A Study of the Molecular Make up of Sakurai's Object

A STUDY OF THE MOLECULAR MAKE UP OF SAKURAI’S OBJECT USING ALMA

A thesis submitted to the University of Manchester for the degree of Master of Science in the Faculty of Science and Engineering

November 2020

By Phoebe Stainton School of Physics and Astronomy Contents

Abstract 11

Declaration 12

Acknowledgements 15

1 Stellar Evolution 16 1.1 Motivation ...... 17 1.2 Overview of Evolution from the Main Sequence to the White Dwarf Phase ...... 18 1.2.1 Low Mass Stars ...... 18 1.2.2 Low and Middle Intermediate Mass Stars ...... 21 1.3 AGB Evolution ...... 23 1.3.1 Low Mass and Lower Intermediate Mass Stars . . . . 24 1.3.2 Middle Intermediate Mass Stars ...... 25 1.4 Nuclear Reactions During Stellar Evolution ...... 27 1.4.1 Nucleosynthesis in Low Mass Stars ...... 27 1.4.2 Nucleosynthesis in Lower Intermediate Mass Stars . . 29 1.4.3 Nucleosynthesis in Middle Intermediate Mass Stars . 33

2 1.5 Convection and Dredge Up ...... 35 1.5.1 Convection in Low Mass Stars ...... 35 1.5.2 Convection in Low and Middle Intermediate Mass Stars 35 1.5.3 Dredge Up Processes ...... 36 1.6 Post- AGB Evolution and Very Late Thermal Pulses . . . . 40 1.6.1 Very Late Thermal Pulses ...... 40 1.6.2 Post-AGB Evolution in Low and Low Intermediate Mass Stars ...... 41 1.6.3 Post-AGB Evolution in Middle Intermediate Mass Stars ...... 43 1.7 Mass Loss ...... 44 1.7.1 Mass Loss Through Stellar Winds ...... 44 1.7.2 Mass Loss Through Superwinds ...... 46 1.7.3 Mass Loss Models ...... 47 1.8 Shaping of Nebulae ...... 49 1.9 Sakurai’s Object ...... 51

2 Interferometry 56 2.1 Background to Interferometry ...... 57 2.2 The Process of Interferometry ...... 58 2.3 Deconvolution ...... 64 2.3.1 The Högbom CLEAN Algorithm ...... 65 2.3.2 The Clark Algorithm ...... 67 2.3.3 Cotton-Schwab Algorithm ...... 68 2.4 Emission and Absorption from the Atmosphere ...... 70 2.5 The Effects of Baselines on Resolution ...... 71 2.6 The Effects of Baselines on Image Quality ...... 72

3 3 ALMA and Atomic Physics 73 3.1 ALMA ...... 74 3.1.1 Background to ALMA ...... 74 3.1.2 The Scientific Goals of ALMA ...... 75 3.1.3 The Effects of Baselines on ALMA ...... 76 3.2 Atomic Physics ...... 78 3.2.1 Fine Structure: Relativistic Correction ...... 78 3.2.2 Relativistic Energy Correction ...... 79 3.2.3 Fine Structure: The Spin-Orbit Interaction ...... 82 3.2.4 Fine Structure: Combining Relativistic Corrections and the Spin-Orbit Interaction ...... 85 3.2.5 Hyperfine Structure ...... 85 3.2.6 The Effects of Fine and Hyperfine Structure on this Research ...... 86 3.2.7 Example for Carbon ...... 87

4 Data Collection 89 4.1 Making Image Cubes ...... 91 4.1.1 The Continuum Images ...... 91 4.2 The Resolved Nature of Sakurai’s Object ...... 96 4.3 Producing Spectra ...... 98 4.4 Identifying Spectral Lines ...... 100 4.5 Analysing the Spectral Lines ...... 106 4.6 Additional Line Searches ...... 116

4.6.1 HC5N...... 116 4.7 Final Identiﬁcations ...... 120

4 5 Astrochemistry 121 5.1 Environments in Space ...... 122 5.1.1 Diﬀuse Interstellar Medium ...... 122 5.1.2 Circumstellar Medium ...... 122 5.1.3 Giant Molecular Clouds ...... 122 5.2 Synthesis and Ionisation in Space ...... 124 5.2.1 Molecular Synthesis ...... 124 5.2.2 Ionization ...... 124 5.3 Gas Phase Chemical Reactions in Space ...... 126 5.3.1 Bond Formation Reactions: Radiative Association . . 126 5.3.2 Bond Formation Reactions: Associative Detachment 127 5.3.3 Bond Formation Reactions: Dust-Grain-Catalysed Reaction ...... 127 5.3.4 Bond Breaking Reactions: Photodissociation and Col- lisional Dissociation ...... 128 5.3.5 Bond Breaking Reactions: Dissociative recombination 128 5.3.6 Rearrangement reactions: Charge transfer ...... 129 5.3.7 Rearrangement Reactions: Neutral reactions . . . . . 129 5.3.8 Rearrangement Reactions: Ion-molecule reactions . . 129 5.4 Chemistry in Molecular Clouds ...... 131 5.5 Chemistry in Circumstellar Envelopes ...... 132 5.6 Astrochemical Modelling ...... 133 5.6.1 Background to the UMIST Database for Astrochem- istry ...... 133 5.6.2 Background to the Dark Cloud Chemical Model . . . 134 5.6.3 Using the Dark Cloud Chemical Model ...... 136

5 5.6.4 Testing Molecular Carbon ...... 139 5.6.5 Testing Ionic Carbon ...... 143 5.6.6 Testing the Visual Extinction and UV Radiation Field Scaling Factor ...... 145 5.6.7 Limits of the Dark Cloud Chemical Model ...... 147 5.7 RADEX ...... 149 5.8 The Online Version of RADEX ...... 150 5.8.1 Calculating Input Values for the Online Version of Radex ...... 150 5.8.2 Using the Online Version of RADEX ...... 152 5.8.3 Results from the Online Model ...... 153 5.9 The RADEX Source Code ...... 154 5.9.1 Making RADEX Input Files ...... 156 5.9.2 Determining Parameters for Carbon Monoxide Input Files ...... 157

5.9.3 Determining Parameters for HC3N Input Files . . . . 158 5.9.4 Using the RADEX Source Code ...... 158 5.9.5 Limits of the RADEX Source Code ...... 160 5.10 The Final Model and the Time Evolution of Sakurai’s Object162 5.11 Discussion of the Model Results ...... 165

6 Conclusions 170 6.1 Further Work ...... 173

6 List of Tables

4.1 Details of the ALMA Data Sets ...... 90 4.2 Details of the Continuum Images Produced in CASA . . . . 94 4.3 Details of the Bounding Ellipses used in CASA ...... 98 4.4 Initial Line Identifications ...... 103 4.5 Peak Flux ± 3σ, Noise, and Frequency Range Data for Initial Line Identifications ...... 104 4.6 Initial Line Identifications ...... 105 4.7 Additional CN Lines for Spectral Window 8 Band 7 . . . . . 115 4.8 Details of the Additional Lines for Spectral Window 5 Band 6117 4.9 Details of the Additional Lines for Spectral Window 16 Band 6118

5.1 Input abundances for the ﬁrst test models ...... 136 5.2 Input values for test models with a constant C:O ratio . . . 138

5.3 Fractional Output Abundances for HC3N and HC5N..... 139 5.4 Input values for the molecular carbon models ...... 140 5.5 Output Fractional Abundances for Molecular Models . . . . 141 5.6 Input values for the ionic carbon models ...... 144

5.7 HC3N and HC5N output abundances for ionic models . . . . 144 5.8 Details of the Output Values at Diﬀerent Times ...... 159 5.9 Details of the Input Values for the Final Model ...... 162

7 List of Figures

1.1 The interior of an AGB star showing the separation between the layers. (adapted from Lamers and M. Levesque (2017)) . 23 1.2 The three proton-proton chains used for nuclear fusion. PPI produces helium, and PPII and PPIII produce lithium and beryllium (Adelberger et al. (2011)) ...... 27 1.3 The NeNa cycle shown in context with the CNO cycle and MgAl cycle. Orange indicates short lived nuclei, whilst green nuclei are stable and long lived. 26Al is long lived in its ground state but will quickly decay in 26Mg when in its metastable state. (Boeltzig et al. (2016)) ...... 31

2.1 A schematic of a radio interferometer consisting of two dishes pointed at a source...... 59

3.1 The Atomic Levels of Carbon with the Fine and Hyperﬁne Splitting ...... 88

4.1 A CASA FITS Image of the Continuum for the 2017 Data. The oval in the bottom left hand corner shows the beam size 92 4.2 A CASA FITS image of the continuum for band 6 from the 2014 data ...... 93

8 4.3 A CASA FITS image of the continuum band 7 from the 2014 data. This image does not include spectral windows 4 or 5 . 94 4.4 A UV Distance vs Amplitude Plot for all Spectral Windows in the 2017 Data Set ...... 97 4.5 Spectral Window 25 in velocity space with respect to the identiﬁed H13CN line ...... 106 4.6 Spectral Window 31 in velocity space with respect to the identiﬁed HNC line ...... 107 4.7 Spectral Window 31 in velocity space with respect to the

identiﬁed HC3N line ...... 107 4.8 Spectral Window 2 Band 6 in velocity space with respect to

the identiﬁed HC3N line ...... 108 4.9 Spectral Window 3 Band 6 in velocity space with respect to the identiﬁed CO line ...... 108 4.10 Spectral Window 5 Band 6 in velocity space with respect to

the HC3N line ...... 109 4.11 Spectral Window 5 Band 6 in velocity space with respect to the 13CN line ...... 109 4.12 Spectral Window 10 Band 6 in velocity space with respect

to the HC3N line ...... 110 4.13 Spectral Window 16 Band 6 in velocity space with respect to the CN line found in the absorption feature ...... 110 4.14 Spectral Window 1 Band 7 in velocity space with respect to

the HC3N line ...... 111 4.15 Spectral Window 7 Band 7 in velocity space with respect to the 13CO line ...... 111

9 4.16 Spectral Window 8 Band 7 in velocity space with respect to the CN line ...... 112 4.17 Spectral Windows 31 and 5 Band 6 in velocity space with

respect to HC3N...... 117

5.1 Time Evolution of Sakurai’s Object as Predicted by Model 10142 5.2 Time Evolution of Sakurai’s Object as Predicted by Model 11143 5.3 Time Evolution of Sakurai’s Object as Predicted by the Fi- nal Model ...... 162 5.4 Time Evolution of HCN, HNC, and CN ...... 163

10 Abstract

This work will aim to use the abilities of ALMA, the UDfA Dark Cloud model, and RADEX to determine likely molecules in Sakurai’s Object and attempt to predict a possible evolutionary path. From ALMA observations

13 it can be concluded that HC3N, CO, CO, and HNC are abundant. Models made using the UDfA Dark Cloud Model suggest these abundances are likely to increase. Whilst it was possible to ﬁnd an evolutionary model, the fast evolution of Sakurai’s Object means that it is likely to need adjustments as more observations are taken, meaning this research provides a foundation for a signiﬁcant amount of further work. Work with RADEX suggest that the temperature of Sakurai’s Object may sit at approximately 20K, and that some lines - such as CO - may be optically thick.

11 Declaration

No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualiﬁcation of this or any other university or other institution of learning.

12 Copyright

i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the Intellectual Property) and any reproductions of copyright works in the thesis, for example graphs and tables (Re- productions), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions.

13 iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://www.campus.manchester.ac.uk/medialibrary/ policies/intellectual- property.pdf), in any relevant Thesis restriction decla- rations deposited in the University Library, The University Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in The University’s policy on presentation of Theses.

14 Acknowledgements

I would like to thank my supervisor, Professor Albert Zijlstra, and my co- supervisor, Dr. Iain McDonald, for their continued direction and support. Thanks must also go to Dr Adam Avison and Dr George Bendo from the ALMA regional team who were kind enough to give up their time to teach me. I must of course thank my parents, Sally and Alan, my brother, Harry, and my partner, Harris, for their continued love and encouragement. This would not have been possible without you all.

15 Chapter 1

Stellar Evolution

16 CHAPTER 1. STELLAR EVOLUTION 17

1.1 Motivation

Since its discovery in 1996, Sakurai’s Object has posed many interesting questions. The primary focus of this work is to establish what molecules are currently present in the spectrum of Sakurai’s Object, as this may provide an insight into its current stage of evolution, how quickly it has evolved up to this point, and what stages it may evolve through next. This work will aim to use data from ALMA observations and the computational capacities of CASA to determine what molecules are in the spectrum produced by Sakurai’s Object. This information will then be used to create chemical models using the dark cloud code from the UMIST Database for Astrochemistry (UDfA). These models will provide insight into how the abundances of molecules will change over time, as well as allowing for a range of inital conditions to be tested. Finally, these chemical models will be used in RADEX in an attempt to analyse physical properties such as line strengths. With this information, it may be possible to improve upon current evolutionary models, especially if more insight is gained into the process before, during, and after a VLTP. CHAPTER 1. STELLAR EVOLUTION 18

1.2 Overview of Evolution from the Main

Sequence to the White Dwarf Phase

Stars can be categorised by their mass using the criteria utilised by Karakas and Lattanzio (2014). Low mass stars are deﬁned by as having a mass

within the range 0.8M and 2M , lower intermediate mass stars fall in the range 2 and 7M , and middle intermediate mass stars have masses between

7 and 9.5M . The evolutionary paths described below assume that the star is either alone, or has only insigniﬁcant interactions with any companion stars.

1.2.1 Low Mass Stars

All stars will undergo a main sequence phase where hydrogen is synthesised into helium in the core, but in cooler regions outside the core, rarer isotopes such as helium-3 and carbon-13 can be produced (Karakas and Lattanzio (2014)). The energy produced in all these reactions is transported to outer layers of the star by radiation. Low mass stars use the proton-proton (or PP) chain to synthesise their helium (Campbell et al. (2010)). As the main sequence progresses, the core becomes depleted in hydrogen and is now helium rich (Karakas and Lattanzio (2014)). Whilst hydrogen burning in the core ceases, it continues in a thin shell surrounding the core, keeping the core and envelope separate (Karakas and Lattanzio (2014)).

At this point, it is important to consider the Schönberg-Chandrasekhar limit. This the maximum mass for an isothermal core that is not undergoing fusion but is still supporting its envelope. At the start of hydrogen CHAPTER 1. STELLAR EVOLUTION 19 shell burning, the cores of low mass stars are still below the Schönberg- Chandrasekhar limit, and consist of cold, dense gas where most of the pressure is supplied by degenerate electrons. As the hydrogen shell produces new helium via the CNO cycle, the helium is “dumped” onto the core below (Chieffi et al. (2001)), increasing its mass beyond the Schönberg- Chandrasekhar limit. Once the core has exceeded the limit, the core slowly contracts and develops a steep temperature gradient. Due to the high temperature sensitivity of the CNO cycle, the rate of fusion in the hydrogen shell increases, thus increasing the amount of energy being produced, which leads to an increase in stellar luminosity. However, the increase in luminosity is limited by the expansion of the envelope, which must be done to conserve gravitational potential energy (Chieffi et al. (2001)). At this point, the star is beginning its ascent of the red giant branch (RGB).

During the ascent of the RGB, low mass stars will return to thermal equilibrium and convective stability, allowing the convective envelope to extend further into the star from the surface to just outside the hydrogen burning shell. This will enable the star to undergo the ﬁrst dredge up, where unprocessed products from the surface are brought down into the star by convection to be processed (Campbell et al. (2010)). At the same time, already processed material will be brought to the surface (see section for 1.5.3 full details).

As the star continues ascending the RGB, the pressure and temperature will continue to increase. However, the temperature rise in these stars is impeded by neutrino emission (Campbell et al. (2010)). The core material will become strongly degenerate before helium burning can occur, which is important as nuclear burning in a degenerate material is thermally unstable CHAPTER 1. STELLAR EVOLUTION 20 and will cause thermonuclear runaway (Chieffi et al. (2001)). This occurs when the energy released by hydrogen burning increases the temperature, which in turn causes an increase in the rate of hydrogen burning that cannot be controlled. In the case of low mass stars, this runaway causes an explosive, off centre ignition of helium within the core, which is commonly referred to as a helium core flash (Dearborn et al. (2006)) and signals that the star is near the end of its evolution on the Red Giant Branch.

