Investigating the Formation Mechanism of Polycyclic Aromatic Hydrocarbons
and
Adapting Particle Swarm Optimization Techniques to Search Large Data Sets
A Thesis presented to
the Faculty of the Graduate School
at the University of Missouri
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
by
Daniel P. Caputo
Dr. Angela Speck, Thesis Supervisor
MAY 2010 To God for giving me the ability to understand and the
objects to observe
To my mother for developing that ability Acknowledgements
I would like to thank:
My adviser Angela Speck, without whom I would have never had a desire to con- tinue my studies. Without Angela’s teaching, motivation, pushing, and encouragement
I would never have accomplished any of this work, I likely would never have tried.
Kevin Volk, for oh so many things...for being able to reducing Michelle data faster than the telescope could take it, and guidance in reducing NIRI data, for giving me technical justification, answering innumerable questions (often more than once), and for being an all-around good Canadian.
Aigen Li, for starting me down this topic with the oh so misleading “It should only take a long weekend” statement.
Paul Miceli for reminding me to pursue excellence.
The members of my committee, for reading and editing and commenting and cri- tiquing and helping me finish my thesis.
NOAO and the Gemini telescope team who worked hard to make sure I would be able to get data.
Of the utmost aid was Samantha and my Mom who gave me encouragement all the while putting up with me being difficult, tired, preoccupied, always busy, and never having enough time. The help that their encouragement and love provided me cannot be underestimated and I fear not well known.
ii Contents
Acknowledgements ii
List of Tables v
List of Figures vi
Introduction 1
2 Stellar Evolution 5
2.1 The Hertzsprung-Russell Diagram ...... 5
2.2 The Birth of Stars ...... 8
2.3 The Red Giant Branch ...... 9
2.4 The Horizontal Branch ...... 11
2.5 The Asymptotic Giant Branch ...... 12
2.5.1 Mass-Loss ...... 14
2.6 Protoplanetary Nebula ...... 16
2.7 Planetary Nebula ...... 17
iii 3 Carbon Chemistry 19
3.1 Introduction ...... 19
3.2 Bonds ...... 19
3.2.1 Aromatics and Aliphatics ...... 25
3.3 Carbon Allotropes ...... 25
4 Polycyclic Aromatic Hydrocarbons 29
4.1 Introduction ...... 29
4.2 PAH’s Vibrational Energy ...... 34
4.3 Stochastic Heating ...... 37
4.4 The Role of Aliphatics ...... 42
4.5 Formation Mechanisms ...... 44
4.5.1 Bottom-up ...... 45
4.5.2 Top-down ...... 47
4.5.3 Distinguishing Between Mechanisms ...... 48
5 Observational Investigations of the Presence of PAHs Around Carbon
Stars 50
5.1 Introduction ...... 50
5.2 Methods and Instruments ...... 54
5.3 Observations ...... 57
5.4 Discussion ...... 58
iv 6 Particle Swarm Optimization 67
6.1 Introduction ...... 67
6.2 Standard PSO ...... 69
6.2.1 The Algorithm ...... 71
6.3 Modified PSO ...... 74
6.3.1 The Algorithm ...... 78
7 Conclusion 83
7.1 PAH...... 83
7.2 PSO ...... 84
References 85
v List of Tables
3.1 Bond Lengths and Energies ...... 25
5.1 Observations and Results ...... 59
vi List of Figures
2.1 A Hertzsprung-Russell Diagram ...... 6
2.2 Paths of Stellar Evolution ...... 7
2.3 Interior of an AGB Star ...... 13
4.1 Ovalene ...... 30
4.2 The First Detection of an UIBs...... 31
4.3 PAH Features ...... 32
4.4 Mono, Duo, Trio, Quartet C-H Bending Modes ...... 35
4.5 Estimated Absorption Cross Sections ...... 38
4.6 The Bottom-Up Mechanism–Acetylene to Benzine ...... 45
4.7 The Bottom-Up Mechanism–One Benzine, Two Benzine ...... 46
4.8 The Bottom-Up Mechanism–Benzine to Coronene ...... 47
5.1 Observed Spectra ...... 60
vii Introduction
The Unidentified Infrared Bands (UIBs) are a set of emission features, first seen by Gillett and his fellow workers in 1973, who’s carrier was not unidentified quickly, and even still there are some who think it is not clear. The most accepted carrier for the UIBs are a family of molecules called Polycyclic Aromatic Hydrocarbons (PAHs).
One of the unique aspect to the UIBs is how ubiquitous they seem to be, having been spotted in very wide array of astronomical environments, and are so abundant as to often dominate images of galaxies when viewed in the wavelengths the UIBs emit at.
With what seems to be so much material, particularly carbon, tied up in PAHs it becomes important to understand as much as we can about these molecules to aid in the understanding of the chemical evolution of the universe. This is exactly what has been happening in the astronomical community, much work has gone into understanding PAHs and what role they have, and continue to play in the evolving universe. Yet, with all of this work just how these molecules form in astronomical
1 conditions is not well understood. The work I have undertaken is to attempt to fill in some of the missing pieces in exactly how these molecules form.
PAHs are expected to form in the circumstellar shells around carbon-stars (C- stars) and are seen around the objects these stars evolve into (protoplanetay nebula and planetary nebula); however, direct observations of the UIBs from C-stars are rare. When the UIBs are detected around C-stars it is usually when the C-star is in a binary system with another star which is much hotter (i.e. the companion has a hard radiation field). This is often attributed to the fact that these stars lack the hard radiation field (ultraviolet) needed to excite PAHs, however it has been shown that large and/or ionized PAHs should not need ultraviolet radiation to be excited.
This leaves two possibilities, 1) the PAHs around C-stars are small and thus need the ultraviolet radiation that these stars lack, or 2) PAHs are not forming around these stars but do form around the planetary nebula which they evolve into.
We have obtained time on the Gemini North telescope, an 8 meter class telescope on Mauna Kea, to investigate if PAHs form around C-stars with a hot companion. The premise of the observations is that the PAH formation mechanism could be determined if, by using spatially resolved spectroscopy from the telescope, the location of PAH emission could be determined with respect to the C-star and its hot companion. One of the formation mechanism requires UV photons to eject the PAHs from the surfaces of grains, but is likely to produce large PAHs which do not need UV photons to be excited, whereas, the other purposed mechanism does not need UV photons for formation, but lead to smaller PAHs which need UV photons for excitation. Consequently the
2 distribution of the UIBs should be different which we hope to detect.
One of the difficulties associates with this research was finding data that was already in the public archives which would be applicable to my search for the UIBs and PAH formation. There is in fact, a great deal of infrared observational data that is publicly available, and could help in testing the PAH formation hypotheses; however, the amount of data is so vast that searching the public archives presents its own challenges. How to find UIB emission in such such large sets of data that was useful to my purpose? This leads directly into the second portion of this work.
A mounting challenge in astronomy today is the increasing amount of data. Soon there will be observational surveys that expect to obtain ≈30 TB of data per night, presenting an enormous archive which will need to be searched efficiently. The Large
Synoptic Survey Telescope (LSST) expects to produce ≈30 TB of data per night culminating in a 10 year database of some 60 TB just for the raw data!1 For many publicly available datasets (including Spitzer, ISO and HST), much of the data was collected for a specific science project with a well-defined scientific goal. However, much of that data will be useful for other, unrelated projects, and hence these archives of observations are mined. How is another observer to find the small set of data that
fits his study parameters within the vast dataset? Or consider why it is that with all of the processing power available today graduate students spend countless days, weeks, or even months pouring over a computer screen trying to screen out good models from bad models, or categorize simple data? Computers have amazing potential in this
1http://www.lsst.org/lsst/science/science-faqq18
3 area, but are only being put to limited use.
To this end I, along with Ryanne Dollan, have begun the development of a modi-
fied Particle Swarm Optimization algorithm which should be more efficient at sifting through extremely large sets of data or models. This algorithm is very general and as such can be used in many different applications. I offer an application to searching a model set to find useful data as well determine any degeneracies that may exist. It is my hope that this algorithm will make it easier for scientist to find useful data with less effort so more energy can be directed to the science at hand.
In chapters 1 through 4 I will discuss the UIBs and PAH formation. Chapter 2 will deal with stars and how they form to provide a basis of the environments PAHs may be forming in. Chapter 3 addresses carbon based chemistry, which will be vital to our understanding of how these molecules may form. Chapter 4 is dedicated to the physics of PAHs: such as how do they emit, what energy is needed to excite them, and explaining what the proposed mechanisms for formation are. Chapter 5 covers the new observations we have obtained trying to understand the PAH formation mechanism.
Chapter 6 covers much of my work on finding a better way to use computers to search through vast amounts of data. Specifically I compare and discuss the advancements of the new algorithm over the current algorithm and give specific ways this may be helpful in astronomy.
4 Chapter 2: Stellar Evolution
2.1 The Hertzsprung-Russell Diagram
The two most obvious stellar observables are the star’s brightness (luminosity) and its color. As stars are nearly blackbodies, their light output of a given wavelength is given by Planck’s function: 2hc2 λ5 Bλ = hc (2.1) e λkT − 1 where h is Planck’s constant, c is the speed of light in vacuum, λ is wavelength, k is
Boltzmann’s constant, and T is the temperature of the star where it becomes optically thick, i.e. where it becomes opaque. The color of a star is determined by the peak wavelength in the given star’s blackbody, or Planck, function. This peak wavelength 2898 can easily be found by using Wien’s law: λ = where λ is in µm and max T max T is in K. It is clear that the star’s color is determined by its temperature. Two
5 independent researcher, Hertzsprung and Russell, plotted a large random sample of stars in color-brightness space and found that the distribution is not random. Figure
2.1 shows that within a color-brightness plot (also known as a Hertzsprung-Russell, or H-R, diagram) stars are concentrated into certain parts of the plot. The main
Figure 2.1: An example of a Hertzsprung-Russell diagram. This is a plot of Luminosity versus
Temperature of stars in the local neighborhood. Note the symbol along the y-axis refers to the
Sun, i.e. L ≡ LSun. The “O B A F”... sequence on the x-axis is a classification system that is ultimately based on the temperature of the star. Credit:ESO diagonal region, extending from the top left to the bottom right, is called the main sequence, where stars spend the vast majority of their lives, about 90% in fact. Over their lifetimes stars’ surface properties (i.e. luminosity, L, and temperature, T) vary as different physical processes become dominant and hydrostatic equilibrium is lost and
6 regained. Consequently stars move through the space on the H-R diagram. The exact path a given star takes from the main sequence is highly dependent on the mass of the star while it is on the main sequence. Figure 2.2 shows the paths taken on the H-R diagram for several stars of various masses. Due to the nature of the research at hand the following description of stellar evolution will be limited to the general path taken by stars from about 2 M to about 4 M . Stars in this mass range will eventually end up with enough carbon in their atmospheres to allow large carbon molecules to form.
Figure 2.2: Example paths of stellar evolution for stars with various main sequence masses overlaid on an H-R diagram. From: Speck (2007)
7 2.2 The Birth of Stars
2
Atoms, molecules and dust grains collect in empty space to form a cloud of material.
As gravity acts on this cloud it begins to contract to a smaller, more dense cloud, the contraction converts gravitational potential energy into kinetic energy which begins to heat the cloud. The heat increases the internal pressure of the cloud, as the star begins life we find gravity has collapsed the pre-stellar material into a dense sphere of gas, when the center of the sphere has been compressed sufficiently to allow nuclear fusion to begin a star has been born. Nuclear fusion results in a change of the chemical composition of the core as well as emitting photons and particles which act to increase the temperature of the star. Heating increases gas pressure, exerting an outward acting force, and the photons exert a radiative pressure outward. These forces, once balanced, reach a steady state called hydrostatic equilibrium. Upon starting fusion in its core and reaching hydrostatic equilibrium the star joins the main sequence on the
Hertzsprung-Russel diagram.
A star will spend most of its life on the main sequence where it is burning through the hydrogen fuel in its core. Eventually the hydrogen atoms in the core of a star get completely processed into helium and there is no more fuel left to continue the nuclear process which has been occurring. Consequently the kinetic energy source has gone
2Carroll and Ostlie’s classic astronomy text “An Introduction to Modern Astrophysics” was used for reference throughout this chapter.
8 and the pressure in the gas drops as energy is radiated away. At this point the star loses hydrostatic equilibrium, as gravity begins to overcome pressure, and the star moves off the main sequence towards the red giant branch.
