.


Several reactions contribute to the formation of HC_5N and HC_7N, and their fraction changes with time.
The following types of reactions largely form these species:

    H_2C_nN^+ + e^-→HC_nN + H,


    N + C_nH^-→HC_nN + e^-,

and

    N + C_n+1H→HC_nN + C,

where n=5, 7.

Cyanopolyynes are mainly destroyed by reactions with C^+ before 5 × 10^3 yr and reactions with C between 5 × 10^3 and 2 × 10^5 yr:

    HC_nN + C^+→H + C_n+1N^+,


    HC_nN + C^+→CN + C_nH^+,

and 

    HC_nN + C→H + C_n+1N,

where n=3,5,7.



 §.§ Cyanopolyyne Chemistry during the Warm-up period
 









Figure <ref> shows  cyanopolyyne abundances in the gas phase, dust surface, and bulk of the icy mantle during the warm-up period for the slow, three-phase model M3.
The zero of time is the starting time of the model calculation in the free-fall collapse stage.
The left-hand side of each abscissa corresponds to the start of the warm-up period, at around 5 × 10^5 yr.  
Note that the temperature is followed with time by a black dashed line.
The formation mechanisms of cyanopolyynes are basically the same in all of the models, depending on the temperature.
We use Model M3  because we can investigate the temperature dependence of cyanopolyyne chemistry during the warm-up period in most detail.



  §.§.§ HC_3N
 

The HC_3N abundance, especially in the gas phase, begins an increase around t =7 × 10^5 yr when the temperature reaches 25 K and the WCCC chemistry onsets <cit.>.
Figure <ref> shows the CH_4 abundances in the gas phase, dust surface, and bulk of the icy mantle of Models M3 and M6.
The gas-phase CH_4 abundance steeply increases and the abundances in dust surface and ice mantles decrease at t =7 × 10^5 yr.
At that time, methane (CH_4) desorbs into the gas phase from the dust surface, and then CH_4 reacts with C^+ leading to the formation of C_2H_2 via the electron recombination reactions involving C_2H_3^+ and C_2H_4^+ <cit.>. 
The C^+ ion is formed by the reaction between CO and He^+.
C_2H_2 reacts with CN to form HC_3N:

    C_2H_2 + CN→HC_3N + H.

This reaction was suggested as the main formation pathway of HC_3N based on observations of its three ^13C isotopologues toward the G28.28-0.36 MYSO <cit.>.
Therefore, our model result and the observational result reach the same conclusion. 
Small subsequent peaks in the HC_3N gaseous abundance  correspond to an enhancement in Reaction (<ref>), which relates to both the CN and C_2H_2 abundances.
For example, the CN abundance sharply increases due to its direct desorption from dust grains around t = 7.7 × 10^5 yr (T ≃ 31 K).
Around t = 9.3 × 10^5 yr (T ≃ 55 K), the gas-phase C_2H_2 abundance increases  because of its desorption from dust grains.  The increases in the gas phase values of CN and C_2H_2 lead to separate enhancements in the HC_3N gas phase abundance through Reaction (<ref>).   

At these low temperatures, HC_3N formed in the gas phase is partially depleted onto dust grains following each enhancement and accumulates in the bulk of the icy mantle.
The result is a pattern for the HC_3N abundance vs time that resembles a spectrum.
At t ≃ 1.1 × 10^6 yr (T ≃ 90 K), HC_3N sublimates from dust grains and reaches its peak abundance in the gas phase. 
The peak abundance in the gas phase is consistent with that of the bulk of the icy mantle, as shown in panel (a) of Figure <ref>.



  §.§.§ HC_5N
 

HC_5N is mainly formed by the following reaction in the warming gas (T > 25 K):

    C_4H_2 + CN→HC_5N + H,

while the precursor C_4H_2 is produced by the reaction

    CCH + C_2H_2→C_4H_2 + H,

and the radical CCH is formed by the electron recombination reaction of C_2H_3^+.
The ion C_2H_3^+ is formed by the reaction between CH_4 and C^+, as discussed  in the preceding section.
The gas-phase species C_4H_2 sharply increases at t = 1.0 × 10^6 yr (T ≃ 73 K) via its direct sublimation from dust grains.
Owing to increases in the C_4H_2 abundance, Reaction (<ref>) is enhanced, leading to an increase in the HC_5N  abundance. 
The radical CCH also reacts with HC_3N in the gas phase to produce HC_5N by the reaction

    CCH + HC_3N→HC_5N + H.