The helium core ﬂash will occur when the core of the star is at around

0.5M , and the temperature will rise drastically over a period of a few seconds. During this increase in temperature, the density will remain almost constant, and a large amount of energy is produced via the triple alpha process (Campbell et al. (2010)). However, the majority of the energy is absorbed by the envelope or used to lift core degeneracy, quenching the process and making it difficult to observe. The core temperature will now be high enough to remove the degeneracy of the gas, allowing the core to expand and create a stable environment for helium burning. As the core expands, the envelope must contract, which causes the temperature of the envelope to rise (Karakas and Lattanzio (2014)) and the temperature of the hydrogen burning shell to decrease. The temperature decrease in the shell reduces the reaction rate, and therefore decreases the rate of energy production. Combined with the decrease in radius, this causes the luminosity of the star to drop. The star will now move onto the horizontal branch, where it will burn helium in its core via the triple alpha process (Chieffi et al. (2001)). Eventually, the helium in the core will become exhausted and the star will move onto the asymptotic giant branch (ABG) (Chieffi et al. (2001)). CHAPTER 1. STELLAR EVOLUTION 21

1.2.2 Low and Middle Intermediate Mass Stars

Unlike low mass stars, low and middle intermediate mass stars on the main sequence will process hydrogen via the CNO cycle (Karakas and Lattanzio (2014)). This has a temperature dependency proportional to T16−20, which is signiﬁcantly higher than the dependence of T4 of the PP chain (Karakas and Lattanzio (2014)). The higher temperature dependence of the CNO cycle means that stars using this process have steep energy gradients, which cause the star to have a convective core and a radiative envelope (Karakas and Lattanzio (2014)). The composition of the core is uniform because of the continuous mixing within, which balances out any non-uniformities induced by nuclear reactions.

Another diﬀerence between low mass stars and intermediate mass stars is that intermediate mass stars do not undergo a core helium ﬂash. This is because the cores of these stars are not degenerate, so helium will be gently -rather than violently- ignited when their cores reach 108K (Chiosi (1997)) and can begin the triple alpha process. Once helium has been ignited, it will continue to burn in the convective core of the star. Hydrogen burning will continue in a shell surrounding the core, and this shell will provide most of the luminosity (Karakas and Lattanzio (2014)).

Inside the helium core, helium is fusing into carbon via the reaction:

4 4 4 12 2He +2 He +2 He −→6 C + γ (1.1) which releases 7.275MeV of energy. This carbon is then processed in the reaction:

12 4 16 6 C +2 He −→8 O + γ (1.2) CHAPTER 1. STELLAR EVOLUTION 22 which releases 7.162MeV of energy and increases the abundance of oxygen (Karakas and Lattanzio (2014)). As the energy produced by these reactions is signiﬁcantly less than the 26.73MeV produced when hydrogen in fused into helium via the proton-proton chain, the period of core helium burning is signiﬁcantly shorter. Also, by fusing helium into carbon and then oxygen, a discontinuity in opacity has been formed at the edge of the convective core (Castellani et al. (1971)). This means that there is no stable point at the edge of the core, allowing the convective core to grow (Karakas and Lattanzio (2014)). As the rate of helium burning increases, the rate of hydrogen burning in the shell will decrease, causing the temperature of the shell to drop. As this shell is at the base of the envelope, the envelope begins to cool and contract, and the star leaves the RGB for the AGB. CHAPTER 1. STELLAR EVOLUTION 23

1.3 AGB Evolution

When stars reach the AGB they have an electron degenerate CO core surrounded by a helium burning shell (Karakas and Lattanzio (2014)). The helium burning shell provides most of the energy as the electron degeneracy slowly increases within the core. Above the helium burning shell is a layer of helium commonly known as the intershell region, and this sep- arates the helium burning shell from the hydrogen burning shell (Becker and Iben (1979)).The hydrogen burning shell is at the base of the hydrogen rich envelope.

Figure 1.1: The interior of an AGB star showing the separation between the layers. (adapted from Lamers and M. Levesque (2017)) CHAPTER 1. STELLAR EVOLUTION 24

1.3.1 Low Mass and Lower Intermediate Mass Stars

In both low and lower intermediate mass stars, the hydrogen burning shell produces helium, which is “dumped” onto the helium layer below, increasing its mass (Chiosi (1997)). The helium shell below will convert helium from the helium layer into carbon and oxygen, which can then be dumped onto the CO core, increasing its mass (Chiosi (1997)). As the star evolves up the AGB, the helium shell begins to run out of fuel and becomes thin- ner. This leads it to become thermally unstable (Chieﬃ et al. (2001)). Eventually, this thermal instability leads to a thermal pulse, during which helium is violently burned in a poorly controlled reaction (Karakas and Lat- tanzio (2014)). At this point, the star has left the early AGB phase and has entered the thermally pulsating AGB phase (TP-AGB phase). Ther- mal pulses are now able to occur repeatedly in the star (Schwarzschild and H¨arm(1965)).

During the TP-AGB, there are long periods of quiet hydrogen shell burning, known as the interpulse phase, punctuated by thermal pulses due to instabilities in the helium burning shell (Karakas and Lattanzio (2014)). The explosive burning of helium during the pulse can produce a convective region that will begin in the helium burning shell and extend through the helium intershell to just below the hydrogen burning shell (Karakas and Lattanzio (2014)). However, as the pulse is short lived, this convective region is not permanent, and it will gradually get smaller as the pulse weak- ens. This is called the power down phase (Karakas and Lattanzio (2014)). Whilst in the power down phase of the pulse, much of the energy produced will be absorbed by the overlying layers, causing them to expand and cool (Chieffi et al. (2001)). This will “switch off” the hydrogen burning shell CHAPTER 1. STELLAR EVOLUTION 25 and allow the third dredge up to occur (see section 1.5.3). This will cause carbon to be brought to the surface, causing the carbon abundance in the envelope to rise (Chieffi et al. (2001)).

After the third dredge up, the star will slowly begin to contract, decreasing in radius whilst increasing in temperature (Karakas and Lattanzio (2014)). This reignites the hydrogen burning shell, which will burn in a stable man- ner due to its low sensitivity to temperature. This marks the beginning of a new interpulse phase, and the thermal pulse cycle can now repeat (Karakas and Lattanzio (2014)). Thermal pulses repeat with a period of roughly 10,000 years (Herwig (2005)), driving the TP-AGB phase and causing the CO core to grow with each pulse.

1.3.2 Middle Intermediate Mass Stars

Middle intermediate mass stars are able to ignite carbon oﬀ centre under degenerate conditions, meaning that they will undergo evolution on the “super-AGB” (Karakas and Lattanzio (2014)). The ignition of carbon will occur when the temperature of the star reaches roughly 600-650MK. At this point, middle intermediate mass stars will have a convective shell that begins at the point of carbon ignition and extends outwards (Karakas and Lattanzio (2014)). As the carbon fuel is depleted, the rate of carbon burning will begin to slow, allowing the star to begin to contract (Karakas and Lattanzio (2014)). This causes secondary convection zones to be formed, allowing carbon burning to move to the centre of the star and process all the remaining carbon (Karakas and Lattanzio (2014)). This will leave the star with a O-Ne core surrounded by an inactive CO shell, a helium burning shell, a hydrogen burning shell, and a convective envelope (Karakas and CHAPTER 1. STELLAR EVOLUTION 26

Lattanzio (2014)).

When these stars reach the TP-AGB phase, they have a very similar evolution to low and lower intermediate mass stars. The main diﬀerence is that the thermal pulses seen in middle intermediate mass stars are not as strong as those in other types of stars (Karakas and Lattanzio (2014)). The thermal pulses in low and lower intermediate mass stars usually reach

8 luminosities of roughly 10 L (Karakas and Lattanzio (2014)), whereas those in middle intermediate mass stars are usually two orders of mag-

6 nitude lower, reaching luminosities of roughly 10 L (Siess (2007), Siess (2010)). The pulses in super-AGBs also have a shorter duration and repeat roughly every 100 years (Karakas and Lattanzio (2014)). CHAPTER 1. STELLAR EVOLUTION 27

1.4 Nuclear Reactions During Stellar Evo-

lution

The nuclear reactions that occur in stars during their evolution provides many of the elements that we see on Earth. However, not all stars are able to synthesise every element, and in this section we will discuss the diﬀerent contributions made by each mass group.

1.4.1 Nucleosynthesis in Low Mass Stars

All stars will begin nuclear fusion by burning hydrogen into helium in their cores. Stars with masses of < 2M will burn their hydrogen via the various branches of the PP chains (Karakas and Lattanzio (2014)). The PP chains are illustrated below in Figure 1.2.

Figure 1.2: The three proton-proton chains used for nuclear fusion. PPI produces helium, and PPII and PPIII produce lithium and beryllium (Adel- berger et al. (2011))

During their AGB evolution, many stars will reach a temperature of 2.5 CHAPTER 1. STELLAR EVOLUTION 28 x 106K, allowing them to form lithium from the helium they have already synthesised. The main isotope of lithium seen in stars is 7Li, which is formed via a process known as the Cameron-Fowler Mechanism (Cameron and Fowler (1971)). This mechanism postulates that some 3He created during hydrogen burning will capture an alpha particle to become 7Be, which can then capture an electron to produce 7Li (Cameron and Fowler (1971)). The ﬁrst stage of the process, which is also known as the PPII chain, can be written as:

3 7 2He + α −→4 Be + γ (1.3) and the second stage can be written as:

7 − 7 4Be + e −→3 Li + νe (1.4)

Alternatively, after the ﬁrst stage the beryllium can be used in the PPIII chain, the reactions for which are illustrated in Figure 1.2. Once there is no 3He left in the envelope, the production of 7Li is forced to stop, as there is no other source of 3He.

Stars can also produce 6Li, but this is highly unstable and soon reacts. The ﬁrst reaction is:

6 7 p +3 Li −→4 Be. (1.5)

The beryllium then undergoes the reaction: CHAPTER 1. STELLAR EVOLUTION 29

7 − 7 4Be + e −→3 Li + ν (1.6) which produces a stable isotope of lithium. However, this lithium can still react with a free proton in the reaction:

7 8 3Li + p −→4 Be (1.7)

4 to give an unstable isotope of beryllium which will decay to form 2 2He, releasing energy in the process.

It is currently unclear how much 7Li low and intermediate mass stars contribute to the galaxy (Romano et al. (2001); Travaglio et al. (2001)), but Prantzos (2012) concluded that nucleosynthesis from the Big Bang could have contributed a maximum of 30% of solar lithium, and other sources, such as AGBs or novae, must have contributed at least 50%. However, observations of stellar yields (Karakas (2010b)) show that only a small number of intermediate mass AGBs produce more lithium than they destroy. For there to be a net production of lithium, hot bottom burning (see section 1.4.2) must take place during the period of highest mass loss (Karakas and Lattanzio (2014)) as this is the only way for the lithium to be removed from the star via winds before being destroyed.

1.4.2 Nucleosynthesis in Lower Intermediate Mass Stars

Lower intermediate mass stars will burn their hydrogen via the CNO cycle, which can be seen below in Figure 1.3, before continuing to undergo the fusion processes outlined above. The CNO cycle uses 4 hydrogen atoms in CHAPTER 1. STELLAR EVOLUTION 30

a series of 6 reactions to provide an atom of helium, along with maintaining levels of carbon, nitrogen, and oxygen within the star.

Both lower and middle intermediate mass stars over 4M can undergo a process called hot bottom burning (HBB) during their AGB or super AGB phase (Karakas and Lugaro (2016)). This process occurs at the base of the envelope (Lattanzio (1992)) which is near the top of the hydrogen burning shell (Karakas and Lattanzio (2014)). HBB occurs when the convective region of a star extends from the envelope into underlying layers, acquiring material from the region of the star that is undergoing nuclear fusion (Ventura et al. (2011)). The bottom of the convective region is now also undergoing nuclear fusion, including the NeNa cycle and the MgAl cycle (Karakas and Lattanzio (2014)). However, for these two cycles to work, the base of the envelope must reach temperatures of around 90MK to allow proton capture nucleosynthesis to occur (Karakas and Lattanzio (2014)).

The NeNa chain produces 23Na from 20Ne, with the 23Na being destroyed to release energy and return to 20Ne, thus beginning the cycle again (Karakas and Lattanzio (2014)). The rate at which 23Na is destroyed can be used to determine the yields of Na (Izzard et al. (2007)).

Another use for the 23Na produced in the NeNa cycle is the MgAl cycle. This process occurs in the helium shell via the triple alpha process (Ventura et al. (2011)) and it will eventually alter the abundances of magnesium and aluminium observed in the star (Karakas and Lattanzio (2014)). Figure 1.3 illustrates the reactions that occur in both the NeNa and MgAl cycles. CHAPTER 1. STELLAR EVOLUTION 31

Figure 1.3: The NeNa cycle shown in context with the CNO cycle and MgAl cycle. Orange indicates short lived nuclei, whilst green nuclei are stable and long lived. 26Al is long lived in its ground state but will quickly decay in 26Mg when in its metastable state. (Boeltzig et al. (2016))

Whilst all stars undergo thermal pulses, during which there are large amounts of nucleosynthesis, some of the most interesting processes occur in lower and middle intermediate mass stars. The main reactions are the triple alpha reaction:

4 12 32He −→6 C (1.8)

and the reaction:

12 16 6 C + α −→8 O + γ. (1.9)

The triple alpha reaction is the main energy source during thermal pulses as the other reaction requires a large quantity of spare 12C to be activated, so it is rarely producing energy during a pulse (Karakas and Lattanzio (2014)). These reactions mean that the composition of the intershell helium layer is altered, with 12C now making up around 20-25% of the intershell by mass, but 4He still makes up around 70-75% (Karakas and Lattanzio (2014)). The exact composition will depend on mass and composition of the intershell CHAPTER 1. STELLAR EVOLUTION 32

before the pulse, the duration of the pulse, and the peak temperature and density during burning (Karakas and Lattanzio (2014)). As these are all dependent on mass and/or metallicity, the composition is fundamentally dependent on these parameters. If these reach the required values, it is possible to create small amounts of 22Ne, 17O, 23Na, 25Mg, 26Mg, and 19F (Karakas and Lattanzio (2014)).

When low and middle intermediate mass stars undergo thermal pulses, the isotopic ratios that are observed will change. The 14N/15N ratio can be increased if mixing occurs that includes material that has seen at least some H burning, like material from the ﬁrst and second dredge ups (see section 1.5.3). This is because large amounts of carbon and oxygen are converted into nitrogen (Kotok (1967)), and some of this is dredged up to the surface before it can be used in other reactions. However, if the material hasn’t seen any H burning, such as that from the third dredge up (see section 1.5.3) the ratio is largely unchanged.

Fluorine is produced by reactions in the helium intershell, with the main one producing nitrogen that can be burnt via 15N(α, γ)19F (Forestini et al. (1992)). However, 15N is easily destroyed by proton capture in the CNO cycle, so it is diﬃcult to maintain enough 15N for ﬂuorine to be synthesised (Karakas and Lattanzio (2014)). This problem is mitigated if protons can be produced by other reactions such as 14N(n,p)12C (which itself requires free neutrons), then the CNO cycle reaction 18O(p, α)15N can produce enough 15N for 19F to be synthesised (Karakas and Lattanzio (2014)).

There is also some 23Na and 27Al in the intershells of stars, which was synthesised in the NeNa cycle and MgAl cycle (Karakas and Lattanzio (2014)). CHAPTER 1. STELLAR EVOLUTION 33

When the NeNa cycle occurs, the ﬁnal abundance of 22Ne is roughly 2% (Fujimoto and Sugimoto (1982)). If the temperature of the intershell rises

above 3×108K during the next thermal pulse, the reactions 22Ne(α,n)25Mg (Fujimoto and Sugimoto (1982)) and 22Ne(α,γ)26Mg will occur at similar rates in the helium shell (Angulo et al. (1999); Longland et al. (2012);

Wiescher et al. (2012)). The 22Ne(α,n)25Mg reaction is a major source of free neutrons for the synthesis of heavy elements by the s-process (Iben (1975); Wiescher et al. (2012)), but both of these reactions require very high temperatures that are not normally achieved by stars with a mass less than 4M (Karakas et al. (2006)). However, if temperatures get too high, it is possible to breakout of the Mg-Al cycle via 27Al(p,γ)28Si, which would cause there to be correlations between Al and Si (Ventura et al. (2011)).