2.3 The Red Giant Branch
In the Red Giant Branch (RGB) phase of life, marked by points “E” in Figure 2.2, the star has exhausted the hydrogen supply in its core which has now been synthesized into helium. The temperature and density of the core are not great enough to ignite the helium core. This phase of life is characterized by the ignition of a hydrogen shell around the core, the exact mechanism for which depends on the mass of the star. Since the core is no longer burning there is a decrease in gas and radiation pressure causing the core to contract. The contracting core releases gravitational potential energy into the shell surrounding the core allowing it to begin burning its hydrogen. As the core continues to collapse it releases more energy into the hydrogen-burning shell leading to higher fusion rates allowing the shell to releasing more energy than the core had previously been. The high energy output by the hydrogen-burning shell injects energy into the non-burning envelope which causes this gas to expand, and thus, the star’s radius increases and effective temperature decreases, explaining the overall reddening of the star that occurs during this phase of its life.
As the star continues its evolution convection currents begin to form. Initially the convection is constrained to near the surface of the star. The convection is the result
9 of an increase in opacity in the stellar photosphere, which is due to the increase in
H− ions as the result of the reddening (or cooling) during the previous phase. The convection currents deepen over time and begin mixing the material that has been synthesized into the upper structure of the star, this is called the first dredge up.
The dredge up changes the concentrations of elements in the star’s photosphere and is detectable by observation.
As the star evolves along this branch the temperature and density in the core increase and eventually allow for quantum tunneling between He atoms. This begins an efficient triple α process, which is defined as follows:
4 4 8 2He +2 He ⇐⇒ 4Br (2.2) 8 4 12 4Br +2 He =⇒ 6C + γ . The star is now at the top of the Red Giant Branch, points “G” in Figure 2.2.
An interesting event is believed to occur in stars with mass lower than about 1.8
M at the tip of the Red Giant Branch. In these stars the triple-α process occurs like above as the result of the increasing of the temperature and density, however here the whole of the star’s core ignites almost simultaneously. This is the result of the star having an electron-degenerate core and the temperature sensitivity of the triple
α process. Because the core is degenerate, unlike ordinary matter, the nuclei of the gas is organized in a regular and periodic spacing like a crystal and the electrons form a sort of sea in which the nuclei are in suspension. Degenerate matter does not obey the ideal gas law and as such the pressure is not dependent on the temperature. The electron sea is what is providing the extra pressure, degeneracy pressure, preventing
10 the core from continued collapse and is a near perfect conductor of heat. So as one part of the core ignites the heat is almost instantaneously distributed throughout the core and so the entire helium core will ignite at nearly the same time. This is referred to as the helium core flash, and releases an immense amount of energy in a very short period of time. As the core heats, from the nuclear reactions, it will eventually break the degeneracy, expand and then cool, slowing the helium burning.
2.4 The Horizontal Branch
With an active triple-α process occurring the production of carbon (C) begins. After enough C is produced oxygen (O) is able to form via alpha particle capture. Alpha particle capture is the process by which a larger atom captures a He atom, which is called an alpha particle for historical reasons, as shown here:
12 4 16 6C +2 He =⇒ 8O + γ. (2.3)
The additional energy gained from the now burning He results in the expansion of the core, thus pushing the hydrogen-burning shell outward. The hydrogen-burning shell, which is still the primary energy source, cools due to being pushed outward thus decreasing the rate of hydrogen-to-helium synthesis, this decreases the number of photons emitted and so the luminosity drops leading to a contracting star and thus an increasing effective temperature. The star has now passed well beyond the top of the Red Giant Branch, and is moving to the left on the H-R diagram as seen in points
“J” in Figure 2.2.
11 2.5 The Asymptotic Giant Branch
This stage of evolution is the most relevant to the research discussed here is shown as points “K” in Figure 2.2. Most of the stars observed for this work are in this phase of life. On the H-R diagram the star is moving asymptotically toward a line extended up from the Red Giant Branch, hence the name. During this phase of its life a star will lose a large fraction of its mass, experience two more dredge up phases, and exhibit periodic variations in its luminosity with an overall increase in luminosity but a small decrease in effective temperature.
The stellar structure at this phase is one of a non-burning, degenerate carbon and oxygen core surrounded by a thin helium-burning shell, and outside of that is a hydrogen-burning shell, followed by the non-burning hydrogen envelope as seen in
Figure 2.3. Early in this phase the helium-burning shell is producing most of the energy. The star is expanding causing the effective temperature to decrease. The convection zone deepens into the helium-rich region which again changes the chemical composition of the star’s outer layers, in addition to dredging up helium, nitrogen is also dredged from this layer to the outer portion. This is referred to as second dredge up phase.
As the hydrogen shell begins burning strongly it becomes the primary energy pro- ducer within the star. The hydrogen shell burns hydrogen synthesizing helium, this so-called helium ash is incorporated into the helium shell below. The helium burning shell is thinning due to its own synthesis of material into other elements and eventually
12 Figure 2.3: A schematic of the interior of an AGB star. Note that this is not to scale, the core and two shells are in fact extremely small compared to the hydrogen envelope. Credit:NOAO extinguishes. But as more helium is added from the hydrogen shell the helium shell becomes, at its base, degenerate and as the temperature increases the degeneracy is overcome rather suddenly and just as in the case of the helium core flash and there is a helium shell flash. While this flash produces much less energy than the helium core
flash it is does drive the hydrogen shell outward, which as a result cools and causing the nuclear reaction rate in the shell to drop. The hydrogen shell will heat again as it contracts back toward its original depth and again increase its helium production leading to more helium ash being deposited in the layer below it and the cycle will be repeated.
With a decrease in the reaction rate in the hydrogen shell the luminosity of the star decreases, the star begins to contract with the decrease in radiation pressure and so the
13 effective temperature increases. Then as the hydrogen shell heats again the luminosity will return to normal levels. This drop and then recovery of luminosity produces an observable effect in luminosity, radial, and effective temperature pulsations over time.
On a shorter time scale, there are pulsations due to changes in the opacity of the star. As the star expands, the surface cools allowing for H+ to recombine with free electrons, decreasing the opacity at the surface, allowing more radiation to escape.
With more radiation escaping, the star cools thus the surface begins to contract. As the surface contracts the hydrogen again becomes ionized and the opacity goes back up. The increased opacity causes more radiation pressure pushing the surface outward, and the cycle begins again.
2.5.1 Mass-Loss
Another important aspect of the Asymptotic Giant Branch (AGB) phase is that they
−4 lose mass. Stars in this phase can loss as much as 10 M per year. This mass loss is believed to be driven by the helium flash pulsations and fluctuation in opacity as described above, as well as the resulting changes in stellar radii and mass. As the star pulsates its radius and luminosity change, as the hydrogen shell’s nuclear reaction rate decreases the stellar radius and luminosity decrease, this leads to less radiation pressure and a higher surface gravity; however, as the reaction rate increases so does the stellar radius and luminosity which increases radiation pressure at the same time that the surface gravity is dropping. Additionally, as the star expands outward there
14 is an additional radial component of velocity provided to the material at the surface, this acts to effectively decrease the temperature needed for a particle to achieve escape velocity. Moreover, as the star ages it is losing mass via the winds described here and the nucleosynthesis that is continuing in its interior, this also adds to the decrease in surface gravity and so as the star progresses through this phase the mass loss should in fact increase. And lastly, as the gas from the star leaves the surface, with what might be a typical temperature of 3000 K, the gas cools and forms dust grains. The effect of the gas forming into molecules and then dust grains is two-fold: (1) the dust grains have a much larger cross sectional area than molecules and so the radiation pressure on the grains is much larger than the gas so as the gas forms dust grains the grains are accelerated away from star, and (2) to decrease the partial pressure of the gas, causing something like a partial vacuum, which drives more mass loss. All of these factors lead to strong stellar winds and cause these stars to lose extremely large fractions, ≈65–75% of their initial mass.
The pulsations caused by the helium shell flashes result in a convection zone form- ing between the hydrogen and helium burning shells. Thus, material produced in the helium shell is mixed into the hydrogen shell closer to the surface. At the same time the already present outer convection zone deepens, and for stars greater than
≈ 2M the two zones will merge allowing for the processed material from the helium shell, notably carbon, to rise to the stellar surface. This is called the third dredge-up phase, which can occur multiple times due to the periodic nature of the helium shell
flashes. As more carbon is transported to the surface the ratio of carbon to oxygen
15 (C/O) begins to increase. The cosmic C/O ratio is believed to be ≈0.4, as this ratio increases at the stellar surface the chemistry also changes. When the C/O ratio is exactly 1 all of the available carbon and oxygen get tied up in carbon monoxide (CO) preventing any other carbon or oxygen based chemistry. If the C/O ratio is less than
1, all of the carbon gets tied up in CO and the remaining oxygen can be involved in chemistry. If the C/O ratio is greater than 1, all of the oxygen gets tied up in CO and the remaining carbon can do chemistry. AGB stars with C/O ratios greater than
1 are called carbon stars (C-stars) and it is this type of star that is important to the following work.
2.6 Protoplanetary Nebula
The post-AGB or protoplanetary nebula (PPN) phase, sometimes called the pre- planetary nebula, is a transition phase in the life of a star, it occurs after the AGB phase and brings the star to the beginning of the planetary nebula phase. During the AGB phase the helium-burning shell is still adding carbon and oxygen ash to the degenerate core, increasing the core’s mass. The star continues throwing off layers of material, eventually so much material is lost during its pulsations that the shell sur- rounding the star become optically thick, meaning that the shell is opaque to visible starlight.
The central star is too cool to ionize the expelled material, but outer layers are so sparse they begin to contract and the temperature increases. As temperature
16 increases, but luminosity remains the same, the object moves to the left on the H-R diagram. Temperatures in the PPN phase will reach up to ≈30,000 K before becoming a planetary nebula.
2.7 Planetary Nebula
The planetary nebula3 (PN) phase, like the PPN, does not actually refer to the star itself, but rather to the expanding shells of dust and gas around the star. Once the effective temperature of the central star, the star at the center of the nebula which has given off the its outer layers, reaches ≈30,000 K there is adequate ultraviolet radiation to ionize or exciting the expanding circumstellar shell. The ionization/excitation of the circumstellar material is the boundary between the PPN and PN phases.
The object continues moving to the left on the H-R diagram. So much of the stellar material has been thrown off and expanded so far away from the central star the opacity of the shell drops and what was once the core of the star becomes viable.
The effective temperature of the central star can reach temperatures on the order of
105 K.
Eventually the circumstellar material has drifted so far away and the star has cooled enough that the material is no longer being excited by the central object. The material continues to move away and joins the interstellar medium (ISM), to which
3The name planetary nebula is a misnomer, as these objects have nothing to do with planets, however when first seen by astronomers in the 18th century through small telescopes they looked much like the gas giant planets and so they have ever since carried the name.
17 PN are believed to contribute about 1 to 5 M per year in the Milky Way galaxy.
This material will mix with the ISM and eventually find its way into a cloud which will collapse to form a star and the circle of stellar life will begin all over again.
18 Chapter 3: Carbon Chemistry
3.1 Introduction
Because we are interested in C-stars and the carbon-dominated dust chemistry that surrounds them, it is important to understand how carbon behaves chemically. In this chapter I will examine how carbon bonds, the various structures carbon forms, and how the structure of a molecule plays an important role in its physical properties.
3.2 Bonds
There are different types of bonds which hold our chemical world together including ionic, covalent, and hydrogen bonds. Fundamentally bonding is a method for atoms and molecules to reach a more energetically favorable state. Ionic, and covalent bonds
19 will be briefly explored as well as hybrid orbitals and aromatic bonds4.
Ionic bonds are the result of one or more atom “donating” an electron(s) to another atom which must result in the reduction of the potential energy, else the bond would not be stable. The donating atom becomes positively charged, a cation, and the recipient of the electron becomes negatively charged, or an anion, and the resulting electrostatic force is what maintains the bond. The strength of the bond is determined by the so-called lattice energy which is the enthalpy of formation of the molecule, which must be exothermic for a stable bond. The strength is directly proportional to the product of the number of electrons donated and the number of the electrons received, that is the charge number of the anion and of the cation.
