Chemical Modeling of Interstellar Molecules in Dense Cores

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Donghui Quan, M.S.

Graduate Program in Chemical Physics

The Ohio State University

2009

Dissertation Committee:

Professor Eric Herbst, Advisor

Professor Frank C. De Lucia

Professor Anil K. Pradhan

Donghui Quan

2009

Abstract

There are billions of stars in our galaxy, the Milky Way Galaxy. In between the stars is where the so-called “interstellar medium” locates. The majority of the mass of interstellar medium is clumped into interstellar clouds, in which cold and hot dense cores exist. Despite of the extremely low densities and low temperatures of the dense cores, over one hundred molecules have been found in these sources. This makes the field of astrochemistry vivid. Chemical modeling plays very important roles to understand the mechanism of formation and destruction of interstellar molecules. In this thesis, chemical kinetics models of different types were applied: in Chapter 4, pure gas phase models were used for seven newly detected or confirmed molecules by the Green Bank Telescope; in

Chapter 5, the potential reason of non-detection of O2 was explored; in Chapter 6, the mysterious behavior of CHNO and CHNS isomers were studied by gas-grain models. In addition, effects of varying rate coefficients to the models are also discussed in Chapter 3 and 7.

Dedication

Dedicated to my parents Quan He (全和), Li Lianxiang (李廉祥 ) and my wife

Wang Jing (王璟)

iii

Acknowledgements

First of all, I would like to thank my advisor, Professor Eric Herbst, who has always been supportive in all means: a mentor in my graduate study, a guide in astrochemical research, and a kind “father” in the life.

My most appreciation also goes to my thesis committee: Professor Frank C. De Lucia and Professor Anile K. Pradhan, who give precious opinions and helpful comments on the research and thesis writing.

I would also like to thank my collaborators: Professor Ian Smith, for evaluating new rates of C + Cn reactions; Professor Dahbia Talbi, for estimating possible formation channels of c-C3H2O; Professor Murray McEwan, for suggestions of + + maximum branching ratio of C2H3 + CO to form C3H3O ; Professor Hua Guo, for theoretical calculations of O + OH reaction rate coefficient; Dr. David Woon, for estimating useful data for CHNO and CHNS isomers; Dr. Sandra, Brünken, for detailed information of Sgr B2 physical conditions and CHNO isomers detection; Professor Yoshihiro Osamura, for evaluating possible neutral-neutral destruction channels of CHNO isomers. Without their beneficial discussion and numerous helps, works in this thesis would not be possible.

My thankfulness is also to former and current group members: Dr. Oscar Osamara, Dr. Herma Cuppen, Dr. Robin Garrod, Dr. Valentine Wakelam, Dr. Qiang Chang, Dr. George Hassle, Paul Rimmer, Nanase Harade, Yezhe Pei. With everybody’s efforts, the group is like a big warm family.

I want to thank my parents, who raised me, educated me, and supported me in all occasions. I want to thank my beloved wife, Jing, who always has confidence in me and accompanies me through all the difficulties and happy times.

Vita

Nov. 1978 ...... Born - Taizhou, Jiangsu, China P. R.

1998...... B.S. - Chemical Physics, University of

Science and Technology of China,

Anhui, China

2003...... M.S. - Chemical Physics, University of

Science and Technology of China,

Anhui, China

2003 to present ...... Graduate Research Assistant

Graduate Program of Chemical

Physics, The Ohio State University,

Columbus, Ohio, USA

Publications

(1) D. Quan, E. Herbst, and Y. Osamura ”Gas-grain Modeling of Cyanic Acid,

Isocyanic Acid, Fulminic Acid, and Isofulminic Acid in Hot, Lukewarm, and Cold

Cores” (in preparation )

(2) N. Marcelino, S. Brünken, J. Cernicharo, D. Quan, E. Roueff, E. Herbst, and

P. Thaddeus, “The Puzzling Behavior of HNCO Isomers in Molecular Clouds”,

(submitted to A&A)

(3) V. Wakelam, J.C. Loison, D. Talbi, D. Quan, and F. Caralp ”A Sensitivity study of the neutral-neutral reactions C + C3 and C + C5 in Cold Dense

Interstellar Cores” Astronomy & Astrophysics 495, 513 (2009)

(4) D. Quan, E. Herbst, T. J. Millar, G. E. Hassel, S. Lin, H. Guo, P. Honvault, and D. Xie ”New Theoretical Results Concerning the Interstellar Abundance of

Molecular Oxygen” The Astrophysical Journal, 681, 1318 (2008)

(5) D. Quan and E. Herbst ”Possible gas-phase syntheses for seven neutral molecules studied recently with the Green Bank Telescope” Astronomy &

Astrophysics 474, 521 (2007)

(6) I. W. M. Smith, A. M. Sage, N. M. Donahue, E. Herbst and D. Quan ”The temperature-dependence of rapid low temperature reactions: experiment, understanding and prediction” Faraday Discussions 133, 137 (2006)

Fields of Study

Major Field: Astrochemistry and Astrophysics

Table of Contents

Abstract ...... ii

Dedication ...... iii

Acknowledgements ...... iv

Vita ...... v

List of Tables ...... xii

List of Figures ...... xiv

Chapter 1: Introduction ...... 1

1.1 Interstellar medium and interstellar clouds ...... 1

1.2 Interstellar molecules ...... 4

1.3 Astrochemistry ...... 8

1.4 References ...... 15

Chapter 2: Chemical Models ...... 18

2.1 Modeling Method ...... 18

2.2 Gas-Phase Model ...... 20

2.2.1 Physical conditions of the gas model ...... 21

2.2.2 Species in the gas model ...... 23

2.2.3 Chemical reactions and the rate coefficients ...... 23

vii

2.3 Gas-Grain Model ...... 31

2.3.1 Physical parameters of dust particles ...... 32

2.3.2 Surface species ...... 33

2.3.3 Surface reactions and gas-grain interactions ...... 34

2.4 Application of the models ...... 38

2.5 References ...... 38

Chapter 3: Inclusion of New Rapid Low Temperature Reaction Rate Coefficients

...... 40

3.1 New Rates ...... 40

3.2 Gas phase model settings ...... 41

3.3 Results and comparison to former models and observances ...... 42

3.4 References ...... 47

Chapter 4: Gas-phase modeling of GBT Molecules in TMC-1 and Sgr B2...... 49

4.1 Observational results ...... 49

4.1.1 Molecules in TMC-1 ...... 50

4.1.2 Molecules towards Sgr B2 ...... 51

4.2 Synthesis of detected molecules ...... 52

4.2.1 Synthesis of observed molecules in TMC-1 ...... 60

viii

4.2.2 Synthesis of observed molecules towards Sgr B2(N) ...... 64

4.3 Modeling results and comparison with observances ...... 67

4.3.1 TMC-1 ...... 67

4.3.2 Halo of Sgr B2(N) ...... 73

4.4 Conclusion ...... 75

4.5 References ...... 77

Chapter 5: Interstellar Abundance of Molecular Oxygen ...... 79

5.1 Background of O2 problem in cold cores ...... 79

5.1.1 Review of the history of modeling attempts ...... 80

5.1.2 Rate of O + OH reaction ...... 81

5.1.3 O2 factional abundance upper limits set by observers ...... 82

5.2 Modeling settings and general discussion of O + OH reaction effects ... 83

5.2.1 Modeling method and settings ...... 83

5.2.2 Effects of O + OH reaction rate coefficient change on related species

5.3 Modeling results and comparison to observations ...... 86

5.3.1 OH and O2 ...... 86

5.3.2 Other affected species ...... 93

5.3.3 High sulfur calculations ...... 96

5.3.4 Warmer sources ...... 100

5.4 Conclusion ...... 101

5.5 References ...... 102

Chapter 6: Gas-grain modeling of CHNO isomers and CHNS isomers ...... 106

6.1 Background of CHNO isomers study ...... 106

6.1.1 Observational results ...... 106

6.1.2 Possible gas-phase syntheses ...... 108

6.2 Gas-grain models for CHNO isomers ...... 110

6.2.1 New reactions ...... 110

6.2.2 Gas-grain modeling settings ...... 124

6.3 Results ...... 126

6.3.1 Hot cores ...... 127

6.3.2 Hot core environments ...... 129

6.3.3 Lukewarm corino ...... 131

6.3.4 Cold cores ...... 133

6.4 CHNS isomers ...... 136

6.5 Discussion ...... 139

6.6 References ...... 142

Chapter 7: Sensitivity Method ...... 146

7.1 Introduction ...... 146

7.2 Chemical models ...... 148

+ 7.3 H3 + O case study ...... 149

7.4 C + Cn case study ...... 156

7.5 Conclusion ...... 159

7.6 References ...... 159

References ...... 161

List of Tables

Table 1.1 Detected interstellar molecules...... 5

Table 2.1 Physical parameters for typical cold interstellar clouds...... 21

Table 2.2 Typical non-zero initial fractional abundances...... 22

Table 2.3. Examples of types of reactions...... 30

Table 2.4 Major physical parameters for dust particles and gas-grain interactions.

...... 32

Table 2.5. Examples of additional types of reactions and processes to the model.

...... 37

Table 3.1 List of Modified Reaction Rate Coefficients in New Rapid Low

Temperature Reaction Study...... 41

Table 3.2 Comparison of some calculated and observed fractional abundances with respect to H2 in L134N...... 43

Table 3.3 Comparison of some calculated and observed fractional abundances with respect to H2 in TMC-1...... 45

Table 4.1 GBT molecules chemistry...... 53

Table 5.1 k1 values at 10K used in O2 study...... 86

Table 6.1 Additional gas-phase reactions for CHNO isomer study...... 114 xii

Table 6.2 Additional surface-related reactions for CHNO isomer study...... 121

Table 6.3 Physical parameters of the CHNO models...... 125

Table 7.1 Studied reactions with their rate coefficients. Coefficients also multiplied by factors of 3.125, 2, 1.1 for comparison...... 154

xiii

List of Figures

Figure 1.1. Collaboration in astrochemistry...... 9

Figure 4.1. Calculated fractional abundances of CH3C3N and CH2CCHCN...... 69

Figure 4.2. Calculated abundance ratio of cyanoallene to methyl cyanoacetylene plotted vs. parameter δ...... 70

Figure 4.3. Calculated fractional abundances of C4H3N isomers vs. time...... 71

Figure 4.4. Calculated fractional abundances of methyl cyanodiacetylene

(CH3C5N) and methyl triacetylene (CH3C6H) plotted vs. time...... 72

Figure 4.5. Calculated fractional abundance of ketenimine plotted as a function of time...... 73

Figure 5.1. Fractional abundance of OH with respect to H2 plotted as a function of time for four different k1 values...... 88

Figure 5.2. Fractional abundance of O2 with respect to H2 plotted as a function of time for four different k1 values...... 89

Figure 5.3. Same as Figure 5.1 except that C-rich abundances relevant to TMC-1 are used...... 91

Figure 5.4. Same as Figure 5.2 except that C-rich abundances relevant to TMC-1 are used...... 92

xiv

Figure 5.5. Percentage of significantly affected species plotted against time. .... 94

Figure 5.6. Fractional abundances of NO and SO2 with respect to H2 plotted against time for four different values of the rate coefficient k1...... 96

Figure 5.7. Fractional abundance of O2 with respect to H2 plotted against time for four k1 values...... 98

Figure 5.8. Same as Figure 5.7 except that horizontal lines are observational results towards TMC-1, dashed lines and dotted lines are calculated abundances for C-rich cases (both for low-metal and high-sulfur)...... 99

Figure 6.1. Temperature settings of four gas-grain models applied for CHNO isomers study...... 126

Figure 6.2. Fractional abundance of CHNO isomers with respect to H2 plotted as a function of time for hot cores...... 129

Figure 6.3. Same as Figure 6.2 except that the warm envelope model is used and compared to Sgr B2 (OH) observation...... 131

Figure 6.4. Fractional abundance of CHNO isomers with respect to H2 plotted as a function of time for lukewarm corino...... 133

Figure 6.5. Fractional abundance of CHNO isomers with respect to H2 plotted as a function of time for cold cores...... 135

Figure 6.6. Fractional abundance of CHNS isomers with respect to H2 plotted as a function of time for Sgr B2...... 137

Figure 6.7. Fractional abundance of CHNS isomers with respect to H2 plotted as a function of time for TMC-1...... 138

+ Figure 7.1. Number of “significantly” changed species versus time in H3 + O case...... 149

Figure 7.2. S and SR values as functions of time...... 152

+ Figure 7.3. SFR values as functions of time in H3 + O study...... 155

+ Figure 7.4. SFR values as functions of time in H3 + O study...... 157

Figure 7.5. Fractional abundances of several important or observed species concerning TMC-1 vs time...... 158

xvi

Chapter 1: Introduction

1.1 Interstellar medium and interstellar clouds

The universe includes our galaxy, the Milky Way, as well as a large number of external galaxies. Each galaxy contains billions of stars. In between the stars, there is no vacuum; instead, this is where the so-called “interstellar medium” exists. In the Milky Way, about 10% of the matter is in the interstellar medium whereas in external galaxies it can be significantly less. In this thesis, the topic will be focused on the Milky Way and hereafter all specific values discussed concern the Milky Way.

The interstellar medium is heterogeneous in density and temperature (Lis et al. 2006; Tielens 2005). Most of the matter is clumped into clouds, leaving the inter-cloud space full of extremely dilute gas with a density of n ≈ 0.1 cm-3.

Unshielded interstellar radiation can easily break up small molecules (if there are any) and no molecules have been observed in the inter-cloud gas.

On the other hand, molecules exist in the colder portions of the medium, which consist of “clouds”. In the interstellar clouds, most of the mass is in the gas phase, where the most abundant element is hydrogen and the next most 1

abundant one is helium, which processes about 10% of the hydrogen abundance for our galaxy. These two elements are believed to have been produced in the

Big Bang. Heavier elements, including carbon, nitrogen, oxygen, and others, are produced in stellar interiors and propagated to interstellar clouds. All these elements have much lower abundances than hydrogen; indeed they are four or more orders of magnitude less abundant by number. Besides the gas, interstellar clouds also contain tiny dust particles. These particles make up about 1% of the cloud’s mass and the dust-to-gas ratio by number is approximately 1.33 × 10-12.

IR absorption reveals that dust particles are mostly made of silicates and carbon; in warmer regions IR emission shows characteristics of polycyclic aromatic hydrocarbons (PAHs). In the denser cold regions of the clouds, dust particles are covered by mantles of ice, which are a mixture of mostly water, carbon monoxide and carbon dioxide. Theoretical and observational studies suggest that radius of these particles ranges from 0.02 to 0.5 µ (Mathis et al. 1977; Draine & Lee 1984).

Interstellar clouds can be classified by density. “Diffuse” clouds are those of density n ≈ 100 cm-3. These clouds are quite transparent to radiation from background stars. Their visual extinction for the visible and ultraviolet photons is less than one mag. The typical gas temperature of diffuse clouds is 50-100 K.

Due to the strong radiation in these regions, most molecules can be easily destroyed or ionized and thus have fairly low abundances. Only a small number of diatomic and triatomic gas phase molecules have been found in the diffuse

regions and they are of low abundances except for molecular hydrogen. This species can be actively produced on dust surfaces from two hydrogen atoms, and then released into the gas phase, leading to a comparable number density to atomic hydrogen. Because dust particles tend to be formed from heavy elements, compared with the cosmic elemental abundances, “depletions” of these elements in the gas phase range from factors of a few for carbon and oxygen to much greater values for silicon, iron, and calcium.

“Dense” clouds contain much more matter than diffuse clouds. Although small and relatively homogeneous dense clouds, known as globules, can occur, the larger dense clouds are heterogeneous in density, and are known as

“assemblies” or “giant” clouds depending on size. In these large clouds, dense

“cold cores” exist among more diffuse material. The typical density of a cold core is 104 cm-3 and the temperature is only 10-20 K. The interior can be shielded from radiation mainly due to the dust particles. As the result, molecules in these regions are destroyed much more slowly by the radiation than in the diffuse clouds. The major form of hydrogen in the dense clouds is H2. Many other molecules have also been detected. The two best-known cold cores are TMC-1 and L134N. In the former, more than 50 molecules have been detected, and in the latter, the number is over 40.

Although dense cold cores are called quiescent cores because of the low internal motion, they are not indefinitely stable. Some will disperse while others

collapse. The collapse starts in an isothermal manner. After a certain length of time, a central dense condensation develops, which can have a high density of

106 cm-3 or more and a very low temperature, perhaps as low as 5 K. Such objects are known as “prestellar cores”. When the central condensation of the prestellar core becomes sufficiently dense to be optically thick to cooling radiation, it can no longer remain cool but starts to heat up, becoming a protostar.

This process can lead to the formation of solar-type stars. As the protostar heats up, it warms its environment and forms a hot corino around itself. Larger and warmer structures, known as hot cores, are associated with high-mass star formation. With temperatures ranging from 100-300 K depending on the mass of the protostar, hot cores and their corinos show a rich chemistry that is quite different from that of cold cores.

1.2 Interstellar molecules

The interstellar medium, especially the part consisting of cold and hot dense cores, provides a hotbed for the formation of molecules. In the late 1930’s and early 1940’s, optical astronomers detected the first interstellar molecules, CH,

CN, CH+ (Swings & Rosenfeld 1937; McKellar 1940; Douglas & Herzberg 1941).

However, not until in the 1960’s were new molecules detected (Weinreb et al

1963). After that, the field of molecular astronomy became vivid with immense improvement in observational techniques so that many more molecules have

been detected. Table 1.1 lists detected gas phase molecules in all phases of the

interstellar medium, mainly in dense clouds, and in very old stars that have large

circumstellar shells of gas and dust similar in physical conditions to cold cores

(CDMS 2009; Woon 2009). Most of these detected molecules are organic ones,

ranging in size from 2 to 13 atoms. As for the abundances, the most abundant

molecule in dense regions is H2. The second abundant one is CO, which has a

-4 fractional abundance with respect to H2 of 10 . Others include neutral molecules,

radicals, cations, and anions. Molecular cations have fractional abundances of at

most 10-8. The most abundant polyatomic species have fractional abundances of

10-6. Moreover, most organic species found in cold cores are very unsaturated,

such as the radical series CnH and HC2nCN, while in hot cores, more saturated

ones, such as methanol, ethanol, methyl formate, etc. are detected (Lis et al.

2006).

Table 1.1 Detected interstellar molecules.

2 3 4 5 6 7 & 8 9+ atoms atoms atoms atoms atoms atoms atoms

+ H2 H3 CH3 CH4 C2H4 7 atoms 9 atoms

CH CH2 NH3 SiH4 CH3OH CH3CHO CH3CHCH2

+ + + CH NH2 H3O H2COH CH3SH CH3NH2 CH3OCH3

Continued on next page

Table 1.1 Continued

NH H2O H2CO H2CNH CH3CN CH3CCH CH3CONH2

OH H2S HCCH C3H2 CH3NC C2H3OH CH3C4H

HF CCH H2CN c-C3H2 CH2CNH c-CH2OCH2 C8H

+ - HCl HCN HCNH CH2CN NH2CHO C2H3CN C8H

SH HNC H2CS NH2CN c-C4H2 HC5N HC7N

+ C2 HCO C3H CH2CO l-C4H2 C6H C2H5CN

+ - CN HOC c-C3H HCOOH HC2CHO C6H C2H5OH

CO HCO HCCN C4H c-C3H2O

+ + - + CO N2H HNCO C4H HC3NH 8 atoms 10 atoms

+ CF HCP HOCN HC3N C5O C2H6 C2H5CHO

CP HNO HCNO HC2NC C5N HCOOCH3 CH3COCH3

+ + CS HCS HOCO HNCCC HC4N CH3COOH (CH2OH)2

SiC C3 HNCS C5 C5H HOCH2CHO CH3C5N

? ? N2 C2O HSCN C4N l-HC4H C2H3CHO

- NO C2S C3N C4Si C5N CH3C3N 11 atoms

PN c-C2Si C3O HCOCN CH2CCHCN CH3C6H

Continued on next page 6

Table 1.1 Continued

NS CO2 C3S H2C6 HC9N

SiN OCS c-SiC3 C7H C2H5OCHO

+ SO N2O HOCO H2NCH2CN

+ - SO SO2 C3N 12 atoms

? PO SiCN PH3 C6H6

SiO SiNC n-C3H7CN

AlO AlNC

FeO? MgCN 13 atoms

AlF MgNC HC11N

NaCl NaCN

AlCl HCP

KCl CCP

SiS

Note: those with a question mark are tentative detections.

Theoretical studies (Stief et al. 1972; Roberge et al. 1991) show that

unshielded interstellar radiation can easily destroy small molecules at a “large”

rate on the order of 10-10 s-1. This introduces a short lifetime of about 300 years and makes these molecules unable to travel through unshielded regions.

Therefore most molecules detected must have been formed at or near locations where they are observed. The precursor material, however, is from ejecta of stars, which contains atoms and dust particles. Still, there are many questions remaining, such as: How are these interstellar molecules formed? What are the underlying chemical reactions? How do they evolve with time and what will be the final products these molecules will lead to? These questions belong to the interdisciplinary study of astrochemistry.

1.3 Astrochemistry

As shown in Figure 1.1, understanding the chemistry underlying the behavior of interstellar molecules requires knowledge of several fields.

Observational groups detect new molecules and report them. Modeling groups then set up chemical models to understand the mechanism and make predictions of possible future detections. Experimental groups study the spectroscopy and rate coefficients of molecules, trying to simulated physical conditions for interstellar medium although the extremely low densities of the sources can hardly be reached. Quantum chemists calculate rate coefficients. They both provide needed information to observers and modelers. All these efforts make current understanding of interstellar molecules possible.

Figure 1.1. Collaboration in astrochemistry.

The synthesis of most observed molecules can be explained by chemical reactions either in the gas or on the surface of the dust particles. The abundance of many interstellar molecules can be well explained by the gas phase chemistry while others cannot. For the latter, surface chemistry or a combination of gas phase and surface chemistry can usually give explanation.

A good example is the formation of interstellar molecular hydrogen. During the early stages of the formation of interstellar clouds from stellar ejecta, the material is diffuse and inadequate for molecular development due to the low density and high radiation field. Nevertheless, even under these circumstances, molecular hydrogen is formed efficiently (Tielens 2005). With the low density, the only possible gas-phase reaction that produces a diatomic species from atoms is

radiative association, in which the product can be stabilized by the emission of a photon. For H2, the following reaction stands out:

H + H → H2 + hν. (1.1)

However, this process is inefficient and cannot reproduce the large abundance of molecular hydrogen (Tielens 2005). An alternative route is via the reactions:

H + e- → H- + hν, (1.2)

- - H + H → H2 + e . (1.3)

These processes are still too slow to produce much H2 under the cold interstellar conditions. Experimental and theoretical studies show that the effective formation of H2 occurs on dust particles by successive adsorption of two hydrogen atoms

(Lis et al. 2006). Moreover, this reaction is exothermic and provides enough energy for H2 to be desorbed into the gas phase (Williams & Brown 2007). After a significant amount of gaseous H2 is produced, H2 at the edge of the cloud can absorb photons and can shield inner ones against photodissociation.

Once there is sufficient amount of H2 in the gas, gas phase reactions can occur, and lead to production of most of the species seen in diffuse clouds and dense cores. The extreme conditions in the interstellar medium put severe restrictions on the possible gas phase reactions that can occur. The low density and low temperature prevent most reactions that can happen on the earth. In general, low density prevents three-body processes, where three molecules are

required to collide to occur, while low temperatures rule out endothermic reactions or exothermic reactions with activation barriers. The chemical processes that dominate the gas-phase chemistry are thus exothermic reactions without any activation barriers.