The species HC_5N formed in the gas phase is partially accreted into the bulk of the icy mantle, as is the case for HC_3N.
At t = 1.2 × 10^6 yr (T ≃ 115 K), HC_5N is desorbed into the gas, and reaches its peak abundance.
This abundance corresponds to that in the bulk of the mantle, right before desorption, as shown in panel (b) of Figure <ref>, in a similar manner to  HC_3N.
The subsequent decrease is caused by  reaction with HCO^+ and other protonated ions.



  §.§.§ HC_7N
 

After the temperature reaches 25 K, HC_7N is efficiently formed by the following reaction:

    C_6H_2 + CN→HC_7N + H.

The C_6H_2 species is formed by the reaction between CCH and C_4H_2, which is similar to Reaction (<ref>).
In addition, gaseous C_6H_2 reaches its peak abundance just after its direct sublimation from dust grains at t=1.2 × 10^6 yr (T ≃ 94 K) and the reaction rate of Reaction (<ref>) increases.
This leads to an increase in the HC_7N abundance. 
The  HC_7N species is also produced by the reaction

    CCH + HC_5N→HC_7N + H.


Analogously to the cases of HC_3N and HC_5N, HC_7N  also accumulates on the dust surface and in the bulk of the icy mantle and is desorbed into the gas phase around t = 1.3 × 10^6 yr (T ≃ 145 K).
The peak abundance of HC_7N in the gas phase is comparable to that on the dust surface, not in the bulk of the icy mantle, as shown in panel (c) of Figure <ref>.

Besides adsorption onto dust grains, cyanopolyynes are efficiently destroyed by the reactions with HCO^+ and other ions during the warm-up period:

    HC_nN + HCO^+→H_2C_nN^+ + CO,

where n = 3,5,7.

The peak abundance of HC_5N is higher than that of HC_3N, which may not be realistic.
Occasionally the largest species in a sequence, such as HC_7N (if it is truly the largest) is not described well in a network.
The high HC_5N abundance may reflect that there are unknown important destruction reactions of cyanopolyynes both in the gas phase and dust surface.
For example, radicals can move on dust grains during the warm-up period and reactions between cyanopolyynes and radicals may decrease the abundances of cyanopolyynes on dust surface and ice mantles.
However, our current reaction networks does not contain such reactions, while photodissociation destruction processes are included.
Besides photodissociation processes, if other destruction reactions of cyanopolyynes on dust surface exist, the longer cyanopolyynes will be more affected because longer cyanopolyynes stay longer time due to higher sublimation temperatures in our current model.

In summary, the cyanopolyynes are produced by a combination of neutral-neutral and ion-neutral gas-phase  reactions during the warm-up period (T > 25 K) and accumulate on and in the dust mantles before the temperature reaches their sublimation temperatures.
The sublimation of first CN and secondly the C_2nH_2 (n=1,2,3) species enhances key reactions  to form the cyanopolyynes, which partly accrete onto dust mantles.
As the temperature rises, the pattern of enhancements in the production of the gaseous  cyanopolyynes followed by  partial accretion onto grains leads to a characteristic spectral-type pattern.
When the temperature rises past the sublimation temperatures of cyanopolyynes, they desorb into the gas, and reach their peak abundances.  
The spectral-type abundance profile is best seen in the slow models, but exists to a lesser extent in the faster models too.
Cyanopolyynes are mainly destroyed by reactions with HCO^+ and other protonated ions in the gas phase and their abundances decrease.



§ DISCUSSION
 



 §.§ Comparisons of Cyanopolyyne Abundances among Models
 






ccccccccc

The peak calculated abundances of cyanopolyynes in the gas phase and the corresponding temperature 
0pt

Model     2cHC_3N          2cHC_5N          2cHC_7N 

2-35-68-9
     Abundance     T (K)           Abundance     T (K)          Abundance     T (K)

M1     3.62 × 10^-8     200         1.08 × 10^-7     200         6.03 × 10^-8     200 

M2     2.79 × 10^-8    200         7.66 × 10^-8     200         6.20 × 10^-8     200 

M3     4.39 × 10^-8     98         1.14 × 10^-7     129         5.19 × 10^-9     162 

M4     1.98 × 10^-8     200         8.97 × 10^-8     200         6.41 × 10^-8     200 

M5     2.15 × 10^-8     96         4.42 × 10^-8     200         1.45 × 10^-8     200 

M6     1.11 × 10^-8     92         5.02 × 10^-8     129         6.44 × 10^-10     162 

	


Figure <ref> shows comparisons of the cyanopolyyne abundances in the gas-phase during the warm-up period, among all models, while Table <ref> summarizes the peak abundances during the warm-up and hot-core periods of cyanopolyynes in the gas phase and the corresponding temperatures in each model.  
In the fast and medium warm-up  models (red and green lines), cyanopolyynes reach higher abundances in the gas phase after their desorption.
Given the rapidity of desorption,  their peak abundances do not correspond to their abundances on the dust surface or bulk of the icy mantle during the desorption.  
The post-desorption syntheses in the gas phase are particularly important for the longer chains.
One possible reason for their importance  is that there is not enough time to accumulate on dust surfaces or in the bulk of the icy mantles during the short heating timescale.  
On the other hand, accumulation on dust surface and in the bulk of the icy mantle play essential roles in producing the high cyanopolyyne abundances during the warm-up period when there is enough time for cyanopolyynes to adsorb onto dust grains.
This seems to depend on the assumed initial density.