Covalent bonds are formed by the sharing of valence electrons to reduce the poten- tial energy of the system. This would be the result of two or more atoms not having a full valence electron shell, each sharing one or more electron so that each atom tends to have a complete valence shell. Consider the diatomic molecule C2, it would have the following structure C..¨=C..¨ 5 where each dot represents one unbonded electron and the lines represent two shared electrons. Counting the total number of electrons rep- resented in the figure there are a total of 12 electrons, four unbonded electrons on each atom and four bonded electrons, as expected since each carbon atom has six valence electrons available to react. However, when the electrons are counted with respect to each atom including all four bonded electrons both atoms seem to have eight elec-
4Kotz and Treichel’s introductory chemistry text was used as a reference throughout this chapter 5Typically the dots are inferred, thus C..¨=C..¨ ≡ C=C
20 trons and so the atoms are said to be sharing four electrons, which corresponds to a full valence shell. Whereas the strength of ionic bonds is proportional to the charge numbers of the cat- and anions, the strength of the of covalent bonds is dependent on, among other factors, the angle between the atoms which are bonded. Covalent bonds are, in general, much stronger than ionic bonds. Covalent bonds can fundamentally be broken down into sigma (σ) bonds, pi (π) bonds, and delta (δ) bonds.
σ bonds are the strongest type of covalent bonds. σ bonds are characterized by its symmetry with respect to the axis of the bond. Such symmetry can arise from for example, s − s orbital, s − p orbital, and p − p orbital bonds as long as the p orbitals are directed along the axis of the bond. π bonds are the result of the two lobes of one p orbital overlapping with another, parallel p orbital, for this to happen both p orbitals must be aligned perpendicular to the plane of the molecule. Because the p−p orbitals must be parallel, rather than head on as in σ bonding, there is less orbital overlap which causes these bonds to be less strong than σ bonds. δ bonds form when four lobes from one electron orbital overlap four lobes of another electron orbital in the other atom involved in the bonding. In cases where there are multiple covalent bonds between two atoms, such as in the case of C = C the first bond will be a sigma bond and each successive bond will be either one or more π bonds or a δ bond, for carbon it will tend to be π bonds.
This simple bonds described above work well for simple molecules like C = C, however as molecules become more complicated these bond structures do not corre- spond to observation. For example, according to the bonding scheme described above
21 methane (CH4) should have one hydrogen atom bonded via a σ bond and the other three bonded via π bonds. But based on the previous analysis carbon has only two electrons free to bond, as the other two are paired in the s orbital which has a lower energy state than the p orbital and hence the two in the s orbital would have to be ex- cited to the p orbital. Additionally, this would imply that methane is not symmetric, yet experiments show that it is symmetrically arranged in a tetrahedral. Furthermore, this would not minimize the energy of the molecule since there is an electrostatic re- pulsion force between the hydrogen atoms attempting to maximize the angel between themselves. If methane was arranged with one σ and three π bonds the electrostatic repulsion would not be minimized. Clearly a different or modified theory is needed to describe many of the molecules that carbon can form.
This modification comes in the form of orbital hybridization. A hybrid orbital is created by mixing the s, p, and/or d orbitals of an atom to create an equal number of hybrid orbitals. In the case of methane each hydrogen needs to bond with one of the four available valance electrons of the carbon atom, two of which are in the s orbital and the other two occupy two of the three p orbitals (px, py, and pz), since four bonds are needed all four orbitals will be used. The hybrid orbitals that form from one s orbital and three p orbitals is referred to as sp3 orbitals. Each of the sp3 orbitals is expected to be 109.5◦ which provides the greatest separation between the four hydrogen atoms in three dimensional space.
There exist the sp2 and sp1 hybrid orbitals as well, each is the hybridization of an s orbital with two p orbitals or one p orbital respectively. For examples of cases
22 where these occur consider C2H4, ethene, where the carbon-carbon pair form a double bond. Here each carbon atom hybridizes its valance s orbital with two of its p orbitals to form three sp2 orbitals, each with one non-hybridized p orbital. This allows for the carbon-carbon bonds to be the result of sp2-sp2 and p-p bonding, and each of the hydrogen atoms to bond to an sp2 orbital. Each of the sp2 orbitals are in plane with a 120◦ separation from each other and the remaining p orbital is perpendicular to the sp2 plane. In the case of the sp1 hybrid orbitals one s orbital hybridizes with one p orbital, leaving two p orbitals each perpendicular to the plane of the sp1 orbitals as
1 well as to each other. One molecule that has sp orbitals is acetylene, C2H2, which has a carbon-carbon triple bond. In acetylene the carbon-carbon bonds consist of the
1 1 px-px, pz-pz, and one sp -sp bonds with one hydrogen bonded to each of the carbons via the remaining sp1 orbitals. The bond angels between the sp1 orbitals is 180◦ and the p-p-sp1 bonds are all perpendicular to each other.
One additional complication needs to be considered: when, for example, carbon bonds with itself it can form chains or rings, in the case where it forms rings the energy required to break the molecule is often greater than expected using the above analysis. As expected from above a molecule of six carbon atoms in a ring with six hydrogen atoms (benzene or C6H6), one attached to each of the carbon atoms, the carbon would form sp2 hybrid orbitals with one remaining electron in a p orbital perpendicular to the plane of the molecule. One of the three sp2 orbitals is involved in bonding the hydrogen, the other two in bonding to the two adjacent carbon atoms.
This leaves the six p orbitals, one from each carbon atom, properly aligned to form π
23 bonds; however, each p orbital can bond with either the p orbital of the carbon to its left, or to its right, but only one. And this is how the structure of these molecules is often drawn, six atoms with double bonds between three and single bonds between the others. But when examined in the laboratory the bond lengths, which correspond to the number of bonds between two atoms (see Table 3.1), between all six of the carbon atoms is the same length. Additionally as mentioned earlier, the energy required to break benzene apart in the laboratory is greater than predicted by this theory. The key to understanding how each bond has the same length is to realize that each p orbital bonds with the carbon atom to the right AND left, effectively creating 1.5 bonds between each carbon atom6. This hypothesis explains the equal bond length between all of the carbon atoms in benzene and is supported experimentally given that the bond length between carbon atoms in benzene is 139 pm which is between the average lengths of single and double bonded carbon (154 pm and 134 pm respectively).
Starting from the idea that π bonds exist between all of the carbon atoms it becomes clear that there is a continuous π electron cloud above and below the plane of the molecule. 6Expecting there to be three single bonds and three double bonds, for a total of nine bonds, divided equally between six bond sites gives 3 + (3 × 2) = 9 bonds 9 bonds ÷ 6bond sites =
1.5 bonds per site.
24 Bond Type Bond Length (pm) Bond Energy (kJ/mol)
Single 154 346
Double 134 602
Triple 121 835
Benzene (C-C bond) 139
Table 3.1: The average bond length, and bond energy for various C-C bonds.
3.2.1 Aromatics and Aliphatics
Aromatic compounds are ones which are dominated by aromatic bonds, such as ben- zene, these types of molecules are very stable. Aliphatics on the other hand are carbon based molecules with sp1 and sp3 bonds in addition to the sp2 bonds found in aromat- ics. Because of the lack of aromatic bonds, and the stability that results from those bonds, aliphatic molecules are much less stable than aromatic molecules. A mixture of aromatic and aliphatic molecules is often referred to as hydrogenated amorphous carbon. As will be discussed later aromatics, as well as perhaps aliphatics and hy- drogenated amorphous carbon will play an important role in much of the following research.
3.3 Carbon Allotropes
An allotrope refers to the way that some elements are able to be arranged with different bond structures. For one element, in the same state of matter, there may be several
25 ways to arrange the atoms to create stable structures which produce different chemical and physical effects, these arrangements are called allotropes. Carbon is an element with many allotropic structures, including: diamond, graphite, amorphous carbon, fullerene (i.e. C60, commonly called buckyballs), as well as other allotropes such as carbon nanobuds and carbon nanofoam.
Diamond and graphite are the two most commonly known allotropes of carbon.
Known since ancient times, diamonds are a crystal arranged in a variation of the face centered cubic lattice, where the carbon atoms are periodic in regular tetrahedrons.
1 The basic face centered cubic lattice has four atoms per cell, 8 at each of the eight
1 corners as well as 2 at the center of each of the six sides, whereas a diamond has the basic face centered cubic structure with four additional atoms within the lattice this structure is known as the diamond cubic. Each atom in the diamond cubic structure is connected with four other atoms in a non-planar hexagonal shape. Graphite on the other hand is carbon arranged in sheets of planar hexagonal rings with each atom connected to only three adjacent atoms. A single sheet of hexagonal rings of carbon is called graphene; graphite can be thought of as simply stacking layers of graphene which are bond to each other not by the common chemical bonds, but very loosely bonded by Van der Waals interaction7.
Graphite is blackish gray, diamonds are transparent in the optical; graphite is a very soft material (used for example in pencil lead) whereas diamonds are the hardest naturally occurring bulk mineral (used on drill tips for example); graphite is an elec-
7Van der Waals interactions are the resulting force between dipoles.
26 tric conductor, but pure carbon diamond (diamond without impurities) is an electric insulator. Thermodynamically graphite is the most stable of all allotropes of carbon; given enough time and/or heat diamond will turn into graphite8. Even though both graphite and diamond are composed entirely of carbon all of these differences are the result of exactly how the carbon is structured.
Other carbon allotropes include, amorphous carbon which is carbon that is ar- ranged in no particular arrangement; it has no long-range order, though it can, and likely will, have short-range order. Amorphous carbon can be difficult to characterize outside of its lack of long-range order since one sample of amorphous carbon need not, molecularly, appear like another sample. However, one method of characterization is by the ratio of sp2 to sp3 bonds.
Unlike diamond or graphite which each has a set structure or amorphous carbon which has no set structure, fullerenes are a family of molecules which are characterized by their molecular shape. Fullerenes are much like graphene in structure, but usually with the inclusion of pentagonal rings9 which cause the planar sheets of graphene to curl into the third dimension, and eventually fully encapsulate a volume, these sorts of fullerenes are usually spherical or ellipsoidal in shape. Another sort of fullerene, nan- otubes, often have only hexagonal rings in their length and can be thought of as a sheet
8So in fact, diamonds are not forever, it might be more honest to give one’s fianc´eea ring with a graphite top if the idea is to represent the eternal nature of one’s love for the other. Though it would likely end up just creating black marks all over everything it rubbed against, additionally there is much less money to be made by selling graphite rings. 9Though less common, fullerenes can also include other ring shapes such as heptagonal rings.
27 of graphene that has been rolled into a cylinder. All fullerenes are hollow structures, but they can be caused to encapsulate another molecule, even other fullerenes.
28 Chapter 4: Polycyclic Aromatic
Hydrocarbons
4.1 Introduction
Polycyclic aromatic hydrocarbons (PAHs) consist of a group of aromatic six-member carbon rings with hydrogen atoms extending from the edge of the molecule. Aromatic six-member carbon rings are simply closed, hexagonal rings of carbon atoms with sp2 bonds between each carbon atom as well as a continuous π electron cloud above and below the plane of the molecule, the simplest molecule like this is benzine (see Chapter
3). In PAH molecules many of these hexagonal rings combine to form a sheet of co- planar rings much like graphene, but with hydrogen atoms bound to the edge of the sheet (See figure 4.1 for an example of a PAH molecule).
29 Figure 4.1: A drawing of the PAH molecule Ovalene, C32H14, with out the hydrogens drawn.
Gillett et al. (1973) first detected an 11.3 micron emission feature in two planetary nebulae (see Chapter 2) NGC 7027 and BD+30◦3639 which could not be explained by known emission lines (see Figure 4.2). Their observations were the first instance of what would become called the Unidentified Infrared Bands (UIBs). The UIBs are a set infrared emission features, the strongest of which are centered at 3.3, 6.2,
7.7, 8.6, and 11.25 µm (see Figure 4.3. The UIBs have now been found in almost every conceivable astronomical environment (Tielens et al. 1999) including, regions in space with ionized hydrogen called Hii regions (Peeters et al. 1999), as well as the interstellar medium (ISM), in our own galaxy and other galaxies. Since their discovery in the early 1970’s, there have been many proposed carriers, for the UIBs including: magnesium carbonate (Gillett et al. 1973), calcium carbonate (Cherchneff et al. 1999), hydrogenated amorphous carbon (HAC; Jones et al. 1990), coal (Papoular et al. 1993), nanodiamonds, and PAHs (Leger Puget 1984; Allamandola et al. 1985).
In recent years PAHs have become widely accepted as the most likely carriers of the
30 Figure 4.2: The first published astronomical spectra exhibiting excess at 11.3 µm. This would be identified as one of a set of features which always appeared together, the Unidentified Infrared Bands.
31 Figure 4.3: Some of the UIBs with the associated molecular modes. From Draine (2003).
UIBs.