The most important type of barrierless reactions in the interstellar circumstances are ion-molecules reactions (Herbst 2005). Ions can be formed by a variety processes. The dominant one is ionization by cosmic rays, which are high-energy bare nuclei travelling at velocities near the speed of light. When cosmic ray protons (CRP) enter the interstellar clouds, they can ionize H2 and He directly. For example:

+ - H2 + CRP → H2 + e + CRP’. (1.4)

Moreover, the generated secondary electrons can themselves ionize H2, as well as other atoms and molecules:

- + - - H2 + e → H2 + e + e , (1.5) and

A + e- → A+ + e- + e-, (1.6)

Other neutral species can also be ionized via processes shown below:

* H2 + CRP → H2 + CRP, (1.7)

* H2 → H2 + hν, (1.8)

hν + A → A+ + e-. (1.9)

+ Once formed, H2 immediately (within a day or so) reacts with H2 via a well-

+ studied ion-molecule reaction to form the well-known triangular ion H3 :

+ + H2 + H2 → H3 + H. (1.10)

Ion-molecule reactions play an important role in synthetic interstellar chemistry.

The synthesis of water gives a good example. This synthesis starts from the following ion-molecule reaction:

+ + O + H3 → OH + H2. (1.11)

Then the hydroxyl ion is depleted quickly by two hydrogen atom transfer reactions with H2. These reactions are also ion-molecule reactions:

+ + OH + H2 → H2O + H, (1.12)

+ + H2O + H2 → H3O + H. (1.13)

+ The oxonium ion, H3O , does not react with H2. Instead, it reacts with electrons in dissociative recombination to form water molecule and the hydroxyl radical.

+ - H3O + e → H2O + H, (1.14)

+ - H3O + e → OH + H + H. (1.15)

Another type of important reactions are the neutral-neutral reactions. The requirement of no activation energy barriers is of course still valid (Smith et al.

2004). For example, starting from the hydroxyl radical formed in reaction 1.15,

neutral-neutral reactions involving at least one radical can then lead to the diatomics O2, NO, and N2:

OH + O → O2 + H, (1.16)

OH + N → NO + H, (1.17)

NO + N → N2 + O. (1.18)

Atomic carbon is a particularly reactive atom. It can not only react with radicals and semi-radicals such as O2, but also react with a variety of non- radicals, e.g., unsaturated hydrocarbons. In addition, CN and CCH have the same ability (Sims 2006; Smith et al. 2006).

+ C is detected in diffuse clouds. Its ion-molecule reaction with H2 is endothermic:

+ + C + H2 → CH + H, (1.19) and unlikely to occur except possibly in shocks. Instead the reactant can lead to addition by emission of a photon. This reaction is called radiative association

(Herbst 2006):

+ + C + H2 → CH2 + hν. (1.20)

Neutral species can also have radiative association reactions. For example,

C + H2 → CH2 + hν. (1.21)

Besides positive ions, negative molecular ions also play a role in interstellar chemistry. Herbst (1981) suggested they could be formed in space via radiative attachment, i.e., attaching one electron to the neutral species and stabilizing the product by emitting one photon:

A + e- → A- + hν. (1.22)

Negative ions, or anions, can also be produced by so-called dissociative attachment, in which electrons attached to neutrals and break a chemical bond, e.g.:

- - e + C2H2 → C2H + H, (1.23) although many of this type of reactions are endothermic.

To destroy anions, associative detachment reactions with atomic hydrogen are important:

A- + H → AH + e-. (1.24)

In addition to gas-phase reactions, many surface reactions can also occur and sometimes produce molecules that cannot be formed efficiently in the gas.

For example, as presented earlier, H2 is mainly formed on grain surfaces and desorbed into the gas to start the chemistry there. The surface chemistry starts from accretion of gas-phase species onto the dust grains. Under the low temperature, the accretion is dominantly by weak long-range forces, e.g., the van der Waals force. This leads to physisorption, with binding/desorption energies ED

ranging from 0.03-0.5 eV. Once on the grain and thermalized to the grain temperature, the weakly-bound species can diffuse to other sites on the grain via a random-walk. The potential barrier for such motion, labeled Eb, is normally smaller than the desorption energies. When two atoms/molecules meet each other, a chemical reaction may occur. Besides H2 formation, several organic molecules can also be formed via this method. For example, gas phase chemistry cannot make sufficient methanol and the molecule can be formed on the surface (Zainab et al. 2005):

H + CO → HCO, (1.25)

H + HCO → H2CO, (1.26)

H + H2CO → H3CO, (1.27)

H + H3CO → CH3OH, (1.28)

At low temperatures, species other than light ones, H, H2, and He cannot be desorbed efficiently from the surface by thermal evaporation. Alternative routes by cosmic rays (Léger et al. 1985), photons (Westley et al. 1995; Öberg et al.

2009a, b), and by released energy from exothermic chemical reactions (Allen &

Robbinson 1975; Duley & Wiliams 1993; Garrod et al. 2007) are suggested.

1.4 References

Allen, M., and Wiliams, D.A. 1993, Non. Not. R. Astron. Soc., 260, 37 15

CDMS, 2009, the Cologne database for molecular spectroscopy, http://www.astro.uni-koeln.de/cdms

Douglas, A.E., and Herzberg, G. 1941, ApJ, 94, 381

Draine, B.T., and Lee, H.M. 1984, ApJ, 285, 89

Garrod, R.T., Wakelam, V., and Herbst, E. 2007, A&A, 467, 1103

Herbst, E. 2005, J. Phys. Chem. 109, 4017

Herbst, E. 2006 Gas Phase Reactions. In GWF Drake (ed.) Handbook of Atomic,

Molecular, and Optical Physics, pp. 561-573, Springer Verlag, Leipzig

Léger, A., Jura, M., and Omont, A. 1985, A&A, 144, 147

Lis, D., Blake, G.A., Herbst, E. (eds). 2006, Astrochemistry: Recent Successes and Current Challenges, Cambridge University Press, Cambridge

Mathis, J.S., Rumpl, W., and Nordsieck, K.H. 1977, ApJ, 217, 425

McKellar, A. 1940, Publ. Astron. Soc. Pac., 52, 187

Öberg, K.I., Garrod, R.T., van Dishoeck, E.F., and Linnartz, H. 2009a ApJ, 693,

1209O

Öberg, K.I., van Dishoeck, E.F., and Linnartz, H. 2009b A&A, 496, 281O

Smith, I.W.M., Herbst, E., and Chang, Q. 2004, Mon. Not. R. Astron. Soc. 350,

323

Swings, P., and Rosenfeld, L. 1937, ApJ, 86, 187 16

Tielens, A.G.G.M. 2005, The Physics and Chemistry of the Interstellar Medium,

Cambridge University Press, Cambridge

Weinreb, S., Barrett, A.H., Meeks, M.L., and Henry, J.C. 1963, Nature, 200, 829

Westley, M.S., Baragiola, R.A., Johnson, R.E., and Baratta, G.A. 1995, Nature,

373, 405

Williams, D., Brown, W.A., Price, S.D., Rawlings, J.M.C., and Viti S.2007 Ast. &

Geophys. 48: 1.25

Woon, D.E. 2009, http://www.astrochymist.org/

Zainab, A., Takeshi, C., Yuka, K. et al. 2005, ApJ, 626, 262

Chapter 2: Chemical Models

To study the rich chemistry in interstellar medium, chemical reaction models based on kinetics are used. In this chapter, one of the major chemical models, the OSU chemical reaction network, will be introduced in detail. In Section 2.1, the kinetics and mathematics underlying the model will be briefly reviewed. In the following sections, the construction, including physical conditions, reactions and their rate coefficients for the OSU pure gas phase and gas-grain models will be presented.

2.1 Modeling Method

The formation and destruction of a species are governed by chemical kinetics. For example, if a species C is formed by the following two reactions:

A1 + B1 → C, (2.1)

A2 + B2 → C + E, (2.2)

and reaction constants for reactions 2.1 and 2.2 are k1 and k2, the formation rate of C will be:

Rform = k1 [A1] [B1] + k2 [A2] [B2]. (2.3)

Assuming C can be destroyed by three reactions:

D1 + C → P1, (2.4)

D2 + C→ P2 + P3, (2.5)

C → P4, (2.6)

with reaction constants k3 – k5 respectively, the total destruction rate will be:

Rdes = k3 [D1] [C] + k4 [D2] [C] + k5 [C]. (2.7)

Change rate of C concentration will then be:

d[C]/dt = Rform - Rdes= k1 [A1] [B1] + k2 [A2] [B2] - k3 [D1] [C] - k4 [D2] [C] - k5[C]. (2.8)

Similarly, once the reactions relating to all included species are studied, an ordinary differential equation can be set up for each species:

dni / dt = ΣjΣlkjlnjnl − Σmkimninm + Σokiono − Σpkipni. (2.9)

In the equation above, the left side is the time derivative of species i’s concentration; the first term of the right side of the equation is the formation rate via second-order reactions; the second term is the destruction rate via second- order reactions; while the third and fourth terms are formation and destruction rates of first-order reactions, respectively. Here n stands for the actual concentration, k for the rate constants of the reactions. In history, since the precise solution of many of this kind of equations can be difficult, steady state

estimations were used often. At the steady state, concentration of each species is not changed and the formation rate equals to destruction rate. Nowadays, this is no longer a problem. Fast computers can easily integrate hundreds of coupled differential equations, as shown above. Therefore, when the reactions of known interstellar species, as well as the species connected to them, are included into the model, chemical modeling becomes a purely mathematical problem. All the differential equations can be integrated together and give the species’ concentrations as functions of time.

2.2 Gas-Phase Model

The pure gas phase model usually applied is a pseudo time dependent model. In the model, the physical conditions, including the total density, temperature, cosmic ray ionization rate, visual extinction, as well as elemental abundances, are all fixed by a single set of parameters while over four thousand chemical reactions that occur among more than four hundred interstellar species cause the species’ abundances to evolve with time. This model is mostly applicable to homogeneous systems and has been successful in reproducing molecular concentrations in many sources (Smith et al. 2004; Smith et al. 2006).

2.2.1 Physical conditions of the gas model

The first step to set up the pseudo time dependent model is to generate a set of parameters to describe the physical conditions. Table 2.1 shows the standard values that are usually used for cold interstellar clouds.

Table 2.1 Physical parameters for typical cold interstellar clouds.

Parameter Physical meaning Typical value

-3 4 nH (cm ) total density 2 × 10

T (K) temperature 10

ζ (s-1) cosmic ray 1.3 × 10-17

ionization rate

Av visual extinction 10

To start, initial abundances of all species must also be defined. Table 2.2 shows a set of typical non-zero initial fractional abundances, which are abundances with respect to total density. These depend on the chosen elemental abundances. Typical values used are so-called “low-metal” abundances, which are successful to model the dense cores in the Milky Way. These initial non-zero abundances also put constraints to elemental abundances as the chemical evolvement will not involve nuclei reactions and each element’s total abundance should be conserved. 21

Table 2.2 Typical non-zero initial fractional abundances.

Species Typical value

He 6.00 × 10-2

N 2.14 × 10-5

O 1.76 × 10-4

-1 H2 5.00 × 10

C+ 7.30 × 10-5

S+ 8.00 × 10-8

Si+ 8.00 × 10-9

Fe+ 3.00 × 10-9

Na+ 2.00 × 10-9

Mg+ 7.00 × 10-9

P+ 3.00 × 10-9

Cl+ 4.00 × 10-9

F+ 6.60 × 10-9

2.2.2 Species in the gas model

In the standard pure gas phase model, more than 400 species are included in the network. These species include over one hundred observed interstellar molecules towards various interstellar sources, as well as other related species. About two-fifth of the species are neutral atoms or molecules.

Apart from that, most of the other species are cations. As discussed in Chapter 1, cations play very important roles in interstellar chemistry. A complete list of these species can be found at http://www.physics.ohiostate.edu/~eric/research.html.

2.2.3 Chemical reactions and the rate coefficients

Under the physical conditions shown in Table 2.1, the total density is extremely low (compared to normal conditions on the earth, where the density is more than 2 × 1019 cm−3) and the temperature is low. As discussed in Chapter 1, the low-density makes three-body reactions unable to happen. The low- temperature makes reactions with relatively high activation energy too slow to occur. Activation energy more than 1 eV will lead to very small reaction rates at T

< 100 K. Only reactions with high rate coefficients are important (Herbst, 2005).

At http://www.physics.ohio-state.edu/~eric/research.html, a list of gas- phase interstellar chemical reactions is shown. In total, there are fourteen types

of reactions considered. In the following, the method of estimating each type of reaction rate constant, if they have not been measured, will be discussed.

Type 0 reactions are gas-grain interaction reactions. In the gas model, dust particles are not really included. However, the effects of dust cannot really be eliminated since the first step of all the interstellar chemistry starts from formation of H2 on grains, as shown earlier in Chapter 1. Also, some of the heavy elements’ cations, e.g., Fe+, can interact with dust grains. Therefore, Type 0 reactions are added in the gas model.

Type 1 reactions are the ionization reactions caused by cosmic rays. This type of reaction is the main source of ion formation. In the model, an overall rate is used to represent the ionization rates from both cosmic rays or cosmic ray induced photons and ‘secondary electrons’, as discussed earlier in Section 1.3. A parameter labeled the ‘cosmic ray ionization rate’ ζ has been applied to represent the rate of Type 1 reactions. ζ is a first-order rate coefficient with a value of 1-5 ×

10−17 s−1 for a typical dense core and one or two orders of magnitude higher for diffuse clouds. In the model, a typical value of 1.3 × 10−17 s−1 is used, as shown in Table 2.1. Type 1 reaction rates then can be represented as k = α × ζ, (2.10) where α is the scaling factor since different species can have different interacting cross sections with cosmic rays. ζ values of H2 and He add up to 1. For other species, ζ > 1 due mainly to photons (Gredel et al. 1989) 24

Another type of reaction that is similar to Type 1 reactions is Type 13, which consists of photo-ionization and photo-dissociation reactions caused by external UV photons. Visual extinction is used to represent the penetration ability of photons in different sources. Rate coefficients of Type 13 can be fit to the expression k = αe−Av , (2.11)

where Av is the visual extinction and α is the rate constant at the cloud edge

(where Av = 0). α depends on the nature of species, as well as the wavelength of photons.

After being produced by Type 1 or Type 13 reactions, cations can react with neutral species in so-called ion-neutral reactions. This type of reaction is identified as Type 2 in the gas phase model. More than half of the reactions in the chemical reaction network are Type 2 reactions. Many ion-molecule reactions obey this constraint as discussed above that they are exothermic without barriers.

This type of reaction can be grouped into two sub-types: reactions with polar and with non-polar neutral species. Methods of estimating the rate coefficients are different for these two sub-types. The Langevin model is used to estimate unmeasured reaction rate constants of reactions with non-polar molecules. In the method, the long-range ion-induced dipole potential is considered and the polarizability is assumed to be a scalar.

Assuming that all trajectories that overcome the centrifugal barrier can lead to reaction, the Langevin rate coefficient is calculated to be

1/2 kL = 2πe (α/µ) , (2.12) where α is the dipole polarizability and µ is the reduced mass (Herbst, 2006a). A

-9 3 -1 typical value of kL is 10 cm s .

Estimation of reactions with polar species starts from the locked-dipole method

(Herbst, 2006b). In this method, the rotation of the dipole is neglected and it is

‘locked’ onto the incoming ion as a linear configuration. The rate coefficient is predicted to have the form

1/2 kLD = [1 + (2/π )x] kL, (2.13)

where kL is the Langevin rate coefficient, and

1/2 x = µD / (2αkBT) , (2.14)

where µD is neutral dipole moment. The result from this method is usually too large since it represents a limit when the temperature approaches zero and reaches the real ‘locked-dipole’ situation. An empirical method called the

‘trajectory scaling approach’ is then applied to estimate rate coefficients of reactions between ions and polar neutrals (Herbst & Leung 1986). Here

kTS = [0.62 + 0.4767x] kL, (2.15) where x is calculated in the same way as in the ‘locked-dipole’ method. When x is large, kTS has the same temperature dependence as x, which is inversely 26

proportional to the square root of T. Many ion-molecule reactions have their rate coefficients measured in laboratories and can be used in the model (Anicich,

2003; Woodall et al. 2007).

Type 4 reactions are another type of reaction between cations and neutral species. Unlike Type 2 reactions, this type of reaction, known as radiative association, produces addition products of the reactants and emits extra energies by ejecting photons. Since experimental measurements of association rate coefficient are usually made under high densities where the product is stabilized by collision rather than emission of a photon, modifications must be made. The whole process of radiative association can be separated into three fundamental reaction steps: formation of an intermediate complex; dissociation of the complex

(backward reaction); radiative stabilization of the complex (which leads to the product). The symbols k1, k−1, and kr stand for the rate coefficients of these three fundamental reactions, respectively. If the complex is at steady-state concentration, the overall reaction rate constant for radiative association can be calculated to be

kra = k1kr / (k−1 + kr). (2.16)

Normally k−1 is much bigger than kr, in which case the equation can then be simplified to

kra = (k1 / k−1) kr. (2.17)

In a similar manner, the overall three-body rate coefficients when collisional stabilization dominates can be calculated as

k3b = (k1 / k−1) k2, (2.18)

where k2 is the rate coefficient of collision stabilization of the complex (instead of

−10 3 −1 radiative stabilization). A typical k2 value is 10 cm s , while kr can be estimated from the average Einstein A coefficient for vibrational emission to be ≈

102−3 s−1. Therefore, the room temperature rate coefficient of radiative association can be estimated as

kra = (kr / k2) k3b. (2.19)

From basic statistical theory, the temperature dependence of either type of associative reaction is T−r/2, where r is the total number of rotational degrees of freedom of the reactants (Bates & Herbst, 1988).

Type 9, 10, and 11 reactions are all related to cations. Type 9 reactions are dissociative recombination reactions. When electrons collide with molecular cations, the charge will be neutralized and the parent neutral will break down into smaller species. Measured dissociative recombination rate coefficients are typically 10−6−7 (T/300)−0.5 cm3 s−1. If not measured, rate coefficients of this type of reactions can be estimated as

2 1/2 kdr = e Rcrits (8π / (mekBT)) , (2.20)

where Rcrit is the critical distance within which cations and electrons can react with each other (Weston & Schwarz, 1972). In this method, it is assumed that when cations and electrons attract each other by the Coulomb long-range potential and reach the critical distance, the dissociative recombination reaction will occur. The breaking up of the cations can produce all kinds of exothermic products with various branching ratios. Type 10 reactions are radiative recombination reactions, which are also reactions between cations and electrons.

Electrons can attach to cations and form neutral species, where the extra energies are taken away by escaping photons. Type 11 reactions are recombination reactions between cations and anions. As will be discussed later, anions, or negative ions, can be formed in interstellar clouds. Thus positive and negative ions can neutralize each other.

Neutral species are reactants in Type 2, 4, 10 reactions. In addition, neutral-neutral reactions are also very important. Types 6, 7, 8 reactions in the chemical reaction network are all neutral-neutral reactions. Of course the reactions included all have zero activation, energy barriers to comply with the low temperature circumstances. Rate coefficients of these three types of reactions can be taken either from laboratory experiments, from quantum chemical calculations, or from estimations (Smith et al. 2004).

Besides cations and neutral species, anions, or negative ions, are also included in the gas-phase model. Anions are formed via electron attachment

reactions, which are Type 12 reactions in the model. Similar to radiative association reactions between cations and neutral species (reaction type 4), the process of electron attachment is assumed to have three fundamental steps: electron attachment; electron detachment of the complex; and radiative stabilization.

Table 2.3. Examples of types of reactions.

Reaction Reaction Example

Type

0 Gas-grain interaction H + H + GRAIN → H2 +

GRAIN

+ − 1 Cosmic-ray ionization H2 + CRP → H2 + e

- + − - H2 + e → H2 + e + e

C + CRPh → C+ + e−

C + e- → C+ + e− + e-

+ + 2 Cation-neutral reactions C + CH → C2 + H

3 Anion-neutral reactions C− + NO → CN− + O

4 Radiative association C+ + H → CH+

− − 5 Associative detachment C + C → C2 + e

Continued on next page 30

Table 2.3 Continued

6 Collisional ionization O + CH → HCO+ + e−

7 Neutral-neutral reactions C + CH → C2 + H

8 Neutral-neutral radiative association C + C → C2

+ − 9 Dissociative recombination C2 + e → C + C

10 Radiative recombination C+ + e− → C

11 Cation-anion recombination C+ + C− → C + C

12 Electron attachment C + e− → C−

13 Photo-ionization & photo-dissociation C + hν → C+ + e-

2.3 Gas-Grain Model

As introduced in Chapter 1, the interstellar medium is dusty. Dust particles play a critical role in the formation of H2 on their surfaces. Moreover, big organic molecules can be formed on the grain surface and then desorbed into the gas via thermal or non-thermal routes (Garrod et al. 2007). Therefore, a chemical modeling method combining both gas-phase and grain surface reactions is necessary. The OSU astrophysics and astrochemistry group have developed gas-grain models to accomplish this task (Hasegawa et al. 1992; Ruffle & Herbst,

2001a, b, c; Garrod & Herbst, 2006; Garrod et al. 2007).

2.3.1 Physical parameters of dust particles

As in the case of the pure gas phase model, the first step to set up the gas-grain model is to define a set of parameters to describe the physical conditions of the system. As the gas-grain model includes both gas phase and dust particles, besides those listed in Table 2.1 for the gas physical parameters, additional ones are needed for the dust particles. Major ones are listed in Table

2.4.

Table 2.4 Major physical parameters for dust particles and gas-grain

interactions.

Parameter Physical meaning Typical value

Tdust (K) dust temperature depending on the source

d / g dust to gas ratio by mass 0.01

STICK0 sticking coefficient for 0.5

neutral species

RD grain radius 1 × 10-5 cm

TNS number of sites per grain 1 × 106

aRRK coefficient for non-thermal 0.01

desorption by reaction

Tdust is the dust temperature and depends on the nature of the source.

Usually in the model, it’s equal to gas temperature. Dust to gas ratio by mass, d/g, along with the total density, and the radius, can determine the dust particle density. STICK0 is the sticking coefficient for neutral species, or in other words, the chance for a neutral species to stick to the dust upon collision and become a surface species. TNS is the number of sites per grain and is needed to convert species concentrations to numbers on the surface. The aRRK coefficient is a parameter that specifically defines non-thermal desorption driven by energies from exothermic surface reactions (Garrod et al. 2007).

2.3.2 Surface species

About 200 surface species are added to the gas-phase model. Since there is excess amount of electrons, positive ions can collide with them on grains to form neutrals that come off. To simplify the problem, at the current stage, only neutral surface species are considered. In the gas-grain network, the letter “J” is used as the prefix for the surface species to distinguish them from gas species, e.g., JCO means CO on the surface and CO means the gas-phase CO.

2.3.3 Surface reactions and gas-grain interactions

Several types of reactions and processes are added into the gas-phase network, making the total number of reactions to be over 6000. The first type of process added is the accretion of gas-phase species onto the surface to form adsorbates. This process occurs at a rate defined by the product of the collision rate, treating the dust particles as a normal species and the chance for addition is the parameter STICK0 defined in Table 2.4:

Racc,I = STICK0 σd ni nd, (2.24)

where ni is the concentration of species i, nd is the dust density, is the thermal velocity, and σd is the geometrical dust-grain cross section.

In addition to accretion, grain-surface chemical reactions are added, particularly those that occur by a diffusive (random-walk) mechanism known as the Langmuir-Hinshelwood mechanism. The surface of dust particles is smooth but has potential valleys and barriers. Therefore many ‘traps’ exist on the surface like the valleys on the earth. When two atoms/molecules, A and B, reach each other in a particular valley, they may have a chance to react. When the chemical reaction between A and B does not have activation energy, the surface reaction rate is simply given by the sum of the diffusion rates:

dNA / dt = −(kdiff,A + kdiff,B) NANB = −KABNANB, (2.25)

where NA and NB are numbers of sites on an average grain occupied by A and B, respectively, and

−Eb,i/T kdiff,I = khop,I / N = ν0e / N, (2.26)

where Eb,i is the diffusion barrier between two adjacent sites, N is the total number of sites, and

2 1/2 12 −1 ν0 = (2nsEb / (π m)) ≈ 10 s . (2.27)

When there is an activation energy barrier Ea for the chemical reaction, to simplify the problem, a factor of κ is introduced so that the rate coefficient will be:

KAB’ = κ × KAB. (2.28)

The factor κ can be estimated by a simple method or a complex one. In the simple method, κ is either a hopping probability or tunneling probability concerning the chemical reaction energy barrier Ea, whichever is bigger. The hopping probability is simply given by Boltzman factor:

κ = e−Ea/T, (2.29) and the tunneling probability is:

−2(α/ħ)(2µEa) κ = Ptunn = e , (2.30) where α is the width of the rectangular potential barrier. In the complex method, a competition between diffusion barrier Eb (via hopping) and chemical reaction (via hopping or tunneling) is considered. The expression is

κ = kchem(khop,A + khop,B) / (kchem + khopp,A + khopp,B), (2.31)

where khop,A and khop,B are hopping rates of A and B, respectively, over the diffusion barrier Eb, and kchem is the tunneling or hopping rate over the chemical reaction activation barrier, whichever is larger:

−Ea/T kchem = khop = νe , (2.32) or:

−2(α/ħ)(2µEa) kchem = ktunn = νPtunn = νe . (2.33)

When two species react exothermically on the surface, there is a chance for the products to desorb into the gas. RRK theory is used to quantify this effect.