1.4.3 Nucleosynthesis in Middle Intermediate Mass

Stars

The nucleosynthesis that occurs in middle intermediate mass stars is similar to that in low and lower intermediate mass stars. Middle intermediate mass stars will burn hydrogen into helium via the CNO cycle and will undergo HBB, the NeNa cycle, and the MgAl cycle. The main diﬀerence is that middle intermediate mass stars can have intershells with temperatures in excess of 400MK, and envelope bases with temperatures over 100MK (Karakas and Lattanzio (2014)). This means that all middle intermediate mass stars will undergo these processes, whereas only the heaviest lower intermediate mass stars will. Siess (2010) calculated that middle intermediate mass stars will produce detectable amounts of 13C, 14N, 17O, 22Ne, 23Na, CHAPTER 1. STELLAR EVOLUTION 34

25Mg, 26Mg, and 26Al through the CNO, NeNa, and MgAl cycles. CHAPTER 1. STELLAR EVOLUTION 35

1.5 Convection and Dredge Up

1.5.1 Convection in Low Mass Stars

As previously discussed, low mass stars burn their hydrogen using the PP chain, which has a temperature dependence of T4. This means that the rate of energy production is low, and so the energy will be transported away from the centre of the star via radiation, giving the star a radiative core (Palla and Stahler (1993)). These stars also have envelopes with temperatures cool enough to prevent hydrogen from being ionized, meaning high energy photons from deep within the star are absorbed by hydrogen when they reach the envelope. This increases the opacity of the envelope, making it convective (Guenther (2001)). The convective envelope of the star can now take unprocessed material (e.g. hydrogen and helium) down to hotter regions of the star to undergo nucleosynthesis. At the same time, processed material from the inner regions will be transported to the envelope, changing the observed chemical composition (Karakas and Lattanzio (2014)). This transportation process is known as a “dredge up”. The material dredged up from the star is vital for galactic chemical evolution, as it can be lost to the interstellar medium (ISM) via winds (Campbell et al. (2010)), where it will be used in the formation of new stars that will continue to produce more chemical elements.

1.5.2 Convection in Low and Middle Intermediate

Mass Stars

Stars with M ≥ 2M burn their hydrogen via the CNO cycle, forcing most of the nuclear burning to occur in the hotter central regions of the star CHAPTER 1. STELLAR EVOLUTION 36

(Guenther (2001)). The rate of energy production in the CNO cycle is so high that the star must use convection to remove the excess energy and remain in equilibrium, so the inner regions become convective (Guenther (2001)). The convective region extends from the area of the star where helium burning is taking place (usually the core) to near the base of the hydrogen burning shell (Guenther (2001)). This convective core can reach temperatures that enable the hydrogen burning shell to produce nitrogen from hydrogen (Chieﬃ et al. (2001)). The hydrogen burning shell is domi- nated by the CNO cycle, meaning the shell is hot enough to produce some carbon via the triple α process (Chieﬃ et al. (2001)). Some of this carbon is then burnt in a reaction that produces some nitrogen in the hydrogen burning shell, which allows for the continuation of the CNO cycle.

1.5.3 Dredge Up Processes

It is important to note that the names of the dredge ups are determined by the evolutionary state of the star, and not the order in which the star experiences them. This means that it is possible for a star to undergo the FDU and TDU, but not the SDU, as is the case with some lower mass stars.

The ﬁrst dredge up (FDU) happens as a star ﬁnishes its main sequence and enters the red giant branch (Karakas and Lattanzio (2014)). This dredge up takes material from the surface of the star into the hotter, central regions for nucleosynthesis via convection, whilst simultaneously transporting previously synthesised material to the surface (Karakas and Lattanzio (2014)). For the FDU, there is a decrease in both the 12C/13C and C/N ratios as the surface abundances of 13C and 14N increase (Carretta et al. (1998)). CHAPTER 1. STELLAR EVOLUTION 37

The surface abundance of 4He also increases, but the abundances of both lithium and beryllium decrease, and the abundance of 12C drops by around 30% (Karakas and Lattanzio (2014)). There will also be an increase in the abundance of 17O, but a decrease in the abundance of 18O, increasing the observed ratio of 17O/16O and decreasing the observed ratio of 18O/16O. This is due to the CNO cycle producing 17O but destroying 18O.

It is also noticeable that the 12C/13C ratios observed by Forestini and Char- bonnel (1997) and Karakas (2010a), both showed lower values than the authors had expected. The lack of 12C means that the rate of the reaction

12C(α, γ)16O is much lower than expected, and less oxygen is produced. This means that the intershell is only around 2% 16O (Boothroyd and Sackmann (1988)), which limits the amount of nucleosynthesis that can happen afterwards. However, if there is some convective overshoot at the inner border of the ﬂash driven convective zone, Herwig (2000) concluded that some carbon and oxygen from the CO core will be mixed into the intershell, giving abundances of roughly 40% for carbon and 20% for oxygen (Karakas and Lattanzio (2014)). This is particularly important for galactic chemical abundances as AGBs provide about one third of the 12C in the galaxy (Karakas and Lattanzio (2014)), with core collapse supernovae and Wolf-Rayet stars providing another third (Dray et al. (2003)).

The second dredge up (SDU) occurs at the end of core helium burning, providing that the star has a mass between 4M - 8M (Karakas and Lattanzio (2014)). As discussed previously, AGB stars undergo nuclear burning in 2 shells. The energy produced by these shells causes the outer layers of the star to expand and cool, producing a convective region that penetrates deep within the star (Chieﬃ et al. (2001)). Having already CHAPTER 1. STELLAR EVOLUTION 38

undergone a dredge up prior to reaching the AGB, stars with M > 4M will now undergo their SDU, which will increase the abundance of CNO products by penetrating much further into the star than the ﬁrst dredge up (Boothroyd and Sackmann (1999)). This causes the surface abundances of 4He and 14N to increase, and the abundances of 12C and 16O to decrease as they are taken deeper into the star (Charbonnel (1995)).

During the SDU, material is moved around the star for processing. In some stars the convection will end closer to the core than the helium burning shell, causing carbon, and sometimes oxygen, to be dredged to the surface (Doherty et al. (2014); Gil-Pons et al. (2013)) in a process called a dredge out. These dredge outs were first noted by Ritossa et al. (1996), and show hydrogen diffusing into helium burning convective zones, causing the hydrogen to be mixed to such extreme temperatures that it causes a hydrogen flash.

The third dredge up (TDU) will occur when a star is on the AGB and experiences a helium shell flash (Karakas and Lattanzio (2014)). The helium flash can produce large temperature gradients within the star, allowing a new convective zone to form near the carbon rich core. If this convection zone merges with the one in the envelope to form a single large convective zone, core carbon can be dredged up to the surface (Karakas and Lattanzio (2014)). This will dramatically alter the surface composition of the star, and the amount of carbon observed will increase, allowing the star to be classified as a carbon – or C - star. This will alter the ratios seen at the surface of the star (Karakas and Lattanzio (2014)). Any carbon that does reach the envelope is likely to be converted into nitrogen via the CNO cycle, meaning that the addition of carbon also causes an enrichment in the CHAPTER 1. STELLAR EVOLUTION 39 amount of nitrogen (Chieffi et al. (2001)).

The dredging up of carbon to the surface is incredibly important in middle intermediate mass stars, as these stars are only capable of having a TDU if they fulﬁl speciﬁc criteria. For stars with a large CO core, a TDU is likely if there is a dredge up of carbon rich material (Chiosi (1997)). For stars with a smaller core, there must be some form of extra mixing in the intershell region (Iben and Renzini (1982)), or convective overshoot (Hollowell and Iben (1989)). As all of these processes require carbon rich material in the external layers, the TDU is highly dependent on the carbon composition of the star. CHAPTER 1. STELLAR EVOLUTION 40

1.6 Post- AGB Evolution and Very Late Ther-

mal Pulses

1.6.1 Very Late Thermal Pulses

During a very late thermal pulse (VLTP), there is violent hydrogen burning (Miller Bertolami and Althaus (2007)) that triggers a helium ﬂash and a thermal pulse in the same way as on the TP-AGB phase. Any star that reaches the AGB phase may undergo this process, meaning that stars with a mass between 0.6 - 10 M may undergo a VLTP.

During this pulse, the hydrogen shell is almost completely extinguished, allowing a pulse driven convective zone to reach the hydrogen rich envelope (Miller Bertolami and Althaus (2007)). This means that convection can now take hydrogen rich material into the carbon rich interior to be burnt (Miller Bertolami et al. (2006)), as hydrogen must be burnt with 12C during a VLTP to maintain stability (Miller Bertolami and Althaus (2007)). Once the hydrogen has been moved down into a hotter region of the star, almost all of it will be burnt via two sets of reactions. The ﬁrst set is the single equation:

12 13 13 + 6 C + p −→7 N + γ −→6 C + e + ve (1.10)

(Miller Bertolami and Althaus (2007)).

The second set adds the reaction:

13 14 6 C + p −→7 N + γ (1.11)

(Miller Bertolami and Althaus (2007)) to equation 1.10.These reactions CHAPTER 1. STELLAR EVOLUTION 41 work alongside each other at the same rate, so there is never an excess of any intermediate products.

It is important to note the differences between very late thermal pulses (VLTPs) and late thermal pulses (LTPs). Whilst both LTPs and VLTPs are helium shell flashes that serve to dredge up helium and metals whilst moving hydrogen to the core, these flashes occur at different points in a star’s evolution (Lawlor (2019)). For VLTPs the helium shell flash occurs on the white dwarf cooling branch when the helium shell flash zone convec- tively engulfs the remainder of the hydrogen rich envelope (Althaus et al. (2019)). The hydrogen is processed in the deeper interior levels of the star (Iben and MacDonald (1995)) before being ejected. For LTPs, the helium shell flash occurs on the horizontal track (Blöcker (2001)) as these stars have more mass in their helium shells compared to stars that undergo VLTPs (Lawlor (2019)). In this case, the envelope does not undergo nucleosynthesis after ingestion, but the hydrogen is instead diluted by the extension of the convective envelope caused by the star returning to the AGB after the LTP (Althaus et al. (2019)). The hydrogen will be eventually be burnt as the star contracts when turning on to the white dwarf cooling track (Althaus et al. (2005)). This process produces white dwarfs with hydrogen

−6 −7 masses between 10 – 10 M (Althaus et al. (2005)).

1.6.2 Post-AGB Evolution in Low and Low Interme-

diate Mass Stars

When stars are nearing the end of their AGB phase, they will be undergoing thermal pulses whilst losing mass through stellar winds (see section 1.7). CHAPTER 1. STELLAR EVOLUTION 42

At some point during a thermal pulse, mass loss will end. If the end point is during a period of hydrogen burning, the star will be left with a thin layer of hydrogen rich material, but if the end occurs during helium burning, the envelope will mainly be made of helium (Karakas and Lattanzio (2014)). As hydrogen burning occurs for a longer period during a thermal pulse, it is more likely that the former will occur, meaning that the white dwarf that will follow is more likely to have hydrogen lines in its spectra. Once mass loss has stopped, the CO core of the AGB is exposed and surrounded by an optically thick shell of ejected material (Bloecker (1995)), which has a denser inner region. This shell will only allow the star to radiate in the infrared and radio, and OH molecules will be observed, leading the star to be considered an OH/IR star (Bloecker (1995)). The central star will have an internal structure consisting mainly of degenerate electrons, which can radiate photons to the surface.

The core will now contract, causing the shell to expand slightly and become optically thin (Bloecker (1995)), and the temperature of the core to rise. When the core has reached approximately 25,000K, the radiated photons will be energetic enough to ionise the nebula (Engels (2005)), causing the nebula to emit light. The nebula and star will now evolve at a constant luminosity towards higher temperatures, meaning the radius must decrease (Engels (2005)).

The final nuclear reactions are now taking place in a thin shell on top of the core, but this will cease when the star turns onto the white dwarf cooling track (Engels (2005)). The star has a temperature of roughly 104 - 105K on the track, but as the interior is fully degenerate, there can be no nuclear reactions taking place (Engels (2005)). Due to the lack of nuclear reactions, CHAPTER 1. STELLAR EVOLUTION 43 the temperature begins to decrease, as does the luminosity. However, some luminosity is produced as the internal energy is radiated away (Bloecker (1995)). This process is very slow as degenerate matter lacks available quantum states, meaning it is difficult for the star to absorb and reemit photons (Bloecker (1995)). However, eventually this process will cool the surface of the star, allowing for the radius to increase and the nebula to disperse (Engels (2005)). The star has now reached its final state as a CO white dwarf.

1.6.3 Post-AGB Evolution in Middle Intermediate Mass

Stars

Like low and lower intermediate mass stars, middle intermediate mass stars consist of a core surrounded by a weakly bound envelope, but middle intermediate mass stars have O(Ne) cores rather than CO (Karakas and Lattanzio (2014)). They too will evolve at a constant luminosity, increasing in temperature and decreasing in radius, before forming a planetary nebula. They will then evolve onto the white dwarf cooling track before ending their lives as O(Ne) white dwarves. CHAPTER 1. STELLAR EVOLUTION 44

1.7 Mass Loss

1.7.1 Mass Loss Through Stellar Winds

Mass loss in stars occurs primarily on the RGB and AGB, and the most common mechanisms for mass loss are winds.

However, stellar winds and their stronger counterparts, superwinds, are poorly understood (Prialnik (2000)). There is a correlation between the increasing luminosity of a cool star and its mass loss rate, but this mass loss rate is not always driven by radiation pressure. The outer layers of cool stars allow atoms and molecules to form dust at a few stellar radii (Höfner and Olofsson (2018)), and the wind around cool stars in then driven by radiation pressure on the dust. The increase in radiation pressure then accelerates the dust, allowing it to reach escape velocity, vesc and flow away from the star (Höfner and Olofsson (2018)). This material can also drag other material with it.

If the mass loss rate is given by M˙ , then the mass ejected during a time interval of δt will be M˙ δt. This mass will be travelling at escape velocity, vesc, which it will have reached by absorbing some of the momentum carried by the radiation. If we take the momentum of the radiation to be (L/c)δt, and the fraction absorbed to be φ0 , then we get the equation:

0 L Mδtv˙ = φ δt (1.12) esc c

As 2GM v2 = , (1.13) esc R CHAPTER 1. STELLAR EVOLUTION 45

Equation 1.13 can be substituted into 1.12 to give:

0 v LR M˙ = φ esc , (1.14) 2c GM which describes the mass loss rate with respect to mass, radius, luminosity, and the fraction of the radiation absorbed.

Observations have shown that stars can have mass loss rates that range

9 −4 from 10 – 10 M per year (Engels (2005)). When the Reimers formula (Reimers (1975)):

˙ −13 L R M −1 M ≈ 10 (M yr ) (1.15) L R M

˙ −6 −1 is used to analyse stellar winds, M ' 10 M yr , which suggests the momentum transfer is eﬃcient enough to cause stellar winds and be the main cause of mass loss.

Stellar winds are usually comprised of molecular species, with AGB winds being particularly abundant in CO. Depending on the C:O ratio of the star, the wind itself may be either O or C rich, and the dust in the wind may be comprised either primarily of metal silicates or carbon based molecules. Nucleosynthesis products are lost via winds, with stars similar in mass to the Sun producing similar winds due to the input metallicities being approximately solar. CHAPTER 1. STELLAR EVOLUTION 46

1.7.2 Mass Loss Through Superwinds

Superwinds are signiﬁcantly stronger than stellar winds, which means that the ejecta form a dense shell around the central star instead of leaving behind diﬀuse material (Prialnik (2000)). The existence of superwinds is proven in part by the relatively low number of bright stars on the AGB of a Hertzsprung-Russell Diagram (Prialnik (2000)). The number of stars is expected to be proportional to the time that the stars spend with both a hydrogen and helium burning shell, but we see fewer than we expect, meaning that something must stop some of the stars reaching this point (Prialnik (2000)).

As previously discussed, AGB stars convert hydrogen into carbon and oxygen, causing their cores to grow whilst their envelopes shrink. If we let Q be the amount of nuclear energy released per unit mass during this process, and L be the average luminosity over a thermal pulse cycle, then we know from thermal equilibrium that:

˙ L −11 L −1 Mc = ≈ 1.2 × 10 M yr , (1.16) Q L

˙ where Mc is the change in mass of the core with respect to time (Prialnik (2000)).

As: L M = 6 × 104 c , (1.17) L M − 0.5 substituting 1.17 into 1.16 gives: CHAPTER 1. STELLAR EVOLUTION 47

dM c = 7.2 × 10−7yr−1dt (1.18) Mc − 0.5M

Prialnik (2000).

The mass of the core is limited by the Sch¨onberg-Chandrasekhar limit, which means that we can integrate the above equation to get an upper limit on the amount of time a star spends burning two shells (Prialnik

(2000)). If the lower limit is taken to be the initial core mass Mc,0, which

must be greater than 0.5M , and the upper limit is taken to be MCh, then the time a star spends in the double burning phase is:

6 MCh − 0.5M τAGB < 1.4 × 10 ln yr (1.19) Mc,0 − 0.5M

(Prialnik (2000)).