UIBs have been attributed to PAHs because their vibrational modes produce spec- tral features very similar to the observed UIBs. In addition, PAHs are able to emit in low and high intensity radiation fields (Li et al. 2002), and have the unusual capac- ity to be stochastically heated, i.e., heated to high temperatures by a single photon
(Draine et al. 2001). Using laboratory experiments Allamandola et al. (1999), found that the spectra of a mixture of neutral and positively charged PAHs is consistent with that of the UIBs. While there is still some debate about the carriers of the UIBs and even new ideas being put forward (e.g. Bernstein & Lynch 2009), from now on we will assume that the UIBs are in fact carried by PAHs and thus the two acronyms will be used interchangeably.
32 UIBs have be identified in nearly every direction observed. The ubiquitous nature of PAHs in the universe is one reason they have received so much attention; something this common must play an important role in the chemistry of the universe. It has only been in the last several years that PAHs have become the most accepted candidate carriers for the UIBs, however there is still much that is unknown about their na- ture. One very important question that remains unanswered is exactly how are PAHs formed? On the earth, PAHs are very common, forming from the burning of coal or other hydrocarbons; they are the principal constituents of soot (Cherchneff et al.
1999). However, in space, where there is no oxygen atmosphere in which combustion can occur, neither coal nor hydrocarbons can burn; so exactly how they are formed so abundantly as to populate the universe is still not well understood.
In the remainder of this chapter several topics will be discussed, including under- standing the radiation needed to excite PAHs, and how various physical parameters of the PAH molecule will affect the energy of photons that can be absorbed and emitted.
The exact emission from the bending and stretching of different bonds within PAHs will also be described. Stochastic heating plays an interesting role in PAH emission, the physical nature of stochastic heating will be examined, as will the need for a care- ful definition of temperature when attempting to understanding the behavior of single molecules. Aliphatics, which are carbon-based molecules like PAHs but with a slight difference in structure, will be discussed. And the role aliphatics may play in UIB emission as well as in PAH formation is discussed. Then formation mechanisms will be explored, discussing both the bottom-up and top-down mechanisms.
33 4.2 PAH’s Vibrational Energy
Though PAHs have been observed in many astronomical environments, it was initially believed that ultraviolet (UV) was needed to excite PAHs because UIB emission was only seen in environments with hard radiation fields. However, due to some of the work reproduced here it is now believed that most radiation fields are capable of exciting at least certain PAHs. When a molecule, such as a PAH, absorbs a photon it must release the associated energy in some way so as to remain in equilibrium, if it is unable to do so then the molecule will heat up and will eventually be dissociated. PAHs release this energy by the stretching and bending of the bonds holding the molecule together.
When these bonds vibrate or bend they release energy, each stretch and bend of a bond releases a very specific frequency of electromagnetic radiation which can be used to identify that state. For example, when a carbon-carbon bond stretches, it releases energy in the form of a photon with a wavelength of 6.2 or 7.6 µm. When a carbon– hydrogen bond stretches, it releases energy as a photon with a wavelength of 3.3 µm.
As a carbon-hydrogen bond bends in the same plane as the plane of the PAH molecule, it emits at 8.6 µm; and, when a carbon-hydrogen bond bends out of the molecular plane, it emits at either 11.3, 12.0, 12.7, or 13.5 µm (see figure 4.3).
What determines the wavelength of the emitted photon from the bending of the carbon-hydrogen bond is the number of hydrogen atoms attached to the benzene ring
(see figure 4.4). If there is only one hydrogen atom attached to the benzene ring, then the 11.3 feature will be visible; if there are two hydrogen atoms extending from the
34 Figure 4.4: Various PAH molecules with the C-H in-plane modes labeled which cause the higher wavelength UIB features as seen in Figure 4.3. Adapted from Draine 2003.
35 ring, then the 12.0 feature will be observed; and likewise for three hydrogen atoms the 12.7 feature will be present, and if there are four hydrogen atoms bonded to the benzene ring that is bending the 13.5 feature will be present.
A molecule can only absorb and emit certain energies, that is, only certain wave- lengths of light. Other wavelengths of light will not interact with the molecule. The wavelength of light that the molecule can absorb or emit is based on the energy levels of the molecule (see Equations (4.1) – (4.3)). Eni, `i − Eni−1, `i−1 `i = 1, 2, 3,... Ephoton = (4.1) Eni, `i − Eni−1, `i+1 `i = 0, 1, 2,... where Ephoton is the energy of the photon being absorbed, n and ` are quantum numbers for vibrational and rotational modes, respectively. This leads to rκ 2 + ` ~ ~ µ i µa2 Ephoton = (4.2) rκ 2 + (` + 1) ~ ~ µ i µa2 where κ is the second spatial derivative of the bond potential energy, µ is the reduced m m mass ≡ 1 2 of the two atoms at either end of the bond, and a the bond m1 + m2 length. Finally, this can be rewritten as:
rκ 2 E = ± I ~ photon ~ µ µa2
I = 1, 2, 3,... (4.3)where now I is simply taking the place of the ` term. The analogy to the classical simple harmonic oscillator is apparent where κ would be the spring
36 rκ constant and µ the mass. Then would be the angular frequency of the oscillator. µ As expected, we can see a relationship between the quantum mechanics that describe how molecules behave and classical mechanics.
It is well accepted that PAHs absorb strong UV radiation; however, laboratory studies have shown a sharp cutoff of absorption by PAHs in the UV (Li & Draine,
2002). Li & Draine (2002) address this issue by making a distinction between the
PAHs used in laboratory experiments which were “small, neutral PAHs [...] with little or no absorption in the visible“ and PAHs in astronomical environments. For instance,
Draine and Li (2001) estimate PAHs within the Milky Way have an average number of carbon atoms per PAH of approximately 100. They note that the largest PAH studied in the laboratory was C48H20, with only half the number of carbon atoms as the average PAH in the Milky Way. Li and Draine (2002) show that, for larger and ionized PAHs, the absorption edge shifts to longer wavelengths (see figure 4.5).
4.3 Stochastic Heating
Stochastic heating results from the absorption of a single photon, which causes a dramatic spike in temperature (Draine and Li, 2001). This type of heating is important for very small grains/large molecules, such as PAHs, because they are small enough for the entire particle to be heated by a single photon. Larger grain would not be as significantly excited by a single photon due the dispersion of the photons energy throughout the grain and thus the energy added by the photon per atom/bond is much
37 Figure 4.5: Estimated absorption cross sections per carbon atom, with number of carbon atoms,
NC , = 20, 35, 50, 70, 100, and 200. The top panel is for ionized PAHs while the bottom for neutral
PAHs. From: Li and Draine (2002).
38 less. As PAHs are very stable molecules they absorb UV photons quite well, which provide a large amount of energy per bond of the PAH. Of course, this energy per bond varies with the exact energy of the incident photon and the number and type of bonds in a particular PAH.
As the energy of the photon is dispersed though the bonds of the molecule, it is said to be heated. Draine and Li (2001) are very careful in their definition of temperature which they base on the average energy, E (T ) of all the vibrational modes, the modes are indexed by j and given as:
N X ωj E (T ) = ~ (4.4) ~ωj j=1 exp kT −1
th where ωj is the fundamental frequency of the j vibrational mode, k is Boltzmann’s constant, T is the temperature, and N is the total number of vibrational modes.
It is important to note the difference between a vibrational mode, j, and the vibrational level, u. Each PAH molecule can have Nm = 3Na − 6 distinct vibrational modes since there are a total of 3Na degrees of freedom and 6 degrees of freedom come half from rotational and half from translational degrees of freedom. Here Nm is used to represent the number of modes and Na is the number of atoms in the PAH.
Each vibrational mode is simply a single way that the PAH molecule can vibrate. It maybe of interest to note that vibrational modes are often approximated as a harmonic oscillator; this approximation was used by Draine and Li to calculate the number of vibrational states or sets of unique vibrational modes for the whole molecule. The vibrational level is however, a vibration that occurs at one discrete energy level. If
39 the modes are assumed to be quantum harmonic oscillators then only certain, discrete energy levels can be occupied and it is these energy levels that the vibrational level refers to.
From (4.4) the temperature, T (Eu), where u is a vibrational level, can be defined for large grains such that E(T ) = Eu,where E(T ) is the expectation value for the vibrational energy E when in contact with a heat bath at temperature T . However, for small grains, there may be only a few vibrational modes excited with many vibrational degrees of freedom. Since by (4.4) T is summed over all the vibrational modes, j, the effect according to Draine and Li is that T will be calculated to be lower than its measured emission would require. It is important to note that temperature is being used to determine the energy emission from a vibrational mode. Thus, they claim temperature is not well defined using the methods of (4.4) for small grains. So, in an attempt to match the observed emission of molecules like PAHs, Draine and Li find a temperature model of a vibrational level based on observed emission to be: ω ~ 1 E ≤ ω k ln 2 u ~ 20 Tu = (4.5) T (Eu) Eu > ~ω20 where Tu is the temperature of the vibrational level u, and ω1 is the single vibrational
th mode of interest, and ω20 is the 20 vibrational mode. They also note that, while ω20 is arbitrary, the idea of temperature is questionable with so few degrees of excitation and that when this definition for temperature is used the results are in fair agreement with their model. Note that for the case where Eu > ~ω20 there is no need to use this new model for Tu, and so Tu can be found based on (4.4).
40 Since they are interested in single photon or stochastic heating, Draine & Li (2001)
find a critical grain size below which stochastic heating is an important effect. They
find this critical size NC,sph, the number of carbon atoms per grain, to be:
−0.60 5 u NC,sph ≈ 5 × 10 (4.6) uE
based on, τrad (Nsph) = τabs (Nsph) where uE is the local radiation field,
Z ∞ −1 cuν τabs ≡ Cabs (hν) dν (4.7) 0 hν which is the mean time between photon absorption events, and the radiative cooling time
Eu τrad (Eu) ≡
. Here abs and rad refer to absorption and radiative, respectively; Cabs is the absorp- tion cross section, uv is the intensity of radiation at a specific frequency, l represents energy levels below u, Tlu is the downward transition rate, and all other variables have been previously defined or are common physical constants. In the case when the grain size is less than the critical size, the grain will absorb a single photon, be heated dramatically, and then cool quickly. Such a grain will spend much of its time between absorption events with energy much less than the average energy of the photons it is able to absorb. However, grains with more atoms then this critical number will be heated by absorption without enough time between absorption events so that they are heated to energies larger than the local radiation field.
41 As a result of stochastic heating, Draine & Li (2001) conclude that the ratio of the intensity of the emission bands is strongly dependent on the size of the PAH. Small
PAHs should tend to radiate more strongly at the 6.2 and 7.7 µm features whereas larger PAHs will tend to emit more strongly at increasingly longer wavelengths. The ability to determine a relative size of PAHs can be useful in determining the how these molecules form as will be discussed later in this chapter.
4.4 The Role of Aliphatics
Due to subtle variations in the peak positions and relative strengths of the features of the observed UIBs, several classes have been defined to help organize the UIB emissions. Peeters et al. (2002) organized the PAH emission from some 57 sources into class A, B, and C. The class A carbon-carbon stretching features are found at
6.22 and 7.65 µm, and their source is usually HII regions, reflection nebulae, galaxies, and clusters of Herbig Ae/Be stars i.e., large, pre-main sequence stars (Sloan et al.
2007). Class B shows features shifted from the class A location, to 6.26 and 7.85 µm, respectively; and these sources are typical of planetary nebulae and isolated Herbig
Ae/Be stars. Finally, class C sources are the rarest and include the Egg Nebula, which has its 6.22 micron features shifted to 6.26 µm with no emission seen near the usual
7.65 micron feature but with an additional feature around 8.2 µm. Peeters et al.
(2002) determined where these features peaked after subtracting a continuum from the spectra of each of the 57 sources, here one must be cautious because the chosen
42 continuum can have an impact, sometimes a significant impact, on where features peak; and because much of the classification is based on the peak position it should be understood that these positions may vary.
Sloan et al. (2007) discovered a class C PAH source within the spectra of HD
100764, only the seventh known source at the time. Geballe et al. (1989) also observed, in the Orion Bar, what would later be classified as a class C PAH source, which was revisited and confirmed by Sloan et al. (2007); Joblin et al. (1996) also observed class C features in NGC 1333 and NGC 2023. In all seven known class C sources, the radiation field has very low energy. It was argued in all three of the aforementioned papers that there must be other particles causing the observed shifts in UIBs.
Another hydrocarbon could play a role in discovering how PAHs are formed. As mentioned earlier, PAHs are aromatic rings of carbon with hydrogen at the edges.
What makes these rings aromatic is the dominance of sp2 bonds between the carbon atoms; however, aliphatics are similar but are composed of sp1 and sp3 bonds in addition to the sp2 bonds (Sloan et al. 2007). This variation in bond types is what
Geballe et al. (1989), Sloan et al. (2007), and Joblin et al. (1996) argue is causing the shift detected in what are now referred to as the class C UIBs.