When we compare the peak abundances in Model M3 (slow; 3-phase) with those in Model M6 (slow, 2-phase), we find that the peak abundances in M3 are higher  by a factor of 2 – 8, as shown in Table <ref>.
These different peak abundances between Models M3 and M6 support the hypothesis that accumulation of cyanopolyynes in the bulk of the icy mantle enhances their abundances in the gas phase after their desorption at higher temperatures, because, basically, the ice prevents the gas phase destruction of cyanopolyynes by maintaining their peak abundances unaltered in the mantles.



 §.§ Comparisons with Observations
 

Table <ref> contains summaries of the observed abundances of HC_5N, CH_3CCH, and CH_3OH in three MYSOs <cit.> and the peak calculated abundances in each model.
We excluded HC_3N because its column densities and excitation temperatures in the observed MYSOs seem to include large uncertainties <cit.>.
These observations were carried out using  single-dish telescopes and thus, because of beam dilution, the derived abundances and rotational temperatures are  lower limits <cit.>. 
Hence, our criterion for reproduction is that the model produces more than the observed lower limit in the following sections.

We found that the maximum model abundances of the three gas-phase species are higher than the observed lower limits in all of the models.
We also derived their abundances in L1527, a low-mass WCCC source,  and found, once again that the model peak abundances exceed the observed lower limits.  

cccc

Lower limits of observed abundances in MYSOs and the peak calculated abundances  of HC_5N, CH_3CCH, and CH_3OH 
0pt

Source/Model     HC_5N     CH_3CCH     CH_3OH

Observationa             

G12.89+0.49     5.0^+3.1_-2.7× 10^-10     2.1^+1.4_-1.1× 10^-8     6.0^+9.0_-4.5× 10^-8 

G16.86-2.16     (8.0 ± 3.5) × 10^-10     1.6^+0.95_-0.75× 10^-8     4.4^+5.5_-2.9× 10^-8 

G28.28-0.36     2.1^+1.3_-1.0× 10^-9     3.8^+2.6_-2.2× 10^-8     2.3^+3.5_-1.7× 10^-8 

L1527 (WCCC)b     (1.2 ± 0.3)× 10^-10     (1.07 ± 0.05)× 10^-9     (1.1 ± 0.2)× 10^-9 

             

Model             

M1     1.08 × 10^-7     9.27 × 10^-7     6.32 × 10^-6 

M2     7.66 × 10^-8     9.23 × 10^-7     4.76 × 10^-6 

M3     1.14 × 10^-7     2.42 × 10^-7     9.66 × 10^-8 

M4     8.97 × 10^-8     9.61 × 10^-7     3.60 × 10^-6 

M5     4.42 × 10^-8     9.03 × 10^-7     3.02 × 10^-6 

M6     5.02 × 10^-8     2.80 × 10^-7     6.46 × 10^-8 


aAbundances taken from <cit.> and converted to abundances with respect to total hydrogen.
bColumn densities of HC_5N, CH_3CCH, and CH_3OH taken from <cit.> and N(H_2) value of 2.8 × 10^22 cm^-2 taken from <cit.>. The abundances with respect to H_2 are converted to abundances with respect to total hydrogen.
	







cccccccc

The range of age and lower limit of temperature constrained by comparisons with the observational results in G28.28-0.36 
0pt

     3cAge (yr)          3cLower limit of temperature (K) 

2-4 6-8
Model     HC_5N     CH_3CCH     CH_3OH          HC_5N     CH_3CCH     CH_3OH

M1     5.94 × 10^5 - 2.48 × 10^6     4.71 × 10^5 - 7.19 × 10^5     4.75 × 10^5 - 7.19 × 10^5         200     84     100 

M2     5.92 × 10^5 - 2.64 × 10^6     5.64 × 10^5 - 6.39 × 10^5     5.79 × 10^5 - 6.39 × 10^5         120     84     100 
 
M3     1.21 × 10^6 - 1.44 × 10^6     1.07 × 10^6 - 1.16 × 10^6     1.16 × 10^6 - 1.19 × 10^6         118     82     105 

M4     5.94 × 10^5 - 1.70 × 10^6     4.70 × 10^5 - 5.94 × 10^5     4.74 × 10^5 - 5.94 × 10^5         200     78     98 
 
M5     5.90 × 10^5 - 1.64 × 10^6     5.59 × 10^5 - 6.39 × 10^5     5.74 × 10^5 - 6.39 × 10^5         118     78     96 
 
M6     1.19 × 10^6 - 1.44 × 10^6     1.05 × 10^6 - 1.12 × 10^6     1.13 × 10^6 - 1.17 × 10^6         112     78     98 


	