Modeling the surface-molecule bond as an additional vibrational degree of freedom, the theory gives the standard RRK probability for an energy E > ED as following:

s-1 P = (1 – ED / Ereac) . (2.34)

where ED is the desorption barrier of the product molecule, Ereac is the energy released from the reaction, and s is the number of vibrational modes. The excess energy can either be lost into the solid or can be used for desorption. If it is simply assumed that relaxation occurs at the frequency of energy transfer, the probability of desorption is too great. Therefore, an empirical parameter labeled aRRK (defined in Table 2.4) is used to represent this effect and fraction f for the portion of product to escape into the gas phase is calculated from the expression:

f = aRRKP / (1 + aRRKP). (2.35)

Species on the grains can also evaporate into the gas phase via thermal desorption, more commonly known as evaporation. The rate of this process is as the following:

-Ed/T ktherm,desorp = α e . (2.36)

In addition, cosmic rays and internally generated photons can also desorb or dissociate the surface species. Rates of dissociation reactions are represented in similar way to those in the gas phase (equations 2.2 and 2.3).

Table 2.5. Examples of additional types of reactions and processes to the

model.

Reaction Reaction or Process Example

Type

14 diffusive grain surface reactions and JC + JC → JC2

non-thermal desorption by exothermic JC + JC → C2 energy

15 thermal evaporation JC3N → C3N

16 cosmic ray induced desorption JC2S + CRPh → C2S

17,18 cosmic ray induced photodissociation JC2H + CRPh → JC2 + JH

Continued on next page

Table 2.5 Continued

19,20 photodissociation JHCO + hν → JCO + JH

99 accretion C3 → JC3

2.4 Application of the models

In using the networks in models, the physical conditions must be carefully chosen to simulate the actual studied system. As can be seen in the studies that will be presented in the next several chapters, varying the physical conditions can lead to very different results. Also, when new species are added to the network, all related species and their reactions, including both effective formation and destruction routes, should also be included.

2.5 References

Anicich V.G. 2003, Jet Propulsion Laboratory

Bates D.R., & Herbst E. 1988, In TJ Millar & DA Williams (eds). 17-40, Kluwer

Academic Publishers, Dordrecht

Garrod, R., & Herbst, E. 2006, A&A 457, 927

Garrod, R., Wakelam, V., & Herbst, E. 2007, A&A 467, 1103

Gredel, R., Lepp, S., Dalgarno, A., & Herbst, E. 1989, ApJ, 347, 289

Hasegawa, T.I., Herbst, E., & Leung, C.M. 1992, ApJS, 83, 167

Herbst, E., and Leung, C.M. 1986, ApJ, 310, 378

Herbst, E. 2005, JPC, 109, 4017

Herbst E. 2006a, Gas Phase Reactions. In GWF Drake (ed.) Handbook Atomic,

Molecular, and Optical Physics, 561-573, Springer Verlag, Leipzig

Herbst E., & Leung C.M. 2006, ApJ, 310, 378

Petrie S., & Herbst E. 1997, ApJ, 491, 210

Smith, I. W. M., Herbst, E., & Chang, Q. 2004, MNRAS, 350, 323

Smith, I.W. M., Sage, A. M., Donahue, N. M., Herbst, E., & Quan, D. 2006, in

Chemical Evolution of the Universe. Faraday Discussions No. 133, 137

Weston Jr R.E., & Schwarz HA. 1972 Chemical Kinetics. Prentice-Hall,

Englewood Cliffs

Woodall, J., Agundez, M., Markwick-Kemper, A.J., & Millar, T.J. 2007, A & A, 466,

1197 and http://www.udfa.net

Chapter 3: Inclusion of New Rapid Low Temperature Reaction Rate

Coefficients

Smith et al. (2006) estimated several important rapid neutral-neutral reaction rate coefficients at low temperature. In this study, these new rate coefficients are included into the gas-phase model and the results are compared with those of the former model and observances.

3.1 New Rates

As introduced in Chapter 2, ion-molecule reactions play an important role in the chemical reaction network. Another class of reactions of much importance are the neutral-neutral reactions (Bettens et al. 1995; Terzieva & Herbst 1998; Le

Teu et al. 1999; Smith et al. 2004; Smith et al. 2006). Smith et al. (2006) estimated low-temperature rate coefficients for several fast neutral-neutral reactions that may occur under the restricted physical conditions of low densities and low temperatures. These reactions (see Table 3 in Smith et al. (2006)) are added (if not included before), modified (if existing in osu.2003) to the osu gas phase model. 40

3.2 Gas phase model settings

This study is based on the gas-phase chemical reaction network, osu.2005. To compare the results to those from former model, two networks are used. One is the former model, osu.2005. The other is the modified model, with the important neutral-neutral reactions updated. Related reactions with their rate coefficients are listed in Table 3.1. Modeling results will be compared to two typical cold dense cores, L134N, and TMC-1. The typical settings of physical conditions are the same as listed in Tables 2.1 and 2.2 except for Oxygen elemental abundance. For L134N, standard oxygen abundance (as shown in

Table 2.2) is used. For TMC-1, oxygen abundance is 6.10 × 10-5 against total density.

Table 3.1 List of Modified Reaction Rate Coefficients in New Rapid Low

Temperature Reaction Study.

Old rate coefficients in New rate coefficients

3 -1 3 -1 Reaction osu.2005 (cm s ) (cm s )

@ 10K @ 10K

C + C2 → C3 not included 1.00 × 10-13

C + C3 → C4 1.00 × 10-10 1.00 × 10-12

Continued on next page 41

Table 3.1 Continued

C + C4 → C2 + C3 1.00 × 10-13 1.00 × 10-10

C + C5 → C6 1.00 × 10-10 removed

C + C5 → C3 + C3 not included 3.00 × 10-10

C + C6 → C2 + C5 1.00 × 10-13 5.00 × 10-11

C + C6 → C3 + C4 not included 5.00 × 10-11

C + C7 → C8 1.00 × 10-10 removed

C + C7 → C3 + C5 not included 3.00 × 10-11

C + C8 → C4 + C5 not included 3.00 × 10-11

C + C8 → C3 + C6 not included 3.00 × 10-11

C + C8 → C2 + C7 1.00 × 10-13 3.00 × 10-11

3.3 Results and comparison to former models and observances

A large number of gas-phase molecules have been observed towards the two cores of L134N and TMC-1, especially unsaturated organic species. L134N has more than 40 different molecules and TMC-1 has more than 50. An earlier study using the osu.2003 shows that the kinetic model is best fit to observations around 105 years (Wakelam et al. 2006). When the uncertainties both from calculations, including former model (osu.2005) and modified model, and 42

observations are considered, a “good” agreement is reached if the values from calculation and observation are within a factor of 10. Comparisons of the

5 calculated fractional abundances (with respect to H2) around 10 years with

L134N and TMC-1 observations are listed in Tables 3.2 and 3.3, respectively.

Table 3.2 Comparison of some calculated and observed fractional

abundances with respect to H2 in L134N.

Species Observed Old Calculated New Calculated

Abundance Abundance Abundance

CH 1 × 10 -8 8.18 × 10-9 2.13 × 10-9

CO 8 × 10-5 7.81 × 10-5 1.35 × 10-4

CN 8.2 × 10-10 9.08 × 10-9 1.98 × 10-9

CS 1.7 × 10-9 9.14 × 10-9 5.16 × 10-9

SO 3.1 × 10-9 8.4 × 10-11 8.43 × 10-9

OH 7.5 × 10-8 6.96 × 10-9 1.00 × 10-8

HCN 1.2 × 10-8 3.61 × 10-8 2.63 × 10-9

HNC 4.7 × 10-8 3.93 × 10-8 2.35 × 10-9

-8 -9 NH3 9.1 × 10 6.94 × 10 7.91 × 10-9

CCH ≤ 5 × 10-8 8.92 × 10-9 5.75 × 10-9

Continued on next page 43

Table 3.2 Continued

-10 -9 C3H 3 × 10 7.23 × 10 3.49 × 10-9

-9 -9 C4H 1 × 10 5.13 × 10 1.97 × 10-9

-9 -9 c-C3H2 2 × 10 5.57 × 10 2.25 × 10-8

-9 -11 C3H4 ≤ 1.2 × 10 1.57 × 10 1.21 × 10-10

-10 -10 -9 HC2CN 8.7 × 10 1.19 × 10 8.32 × 10

-10 -10 -10 HC4CN 1 × 10 2.68 × 10 6.11 × 10

-11 -11 -11 HC6CN 2 × 10 7.77 × 10 5.13 × 10

-10 -10 C3N ≤ 2 × 10 5.05 × 10 2.19 × 10-10

-11 -9 C3O ≤ 5 × 10 1.16 × 10 4.19 × 10-10

-10 -10 -10 C3S ≤ 2 × 10 7.50 × 10 5.03 × 10

-8 -9 -7 H2CO 2 × 10 7.30 × 10 1.18 × 10

HCO+ 1 × 10-8 5.63 × 10-9 3 × 10-9

+ -10 -10 -10 N2H 6.8 × 10 1.51 × 10 1 × 10

For each cloud, the percentage of molecules with calculated abundances in agreement with observed values is around 70-80%. Those that are not in good 44

agreement are marked as bold italics. There are several potential reasons for the remaining disagreements: possible errors or incompleteness in the gas phase network used; the need for surface chemistry; more complex physical conditions.

Table 3.3 Comparison of some calculated and observed fractional

abundances with respect to H2 in TMC-1.

Species Observed Old Calculated New Calculated

Abundance Abundance Abundance

CH 2 × 10-8 2.36 × 10-8 1.81 × 10-8

-8 -8 -8 C2 5 × 10 8.38 × 10 6.53 × 10

CO 8 × 10-5 1.17 × 10-4 6.23 × 10-5

CN 5 × 10-9 3.93 × 10-7 4.12 × 10-8

CS 4 × 10-9 9.28 × 10-8 3.97 × 10-8

SO 2 × 10-9 1.84 ×10-10 5.02 × 10-11

OH 2 × 10-7 7.68 × 10-9 8.06 × 10-9

HCN 2 × 10-8 5.62 × 10-8 1.89 × 10-7

HNC 2 × 10-8 5.63 × 10-8 1.92 × 10-7

-8 -8 -8 NH3 2 × 10 2.08 × 10 1.37 × 10

Continued on next page

Table 3.3 continued

CCH 2 × 10-8 1.98 × 10-8 7.9 × 10-9

-8 -8 -8 C3H 1 × 10 1.85 × 10 1.74 × 10

-8 -7 -8 C4H 9 × 10 1.16 × 10 1.83 × 10

-10 -9 -9 C5H 6 × 10 5.47 × 10 1.65 × 10

-10 -8 -10 C6H 2 × 10 1.43 ×10 5.41 × 10

-8 -8 -8 c-C3H2 1 × 10 2.03 × 10 1.02 × 10

-9 -10 -11 C3H4 6 × 10 3.27 × 10 4.32 × 10

-8 -9 -8 HC2CN 2 × 10 6.03 × 10 1.02 × 10

-9 -9 -10 HC4CN 4 × 10 3.08 × 10 6.41 × 10

-9 -10 -10 HC6CN 1 × 10 3.40 × 10 1 × 10

-10 -10 -12 HC8CN 5 × 10 1.17 × 10 9.7 × 10

-10 -9 C3N 6 × 10 2.48 × 10 2.36 × 10-10

-10 -10 C3O 1 × 10 5.79 × 10 3.39 × 10-11

-9 -10 C3S 1 × 10 6.98 × 10 8.99 × 10-10

-8 -7 H2CO 5 × 10 1.45 × 10 1.91 × 10-8

Continued on next page

Table 3.3 continued

HCO+ 8 × 10-9 6.05 × 10-9 3.22 × 10-9

+ -10 -10 -10 N2H 4 × 10 5.48 × 10 5.25 × 10

From the tables, it can be concluded that with the newest network, the agreement with L134N observation is 73%, slightly worse than that with the former osu.2005 model, which is 78%; whereas for TMC-1CP, the agreement has risen from 75% to 80%. Therefore, inclusion of the new estimation of the neutral-neutral reaction rate coefficients and new reactions does not have a strong influence on the overall agreement, for both the L134N and TMC-1 cases, although individual species may have notable changes.

3.4 References

Bettens, R. P. A., Lee, H.-H., and Herbst, E. 1995, ApJ., 443, 664

Le Teu, Y. H., Millar, T. J., and Markwick, A. J. 1999, A&A, 146, 157

Smith, I. W. M., Herbst, E., and Chang, Q. 2004, Mon. Not. R. Astron. Soc., 350,

323.

Smith, I.W. M., Sage, A. M., Donahue, N. M., Herbst, E., & Quan, D. 2006, in

Chemical Evolution of the Universe. Faraday Discussions No. 133, 137

Terzieva, R., and Herbst, E., 1998, ApJ., 501, 207

Wakelam, V., Herbst, E., & Selsis, F. 2006, A&A, 451, 551

Chapter 4: Gas-phase modeling of GBT Molecules in TMC-1 and Sgr B2

In this chapter several applications of the pseudo time dependent gas-phase approach will be presented. Syntheses for seven neutral molecules detected by the Green Bank Telescope in the year of 2006 will be discussed. In Section 4.1, the observations and fractional abundances will be introduced. In Section 4.2, the chemical reaction network and the most important synthetic pathways will be described. In Section 4.3, modeling results will be discussed and compared with observations. In Section 4.4, conclusions and further discussions of this study will be made.

4.1 Observational results

In the year 2006, with the 100-meter Green Bank Telescope (GBT), seven interstellar molecules were detected for the first time or confirmed towards two sources. Towards the cold core Taurus Molecular Cloud -1 (TMC-1), cyanoallene

(CH2CCHCN) and methyl triacetylene (CH3C6H) were detected; and methyl cyanoacetylene (CH3CCCN) and methyl cyanodiacetylene (CH3C5N) were confirmed. Towards the environments of the hot-core source Sagittarius B2 (N) 49

(Sgr B2 (N)), cyclopropenone (c-C3H2O), ketenimine (CH2CNH), and acetamide

(CH3CONH2) were found.

4.1.1 Molecules in TMC-1

As demonstrated in earlier chapters, the typical cold dense core TMC-1 has many interstellar molecules detected (Smith et al. 2006). In this study, four newly detected or confirmed molecules in 2006 will be discussed.

In Lovas et al. (2006), the authors identified cyanoallene (CH2CCHCN), which was detected for the first time, and confirmed an isomer of methyl cyanoacetylene (CH3CCCN). In their study, cyanoallene was found to be the more abundant one. Column densities were determined to be 2 × 1012 cm-2 and

4.5 × 1011 cm-2 for cyanoacetylene and cyanoallene, respectively. Chin et al.

(2006) reported a similar observation with the 100-m Effelsberg telescope. A variety of authors have discussed the possible formation mechanism of methyl cyanoacetylene. Schwahn et al. (1986) started with the formation of protonated

+ methyl cyanoacetylene via the radiative association of CH3 and propiolonitrile

(HCCCN), followed by dissociative recombination with electrons to form

CH3CCCN. On the other hand, Balucani et al. (2002) suggested both of these isomers (cyanoacetylene and cyanoallene), as well as a third isomer, 3- cyanomethalacetylene (HCCCH2CN), can be formed from the neutral-radical

reactions between C3H4 in its isomeric forms allene (H2CCCH2) and methyl acetylene (CH3CCH) and the cyano (CN) radical.

After its first detection by Snyder et al. (1984), the next member of the methyl cyanopolyyne family (CH3(CC)nCN), methyl cyanodiacetylene, methyl cyanodiacetylene (CH3C5N), was confirmed by Remijan et al. (2006) and Snyder et al. (2006). Column density of this species was determined a value of 7.4 ×

1011 cm-2.

The methyl polyynes (CH3C2nH) are another family of hydrocarbons in

TMC-1. Snyder et al. (1984) found some evidence of existence of the largest member of this group, methyl triacetylene (CH3C6H) in this source. In 2006,

Remijan et al. (2006) detected this molecule and assigned the column density to be 3.1 × 1012 cm-2.

4.1.2 Molecules towards Sgr B2

The galactic center source Sgr B2 is a prime region for many interstellar species. In 2006, towards its hot core Sgr B2(N), three species were detected via their spectral transitions in absorption towards the source and thus probably derived from a cold halo of material surroundings of the hot core.

Lovas et al. (2006b) reported the detection of ketenimine (CH2CNH) with a column density of 1.5 × 1015 cm-2, corresponding to a fractional abundance of

-9 (0.1-3.0) ×10 with respect to H2. The authors suggested a possible formation route by isomerization of methyl cyanide (CH3CN) with energy supplied by shocks.

Hollis et al. (2006a) detected cyclopropenone (c-C3H2O) with a column

13 -2 density of ≈ 1 × 10 cm , corresponding to a fractional abundance against H2 of

≈ 6 ×10-11. Hollis et al. (2006a) maintained that this species may be formed from some type of oxygen addition to simpler ring species, e.g., c-C3H2, which is also present towards the same source.

Hollis et al. (2006b) found another molecule, acetamide (CH3CONH2) with a column density of 1.8 × 1014 cm-2. The authors believed that a synthesis of this species involves the exothermic association reaction between formamide

(HCONH2) and methylene radical (CH2) in the presence of shock phenomena, although radiative association reactions normally are fastest under low-energy conditions.

4.2 Synthesis of detected molecules

Based on the gas-phase chemical reaction network, osu.01.2007, which contains 452 species and 4431 reactions, the newly detected molecules and related species, as well as numerous reactions, were added to the network. To model the two sources where they molecules were seen, typical values of

physical conditions as shown in Table 2.1 were used for both TMC-1 and the cold halo around Sgr B2 (N) for all the molecules except for the warmer region where ketenimine was detected, where T = 50K. As for the elemental abundances, typical low-metal abundances as listed in Table 2.2 were used except that for TMC-1, where a lower Oxygen fractional abundance of 6.10 × 10-5 with respect to total density was applied. Reactions added to the OSU network to treat the chemistry of the GBT molecules, including both formation and destruction reactions, are listed in Table 4.1 along with their rate coefficients k and references. Table 4.1 also includes existing reactions in the network concerning these molecules. For bimolecular reactions, the rate coefficients are parameterized as k = α × (T/300)β × e-γ/T, whereas for cosmic-ray induced photodissociation, k = α × ζ.

Table 4.1 GBT molecules chemistry.

Reaction α β γ Ref.

(units: see

references)