This means that the superwind must prevent some stars from reaching this point in their evolution by stripping them of their envelopes, explaining the strange results from H-R diagrams. In fact, mass loss due to superwinds is thought to be so extreme that any star subjected to one could only grow its

core by around 0.1M (Justtanont et al. (2013)) before the entire envelope is removed. Stars that do survive the superwind are usually left with cores between 0.6 – 1.1 M , despite starting oﬀ with initial masses between 1M

< M < 9M .

1.7.3 Mass Loss Models

Instead of observations, it is very common that models are used to estimate the mass loss rates of stars. The models are simplistic as shock and dust CHAPTER 1. STELLAR EVOLUTION 48

driven winds (Winters et al. (2013)) make it diﬃcult to observe the stars at wavelengths shorter than the infrared (Habing (1996); Uttenthaler (2013)). Habing (1996) showed that stars on the upper part of the AGB have con- tinuously increasing mass loss rates, and Groenewegen et al. (2009) and

−7 Justtanont et al. (2013) showed that these rates varied from 10 M per

−4 year for short period Mira variables to 10 M per year for long period variables, supporting the previous observations that mass is not lost from a star at a continuous rate.

Mass loss also has an impact on other properties of the star. If mass loss is occurring during the planetary nebula phase, it can alter the rate at which a planetary nebula nucleus (PNN) can evolve. Almost all PNNs are losing mass (Perinotto (1989)), and there is a strong correlation between the observed terminal wind velocities of the PNN and its Teff (Heap (1986)) which is supported by the idea that winds are driven by radiation pressure (Pauldrach et al. (1988)). These winds have velocities of approximately 1000 kms−1, and mass loss rates around 3 orders of magnitude lower than those at the end of the AGB phase (Cerruti-Sola and Perinotto (1989); Perinotto (1989)). This suggests that the wind has increased in speed as the star has evolved from the AGB to the PN phase (Kwok et al. (1978)).

Whilst it is still unclear how much mass is lost from a star during the RGB phase, estimates put it as high as 30% of the original mass of the star (Karakas and Lattanzio (2014)). CHAPTER 1. STELLAR EVOLUTION 49

1.8 Shaping of Nebulae

Planetary and protoplanetary nebulae evolve from the mass loss envelopes around AGB stars, which consist of the products of nucleosynthesis reactions that the star underwent earlier in its evolution (Karakas and Lugaro (2010)). The AGB stars themselves are spherically symmetric, but their envelopes have a range of morphologies, and around 80% of protoplanetary nebulae are not spherically symmetric, instead having bipolar or multipo- lar morphologies (Sahai (2009)). In order to reshape the nebulae, external forces - such as winds - must be incorporated. The “generalised interacting- stellar-winds” (GISW) model proposes an isotropic wind that originates in the central star of the planetary nebula. Travelling at over 1000km s−1, the wind expands within the “equatorially dense” circumstellar envelope and produce an array of axisymmetric shapes (Balick and Frank (2002)). The speed and direction of the wind is likely impacted by “a jet of high-speed collimated outﬂow” (CFW) that occurs early in the post AGB phase, or late in the AGB phase (Sahai (2009)). Either way, to break the symme- try the CFW will need to change direction as it travels, or it must have multiple components in diﬀerent directions.

Another solution to the problem of asymmetric planetary nebulae (PNs) and protoplanetary nebulae (PPNs) was suggested by Moe and De Marco (2006) and Soker (2006). Both concluded that it was possible that all asymmetric PNs and PPNs were part of a binary system, as it was already well established that binarity strongly impacted the characteristics of mass loss in evolved stars (Sahai (2009)). However, directly observing binary systems is notoriously diﬃcult due to observational limitations (e.g dust CHAPTER 1. STELLAR EVOLUTION 50 clouds). Indirect observing is also diﬃcult as AGB stars are naturally variable and undergo thermal pulses, making radial-velocity and photometric variability measurements inappropriate for observing these stars.

The simplest scenario in which a planetary nebula forms is when a progenitor star loses its external envelope at the end of the AGB phase and begins the cooling sequence that will lead to a white dwarf. As the central star evolves, it will become hot enough to ionise the material it has just ejected (Abell and Goldreich (1966);Paczy´nski(1970)), however, if the central star evolved too quickly the gas is only ionised for a short time, reducing the probability that the nebula will be detected. Conversely, if the star evolves too slowly, the gas may have already dispersed too much to be detectable (Miller Bertolami (2014)). CHAPTER 1. STELLAR EVOLUTION 51

1.9 Sakurai’s Object

Initially described as a slow nova, Sakurai’s Object (V4334 Sgr) is the central star of an old planetary nebula that underwent a very late thermal pulse (VLTP) shortly before its discovery in 1996 by Yukio Sakurai (Nakano et al. (1996)). In the Milky Way, it is expected that a VLTP will be observed every 10 years (Zijlstra (2002)), but the VLTP seen in Sakurai’s Object was only the second case documented, with the other being V695 Aql in 1918 (Clayton and De Marco (1997)).

During the VLTP experienced by Sakurai’s Object, which will occur in roughly 10% of all central stars of planetary nebulae (Iben and MacDonald (1995)), what was left of the original hydrogen rich envelope was taken into the helium burning shell via convection, allowing the material to be processed and ejected soon after (Zijlstra et al. (2005)). This formed a hydrogen deﬁcient nebula inside the old PN, which is currently expanding at around 300kms−1 inside the old nebula (van Hoof et al. (2015)) and has been ionised by a shock (van Hoof et al. (2007b)). The formation of the hydrogen poor nebula had never been observed due to restrictions on instruments, stellar extinction, or a combination of the two (Zijlstra et al. (2005)). V605 Aql formed its hydrogen poor nebula after an outburst between 1918-1924 (Clayton and De Marco (1997); Lechner and Kimeswenger (2004)), but it was only seen 60 years later as a hot Wolf-Rayet star (Seitter (1987)) with a hydrogen poor nebula (Zijlstra et al. (2005)).

After the VLTP, Sakurai’s Object brightened and became a very cool born again AGB star, with a spectrum that resembled a carbon star (Van de Steene et al. (2016)). A few years later, dust formation began in the new CHAPTER 1. STELLAR EVOLUTION 52 ejecta, obscuring the central star (Van de Steene et al. (2016)).

In order to determine the geometric structure of Sakurai’s Object, the Very Large Telescope Interferometer (VLTI) at ESO was used, and a dust rich disk was detected (van Hoof et al. (2018)). Further observations revealed that the disk had dimensions of 105 x 140 AU, assuming the distance to Sakurai’s Object is approximately 3.5 kpc (Chesneau et al. (2009)). As the gaseous material in the disk is lacking hydrogen, the disk must have been formed during the VLTP, and must have been formed in or before 1997, as the disk obscures the central star (van Hoof et al. (2018)). The bipolar lobes were found using the NIRI/Altair instrument on Gemini in 2010 and 2013 (Hinkle and Joyce (2014)), and the expansion of this structure is obvious. It is also important to note that the central star is showing signs of brightening in the near IR, and that the whilst the old PN is roughly spherical, the new ejecta is bipolar (van Hoof et al. (2018)).

Zijlstra et al. (2005) also used the VLA to observe Sakurai’s Object. The observations were conducted at 8.6 GHz in CnB configuration. From the data collected, a continuum-subtracted image was produced (see Figure 1 of Zijlstra et al. (2005)) which showed that the planetary nebula of Sakurai’s Object has a diameter of approximately 40 arcseconds, and an integrated radio flux of 1.5 ± 0.2mJy. The central star was recorded as having an integrated flux of 100 ± 30µJy, and shows evidence of some sort of double structure (Zijlstra et al. (2005)).

Sakurai’s Object emits in wavelengths from the optical to radio (van Hoof et al. (2018)), but the ﬁrst emission line detected was HeI 1083nm, and it was discovered by Eyres et al. (1999). Two years later, optical forbidden CHAPTER 1. STELLAR EVOLUTION 53 lines from neutral and singly ionised nitrogen, oxygen, and sulphur were discovered by Kerber et al. (2002), along with very weak H alpha (van Hoof et al. (2018)).

Between 2001 and 2007 it was noted that the optical spectrum declined in flux, and the level of excitation also decreased (Van de Steene et al. (2016)). This, along with the absence of the HeI 1083nm emission line in 1997, provided evidence for a shock occurring in 1998 that was then followed by cooling. A possible explanation is that these signals are caused by some of the fastest material ejected in the VLTP hitting older ejecta from the star (Van de Steene et al. (2016)). In 2008, the fluxes of optical lines started to increase again, and a sudden jump in the flux of [OII] suggested that a second shock may have occurred (Van de Steene et al. (2016)). HeI 587.6nm and HeI 706.5nm were then detected in 2008, followed by HeI 667.8nm in 2009 (van Hoof et al. (2015)). New lines have been emerging in the optical spectrum since 2013 – some of which are electronic transitions of CN - and some show signs of being formed either very close to the central star, or in the disk (Van de Steene et al. (2016)). A PV diagram of [NII] 658.3nm showed emission lines that had been both red shifted and blue shifted. These lines came from two different regions of the source, with the red shifted lines coming from a region displaced by -0.18 arcseconds from the continuum, and the blue shifted lines coming from a region displaced by 0.24 arcseconds with respect to the continuum (van Hoof et al. (2018)). It was suggested that these lines – along with other optical forbidden lines – originated in bipolar lobes (Hinkle and Joyce (2014)).

Observations have also been taken using ALMA. Between 2004-2007, the radio flux at 8GHz was increasing, and was interpreted as evidence that CHAPTER 1. STELLAR EVOLUTION 54 carbon was beginning to undergo photoionisation (van Hoof et al. (2007a)). However, more recent data suggests that the source has faded, as flux levels have returned to those seen in 2004-2005 (van Hoof et al. (2018)). As this is inconsistent with carbon photoionisation, the change in flux was likely due to a shock (van Hoof et al. (2018)).

In 2015, observations using ALMA obtained a band 6 spectral scan, an incomplete band 7 spectral scan that was rejected in quality control, and a continuum image (van Hoof et al. (2018)). The band 6 scan detected

13 13 13 lines for CO, CO, CN, possibly some blended CN, HC3N, HC CCN, HCC13CN, and maybe H13CCCN (van Hoof et al. (2018)). The emission from CO and HC3N is unresolved and coincides with the position of the central star (Van de Steene et al. (2016)), as does the ALMA continuum (van Hoof et al. (2018)), suggesting that these lines likely originate from the disk (Van de Steene et al. (2016)). CN and 13CN emission lines are spatially resolved, and instead coincide with the bipolar lobes detected by Hinkle and Joyce (2014), suggesting that CN may have been formed when a shock caused HCN to disassociate in the lobes.

Prior to its discovery, evolutionary models had been created for stars like Sakurai’s Object, but none accurately predicted the speed at which the star would evolve (van Hoof et al. (2015)). Most models predicted that Sakurai’s Object would take several hundred years to become a reborn planetary nebula, but this stage will likely be reached much faster (Zijlstra et al. (2005)). There were several evolutionary models suggested, but all focused on a hydrogen ingestion ﬂash (HIF) in the helium burning shell (van Hoof et al. (2015)). Models suggested by Herwig (2001) and Lawlor and MacDonald (2003) assumed that HIFs would suppress convection, pushing CHAPTER 1. STELLAR EVOLUTION 55 hydrogen burning to the surface. This claim was investigated using 3D hydro models, which demonstrated hydrogen ingestion occurs via a global non-radial instability, allowing for transitions between spherically symmetric states (Herwig et al. (2011); Herwig et al. (2014)). Miller Bertolami et al. (2006) suggested that it would also be possible to achieve the same speed of evolution using very small time steps instead of changing the mixing physics. Whichever model is used, all could be improved by using the evolution of the stellar temperature as a constraint, but this is now much more diﬃcult given the heavy dust layer obscuring the star (van Hoof et al. (2015)).

The model in Herwig (2002) describes an evolution from the pre-white dwarf phase to the AGB phase in approximately 3 years, which is supported by the study conducted by (Duerbeck et al. (2000)). It is suggested that this very fast evolution is due to a hydrogen ﬂashed that is fuelled by a proton ingestion from the envelope to deeper layers of the star (Herwig (2002)). The star will then become a central star of a planetary nebula, and should undergo a second, helium ﬂash driven born again evolutionary phase lasting roughly 100 years (Herwig (2002)). Chapter 2

Interferometry

56 CHAPTER 2. INTERFEROMETRY 57

2.1 Background to Interferometry

Interferometry is a method used to extract information from the interference patterns caused by the superposition of waves (Bryan Bunch et al. (2004)). The interference pattern is caused by two waves of the same frequency combining and undergoing constructive interference, with the exact nature of the pattern being determined by a diﬀerence in phase (Ryle and Hewish (1960)). The diﬀerence in phase can be easily determined if the waves arriving at the interferometer are neither fully in nor out of phase (Ryle and Hewish (1960)).

An interferometer will consist of 2 or more telescopes combining their signals to behave as one large telescope (Hariharan (2012)). This gives a resolution equal to that of one telescope where the diameter is equal to the largest baseline present in the array (Ryle and Hewish (1960). In the case of Sakurai’s Object, the interferometer used is ALMA, which has a maximum baseline of approximately 16km. CHAPTER 2. INTERFEROMETRY 58

2.2 The Process of Interferometry

The following details are based on the VLA (Very Large Array) and cm wave interferometry. Whilst much of this is similar for ALMA, some details - such as calibration - will vary slightly.

The process of interferometry can be described using a source at inﬁn- ity producing plane waves (Perley et al. (1989)). In this case, it can be assumed that the interferometer is made up of 2 identical telescopes separated by vector B (Perley et al. (1989); ALMA Technical Handbook (https://almascience.eso.org/documents-and-tools/cycle8)). A schematic of this set up can be seen in Figure 2.1. If s is the unit vector in the direction of the source, it is possible to calculate the path delay caused by the

separation of the telescopes. The geometric delay, τg, is given by:

B.s (2.1) c

where c is the speed of light (Perley et al. (1989)). CHAPTER 2. INTERFEROMETRY 59

Figure 2.1: A schematic of a radio interferometer consisting of two dishes pointed at a source.

Once the signal has been detected by the antennas, it passes through am- pliﬁers that will identify the frequency band, which will have a width of ∆ν (Perley et al. (1989)). The signals are then sent through a correlator, which is made up of a voltage multiplier and an integrator (Wootten and Thompson (2009)). The correlator combines the signals, so if we consider

the signal from the ﬁrst antenna to be V 1(t), and the signal from the sec-

ond to be V 2(t), the correlator will produce and output proportional to

(Perley et al. (1989)). The signals that were received by each antenna can be broken down into Fourier components, giving:

V 1(t) = v1 cos(2πν(t − τ g)) (2.2) CHAPTER 2. INTERFEROMETRY 60

and

V 2(t) = v2 cos(2πνt) (2.3)

(Perley et al. (1989)).

The response of the correlator, R, will then be given by:

R(τ g) = v1v2 cos(2πντ g) (2.4)

It is now possible to give the output of the interferometer in terms of the radio brightness integrated over the whole sky (ALMA Technical Hand- book, (https://almascience.eso.org/documents-and-tools/cycle8)). Let I(s) be the radio brightness in the direction of unit vector s (see above diagram). If it is assumed that both antennas are identical and are pointing towards an element of the source (dΩ), then the signal power received in terms of the eﬀective collecting area, A(s), is given by:

A(s)I(s)∆νdΩ (2.5)

(Perley et al. (1989)). As the output power is proportional to the received power and the cosine fringe term, the correlator output for the signal em- anating from dΩ is:

dR = A(s)I(s)∆νdΩ cos(2πντ g) (2.6)

(Perley et al. (1989)). Replacing τ g with Equation (2.1) and integrating over the whole surface of the celestial sphere, S, gives an interferometer CHAPTER 2. INTERFEROMETRY 61

response in the form:

Z 2πνB.s R = ∆ν A(s)I(s) cos dΩ (2.7) S c

(Perley et al. (1989)). This equation is only valid if the bandwidth is small enough that any variation in A and I due to ∆ν can be ignored. In addition, the waves must be planar due to the source being at inﬁnity, and the source must be incoherent (Perley et al. (1989)).

During observations, it is usually necessary to centre the ﬁeld of view on a given point on the source, s0. As s = s0 + σ, the equation for R can be written as:

2πνB.s Z 2πνB.σ R = ∆ν cos 0 A(σI(σ) cos dΩ c S c 2πνB.s Z 2πνB.σ − ∆ν sin 0 A(σ)I(σ) sin dΩ (2.8) c S c

(Perley et al. (1989)). It is then possible to deﬁne the normalised antenna

reception pattern An = A(σ)/A0, where A0 is the response at the centre of the beam. The complex visibility of the source can now be written using the equation:

V = |V |eiφv (2.9)

(Perley et al. (1989)).