Because PAHs are composed of sp2 bonds they are able to spread the energy of an absorbed photon very efficiently through the whole molecule, whereas the bonds in aliphatics are more likely to be broken by the same photon which would simply excite a PAH (Sloan et al. 2007). This is because of the ability to effectively distribute energy over the whole molecule that PAHs are more stable than aliphatics. Because
43 of the PAH’s stability, it is expected that PAHs can survive much more harsh envi- ronments, i.e. more intense radiation fields, than aliphatics. Therefore, if both PAHs and aliphatics were to be created, in time there would be an observed depletion of aliphatics compared to PAHs. It is this very process that the Geballe et al. (1989),
Sloan et al. (2007), and Joblin et al. (1996) studies suggested was leading to the variation in observed spectra. Moreover, aliphatics would not be expected to form in many of the harsher environments in which PAHs thrive since the aliphatics would be broken apart before the PAH molecule would be finished forming.
A mixture of aromatics, like PAHs and aliphatics is called hydrogenated amorphous carbon (HAC). In the laboratory a sample of HAC has been shown to have a spectra consistent with that of class C PAH sources (Sloan et al. 2007; Scott 1997). From this evidence, Sloan et al. (2007) suggests that PAH spectra evolve from HAC-based conglomerates, which are broken down due to exposure to intense radiation fields.
This process results in a higher PAH concentrations over time. They also suggest that class C PAH sources have lower intensity radiation fields, while class B and A sources exist in higher intensity fields which explains why C class sources often show HAC-like features.
4.5 Formation Mechanisms
Formation of PAH in space is still not well understood. Two hypotheses however, are competing for acceptance: 1) the bottom-up method; and 2) the top-down method.
44 4.5.1 Bottom-up
The bottom-up mechanism begins with a seed molecule that is altered in some way to form the building blocks of the PAH molecule. Specifically, the most common method for the bottom-up formation mechanism begins with acetylene (C2H2) as the seed to which a hydrogen atom is added. The addition of the hydrogen breaks the π bond in the carbon-carbon triple bond to become a carbon-carbon double bond forming the radical C2H3. This new molecule is now free to react with another acetylene molecule breaking its triple bond and resulting in C4H5. The C4H5 molecule then loses two hydrogen atoms, one at a time, producing C4H3 which reacts with one more acetylene to form C6H5. This molecule will take the more stable aromatic form with alternating double and single bonds between the carbon atoms. This process is demonstrated in
figure 4.6. Now a single aromatic benzene ring has formed; but this is simply a cyclic
Figure 4.6: A pathway from C2H2 to one benzine ring. From Allamandola et al. (1989)
45 aromatic hydrocarbon, not the polycyclic aromatic hydrocarbon we seek.
To form a polycyclic aromatic hydrocarbon from a cyclic aromatic hydrocarbon
(see figure 4.7), an acetylene molecule with a missing hydrogen atom bonds with the
Figure 4.7: Building up one benzine ring into two attached rings through the addition of acetylene.
From Allamandola et al. (1989) unpaired electron on a carbon atom. The aromatic ring then must lose a hydrogen so a new unpaired electron is available to create another carbon receptacle. This new receptacle site bonds with another acetylene molecule. Now the whole molecule is an aromatic ring with all the material needed to form a second ring; and, just like the last step in forming the single aromatic ring, the second ring will take the more stable aromatic form. Finally, a PAH has formed. It may grow into a larger PAH such as
Coronene, C24H12, as shown in Figure 4.8. by first adding another C4H2, then a C2, and then a C4H2 and so forth creating various sizes of PAHs.
46 Figure 4.8: Starting from benzine and using the detailed process shown in Figure 4.7 we show a pathway to Coronene, C24H12. From Allamandola et al. (1989)
4.5.2 Top-down
The second mechanism by which PAHs may form is called the top-down method. This theory proposes that there are carbon rich dust grains and that PAH molecules can form on their surface. Subsequently, a PAH molecule can be desorbed from the surface of the grain by photo-dissociation. The strength of this theory is that, in general, this mechanism allows for larger PAHs to be formed than can be formed by the bottom-up mechanism. As described earlier, the larger the PAH, the lower the photon energy needed to excite the molecule, which may help explain how PAHs are seen in so many low-intensity radiation fields.
One way this mechanism may work is to have a high-energy photon incident on the dust grain which holds the material needed for the PAH to form. The environment of
47 the dust grains is often very favorable for molecular formation, in fact, this method is expected to be the way molecular hydrogen is often formed in astronomical environ- ments. As a large grain of amorphous carbon is bombarded with high energy photons it may break apart, or a benzene ring may break off of its edge. This ring is now free to interact with atomic hydrogen, the most abundant element in the universe, which will bond with the outer carbon atoms forming a PAH.
4.5.3 Distinguishing Between Mechanisms
If the top-down mechanism is similar to the actual mechanism by which PAHs are formed, then a binary system containing a C star and a hot companion that shows
PAH emission is still possible. For this mechanism, the PAHs around the C star can be excited by its own radiation field; however, the hot companion provides the high- energy photons needed to break off the benzene chain from the amorphous carbon grain. In this case, one would expect to find PAHs emission from around all sides of the C star in the binary system when observed with high spatial resolution, not just from the side facing the hot companion. This is because the emission from the C star will excite the PAHs, but one would not expect to see such emission around a single
C star due to the lack of hot companion’s high-energy photons which are needed in the formation mechanism.
If the bottom-up mechanism is similar to the actual mechanism by which PAHs are formed, then around a binary system containing a C star and a hot companion may
48 also show PAH emission. However with this mechanism tending to produce smaller
PAHs, which require the higher energy radiation from the hot companion in order to emit (see Figure 4.5 and surrounding text), one would expect to find PAHs emission from only the sides with a direct line of sight to the hot companion. The part of the shell around the C-star which is on the opposite side as the hot companion would not be expected to emit since the only radiation the PAHs there are exposed to is due to the lower energy radiation from the C-star, and thus would not emit. When observed with high spatial resolution may be detectable.
An interesting case may exist wherein the PAHs are formed via the top-down mechanism producing larger PAHs, but the high energy photons from the hot com- panion begin breaking the PAHs into smaller PAHs. In this case one may have results which appear to suggest the bottom-up mechanism however this conclusion would be of course wrong. To clarify this case one could attempted to determine if there exist a size distribution of PAHs around the C-star, this could be done by comparing the ratio of the 3.3-to-11.3 µm features (see de Muizon et al. 1990 and Driane & Li 2001).
If the PAHs were the same size around the C-star then the bottom-up mechanism can be considered, however if there is a large variation in the sizes of PAHs around the
C-star then the PAHs have likely been broken up and this may be suggestive, though not indicative, of the top-down mechanism of formation.
49 Chapter 5: Observational Investigations of the Presence of PAHs Around Carbon
Stars
5.1 Introduction
The so-called UIBs have been widely observed in interstellar media, both in the Milky
Way galaxy and in other galaxies of metallicity down to about -0.5 solar10. These emis- sion features are commonly attributed to polycyclic aromatic hydrocarbons (PAHs;
Leger Puget 1984; Allamandola et al. 1985), and occur at 3.3, 6.2, 7.6-7.9, 8.6 and
11.3 µm (see Figure 4.3). PAHs are excited by absorption of single photons whose
10Metallicity is the abundance of elements larger than helium relative to the abundance of hydrogen and helium
50 energy is then distributed over the whole molecule(Draine & Li 2001; see Section 4.3).
These molecules then emit the energy in the distinctive IR bands (see Section 4.2).
The precise band wavelengths and strength ratios depend on the size, composition and charge of the PAHs (Li & Draine 2002). Furthermore, the wavelength of photons needed to excite PAHs depends on their size. While small PAH need higher energy
(UV) photons, large PAHS (>≈50 C atoms) can be excited by visible or even near-IR photons (Li & Draine 2002). The 3.3um/11.3um ratio has been interpreted to be related to the size of the PAH (de Muizon et al. 1990).
Buss et al. (1991) first detected UIB emission around a C-star, TU Tau, with a hot companion. The emission was attributed to the hard radiation of the hot companion since the UIBs had not been seen in any other spectra of C-stars. Buss et al. (1991) also suggested that PAHs may be present in C-stars without hot companions even though they are not observed in the spectra. Speck et al (1997) observed three C-stars with hot companions (TU Tau, UV Aur, and CS776) and confirmed the observation of UIB emission in TU Tau from Buss et al. (1991) expanding the spectrum’s wavelength range to show, with good signal to noise, the 8.6 and 11.25 µm features. The 11.25
µm feature was also seen in UV Aur; however, no UIR band was detected in CS776.
Uchida et al. (1998) then detected UIB emission in other objects with low UV flux, namely vdB 133. Boersma et al (2006) investigated 50 C-star spectra finding UIB emission in only one, TU Tau, and questions whether UIB emission around TU Tau suggest PAHs are present around other C-stars without hot companions, simply not excited, or if the hot companion is playing some role in the formation of the PAHs.
51 The basic premise of our observational programs is that the PAH formation mech- anism can be determined if, by using spatially resolved spectroscopy from Michelle, the location of PAH emission could be determined with respect to the C-star and its hot companion. We also hoped to determine how “hot” the hot companion needed to be for UIB emission to be present by observing C-stars with a range of companion spectral types. The top-down formation mechanism requires UV photons to eject the
PAHs from the surfaces of grains, but is likely to produce large PAHs which do not need UV photons to be excited, whereas, bottom-up formation does not need UV photons for formation, but lead to smaller PAHs which need UV photons for exci- tation. Consequently the distribution of UIBs should be different. However, there could exist a case where PAH formation occurs via the top-down mechanism, but fur- ther processing11 by the companion star’s UV field turns the large PAHs into smaller molecules. While the large PAHs would be excited by the C-star radiation alone, the processed smaller PAHs require excitation by the UV from the companion. In this case we may not be able to disentangle the formation mechanisms using the Michelle observations alone. With additional observations using NIRI to obtain the strength of the 3.3 µm we could definitively determine the size of the PAHs and determine if there is a distribution of sizes with respect to the star system. A distribution of size would be expected if the UV from the companion was processing the PAHs.
In order to attempt to distinguish which of the two formation mechanisms dominate around C-stars we obtained observing time on the Gemini North telescope on Mauna
11This refers to, in this case, breaking apart the PAH molecule due to the UV from the companion.
52 Kea. The first proposal, entitled “NIRI/Altair imaging of PAH bands around carbon stars: determining the formation and processing mechanisms of organic molecules”, was approved for 20 hours of classical observing time to obtain photometric data in
February of 2009, and the second proposal, entitled“PAH Formation around Carbon
Stars and the Limit of the Hot Companion”, was approved for 20 hours of classical observing time to obtain spectral data during January 2010. The first observing run provided very little to no viable data due to poor weather, however the second run provided usable data.
The initial goal of these observations was to detect UIB emission and determine if there is a non-symmetric distribution of emission, which is the reason for taking the spectra of each object twice with the spectra perpendicular to each other. If we
find a difference in the distribution of emission, implying a difference in where the
PAHs are being excited, then we may conclude that the PAHs are small, needing the UV from the hot companion to be excited, this would suggest the bottom-up formation mechanism. However, if the UIB emission is the same in both directions then this implies that the C-star is able to excite the PAHs and so they must be large suggesting the hot companion is need in the formation of the PAHs, via the top-down mechanism.
53 5.2 Methods and Instruments
For our observations we used the Gemini North telescope which is an 8.1 meter di- ameter telescope on the summit of Mauna Kea on the island of Hawaii, there is an identical or twin telescope, Gemini South, on the summit of Cerro Pachon in Chile.
In the first observation run Gemini’s instrument the Near InfraRed Imager and spec- trometer (NIRI) was used along with the adaptive optics system ALTtitude conjugate
Adaptive optics for the InfraRed (ALTAIR). The NIRI instrument is an infrared de- tector operating from about 1 to 5 µm. It has three cameras, we used the f/32 camera with a field of view of 22×22 arcseconds2, in addition we used three narrow band
filters, namely: the K-continuum (centered at 2.090 µm), the H2 1-0 S(1) (centered at 2.122 µm), and the hydrocarbon filter (centered at 3.295 µm). These filters were chosen such that the hydrocarbon filter would show any UIR emission, capturing the
3.3 µm feature and the other two filters were “off-band” meaning they would show light from the object that was not UIR emission, but light being emitted by the object itself. With light measured in two different bands near the band of interest which only show only the blackbody emission, this is emission which contains no molecular or dust features, one can estimate an average slope of the blackbody curve in the region near the off-band filters. If the off-band filters are chosen close to the on-band filter, in terms of wavelength, then after finding the average slope of the blackbody, the continuum in the on-band filter can be extrapolated, and then the continuum can be subtracted from the on-band filtered image and what remains is an approximation of
54 the excess, do to in this case, UIB emission.