We are particularly interested in G28.28-0.36, because this source shows a uniquely  high HC_5N/CH_3OH feature, discussed below, among the observed sources <cit.>.  In addition, G28.28-0.36 shows a relatively high HC_5N abundance, as derived with the  single-dish observations <cit.>.
In the Orion KL hot core, the HC_5N abundance with respect to H_2 was derived to be 1.7 × 10^-10 <cit.>.
Therefore, the HC_5N abundance in G28.28-0.36 is higher than that in the Orion KL hot core by more than one order of magnitude.
As  already mentioned in Section <ref>, the HC_5N abundance in G28.28-0.36 is higher than that in L1527 by a factor of 20, as shown in Table <ref>.
The particularly high HC_5N abundance in G28.28-0.36 cannot be explained by warm carbon-chain chemistry (WCCC) in the lukewarm envelope <cit.>.

We now compare our model results with the lower limits of HC_5N, CH_3CCH, and CH_3OH in G28.28-0.36 in order to constrain the minimum temperatures in the warm-up period where they reside.
Figure <ref> shows the model results with the lower limits to molecular abundances in G28.28-0.36 as horizontal black dashed lines.
Table <ref> summarizes the range of ages and lower limits of temperature constrained by the comparisons between the model results and the observed lower limits. 
The range of ages is determined as the continuous times when the model abundances are higher than the observed lower limits.

The observed lower limit of HC_5N is reproduced only at ages after it desorbs from dust grains in all the models.
Therefore, the chemistry in the lukewarm temperature  range of 25 < T < 100 K cannot explain the high HC_5N abundance in G28.28-0.36, because its desorption temperature is higher than 100 K. 
The ages when the temperature reaches at the HC_5N sublimation temperature of ∼ 115 K are 5.9 × 10^5 yr and 1.2 × 10^6 yr in the Medium and Slow warm-up models, respectively.
In the Fast warm-up models, further gas-phase formation is needed to reproduce the observed HC_5N abundance.
Hence, the lower limit of the observed HC_5N abundance cannot be reproduced at its sublimation temperature (t ∼ 4.8 × 10^5 yr).

The carbon-chain species CH_3CCH,  shown in the middle panels of Figure <ref>, is formed in the gas phase during the warm-up period triggered initially by desorption of CH_4 via the following reactions:

    CH_4 + C^+→C_2H_3^+ + H,


    CH_4 + C_2H_3^+→C_3H_5^+ + H_2,

followed by

    C_3H_5^+ + e^-→CH_3CCH + H.

The CH_3CCH is subsequently adsorbed onto dust grains, in analogy with the cyanopolyynes, and starts to desorb at temperature of 70 K. 
The minimum temperature at which its lower limit observed in G28.28-0.36 (3.8^+2.6_-2.2× 10^-8) is reproduced occurs only after its desorption from dust grains at ≈ 80 K, corresponding to ages of 4.7 × 10^5 yr, 5.6 × 10^5 yr, and 1.1 × 10^6 yr in the Fast, Medium, and Slow warm-up models, respectively.
Its abundances decrease more rapidly compared to those of HC_5N, and the ranges of time which can reproduce the observed abundance become narrower.
Unlike HC_5N, CH_3CCH is destroyed by the reaction with atomic oxygen, leading to CO + C_2H_4.
This reaction seems to contribute to the faster destruction of CH_3CCH.
 
The lower panels of Figure <ref> show the results for CH_3OH, which is not a species produced by WCCC, because its sole production occurs on the grains via hydrogenation of CO.
Nevertheless, its lower limit observed in G28.28-0.36 is also reproduced only after it desorbs into the gas phase at temperatures above ∼ 100 K.
The corresponding ages of the CH_3OH sublimation are 4.8 × 10^5 yr, 5.8 × 10^5 yr, and 1.1 × 10^6 yr in the Fast, Medium, and Slow warm-up models, respectively.
Methanol is destroyed by reactions with ions such as HCO^+.