If the real and imaginary parts are then separated, it is possible to write:

Z 2πνB.σ A0|V | cos(φv) = A(σ)I(σ) cos dΩ (2.10) S c CHAPTER 2. INTERFEROMETRY 62 and Z 2πνB.σ A0|V | sin(φv) = − A(σ)I(σ) cos dΩ (2.11) S c

(Perley et al. (1989)). When equations 2.10 and 2.11 are substituted into equation 2.8, the result is:

2πνB.s R = A ∆ν|V | cos 0 − φ (2.12) 0 c ν

In this equation, the cosine term is the fringe pattern produced by the waves, and both the amplitude and phase of V can be obtained during calibration (Perley et al. (1989)). As the observing frequency, ν, is proportional to the frequency of the fringe term, fringe patterns within a range of frequencies can essentially be combined by using a ﬁnite bandwidth. This will cause the interferometer response, R, to become:

dR = A0|V | cos(2πντ g − φν)dν (2.13)

The ideal response from an interferometer would then resemble a rectan- gular step function, and can be written as:

Z ν0+∆ν/2 R = A0|V | cos(2πντ g − φν)dν (2.14) ν0−∆ν/2 which can then be evaluated to:

π∆ντ g R = A0|V |∆ν sin cos(πν0τ g − φν) (2.15) π∆ντ g

where ν0 is the central frequency of the passband used for observing.

By the end of the process, a series of fringes will have been collected. These CHAPTER 2. INTERFEROMETRY 63 fringes will have amplitudes that are produced when the source intensity distribution undergoes a Fourier transform. These fringes will then be removed by inserting electronic delays, leaving only the response. A computer can then be used to extract information about both the amplitude and phase of the source at diﬀerent points, and this information is used to construct an image.

As is expected, a greater number of readings provides a more accurate image, but this must be balanced with practicalities such as the time taken to compute the extra readings and the space available to store the data. CHAPTER 2. INTERFEROMETRY 64

2.3 Deconvolution

The major issue that arises with an interferometer is that the response is never measured over the whole u,v plane (Perley et al. (1989)). In theory, this is possible at a single frequency, but it would require an array with enough antennas to provide baselines covering all possible separations and orientations, making it too expensive. This means that an incomplete data set will be collected, and there will be an infinite number of final images that would fit with the collected data.

The ideal image, I(x, y), is produced by a full u,v response function, I(u, v), which is given by:

ZZ I(x, y) = I(u, v)e2πi(ux+vy)dudv (2.16)

However, we are left with what is known as the ’dirty image’, which is given by:

ZZ 2πi(ux+vy) ID(x, y) = I(u, v)S(u, v)e dudv. (2.17)

This occurs because of the sampling function, S(u,v). In areas of the u,v plane that have been sampled, this is 1, and in areas where no sampling has been done, this is 0.

By using the convolution theorem, the right hand side of equation 17 can be written as:

ID(x, y) = I(x, y) ∗ B(x, y) (2.18) CHAPTER 2. INTERFEROMETRY 65 where ZZ B(x, y) = S(u, v)e2πi(ux+vy)dudv. (2.19)

B(x,y) is therefore the Fourier transform of the sampling function, S(u,v), and is deﬁnition of the dirty beam. If the locations of the telescopes are accurately known, then the sampling function and the dirty beam are also accurately known, and calculating the image I(x,y) requires deconvolution (Perley et al. (1989). However, some additional information is required to do this, and this can be supplied by one of several CLEAN algorithms.

2.3.1 The H¨ogbom CLEAN Algorithm

The first CLEAN algorithm was developed in 1974 by J. Högbom, and it solves the convolution equation by assuming that a radio source is a collection of point sources in an empty field of view (Perley et al. (1989)). The strength and position of each point is found using an iterative program that can be run with or without user interaction, and it will produce a deconvolved – or “CLEAN” – image, which consists of the sum of the points convolved with a “CLEAN” beam (Perley et al. (1989)). The CLEAN beam is usually Gaussian, as this minimises the effect of higher spatial frequencies on the final image (Perley et al. (1989)).

The Högbom algorithm is the most used variant of CLEAN, and it begins by determining the strength and position of the brightest pixel in the input – or “dirty”- image (Perley et al. (1989)). If there is an obvious source of flux in the image, the user may draw a CLEAN window around the source, instructing the algorithm to locate the strongest pixel in the window (Perley et al. (1989)). The dirty beam is then subtracted from the dirty image at CHAPTER 2. INTERFEROMETRY 66 the point of the brightest pixel to give a new image, and this process is repeated until the peak flux is below a level predetermined by the user (Perley et al. (1989)). If too few iterations of the algorithm are used, extended structure in the image is not very clear. Whilst the total number of iterations remains a choice for the user, it is common to only stop when there is no noticeable difference in the image before and after an iteration has been performed (Perley et al. (1989)). The point source model is then convolved with a “CLEAN” beam, which is usually a Gaussian that has been fitted to the central lobe of the dirty beam, and the residuals of the dirty image are added to the CLEAN image to give a final product (Perley et al. (1989)).

The Högbom algorithm has been analysed in Schwarz (1978) and Schwarz (1979). It was concluded that in the noise-free case, the least squares minimisation of the difference between the observed and model visibilities produces a unique answer if the number of cells in the model is smaller than the number of independent visibility measurements contributing to the dirty image and beam (Schwarz (1978); Schwarz (1979)). This is only true if the real and imaginary parts of the visibilities are counted separately. As this is unaffected by the distribution of u-v sample points, super resolution is possible if there are enough data points (Schwarz (1978); Schwarz (1979)).

However, in practice there is always noise in an image. All instruments have a minimum level of thermal noise that is non-zero, and there are almost always a noise contribution from residual calibration errors. The CLEAN algorithm makes use of a fast Fourier transform (FFT) to calculate the dirty image and beam (Perley et al. (1989)), which causes information CHAPTER 2. INTERFEROMETRY 67 about the derivatives of the visibility function that the super resolution is based on to be lost. Therefore, the decision is usually taken to produce a more accurate ﬁnal image rather than one with increased resolution.

Crucially, Schwarz (1978) and Schwarz (1979) produced three conditions that are required for the CLEAN algorithm to converge. They are: the beam must be symmetric, it cannot have negative eigenvalues, and there cannot be spatial frequencies in the dirty image that are not also in the dirty beam (Schwarz (1978); Schwarz (1979)). An ideal image and beam will obey all three criteria, but errors can cause the beam and image to break one or more of these conditions, causing the algorithm to eventually diverge (Perley et al. (1989)).

The CLEAN beam suppresses high spatial frequencies in the images, as these are not well modelled by the CLEAN algorithm (Perley et al. (1989)). Whilst this can cause real sources to be removed from the image, without suppression the images produced are inaccurate. The CLEAN beam is usually designed by ﬁtting a Gaussian to the centre of the dirty beam, but some cases may require the size of the CLEAN beam to be scaled (Perley et al. (1989)).

2.3.2 The Clark Algorithm

In 1980, Clark adapted H¨ogbom’s original algorithm to produce the Clark algorithm. Clark decided that as the CLEAN beam is a convolution, there would be situations where a 2D FFT would be more eﬃcient.

Clark’s Algorithm determines the rough positions and strengths of any components using a small patch of the dirty beam, and then utilises the CHAPTER 2. INTERFEROMETRY 68 original H¨ogbom CLEAN. The algorithm then uses a minor cycle that begins with a segment of the beam (including the highest exterior side lobes) being selected to represent the beam patch (Perley et al. (1989)). Points are selected from the dirty image if they have an intensity higher than the largest exterior sidelobe of the beam patch, and a H¨ogbom CLEAN is then performed using the beam patch and the selected points of the dirty image (Perley et al. (1989)). If the remaining points no longer have an intensity higher than the highest exterior sidelobe, the program stops, but otherwise it will repeat this process until that condition is met. This will produce a point source model, which can then be used in a FFT in the major cycle (Perley et al. (1989)). This is then multiplied by the weighted sampling function and is then transformed back, before being subtracted from the dirty image (Perley et al. (1989)).

2.3.3 Cotton-Schwab Algorithm

In 1984, Cotton and Schwab developed Clark’s algorithm so that the major cycle subtraction of the CLEAN components was performed on ungridded visibility data (Schwab (1984)). This means that noise and gridding data can be removed by the inverse Fourier transform of the CLEAN components from each u-v sample (Schwab (1984)). If there is a small number of CLEAN components, it is possible to use a direct Fourier transform, but the accuracy of this method is limited by the accuracy of the equipment used (Perley et al. (1989)). For a large number of CLEAN components, the FFT method is used, but this brings in errors due to the interpolation between sampled areas. However, a large number of samples may mean that the process becomes very expensive due to the computing power required, CHAPTER 2. INTERFEROMETRY 69 so a balance must be reached.

The main advantage of the Cotton-Schwab algorithm is the increased accuracy achieved by removing the grid, but it also has the advantage of being able to CLEAN several fields at the same time, providing they are all near each other (Perley et al. (1989)). In a minor cycle, the fields undergo a CLEAN independently of each other, but in major cycles the CLEAN components are removed from all fields at the same time (Perley et al. (1989)). The residual image for each field is calculated in a way that includes the w term, meaning the Cotton-Schwab algorithm also accounts and corrects for distortions caused by non-coplanar baselines (Perley et al. (1989)). CHAPTER 2. INTERFEROMETRY 70

2.4 Emission and Absorption from the At-

mosphere

The troposphere is the region of the Earth’s atmosphere that is closest to the surface and contains 99% of the water vapour in the atmosphere. The troposphere is approximately 78% nitrogen, 21% molecular oxygen, and contains traces of other molecules. Both the water vapour and molecular oxygen found in the troposphere can absorb radio waves and attenuate the signal (Perley et al. (1989)), which will reduce the signal picked up by an interferometer.

At 60GHz and 118GHz, the main source of absorption is molecular oxygen, and at the centre of these transitions lies an opaque atmosphere (Perley et al. (1989)). Water vapour is the main absorption source at all other frequencies, but it is strongest at 22 GHz and 183GHz (Perley et al. (1989)). Ozone can also cause problems at some mm wavelengths.

The attenuation of the source is important in interferometry as it has a direct impact on the antenna temperature, which can be written as:

τν sec(z) −τν sec(z) Tse + Tatm(1 − e ), (2.20)

where τν is the opacity of the atmosphere at a given frequency, ν,Ts is the attenuated source signal, and Tatm is the temperature of the atmosphere.

In practical terms, a system with a higher temperature will be one with a higher noise. This makes it easy for noise to cover measurements, so only measurements that are more extreme will be registered. CHAPTER 2. INTERFEROMETRY 71

2.5 The Eﬀects of Baselines on Resolution

To understand the resolution of an interferometer, it is helpful to ﬁrst consider the Rayleigh criterion, which can be written as:

1.22λ θ = (2.21) D

where θ is the angular resolution in radians, λ is the wavelength of the radiation in meters, and D is the diameter of the aperture in meters. In general, this equation shows that, for any given wavelength, a larger diameter will provide a better resolution.

This provides a major advantage for interferometers, as their apertures will be equal to the longest baseline in a conﬁguration, not the diameter of the dish. This allows them to have values of D that are kilometers rather than meters in size, providing a better angular resolution than a single dish.

However, this comes with the draw back that the shortest baseline will determine the largest angular scale of the target that the interferometer can image. Any emission that can be considered smooth on larger scales will not give a correlated signal. CHAPTER 2. INTERFEROMETRY 72

2.6 The Eﬀects of Baselines on Image Qual-

ity

For all interferometers, the image quality is enhanced by using more u-v points. Increasing the u-v coverage reduces the number of ’gaps’ in the data that require interpolation, so fewer guesses are required to form a complete image. This in turn reduces the number of sidelobes, meaning the image produced is more accurate. The easiest way to achieve this is to have as many diﬀerent baselines as possible, with one example being the thousands of baselines provided by the ALMA antennas. This increases the u-v coverage, but increases the overall cost.

Longer observations allow for more of the u-v plane to be ﬁlled as the Earth rotates, improving the imaging accuracy for arrays with fewer antennas. In all cases, the data will require calibration to remove instrumental eﬀects, time-dependent atmospheric distortions of the signal, and any other distortions. Chapter 3

ALMA and Atomic Physics

73 CHAPTER 3. ALMA AND ATOMIC PHYSICS 74

3.1 ALMA

3.1.1 Background to ALMA

The following description of ALMA is based on that found in Wootten and Thompson (2009). The Atacama Large Millimetre/Submillimetre Array (ALMA) is a radio telescope in the Atacama Desert in northern Chile. Whilst much of the light ALMA is targeting has wavelengths of around 1mm and is therefore in the radio and infrared, ALMA can operate at wavelengths between 0.32-3.6mm. This light mainly comes from some of the coldest, earliest, and most distant galaxies in the Universe, and the emission is not observable in the visible range.

ALMA has 2 arrays of antennas, with each antenna acting as a mirror by focussing incoming radiation onto a detector to be measured. The main array consisting of 50 12m diameter antennas that can be reconfigured to give baselines between 150m to 16km. The second array is called the Atacama Compact Array (ACA) and is made up of 4 antennas with a 12m diameter, and a further 12 with a 7m diameter, giving a maximum baseline of around 50m. The antennas themselves are built on foundations and have alt-azimuthal mounts and quadripods. The quadripods hold the subreflectors and enable them to be moved in such a way that the beam can jump between 2 positions on the sky that are separated by around 2 beamwidths. This provides ALMA with both on source and off source measurements at the same time, reducing the chance of discrepancies due to external factors such as the weather. The ACA is primarily used to study extended objects and provide total power measurements but can also be used in tandem with the main array, where it will operate as the “zoom”. CHAPTER 3. ALMA AND ATOMIC PHYSICS 75

When in use with the main array, the ACA will be able to focus on smaller areas of the sky and provide a more in depth view of that region.

3.1.2 The Scientiﬁc Goals of ALMA

Upon its inception, ALMA was set 3 scientiﬁc goals. The ﬁrst goal is to detect emission from CO molecules or C+ ions from a galaxy with a luminosity similar to the Milky Way at a redshift of 3. This should be done in under 24 hours of integration. This determines the collecting area, as the sensitivity cannot be increased by enlarging the bandwidth (Wootten and Thompson (2009)) as the line width must always be smaller than the baseline for spectral line detections.

The second goal is to image the kinematics of gas in protostars and protoplanetary disks around young stars similar to our Sun. These stars are at distances of around 150 pc, which enables the physical, chemical, and magnetic fields to be studied more closely, and also allows planet formation in the disk to be observed (Wootten and Thompson (2009)). To measure the magnetic fields of the stars, ALMA must be able to measure the polarized components of the incoming waves, and to measure the chemical properties, the bandwidth must be able to simultaneously measure more than one emission line (Wootten and Thompson (2009)). This goal determines the angular resolution, as it must be finer than 0.03” at 150 pc (Wootten and Thompson (2009)).

ALMA’s third goal is to provide high quality imaging for astronomers worldwide, which requires the telescope to be able to correct for imaging errors (Wootten and Thompson (2009)). This is primarily achieved by CHAPTER 3. ALMA AND ATOMIC PHYSICS 76 an on-site team, the use of computer techniques, and combining multiple pointings to produce each image, but ALMA’s location reduces the likelihood of external factors causing errors. With the Atacama Desert being one of the driest on Earth, the water column is only around 1mm, meaning that observations in the millimetre and submillimetre range – which would normally be prevented by water vapour in the atmosphere - can be made (Wootten and Thompson (2009)). The median temperature is -2.5 degrees Celsius and the average wind speed is 10.4 ms−1 (Chesneau et al. (2009)). Phase errors - which are similar to optical seeing errors - can be caused by ﬂuctuations in atmospheric refraction, whereas absorption and emission in the atmosphere cause amplitude errors and noise. ALMA can correct these using water vapour radiometry and system temperature measurements alongside astrophysical calibrators.

3.1.3 The Eﬀects of Baselines on ALMA

As mentioned in the previous chapter, the angular resolution is dependent on the baseline. The 12m array of 50 dishes can be configured to give shorter baselines between 15m and 160m in the most compact configuration. This increases the sensitivity of the array to extended emission. It is important to note that this will reduce the resolution, but in this research compact and medium configurations were used with baselines up 1 km.