-10 C3H4 + CN →C4H3N +H 4.10 × 10 0 0 1

3 C4H3N (CR) → C3N + CH3 1.50 × 10 0 0 2

Continued on next page

Table 4.1 continued

+ + −8 C4H3N + H3 →C4H4N + H2 1.08 × 10 -0.5 0 2

+ + −9 C4H3N + HCO → C4H4N + CO 4.11 × 10 -0.5 0 2

+ + −9 C4H3N + He →CH3 + C3N + He 9.49 × 10 -0.5 0 2

+ + −8 C4H3N + H →CH3 + HC3N 1.85 × 10 -0.5 0 2

+ + −9 C4H3N + C → C2H3 + C3N 2.90 × 10 -0.5 0 2

+ −9 C4H3N + C+ → C4H3 + CN 2.90 × 10 -0.5 0 2

+ + −9 C4H3N + H2 →C4H4N +H 1.00 × 10 0 0 2

+ + −10 C4H5 + N →C4H4N +H 1.00 × 10 0 0 2

+ + −11 CH3+ + HC3N → C4H4N + hν 8.60 × 10 -1.4 0 2

+ + −9 C4H4N + C → C5H3N +H 1.00 × 10 0 0 2

+ − −6 C4H4N +e → C4H3N +H 1.00 × 10 -0.3 0 2

+ − −6 C4H4N +e → CH3 + HC3N 1.00 × 10 -0.3 0 2

−10 CH3C4H + CN → CH3C5N +H 4.10 × 10 0 0 1,3

3 CH3C5N (CR) →C5N + CH3 1.50 × 10 0 0 2

+ + −9 CH3C5N + C → C6H3 + CN 6.24 × 10 -0.5 0 2

Continued on next page

Table 4.1 continued

+ + −8 CH3C5N + H → CH3 + HC5N 2.03 × 10 -0.5 0 2

+ + −8 CH3C5N + He →CH3 + C5N + He 1.04 × 10 -0.5 0 2

+ + −8 CH3C5N + H3 → C6H4N + H2 1.19 × 10 -0.5 0 2

+ + −9 CH3C5N + HCO → C6H4N + CO 4.34 × 10 -0.5 0 2

+ + −10 C6H5 + N →C6H4N +H 1.00 × 10 0 0 2

+ + −11 CH3 + HC5N → C6H4N + hν 8.60 × 10 -1.4 0 2

+ + −9 C6H4N + C → C7H3N +H 1.00 × 10 0 0 2

+ − −6 C6H4N + e →CH3+ HC5N 1.00 × 10 -0.3 0 2

+ − −6 C6H4N + e →CH3C5N +H 1.00 × 10 -0.3 0 2

−10 CCH + CH3C4H → CH3C6H +H 1.80 × 10 0 0 1,3

−12 C6H + CH4 →CH3C6H +H 7.00 × 10 0 0 3

+ − −7 C7H5 + e →CH3C6H +H 3.50 × 10 -0.5 0 2

+ − −7 C7H5 + e →C7H2 + H2 +H 3.50 × 10 -0.5 0 2

+ + −10 C2H4 + C5H2 →C7H5 +H 5.52 × 10 -0.5 0 2

+ + −10 C4H2 + C3H4 →C7H5 +H 6.42 × 10 -0.5 0 2

Continued on next page

Table 4.1 continued

+ + −9 C4H3 + C3H3 →C7H5 +H 1.65 × 10 -0.5 0 2

+ + −10 C5H2 + C2H4 →C7H5 +H 5.00 × 10 0 0 2

+ + −10 C6H2 + CH4 → C7H5 +H 8.00×10 0 0 2

+ + −13 C3H3 + C4H2 →C7H5 + hν 1.00 × 10 -2.5 0 2

+ + −9 C5H3 + C2H2 →C7H5 + hν 1.00 × 10 0 0 3

+ + −10 C7H5 + N →C7H3N + H2 1.00 × 10 0 0 2

3 CH3C6H (CR) →C6H + CH3 1.50 × 10 0 0 2

+ + −10 CH3C6H + C → C7H3 + CH 9.00 × 10 -0.5 0 2

+ + −10 CH3C6H + C → C8H2 + H2 9.00 × 10 -0.5 0 2

+ + −9 CH3C6H + H → C7H3 + H2 2.92 × 10 -0.5 0 2

+ + −9 CH3C6H + H → C7H4 +H 2.92 × 10 -0.5 0 2

+ + −9 CH3C6H + He →C7H2 + H2 + He 1.49 × 10 -0.5 0 2

+ + −9 CH3C6H + He →C7H3 + H + He 1.49 × 10 -0.5 0 2

+ + −9 CH3C6H + H3 → C7H5 + H2 3.40 × 10 -0.5 0 2

+ + −9 CH3C6H + HCO → C7H5 + CO 1.25 × 10 -0.5 0 2

Continued on next page

Table 4.1 continued

−10 CH3C6H + C → C8H2 + H2 7.40 × 10 0 0 2

+ − −7 CH3CNH + e → CH2CNH +H 1.00 × 10 -0.5 0 3

+ + −9 CH2CNH + C → C2H3 + CN 1.83 × 10 -0.5 0 4

+ + −9 CH2CNH + H → CH2CN + H2 2.82 × 10 -0.5 0 4

+ + −9 CH2CNH + H → CH3CN +H 2.82 × 10 -0.5 0 4

+ + −9 CH2CNH + He →CN + CH3 + He 2.02 × 10 -0.5 0 4

+ + −9 CH2CNH + He →CH3 + CN + He 2.02 × 10 -0.5 0 4

+ + −9 CH2CNH + H3 → CH3CNH + H2 3.33 × 10 -0.5 0 4

+ + −9 CH2CNH + HCO → CH3CNH + CO 1.35 × 10 -0.5 0 4

+ + −9 HCN + CH3 → CH3CNH + hν 9.00 × 10 -0.5 0 2

+ − −7 CH3CNH + e → CH2CN + H + H 1.00 × 10 -0.5 0 3

+ − −7 CH3CNH + e → CH3CN + H 1.00 × 10 -0.5 0 3

+ + −9 CH3CN + H3 → CH3CNH + H2 9.10 × 10 -0.5 0 2

+ + −9 CH3CN + HCO → CH3CNH + CO 3.70 × 10 -0.5 0 2

+ + −9 CH3CN + H3O → CH3CNH + H2O 4.22 × 10 -0.5 0 2

Continued on next page

Table 4.1 continued

+ + −9 CH3CN + HOCO → CH3CNH + CO2 3.28 × 10 -0.5 0 2

−11 c-C3H2 + OH → c-C3H2O + H 1.00 × 10 0 0 5

+ + −10 c-C3H4 + O →c-C3H3O + H 2.00 × 10 0 0 6

+ + −16 C2H3 + CO → c-C3H3O + hν 2.00 × 10 -2.5 0 7

+ − −7 c-C3H3O + e →c-C3H2O + H 1.00 × 10 -0.5 0 3

+ − −7 c-C3H3O + e →C2H3 + CO 1.00 × 10 -0.5 0 3

+ + −8 c-C3H2O + H3 →c-C3H3O + H2 1.01 × 10 -0.5 0 4

+ + −9 c-C3H2O + HCO →c-C3H3O + CO 3.91 × 10 -0.5 0 4

+ + −9 c-C3H2O + H3O →c-C3H3O + H2O 4.29 × 10 -0.5 0 4

+ + −8 c-C3H2O + He → C3H2 + O + He 1.22 × 10 -0.5 0 4

+ + −8 c-C3H2O + H →C3H2 + OH 1.71 × 10 -0.5 0 4

+ + −9 c-C3H2O + C →C3H2 + CO 5.41 × 10 -0.5 0 4

+ + −9 NH2CHO + CH3 → CH3CHONH2 + hν 1.00 × 10 0 0 3

+ − −7 CH3CHONH2 + e → CH3CONH2 + H 1.00 × 10 -0.5 0 3

+ − −7 CH3CHONH2 + e → CH3 + NH2CHO 1.00 × 10 -0.5 0 3

+ + −13 CH3CHO + NH4 → CH3CHONH4 + hν 1.00 × 10 -3.0 0 8

Continued on next page 58

Table 4.1 continued

+ − −7 CH3CHONH4 + e →CH3CONH2 + H2 + H 1.00 × 10 -0.5 0 3

+ − −7 CH3CHONH4 + e →CH3 + NH2CHO + H2 1.00 × 10 -0.5 0 3

+ + −9 CH3CONH2 + C → CH3CONH2 + C 4.60 × 10 -0.5 0 4

+ + −8 CH3CONH2 + H → CH3CONH2 + H 1.47 × 10 -0.5 0 4

+ + −9 CH3CONH2 + He →CH3CONH2 + He 5.20 × 10 -0.5 0 4

+ + −9 CH3CONH2 + He →CH3 + CO + NH2 + He 5.20 × 10 -0.5 0 4

+ + −9 CH3CONH2 + H3 → CH3CHONH2 + H2 8.60 × 10 -0.5 0 4

+ + −8 CH3CONH2 + HCO → CH3CHONH2 + CO 3.30 × 10 -0.5 0 4

+ + −9 CH3CONH2 + H2 → CH3CHONH2 + H 1.00 × 10 0 0 3

+ − −7 CH3CONH2 + e → CH3 + NH2 + CO 1.50 × 10 -0.5 0 3

Note: The parameter α is in units of cm3 s−1 for bimolecular reactions and is unitless for cosmic ray processes.

References:1, Carty et al. (2001); 2, osu.01.2007; 3 estimation according to analogous reaction rates; 4, calculation based on method of Chesnavich et al.

(1980); 5, D. Talbi, private communication; 6, Prodnuk et al. (1992); 7, Scott et al.

(1995); 8, Adams et al. (2003).

4.2.1 Synthesis of observed molecules in TMC-1

One important formation channel for the synthesis of cyanoacetylene and cyanoallene is the neutral-radical reaction involving the radical CN and the hydrocarbons methyl acetylene (CH3CCH) or allene (CH2CCH2) where the former molecule is a well-known interstellar species while the latter has never been detected due to its nonpolar structure. To compute abundances of the products, the two neutral reactants, methyl acetylene and allene, were not treated individually in the network. Instead, the sum of their abundances was considered and an overall species C3H4 was used to represent both of these two isomers. In addition, a parameter δ = [CH3CCH]/[C3H4] was added to stand for the portion of methyl acetylene among the total C3H4. This parameter can be varied for use in the chemical reaction network. This reaction channel has been studied via the CRESU technique (Carty et al. 2001) and found to have temperature-independent rate coefficients in the range 15-295 K of 4.1 × 10-10 cm3s-1. Balucani et al. (2002) published a subsequent combined crossed-beam and ab initio study for the reaction channels shown below:

CH3CCH + CN → CH2CCHCN + H, (4.1)

CH3CCH + CN → CH3CCCN + H, (4.2)

CH2CCH2 + CN → CH2CCHCN + H, (4.3)

CH2CCH2 + CN → HCCCH2CN + H, (4.4)

where the branching ratio between reactions (4.1) and (4.2) is 1:1 and between

(4.3) and (4.4) is 9:1. The third isomer 3-cyano methylacetylene (HCCCH2CN) was not detected in the interstellar medium possibly due to its much smaller dipole moment than the other two isomers. When k was used as the total reaction rate coefficient for reactions C3H4 + CN → C4H3N + H, the production rate of cyanoallene would be [0.5×δ + 0.9×(1-δ)] × k, while those for methyl cyanoallene and 3-cyano methylacetylene would be [0.5×δ] × k and [0.1×(1-δ)] × k, respectively.

In addition to the neutral-radical channels, the three C4H3N isomers can be formed from ion-molecule channels, which lead initially to the production of a

+ protonated ion precursor, C4H4N . This precursor may be a combination of several isomers. After being formed, dissociative recombination between this precursor and electrons leaded to the formation of three C4H3N isomers:

+ - C4H4N + e → CH2CCHCN + H, (4.5)

+ - C4H4N + e → CH3CCCN + H, (4.6)

+ - C4H4N + e → HCCCH2CN + H. (4.7)

The relative rates of the production isomers were assumed to be the same as from the neutral-radical pathways. This assumption is reasonable since the structures of the isomeric ions are related in an intimate manner to those of the

C4H3N isomers. Calculations in this study showed that the neutral-radical

channels are the more important. Once formed, the neutral C4H3N molecules are

+ + destroyed via standard ion-molecule reactions with cations such as HCO , H3 ,

C+ and He+, as well as via photodissociation caused by cosmic-ray induced photons. Some of the cation-molecule reactions protonate the C4H3N species, which can be reformed via dissociative recombination (reactions 4.5 – 4.7) with less than 100% efficiency since other product channels were included.

As for the third TMC-1 molecule in this study, methyl cyanodiacetylene

+ (CH3C5N), one formation channel from the dissociative recombination of C6H4N was included in former models (osu.01.2007):

+ - C6H4N + e → CH3C5N + H. (4.8)

Besides reaction (4.8), a reaction between CN and CH3C4H, likely to be more efficient, was also added:

CN + CH3C4H → CH3C5N + H. (4.9)

This reaction is in analogy with the measured formation of methyl cyanoacetylene (Carty et al. 2001). The rate coefficient of reaction (4.9) was chosen to possess the same parameters as measured for CN + CH3CCH (Carty et al. 2001). After being formed, methyl cyanodiacetylene can be destroyed via cation-molecule reactions and cosmic ray induced photodissociation.

For the last GBT molecule observed in TMC-1, methyl triacetylene

+ (CH3C6H), the dissociative recombination of the precursor cation C7H5 was already in former models (osu.01.2007):

+ - C7H5 + e → CH3C6H + H. (4.10)

Again, as this reaction is not sufficiently efficient, two neutral-radical formation reactions were added to the reaction network:

CCH + CH3C4H →CH3C6H + H, (4.11)

C6H + CH4 →CH3C6H + H. (4.12)

Reaction (4.11) was assumed to proceed at the same rate as the reaction between CCH and CH3CCH, which was studied in the laboratory by Carty et al.

(2001). The latter reaction was also included to the network. Reaction (4.12) was based on the reaction between CCH and CH4, which was only studied at 300K

(Laufer & Fahr 2004), and has a rate below the standard neutral-radical value, possibly suggesting a small activation energy barrier. It was assumed that reaction (4.12) has a rate independent of temperature. Once produced, methyl triacetylene is depleted by reactions similar to other GBT molecules observed in

TMC-1, plus a destruction channel by atomic carbon.

4.2.2 Synthesis of observed molecules towards Sgr B2(N)

Ketenimine (CH2CNH) is mainly formed by the dissociative recombination

+ of protonated acetonitrile, CH3CNH , which can also serve as a precursor for acetonitrile (CH3CN) and the cyanomethyl radical (CH2CN):

+ - CH3CNH + e → CH2CNH + H, (4.13)

+ - CH3CNH + e → CH3CN + H, (4.14)

+ - CH3CNH + e → CH2CN + H + H. (4.15)

The branching ratio between reactions (4.13) – (4.15) was assumed to be 1:1:1.

If this is the case, ketenimine should also be detectable in TMC-1 along with acetonitrile and cyanomethyl, since these two species were already detected there. After being formed, the ketenimine molecules were destroyed by reactions with relatively abundant cations.

Deducing a reaction pathway for the formation of cyclopropenone (c-

C3H2O) was a somewhat a difficult task (Hollis et al. 2006a). The cyclic molecule, c-C3H2, may serve as a natural precursor to cyclopropenone through some reaction with an oxygen-containing species:

c-C3H2 + O2 → c-C3H2O + O, (4.16)

c-C3H2 + O → c-C3H2O + hν, (4.17)

c-C3H2 + OH → c-C3H2O + H. (4.18)

However, only reaction (4.18) does not have a barrier according to quantum chemical calculations (Talbi, private communication). As for the cation-molecule

+ pathways leading to the protonated precursor c-C3H3O , which can then undergo the dissociative recombination to form cyclopropenone:

+ - c-C3H3O + e → c-C3H2O + H. (4.19)

+ the c-C3H3O might be produced by various cation-neutral reactions between cations with a three-carbon cyclic structure and oxygen-containing molecules/atoms such as:

+ + c-C3H2 + H2O → c-C3H3O + H, (4.20)

+ + c-C3H3 + O → c-C3H2O + H, (4.21)

+ + c-C3H2O + H2 → c-C3H3O + H, (4.22)

+ + c-C3H4 + O → c-C3H3O + H. (4.23)

Among these four possible channels, reaction (4.20) was studied in the laboratory and found not to occur at room temperature (Prodnuk et al. 1992), while the two step synthesis (4.21 and 4.22) fails because reaction (4.22) is endothermic. Only reaction (4.23) remains a possible pathway to form protonated cyclopropenone starting from a three-carbon ring. In addition, the radiative

+ + association between C2H3 and CO might also produce c-C3H3O :

+ + C2H3 + CO → c-C3H3O + hν. (4.24)

However, this reaction was studied in the three body limit by Scott et al. (1995),

+ who found the dominant product to be protonated propadienone (H2CCHCO ).

These authors used their results to rule out reaction (4.24) as a source of protonated propynal, which would then lead to propynal, a known interstellar molecule actually detected towards Sgr B2 (N) (Hollis et al. 2004).

Cyclopropenone is destroyed by abundant cations.

For the third detected molecule in the halo surrounding Sgr B2 (N), acetamide (CH3CONH2), Hollis et al. (2006b) suggested the main formation method might be the exothermic neutral-radical reaction between formamide and the methylene (CH2) radical:

NH2CHO + CH2 → CH3CONH2 + hν. (4.25)

However, this reaction involves a spin flip and thus probably an energy barrier. In addition, it is an association reaction, which must occur via radiative stabilization in the low-density interstellar medium. Therefore, other formation channels are needed. A likely radiative association reaction involving formamide is the cation- molecule association:

+ + NH2CHO + CH3 → CH3CONH2 + hν, (4.26) followed by the dissociative recombination:

+ - CH3CHONH2 + e → CH3CONH2 + H. (4.27)

The reaction rate coefficient for (4.26) was assumed to be efficient and the

Langevin value of 1 × 10-9 cm3s-1 at 10K was used. A second radiative association reaction involving acetaldehyde (CH3CHO) and the ammonium ion was also considered:

+ + CH3CHO + NH4 → CH3CHONH4 + hν, (4.28) which is followed by the dissociative recombination with electrons to form acetamide. The reaction rate of this reaction was also assumed be large at 10K.

The main destruction channels of acetamide are through cation-molecule reactions.

4.3 Modeling results and comparison with observances

4.3.1 TMC-1

Figure 4.1 shows calculated fractional abundances against molecular hydrogen for the two observed C4H3N isomers, methyl cyanoacetylene and cyanoallene, near their peak early-time values (t = 1 × 105 yr) as a function of the parameter δ, which is the ratio of the abundance of methyl acetylene to the total abundance of methyl acetylene and allene. Observed fractional abundances against H2 of these two species are shown in the figure as the horizontal lines.

These observed values were determined from the detected molecular column densities by Lovas et al. (2006a) and the assumption that the H2 column density 67

is 1022 cm-2. From the figure, it can be seen that at early-time the calculated abundance of cyanoallene (right panel) is in reasonable agreement with observation for all δ values. The worst agreement occurs as δ approaches unity, but even here the calculated abundance is low by a factor less than two. The role of δ is more important for methyl cyanoacetylene case (left panel); the calculated abundance is almost an order of magnitude low when δ is near zero but increases very rapidly with increasing δ. This result is reasonable because, as discussed in Section 4.2.1, methyl acetylene is the main source of methyl cyanoacetylene and δ is the fraction of methyl acetylene among C3H4 isomers.

The best fit value of δ can be obtained from the ratio between cyanoallene and methyl acetylene at early-time, where the observed value is 4.5. Figure 4.2 shows the calculated ratio plotted against δ; from the figure, the best agreement between calculations and observation occurs at δ = 0.35. Thus, the best fit gives that the abundance of methyl acetylene is 35% and that of allene 65% of the overall C3H4 abundance.

Figure 4.1. Calculated fractional abundances of CH3C3N and CH2CCHCN.

5 X (against H2) is plotted vs. the parameter δ (see text); t = 1 × 10 yr. Left panel,

CH3CCCN; right panel, CH2CCHCN. Observed values shown as horizontal lines.

Figure 4.2. Calculated abundance ratio of cyanoallene to methyl cyanoacetylene

plotted vs. parameter δ.

Time = 1 × 105 yr. Observed ratio of 4.5 plotted as horizontal line.

With δ = 0.35, the calculated fractional abundances of methyl cyanoacetylene and cyanoallene are plotted against time in Figure 4.3. The similarity between the two figures stems from the fact that they are produced from C3H4 isomers with a constant abundance ratio and destroyed in a similar manner. In both cases, the molecular abundances peak at times slightly greater than 105 yr and are in excellent agreement with observation from 105 yr through

107 yr. Furthermore, the predicted abundance of the third isomer, 3- 70

-11 cyanomethylacetylene (HCCCH2CN), is ≈ 1 × 10 at early time. This value is lower than those for methyl cyanoacetylene and cyanoallene by factors of ≈ 4 and ≈ 16, respectively.

Figure 4.3. Calculated fractional abundances of C4H3N isomers vs. time.

Left panel, CH3CCCN; right panel, CH2CCHCN; δ = 0.35. Observed abundances shown as horizontal lines.

The calculated fractional abundances of methyl cyanodiacetylene and methyl triacetylene are shown in Figure 4.4 as functions of time. Observed factional abundances of these two species are plotted as horizontal lines in the figure. The observed value for methyl cyanodiacetylene is ≈ 8 × 10-11 (Snyder et al. 2006; Remijan et al. 2006) and for methyl triacetylene is 3 × 10-10 (Remijan et al. 2006). As shown in the figure, the calculated abundance for methyl cyanodiacetylene is in excellent agreement with observation from times starting

5 at 10 yr. Therefore, the synthesis from the reaction between CN and CH3C4H is quite superior to the cation-molecular pathways, which were found inadequate by

Snyder et al. (2006). For methyl triacetylene, the calculated fractional abundance is in poorer agreement with the observation; after 2 × 105 yr, calculated values are almost one order of magnitude too low. Nevertheless, when uncertainties in observations and calculations are both considered, an overlap of Gaussian distributions will occur if observational uncertainties are assumed to be a factor of three and calculated uncertainties similar to those found for TMC-1 by Wakelam et al. (2006).

Figure 4.4. Calculated fractional abundances of methyl cyanodiacetylene

(CH3C5N) and methyl triacetylene (CH3C6H) plotted vs. time.

Left panel, CH3C5N; right panel, CH3C6. Observed abundances shown as horizontal lines.

4.3.2 Halo of Sgr B2(N)

In Figure 4.5, ketenimine modeling results are shown. The calculated fractional abundance is plotted as a function of time. The range of observed abundances is plotted as the gray area. In this case, the assumed temperature has been raised to 50K from 10K and the result is an increase of a factor of three in the peak calculated abundance. The early-time abundance at either temperature is well within the observed range.

Figure 4.5. Calculated fractional abundance of ketenimine plotted as a function of

time.

The shadowed region represents the range of observed values. T =50K results are shown. 73

In complete contrast to the case of ketenimine, the cold gas-phase model fails for the case of acetamide (CH3CONH2). When compared with the observed fractional abundance of 1.1 × 10-9 determined by Hollis et al. (2006b), the calculated peak value is about six orders of magnitude too low. The huge discrepancy derives from the fact that the starting materials, formamide and acetaldehyde, themselves have small abundances. To boost the abundance of formamide (NH2CHO), the following possible radiative association reaction

+ between NH4 and H2CO was also considered:

+ + NH4 + H2CO → NH4CH2O + hν, (4.29) followed by dissociative recombination. This reaction has been studied and known to occur under high-density conditions (Adams et al. 1980), but even with the assumption that a large rate coefficient was used, formamide still has a low abundance. The calculated ratio of acetamide abundance over that of formamide at early time is 0.003 while the observed abundance ratio in the cold halo region is 0.1 - 0.5 (Hollis et al. 2006b). So, it would appear that formamide is not the proper precursor in any event.

Finally, the case of cyclopropenone is somewhat ambiguous. If the

+ radiative association reaction between C2H3 and CO (Scott et al. 1995) does lead to protonated cyclopropenone, then a peak fractional abundance exceeding

10-10 for cyclopropenone is computed for early-time. This abundance compares 74

favorably with the observed value of 6 × 10-11 (Hollis et al. 2006a). However, it is more likely that the dominant product of the radiative association is not the ring- closure product but instead protonated propadienone, so that the production rate of cyclopropenone via this route is at best ≈ 1-5% of that of propadienone

(McEwan, private communication). In that case, the peak calculated fractional abundance lies well below the observed value. When the association reaction

(reaction 4.24) is ruled out, two other pathways remain: the neutral-radical reaction involving c-C3H2 and OH; and the cation-molecule reaction between

+ + C3H4 and O. As the C3H4 abundance is low, the neutral-radical channel dominates but only leads to the production of a fractional abundance for cyclopropenone of 6 × 10-12 at early time, which is an order of magnitude low.

Given the difficulty of deducing the proper H2 column density in this source as well as the uncertainty in the calculated abundance (Wakelam et al. 2006), the cold gas-phase production mechanism cannot be ruled out.

4.4 Conclusion

The pseudo time dependent low temperature pure gas-phase model works well for all TMC-1 molecules whether they are newly detected or confirmed by the use of the GBT while the performance of the model is rather poor for two of the three new molecules detected towards Sgr B2 (N). Sgr B2 (N) is a complex hot core source with a core-halo type structure, from which organic molecules

can be detected in absorption. Although such molecules may currently be existing under the cold conditions of the halo, it is certainly not clear where their origin was. They could be formed by gas-phase processes in the outer regions where they are detected. This assumption is not supported by this study. The failure of gas-phase models to reproduce earlier observed abundances of propenal (CH2CHCHO) and propanal (CH3CH2CHO) towards the same source

(Hollis et al. 2004) also suggests that these molecules may not be formed in the gas phase.

A second possible origin of organic molecules in Sgr B2 (N) is that they could be generated on the granular surfaces. This assumption raises new problems; in particular, how do the molecules leave the grains in a cold region?

One possibility is that non-thermal desorption, such as those via the energy generated by exothermic surface chemical reactions (Garrod et al. 2007), can lead to sufficient concentrations of these molecules (or their precursors) in the gas-phase.

Another possibility often invoked when discussing the galactic center region is that intermittent shock waves pervade the medium and sputter molecules off the grain surfaces.

Yet a fourth possibility is that the molecules are formed in the warmer (hot core) region and then diffuse throughout the halo. A former study showed that a

surface temperature of 40K can lead efficient evaporation of many organic molecules from the surface (Garrod & Herbst 2006).

4.5 References

Adams, N.G., Smith, D., & Paulson, J.F. 1980, J. Chem. Phys., 72, 288

Adams, N.G., Babcock, L.M., Mostefaouoi, T.M. & Kerns, M.S. 2003, Int. J. Mass.

Spectrom., 223, 459

Balucani, N., Asvany, O., Kaiser, R.-I., & Osamura, Y. 2002, J. Chem. Phys. A,

106, 4301

Carty, D., Le Page, V., Sims, I.R., & Smith, I.W.M. 2001, Chem. Phys. Lett., 344,

310

Chesnavich, W.J., Su, T., & Bowers, M.T. 1980, J. Chem. Phys., 72, 2641

Chin, Y., Kaiser, R.-I., Lemme, C., & Henkel, C. 2006, in Astrochemistry, From

Laboratory Studies to Astronomical Observations, AIP Conf. Proc., 855, 149

Garrod, R.T., & Herbst, E. 2006, A&A, 457, 927

Garrod, R.T., Wakelam, V., & Herbst, E. 2007, A&A, 467, 1103

Graedel, T.E., Langer, W.D., & Frerking, M.A. 1982, APJS, 48, 321

Hollis, J.M., Jewell, P.R., Lovas, F.J., Remijan, A., & Møllendal, H. 2004, ApJ,

610, L21

Hollis, J.M., Remijan, A.J., Jewell, P.R., & Lovas, F.J. 2006a, ApJ, 642, 933

Hollis, J.M., Lovas, F.J., Remijan, A.J., et al. 2006b, ApJ, 643, L25

Laufer, A.H. & Fahr, A. 2004, Chem. Rev., 104, 2813

Lovas, F.J., Remijan, A.J., Hollis, J.M., Jewell, P.R., & Snyder, L.E. 2006a, ApJ,

637, L37

Lovas, F.J., Hollis, J.M., Remijan, A.J., & Jewell, P.R. 2006b, ApJ, 645, L137

Prodnuk, S.D., Gronert, S., Bierbaum, V.M., & DePuy, C.H. 1992, Org. Mass.

Spectrom., 27, 416

Remijan, A.J., Hollis, J.M., Snyder, L.E., Jewell, P.R., & Lovas, F.J. 2006, ApJ,

643, L37

Schwahn, G., Schieder, R., Bester, M., & Winnewisser, G. 1986, J. Mol.