In summary, the lower limits of all of these species derived in G28.28-0.36 can be reproduced only after desorption from dust grains. 
The observed species in G28.28–0.36 seem to reside in higher temperature regions when compared with WCCC sources.
The HC_5N and CH_3OH abundances do not become higher than the observed abundances at the same age in the Slow warm-up models, although their peaks can be higher than the observed ones at different ages (Table <ref>).





We now return to a comparison of  theory and observation concerning the abundance ratio of HC_5N to methanol in G28.28–0.36.
The derived N(HC_5N)/N(CH_3OH) column density ratio in G28.28–0.36 (0.091^+0.109_-0.039) is higher than that in the other three MYSOs by more than one order of magnitude <cit.>.
This ratio will be much lower in some HC_5N-undetected MYSOs than the HC_5N-detected MYSOs.
In fact, <cit.> did not detect HC_5N in half of their target MYSOs. 

Figure <ref> shows temporal dependence of the HC_5N/CH_3OH abundance ratio of Models M1 – M3.
Because the individual abundances of  both HC_5N and CH_3OH can be reproduced only after desorption from the gas, we investigated the ratio of their abundances only in this region.
The actual investigated ranges of age are 4.75 × 10^5 – 2.48 × 10^6 yr, 5.79 × 10^5 – 1.02 × 10^6 yr, and 1.16 × 10^6 – 1.3 × 10^6 yr for Models M1, M2, and M3, respectively.
The closest calculated values to the observed ratios  are ∼ 0.20 at 6 × 10^5 yr (T = 200 K) in Model M1 and ∼ 0.16 at 1.2 × 10^6 yr (T ≃ 115 K) in Model M3.
In the case of Model M2, the calculated ratio with the current time resolution changes too rapidly and we could not find the exact value and age when the observed ratio is reproduced.
From Figure <ref>, the observed ratio may be reproduced around 8 × 10^5 yr (T = 200 K) in Model M2.
All of these ages correspond closely to the time when HC_5N reaches the peak abundances.
These results may suggest that desorption of HC_5N or its further gas-phase formation have just started in hot regions in G28.28–0.36.



 §.§ Effects of Cosmic Ray Ionization Rates on HC_5N Abundance
 

<cit.> suggested that a high cosmic-ray ionization rate of ζ≃ 4 × 10^-14 s^-1 can reproduce their observational results for cyanopolyynes in OMC-2 FIR4.
The observational results of the c-C_3H_2 abundance were also reproduced by such a high cosmic-ray ionization rate <cit.>.
In addition to runs with the common cosmic-ray ionization rate of ζ = 1.3 × 10^-17 s^-1, we ran our models with high cosmic-ray ionization rates of ζ = 3.0 × 10^-16 s^-1 and 4.0 × 10^-14 s^-1, as <cit.> had done.
Such high cosmic-ray ionization rates could be possible in protostellar systems <cit.>.
Our results for gas-phase HC_5N abundances using these three ionization rates are shown in Figure <ref>. 
We used  Models M3 and M1 with Slow and Fast warm-up timescales in panels (a) and (b), respectively.

In panel (a), the peak abundances decrease with an increase in the cosmic-ray ionization rate. 
This is caused by the fact that HC_5N is destroyed in the gas phase by reaction with H^+ and other ions before it is adsorbed onto dust grains.
The H^+ ion destroys HC_5N most efficiently after 7 × 10^5 yr:

    HC_5N+ H^+→H + HC_5N^+.

This reaction is essential especially in the model with the cosmic-ray ionization rate of 4 × 10^-14 s^-1.
The HC_5N^+ ion partly reacts with H_2 to form H_2C_5N^+, which contributes to re-formation of HC_5N through the electron dissociative recombination reaction.
However, the reaction between HC_5N^+ and H_2 is much less effective compared to the electron dissociative recombination of HC_5N^+ to form C_5N and H, because the electron abundance becomes high in conditions with high cosmic-ray ionization rates.
Polyatomic ions such as HCO^+ and H_3^+ react with electrons, leading to dissociative recombination, more rapidly than H^+, and hence the relative abundance of H^+ to polyatomic ions becomes high. 
Thus, the H^+ becomes a reaction partner of HC_5N.
In the model with the cosmic-ray ionization rate of 3.0 × 10^-16 s^-1, on the other hand, the HCO^+ ion is the main contributor to the destruction of HC_5N after 10^6 yr:

    HC_5N + HCO^+→CO + H_2C_5N^+.