Because some of these objects may have extended emission, that is emission origi- nating from the space exterior to the objects surface, in this case extended emission at
3.3 µm would be interpreted as the result of PAH molecules emitting, it is important to verify whether any apparent extended emission is real and not the result of a limita- tion of the observation. It may seem that by the virtue of the detector recording light exterior to the objects surface that light can is guaranteed to be extended emission, however due to possible defects in the detector, in the filter, and blurring of the image by the atmosphere12 there can appear to be extended emission when in fact there is none. If another star were to be used as a standard to compare the object of interest to it, it should have no extended emission at the wavelength of interest but should be as near as possible to the same brightness and be as near as possible in elevation13, and observed near the same time as the object of interest. By using a such a standard one could analyze how the atmosphere/filter/detector system is effecting the primary observation. If the standard has a tight, round point spread function (PSF), (the PSF is the way the light from a point source becomes spread out over the detector due
12Because the atmosphere is comprised of many layers that move with respect to each other with pockets of higher and lower density/temperature the light passing through the atmosphere becomes smeared out. This is referred to as seeing, if the light is very smeared out it is said to be bad seeing, but if the light is not very smeared out it is said to be good seeing. 13By having similar elevations the light from the standard star would pass through the nearly the same amount of atmosphere as the the light from the object of interest, which will hopefully provide a good estimate for the seeing
55 to optical effects such as the ones listed above), then any extended emission seen in the object of interest may be real, however if the PSF of the standard is very large and/or non-symmetric it can be difficult or impossible to determine if any apparent extended emission in the object of interest is real or not. To help track general trends in the change of the atmosphere standard stars are usually observed both before and after the observation of the object of interest. Additionally, the off-band filters are used here to make sure that any apparent extended emission is not simply light being scattered by material surrounding the object. In this case, since we know that in the off-band filters the light is not UIB emission, if there was real extended emission the emission should be seen in the on-band filter, but not in the off-band filters. If the apparent extended emission is found in the off-band filters as well then it is likely due, at least in part, to scattered light from the central source and not UIB emission.
ALTAIR is the adaptive optics system that can be used with NIRI. Adaptive optics refers to deforming the parabolic mirror to adjust for variations in the seeing. In the case of ALTAIR there are 177 actuators under the main mirror deforming it so as to correct for seeing. ALTAIR uses a wavefront sensor which detects changes in a guide star to calculate how the mirror should be deformed to minimize the effects of seeing.
The guide star can be either a natural star or the system can monitor a Laser guide star which is used by monitoring how a Laser’s path is altered by the atmosphere. In either case the correction, or deformation, of the mirror is done up to a rate of 1kHz, meaning that every microsecond the mirror deformation is being updated to reduce the effects of seeing.
56 In January 2010 we were granted 20 hours of time at Gemini North to use the
Michelle instrument. Michelle is a mid-infrared instrument, observing from 7 to 20
µm capable of spectroscopy as well as imaging. In order to test the hypotheses in question we want get spatially resolved spectroscopic information. We also need to know the structure of the system, i.e. where is the hot companion. With this in mind, for each Cstar binary system in our sample we took narrow band images mid-IR, mid-IR spectra and optical images. During this run most of the telescope time was dedicated to spectroscopy of the eight objects listed in Table 5.1. We also imaged the objects using Michelle in five filters14. Both of the off-band filters are useful in the methods described above regarding continuum subtraction. The on-band filters are useful in determining the distribution of any UIB emission found. We also used the
Gemini Multi-Object Spectrograph (GMOS) to image the binary systems in order to locate, when resolvable, the companion star with respect to the C-star.
5.3 Observations
In the first run, using NIRI, we obtained photometry for twelve objects, namely:TU
Tau, UV Aur, V569 Pup, IV CMa, V767 Mon, SZ Sgr, V Hya, HD 75021, CIT 6, Y
Cvn, IRAS 07134+1005, and AG Ant. Unfortunately, poor weather compromised all the observations. 14Namely, the Si-1 filter (containing the 7.7 µm UIB feature), the Si-2 filter (containing the 8.6
µm UIB feature), and the Si-5 filter (containing the 11.3 µm UIB feature), as well as two off-band
filters, the Si-4 filter and the Si-6 filter.
57 In the second run, using Michelle, we obtained spectroscopic data for eight objects namely:AG Ant, CY CMi, IV CMa, RY Mon, V767 Mon, V Hya, Y Cvn, and UZ Pyx.
Most of these objects were C-stars with the exception of CY CMi and possibly AG
Ant which are post-AGB objects (Justtanont et al. 1996 and Waelkens & Waters 1987 respectively). Michelle provides Mid-Infrared spectra ranging from ≈7-14 µm. In our observations the spectra are generally reliable from ≈8-13 µm, and any data beyond this range may need further scrutiny due to the atmosphere not being as transparent at the edges of the range.
Figure 5.1 shows spectra collected of the eight objects in our observations; the two spectra in most panels show a vertical and a horizontal slice of the object. Because we are using long-slit spectroscopy we choose which direction to lay the slit across the object, and because we want to detect differences in the spacial distribution of UIB emission we lay the slit one way, take a spectrum, then rotate it 90◦ and take another spectrum. The red lines running vertically in each panel are placed at the various UIB emission wavelengths. The first three red lines, which are thicker, occur at typically strong 7.7, 8.6, and 11.25 µm UIB emission, the last three thinner red lines occur at the weaker 12.0, 12.7, and 13.55 µm UIB emission features.
5.4 Discussion
Of the eight objects we observed only one, AG Ant, showed clear evidence for UIB emission at the typical wavelengths. This is also a possible post-AGB object, a PPN,
58 Object RA & Dec Companion’s UIBs Interesting Results
Spectral De-
Type tected?
AG Ant 10:18:7.59 B9 Yes Typical UIB emission.
-28:59:31.2
V767 Mon 07:50:4.05 A6 No Interesting in only that there is nothing
-00:52:55.3 interesting.
RY Mon 07:06:56.48 - F3 No Shows broad 8.5 and 11.3 µm features.
07:33:26.52
CY CMi 07:16:10.26 F5 Yes Maybe class B or C type UIB emission.
09:59:47.99
V Hya 10:51:37.26 - K0 No Shows broad 8.5 and 11.3 µm features.
21:15:0.32
UZ Pyx 08:46:36.33 - K1 No None.
29:43:41.2
Y Cvn 12:45:7.83 Unknown No Have data from more than 10 years ago
45:26:24.92 which may show changes in the object.
IV CMa 06:23:39.12 - Unknown No Shows broad 8.5 and 11.3 µm features.
27:03:56.68
Table 5.1: Objects from Michelle observations, in descending order of object/companion’s temper- ature when known.
59 Figure 5.1: Spectra taken using Michelle, with60 wavelength along the x-axis and flux along the y-axis. The vertical lines reference the strong UIB lines at 7.7, 8.6, 11.25 µm and the weaker UIB lines at 12.0, 12.7, and 13.5 µm. The two spectra in each of the panels, with the exception of panel
“e”, are spectra taken at 90◦ of each other. and thus the radiation field due to the object is expected to be very hard, and UIB emission is known to occur in these type of objects. However, the spectrum of AG
Ant, in this wavelength range does not show what is typically expected of a post-AGB object whereas CY CMi looks very much like what is expected of such objects. It may be worth additional observations in other wavelength bands to get a more complete understanding of what the continuum is like to see if this object has been wrongly classified.
Of the remaining seven objects the spectral type of the companion is know for
five of the objects. Table 5.1 lists the objects with the spectral type of the object or the known companion. Of the five with known spectral types only V767 Mon can be considered to be in a hard radiation field, to have a hot companion. With a spectral type of A6, V767 Mon’s companion’s blackbody will peak in the UV15, if this object has UIB emission it is certainly not strong. The spectrum we obtained from V767
Mon is much too noisy to say whether or not there is UIB emission definitively, but we can conclude that if there, it must be weak.
CY CMi shows what may be the 7.7 µm UIB feature offset to ≈7.8 µm, the 11.25
µm feature offset to 11.3-11.4 µm, and one could anticipate finding the weaker 12.0,
12.7, and perhaps even the 13.55 µm features in the abundance of features beginning at around 12 µm. It was suggested earlier that the data outside of ≈8-13 µm range may be unreliable and one must be critical of this regime. In this case however, the
15 2898 Recall the peak wavelength of a blackbody is given by Wien’s Law, λpeak = T where λ is in
µm and T is in K
61 general trend of the spectrum looks to be reliable in the wavelengths short of 8 µm, and the feature at 7.8 µm looks very strong and well defined, which leads to the conclusion that the feature is real. There seems to be a notable lack of the 8.6 µm feature, a feature due to in-plane C − H bending. For these observations the UIB emission seems to follow some combination of the class B and class C emission, with the exception that there does not seem to be an 8.6 µm feature. Sloan et al. (2007) claims that class B spectra show the 7.7 µm feature centered at 7.9 µm, while the class C spectra were sifted to around 8.2 µm, clearly this cannot be categorized as class C based on this feature. However, for the 11.25 µm feature the claim is that A and B class spectra range between 11.21 and 11.30 µm with an average of 11.26 µm, while for the C class that feature seemed to be shifted to the 11.36-11.42 µm range.
Evidently the spectrum of CY CMi demonstrates C class bands at longer wavelengths and B class bands at shorter one. Yet there does not seem to be the 8.6 µm feature present which remains perplexing.
The other three objects with known companion types: RY Mon, V Hya, and
UZ Pyx having companion spectral types of F3, K0, and K116 respectively, show no detectable UIB emission. However, the two hottest of the three, RY Mon and V Hya, show broad features at ≈8.5 and 11.3 µm. The 11.3 µm feature is a well known
SiC emission feature. With the spectra we obtained it is unclear whether the 8.5
µm feature is due to emission, or absorption on either side of the feature. In order
16All three of these companions should be peaking in the visible, with the F3 companion signifi- cantly more blue than the other two.
62 to determine which is the case we would need to be able to identify the underlying continuum; this might be possible if the spectra ranged over a longer wavelength.
Given that the C-star with the coolest companion, UZ Pyx, does not show these two features it may imply a temperature dependency, though with only three data points it is hard to suggest a correlation, furthermore the appearance of these features may have a dependence on the C/O ratio, which is not known or accounted for here.
Y Cvn also shows the 11.3 and a weak 8.5 µm features. The feature in this very object was looked at by Speck et al. (2005; see section 2.3 and Fig. 3 of that paper) in the same wavelength range but with lower resolution. They concluded that these features were likely do to amorphous SiC which, according to laboratory data shows two peaks, one that directly fits the 11.3 µm feature and another with a peak around ≈9 µm. They suggest the “reason for differences in peak positions between the laboratory spectra and the observed astronomical absorption features are due to the effects of self-absorption and grain size”. However, in the modeling that Speck et al. (2005) preforms when the effects of self-absorption and grain size are considered the primary result is to shift the 11.3 µm feature, with very little effect on the 9
µm feature. For the case of Y Cvn the 11.3 µm position fits quite well without any shifting, it is the 9 µm feature that is shifted to ≈8.5 µm. It should be noted however, that in the spectrum obtained here the strength of both features seems diminished compared to the strength of the features in Speck et al. (2005) which had originally been published in Speck et al. (1997); furthermore, both features in the Speck et al.
(2005) data is much more sharply peaked than in the spectrum observed here which is
63 more flat topped. The Y Cvn spectrum observed here in fact seems to have evidence of incomplete self-absorption in the form of horns at ≈11 and 11.5 µm. This may very well be observational evidence of an evolving dust shell around Y Cvn, and aside from the shifting of the peak of the 11.3 µm feature, such evolutionary changes are exactly as predicted in Speck et al. (2005).
Another possibility for the 8.5 µm feature is the result of absorption on either side of the apparent feature so as to reduce the flux leaving a continuum level of flux at 8.5
µm. Speck et al. (2006) provide a good example of how this might happen in a C-star environment. The absorption features examined in Speck et al. (2006), due to C2H2, does produce an apparent feature, a “bump” in the flux, near 8.5 µm (see Fig. 2 in
Speck et al. 2006 for an example). Without spectra covering a larger wavelength range, allowing us to determine the underlying continuum, we will be unable to distinguish, in any definitive way, between the two cases of emission or absorption.