Spectrosc., 116, 263

Scott, G.B.I., Fairley, D.A., Freeman, C.G., Maclagan, R.G.A.R., & McEwan, M.J.

1995, IJMSIP, 149/150, 251

Snyder, L.E., Wilson, T.L., Henkel, C., Jewell, P.R., & Walmsley, C.M. 1984,

BAAS, 16, 959

Snyder, L.E., Hollis, J.M., Jewell, P.R., Lovas, F.J., & Remijan, A. 2006, ApJ, 647,

412

Wakelam, V., Herbst, e., & Selsis, F. 2006, A&A, 451, 551

Chapter 5: Interstellar Abundance of Molecular Oxygen

One continuing problem for modelers of the chemistry of cold cores is the low abundance/non-detection of molecular oxygen in these regions. In chemical models, a neutral-neutral reaction between O and OH is believed to be the main formation pathway of O2 in interstellar medium. In this chapter, several experimentally/theoretically determined rates of this reaction will be applied to the pseudo time dependent gas-phase model. This is to attempt to reveal effects of varying the rate and the possible reason for the low O2 abundance. In Section

5.1, the background of the O2 problem will be reviewed. In Section 5.2, modeling settings and effects of varying the O + OH reaction rate will be introduced. In

Section 5.3, the modeling results of directly related species, O, O2, OH, as well as other affected species will be presented. In Section 5.4, conclusions of the study and prediction for possible further detections will be discussed.

5.1 Background of O2 problem in cold cores

The lack of detection of O2 in the gas phase of cold interstellar cores such as TMC-1 and L134N is inconsistent with former and current gas-phase modeling

results. Compared with the upper limits set by observational groups (Pagani et al.

2003; Smith et al. 2004; Ohishi et al. 1992), chemical models give much too large fractional abundances of O2 at early time or steady states, usually two to three orders of magnitude too high (Bergin et al. 2000; Wakelam et al. 2006; Larsson et al. 2007).

5.1.1 Review of the history of modeling attempts

Bergin et al. (2000) ran steady state models for the gas-phase chemistry for cold interstellar cores. In their models, calculated O2 and H2O abundances are too big when compared to observations. A large number of solutions to this discrepancy were suggested, as discussed in Larson et al. (2007) and Wakelam et al. (2006): the clouds might be very young; pseudo-time-dependent gas-phase models of the chemistry of the large number of species seen in TMC-1 and

L134N work best at early times around 105 yr, etc. In the original calculations by

Bergin et al. (2000), the O2 abundance is rather low at early time while the H2O abundance is already too large to explain observations. In Wakelam et al. (2006) where an updated version of OSU chemical reaction network at that time was applied, the H2O problem was partially solved. With a criterion for “agreement” between observation and model abundances based on the overlap of Gaussian error functions, the abundance of water is sufficiently low over a wide range of times. This explained the lack of detectability of H2O in most cold sources, 80

although the severe upper limits in B68 and ρ Oph D may still present problems.

5 However, the O2 problem remained for times after 10 yr while agreement at later times may be achieved in gas-phase models by changing the standard elemental abundances applied to carbon-rich ones. This changing of elemental abundances should be taken only with much care to preserve the agreement for other species. Other solutions to the O2/H2O problems involve shocks, turbulence, bistability, and grain chemistry (Bergin et al. 2000; Charnley et al. 2001; Spaans

& van Dishoeck 2001; Viti et al. 2001; Willacy et al. 2002; Roberts & Herbst

2002).

5.1.2 Rate of O + OH reaction

The problem of O2 has been complicated by the lack of knowledge of the rate coefficient at the standard cold core temperature of 10K for its major formation reaction:

O + OH → O2 + H. (5.1)

Not long before this study, the rate coefficient k1 used in the OSU network was estimated from higher temperature measurements and had the expression 7.5 ×

10-11 (T/300)-0.25 cm3s-1. This leads to a value of 1.76 ×10-10 cm3s-1 at 10K. The value in the other major chemical reaction network, RATE99 (Le Teuff et al.

2000), was 1.77 × 10-11 e178/T cm3s-1, but pertains only to temperatures above

150K. Using experiments in the temperature range 39-142K with the CRESU

(Cinètique de Rèaction en Ecoulement Supersonique Uniforme) technique, Carty et al. (2006) suggested the rate coefficient is a constant 3.5 × 10-11 cm3s-1.

Although the temperature independence of the CRESU result is valid, the value itself may be somewhat low (Smith & Stewart 1994; Robertson & Smith 2006).

Xu et al. (2007b) undertook quantum mechanical calculations of the reaction rate coefficient at low temperature by a variety of approaches. With the

J-shifting approximation, they obtained a rate coefficient that decreases as the temperature drops from 100 to 10K. At 40K, the calculated rate coefficient was determined to be about a half of the experimental value. At 10K, the calculated rate coefficient fell to a very low value of 5.4 × 10-13 cm3s-1, which is significantly under the 39K experimental value. Later Lin et al. (2007) removed the J-shifting approximation and showed the calculated rate coefficient at 10K to be about

1/4.5 of the experimental value at 39K.

5.1.3 O2 factional abundance upper limits set by observers

For O2, with the Odin satellite observers determined upper limits for its

-7 -8 fractional abundance with respect to H2 to be 1.7 ×10 in L134N and 7.7 × 10 in

TMC-1 (Pagani et al. 2003). Because the effects of varying the rate coefficient for the reaction between O + OH will be studied, modeling results may also lead to

varying OH abundances, which can be compared to observations. Harju et al.

(2000) determined the fractional abundance in TMC-1 to be 2 × 10-7 from mapping the cloud at 1665 MHz using the Effelsberg 100m telescope. For L134N, the observed fractional abundance was determined to be 7.5 × 10-8 (Smith et al.

2004; Ohishi et al. 1992).

5.2 Modeling settings and general discussion of O + OH reaction effects

5.2.1 Modeling method and settings

In this study, the standard osu.01.2007 gas-phase chemical network has been utilized with the standard parameters for cold cores, as shown in Table 2.1.

Two sets of low-metal elemental abundances were applied. For L134N, the standard low-metal abundances, which is listed in Table 2.2, were used and for

TMC-1, O abundance is 6.10 × 10-5. The latter was proved most useful in improving agreement at early time with observation for the more than 50 detected molecules in TMC-1 (Wakelam et al. 2006). In addition, to allow for a possible high sulfur abundance in the gas phase, a sulfur abundance two orders of magnitude higher than the so called “low-metal” one, while other elemental abundances remained the same, was also utilized.

5.2.2 Effects of O + OH reaction rate coefficient change on related species

To explore the effects of rate coefficient k1 of reaction (5.1), four different k1 values were used. These values are listed in Table 5.1. To discuss the chemistry of O2 and its precursor OH in this case, two simplifying terms for reaction (5.1) are used: dominant and rate limiting. The term “dominant” here means that the reaction is the major route for the formation of O2, while the term

“rate limiting” means that the reaction is the major process for the destruction of

OH. When the reaction is both dominant and rate limiting, a change in its rate coefficient should not affect the O2 abundance and strongly affect the OH abundance. This can be shown mathematically under steady state conditions.

Assume that OH is depleted by reaction (5.1), as well as by reactions with cations and other neutrals. The steady state approximation can give the following equation:

+ [OH] = f / (k1[O] + ki[I ] + kn[N]), (5.2)

where f is the OH formation rate, ki and kn are the rate coefficients for OH destruction by cations I+ and neutrals N other than O, respectively, and the brackets refer to concentration. When reaction (5.1) is rate limiting, the abundance of OH reduces to the expression

[OH] = f / (k1[O]), (5.3)

Thus, an increase in the value of k1, will reduce the OH abundance, as long as it does not affect the O abundance strongly.

A similar steady state approximation can be derived for the O2 abundance, given by the expression

+ [O2] = (k1[O][OH] + f’) / (kc[C] + ki[I ]), (5.4)

where f’ represents other formation routes to O2 other than from reaction (5.1), and kc is the rate coefficient for O2 destruction with atomic carbon. If reaction (5.1) is dominant and at the same time it is rate limiting, the O2 abundance can be given by the following equation:

+ + [O2] = (k1[O][OH]) / (kc[C] + ki[I ]) ≈ f / (kc[C] + ki[I ]). (5.5)

In this case, the O2 abundance is independent of k1. When the reaction is not dominant (for the formation of O2), a change in its rate coefficient will also not affect the O2 abundance directly since the numerator of equation (5.4) will be f’.

Also, if the reaction is not rate limiting, change of its rate coefficient will not affect the abundance of OH strongly and so will affect O2 abundance if it is still dominant. Finally, if reaction (5.1) is neither dominant nor rate limiting, neither of the species will be affected. It must be remembered, however, that in a complex network of reactions, the terms “rate limiting” and “dominant” often have to be qualified. For example, this reaction can be rate limiting for OH only within a

limited range of k1 values, because other reactions can become more important as k1 decreases.

Table 5.1 k1 values at 10K used in O2 study.

3 -1 k1 (cm s ) Remarks Reference

1.76 × 10-10 osu.01.2007 Smith et al. (2004)

3.5 × 10-11 Experimental (39-142K) Carty et al. (2006)

7.84 × 10-12 Theoretical without J-shifting Quan et al. (2008)

5.4 × 10-13 Theoretical with J-shifting Xu et al. (2007b)

5.3 Modeling results and comparison to observations

5.3.1 OH and O2

Figures 5.1 and 5.2 show results for the fractional abundances of OH and

O2 with respect to H2 in L134N as functions of time, respectively. From Figure 5.1, it can be seen that the abundance of OH increases with time until about 106 yr, after which steady state is reached and the OH abundance does not change with time. The dependence of the abundance of OH on the value of k1 also increases as time increases, so that at steady state there is a two orders of magnitude divergence between the lowest abundance, corresponding to the highest value of k1, and the highest abundance, corresponding to the lowest value of k1. From the 86

discussion in Section 5.2.2, it appears that reaction (5.1) would be rate limiting at late times near steady state. Detailed model results show, however, that the reaction is not the only important destruction process for OH at late times, especially when the smallest k1 value is applied, and that reactions with protonating ions also contribute. At earlier times, OH is depleted mainly by reaction with C+, as well as with neutral C an N. The two boxes in Figure 5.1 show the time range that the calculated OH abundance is within a factor of 3 and a factor of 10 of the observed value. The time range of course depends on k1, too.

If the factor-of-3 criterion for agreement between theory and observation for OH is used, from Figure 5.1 it can be seen that for the highest value of k1, agreement starts only at times later than 106 yr, while for the lowest value, agreement is best around 105 yr but rapidly deteriorates with increasing time. The agreement is reasonable over the largest period of time for the experimental rate coefficient. If the factor-of-10 criterion is used, the constraints are less tight.

Figure 5.1. Fractional abundance of OH with respect to H2 plotted as a function

of time for four different k1 values.

O-rich abundances relevant to L134N are used. Horizontal line: OH observation

-10 towards L134N; dashed line: calculated OH abundance with k1 = 1.76 × 10

3 -1 -11 3 -1 -12 cm s ; dotted line: k1 = 3.5 × 10 cm s ; dash-dotted line: k1 = 7.84 × 10

3 -1 -13 3 -1 cm s ; dot-dot-dashed line: k1 = 5.4 × 10 cm s . The boxes delineate the regions where agreement between observation and theory is within a factor of 3

(solid line) and a factor of 10 (dotted line).

Figure 5.2. Fractional abundance of O2 with respect to H2 plotted as a function of

time for four different k1 values.

O-rich abundances relevant to L134N are used. See Figure 5.1 for caption of the curves.

As for the results shown in Figure 5.2, the O2 fractional abundance increases steadily with time until reaching a very high steady state value of

-4 6 almost 10 with respect to H2 somewhat after 10 yr, which is the same as shown before by Bergin et al. (2000). Before this time, the abundance of O2

5 depends directly on the value of k1. For example, at a time of 10 yr, O2 fractional

-9 -7 abundances range from ≈ 10 for the lowest value of k1 to almost 10 for the 89

5 highest value of k1. When the time increases to 3 × 10 yr, all abundances increase strongly but the smaller abundances increase the more strongly so that the differences become much smaller. Regarding the observed O2 upper limit, all four models reach the limit around (2-3) × 105 yr. At late times, detailed modeling results show that reaction (5.1) accounts for between 40% and 60% of the O2 production. The reaction’s importance depends on the value of k1, and so is close to dominant as well as rate limiting. Other important formation pathways of

+ 5 O2 include HOCO + O. At times before 10 yr, the reaction is clearly dominant

(near 100% of the O2 production), but not rate limiting.

C-rich abundances were applied for modeling TMC-1. Results are shown in Figures 5.3 and 5.4. The former shows the OH abundance and the latter shows the O2 abundance. The separation among the OH abundances for differing values of k1 is generally not large, because reaction (5.1) is not rate limiting, since a lower oxygen elemental abundance is used. Once again, the solid box delineates the regions of factor-of-3 agreement; in this case, the figure shows however that there is some difference among the different values of k1. In

6 particular, the largest value of k1 leads to agreement only at times over 10 yr, while the other three rate coefficients all lead to agreement with observation for times over (2-3) × 105 yr. When a criterion of factor-of-10 is used as the criterion, looser constraints are shown, especially for the largest value of k1.

Figure 5.3. Same as Figure 5.1 except that C-rich abundances relevant to TMC-1

are used.

In Figure 5.4, the four curves for O2 show considerable dispersion at most times, indicating that reaction (5.1) is not dominant. Furthermore, the four values of the O2 abundance increase monotonically from the beginning of the calculation until a time near 5 × 105 yr, when peak abundances are reached. The calculated abundances then decrease until a time near 2 × 106 yr, when steady state is eventually reached. The “bump” is correlated with a decline in the abundance of atomic carbon, which is related to O2, since the following reaction

C + O2 → CO + O (5.6) 91

is always the main destruction reaction of O2 during this time range. With the lowest of the four k1 values used, the calculated O2 fractional abundance essentially lies below the upper limit set up by observers for all times. With the highest k1 value, the calculated abundance becomes too large at a little more

5 than 10 yr. The middle two k1 values yield results in between these two extremes.

Figure 5.4. Same as Figure 5.2 except that C-rich abundances relevant to TMC-1

are used.

To summarize the O2 problem with both sets of abundances (O-rich and

C-rich), at the optimum early-time ages for L134N and TMC-1 determined by 92

Wakelam et al. (2006) there is no major discrepancy with the observed upper limit of O2. Nor is there a discrepancy of note with the observed abundance of

OH if the larger uncertainty in the observed abundance is chosen. If one insists on a later time or even steady state solution, however, O-rich abundances produce a single very large abundance of O2 for all k1 values, whereas C-rich abundances generally produce an overly large abundance of O2 only with the largest value of k1, which probably does not pertain to 10K. Moreover, the large abundance does not exceed the upper limit by more than one order of magnitude.

For OH at late times, only the smallest k1 value under O-rich conditions gives trouble when the larger uncertainty is chosen.

5.3.2 Other affected species

Apart from affecting the reactants and products directly involved in reaction (5.1), a change in the value of k1 can influence many other species. The results at the two extreme cases with the largest and the smallest k1 values at

10K were investigated. Figure 5.5 shows the percentage of affected species for both O-rich and C-rich cases as a function of time using the criterion of a factor of

10 change in abundance as “significant”.

Figure 5.5. Percentage of significantly affected species plotted against time.

Upper panel: O-rich case; lower panel: C-rich case.

For the O-rich case, up to 30% of the 452 species in the model are significantly affected at one time or another. Following the example of OH, however, these effects occur overwhelmingly at > 105 yr and so will not change the overall agreement with observation at early times. For the C-rich elemental abundances, the effects of the change in k1 are much smaller. Using the same criterion, only 2% of the species in the model are significantly affected. The affected species are connected to the reactants or products of reaction (5.1) via reaction pathways. Since there is much less atomic oxygen in the C-rich case 94

and the OH abundance is less dependent on changes in k1, far fewer species are strongly affected.

Figure 5.6 shows two examples of NO and SO2, which are both somewhat affected by the reaction (5.1) rate change. The horizontal lines in these figures are the observed abundance for NO and the upper limit for SO2 in L134N and the observed abundances of both in TMC-1 (Ohishi et al. 1992; Smith et al. 2004). In the case of NO, the radical is produced via the neutral-neutral reaction between

N and OH and follows the OH abundance closely. Not only does the general increase of OH with time, which occurs with both sets of elemental abundances, lead to a similar increase for NO, but for O-rich abundances, the large dispersion among the four OH curves at late times leads to a similar dispersion for NO. For

SO2, the situation is similar although the effect is somewhat smaller for O-rich abundances than for the case of NO. The reason is that the two main formation reactions for SO2 are the reactions between the radical SO and O or OH; both of these reactant partners are reactants in reaction (5.1).

Figure 5.6. Fractional abundances of NO and SO2 with respect to H2 plotted

against time for four different values of the rate coefficient k1.

The observed fractional abundances or upper limits (Ohishi et al. 1992; Smith et al. 2004) are depicted as solid horizontal lines. C-rich abundances pertain to

TMC-1 and O-rich abundances to L134N. Legend for k1 values of different curves is the same as that in Figure 5.1.

5.3.3 High sulfur calculations

Although chemical models of cold dense clouds often use a low abundance of sulfur to improve the overall agreement with observation, there is

little or no evidence of any depletion of this element in diffuse clouds. Therefore high-sulfur abundances were also applied to the problem. “High-sulfur” here means sulfur abundance is two orders of magnitude greater than listed in Table

2.2. This is a value close to what is obtained in diffuse clouds. Other elemental abundances are kept the same as those in the standard low-metal abundances.

Figures 5.7 and 5.8 show the comparisons of the calculated O2 abundances versus time for models with high and low sulfur; Figure 5.7 shows the O-rich case, while Figure 5.8 shows the C-rich case. In both cases, use of the higher sulfur abundance reduces the calculated O2 abundance. In the O-rich case this effect starts at ≈ 103 yr and increases as time evolves. The largest effect, which is about one order of magnitude, occurs at late times, when the lowest k1 value is used. Nevertheless, the use of the high sulfur abundance only increases the time at which the calculated O2 abundance surpasses the observed upper limit by a factor of a few. In the C-rich case, the effect is more significant: starting from ≈

3 10 yr, the effect can be as large as four orders of magnitude. Moreover, for all k1 values utilized, the calculated O2 abundance lies below the upper limit for all times. In addition, use of the C-rich abundances reduces the calculated H2O abundance by a significant amount at late times; the large early-time value is not changed much.

Figure 5.7. Fractional abundance of O2 with respect to H2 plotted against time for

four k1 values.

Horizontal solid lines are observational values towards L134N; dashed lines are

“low-metal” (O-rich) model results, while dotted lines are high-sulfur (and O-rich)

-10 3 -1 model results. Upper left panel: k1 = 1.76 ×10 cm s ; upper right panel: k1 =

-11 3 -1 -12 3 -1 3.5 ×10 cm s ; lower left panel: k1 = 7.84 ×10 cm s ; lower right panel: k1 =

5.4 ×10-13 cm3s-1.

Figure 5.8. Same as Figure 5.7 except that horizontal lines are observational results towards TMC-1, dashed lines and dotted lines are calculated abundances

for C-rich cases (both for low-metal and high-sulfur).

As for the OH abundance, it decreases sharply in the C-rich case, by an order of magnitude or more, resulting in worse agreement with observation for all times. This reduction leads to no late-time dependence on k1. The overall agreement in TMC-1 (C-rich case) is worsened dramatically when high-sulfur abundances are applied. With the order-of-magnitude criterion, the agreement at early time goes from ≈ 80% of the observed molecules to ≈ 60%. On the other hand, the overall agreement in L134N (O-rich case) remains about the same. 99

Therefore, it would seem that the use of high sulfur abundance is not helping, especially in the C-rich case.

5.3.4 Warmer sources

Dark cold cores, such as TMC-1 and L134N, are not the only cloud cores searched unsuccessfully for O2. Goldsmith et al. (2000) reported a large number of negative results with the SWAS satellite towards a variety of warmer cores such as OMC-1. Towards one of these cores, ρ Oph A, a well-known star- forming region, later observations with the Odin satellite revealed a tentative

-8 detection of O2 with fractional abundance of 5 × 10 relative to H2 (Larsson et al.

2007). To simulate the possible effect in warmer surroundings, a homogeneous warm gas-phase model was applied. This model is similar to those discussed above for cold cores, but with physical conditions n = 106 cm-3 and T = 40K, and the use of the 39K experimental value for the rate coefficient of the O + OH reaction. The results of the constant-temperature warm gas-phase model for O2 are not very distinguishable from the low-temperature models with a k1 value of

3.5 × 10-11 cm3s-1. In Quan et al. (2008), a warm-up gas-grain model where the temperature was increased after 105 years, was applied and achieved reasonable agreement with both the upper limits detected by SWAS (Goldsmith et al. 2000) and the tentative detection of Larsson et al. (2007) in ρ Oph A.

100

5.4 Conclusion

The major purpose of this study is to explore the effect of changes in k1 on the abundance of O2 in cold sources. New calculations of the rate coefficient for reaction (5.1) show that k1 decreases significantly when temperature drops from its value at 39K, which is the lowest experimentally determined temperature

(Carty et al. 2006). Without the J-shifting technique, the calculated rate coefficient is ≈ 4.5 times lower than the experimental value at 39K, but with J- shifting approximation, the value is ≈ 65 times lower than experiment. Application of pseudo-time-dependent models has revealed the effect of changing the k1 value on the level of agreement between observed and calculated abundances of

O2, its precursor OH, and, other affected species in two typical cold cores: TMC-1 and L134N.

Since only upper limits for O2 can be determined in these sources, a reasonable calculated abundance would be approximately at or below the limits.

With this criterion, the situation for L134N, which is modeled with O-rich elemental abundances, is that all k1 values utilized lead to good agreement with observation for times through ≈ (1-2) × 105 yr only and reach poor agreement shortly thereafter. The situation regarding O2 for O-rich abundances discussed by

Bergin et al. (2000) has not been changed appreciably by variation of k1. Nor does the use of high-sulfur abundance change the situation substantially. The

101

case of TMC-1, which is modeled with C-rich elemental abundances, is different.

The highest k1 value leads to an O2 abundance that exceeds the upper bound for

5 all times later than 2 × 10 yr, as in the O-rich case, but the three lower k1 values lead to O2 abundances that are significantly above the observed upper limit for smaller periods of time. When the high-sulfur abundance is used, all four k1 values lead to good agreement with observation at all times. A loose constraint on the value of k1 can be obtained by comparison of calculated and observed OH abundances in both sources over ranges of time for which the O2 agreement is reasonable. This analysis leads to the superiority of the experimental and high- order theoretical values for k1 over the more extreme upper and lower values.

To make a more complete study, some models with the extraordinarily

-15 3 -1 small rate coefficient of k1 = 1.0 × 10 cm s were run. In this case, for O-rich conditions, the amount of O2 produced at late times is significantly less, and it is produced mainly via other processes. The calculated fractional abundance of ≈

10-5 is still well above the observed upper limit in L134N. For C-rich conditions, on the contrary, the calculated O2 fractional abundance lies below the observed

TMC-1 upper limit at all times.

5.5 References

Bergin, E.A., & Snell, R.L. 2002, ApJ, 581, L105

102

Bergin, E.A. et al. 2000, ApJ, 539, L129

Carty, D., Goddard, A., Köler, S.P.K., Sims, I.R., & Smith, I.W.M. 2006, J. Phys.