The formed H_2C_5N^+ will react with electrons and partly (∼ 45 %) will go back to HC_5N. 
As discussed in the previous sections, the accumulation of HC_5N onto dust surface and in ice mantles is an important process in the slow warm-up models. 
However, the HC_5N destruction by ions works efficiently in the high cosmic-ray ionization models, and the accumulation of HC_5N is suppressed, leading to the lower HC_5N abundances.
The HC_5N abundances in models with  the two higher cosmic-ray ionization rates cannot reproduce its observed abundance in G28.28–0.36 even at peak abundance.
However, there is no significant difference in peak abundance among the fast warm-up models with different cosmic-ray ionization rates in panel (b).
With the highest cosmic-ray ionization rate, HC_5N continues to be formed by Reaction (<ref>) efficiently, while the reaction is less efficient due to the significantly lower abundance of C_4H_2 in the models with the cosmic-ray ionization rate of 3.0 × 10^-16 s^-1 after ∼ 1 × 10^6 yr.  
This highest cosmic-ray ionization model can reproduce the observed abundance in G28.28–0.36 for all times after 4.86 × 10^5 yr (T ≥ 170 K).

The HC_5N abundance in the slow warm-up model with cosmic-ray ionization rate of 4.0 × 10^-14 s^-1 is significantly lower than in the same cosmic-ray ionization rate model with fast warm-up. 
The difference between slow and fast warm-up models is caused by the different abundances of H^+ and H_3^+, which in turn are related to the abundances of H and H_2. 
In the slow warm-up model, the H_2 formation rate is slowed down by an exponential factor of the form exp(-E_diff/T), where E_diff is known as the diffusion barrier and T is the temperature.
The diffusion barrier slows the average motion of the reacting hydrogen atoms.
The destruction rate of H_2 is larger than its formation rate in such a high cosmic-ray ionization condition. 
The retarding effect of the diffusion barrier is lessened in the fast warm-up model because of the higher temperatures even at early times.
Hence, the H abundance is higher than that of H_2 in the slow warm-up model, while the H_2 abundance is higher in the fast warm-up model.
In the slow warm-up model, the H^+ ion is efficiently formed by the ionization of H atom by cosmic rays. 
On the other hand, in the fast warm-up model, the H^+ ion is formed by the reaction between H_2 and cosmic rays, leading to H, H^+, and electrons, which is slower than the ionization of H atoms by cosmic rays.
Hence, the formation of the H^+ ion is more efficient in the slow warm-up model. 
Cosmic rays also produce H_2^+ from H_2 ionization.  
The H_2^+ ion subsequently reacts with H_2 forming the H_3^+ ion in the fast warm-up model, whereas H_2^+ reacts with H to form H_2 and H^+ in the slow warm-up model.
Therefore, in the slow warm-up model, the H^+ abundance is larger than that of H_3^+, while the opposite is true in the fast warm-up model.
 
The H^+ ion contributes to destruction of HC_5N to form HC_5N^+ in the slow warm-up model. 
The reaction between HC_5N^+ and electrons cannot produce HC_5N.
In the fast warm-up model, on the other hand, the reactions with H_3^+ and HCO^+ destroy HC_5N, and both reactions form H_2C_5N^+, which reacts with electron and partially goes back to HC_5N. 
Reaction (<ref>) continues to form HC_5N in both models and this reaction is particularly important for the slow warm-up model. 
The C_4H_2 molecules are formed from large hydrocarbons (e.g., C_4H) and their ions (e.g., C_4H_3^+) in both models, not bottom-up formation starting from CH_4. 
Therefore, the carbon-chain formation starting from CH_4 is no longer an important formation mechanism of cyanopolyynes for the highest cosmic-ray ionization models.

In summary, the lower limit of HC_5N observed in the G28.28–0.36 MYSO can be reproduced with temperatures above ∼ 115 K in all of the models with the typical cosmic-ray ionization rate of 1.3 × 10^-17 s^-1.
In the case of the Slow warm-up timescale, the models with high cosmic-ray ionization rates cannot reproduce the observed abundance of HC_5N in G28.28–0.36.
On the other hand, the model with Fast warm-up timescale and the highest cosmic-ray ionization rate can maintain the high abundance of HC_5N.








 §.§ Comparisons among Carbon-Chain Species
 





We found unusual features of the cyanopolyynes during the warm-up period; in particular, they are formed initially in the gas phase, subsequently  accumulate in the bulk of the icy mantle, and then desorb into the gas phase, with their gas-phase peak abundances attained when they desorb.
The carbon-chain molecule CH_3CCH shows a similar feature (Section <ref>).