If we start by focusing on 1 of ALMA’s 12m dishes and assume that the incoming radiation has a wavelength of 1mm, we therefore have:

1.22(1 × 10−3) θ = , (3.1) 12 CHAPTER 3. ALMA AND ATOMIC PHYSICS 77

where θ is in radians. This gives each antenna a primary beam width of 21.0” to 3 signiﬁcant ﬁgures.

However, as ALMA works as an interferometer, the resolution is determined by the maximum baseline, which is 16km. Using the same assumption as before, the resolution is now given by:

1.22(1 × 10−3) θ = (3.2) 16000

When converted into arcseconds, this gives a resolution of 0.016”.

If we use the same reasoning for the 7m diameter dishes found in the ACA, the primary beam width is 36.0” (3 signiﬁcant ﬁgures). As the maximum baseline of the ACA is 50m, the resolution is 5.03”. It is important to clarify here that the primary beam is the sensitivity of the array with respect to direction, whereas the resolution is the minimum angle required for two close objects to be seen as separate bodies. CHAPTER 3. ALMA AND ATOMIC PHYSICS 78

3.2 Atomic Physics

All spectral lines will have wavelengths that can be calculated using the Schr¨odingerequation if it is assumed that the electrons have no spin and are non-relativistic. However, when spin and the eﬀects of relativistic electrons are accounted for, the energy levels are no longer degenerate, and the spectral lines split.

When examining the spectral lines observed by ALMA, it is important to consider the possible impacts of both fine and hyperfine structure. The fine structure of a line is denoted by the J number it is assigned, and hyperfine structure is denoted with an F number. What follows below is based on the physics used when examining hydrogen, but it can be expanded upon to include larger atoms.

3.2.1 Fine Structure: Relativistic Correction

Fine structure in atoms is partially caused by the relativistic corrections that must be made to the non-relativistic Schr¨odinger equation. Without relativistic corrections, the time-independent Schr¨odingerequation for a hydrogen atom can be written as:

e2 − ~ ∇2 − ψ(r) = Eψ(r) (3.3) 2m 4π0r

where: 2 ˆ ~ 2 e H0 = − ∇ − (3.4) 2m 4π0r is the leading term in the Hamiltonian, and m is the reduced mass. CHAPTER 3. ALMA AND ATOMIC PHYSICS 79

When fine structure is considered, two additional terms must be added to ˆ the Hamiltonian. The first of these is hrel, which is a relativistic correction ˆ to the non-relativistic kinetic energy. The second is hSO, which accounts for the magnetic spin orbit interaction. The addition of these terms prevents the Schrödingerequation from being solved analytically, but the fine structure is small enough that perturbation theory can be used to calculate the change in the spectra due to the new terms.

3.2.2 Relativistic Energy Correction

The original equation for the energy shift in the nth energy level is given by the expectation value of the perturbation hˆ:

ˆ ∆E =< ψnlmlms |h|ψnlmlms > (3.5)

where

|ψnlmlms > (3.6) is the unperturbed energy eigenstate and hˆ is the energy of the perturba- ˆ tion, which is hrel in this case.

The ﬁrst order relativistic energy correction is:

pˆ4 − (3.7) 8m3c2

Substituting this into equation 3.5 gives the energy shift:

pˆ4 ∆E =< ψ | − |ψ > (3.8) nlmlms 8m3c2 nlmlms CHAPTER 3. ALMA AND ATOMIC PHYSICS 80

However, it is easier to express the operator as:

pˆ4 1 − ≈ (Hˆ − Vˆ )2 (3.9) 8m3c2 2mc2 0

Substituting this into equation 3.8 gives:

1 ∆E =< ψ | − (Hˆ 2 − Hˆ Vˆ − Vˆ Hˆ + Vˆ 2)|ψ > (3.10) nlmlms 2mc2 0 0 0 nlmlms

As ˆ < ψnlmlms |H0|ψnlmlms >= En (3.11) and

2 ˆ e < ψnlmlms |V |ψnlmlms >=< ψnlmlms | − |ψnlmlms > (3.12) 4π0r

it is possible to rewrite 3.10 as

2 2 2 ! 1 2 e 1 e 1 ∆E = − 2 E + 2E < > + < 2 > (3.13) 2mc 4π0 r 4π0 r

Using the following radial integrals:

1 1 < 2 >= 2 (3.14) r n a0

and 1 1 1 < 2 >= 1 3 2 (3.15) r l + 2 n a0 CHAPTER 3. ALMA AND ATOMIC PHYSICS 81

equation 3.13 can be written as:

2 2 2 1 2 e 1 e 1 1 ∆E = − 2 (E + 2E 2 + 1 3 ) (3.16) 2mc 4π0a0 n 4π0a0 l + 2 n

where a0 is the Bohr radius, n is the principal quantum number, and l is the orbital angular quantum number.

We can then use: 1 1 E = − α2mc2 (3.17) 2 n2

and e2 = α2mc2 (3.18) 4π0a0

to write equation 3.16 as

α4mc2 1 1 1 1 ∆E = − 4 − 4 + 3 1 (3.19) 2 4n n n l + 2

where α is the ﬁne structure constant.

This can be simpliﬁed to:

2 1 2 2 1 α 3 n ∆E = − α mc 2 − 2 − 1 (3.20) 2 n n 4 l + 2

As: 1 1 E = − α2mc2 (3.21) n 2 n2

equation 3.20 can be divided through by En to give:

∆E α2 3 n = − 2 − 1 (3.22) En n 4 l + 2 CHAPTER 3. ALMA AND ATOMIC PHYSICS 82

where ∆E is the relativistic energy shift. En

This shift in the energy level is accompanied by a split, as there can be more than one value of l as l= 0, . . . , n-1. For example, if n = 2 then l = 0, 1, so the n=2 energy level would be split into 2 levels (2s and 2p) when the relativistic corrections are taken into account.

3.2.3 Fine Structure: The Spin-Orbit Interaction

As electrons orbit the nucleus, they generate magnetic ﬁelds. These ﬁelds can be described using the magnetic dipole moment:

µ = IA (3.23) where I is the current and A is the area of the loop. If the electron is orbiting at a radius of r with a velocity v,

A = πr2 (3.24) and e I = − 2πr (3.25) v Substituting 3.24 and 3.25 into 3.23 gives:

e e µ = − mvr = − L (3.26) 2m 2m

where L is the angular momentum of the electron.

As magnetic dipole moments are so small, it is common to quantify them CHAPTER 3. ALMA AND ATOMIC PHYSICS 83

using Bohr magnetons, where:

e µ = ~ . (3.27) B 2m

This means that the angular momentum, L, of the orbiting electron gener-

ates an orbital magnetic moment, µl where:

L µl = −glµB (3.28) ~

where g is the “Land´eg factor”, which equals 1, and L2 = ~2l(l-1)

The spin intrinsically associated with the electron also generates its own magnetic moment, which is referred to as the spin magnetic moment. This is given by: S µs = −gsµB (3.29) ~ where g is again the Land´eg factor, but here equals 2, and

3 S2 = 2s(s + 1) = 2 (3.30) ~ ~ 4

When these two magnetic moments interact, it is known as the spin-orbit interaction. The energy of this interaction in hydrogen can be found by using a reference frame that assumes the electron is at rest and the proton

is orbiting around it. The electron will experience a magnetic ﬁeld, Borbit, due to the proton. This magnetic ﬁeld interacts with the magnetic moment,

µs, that arises due to the spin of the electron. The energy of the spin-orbit interaction is given by:

∆E = −µs.Borbit (3.31) CHAPTER 3. ALMA AND ATOMIC PHYSICS 84

As we already have µs, we only need to determine an expression for Borbit, which can be done using the Biot-Savart law. Using this law gives:

µ e B = 0 r × v (3.32) 4πr3

Substituting L = mr×v into 3.32 gives:

µ e B = 0 L (3.33) 4πmr3

Therefore, the spin-orbit energy in the rest frame of the electron is:

µ e2 ∆E = 0 L.S. (3.34) 4πm2r3

To ﬁnd the resulting energy shift, perturbation theory must gain be applied. However, the mathematical details are beyond the scope of this research, so instead the result will be stated. The energy shift due to the spin-orbit interaction can be written as:

∆E α2 j(j + 1) − l(l + 1) − s(s + 1) = − 1 (3.35) En n 2l(l + 2 )(l + 1)

where j is the total angular momentum quantum number, and s is the spin quantum number.

This means that any energy levels where l > 0 will be split. If we again consider the n = 2 energy level, we can see that the 2s level will not be split as l = 0. However, the 2p energy level has l = 1, meaning that it will be split. The splitting is referred to using the quantum number j, where j

1 1 3 = |l + s|, and s = ± 2 . This means that for the 2p level j = 2 or 2 , giving CHAPTER 3. ALMA AND ATOMIC PHYSICS 85

a 2p level with each j value. An example of this splitting can be seen in Figure 3.1.

3.2.4 Fine Structure: Combining Relativistic Correc-

tions and the Spin-Orbit Interaction

We now have 2 equations for the causes of ﬁne structure, one given by equation 3.22, and another given by equation 3.35. If these two equations are combined, the result is:

∆E α2 3 n = − 2 − 1 (3.36) En n 4 j + 2

3.2.5 Hyperﬁne Structure

The fine structure of atoms can be split further into what is known as hyperfine structure. This splitting is due to nuclear spin producing a nuclear magnetic dipole moment which interacts with the magnetic field generated by orbiting electrons.

The total angular momentum is given by:

F = I + J (3.37) where F is the total angular momentum, I is the nuclear spin, and J is the total electronic angular momentum.

The equation for the hyperﬁne energy splitting is:

ˆ ˆ ∆E = AJ < I.J > (3.38) CHAPTER 3. ALMA AND ATOMIC PHYSICS 86

where AJ is a constant. Therefore, we can square the equation for total angular momentum to get:

F 2 = I2 + J 2 + 2I.J. (3.39)

Rearranging 3.39 gives:

F 2 − I2 − J 2 I.J = . (3.40) 2

Substituting 3.40 into the equation 3.38 gives:

A ∆E = J < Fˆ2 − Jˆ2 − Iˆ2 > . (3.41) 2

Upon simplifying, we are left with:

A ∆E = J (F (F + 1) − J(J + 1) − I(I + 1)). (3.42) 2

If we again return to the example of the n=2 level, the hyperﬁne splitting equation will split every energy level with angular momentum J into a pair

1 of sublevels with angular momentum F = J± 2 .

3.2.6 The Eﬀects of Fine and Hyperﬁne Structure on

this Research

In the case of this research, fine splitting becomes important as it will cause many lines of the same species to be registered due to fine splitting. This can be useful, as transitions with high J numbers require more energy to CHAPTER 3. ALMA AND ATOMIC PHYSICS 87 occur, making them less likely to occur in a cold nebula. However, it also means that the transitions must be considered when deciding if a potential line identification is correct. One factor that makes an identification more likely is a high number of other lines from the same species surrounding it. If most of these lines are due to fine or hyperfine structure, this does not necessarily make the line more likely, as the other lines are from the same gross structure.

3.2.7 Example for Carbon

Carbon is seen in large quantities in Sakurai’s Object, and therefore provides a good example relevant to this research. 12C has a full inner shell, and 4 electrons in the outer shell. This means that the 1s and 2s orbitals will both be full, and the 2p orbital will contain 2 electrons.

For the ﬁrst energy level (the inner shell home to the 1s orbital), n = 1, so l must be 0, meaning that j = 1/2. For the second energy level, n = 2, so l = 0, 1. The 2s orbital is assigned l = 0, and the 2p orbital is assigned l = 1. Using the same principles that were applied to the 1s orbital, it can be clearly seen that the 2s orbital also has j = 1/2. However, for the 2p orbital we must make use of the equation j = |l + s|, where s = ± 1/2, to show that the j values of the 2p orbital are 1/2 and 3/2. This means that the 2p orbital will split into 2 sub levels that are based on their j numbers. This is illustrated in Figure 3.1. Finally, the F numbers can be calculated using F = J ± 1/2, giving the levels shown in Figure 3.1. CHAPTER 3. ALMA AND ATOMIC PHYSICS 88

Figure 3.1: The Atomic Levels of Carbon with the Fine and Hyperﬁne Splitting Chapter 4

Data Collection

The original data used in this research was collected using ALMA. The data referred to as the 2014 data comes from project 2013.1.00516.S, which was released in stages between August 28th 2016 and February 5th 2017. These data cover band 6 and 7. The data referred to as the 2017 data is from project 2017.1.00017.S, which was released on October 17th 2019 and covers band 6. This data was retrieved from the ALMA archive and the calibration provided was applied to produce data ready for imaging. This data was then used to make image cubes, from which spectra were produced. Details for the data sets can be found in Table 4.1, where ’SPWs’ stands for spectral windows, ’Freq’ stands for frequency, ’No.’ stands for number, ’Obs’ stands for observations and ’Spec Res’ stands for spectral resolution.

The Band 7 2014 data consists of 2 observations made on the 25th of July 2015 and another made on the 27th of August 2015.

89 CHAPTER 4. DATA COLLECTION 90

Table 4.1: Details of the ALMA Data Sets

Characteristic 2013.1.00516.S 2013.1.00516.S 2013.1.00516.S 2017.1.00017.S Band 6 7 7 6 Time on Target (s) 310 123 62 1002 Freq Range (GHz) 211.1-245.81 316.21-331.95 320.02 - 336.0 256.11-274.84 No. Obs 5 2 1 4 SPWs per Obs 4 4 or 2 4 13 Spec Res (km/s) 5 7 28 2 Date 24 Jul 2015 25 Jul 2015 27 Aug 2015 28 Sep 2018

On the 25th of July, 2 observations were made, with one taking measurements for 4 spectral windows and the other taking measurements for an additional 2 spectral windows. The total time spent making measurements (not including calibration) was 123 seconds.

On the 27th of August, an additional observing session was run where measurements were taken for 4 spectral windows. These spectral windows were diﬀerent to those observed in July. CHAPTER 4. DATA COLLECTION 91

4.1 Making Image Cubes

In order to make image cubes, a python script was written. This script initially began by deleting any old versions of the spectral cube that had no continuum subtraction. It then imaged the spectral window without continuum subtraction using 500 iterations of the Högbom CLEAN and a natural weighting. Any old images of the continuum were then deleted, and the continuum was imaged using a natural weighting and 500 iterations of the Högbom CLEAN. This imaging process excluded any channels with spectral lines. At this point, any old versions of the continuum subtracted measurement set are deleted, and a new continuum subtracted data set is created. This was done using the ’uvcontsub’ task, which fits polynomials to the continuum only spectral windows in order to estimate the continuum emission. The fit produced is a representative model of the continuum in all channels, so it can be subtracted from the measurement set. Finally, old versions of the image cube for a given spectral window are deleted, and the spectral window can be imaged with continuum subtraction. This produces an image cube for a given spectral window, and this process is repeated for each spectral window in the 2017 data set.

Image cubes for the 2014 data had already been made, but the same process was followed.

4.1.1 The Continuum Images

When subtracting the continuum using the python script, one of four continuum images could be used. For the 2017 data, there is only image available, and this is shown in Figure 4.1. CHAPTER 4. DATA COLLECTION 92

Figure 4.1: A CASA FITS Image of the Continuum for the 2017 Data. The oval in the bottom left hand corner shows the beam size

For band 6 of the 2014 data, there is again only one image, and this is shown in Figure 4.2. CHAPTER 4. DATA COLLECTION 93

Figure 4.2: A CASA FITS image of the continuum for band 6 from the 2014 data

Upon looking at the data available for band 7 from 2014, it was discovered that 2 continuum images had been produced: one with all of the spectral windows, and another that had excluded spectral windows 4 and 5. Spec- tral windows 4 and 5 both sat either in or very close to an atmospheric transmission ’dip’, causing their calibration to be poor. This meant that these spectral windows were signiﬁcantly nosier than the others and de- graded the ﬁnal image. The decision was made to remove them and make a second continuum image (Figure 4.3), which is the image used in this research. CHAPTER 4. DATA COLLECTION 94

Figure 4.3: A CASA FITS image of the continuum band 7 from the 2014 data. This image does not include spectral windows 4 or 5

Table 4.2 outlines the speciﬁcations of each continuum image, with ’Freq’ being short for frequency, ’Dec’ being short for declination, and ’RA’ being short for right ascention.