Chem. A, 110, 33101

Charnley, S.B., Rodgers, S.D., & Ehrenfreund, P. 2001, A&A, 378, 1024

Davidsson, J., & Stenholm, L.G. 1990, A&A, 230, 504

Garrod, R.T., Wakelam, V., & Herbst, E. 2007, A&A, 467, 1103

Goldsmith, P.F. et al. 2000, ApJ, 539, L123

Graff, M.M., & Wagner, A.F. 1990, J. Chem. Phys., 92, 2423

Harding, l.B., maergoiz, A.I., Troe, J., & Ushakov, V.G. 2000, J. Chem. Phys.,

113, 11019

Harju, J., Winnberg, A., & Wouterloot, J.G.A. 2000, A&A, 353, 1065

Hassel, G.E., Herbst, E. & Garrod, R.T. 2008, ApJ

Larsson, B. et al. 2007, A&A, 466, 999

Le Teuff, Y.H., Miller, T.J., & Markwick, A.J. 2000, A&AS, 146, 157

Lin, S.Y., & Guo, H. 2004, J. Phys. Chem. A, 108, 2141

Lin S.Y., Guo, H., Honvault, P., & Xie, D. 2006a, J. Phys. Chem. B, 110, 23641

Lin, S. Y., Xie, D., & Guo, H. 2006b, J. Chem. Phys., 125, 091103

103

Lin S.Y., Guo, H., Honvault, P., Xu, C., & Xie, D. 2008a, J. Phys. Chem., 128,

014303

Lin S.Y., Sun, Z., Guo, H., Zhang, D.H., Honvault, P., Xie, D., & Lee, S.Y. 2008b,

J. Phys. Chem. A, 112, 602

Miller, J. A. 1986, J. Chem. Phys., 84, 6170

Ohishi,M., Irvine,W. M., & Kaifu, N. 1992, in IAU Symp. 150, Astrochemistry of Cosmic Phenomena, ed. P. D. Singh ( Dordrecht: Kluwer), 171

Pagani, L., Bacmann, A., Cabrit, S., & Vastel, C. 2007, A&A, 467, 179

Pagani, L., et al. 2003, A&A, 402, L77

Roberts, H., & Herbst, E. 2002, A&A, 395, 233

Robertson, R., & Smith, G. P. 2006, J. Phys. Chem. A, 110, 6673

Smith, I. W. M., Herbst, E., & Chang, Q. 2004, MNRAS, 350, 323

Smith, I. W. M., & Stewart, D. W. A. 1994, J. Chem. Soc. Faraday Trans., 90,

3221

Spaans, M., & van Dishoeck, E. F. 2001, ApJ, 548, L217

Viti, S., Roueff, E., Hartquist, T. W., Pineau des Foreˆts, G., & Williams, D. A.

2001, A&A, 370, 557

Wakelam, V., Herbst, E., & Selsis, F. 2006, A&A, 451, 551

104

Willacy, K., Langer, W. D., & Allen, M. 2002, ApJ, 573, L119

Xu, C., Jiang, B., Xie, D., Farantos, S. C., Lin, S. Y., & Guo, H. 2007a, J. Phys.

Chem. A, 111, 10353

Xu, C., Xie, D., Honvault, P., Lin, S. Y., & Guo, H. 2007b, J. Chem. Phys.,

127, 024304

Xu, C., Xie, D., Zhang, D. H., Lin, S. Y., & Guo, H. 2005, J. Chem. Phys., 122,

244305

105

Chapter 6: Gas-grain modeling of CHNO isomers and CHNS isomers

Isocyanic acid (HNCO) is a well-known interstellar molecule. Two of its metastable isomers, cyanic acid (HOCN) and fulminic acid (HCNO), have also been observed in various surroundings, including the Sgr B2 giant molecular cloud, several cold cores, and the lukewarm corino L1527 as well. In this study, gas-grain models were applied for four CHNO isomers, including HNCO, HOCN,

HCNO, and HONC. In addition, a very similar study of CHNS isomers will also be discussed later in this chapter.

6.1 Background of CHNO isomers study

6.1.1 Observational results

Isocyanic acid (HNCO) has been detected towards various sources, including photon-dominated regions (Jansen et al. 1995), translucent clouds

(Turner et al. 1999), cold dense cores (Brown 1981; Marcelino et al. 2009a), hot cores (Churchwell et al. 1986; Snyder & Buhl 1972; Martín et al. 2008), a

“lukewarm corino” (Marcelino et al. 2009a), and in assorted clouds throughout

106

the Galactic Center (Menten 2004; Martín et al .2008; Turner 1991). The fractional abundance of HNCO against molecular hydrogen is similar in different sources. In the typical cold core TMC-1, its fractional abundance against molecular hydrogen is 5 × 10-10 (Marcelino et al. 2009a) while in assorted sources in the giant cloud Sgr B2 it is ≈ 0.5-5 × 10-9 (Churchwell et al. 1986;

Brünken et al. 2009a,b). Abundances in the hot cores Sgr B2 (M) and Sgr B2 (N) are somewhat uncertain due partially to the uncertain H2 column density (Liu &

Snyder 1999). The metastable isomer of lowest energy, cyanic acid (HOCN), was identified in Sgr B2 (OH). Its estimated ratio relative to HNCO is 0.4% and its

-11 fractional abundance with respect to H2 is 1 × 10 (Brünken et al. 2009b; Turner

1991). In addition, HOCN has also been detected in and around the hot cores

Sgr B2 (M) and Sgr B2 (N), elsewhere in Sgr B2, and in TMC-1 with a ratio to

HNCO about 1% (Brünken et al. 2009a, b; Marcelino et al. 2009b). An even higher energy isomer, fulminic acid (HCNO), has been detected towards several cold and prestellar cores as well as towards the lukewarm corino L1527. The

HCNO/HNCO abundance ratio was estimated to be about 2% in the sources studied except for TMC-1, where the value is less than 1/300 (Marcelino et al.

2009a). On the other hand, a search for HCNO in hot regions such as Orion, Sgr

B2 ended in negative results (Marcelino et al. 2009a,b).

107

6.1.2 Possible gas-phase syntheses

After HNCO was first detected towards Sgr B2 (Snyder & Buhl 1972),

Iglesias (1977) suggested a gas-phase synthesis of this molecule. The synthesis

+ starts from the ion NCO and consists of two ion-molecule reactions with H2 followed by a recombination reaction with electrons:

+ + NCO + H2 → HNCO + H, (6.1)

+ + HNCO + H2 → HNCOH + H, (6.2)

HNCOH+ + e- → HNCO + H. (6.3)

A similar synthesis was advocated by Brown (1981) to explain the abundance of HNCO in TMC-1, although he assumed that the lower energy

+ isomer H2NCO is the product in reaction (6.2). Iglesias (1977) estimated the

-10 HNCO fractional abundance to be around 10 for a cold cloud at a density nH =

2 ×104 cm-3 with a lower fractional abundance at higher densities. Following these two studies, Marcelino et al. (2009a) reported a gas-phase model for

HNCO, HOCN, and HCNO in a steady-state study of cold dense cores, adding considerably to the ions considered by Iglesias (1977). In their network, HOCN can be formed from the precursor ion HNCOH+ whereas HCNO is formed from the well-studied neutral-neutral reaction between methylene and nitric oxide

(Glarborg et al. 1998):

108

CH2 + NO → HCNO + H. (6.4)

The theoretical results of Marcelino et al. (2009a) for cold clouds at 10K are density-dependent, with the abundance ratio R = HNCO/HCNO ranging from

3 -3 5 -3 0.8 at nH = 2 × 10 cm to a peak of 72 at 2 × 10 cm before it starts dropping at still higher densities. The results are in reasonable agreement with the observed values in cold cores except for TMC-1 where too much fulminic acid (HCNO) is predicted. They are also in agreement with two observations in the lukewarm corino L1527, one towards the protostar and one towards the colder envelope, although the 10K temperature used may be too low (Sakai et al. 2008). Moreover,

5 the predicted abundances of HOCN are very low; e.g., for a cloud of nH = 2 × 10 cm-3, the predicted abundance of HOCN is only 2% of that of HCNO, presumably because there is no neutral-neutral channel analogous ot reaction (6.4) for

HCNO. This low predicted abundance does not support the suggested evidence for HOCN in TMC-1 reported by Brünken et al. (2009b) and Marcelino et al.

(2009a).

In addition to gas-phase syntheses of HNCO, HOCN, and HCNO, possible gas-grain syntheses were also briefly discussed in Brünken et al. (2009b). It has been assumed for some time that HNCO can be produced efficiently on grain surfaces by the hydrogenation of accreted NCO (Hasegawa & Herbst 1993;

Garrod & Herbst 2006). It is of course possible that some HOCN can also be formed in this manner. In cold sources, any of the isomers formed on dust

109

particles would have to desorb into the gas in some non-thermal manner (e.g. photodesorption) to be detected in the gas phase, whereas in hot cores and their environments the ice mantles formed in prior cold eras evaporate at least partially.

6.2 Gas-grain models for CHNO isomers

In the study of CHNO isomers, the Ohio State gas-grain network

(Hasegawa et al. 1992; Hasegawa & Herbst 2001; Garrod & Herbst 2006; Garrod et al. 2007; Hassel et al. 2008) was used. The network contains almost 700 species, including 200 surface species, and over 6000 gas-phase and grain- surface reactions. Starting with the standard model, CHNO isomers and related species, as well as new reactions were added. In the following subsections, added reactions and gas-grain model settings will be introduced.

6.2.1 New reactions

Additional gas-phase reactions are taken from the literature (Iglesias 1977;

Brown 1981; Glarborg et al. 1998), as discussed above in Subsection 6.1.2. The reactions are listed in Table 6.1. It should be pointed out that among all studied

CHNO isomers, only HCNO can be formed in the gas phase via the unique reaction (6.4). In addition, surface processes are also considered and listed in

110

Table 6.2. In each table, the rate coefficients (Table 6.1) or parameters used in obtaining the rate coefficients (Table 6.2) are both listed. The surface reactions are considered to take place via the standard diffusive (Langmuir-Hinshelwood) mechanism on grains of radius 0.1 µ; the reactions are treated by rate equations

(Herbst & Millar 2008). Desorption energies (ED) and diffusion energy barriers (Eb) for the surface species are set to the values discussed in §2.2 of Garrod &

Herbst (2006). For the CHNO isomers, ED is estimated to be 2800K and Eb to be half of the desorption energy.

The gas-phase formation routes of the CHNO isomers are similar to those discussed in Marcelino et al. (2009a). The surface syntheses start from the isocyanate radical NCO, which is formed in the gas mainly by the neutral-neutral reaction between atomic nitrogen and the formyl radical:

N + HCO → NCO + H. (6.5)

Then the product radical can be accreted onto the grains and form the surface species JNCO, where J here designates a species on the grain surface. After that, a surface hydrogen atom can add to the radical, leading to both isocyanic and cyanic acids:

JH + JNCO → JHNCO, (6.6)

JH + JNCO → JHOCN. (6.7)

111

Then the products can be desorbed into the gas phase, either by non-thermal mechanisms during a cold era, or mainly via thermal processes during a warm- up or hot era. Non-thermal desorption mechanisms in the network include processes driven by cosmic rays, and the energy of exothermic reactions. To help destroy the grain species, surface photodissociation via external photons and cosmic-ray-induced photons are also included with rate coefficients equal to those that occur in the gas (Ruffle & Herbst 2001).

The surface synthesis of JHCNO and JHONC follows similar routes to

JHNCO except that their precursor, the radical CNO, is assumed to be produced on grain surfaces via the association of atomic carbon and nitrous oxide:

JC + JNO → JCNO. (6.8)

Once produced, the gaseous CHNO isomers are depleted by accretion onto grains, by photodissociation involving mainly cosmic ray-induced photons,

+ and by chemical reactions with cations (e.g. H3 ) or possibly the abundant neutral atoms C and O. For HNCO, the most stable isomer with a formation enthalpy of -

27.6 kcal/mol (Schuurman et al. 2004), all the reactions with C and O are believed to have barriers and unlikely to occur. For HOCN, which lies higher in energy than HNCO by 25 kcal/mol (Schuurman et al. 2004), its reaction with atomic carbon is exothermic and barrierless for four sets of products (Quan et al.

2009):

HOCN + C → CO + HCN, HCO + CN, H + OCNC, and OH + CNC. (6.9) 112

Its reaction with atomic oxygen to produce the products OH and NCO:

HOCN + O → OH + NCO, (6.10) is exothermic with a small barrier of only 0.24 kcal/mol (120K) and may be important at high temperatures, as occur in the warm-up models (Garrod &

Herbst 2007).

For the case of HCNO, which lies 70 kcal/mol higher in energy than

HNCO (Schuurman et al. 2004), the exothermic reaction with atomic oxygen has been previously studied. Laboratory results show that it has a barrier of (195 ±

120) K and that products including CO dominate (Feng & Hershberger 2007). On the other hand, theoretical results (Miller et al. 1998, 2003) indicate that no barrier exists for rapid reactions to form HCO and NO, or NCO + OH. Here, the laboratory results are chosen. Of the reactions with atomic carbon, the process

C + HCNO → C2H + NO, (6.11) has been found to be exothermic with no energy barrier (Osamura, private communication).

For the highest energy isomer studied, HONC, with energy relative to

HNCO of 85 kcal/mol (Schuurman et al. 2004) the reaction with O:

O + HONC → O2H + CN, (6.12)

113

is exothermic by 11 kcal/mol and assumed to have no barrier. The reaction with

C with the most likely products of CH + CNO is endothermic by 43.6 kJ/mol. In addition, H atoms may also react with the CHNO isomers and destroy them.

Table 6.1 Additional gas-phase reactions for CHNO isomer study.

Reaction α β γ Ref.

(Units vary.

See

footnote.)

HNCO

HNCO → NH + CO (CRPh) 6.00 × 103 0 0 a

+ + -9 H + HNCO → NH2 + CO 7.94 × 10 -0.5 0 a

He+ + HNCO → NCO+ + H + He 5.68 × 10−9 -0.5 0 a

He++ HNCO → HNCO+ + He 5.68 × 10−9 -0.5 0 b

+ + −9 H3 + HNCO → H2NCO + H2 3.69 × 10 -0.5 0 b

+ + −9 H3 + HNCO → HNCOH + H2 3.69 × 10 -0.5 0 b

HNCO → NH + CO (hν) 1.00 × 10−9 0 1.7 b

Continued on next page

114

Table 6.1 continued

HOCN

HOCN → OH + CN (CRPh) 6.00 × 103 0 0 b

+ + -9 H + HOCN → H2O + CN 6.25 × 10 -0.5 0 b

He+ + HOCN → NCO+ + H + He 4.47 × 10−9 -0.5 0 b

+ + −9 H3 + HOCN → HNCOH + H2 8.54 × 10 -0.5 0 b

+ + −9 H3 + HOCN → H2OCN + H2 8.54 × 10 -0.5 0 b

HOCN → OH + CN (hν) 1.00 × 10−9 0 1.7 b

HOCN + O → OH + OCN 1.00 × 10−10 0 0 b

HOCN + C → CO + HCN 1.00 × 10−10 0 0 b

+ + + + + HNCO , HOCN , H2NCO , HNCOH , H2OCN

+ + −8 OCN + H3 → HNCO + H2 1.64 × 10 -0.5 0 b

+ + −8 OCN + H3 → HOCN + H2 1.64 × 10 -0.5 0 b

+ + −9 NCO + H2 → HNCO + H 1.51 × 10 0 0 c,d

+ + −9 NCO + H2 → HOCN + H 1.51 × 10 0 0 b

+ + −9 HNCO + H2 → H2NCO + H 1.51 × 10 0 0 c,d

+ + −9 HNCO + H2 → HNCOH + H 1.51 × 10 0 0 c,d

Continued on next page 115

Table 6.1 continued

HNCO+ + e- → CO + NH 1.50 × 10−7 -0.5 0 a

HNCO+ + e- → H + OCN 1.50 × 10−7 -0.5 0 b

+ - −7 H2NCO + e → HNCO + H 1.50 × 10 -0.5 0 b

+ - −7 H2NCO + e → NH2 + CO 1.50 × 10 -0.5 0 b

+ + −9 HOCN + H2 → HNCOH + H 1.51 × 10 0 0 b

+ + −9 HOCN + H2 → H2OCN + H 1.51 × 10 0 0 b

HOCN+ + e- → OH + CN 1.50 × 10−7 -0.5 0 b

HOCN+ + e- → H + OCN 1.50 × 10−7 -0.5 0 b

HNCOH+ + e- → HNCO + H 1.00 × 10−7 -0.5 0 b

HNCOH+ + e- → HOCN + H 1.00 × 10−7 -0.5 0 b

HNCOH+ + e- → NH + HCO 1.00 × 10−7 -0.5 0 b

+ - −7 H2OCN + e → HOCN + H 1.50 × 10 -0.5 0 b

+ - −7 H2OCN + e → H2O + CN 1.50 × 10 -0.5 0 b

HCNO

HCNO → CH + NO (CRPh) 6.00 × 103 0 0 b

Continued

116

Table 6.1 continued

+ + -8 H + HCNO → CH2 + NO 1.17 × 10 -0.5 0 b

He+ + HCNO → HCNO+ + He 8.39 × 10−9 -0.5 0 b

+ + −9 H3 + HCNO → HCNOH + H2 6.92 × 10 -0.5 0 b

+ + −9 H3 + HCNO → H2CNO + H2 6.92 × 10 -0.5 0 b

−10 HCNO + C → C2H + NO 1.00 × 10 0 0 b

−10 CH2 + NO → HCNO + H 1.00 × 10 0 0 e,b

HCNO → CH + NO (hν) 1.00 × 10−9 0 1.7 b

HONC

HONC → CN + OH (CRPh) 6.00 × 103 0 0 b

+ + -8 H + HONC → H2O + CN 1.45 × 10 -0.5 0 b

He+ + HONC → HONC+ + He 1.03 × 10−8 -0.5 0 b

+ + −9 H3 + HONC → HCNOH + H2 8.54 × 10 -0.5 0 b

−10 HONC + O → O2H + CN 1.00 × 10 0 0 b

HONC → OH + CN (hν) 1.00 × 10−9 0 1.7 b

Continued on next page

117

Table 6.1 continued

+ + + + HCNO , HONC , HCNOH , H2CNO

+ + −9 HCNO + H2 → HCNOH + H 1.51 × 10 0 0 b

HCNO+ + e- → CH + NO 1.50 × 10−7 -0.5 0 b

HCNO+ + e- → H + CNO 1.50 × 10−7 -0.5 0 b

HCNOH+ + e- → HCNO + H 1.00 × 10−7 -0.5 0 b

HCNOH+ + e- → HCN + OH 1.00 × 10−7 -0.5 0 b

+ - −7 H2CNO + e → HCNO + H 1.50 × 10 -0.5 0 b

+ - −7 H2CNO + e → C2H+ NO 1.50 × 10 -0.5 0 b

+ + −9 HCNO + H2 → HNCOH + H 1.51 × 10 0 0 b

+ + −9 HCNO + H2 → H2CNO + H 1.51 × 10 0 0 b

+ + −9 HONC + H2→ HCNOH + H 1.51 × 10 0 0 b

HONC+ + e- → OH + CN 1.50 × 10−7 -0.5 0 b

HONC+ + e- → H + CNO 1.50 × 10−7 -0.5 0 b

HCNOH+ + e- → HONC + H 1.00 × 10−7 -0.5 0 b

Continued on next page

118

Table 6.1 continued

OCN, CNO

O + OCN → CO + NO 1.00 × 10-10 0 0 a

H + OCN → OH + CN 1.00 × 10-10 0 0 b

H + CNO → OH + CN 1.00 × 10-10 0 0 b

OCN → CN + O (CRPh) 1.50 × 103 0 0 a

CNO → CN + O (CRPh) 1.50 × 103 0 0 b

C+ + OCN → CO+ + CN 1.90 × 10−9 -0.5 0 a

He+ + OCN → O+ + CN + He 1.50 × 10−9 -0.5 0 a

He+ + OCN → CN+ + O + He 1.50 × 10−9 -0.5 0 a

+ + −9 H3 + OCN → HNCO + H2 1.64 × 10 -0.5 0 a

+ + −9 H3 + CNO → HOCN + H2 1.64 × 10 -0.5 0 a

C+ + CNO → CO+ + CN 8.98 × 10−9 -0.5 0 b

He+ + CNO → O+ + CN + He 1.99 × 10−8 -0.5 0 b

He+ + CNO → CN+ + O + He 1.99 × 10−8 -0.5 0 b

+ + −9 H3 + CNO → HCNO + H2 1.64 × 10 -0.5 0 b

Continued on next page

119

Table 6.1 continued

+ + −9 H3 + CNO → HONC + H2 1.64 × 10 -0.5 0 b

C + OCN → CO + CN 1.00 × 10−10 0 0 a

O + OCN → CO + NO 1.00 × 10−10 0 0 b

O + CNO → CO + NO 1.00 × 10−10 0 0 b

N + HCO → OCN + H 1.00 × 10−10 0 0 a

CH + NO → CNO + H 1.00 × 10−10 0 0 a,b

OCN → CN + O (hν) 1.00 × 10−11 0 2.0 a

CNO → CN + O (hν) 1.00 × 10−11 0 2.0 b

Note: Bimolecular rate coefficients are tabulated as α × (T/300)β × e-γ/T in units of cm3 s−1. Photodissociation rate coefficients are tabulated as α × (T/300)β × e-γAv in units of s−1. Cosmic-ray-induced photodissociation rate coefficients are tabulated in terms of ζ (s-1).

References: a, Hasegawa et al. (1992); Garrod et al. (2007); Hassel et al. (2008); b, estimation according to analogous reaction rates; c, Iglesias (1977); d, Brown

(1981); e, Glarborg et al. (1998).

120

Table 6.2 Additional surface-related reactions for CHNO isomer study.

Reaction Parameters Ref.

Surface reactions Eb,A (K) Eb,B (K)

JH + JOCN → JHNCO 225 1200 a

JH + JOCN → JHOCN 225 1200 a,b

JC + JHOCN → JCO + JHCN 400 1400 a,b

JH + JCNO → JHCNO 225 1200 a,b

JC + JHCNO → JC2H + JNO 400 1400 a,b

JH + JCNO → JHONC 225 1200 a,b

JO + JHONC → JO2H + JCN 400 1400 a,b

JC + JOCN → JCN + JCO 400 1200 a

JO + JOCN → JCO + JNO 400 1200 a,b

JC + JCNO → JCN + JCO 400 1200 a,b

JC + JNO → JCNO 400 800 a,b

Reaction-induced desorption ED (K) Eexo (K)

JH + JOCN → HNCO 2800 53799 a

JH + JOCN → HOCN 2800 43130 b

Continued on next page 121

Table 6.2 continued

JC + JHOCN → CO + HCN 2050 81678 b

JH + JCNO → HCNO 2800 9435 b

JC + JHCNO → C2H + NO 2137 28018 b

JH + JCNO → HONC 2800 9435 b

JO + JHONC → O2H + CN 3650 5714 b

JC + JOCN → CN + CO 1600 62503 a

JO + JOCN → CO + NO 1600 47751 b

JC + JCNO → CN + CO 1600 95466 b

JC + JNO → CNO 2400 48750 b

Thermal and cosmic-ray desorption ED (K)

JHNCO → HNCO 2800 a

JHOCN → HOCN 2800 b

JHCNO → HCNO 2800 b

JHONC → HONC 2800 b

JCNO → CNO 2400 b

Continued on next page

122

Table 6.2 continued

Cosmic-ray-induced photodissociation α (s-1)

JHNCO → JNH + JCO 6 × 103 ζ a

JHOCN → JOH + JCN 6 × 103 ζ b

JHCNO → JCH + JNO 3 × 103 ζ b

JHONC → JOH + JCN 3 × 103 ζ b

JCNO → JCN + JO 3 × 103 ζ b

Photodissociation α (s-1) γ

JHNCO → JNH + JCO 1.00 × 10-9 1.7 a

JHOCN → JOH + JCN 1.00 × 10-9 1.7 b

JHCNO → JCH + JNO 1.00 × 10-9 1.7 b

JHONC → JOH + JCN 1.00 × 10-9 1.7 b

JCNO → JCN + JO 1.00 × 10-11 2.0 b

Note: The parameters and how they are applied in the formulae for the rate coefficients for assorted process can be found in Hasegawa et al. (1992);

Hasegawa & Herbst (1993); Ruffle & Herbst (2001); Garrod et al. (2007); Herbst

& Millar (2008).

123

References: a, Hasegawa et al. (1992); Garrod et al. (2007); Hassel et al. (2008); b, estimation according to analogous reaction rates.