Figure <ref> shows the abundances of CCH (red), CCS (green), and c-C_3H_2 (blue) during the warm-up period.
The species CCH and CCS show abundance peaks just after the temperature rises to 25 K.
The CCH molecule is efficiently destroyed by the reaction with atomic oxygen (O) during 1.0 × 10^6≤ t ≤ 1.07 × 10^6 yr, when the temperature rises from ≈ 70 K to ≈ 80 K.
The subsequent decrease in the gas-phase CCH abundance is caused by its efficient destruction by reaction with H_2, which occurs efficiently with the temperature of ≥ 90 K, at a time of t ≥ 1.1 × 10^6 yr <cit.>.
Dicarbon sulfide, or CCS, is destroyed by the reaction with atomic oxygen (O). 
The atomic oxygen desorbs at temperatures above 60 K <cit.> at a time of t ≥ 1.0 × 10^6 yr.
Because of these rapid gas-phase reactions, desorption from dust surfaces is not important for the synthesis of gas-phase CCH and CCS.

On the other hand, c-C_3H_2 shows its gas-phase peak abundance after its direct evaporation from the dust surface at temperatures above 90 K at a time of t ≥ 1.1 × 10^6 yr, as is the case for the  cyanopolyynes and CH_3CCH.
The cyclic species c-C_3H_2 is produced in the gas-phase both in the pre-warm-up period and during the warm-up period starting with the sublimation of CH_4.  
The main formation pathway of c-C_3H_2 is the dissociative recombination reaction of c - C_3H_3^+:

    c-C_3H_3^+ + e^-→ c-C_3H_2 + H.

Gaseous c-C_3H_2, formed in the low-temperature portion of the warm-up period, is subsequently adsorbed onto dust grains, from which it desorbs after ∼ 1.0 × 10^6 yr at temperatures T ≥ 65 K.
It is efficiently destroyed by the reaction with H_2 at temperatures above 120 K (t ≥ 1.2 × 10^6 yr).
Hence, the efficient destruction of c-C_3H_2 occurs after it desorbs.
All species in Figure <ref> decrease in abundance with parallel curves after 1.5 × 10^6 yr.

In summary, there are largely two types of carbon-chain species in warm-up regions.
One type shows peak abundances just after their desorption from dust grains; these include cyanopolyynes, CH_3CCH, and c-C_3H_2.
The other type shows peak abundances just after the temperature rises to 25 K (CCH and CCS).
The latter include relatively reactive species, which are easily destroyed in the gas phase.
On the other hand, cyanopolyynes are not destroyed by reactions with H_2 and O, but react with ions such as H^+, H_3^+, and HCO^+, and so eventually decrease.  

Such differences among carbon-chain species seem to explain the observational results in HMPOs <cit.> and massive cluster-forming regions <cit.>.
<cit.> suggested that HC_3N is newly formed in the warm and well-shielded dense gas around HMPOs, and <cit.> reported that the detection rates  for the cyanopolyynes, defined by the number of sources where target molecules were detected divided by the number of total observed sources × 100,  are higher around HMPOs than  in low-mass protostars, but that of CCS is lower.
<cit.> concluded that HC_3N tends to be abundant, whereas  CCS detection is rare in massive cluster-forming clumps, where it has  probably been already destroyed by reaction with O because the dust temperature should be higher than the sublimation temperature of atomic oxygen.  On the other hand, HC_3N can still be abundant in such high temperature regions.



 §.§ Implication for Chemical Diversity around Massive Young Stellar Objects (MYSOs)
 

As  already mentioned in Section <ref>, the different timescales of the starless core phase <cit.> and the penetration of the interstellar radiation field <cit.> were proposed as possible origins of chemical diversity in low-mass star-forming regions.
High-mass stars are usually born in giant molecular clouds (GMCs), and there is a possibility that the formation of high-mass starless cores starts long after the clouds were well shielded against the interstellar radiation field unless GMCs have clumpy structures.
In the former case, there should be enough time for atomic carbon to convert into CO molecules.
In particular, the interstellar radiation field may be important for the outer edge of GMCs but not for the inner regions, as is the well-known case of photon-dominated regions (PDRs).

Chemical diversity can also be caused by the dependence of abundance on the heating rate.  
For example, CH_3OH shows higher peak abundances in those models with a Fast heating timescale.
On the other hand, as discussed above, HC_5N tends to be more abundant in the models with the Slow heating timescale because there is enough time for HC_5N to accumulate in the bulk of the icy mantle before desorption.
This may be one possible origin of the chemical diversity around MYSOs <cit.>. 

The heating timescale of warm-up regions depends not only on stellar masses but also on the relationship between the size of the warming region and the infall velocity <cit.> as given by

    t_h∝R_warm/V_infall,

where t_h, R_warm, and V_infall are the heating timescale, the size of the warm region, and the infall velocity, respectively.
If R_warm becomes larger or V_infall becomes smaller, t_h will be longer.
Such a condition will lead to HC_5N-rich/CH_3OH-poor envelopes around MYSOs, which is similar to the case of G28.28-0.36.