Table 4.2: Details of the Continuum Images Produced in CASA

Image Year Freq Range Dec Pixel RA Pixel Beam Size Source Size rms Noise (GHz) Size (”) Size (”) (”) (”) (Jy) 4.1 2017 265-284 0.05 0.05 0.30 x 0.27 0.35 x 0.29 2.2×10−4 4.2 2014 228-262 0.04 0.04 0.22 x 0.18 0.24 x 0.20 3.2×10−4 4.3 2014 330-356 0.02 0.02 0.18 x 0.14 0.21 x 0.16 5.3×10−4

When the peak flux from each continuum source was measured using a Gaussian fit, the band 6 data for 2014 had a peak flux of 0.022 ± 9.6 × 10−4 Jy/beam. For the band 7 data from 2014, the peak flux was 0.022 ± 1.59 × 10−3 Jy/beam. For the 2017 data, the peak flux was 0.028 ± 6.6 × 10−4 Jy/beam. This increase could suggest that Sakurai’s Object is CHAPTER 4. DATA COLLECTION 95 still evolving, causing an increase in dust mass or dust temperature. Apart from this difference, there seems to be no other discrepancies between the 2 band 6 images. CHAPTER 4. DATA COLLECTION 96

4.2 The Resolved Nature of Sakurai’s Ob-

ject

The ﬁrst property of Sakurai’s Object that can be easily checked using CASA is how resolved the source is. This can be done using the PlotMS tool. By uploading a measurement set to PlotMS and setting the X axis to be a measure of the UV distance and the Y axis to be a measure of the amplitude, a plot is produced (Figure 4.4). In this case, the measurement set contained all the data from the 4 spectral windows in the 2017 data set.

At approximately 700m the ﬂux begins to become more constant, which may suggest that there is an unresolved source within Sakurai’s Object that could account for approximately half of the total ﬂux. However, it is not possible to rule out other causes. CHAPTER 4. DATA COLLECTION 97

Figure 4.4: A UV Distance vs Amplitude Plot for all Spectral Windows in the 2017 Data Set

If Sakurai’s Object was not resolved, the plot would show a ﬂat line with a constant, non-zero amplitude. A resolved source will produce a plot that shows the amplitude decreasing as the UV distance increases, and this takes the shape of a curve. As Figure 4.4 shows a curve of decreasing amplitude, it can be concluded that Sakurai’s Object is resolved. The fairly obvious nature of the curve would also suggest that Sakurai’s Object is well resolved, as a more deﬁned curve suggests a more resolved source.

As Figure 4.4 shows that the continuum is resolved, it would be possible to measure the angular size and frequency variation by ﬁtting a component and deconvolving the beam. CHAPTER 4. DATA COLLECTION 98

4.3 Producing Spectra

After producing the image cubes, it is possible to use CASA to produce spectra. First, a bounding ellipse must be drawn around the source, and this ellipse must include all emission from the source. For the 2017 data, the image cubes showed emission that had a very consistent maximum size, so all the bounding ellipses were kept at a size of 0.9” by 0.9”. For the 2014 data, the maximum emission varied in size, so each bounding ellipse was altered to ensure that as much emission as possible was being contained by the ellipse whilst minimising the background noise.

In order to decide where the centre of the bounding ellipse should be, a Gaussian ﬁt was plotted over the peak channel in each spectral cube, and this gave the coordinates for the peak emission within that ellipse. The size of each bounding ellipse and the centre x and centre y values can be found in Table 4.3. Table 4.3: Details of the Bounding Ellipses used in CASA

Window Band Frequency Range Bounding Ellipse Centre X Centre Y (GHz) (”) 25 6 258.0 - 259.8 0.900 x 0.900 17:52:32:702 -17.41.07.950 31 6 271.1 - 273.0 0.900 x 0.900 17:52:32:702 -17.41.07.905 2 6 227.1 - 228.9 0.942 x 0.802 17:52:32:691 -17.41.07.893 3 6 229.0 - 230.8 1.067 x 0.662 17:52:32:689 -17.41.07.867 5 6 216.7 - 218.5 0.875 x 0.875 17:52:32:700 -17.41.07.915 10 6 234.6 - 236.4 1.295 x 1.118 17:52:32:696 -17.41.07.992 16 6 226.1 - 227.9 0.670 x 0.471 17:52:32:699 -17.41.07.940 1 7 318.1 - 319.9 0.866 x 0.642 17:52:32:695 -17.41.07.944 7 7 329.4 - 331.2 0.690 x 0.474 17:52:32:693 -17.41.07.903 8 7 339.5 - 341.3 0.690 x 0.724 17:52:32:695 -17.41.07.847

Once an ellipse had been drawn, CASA can plot a spectrum of the emission, allowing the frequency that corresponded to the maximum ﬂux to be found. CHAPTER 4. DATA COLLECTION 99

This gave an indication of the frequency of the line in each spectral window that would be causing the emission. CHAPTER 4. DATA COLLECTION 100

4.4 Identifying Spectral Lines

In order to ensure that no relevant data was rejected, it was initially assumed that every peak in each spectral window was due to emission from Sakurai’s Object. Therefore, emission lines with similar frequencies to the peaks seen in each spectral window were identiﬁed using Splatalogue

(https://splatalogue.online//), and their frequencies and EU values were noted. As the lines we are trying to identify are coming from the nebula around Sakurai’s Object, a maximum EU limit of 500K was used for the line in the database. This value deﬁnes the energy needed for the line to reach the upper state, so this limit prevents any higher excitation lines from being included in this research. This limit was chosen as the current dust temperature is estimated to be approximately 180K (Evans et al. (2020)). It can be assumed that when the dust is cool, the gas is probably also cool. Whilst the two are not always in equilibrium and this assumption is not per- fect, no lines were detected that required high dust temperatures. Evans et al. (2020) also found molecular absorption lines, indicating molecules cooler than the dust, further supporting this temperature limit.

Once lines had been identiﬁed, the equation

∆ν v = − × c (4.1) ν was used to calculate the velocities of the lines, where ∆ν is the diﬀer- ence between the measured frequency and the frequency of the line, ν is the measured frequency, and c is the speed of light in a vacuum (3×108 ms−1). CHAPTER 4. DATA COLLECTION 101

As Eyres et al. (2004) calculated a radial velocity of -170 km s−1 ± 30 km s−1 for an absorption, this was the velocity used for absorption lines in this research. For emission lines, Tafoya et al. (2017) calculated velocities of 128 ± 14 km/s for a HCN line, and 123 ± 13 km/s for a H13CN line. Using these two values, an approximate velocity range of 110 - 142 km/s could be found. However, as the smallest channel widths for the 2017 data are 4.31 km/s and 4.52 km/s, this range was expanded to 105 km/s - 147 km/s to prevent any possible identiﬁcations from being missed. This velocity corresponds to a frequency shift of approximately 0.12GHz from the rest frequency.

As the 2017 data had the most obvious emission, these spectral windows were examined ﬁrst to identify possible lines and calculate an approximate velocity range based on our data. A H13CN line was found in spectral window 25, the large peak in spectral window 31 was found to be HNC, and the smaller peak was found to be HC3N. These lines are detailed in Tables 4.4, 4.5, and 4.6, and are shown in Figures 4.5, 4.6, and 4.7. Using the HNC line in spectral window 31 (Figure 4.6), it can be seen that the feature runs from approximately -300 to 500 km/s, as shown by the black dashed lines. The extent of the line was found by determining where the emission returned to approximately zero. The majority of the identiﬁed lines will fall within the brightest part of the feature, which runs from approximately 150km/s ± 100 km/s. This gives a velocity range between 50 km/s to 250km/s, which was then used to identify other possible emission lines.

Once potential line identiﬁcations had been found in Splatalogue, it was CHAPTER 4. DATA COLLECTION 102 necessary to evaluate how likely they were to be causing the features. Com- plicated molecules were ruled out as these are less likely to form on the timescale of the evolution of Sakurai’s Object as they require more atoms and more complicated chemistry. There were also lines that were deemed to be possible, but that lacked additional lines of the same species in the ALMA data. If additional lines had been present, it is likely that the lines would have been bright enough to be detected. It was therefore less likely that these lines alone were able to produce the broad features observed, so these lines were deemed to be slightly less likely but could not be ruled out.

After examining all the possible lines for each spectral window, some windows were found to have no viable candidates. Upon looking again at the image cubes and spectra, it was concluded that any emission found in these spectral windows was likely to be noise. This was concluded either because the emission appeared in only one or two channels (such as spectral windows 18 band 6 and 3 band 7), or because the spectra showed a low peak that didn’t stand out signiﬁcantly from the noise (such as 6 band 6 which had a peak ﬂux of 1.775 ± 2.1 mJy/beam, and a noise of 1.021 mJy/beam of noise). These spectral windows were then discounted.

The lines that were left were then plotted in their respective spectral windows using CASA. This enabled us to see how well the lines overlapped with the peaks in the spectral window at their calculated velocity. If the lines overlapped well, they were likely to be correct identiﬁcations, whereas those with a poor overlap could be ruled out.

The ﬁnal identiﬁcations from this stage of the study can be found in Table CHAPTER 4. DATA COLLECTION 103

4.5. Rows 1, 2, and 3 contain the identiﬁcations from the 2017 data, and all other rows are for 2014 data. Rows 6 and 7 shows the details for the main peak in spectral window 5, whereas row 8 details a minor peak. Row 11 details an absorption feature in spectral window 16, hence the blue shifted velocity. Row 10 details the peak to the right of the absorption feature in spectral window 16, and row 12 details the peak to the left.

Table 4.4: Initial Line Identiﬁcations

Row Window Band Formula Freq Temp EU Intensity Velocity (GHz) (K) (km/s)

1 25 6 H13CN 259.0018 12.4 -1.142 126

2 31 6 HNC 271.9811 13.1 -1.031 145

3 31 6 HC3N 272.8847 160.1 -1.106 141

4 2 6 HC3N 227.4189 131.0 -1.259 168 5 3 6 CO 230.5380 5.5 -4.120 145

6 5 6 HC3N 218.3247 120.5 -1.296 152

7 5 6 HC3N 218.3247 120.5 -1.295 72 8 5 6 13CN 217.4364 5.2 -3.268 170

9 10 6 HC3N 236.5128 141.9 -1.222 139

10 16 6 HC3N 227.4189 131.0 -1.257 88 11 16 6 CN 226.9054 5.4 -4.782 -149

12 16 6 CN 226.6596 5.4 -2.682 166

13 1 7 HC3N 318.3408 259.8 -1.008 147 14 7 7 13CO 330.5880 15.9 -3.666 73

15 7 7 13CO 330.5880 15.9 -3.909 153

16 8 7 CN 340.0196 16.3 -3.063 122 CHAPTER 4. DATA COLLECTION 104

In Table 4.4, ’Temp’ is EU , which is the upper energy level of the transition. ’Freq’ denotes the rest frequency of the line. The intensities provided are from the JPL and CDMS catalogues, which give intensities as the base 10 logarithms of the integrated intensity at a temperature of 300K. They are relative to the strength of the line, and have units of nm2 MHz. All of these transitions are in the ground state, so v=0.

In order to judge how meaningful a detection is, it is important to know the noise level in the cube, as well as the ﬂux produced by the feature. These can be found in Table 4.5, along with the frequency range for each feature. It is important to note that these features are spread over multiple channels, making their detection more signiﬁcant.

Table 4.5: Peak Flux ± 3σ, Noise, and Frequency Range Data for Initial Line Identiﬁcations

Row Window Band Formula Peak Flux Noise Frequency Range (mJy) (mJy) (GHz) 1 25 6 H13CN 125.2 ± 3.1 1.3 258.602 - 259.137 2 31 6 HNC 145.2 ± 5.7 1.9 271.446 - 272.223 3 31 6 HC3N 22.8 ± 5.7 1.9 272.578 - 272.862 4 2 6 HC3N 22.33 ± 3.3 1.1 227.185 - 227.601 5 3 6 CO 33.88 ± 8.7 2.9 230.212 - 230.664 6 5 6 HC3N 22.32 ± 3.6 1.2 217.865 - 218.388 7 5 6 HC3N 21.98 ± 3.6 1.2 217.865 - 218.388 8 5 6 13CN 12.32 ± 3.6 1.2 217.030 - 217.496 9 10 6 HC3N 28.27 ± 5.1 1.7 236.212 - 236.400 10 16 6 HC3N 16.09 ± 6.3 2.1 227.113 - 227.435 11 16 6 CN -7.805 ± 6.3 2.1 226.895 - 227.113 12 16 6 CN 14.94 ± 6.3 2.1 226.322 - 226.895 13 1 7 HC3N 39.44 ± 10.5 3.5 318.099 - 318.471 14 7 7 13CO 34.76 ± 13.2 4.4 330.164 - 330.849 15 7 7 13CO 33.74 ± 13.2 4.4 330.164 - 330.849 16 8 7 CN 77.03 ± 7.8 2.6 339.579 - 340.244

The spectral resolution, J numbers, and velocity ranges of the lines are CHAPTER 4. DATA COLLECTION 105 detailed in Table 4.6. In this table, ’Spec Res’ stands for spectral resolution.

Table 4.6: Initial Line Identiﬁcations

Row Window Band Formula Spec Res Velocity Range J (kHz) (km/s)

1 25 6 H13CN 4.5 -966-1200 3-2

2 31 6 HNC 4.3 -914-1148 3-2

3 31 6 HC3N 4.3 -914-1148 30-29

4 2 6 HC3N 40 -1190-1210 25-24 5 3 6 CO 40 -1200-1200 2-1

6 5 6 HC3N 40 -1251-1269 24-23

7 5 6 HC3N 40 -1251-1269 24-23 8 5 6 13CN 40 -1251-1269 5/2-3/2

9 10 6 HC3N 40 -1149-1171 26-25

10 16 6 HC3N 40 -1184-1216 25-24 11 16 6 CN 40 -1184-1216 2-1

12 16 6 CN 40 -1184-1216 2-1

13 1 7 HC3N 40 -862-858 35-24 14 7 7 13CO 40 -823-817 3-2

15 7 7 13CO 40 -823-817 3-2

16 8 7 CN 40 -808-792 3-2 CHAPTER 4. DATA COLLECTION 106

4.5 Analysing the Spectral Lines

After determining initial identifications of the lines, the spectra were plotted in velocity space with respect to the rest frequency of the identified line. Figures 4.5 to 4.16 show the spectra for each line identified. The red lines in each figure show the peaks in question, and the black dashed lines show the extent of the feature.

Figure 4.5: Spectral Window 25 in velocity space with respect to the iden- tiﬁed H13CN line CHAPTER 4. DATA COLLECTION 107

Figure 4.6: Spectral Window 31 in velocity space with respect to the iden- tiﬁed HNC line

Figure 4.7: Spectral Window 31 in velocity space with respect to the iden- tiﬁed HC3N line CHAPTER 4. DATA COLLECTION 108

Figure 4.8: Spectral Window 2 Band 6 in velocity space with respect to the identiﬁed HC3N line

Figure 4.9: Spectral Window 3 Band 6 in velocity space with respect to the identiﬁed CO line CHAPTER 4. DATA COLLECTION 109

Figure 4.10: Spectral Window 5 Band 6 in velocity space with respect to the HC3N line

Figure 4.11: Spectral Window 5 Band 6 in velocity space with respect to the 13CN line CHAPTER 4. DATA COLLECTION 110

Figure 4.12: Spectral Window 10 Band 6 in velocity space with respect to the HC3N line

Figure 4.13: Spectral Window 16 Band 6 in velocity space with respect to the CN line found in the absorption feature CHAPTER 4. DATA COLLECTION 111

Figure 4.14: Spectral Window 1 Band 7 in velocity space with respect to the HC3N line

Figure 4.15: Spectral Window 7 Band 7 in velocity space with respect to the 13CO line CHAPTER 4. DATA COLLECTION 112

Figure 4.16: Spectral Window 8 Band 7 in velocity space with respect to the CN line

As with all spectra, it is important to note that weaker lines may be dis- torted by noise. As such, only obvious spectral features have been identiﬁed for this research.

Figure 4.9 looks like it should be double peaked, but no credible identiﬁ- cations could be found for the peak on the left. The peak on the right, indicated by the red line, was identiﬁed as a CO line.

Figure 4.10 shows a double peaked feature. Both peaks are caused by HC3N lines with frequencies of 218.3247 GHz (4 decimal places). The peak on left of Figure 4.10 has a peak ﬂux of 21.98 ± 3.6, whereas the peak on the right has a peak ﬂux of 22.32 ± 3.6 1.2 217.865 - 218.388

The peak in Figure 4.11 has been identiﬁed as being caused by a 13CN line. When looking through the possible lines suggested by Splatalogue, another 9 13CN lines were found. They have frequencies ranging from 217.4286 CHAPTER 4. DATA COLLECTION 113

GHz to 217.4967 GHz, and intensities between -5.366 and -2.780. All the additional lines have EU values between 5.24K and 5.25K. These additional lines strongly support the previous identiﬁcation, as they would contribute to the overall strength of the feature.