6.2.2 Gas-grain modeling settings

To simulate the very different circumstances of hot, lukewarm and cold cores, four gas-grain models, including two warm-up models based on models discussed in Garrod & Herbst (2006) and Hassel et al. (2008) on hot cores and corinos, one warm-up model based on the lukewarm corino model for L1527

(Hassel et al. 2008), and one cold core model based on the work in Garrod et al.

(2007) were used. The warm-up models consist of three phases: (i) a cold phase at a temperature of at 10K lasting for 105 years, during which both gas-phase and grain-surface chemistry occur; (ii) a warm-up phase during which temperature increases quadratically 2 × 105 yr, while the surface chemistry produces large organic molecules before the ice mantle fully sublimes; and (iii) a high-temperature, during which gas-phase chemistry acts to deplete the large organic molecules produced in the warm-up and cold phases. With these settings, the length of the cold phase is sufficiently long for the higher density models so that most heavy material has condensed out onto the dust particles.

The densities, final temperatures and other important model parameters of all four models are listed in Table 6.3; the parameters ζ, d/g, and aRRK refer to

124

important physical parameters used in the gas-grain model, as discussed in

Chapter 2. Figure 6.1 shows a plot of temperature vs. time for the models.

Chosen initial non-zero abundances are based on typical oxygen-rich low-metal abundances commonly used as described in Table 2.2.

Table 6.3 Physical parameters of the CHNO models.

Parameter Hot Core Warm Env. Lukewarm Cold Core

-3 6 5 6 4 nH (cm ) 2 × 10 2 × 10 2 × 10 2 × 10

Tasymp (K) 200 50 30 10

ζ (S-1) 1.3 × 10-17 1.3 × 10-17 1.3 × 10-17 1.3 × 10-17

Av 10 10 10 10

d/g 0.01 0.01 0.01 0.01

aRRK 0.01 0.01 0.01 0.01

125

Figure 6.1. Temperature settings of four gas-grain models applied for CHNO

isomers study.

Solid line – hot core model; dashed line – warm envelope model; dash-dotted line – lukewarm corino model; dotted line –cold core model.

6.3 Results

The calculated fractional abundances vs. time of the CHNO isomers for the hot core model, the warm envelope model, the lukewarm model, and the cold core model are shown in Figures 6.2, 6.3, 6.4, and 6.5, respectively. The results will be discussed in the following subsections in the same order.

126

6.3.1 Hot cores

In Figure 6.2, calculated hot core results are compared with observational abundances for HNCO and HOCN of ≈ 1.3 × 10-9 and ≈ 2 × 10-11, respectively, towards Sgr B2 (M) (Brünken et al. 2009a). From the figure, it can be seen that during the cold stage of the hot core model, when the temperature remains at 10

K, the calculated gaseous HOCN abundance lies well below its observed values, while that of gaseous HNCO is within one order of magnitude of observation for only a very short time around 3 × 103 yr. After the warm-up stage begins at 105 yr, a sharp decrease in the solid phase abundances due to sublimation (right panel of Figure 6.2) results in a sharp increase in the gas-phase abundances of all isomers (left panel of Figure 6.2), which peak near the end of the warm-up period, where the temperature is 200 K. At the peak time, the calculated abundance of the dominant isomer HNCO is about 20 times greater than the observed abundance, while that of HOCN is about 100 times bigger than observation. In the final stage of the chemistry, during which the temperature remains at 200 K, the calculated gas-phase abundances of all the four isomers decrease because of the gas-phase chemistry. Overall, the best agreement with observed abundances, using an order-of-magnitude as the criterion, for the two detected isomers, occurs during the final stage of cold phase between 6 - 8 × 104 yr and during the 200 K stage between 6 - 11 × 105 yr. The former occurs at 10 K and

127

the latter has the temperature of 200 K. Since the rotational excitation temperature of the detected isomers is 100 K in this case and Sgr B2 (M) is a hot core, the latter time interval is the more reasonable one, although it occurs at somewhat longer times than previously estimated chemical lifetimes for hot cores of 104-5 yr (Charnley et al. 1992). During this interval, the predicted abundances of HCNO and HONC remain much lower than the abundances of the two lower energy isomers. The observed HNCO abundance in another hot core, Sgr B2 (N), is possibly as high as 10-8 (Brünken et al. 2009a; Liu & Snyder 1999). With the observed abundance of HOCN (Brünken et al. 2009a), the ranges of best agreement for Sgr B2 (N) are similar to those for Sgr B2 (M).

128

Figure 6.2. Fractional abundance of CHNO isomers with respect to H2 plotted as

a function of time for hot cores.

Left panel is abundances in the gas phase and right panel is those on the dust particles. Calculated results are from hot core model and compared to observational results towards Sgr B2 (M) (Brünken et al. 2009a). Column density for molecular hydrogen is estimated as ≈ 3 × 1025 cm-2 (Liu & Snyder 1999).

6.3.2 Hot core environments

Because HNCO and HOCN were also detected in the surroundings of hot cores, the cooler envelopes are simulated with a warm-up model with a peak

129

temperature of 50 K. According to Brünken et al. (2009a), the rotational excitation temperature of the detected isomers around Sgr B2 (M) and (N) is 12-14 K. The calculated results from the warm envelope model are also used to compare to the Sgr B2 (OH) observation. Sgr B2 (OH) is not obviously along the line of sight to a hot core, but consists of matter where the rotational temperature of HOCN is

20 K (Brünken et al. 2009b). Figure 6.3 shows the comparison between the warm envelope model calculations and observations towards Sgr B2 (OH). The observed fractional abundances of HNCO and HONCN are based on the work of

Churchwell et al. (1986), Turner (1991), and Brünken et al. (2009b). The gas- phase calculated results are somewhat similar to those obtained for the hot core model except that the peak values of the gas phase isomers are smaller and the decrease at times following the peak abundance less severe. Moreover, the depletion of surface species after the warm-up is much weaker than that in the hot core, presumably because sublimation remains incomplete at 50 K. Once again, agreement within one order-of-magnitude between model and observation for HNCO and HOCN occurs at two distinct times: one between 1.8-2.2 × 105 yr, during the warm-up stage, and the other between 6.3-11 × 105 yr, during the 50

K stage. In between these two intervals, the predicted HOCN abundance is significantly too large. For this comparison, the temperatures of best agreement during the warm-up stage make more physical sense. Unlike HNCO and HOCN, the HCNO calculated abundance is not very sensitive to time and hovers between 10-12 and 10-11. This is inconsistent with the upper limit of HCNO/HOCN 130

ratio (<10-4) set by observers (Marcelino et al. 2009b). The last isomer studied,

HONC, has a lower predicted abundance than HCNO.

Figure 6.3. Same as Figure 6.2 except that the warm envelope model is used

and compared to Sgr B2 (OH) observation.

The observed HNCO and HOCN fractional abundances are cited from

Churchwell et al. (1986) and Brünken et al. (2009b).

6.3.3 Lukewarm corino

Figure 6.4 shows modeling results for the lukewarm model along with observed abundances for HNCO and HCNO in the lukewarm corino L1527.

131

Unlike the other two warm-up models, the temperature increase does not introduce any significant increase in the gas phase fractional abundances of any isomers, nor does the subsequent hot stage cause an apparent decrease of any isomers except for surface HONC. After a short time of 100 yr, both calculated

HNCO and HCNO fractional abundances in the gas phase remain in very good

(factor of three to order-of-magnitude) agreement with observed abundances except for a brief dip at around 105 yr. The calculated gaseous HOCN abundance is very low until 1 × 104 yr, after which it starts increasing, reaching a detectable value of 7 × 10-11, and remaining abundant afterwards except for a brief dip. The HONC isomer has abundance always below 10-12. As L1527 is a lukewarm corino, calculated results only have physical meanings after T increases to above 30K.

132

Figure 6.4. Fractional abundance of CHNO isomers with respect to H2 plotted as

a function of time for lukewarm corino.

Left panel is the abundances in the gas phase and right panel is those on the dust particles. Calculated results are from the lukewarm model and compared to observational results towards L1527.

6.3.4 Cold cores

Calculated gas-phase and surface abundances for the four isomers are shown for the cold core model in Figure 6.5. This model clearly pertains to the cold cores studied by Marcelino et al. (2009a) but also can pertain to those offset

133

positions in Sgr B2 studied by Brünken et al. (2009a), where the rotational excitation temperatures of HNCO and HOCN are under 10 K. The observed

HNCO abundance in the figure comes from TMC-1. Before 1 × 105 yr, the evolution of each isomer is similar to the three warm-up models. However, after this time, the results of the cold core model are quite distinct since there is no warm-up and much of the material remains on the ice. For HNCO, the gas phase abundance maximizes around 2 × 105 yr at a fractional abundance of 6.7 × 10-10, in excellent agreement with observation. For HCNO, the other isomer detected towards other cold cores but not towards TMC-1, the calculated HCNO/HNCO ratio ranges over the interval 1/10 – 1/200 once a physically significant amount of time has passed. At 1 × 105 yr, which is a typical time for best agreement in cold cores, the HCNO abundance lies about two orders of magnitude lower than

HNCO does, implying a reasonable fit to observed values or, for the case of

TMC-1, an upper limit. As for HOCN, its calculated gas phase abundance is slightly below that of HCNO at a time of 1 × 105 yr and rises significantly above

HCNO after 1 × 106 yr, reaching a fractional abundance with respect to HNCO of more than 1/10 at late times. The tentative observed value of 0.01 for

HOCN/HNCO mentioned by Brünken et al. (2009b) is consistent with the cold core model at times between 5 × 104 and 3 × 105 yr, although the non-detection of HCNO would then be surprising. In addition, HOCN has been detected towards the cold dense cores with a ratio to HCNO around 1 (Marcelino et al.

2009b). When a factor of 3 is used for a reasonably good agreement, this ratio is 134

reproduced within the time range between 2 × 103 – 107 yr. Depending on the age of the source, the isomer HONC might also be detectable.

Figure 6.5. Fractional abundance of CHNO isomers with respect to H2 plotted as

a function of time for cold cores.

Left panel is the abundances in the gas phase and right panel is those on the dust particles. Calculated results are from the cold core model. The horizontal line represents the observed HNCO fractional abundance towards TMC-1.

135

6.4 CHNS isomers

The CHNS isomers constitute a not entirely similar system to that of the

CHNO isomers. HNCS is also a well known interstellar molecule, having been detected by Freking et al. (1979) in Sgr B2 with a fractional abundance against

-11 H2 of 5.8 × 10 . In addition, Irvine et al. (1989) tried searching for HNCS towards cold cores and set upper limits for TMC-1 and L134N. Very recently, a metastable isomer, HSCN was detected towards Sgr B2 (N) with the Arizona

Radio Observatory 12 m telescope (Halfen et al. 2009). The observers also confirmed the detection of HNCS towards this source. The fractional abundances

-12 of HSCN and HNCS relative to H2 were determined to be 4.5 × 10 , and 1.1 ×

10-11. Very unlike to the CHNO isomers case, the CHNS isomers show small differences of the abundances regardless of their stabilities.

Two models analogous to the CHNO study were used for the CHNS isomers: the warm envelope model, which simulates the regions where the isomers were observed around Sgr B2(N), and the cold core model, which simulates regions where only upper limits for HNCS were found. The settings used are the same as those listed in Tables 6.3 and 2.2. As for the added species and reactions, HNCS, HSCN, HCNS, HSNC and related species and reactions analogous to those listed in Tables 6.1 and 6.2 are included.

136

Unsurprisingly, modeling results of CHNS isomers show similar patterns to the CHNO isomers. Figures 6.6 and 6.7 show comparison between calculations and observations/upper limits for Sgr B2 and TMC-1, respectively.

Figure 6.6. Fractional abundance of CHNS isomers with respect to H2 plotted as

a function of time for Sgr B2.

137

Figure 6.7. Fractional abundance of CHNS isomers with respect to H2 plotted as

a function of time for TMC-1.

In the warm envelope modeling results, the HNCS and HSCN abundances show reasonable peaks due to the temperature increase. After the warm-up period, as the temperature stays at 50 K, the CHNS isomers are eventually destroyed and their abundances decrease to a low level. The HNCS abundance peaks at 3 × 105 yr with a value of 1.6 × 10-11, within one order of magnitude of both observed values (Freking et al. 1979; Halfen et al. 2009). At the same time, the HSCN abundance has a peak value of 9.9 × 10-13, also well within one order of magnitude of observation (Halfen et al. 2009). As for the cold core results,

HNCS abundance is always below the upper limit set by Irvine et al. (1989).

138

Calculated fractional abundances confirmed that HNCS can be seen towards hot cores and suggested that it might be found in cold cores. HSCN only has a reasonable abundance towards hot cores while its abundance in cold cores may be too low to be seen. As for the other two isomers included, HCSN and HSNC, their abundances are always low in either warm envelope or cold core models.

Besides the similarities, the CHNS modeling results have some differences from the CHNO modeling results. In general, CHNS isomers have much lower abundances than CHNO isomers, probably because as shown in Table 2.2, sulfur elemental abundance is much smaller than oxygen abundance. The difference between sulfur chemistry and oxygen chemistry may also play a role.

An attempt of to use high metal abundances where the sulfur elemental abundance is increased by a factor of 180, resulted in calculated HNCS and

HSCN peaks in the warm envelope that are only increased by factors of 11 and

13, respectively.

6.5 Discussion

In this study, four OSU gas-grain models were applied to model the abundances of four of the CHNO isomers – HNCO (isocyanic acid), HOCN

(cyanic acid), HCNO (fulminic acid), and HONC (isofulminic acid). The four models are for four different environments: a cold core, in which a constant temperature of 10 K is assumed, and three types of sources in which a gradual

139

quiescent warm-up occurs due to the formation of the star. In the hot core model, the warm up occurs to a temperature of 200 K while in the warm envelope model, which is supposed to simulate the surroundings of a hot core, the warm up produces an asymptotic temperature of 50 K. In addition to these two models, a warm-up model in which temperature increases to 30 K is applied for a lukewarm corino such as L1527 (Sakai et al. 2008).

The four CHNO isomers are produced by a combination of surface chemistry and gas-phase chemistry. For example, in the hot core model, HNCO is initially formed mainly by surface recombination of JH and JNCO followed by non-thermal desorption into the gas, but at 6 × 103 yr, dissociative recombination

+ of H2NCO takes over, while during the warm-up stage, evaporation of JHNCO dominates. For the cold core model, gas-phase reactions play a more prominent role, and one gas-phase reaction (reaction 6.4) is particularly important for the formation of HCNO (Marcelino et al. 2009a).

In all environments observed to date, the most stable isomer (HNCO) is the most abundant, with the other observed isomers (HOCN and HCNO) lower in abundance by a factor of ≈ 100. The most important reason for this dichotomy seems to be the more rapid gas-phase destruction routes for the higher energy isomers, which include reactions with C and/or O atoms involving either zero or very small activation energy. This case is different from the analogous case of

HCN and its higher energy isomer HNC (Herbst et al. 2000), where the higher

140

energy form is of equal or greater abundance in cold sources, but is similar to the case of HC3N and the its higher energy isomers (Osamura et al. 1999). Moreover, it should be noted that the isomers HCNO and HOCN have not been detected in the same source; HCNO is seen in a variety of cold and lukewarm cores

(Marcelino et al. 2009a) but not in TMC-1 or giant clouds, while HOCN is detected in an assortment of sources in Sgr B2 and in several cold dense cores, as well as in L1527 (Brünken et al. 2009b; Marcelino et al. 2009b). This is consistent with the calculated abundances for these two isomers in assorted sources are not that divergent.

In general, the models applied are able to reproduce adequately both the abundance of the dominant isomer HNCO and the minor isomers, HCNO or

HOCN, depending on which is detected in a given source. For the warm-up models of a hot core and its cooler envelope, there are often two periods of best agreement, one during the warm-up period and one during the constant high- temperature phase. For the lukewarm corino case, reasonable agreement occurs over a long period of time including the warm up. For the cold core, the agreement is reasonable during the early-time period usually associated with best overall agreement for gas-phase species, so-called “early time”. The highest energy isomer of the four studied, HONC, has not yet been detected in the interstellar medium but according to the calculations in this study, it should be detectable, although weakly.

141

Finally, the CHNS isomers present another interesting case of how physical environments lead to different abundances of the isomers. With the application of two models analogous to those used for the CHNO isomers, the

HNCS and HSCN calculated abundances are in good agreement with observations towards both hot and cold cores. As in the prediction, HNCS, the most stable isomer, can be seen towards both of the cores while HSCN can be only found towards hot cores and the other isomers – HCNS and HSNC - always have low abundances and should not be detected.

6.6 References

Bergin, E.A., & Snell, R.L. 2002, ApJ, 581, L105

Brown, R. 1981, ApJ, 248, L119

Brünken, S., Belloche, A., Martín, S., Verheyen, L., & Menten, K.M. 2009a, submitted to A&A

Brünken, S., Gottlieb, C.A., McCarthy, M.C., & Thaddeus, P. 2009b, submitted to

ApJ

Brünken, S., Yu, Z., Gottlieb, C.A., McCarthy, M.C., & Thaddeus, P. 2009c, submitted to ApJ

Charnley, S. B., Tielens, A. G. G. M., & Millar, T. J. 1992, ApJ, 399, L71

Churchwell, E., Woon, D., Myers, P.C., & Myers, R.V. 1986, ApJ, 305, 405 142

Feng, W., & Hershberger, J. F. 2007, J. Phys. Chem., A111, 10654

Freking, M.A., Linke, R.A., and Thaddeus, P. 1979, ApJ 234, L143

Garrod, R., & Herbst, E. 2006, A&A 457, 927

Garrod, R., Wakelam, V., & Herbst, E. 2007, A&A 467, 1103

Glarborg, P., Alzueta M.U., Dam-Johansen K., & Miller J.A. 1998, Combustion and Flame, 115, 1

Halfen, D.T., Ziurys, L.M., Brünken, S., Gottlieb, C.A., McCarthy, M.C., and

Thaddeus, P. 2009, ApJ, 702, L124

Hasegawa, T. I., & Herbst, E. 1993, MNRAS, 263, 589

Hasegawa, T.I., Herbst, E., & Leung, C.M. 1992, ApJS, 83, 167

Hassel, G. E., Herbst, E., & Garrod, R. T. 2008, ApJ, 681, 1385

Herbst, E., & Millar, T. J. 2008, In Low Temperatures and Cold Molecules, ed. I.

W. M. Smith (London: Imperial College Press), 1

Herbst, E., Terzieva, R., & Talbi, D. 2000, MNRAS, 311, 869

Iglesias, E. 1977, ApJ 218, 697

Irvine, W.M., Friberg, P., Kaifu, N., Kawaguchi, K., Kitamura, Y., Matthews, H.E.,

Minh, Y., Saito, S., Ukita, N., and Yamamoto, S. 1989, ApJ, 342, 871

Jansen, D.J., Spaans, M., Hogerheijde, M.R., & van Dishoeck, E.F. 1995, A&A,

303, 541 143

Liu, S.Y., & Snyder, L. E. 1999, ApJ, 523, 683

Marcelino, N., Cernicharo, J., Tercero, B., & Roueff, E. 2009a, ApJ, 690, L27

Marcelino, N., Brünken, S., Cernicharo, J., Quan, D., Roueff, E., Herbst, E., &

Thaddeus, P., 2009b, submitted to ApJ

Martín, S., Requena-Torres, M.A., Martín-Pintado, J., & Mauersberger, R. 2008,

ApJ, 678, 245

Menten, K. M. 2004, in The Dense Interstellar Medium in Galaxies, ed. S.

Pfalzner, C.

Kramer, C. Staubmeir, and A. Heithausen (New York: Springer Verlag), 69

Miller, J. A., Durant, J. L., & Glarborg, P. 1998, Combustion and Flame, 135, 357

Miller, J. A., Klippenstein, S. J., & Glarborg, P. 2003, Proceedings of the

Combustion Institute, 27, 234

Osamura, Y., Fukuzawa, K., Terzieva, R., & Herbst, E. 1999, ApJ, 519, 697

Ruffle, D. P., & Herbst, E. 2001, MNRAS, 322, 770

Sakai, N., Sakai, T., Hirota, T., & Yamamoto, S. 2008, ApJ, 672, 371

Schuurman, M. S., Muir, S. R., Allen, W. D., & Schaefer, III H. F. 2004, JCP, 120,

11586

Snyder, L.E., & Buhl, D. 1972, ApJ, 177, 619

Turner, B.E. 1991, ApJS, 76, 617 144

Turner, B.E., Terzieva, R., & Herbst, E. 1999, ApJ, 518, 699

Viti, S., Collings, M. P., Dever, J. W., McCoustra, M. R. S., & Williams, D. A.

2004, MNRAS, 354, 1141

145

Chapter 7: Sensitivity Method

Astrochemical models usually include a large number of reactions, many of which have rate coefficients with uncertainties. This leads to uncertainties in calculated abundances. In this study, a sensitivity method is developed to

+ quantify the effects of rate changes. Two case studies in which H3 + O and C +

Cn rate coefficients are varied will be used to demonstrate the method.

7.1 Introduction

In complex astrochemical models, thousands of reactions are included.

However, many of the reactions are only poorly understood. In particular, rate coefficients are roughly estimated and in many cases, products or branching ratios are undetermined. All these introduce uncertainties to modeling results. On the other hand, not all reactions have equal importance. Even the same changes of rate coefficients in different reactions can lead to very different results.

Normally, these effects are considered by allowing a factor of 10 or, in some cases, a factor of 3, between the calculations and observations. Efforts have been made to quantify these uncertainties. Applying similar methods to different models, Vasyunin et al. (2004, 2008) and Wakelam et al. (2005, 2006) studied

146

the error propagation induced by rate uncertainties in predicted molecular abundances for various environments including dense clouds, diffuse gas, hot cores, and protoplanetary disks. As the result, uncertainties of calculated abundances of the species were quantized. The overlaps between calculated and observational uncertainties were used as the criteria of agreement. In addition, to identify the most important reactions in the reaction networks is very helpful since the modeling results are very sensitive to the reaction rate changes.

These reactions are more worth studying theoretically or experimentally than other reactions. This information is very helpful to astrochemistry study because measuring or estimating reaction rates, especially under the strict conditions of interstellar medium, can take years. With the guideline of “importance” of reactions, the more important ones should be studied with higher priorities. A good example of the necessity for a sensitivity study is the effect of the O + OH

→ O2 + H reaction rate change, which is discussed in Chapter 5 and also in

Quan et al. (2008). A change of several orders of magnitude of the rate coefficient does not affect the O2 abundance significantly because the reaction can be also the dominant destruction route of the reactant OH. When the rate is increased, the OH abundance will decrease accordingly and limit the increase of

O2. On the other hand, a rate change of the reaction C + C3 → C4 can easily affect many species, including one of the most abundant carbon/oxygen containing species, CO (Wakelam et al. 2009).

147

This study is mainly focused on modeling dark cold clouds.

7.2 Chemical models

In the sensitivity study, the models utilized are the Ohio State gas-phase

4 -3 network. The normal settings of T = 10K, nH = 2 × 10 cm , Av = 10 are used.

For the two case studies which will be introduced in the next two sections, two

+ networks at different stage of development were used. For the H3 + O study, osu.2007.01 was applied. The model includes 452 species and 4431 reactions.

For the C + Cn study, an earlier version, osu.2003 was utilized since the purpose is to show how the sensitivity study can actually predict the effect of including, modifying, or removing some of the reactions. The model has 421 species and

4233 reactions. Details of both networks can be found at http://www.physics.ohio-state.edu/~eric/research.html. Different sets of elemental

+ abundances were applied for the two cases, too. In the H3 + O study, both carbon rich and oxygen rich abundances are applied; and in C + Cn study, oxygen rich abundances is used.

148

+ 7.3 H3 + O case study

In January, 2008, Ian Smith suggested an increase of about a factor of 3 for the rate coefficient of the following cation-neutral reaction (Ian Smith, private communication):

+ + H3 + O → OH + H2. (7.1)

The original value used in osu.2007 is 8 × 10-10 cm3 s-1 and the suggested new value is 2.5 ×10-9 cm3 s-1. To evaluate the effect of this rate change causes, the most apparent idea is to count the number of species having their abundances changed by more than a factor of 3. This is similar to results shown in Figure 5.5 in Chapter 5 except that in that case, the number was divided by the total number of species and the percentage change was plotted.