The size of warm regions and their infall velocity relate to other physical conditions.
For example, the size of warm regions depends upon  the luminosity of the central stars, and the density structure <cit.>, while
the infall velocity is related to the density, rotating motion, magnetic field, and radiation pressure <cit.>.
Consequently, the heating timescale is also related to the physical conditions in star-forming regions.
Observations investigating relationships between the chemical diversity and Equation (<ref>) are necessary to constrain the proposed scenario.

The possibility of  UV radiation to cause chemical diversity should be considered in cluster regions.
The first born star should affect its environment and the strong UV radiation it emits can destroy CO molecules to form C and/or C^+, which will be precursors of carbon-chain species.  In that case, we would expect chemical diversity among sources in the same cluster region.
As discussed in Section <ref>, the cosmic-ray ionization rate significantly affects the abundances of cyanopolyynes. 
Cosmic rays can penetrate deeper dense regions compared to the UV radiation. 
Hence, the effects of cosmic rays may be essential particular in the dense cores including hot cores.

The binding energies are affected by significant errors (Table <ref> in Appendix <ref>) and they change with ice-mantle surface composition <cit.>. 
More laboratory work should be dedicated to binding energy measurements; meanwhile, detailed comparison between model predictions and observational results toward star-forming regions will help to put constraints on these important parameters.



§ CONCLUSIONS
 

We have investigated cyanopolyyne chemistry around MYSOs with warm-up hot-core models using the Nautilus code, and motivated by recent observational results toward MYSOs <cit.>.
The main conclusions of this paper are as follows: 


  * Cyanopolyynes are formed via  neutral-neutral and ion-neutral reactions in the lukewarm gas (25 < T < 100 K).
The sublimation of CH_4 and C_2nH_2 from dust grains enhances key reactions for the formation of cyanopolyynes. 
They are simultaneously accumulated on the dust surface and in the bulk of icy mantles in this temperature range.
Cyanopolyynes sublimate into the gas phase when the temperature rises above ∼ 100 K and reach their peak abundances in the gas phase.

  * The carbon chain CH_3CCH shows similar characteristics to cyanopolyynes. It is formed from CH_4 sublimated from dust grains and accumulates onto dust grains before the temperature reaches its sublimation temperature of 70 K. 
After the temperature reaches 70 K, CH_3CCH desorbs from dust grains and shows the gas-phase peak abundance.

  * Models with a longer warm-up period enable these species to accumulate to a greater extent in the bulk of icy mantles.

  * Our model results can reproduce the lower limits of HC_5N, CH_3CCH, and CH_3OH observed in the G28.28-0.36 MYSO, where HC_5N is particularly abundant <cit.>.
Their observed abundances are reproduced best just after their sublimation from dust grains.

  * The species CCH and CCS show their peak abundances just after they are formed in the gas phase triggered by the evaporation of CH_4. 
The chemistry that produces them is the WCCC chemistry.
They are reactive species and destroyed by H_2 or O in the gas phase.
On the other hand, cyanopolyynes, CH_3CCH, and c-C_3H_2 are relatively stable species and can accumulate in the bulk of icy mantles before destruction in the gas phase.
This implies that there are largely two types of carbon-chain species.
Such results seem to explain the higher detection rates of cyanopolyynes than that of CCS in HMPOs and cluster-forming regions.

  * HC_5N-rich and CH_3OH-poor envelopes around MYSOs may reflect different heating timescales.
The heating timescale depends not only on the mass of central stars but also on the relationships between the size of warm regions and their infall velocity, which in turn relate to various physical conditions, including  luminosity, density, magnetic field, rotating motion, and radiation pressure.




K. T. would like to thank the University of Virginia for providing the funds for her postdoctoral fellowship in the Virginia Initiative on Cosmic Origins (VICO) research program. E. H. is grateful for support from the National Science Foundation through grant 1514844.



















Nautilus <cit.>














§ BINDING ENERGY
 

Table <ref> summarizes binding energies of major species and key species in this paper utilized in our model.
These binding energy values and errors are taken from the KIDA database <cit.>.


cccc[h]

Binding energies of major species 
0pt

Species     Binding Energy (K)     Species     Binding Energy (K)

H     650 ± 195     C_2H_2     2587 ± 776 

H_2     440 ± 132     C_4H_2     4187 

C     4000     C_6H_2     5787 

O     1660 ± 60     HC_3N     4580 

N     800     HC_5N     6180 

CO     1150     HC_7N     7780 

CN     1600     CH_3OH     5534 

CH_4     1300     CH_3CCH     4287 

These values are applied for species on amorphous water ice surface <cit.>.
	





























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