In all there are four objects in our sample which show the 8.5 and 11.3 µm features, namely: Y Cvn, RY Mon, V Hya, and IV CMa. These broad features may be hiding
UIB emission, there is no way to know, or it could be that much of the carbon in these systems is tied up in SiC and/or possibly C2H2. C2H2 is required for the bottom-up method of PAH formation, and so these stars maybe forming the preliminary “seed” molecules from which PAHs may later form. It would be interesting to see if there is a correlation, or anti-correlation, between these SiC features and the 21 µm feature as suggested by Speck et al. (2005).
Since we only detected UIB emission in two of the objects the sample size is quite
64 small. Moreover in the two objects we see demonstrating UIB features one of them is a post-AGB object and the other may or may not be, making it difficult for this analysis. Yet we can still learn from AG Ant; the UIB features seen in AG Ant differ by up to 10% and yet it has a radiation field that should be capable of exciting even the smallest PAHs. This may indicate that even a 10% difference in the strength of the features is not sufficient to claim the distribution of emission is evidence of small PAHs only being excited on the side of the C-star facing the hot companion. However, if AG
Ant is a post-AGB object the effect may be do to an asymmetric dust shell resulting in an asymmetric distribution of PAHs.
The other object that may be showing UIB emission is CY CMi, which is very likely a post-AGB object, but if the features seen are in fact UIB emission it is certainty not class A emission, not even typical class B or C. However, the features in both directions seem to have very nearly the same strength. This is not indicative of larger or smaller
PAHs since the radiation field from this object is quite hard; without the NIRI data and the strength ratio of the 3.3/11.25 µm features we cannot conclude anything about the size of the PAHs. Moreover, if the C class UIBs are due to Aliphatic (Slaon et al.
2007) then it may not stand to reason that the excitation of these molecules are as sensitive to size and charge state as the PAHs modeled by Li & Draine (2002).
Another note worthy observation from the data, regarding UIB emission, is the lack of emission in most of these objects. With the exception of AG Ant, the PPN object, and CY CMi, spectral type F5, there is no detected UIB emission in any of the observed C-stars. V767 Mon needs to be observed again to obtain higher signal-
65 to-noise, as the noise in that spectrum could very well be obscuring UIB emission.
It seems that from this data cooler companions to C-stars are many times unable to produce UIB emission. Yet CY CMi, with a cooler companion, seems to be exhibiting
PAH emission. CY CMi may warrant further study as it may be demonstrating a transient state within the Peeters’ classification. However, if V767 Mon does not show
UIB emission with higher signal-to-noise, with its A spectral type companion, then we cannot conclude that if a C-star has a hot companion it will show UIB and thus have emitting PAHs around it, as was the case with CS776 (Speck et al 1997).
Not seeing emission in V767 Mon would be seem to make it less clear as to why
UIB emission is seen in post-AGB objects that evolved from C-stars, but not in many
C-stars, even ones exposed to hard radiation fields. If this is the case then there must be another factor, or combination of factors, which lead to the formation of PAHs in these post-AGB objects. If V767 Mon does not show UIB emission, and we accept that CY CMi is demonstrating UIB emission, then we must conclude that there are not even small PAH around V767 Mon, as they would be exited by UV from the companion, and that UV and available carbon alone are not enough to result in the formation of PAHs.
66 Chapter 6: Particle Swarm Optimization
6.1 Introduction
Particle Swarm Optimization (PSO) is computational algorithm originally developed by Kennedy and Eberhart (1995) to model social behavior, it is considered a member of the artificial life and evolutionary families of algorithms17. PSO is based on the behavior of swarming animals, consider for instance schooling fish, though the oceans are mostly desolate fish are able to find sources of food; many species use schooling behavior to maximize the likelihood of finding food and protection from predators.
If we accept the premise that some fish are more fit for survival when schooling than when alone, one must ask why. A partial answer is with more eyes looking for food and predators the odds of detection is increased. However this is null if there is not some
17These families include ant colony optimization, simulated annealing, and bee colony optimization
67 form of communication between the fish. So there are two factors needed to increase a fish’s fitness: 1) more detectors of food and danger, and 2) an ability to transmit and receive communications about food and danger. Since by virtue of the swarm each creature is more likely to survive than if it were alone, the swarm intelligence is greater than the sum of the intelligence of all of the creatures in the swarm. It is this additional intelligence that PSO attempts to leverage against the optimization of a function. Fundamentally this is what PSO is based on, searching a space for a solution (i.e. food) and accomplishing this more effectively by using multiple detectors
(i.e. fish), called agents, and allowing them to communicate. Since a swarm While this could be used to model social behavior, as it was originally intended to do, it is clearly very capable to find the optimal solutions to a function within a space, this has become its primary use.
The standard PSO is essentially nothing more than what is described above. Yet, if one were to see a graphical representation of these “digital fish” it would not look like any schooling fish seen in nature. This is because the only communication that agents have with each other is where the best solution yet found is, whereas in nature the inter-fish communication is much more sophisticated.
One example of what real fish communicate that is not included in the standard
PSO is communicating distance between neighboring fish. This provides several effects, by this mechanism a fish keeps a minimum distance between itself and all other fish, this aids in predator evasion, and in some fish the spacing between fish is critical to their hunting methods. It is through introducing more realistic forces on the agents
68 that we have tried to produce a more useful and efficient algorithm.
The basic premise of PSO, that it can go through a space and without sampling every point pick out the best solutions in that space is useful in many different applica- tions, scientific ones included. Imagine, for example, having a set of 100,000 radiative transfer models which were created by changing one of a set of parameters at a time.
Now you need to find a ”good solution” i.e. a specific model that matches a single observation. It is a daunting task. Or perhaps what may be of more interest is seeing if there are groups of models which have widely different input parameters but give nearly equal quality of solutions18. Here the question is not if just one out of what may be multiple solutions can be found, but if all solutions can be found. We have developed modifications to the standard PSO in order to (1) improve its efficiency, (2) make it possible to find multiple solutions, or (3) make mapping a parameter space possible.
6.2 Standard PSO
In the standard PSO, agents are placed in a space which then evaluate a function, the
fitness function, at points in the space as they move. The agents are responsible for recording the location with the best result from the fitness function that they find, agent’s or personal best, and if that is the best for the swarm, the global best, then
18For instance, radiative transfer modeling is inherentaly degenerate (see Speck et al. 2009) leading to multiple models that can fit a single spectrum.
69 they communicate this location. Their movements are governed by an equation which is a weighted function of the agent’s personal best as well as the swarm’s global best, and the previous velocity. Entropy is added into the system by two random numbers that adjust the weight of the personal and global best of each iteration.
The entropy is an important part of the system, it makes the system non-determined.
If there were no entropy in the system the path taken by all of the agents would very quickly converge, each of them following a local gradient toward the global best. Pre- mature convergence is an effect of a swarm converging to local optima rather than the global optimum, this is often due the case when a there is a strong local optimum that creates a very strong attractor, limiting the amount of space the swarm will explore.
Entropy is introduced into systems to prevent premature convergence by changing the weighting of how strongly the present global best is attracting each agent. The standard PSO is an improvement in this way over older algorithm such as gradient descent which has no entropy. However, all systems of this nature are susceptible to premature convergence assuming they do not sample each point in the space.
One example of where the standard PSO struggles with premature convergence is the ice cube tray function: consider a space that is shaped like an ice cube tray, it is a plane with periodic minima, all with the same depth. With that in mind, imagine choosing one of the minima at random and making it twice as deep while maintaining the cross section of the “valley”. As the standard PSO explores the space it will find many of the minima, however if it does not find the exact one with twice the depth it will end up converging on one of the minima. As the standard PSO does not have
70 any method to map the space, and reports only one optimum the user will likely never know anything of the topography of the system or that this point was equally as good as many others. With a mapping of the space the user may determine to run the simulation for more time to give the algorithm the chance to explore the space more fully.
In the following section I will explicitly provide the standard PSO algorithm with notes on what is occurring at each step. For this example the swarm is attempting to
find the minimum value for the function f.
6.2.1 The Algorithm
n Let there exist a space R where n is equal to the number of dimensions in Rn, let
n there exist a function f which is defined everywhere within R . Let ~xi be the position
th n and ~vi the velocity vector of the i agent with n components such that ~xi ⊂ R .
Standard-PSO()
1 //Initialize the agents
2 for each i
n 3 do Set agent’s velocity: ~vi ← Random(R )
n 4 Set agent’s position: ~xi ← Random(R ) ~ 5 Set agent’s best: Ai ← ~xi
6 Set global best: G~ ← min fAi
71 7 //Update each agent
8 while Stop condition not met. for each i
9 do Create two random vectors: ~rA, ~rG ← Random[0 → 1]
~ ~ 10 Update agent’s velocity: ~vi ← ω~vi + CG ~rG × ~xi − G + CA ~rA × ~xi − A
11 Update agent’s position: ~xi ← ~xi + ~vi
~ 12 Update agent/global best: if f (~xi) < f Ai
~ 13 then Ai ← ~xi
~ 14 if f (~xi) < f G
~ 15 then G ← ~xi
16 return G~
The Standard-PSO algorithm works as follows:
(3) for each of i agents assign a random velocity vector, who’s components ∈ Rn.
(4) for each of i agents assign a random position vector, who’s components ∈ Rn.
(5) for each of i agents assign it’s current position as the agent’s best position (in this case the minimum).
(6) find the global best by finding the minimum f evaluated at each ~xi.
(8) here we start a loop that will be executed for each agent until a stop condition is met19.
(9) for each agent get two random numbers between 0 and 1.
19The stop condition can be a number of things: Stop after so many iterations, Stop after so many seconds, Stop when some degree of convergence has been met.
72 (10)for each agent update the velocity20:
(10a) multiple the current velocity by some scaling constant ω.
(10bi) scale the constant CG by the random value between [0,1]
(10bii) find the distance the agent is from the global best
(10biii) take the vector product of (10bi) and (10bii).
(10ci) scale the constant CA by the random value between [0,1]
(10cii) find the distance the agent is from it’s best
(10ciii) take the vector product of (10ci) and (10cii).
(10d) sum 10a, 10b, 10c.
(11) for each agent update its position. Note that since each time-step is equivalent, and arbitrary, for each particle we set the time-step to unity so the value of the velocity can simply be added directly to the position without loss of generality.
(12) begin check if agent’s best and global best need to be updated:
(13) if the agent’s best needs to be updated then update here.
(14) if the agent’s best needed to be updated check if the global best needs to be updated, if the agent’s best was not updated this step will not be executed.
(15) if the global best needs to be updated then update here.
(16) the stop conditions of the while loop has been met, so output where the current global best is.
20 ω, CG, and CA are all user definable constants, optimal values of which will often dramatically change the rate of convergence
73 6.3 Modified PSO
The standard PSO is inadequate for the needs explained above. Most importantly, the algorithm needs to be able to show not only where the optimal solution is but where any solution lies within some ±δ. Without the ability to find multiple solutions the degenerate regions of some model’s parameter space can never be found, moreover a map of that space can not be made. We have introduced several new components to the standard PSO algorithm which will provide the capability for the algorithm to map a space, find multiple solutions, and increase the entropy thus reducing the likely hood of premature convergence.
These new capabilities come from adding agent interactions with different types of agents. In the standard PSO there is only one type of agent, in our example “fish”; however, in our modified PSO there are “fish” and “sharks”. The fish are, like in the standard PSO, attempting to find the optima of a function or space but the sharks, acting as predators, are attempting to find the highest concentrations of fish. The sharks have no idea of the underlying space the fish are examining, they are always trying to find where the fish are, and so while the fish’s fitness function will need to be changed for each new application of the algorithm the sharks fitness function will always be the same. Of course, to make the swarm intelligence of use the fish will need to be able to see the shark and communicate about it. The fish will of course try to avoid interactions with the shark agents, and so a new element will have to be added in the fish agents’ velocity update function to include a repulsive force with respect
74 to the shark.
The purpose of the shark agent is multifaceted, first and most clearly this adds entropy into the system, as the fish begin to converge on a solution their concentra- tion increases and so shark agents move toward the schooling fish dispersing the fish allowing for them to explore the more of the space. The shark agents are allowed to
“eat” fish if the shark can catch the fish. Catching a fish is the result of the fish having a strong enough attraction to the part of the space where the shark is and gets too close to the shark. However, when a shark has “eaten” a fish the fish is re-spawned at some random place in the space and with some random velocity, this again serves to increase the entropy of the system allowing for a more through exploration of the space by the fish. When a shark has eaten a certain number of fish a child shark is spawned and the parent shark is restricted to a small radius from where the child shark was spawned. This is used as a method to mark concentrations of fish in the space. A shark agent is more likely to feed on fish where there is a grouping of fish and so it is likely that the place where the shark is restricted to was near an optimum.