+ Figure 7.1. Number of “significantly” changed species versus time in H3 + O

case.

Left panel – carbon rich; right panel – oxygen rich.

149

From the results shown in Figure 7.1, it can be seen that from the left panel for the carbon rich calculation, at most 8 species are affected by a factor of

3 at the same time. Considering the fact that there are a total of 452 species in

+ the model, one would conclude that the rate change of H3 + O does not have a significant effect. Under this condition, the species most strongly affected is H2O2.

Among the 64 times studied, the affected species only have 2 or 4 times where the abundances vary about a factor of 3. For the oxygen rich calculation shown in the right panel of Figure 7.1, the effect of the rate change is larger. At the sharp peak, which is around 2 × 106 years, there are up to 100 species changed by more than a factor of 3. Other times show such changes for fewer than 40 species. Apart from the most strongly affected species H2O2, other significantly

+ + + changed species are HNS , PH2 , C2HO , most of which are species with very low abundances.

From the discussion above, a few points can be seen for the apparent method: first of all, it is not necessarily true that the most strongly affected species are among the direct reactants or products of the reaction having the rate change. The reason is that not all 452 species are equally abundant in the modeling results. One “small” percentage change of a major species may cause significant change of a minor species. For example, H2O2 is not in reaction (7.1) but still most strongly affected when the reaction rate coefficient is changed.

Secondly, as the model is evolving with time, the number of significantly changed

150

species is also a function of time. In other words, at so-called “early time”, which is around 105 years and when the pseudo-time-dependent model fits the observations best, the effect of the rate change can be very different from that at steady state.

The simple counting method can reveal effects of the reaction rate change qualitatively. However, there is still an important question to be answered. There is no apparent reason to choose a factor of 3 as the criterion of more than which for a species to be “significantly” affected. The question is how to quantify the dependence of the abundance changes on the actual change of rate. As Figure

+ 7.1 has shown that under carbon rich conditions, the effect of the H3 + O rate change is insignificant, only the oxygen rich case will be discussed thereafter.

The first step of developing the method is to simply sum up the changes of all species. This quantity must be divided by the rate change to exclude the factor of rate coefficient change. Therefore, the parameter S is defined as follows:

Sj = Σi (∆Xi / ∆kj). (7.2)

Here, j stands for the reaction j and i stands for a species. while X is its abundance and k is the rate coefficient. ∆ represents the new value (where k =

2.5 ×10-9 cm3 s-1) minus the original value (where k = 8 × 10-10 cm3 s-1). S is then the sum of abundance changes of all calculated species divided by the change of reaction rate. This simple criterion raises a new problem since as discussed earlier in this section, not all species are equally abundant. When the S value is 151

calculated, changes from minor species will be overwhelmed by those from major ones. A better parameter, which is labeled SR, is then introduced to avoid this effect:

SRj = Σi (∆Xi/Xoi / ∆kj). (7.3)

With this formulation, fractional changes of the abundance are used instead of absolute changes. Here Xoi stands for the calculated abundance of species i where the original k value is used. Figure 7.2 shows both S and SR values as

+ functions of time for the H3 + O rate change.

Figure 7.2. S and SR values as functions of time.

Upper panel – S; lower panel – SR.

152

From the figure, it can be seen that a relatively high value appears around

2 × 106 years in both S and SR. This corresponds to the sharp peak in the simple counting method shown in the right panel of Figure 7.1. As S actually shows only the changes of the most abundant species, much information has been lost. On the other hand, SR shows a clear time history of the rate change effect. However, a new problem now occurs. All SR values are boosted by dividing the small value of ∆k and this causes SR to have no apparent physical meaning. A further improvement of the parameter can be made as the following:

SFRj = Σi ((∆Xi/Xoi) / (∆kj/koi)). (7.4)

If the abundance of each species is changed at the same factor of a reaction rate coefficient rate change, SFR will equal the number of species as each term will be 1. In other words, if a reaction rate change affects the modeling results significantly, its SFR value should be much more than the number of species. On the other hand, if the SFR value is fairly below the number of species, it must be insignificant.

To validate this method, two other reactions are considered. One is C+ +

+ H2, which is believed to be important since C is the major form of carbon in early stages (as shown in Table 2.2, all carbon element starts from the form of C+) and one of the major destructive cations for many neutral species, and H2 is always

+ abundant. The other one is H3 + SiN, which should be unimportant since SiN 153

always has a low abundance. In addition, non-linear effect may be expected because in the complex chemical network, abrupt change of a rate coefficient may cause it to lose the role as a major formation/destruction route. Apart from the change of a factor of 3.125, changes with factors of 2 and 1.1 are also considered. Settings of different rates are shown in Table 7.1.

Reaction Original rate

(cm s-1)

+ + -10 H3 + O → OH + H2 8.00 × 10

+ + -16 C + H2 → CH2 7.90 × 10

+ + -8 H3 + SiN → HNSi + H2 6.90 × 10

Table 7.1 Studied reactions with their rate coefficients. Coefficients also

multiplied by factors of 3.125, 2, 1.1 for comparison.

Figure 7.3 shows the results of the SFR calculation for the different rate changes for the three reactions, one at a time. The expected unimportant

+ reaction H3 + SiN always shows a small value. It at most reaches unity at late time, indicating that its SFR value is much smaller than the total number of

+ species. The expected important reaction C + H2 shows a very large SFR value at early time. When the time reaches around 5 × 104 years, it decreases to a level comparable with the number of species and mainly stays at this magnitude.

This agrees to the calculated results that the C+ abundance drops after the very

154

+ early stage. The reaction H3 + O has an SFR value in between the other two reactions till 5 × 104. It is mainly between 10 to a few hundred, indicating that this reaction has a moderate importance, especially at late time, where a peak of 287 is reached. Another notable result is the effect of different multiplication factors

+ on the SFR value. The SFR for the C + H2 reaction shows a strong dependence on the rate change factor because the rate itself is actually very small and may be around the edge of changing its role. The other two reactions show reasonable steadiness indicating that their roles are not changed within the range studied.

+ Figure 7.3. SFR values as functions of time in H3 + O study.

155

7.4 C + Cn case study

In this section, the newly developed sensitivity method is applied to evaluate the effect of several C + Cn reaction rate coefficient changes. Smith et al.

(2006) evaluated some of these reactions. They were added to the OSU chemical reaction network, or modified according to new estimations (see Table

3.1 in Chapter 3). In Wakelam et al. (2009), the authors focused on re-evaluating the products and rate coefficients of the following two reactions and derived similar rates to Smith et al (2006):

C + C3 → C4, (7.5)

C + C5 → C3 + C3. (7.6)

The SFR method as defined in equation 7.4 was applied to quantify the effect that these rate changes may cause. However, for some species of really low abundance, their concentrations may change up to several orders of magnitude when other species are not affected much. It is therefore advisable to use an improved parameter, which is labeled an enhanced version of SFR, so- called “SFRT”. In the SFRT method, a species must have abundance higher than a threshold of 1 × 10-10 to be counted into the sum. The time evolution of both these parameters is shown in Figure 7.4.

156

+ Figure 7.4. SFR values as functions of time in H3 + O study.

From the figure, it is clear that the rate change of reaction C + C3 (reaction

7.5) introduces a reasonably large SFR and SFRT values, indicating moderate effects on the whole network. The peak time for both values is around 1 × 105 years and they lie mainly above 400 from 5 × 104 – 5 × 105 years. Moreover, the modification of C + C5 (reaction 7.6) gives a strong additional effect. On the other hand, the other C + Cn reactions except do not show a significant effect on either plot, implying that these reactions are somewhat unimportant. It can also be concluded that for reaction 7.5, the effect is mainly on species more abundant than the threshold of 1 × 10-10 since the SFRT value is approximately equal to the SFR value. On the contrary, the SFRT value for reaction 7.6 is much smaller 157

than its SFR, suggesting that the reaction change affects both abundant and scarce species. To show the actual effects of the C + Cn rate coefficient changes on individual species, a comparison figure of several interstellar species in the typical cold dark dense core, TMC-1, is drawn in Figure 7.5.

Figure 7.5. Fractional abundances of several important or observed species

concerning TMC-1 vs time.

Solid line – osu.2003 calculation; dashed line: only C + C3 is modified; dotted line:

C + C3 and C + C5 reactions are modified; dash dotted line: all C + Cn reactions are modified.

158

7.5 Conclusion

A sensitivity method to quantify the effects of changes in chemical reaction rate constants has been developed in this study. Starting from a simple counting procedure, the method eventually focuses on calculating the sum of the fractional concentration changes divided by the fractional rate constant changes. Shown in

+ a variety of examples, such as changes in the rate coefficients of H3 + O and C

+ Cn, this method clearly reveals the importance of the rate constant changes. In

+ the H3 + O study, the reaction rate constant change shows moderate effect to the species all over the network. Of the other reactions used, the expected

+ important one, C + H2, has a big SFR value which is much larger than the

+ number of species, while the expected unimportant one, H3 + SiN, always has a very small SFR value. In the C + Cn study, it can be concluded that the rate constant changes for both C + C3 and C + C5 have strong effects on the network while the other C + Cn reactions are unimportant. All of these examples validate the SFR parameter as a useful quantitative tool to evaluate the sensitivity of the system to changes in reaction rate coefficients.

7.6 References

Quan, D., Herbst, E., Millar, T. J., et al. 2008, ApJ, 681, 1318

Smith, I. W. M., Herbst, E., & Chang, Q. 2004, MNRAS, 350, 323

159

Smith, I.W. M., Sage, A. M., Donahue, N. M., Herbst, E., & Quan, D. 2006, in

Chemical Evolution of the Universe. Faraday Discussions No. 133, 137

Vasyunin, A. I., Sobolev, A. M., Wiebe, D. S., & Semenov, D. A. 2004, Astron.

Lett., 30, 566

Vasyunin, A. I., Sobolev, A. M., Wiebe, D. S., & Semenov, D. A. 2004, Astron.

Lett., 30, 566

Wakelam, V., Herbst, E., & Selsis, F. 2006, A&A, 451, 551

Wakelam, V., Loison, J.C., Herbst, E., Talbi, D., Quan, D.,& Caralp, F. 2009,

A&A, 495, 513

160

References

Adams, N.G., Smith, D., & Paulson, J.F. 1980, J. Chem. Phys., 72, 288

Adams, N.G., Babcock, L.M., Mostefaouoi, T.M. & Kerns, M.S. 2003, Int. J. Mass.

Spectrom., 223, 459

Allen, M., and Wiliams, D.A. 1993, Non. Not. R. Astron. Soc., 260, 37

Anicich V.G. 2003, Jet Propulsion Laboratory

Balucani, N., Asvany, O., Kaiser, R.-I., & Osamura, Y. 2002, J. Chem. Phys. A,

106, 4301

Bates D.R., & Herbst E. 1988, In TJ Millar & DA Williams (eds). 17-40, Kluwer

Academic Publishers, Dordrecht

Bergin, E.A., & Snell, R.L. 2002, ApJ, 581, L105

Bergin, E.A. et al. 2000, ApJ, 539, L129

Bettens, R. P. A., Lee, H.-H., and Herbst, E. 1995, ApJ., 443, 664

Brown, R. 1981, ApJ, 248, L119

161

Brünken, S., Belloche, A., Martín, S., Verheyen, L., & Menten, K.M. 2009a, submitted to A&A

Brünken, S., Gottlieb, C.A., McCarthy, M.C., & Thaddeus, P. 2009b, submitted to

ApJ

Brünken, S., Yu, Z., Gottlieb, C.A., McCarthy, M.C., & Thaddeus, P. 2009c, submitted to ApJ

Carty, D., Le Page, V., Sims, I.R., & Smith, I.W.M. 2001, Chem. Phys. Lett., 344,

310

Carty, D., Goddard, A., Köler, S.P.K., Sims, I.R., & Smith, I.W.M. 2006, J. Phys.

Chem. A, 110, 33101

CDMS, 2009, the Cologne database for molecular spectroscopy, http://www.astro.uni-koeln.de/cdms

Charnley, S. B., Tielens, A. G. G. M., & Millar, T. J. 1992, ApJ, 399, L71

Charnley, S.B., Rodgers, S.D., & Ehrenfreund, P. 2001, A&A, 378, 1024

Chesnavich, W.J., Su, T., & Bowers, M.T. 1980, J. Chem. Phys., 72, 2641

Chin, Y., Kaiser, R.-I., Lemme, C., & Henkel, C. 2006, in Astrochemistry, From

Laboratory Studies to Astronomical Observations, AIP Conf. Proc., 855, 149

Churchwell, E., Woon, D., Myers, P.C., & Myers, R.V. 1986, ApJ, 305, 405

Davidsson, J., & Stenholm, L.G. 1990, A&A, 230, 504

162

Douglas, A.E., and Herzberg, G. 1941, ApJ, 94, 381

Draine, B.T., and Lee, H.M. 1984, ApJ, 285, 89

Feng, W., & Hershberger, J. F. 2007, J. Phys. Chem., A111, 10654

Freking, M.A., Linke, R.A., and Thaddeus, P. 1979, ApJ 234, L143

Garrod, R., & Herbst, E. 2006, A&A 457, 927

Garrod, R.T., Wakelam, V., and Herbst, E. 2007, A&A, 467, 1103

Glarborg, P., Alzueta M.U., Dam-Johansen K., & Miller J.A. 1998, Combustion and Flame, 115, 1

Goldsmith, P.F. et al. 2000, ApJ, 539, L123

Graedel, T.E., Langer, W.D., & Frerking, M.A. 1982, APJS, 48, 321

Graff, M.M., & Wagner, A.F. 1990, J. Chem. Phys., 92, 2423

Gredel, R., Lepp, S., Dalgarno, A., & Herbst, E. 1989, ApJ, 347, 289

Halfen, D.T., Ziurys, L.M., Brünken, S., Gottlieb, C.A., McCarthy, M.C., and

Thaddeus, P. 2009, ApJ, 702, L124

Harding, l.B., maergoiz, A.I., Troe, J., & Ushakov, V.G. 2000, J. Chem. Phys.,

113, 11019

Harju, J., Winnberg, A., & Wouterloot, J.G.A. 2000, A&A, 353, 1065

Hasegawa, T.I., Herbst, E., & Leung, C.M. 1992, ApJS, 83, 167

163

Hasegawa, T. I., & Herbst, E. 1993, MNRAS, 263, 589

Hassel, G.E., Herbst, E. & Garrod, R.T. 2008, ApJ

Herbst, E., and Leung, C.M. 1986, ApJ, 310, 378

Herbst, E., Terzieva, R., & Talbi, D. 2000, MNRAS, 311, 869

Herbst, E. 2005, J. Phys. Chem. 109, 4017

Herbst, E. 2006 Gas Phase Reactions. In GWF Drake (ed.) Handbook of Atomic,

Molecular, and Optical Physics, pp. 561-573, Springer Verlag, Leipzig

Herbst E., & Leung C.M. 2006, ApJ, 310, 378

Herbst, E., & Millar, T. J. 2008, In Low Temperatures and Cold Molecules, ed. I.

W. M. Smith (London: Imperial College Press), 1

Hollis, J.M., Jewell, P.R., Lovas, F.J., Remijan, A., & Møllendal, H. 2004, ApJ,

610, L21

Hollis, J.M., Remijan, A.J., Jewell, P.R., & Lovas, F.J. 2006a, ApJ, 642, 933

Hollis, J.M., Lovas, F.J., Remijan, A.J., et al. 2006b, ApJ, 643, L25

Iglesias, E. 1977, ApJ 218, 697

Irvine, W.M., Friberg, P., Kaifu, N., Kawaguchi, K., Kitamura, Y., Matthews, H.E.,

Minh, Y., Saito, S., Ukita, N., and Yamamoto, S. 1989, ApJ, 342, 871

Jansen, D.J., Spaans, M., Hogerheijde, M.R., & van Dishoeck, E.F. 1995, A&A,

303, 541 164

Larsson, B. et al. 2007, A&A, 466, 999

Laufer, A.H. & Fahr, A. 2004, Chem. Rev., 104, 2813

Léger, A., Jura, M., and Omont, A. 1985, A&A, 144, 147

Le Teuff, Y.H., Miller, T.J., & Markwick, A.J. 2000, A&AS, 146, 157

Le Teuff, Y. H., Millar, T. J., and Markwick, A. J. 1999, A&A, 146, 157

Lin, S.Y., & Guo, H. 2004, J. Phys. Chem. A, 108, 2141

Lin S.Y., Guo, H., Honvault, P., & Xie, D. 2006a, J. Phys. Chem. B, 110, 23641

Lin, S. Y., Xie, D., & Guo, H. 2006b, J. Chem. Phys., 125, 091103

Lin S.Y., Guo, H., Honvault, P., Xu, C., & Xie, D. 2008a, J. Phys. Chem., 128,

014303

Lin S.Y., Sun, Z., Guo, H., Zhang, D.H., Honvault, P., Xie, D., & Lee, S.Y. 2008b,

J. Phys. Chem. A, 112, 602

Lis, D., Blake, G.A., Herbst, E. (eds). 2006, Astrochemistry: Recent Successes and Current Challenges, Cambridge University Press, Cambridge

Liu, S.Y., & Snyder, L. E. 1999, ApJ, 523, 683

Lovas, F.J., Remijan, A.J., Hollis, J.M., Jewell, P.R., & Snyder, L.E. 2006a, ApJ,

637, L37

Lovas, F.J., Hollis, J.M., Remijan, A.J., & Jewell, P.R. 2006b, ApJ, 645, L137

Marcelino, N., Cernicharo, J., Tercero, B., & Roueff, E. 2009a, ApJ, 690, L27 165

Marcelino, N., Brünken, S., Cernicharo, J., Quan, D., Roueff, E., Herbst, E., &

Thaddeus, P., 2009b, submitted to ApJ

Martín, S., Requena-Torres, M.A., Martín-Pintado, J., & Mauersberger, R. 2008,

ApJ, 678, 245

Mathis, J.S., Rumpl, W., and Nordsieck, K.H. 1977, ApJ, 217, 425

McKellar, A. 1940, Publ. Astron. Soc. Pac., 52, 187

Menten, K. M. 2004, in The Dense Interstellar Medium in Galaxies, ed. S.

Pfalzner, C. Kramer, C. Staubmeir, and A. Heithausen (New York: Springer

Verlag), 69

Miller, J. A. 1986, J. Chem. Phys., 84, 6170

Miller, J. A., Durant, J. L., & Glarborg, P. 1998, Combustion and Flame, 135, 357

Miller, J. A., Klippenstein, S. J., & Glarborg, P. 2003, Proceedings of the

Combustion Institute, 27, 234

Öberg, K.I., Garrod, R.T., van Dishoeck, E.F., and Linnartz, H. 2009a ApJ, 693,

1209O

Öberg, K.I., van Dishoeck, E.F., and Linnartz, H. 2009b A&A, 496, 281O

Ohishi,M., Irvine,W. M., & Kaifu, N. 1992, in IAU Symp. 150, Astrochemistry of Cosmic Phenomena, ed. P. D. Singh ( Dordrecht: Kluwer), 171

Osamura, Y., Fukuzawa, K., Terzieva, R., & Herbst, E. 1999, ApJ, 519, 697

166

Pagani, L., Bacmann, A., Cabrit, S., & Vastel, C. 2007, A&A, 467, 179

Pagani, L., et al. 2003, A&A, 402, L77

Petrie S., & Herbst E. 1997, ApJ, 491, 210

Prodnuk, S.D., Gronert, S., Bierbaum, V.M., & DePuy, C.H. 1992, Org. Mass.

Spectrom., 27, 416

Quan, D., Herbst, E., Millar, T. J., et al. 2008, ApJ, 681, 1318

Remijan, A.J., Hollis, J.M., Snyder, L.E., Jewell, P.R., & Lovas, F.J. 2006, ApJ,

643, L37

Roberts, H., & Herbst, E. 2002, A&A, 395, 233

Robertson, R., & Smith, G. P. 2006, J. Phys. Chem. A, 110, 6673

Ruffle, D. P., & Herbst, E. 2001, MNRAS, 322, 770

Sakai, N., Sakai, T., Hirota, T., & Yamamoto, S. 2008, ApJ, 672, 371

Schuurman, M. S., Muir, S. R., Allen, W. D., & Schaefer, III H. F. 2004, JCP, 120,

11586

Schwahn, G., Schieder, R., Bester, M., & Winnewisser, G. 1986, J. Mol.

Spectrosc., 116, 263

Scott, G.B.I., Fairley, D.A., Freeman, C.G., Maclagan, R.G.A.R., & McEwan, M.J.

1995, IJMSIP, 149/150, 251

Smith, I. W. M., & Stewart, D. W. A. 1994, J. Chem. Soc. Faraday Trans., 90, 167

3221

Smith, I.W.M., Herbst, E., and Chang, Q. 2004, Mon. Not. R. Astron. Soc. 350,

323

Smith, I.W. M., Sage, A. M., Donahue, N. M., Herbst, E., & Quan, D. 2006, in

Chemical Evolution of the Universe. Faraday Discussions No. 133, 137

Snyder, L.E., & Buhl, D. 1972, ApJ, 177, 619

Snyder, L.E., Wilson, T.L., Henkel, C., Jewell, P.R., & Walmsley, C.M. 1984,

BAAS, 16, 959

Snyder, L.E., Hollis, J.M., Jewell, P.R., Lovas, F.J., & Remijan, A. 2006, ApJ, 647,

412

Spaans, M., & van Dishoeck, E. F. 2001, ApJ, 548, L217

Swings, P., and Rosenfeld, L. 1937, ApJ, 86, 187

Terzieva, R., and Herbst, E., 1998, ApJ., 501, 207

Tielens, A.G.G.M. 2005, The Physics and Chemistry of the Interstellar Medium,

Cambridge University Press, Cambridge

Turner, B.E. 1991, ApJS, 76, 617

Turner, B.E., Terzieva, R., & Herbst, E. 1999, ApJ, 518, 699

Vasyunin, A. I., Sobolev, A. M., Wiebe, D. S., & Semenov, D. A. 2004, Astron.

Lett., 30, 566 168

Vasyunin, A. I., Sobolev, A. M., Wiebe, D. S., & Semenov, D. A. 2004, Astron.

Lett., 30, 566

Viti, S., Roueff, E., Hartquist, T. W., Pineau des Foreˆts, G., & Williams, D. A.

2001, A&A, 370, 557

Viti, S., Collings, M. P., Dever, J. W., McCoustra, M. R. S., & Williams, D. A.

2004, MNRAS, 354, 1141

Wakelam, V., Herbst, E., & Selsis, F. 2006, A&A, 451, 551

Wakelam, V., Loison, J.C., Herbst, E., Talbi, D., Quan, D.,& Caralp, F. 2009,

A&A, 495, 513

Weinreb, S., Barrett, A.H., Meeks, M.L., and Henry, J.C. 1963, Nature, 200, 829

Westley, M.S., Baragiola, R.A., Johnson, R.E., and Baratta, G.A. 1995, Nature,

373, 405

Weston Jr R.E., & Schwarz HA. 1972 Chemical Kinetics. Prentice-Hall,

Englewood Cliffs

Willacy, K., Langer, W. D., & Allen, M. 2002, ApJ, 573, L119

Williams, D., Brown, W.A., Price, S.D., Rawlings, J.M.C., and Viti S.2007 Ast. &

Geophys. 48: 1.25

Woodall, J., Agundez, M., Markwick-Kemper, A.J., & Millar, T.J. 2007, A & A, 466,

1197 and http://www.udfa.net

169

Woon, D.E. 2009, http://www.astrochymist.org/

Xu, C., Jiang, B., Xie, D., Farantos, S. C., Lin, S. Y., & Guo, H. 2007a, J. Phys.

Chem. A, 111, 10353

Xu, C., Xie, D., Honvault, P., Lin, S. Y., & Guo, H. 2007b, J. Chem. Phys.,

127, 024304

Xu, C., Xie, D., Zhang, D. H., Lin, S. Y., & Guo, H. 2005, J. Chem. Phys., 122,

244305

Zainab, A., Takeshi, C., Yuka, K. et al. 2005, ApJ, 626, 262

170