If the optimum is a strong one the spawned child shark will eat a number of fish near where it was spawned and then spawn a grandchild shark, now the child shark will be used as a marker as well and so through this continued process the distribution of sharks throughout the space will mark the gradient of the concentration of fish. When the stop condition is met21 what is returned from the function is not just the global best as in the standard PSO, but an array of the locations of all the sharks.
21line 9 of the modified PSO algorithm
75 Another interaction we incorporated is based on a real behavior of fish, namely
fish have a certain volume around them in which they try to keep clear of other fish. If one fish enters another fish’s private space, maybe because there is a predator chasing the first fish, then the second fish will move to keep a certain distance between itself and the other fish. It is from this simple rule that whole schools of fish seem to move in unison. A school of fish can be swimming along in one direction then without notice the whole school seems to change direction instantaneously. an example of what actually happens is one fish detects a predator, then to avoid the predator the fish turns into the space of a neighboring fish, which detecting the violation of its space turns away but into another fish’s space, which turns away and so on. So in fact when these schools seem to change direction instantaneously it is really a very high speed domino effect. We have added a very strong, short-range repulsive force to the fish’s velocity update function based on the distance to near by fish. This serves to fulfill the basic requirement for swarm intelligence that it is good to increase the number of detectors and be able to communicate detections. It also allows for the resolution of the PSO to be set, since the closest any fish will ever come to another fish is fixed by this force.
Now, using the shark agents, we have increased the entropy of the system and found a way to map the distribution of the optima of the space. Another advancement we have made over the standard PSO is to add several schools of fish agents. To continue the metaphor this is akin to having several species of fish searching for food and avoiding predators within our space. As birds of a feather tend to flock together,
76 so in our simulation fish of a scale tend to school together. In order to accomplish this separation by species we have introduced two more forces into the fish agents’ velocity update function: 1) fish experience a medium strength, long-range attractive force toward fish of their own school, 2) fish experience a low strength, medium range repulsive force toward fish of other schools. These forces act to separate out fish by school and lead to each school finding a different optimum, since one school will not settle where another school already is. Because each school will find different optimum the global best for each school may give the location of not the best optimum, but the location of the top set of optima, quality which can be directly overlaid with the map of the space provided by the shark location.
An addition benefit to having multiple schools of fish agents which tend to converge at different optima is to spread out the shark agents. If all of the fish agents were converging to one solution then all of the sharks would converge there as well until the optimum was completely covered with sharks agents that were bond to the location, then the fish would be forced to another optimum where the sharks would converge on until that optimum was also covered with bound sharks, and so on. With multiple schools of fish some of the sharks are likely to move toward one school of fish, while some others towards another school, and so on. This results in a faster mapping of the space.
77 6.3.1 The Algorithm
Simple-Modified-PSO()
1 //Initialize the agents
2 for each i
n 3 do Set agent’s velocity: ~vi ← Random(R )
n 4 Set agent’s position: ~xi ← Random(R )
5 if fish type agent
~ 6 then Set agent’s best: Ai ← ~xi
7 Set global best: G~ ← min fAi 8 //Update each agent
9 while Stop condition not met. for each i
10 do if F ish
11 then Create two random vectors: ~rA, ~rG ← Random[0 → 1]
12 Update “fish” agent’s velocity:
nh ~ ~i 13 ~vi ← ω~vi + CG ~rG × ~xi − G + CA ~rA × ~xi − A + " # X C my-swarm C C C 14 − other-swarms − other-fish − shark 2 3 4 (~x − ~x ) j (~xi − ~xj) (~xi − ~xj) (~xi − ~xj) i j 15 else Update“shark” agent’s velocity:
16 if Distance to fish is ≤ 0.5
17 then ~vi ← ω~vi + β|~xi − close~x f ish|
18 else ~vi ← ω~vi
19 Update agent’s position: ~xi ← ~xi + ~vi
78 20 Update agent/global best:
21 if Fish
~ 22 then if f (~xi) < f Ai
~ 23 then Ai ← ~xi
~ 24 if f (~xi) < f G
~ 25 then G ← ~xi
26 for each swarm
27 do return G~
28 //Enter location of “sharks” into array, “ SHARK ”
29 for each shark
30 do [ SHARK ] ← ~xi
31 return SHARK
The Modified-PSO algorithm works as follows:
(3) for each of i agents assign a random velocity vector, who’s components ∈ Rn.
(4) for each of i agents assign a random position vector, who’s components ∈ Rn.
(6) for each of i “fish” agents assign it’s current position as the agent’s best position
(in this case the minimum).
(7) find the global best by finding the minimum f evaluated at each “fish” agent’s ~xi.
(9) here we start a loop that will be executed for each agent until a stop condition is met22. 22The stop condition can be a number of things: Stop after so many iterations, Stop after so many
79 (10) if the current, ith, agent is a “fish” type agent then update its velocity by:
(11) for each “fish” agent get two random numbers between 0 and 1.
(13)for each “fish” agent update the velocity23 this is the same update function as in the standard PSO:
(13a) multiple the current velocity by some scaling constant ω.
(13bi) scale the constant CG by the random value between [0,1]
(13bii) find the distance the agent is from the global best
(13biii) take the vector product of (10bi) and (10bii).
(13ci) scale the constant CA by the random value between [0,1]
(13cii) find the distance the agent is from it’s best
(13ciii) take the vector product of (10ci) and (10cii).
(13d) sum 13a, 13b, 13c.
(14)here we add four additional terms to the velocity24. Note the summation is over j which refers to agent (of the appropriate type) except the ith agent for which the velocity is currently being updated.
(14a)this is the only positive part of the summation. Here we find the quotient of seconds, Stop when some degree of convergence has been met. 23 ω, CG, and CA are all user definable constants, optimal values of which will often dramatically change the rate of convergence 24 Cmy-swarm, Cother-swarms, Cother-fish, and Cshark are all user definable constants, these values will effect many aspects of the swarm behavior such as: how quickly each swarm will converge to a group, how close agents from one swarm will get to agents from another, the resolution in the algorithm, and how often “sharks” are able to “catch fish”, respectively
80 the constant, Cmy-swarm, and the square of the separation distance between the current
“fish” agent and all other “fish” agents.
(14b-d)these next three terms either slow down the velocity of the agent, or cause it to move away from where it would have been going in the standard PSO.
(14b)find the quotient of the constant Cother-swarms, and the cube of the separation distance between the current “fish” agent and all other “fish” agents.
(14c)find the quotient of the constant Cother-fish, and the fourth power of the separation distance between the current “fish” agent and all other “fish” agents.
(14d)find the quotient of the constant Cshark, and the separation distance between the current “fish” agent and all the “shark” agents.
(14e)sum 14a, 14b, 14c, 14d.
(15)if the current, ith, agent is not a “fish” type agent then it must be “shark” type, then update its velocity by:
(16)if there is a fish who’s distance is less than 0.5 (arbitrary units) then:
(17)for each “shark” agent update the velocity25:
(17a)multiple the current velocity by some scaling constant ω
(17b)find the product of the constant β and the magnitude of the separation distance between the “shark” and the “fish” agents.26
25β is a user definable constant, this constant will help determine how often the “shark” agents will be able to “catch fish” agents 26 Note that since |~xi − close~x f ish| is guaranteed to be less than or equal to 0.5, the term will never 1 contribute more than β. Also note that as the “shark” agent approaches the “fish” agent the rate 2 of change of velocity (i.e. the acceleration) will decrease.
81 (17c)Sum 17a and 17b
(18) if there is no “fish” who is within 0.5 then, the velocity simply changes by a constant factor.
(19) for each agent update its position. Note that since each time-step is equivalent, and arbitrary, for each particle we set the time-step to unity so the value of the velocity can simply be added directly to the position without loss of generality.
(21) only update the agent/global best if the agent is “fish” type.
(22) check if agent’s best need to be updated:
(23) if the agent’s best needs to be updated then update here.
(24) if the agent’s best needed to be updated check if the global best needs to be updated, if the agent’s best was not updated this step will not be executed.
(25) if the global best needs to be updated then update here.
(26) the stop conditions of the while loop has been met.
(27) each swarm will have its own global best, return each one.
(30) record the location of each “shark” in the array [SHARK].
(31) return the array [SHARK].
82 Conclusion
7.1 PAH
The observations made at Mauna Kea have proved interesting but inconclusive. UIB emission was only detected in two of the eight observed objects; thus distinguishing between competing PAH formation mechanisms is not practical. We find in the post-
AGB object CY CMi that the UIB emission is certainly not class A PAH emission, but nether did it fall cleanly into class B or C. It may be that the emission of this object is in a transition between these, artificial, classes and as such it should continued to be observed. As to the strength of the UIB emission in each of the two directions measured they are nearly identical. However since this object has a hard radiation
field we cannot conclude that this is the result of large PAHs, to do that we would need to find the ratio of the strength of the 3.3-to-11.25 µm features and so need to
83 obtain good data from NIRI.
Unexpected results came from four C-star which all exhibited emission around 8.5 and 11.3 µm which may be due to amorphous SiC. The very interesting finding was the change in the spectrum of Y Cvn from when it was observed more than 10 years ago by Speck et al. (1997). These changes mostly followed the predicted evolution of such an object by Speck et al. (2005). For this reason Y Cvn should also continue to be observed to see if these changes continue. We did not detect UIB emission from
V767 Mon, which with a companion of spectral type A6, should be show these features unless they are not there or in someway being masked.
7.2 PSO
Here there are not many conclusions to be drawn. The PSO is an excellent algorithm to use when a function needs to be optimized. The work seems to have much promise in searching through the ever increasing amount of astronomical data. The future challenges lie in producing fitness functions for the needs of the community, so data sets can be searched with ease. Other advancements have been made in addition to the modifications demonstrated here which result in more efficiency in searching a space and better scalability to ever larger sets of data.
84 References
Allain,E., Sedlmayr, E., Leach, S., 1997, A&A, 323, 163
Allamandola, L.J., Hudgins, D.M., Sandford, S.A., 1999, ApJ, 511, L115
Allamandola, L.J., Tielens, A.G.G.M., Barker, J.R., 1985, ApJ, 290, L25
Bernstein, L.S., Lynch, D.K., 2009, ApJ, 704, 226B
Boersma, C., Hony, S., Tielens, A.G.G.M., 2006, A&A, 447, 213
Buss, R.H., Tielens, A.G.G.M., Snow, T.P. 1991, ApJ, 372, 281
Cherchneff, I., 1995, Ap&SS, 224, 379
Cherchneff, I., Cau, P., 1999, IAUS, 191, 215C
Dominy, J.F., 1984, ApJs, 55, 27
Draine B.T., 2003, ARA&A, 341, 241
Draine, B.T., Li, Aigen, 2001, ApJ, 551, 807
Geballe, T.R., Tielens, A.G.G.M., Allamandola, L. J., et al. 1989, ApJ, 341, 278
Gillett, F.C., Forrest, W.J., Merrill, K.M., 1973, ApJ, 183, 87
Joblin, C., Tielens, A.G.G.M.,Allamandola, L.J., Geballe, T., 1996, ApJ, 458, 610
85 Jones, A.P., Duley, W.W., Williams, D.A., 1990, QJRAS, 31, 567
Justtanont, K., Barlow, M.J., Skinner C.J., Roche P.F., Aitken D.K., Smith C.H.,
1996 A&A, 309, 612
Kennedy, J., Eberhart, R., 1995, Proceedings of IEEE International Conference on
Neural Networks, 5, 1942
Leger, A., Puget, J.L., 1984, A&A, 137, L5
Li, A., Draine, B., 2002, ApJ, 572, 232
Papoular, R., Breton, J., Gensterblum, G., Nenner, I., et al. 1993, A&A, 270, L5
Peeters, E., Hony, S., Van Kerckhoven, C., Tielens, A.G.G.M., 2002, A&A, 390, 1089P
Scott, A. 1997, Ph.D. thesis, Univ. Waterloo
Sloan, G.C., et al. 2007, ApJ, 664, 1144
Speck, A.K., Barlow, M.J., 1997, Ap&SS, 251, 115
Tielens, A.G.G.M., Hony, S., van Kerckhoven, C., Peeters, E., 1999, ESASP, 427, 579
Uchida, K.I., Sellgren, K., Werner, M. 1998, ApJ, 493, L109
Waelkens, C.L., Waters, L.B.F.M., 1987, IAUS, 122, 509W
86