There were also 2 isotopologues of HC3N identiﬁed in the frequency range of the feature in Figure 4.11. One was a HC13CCN line with a frequency of

217.3985 GHz, an EU value of 120K, and an intensity of -1.299. The other

13 was a HCC CN line with a frequency of 217.4196GHz, an EU of 120K, and an intensity of -1.299. Whilst these lines are both independently stronger than any of the 13CN lines, the quantity of 13CN lines was deemed to be large enough that the overall intensity would be greater from 13CN.

For Figure 4.12, the peak on the right hand side was identiﬁed as noise. However, on the left hand side the spectrum begins to rise, suggesting that this could be the edge of a feature. Upon examination, a HC3N line was found to be a possible candidate, so the frequency of this line has been used to produce this plot.

Spectral window 16 band 6 is unusual as it is the only window that shows a convincing absorption feature. The absorption feature sits between 2 emission features, as shown in Figure 4.13. This is due to the emission features having positive velocities, and the absorption feature having a negative velocity. The feature on the left in the figure has been identified as being caused by HC3N, but the feature on the right has been identified as being caused by CN. There are also 8 additional CN lines that are either part of the right feature or just outside it, suggesting that there is in fact a CN ’forest’ in the region. These lines have frequencies ranging CHAPTER 4. DATA COLLECTION 114

between 226.6596 GHz to 226.8874 GHz, EU values from 5.43K to 5.45K, and intensities between -3.40 to -2.48.

It is therefore suggested that the absorption feature and emission feature on the right are part of the same feature, potentially caused by a line with both a emission part and an absorption part. Alternatively, noise may be distorting the plot in such a way that a singular emission or absorption feature has been made to look like two features: one absorption and one emission, but the features look to be well above the noise level, so this is unlikely.

It is also possible that Figure 4.13 shows a P Cygni profile. These profiles show strong emission lines alongside blue shifted absorption lines (Israelian and de Groot (1999)), both of which are seen in Figure 4.13. This profile would suggest some sort of outflow is occurring, possibly due to a wind (Israelian and de Groot (1999)). Whilst it is not possible to determine if this is indeed the case here, it should not be overlooked as a possible cause of the shape seen in Figure 4.13.

Whilst the main peak in Figure 4.14 is sharp and narrow, it seems to be part of a broader feature, suggesting that whilst there may be distortion due to noise, there is likely to still be emission in this region.

Figure 4.15 shows a double peaked feature, with both peaks being caused by 13CO with a rest frequency of 330.5880 GHz. They are separated by 80 km/s and the peak on the left has a ﬂux of 34.76 ± 13.2 Jy, whereas the peak on the right has a peak ﬂux of 33.74 ± 13.2 Jy.

Spectral window 8 band 7 has 4 additional CN lines near the peak. These are detailed in Table 4.7. CHAPTER 4. DATA COLLECTION 115

Table 4.7: Additional CN Lines for Spectral Window 8 Band 7

Formula Frequency (GHz) EU (K) Intensity CN 399.9923 16.310 -4.439 CN 340.0081 16.310 -3.061 CN 340.0196 11.335 -3.063 CN 340.0315 11.336 -2.144

These additional lines help to explain the broad nature of the feature, as well as the strength of the feature. Whilst each individual line is not particularly strong, their combined strength would be capable of producing an obvious emission feature, as seen in Figure 4.16. CHAPTER 4. DATA COLLECTION 116

4.6 Additional Line Searches

In order to ensure that no possible candidates were missed, a large search of the Splatalogue database was conducted. This involved searching a frequency range of 217GHz to 343GHz simultaneously for any lines that were deemed to be likely. The lines searched for were: HCN, H13CN, HC15N, H13C15N, CN, 13CN, C15N, 13C15N, HNC, HN13C, H15NC, H15N13C, CO,

13 17 18 13 17 13 18 13 13 13 CO, C O, C O, C O, C O, HC3N, HC CCCN, HC CCN, HCC CN, HCCC15N, H13C13CCN, H13CC13CN, HC13C13CN, HCC13C15N,

None of these searches provided any new identiﬁcations. Some searches - such as that for H13CN - returned no lines, and others - such as that for C15N - only returned lines that were outside the spectral windows but were still within the range given.

4.6.1 HC5N

Although HC5N may be less abundant in Sakurai’s Object, it was still expected due to the potential for its formation during a shock, which Saku- rai’s Object is believed to have undergone. HC5N is also formed in the chemical models discussed in Chapter 5. To ensure that no lines had previously been overlooked, additional searches in Splatalogue were conducted

for HC5N and the isotopologues. A total of 76 lines were found, but only 6 fell into any of the frequency ranges of the lines (see Table 4.5) whilst also having a velocity with the correct sign with respect to the velocity of Sakurai’s Object.

2 of these lines fell into the frequency range for the HC3N feature in spectral window 5 band 6, and they are detailed in Table 4.8. CHAPTER 4. DATA COLLECTION 117

Table 4.8: Details of the Additional Lines for Spectral Window 5 Band 6

Formula Frequency EU Intensity J Velocity (GHz) (K) (km/s)

HC5N 218.2722 294.9 -1.6 82-81 80 HC5N 218.2770 294.9 -1.6 82-81 87

In order to establish how conﬁdently the peak in spectral window 5 band

6 can be labelled as HC3N, the spectrum was plotted with that from the

HC3N peak from spectral window 31 as the identiﬁcation in spectral window 31 was deemed to be incredibly likely. Figure 4.17 shows this overlap.

Figure 4.17: Spectral Windows 31 and 5 Band 6 in velocity space with respect to HC3N

The similarities in the shape of the peaks in Figure 4.17, and the placement of the red lines, shows a strong level of agreement between the two spectral windows. This means it is highly likely that spectral window 5 band 6 is showing emission from a HC3N line rather than a HC5N line, meaning that

no HC5N has been conﬁdently identiﬁed in this spectral window. On top CHAPTER 4. DATA COLLECTION 118

of this, the HC5N lines outlined in Table 4.8 have high J numbers and EU values, meaning that whilst they may have contributed to the emission, they are not the primary cause.

The remaining four lines fall into spectral window 16 band 6. They are detailed in Table 4.9.

Table 4.9: Details of the Additional Lines for Spectral Window 16 Band 6

Formula Frequency EU Intensity J Velocity (GHz) (K) (km/s) HC13CCCCN 226.5673 321.2 -1.6 82-81 44 HC13CCCCN 226.5701 321.2 -1.6 82-81 48 HCCCC13CN 226.6517 321.4 -1.6 Unknown 156 HCCCC13CN 226.6517 321.4 -1.6 Unknown 160

As there is a large ’forest’ of CN lines in the region of both the CN emission and absorption, it is likely that these are the primary cause of the emission. Whilst the HC5N lines have transition frequencies in a similar range, these do not line up well with the peak of the emission or the deep- est part of the absorption. This is achieved by CN lines. In addition to

13 this, both HC CCCCN lines have high J numbers, and EU values twice as high as every line in Table 4.4 except the HC3N line in row 13, making the HC13CCCCN unlikely to be present. Whilst the remaining 2 lines could be present, these two lines alone are unlikely to have caused the broad shape seen, suggesting that whilst these lines may have contributed to the feature, they are not the primary cause.

Investigating the potential presence of HC5N lines provided a good test of the chemical modelling later used on the data. CHAPTER 4. DATA COLLECTION 119

Whilst there are potential HC5N lines in the bands observed, it was determined that they make a negligible contribution. However, its abundance can be used to determine how likely a model is to be accurately representing Sakurai’s Object. CHAPTER 4. DATA COLLECTION 120

4.7 Final Identiﬁcations

From the searches outlined above, the ﬁnal identiﬁcations for the lines seen in Sakurai’s Object remain unchanged from Table 4.4. Chapter 5

Astrochemistry

121 CHAPTER 5. ASTROCHEMISTRY 122

5.1 Environments in Space

Most of the chemical reactions detected in space occur in the interstellar medium (ISM), which is the dilute gas that permeates the space between stars (van Dishoeck (2014)). The ISM is not homogeneous, with kinetic temperatures ranging from 10K to 106K, and densities between 10−4cm−3 to 108 cm−3 (van Dishoeck (2014)). The three main environments that make up the interstellar medium are the diﬀuse interstellar medium, giant molecular clouds, and the circumstellar medium.

5.1.1 Diﬀuse Interstellar Medium

The diﬀuse interstellar medium can be seen as empty space due to the low particle densities of between 1 to 100 cm−1 (Millar and Williams (1993)). The main constituents of this medium are atomic hydrogen and ions. The molecular fraction of these is 0.0-0.1, where the molecular fraction is deﬁned as the number ratio of molecular hydrogen to atomic hydrogen.

5.1.2 Circumstellar Medium

The circumstellar medium is the name given to the area surrounding a star. As stars in different stages of evolution have different characteristics, the UV flux can vary dramatically. This is particularly noticeable when the fluxes from the AGB stage and the post AGB stage are compared.

5.1.3 Giant Molecular Clouds

Giant molecular clouds are colder and denser regions of gas in the ISM, and they contain a large range of molecules, allowing a vast array of reactions CHAPTER 5. ASTROCHEMISTRY 123

to occur inside them (van Dishoeck (2014)). Most of the mass in the interstellar medium is found in these clouds, and they can have diameters of up to 30 pc. Densities within these clouds are usually between 100- 1000 cm−3, with kinetic temperatures ranging between 10-100K (Millar and Williams (1993)).

Within giant molecular clouds there are three subtypes: diﬀuse, translucent, and dense. Diﬀuse molecular clouds consist mainly of atomic species and have molecular fractions between 0.1 – 0.5. Translucent molecular clouds contain predominantly molecular hydrogen and atomic carbon (normally C or C+). Any molecular carbon is usually in the form of CO. In dense molecular clouds, almost all hydrogen and carbon are in molecular form. Hydrogen is found as H2, and carbon is usually found as CO. Whilst

there are other simple molecules present, such as CH and H2O (Millar and Williams (1993)), these have such low number densities that they are almost negligible. CHAPTER 5. ASTROCHEMISTRY 124

5.2 Synthesis and Ionisation in Space

5.2.1 Molecular Synthesis

Molecular synthesis occurs in interstellar clouds, usually through ion-molecule reactions (Millar and Williams (1993)). The reactions are reasonably fast as the charges on the ions will act as an attractive force, making collisions more likely. From Chapter 4, it can be seen that ALMA did not detect ionised species in Sakurai’s Object, implying any ionic species formed by molecular synthesis must have been neutralised. The usual path followed is a neutral gas is ionised and forms small ions, before reacting to form larger ions (Millar and Williams (1993)). These are then neutralised to give the species that are observed by equipment such as ALMA. There were no ionic species detected in the observations used in this research.

5.2.2 Ionization

Gas clouds close to stars are often subjected to photoionization due to the large number of UV photons being emitted by the star. However, molecular clouds contain large amounts of hydrogen and dust grains, both of which prevent visible and UV light from penetrating the inner regions of the cloud (Millar and Williams (1993)). To reach these inner regions infrared photons would be needed, but these are not energetic enough to ionize the molecules, so most molecules are ionized by cosmic rays with the required kinetic energy (Millar and Williams (1993)). The two ionization reactions that may occur with cosmic rays are ionization and dissociative ionization. CHAPTER 5. ASTROCHEMISTRY 125

Ionization can be generally written as:

AB + cr −→ AB+ + e− + cr, (5.1) where cr is a cosmic ray.

Dissociative ionization can be written as:

AB + cr −→ A + B+ + e− + cr. (5.2)

Whilst these are the 2 main ionization reactions, cosmic rays are also involved in dissociation:

AB + cr −→ A + B + cr, (5.3)

and excitation: AB + cr −→ AB∗ + cr, (5.4)

where AB* is in an excited state. CHAPTER 5. ASTROCHEMISTRY 126

5.3 Gas Phase Chemical Reactions in Space

There are several diﬀerent types of gas-phase reactions, which can be broken down into three groups: bond forming, bond breaking, and rearrangement.

5.3.1 Bond Formation Reactions: Radiative Associa-

tion

Radiative association reactions require two reactants to collide and form a single product. Due to conservation laws, the product is usually found in an excited state and must either lose energy via photon emission or decay back to its reactants (Bates and Herbst (1988)). On Earth, this excited product would normally undergo another collision with a third body to get rid of excess energy, but the low collision frequency in the ISM makes this unlikely (Millar and Williams (1993)). If the product can easily emit a photon to reach its ground state, then the reaction will prove to be an efficient way of producing large ions (Millar and Williams (1993)). However, if this is not the case, infrared emission is the only way the product can prevent decay, making the reaction slow and inefficient. Reaction rate coefficients for radiative association range from 10−17cm3s−1 to 10−9cm3s−1 (Millar (2015)). This reaction can be written as:

A + B −→ AB + hν. (5.5) CHAPTER 5. ASTROCHEMISTRY 127

5.3.2 Bond Formation Reactions: Associative Detach-

ment

In these reactions, a negative ion and a neutral species react to form a neutral molecule and an electron (Millar and Williams (1993)). The electron originates from the negative ion and will carry away any excess energy produced in the reaction to comply with conservation laws. The reaction has the general form: A− + B −→ AB + e−. (5.6)

5.3.3 Bond Formation Reactions: Dust-Grain-Catalysed

Reaction

When cool, evolved stars begin to lose mass, dust as well as molecules form within a few to approximately ten stellar radii. Molecules collide with and stick to the grains, forming ice once the wind is far enough from the star to be cool enough.

Reactions on dust grains give products that are highly reactive, increasing the speeds at which other reactions can occur. The most famous reaction that occurs on dust grains is:

H + H −→ H2, (5.7) which requires two H atoms to collide with a dust grain and freeze on to the surface. This allows reactions such as the formation of H2 to occur (Millar and Williams (1993)). Again, conservation laws apply, and so the dust grain removes any excess energy from the reaction. CHAPTER 5. ASTROCHEMISTRY 128

5.3.4 Bond Breaking Reactions: Photodissociation

and Collisional Dissociation

Photodissociation occurs when a molecule absorbs a photon that has ad- equate energy to break a chemical bond (Millar and Williams (1993)). It has the generic form: AB + hν −→ A + B. (5.8)

Collisional dissociation occurs when a molecule collides with a third body (represented as M in equation 5.9) and provides the energy to break a chemical bond. This can be represented by:

AB + M −→ A + B + M. (5.9)

5.3.5 Bond Breaking Reactions: Dissociative recom-

bination

In dissociative recombination, an ion combines with an electron to produce a neutral molecule (Millar and Williams (1993)). However, the product will have large amounts of energy that cannot be removed due to low particle densities reducing the likelihood of a collision with a third body. This causes the product to split into smaller, stable, neutral species, which can be both atomic and molecular. These reactions can have rate constants of 10−6cm3 s−1 (Millar and Williams (1993)), making them very fast and meaning it is diﬃcult to observe the intermediate product from the ﬁrst reaction. CHAPTER 5. ASTROCHEMISTRY 129

5.3.6 Rearrangement reactions: Charge transfer

Neutral species are capable of transferring electrons to ions, causing the ion to dissociate (Millar and Williams (1993)). This can be written generally as: A+ + BC −→ B+ + C + A + energy. (5.10)

When this occurs, the ionisation energy of the original ion (A+) is released, and this can cause the remaining product to split into its constituents (B+ and C) for use in further reactions (Millar and Williams (1993)).

5.3.7 Rearrangement Reactions: Neutral reactions

Throughout the ISM the kinetic temperature is so low that it is not usually possible to overcome the activation barriers for neutral reactions unless a shock occurs (Millar and Williams (1993)). The shock will compress the gas, increase its kinetic temperature and possibly allow the barriers to be overcome. In Sakurai’s Object, there are several high velocity components that suggest shocks are present, meaning that neutral reactions may be seen more frequently.

5.3.8 Rearrangement Reactions: Ion-molecule reac-

tions

Most reactions in the ISM that involve 2 molecules are ion-molecule reactions. These reactions rarely have barriers, meaning the low kinetic temperatures seen in the ISM will not prevent the reactions occurring.

An example of an ion-molecule reaction is hydrogen atom abstraction (Yang CHAPTER 5. ASTROCHEMISTRY 130 et al. (2016)), where one of the faster and more common reactions is:

+ H2 + H2 −→ H3 + H + 1.7eV. (5.11)

+ As the ISM contains a large quantity of both H2 and H2 , this reaction is

+ seen frequently. The H3 ion is then used in proton transfer reactions such as:

+ + H3 + H2O −→ H3O + H2 + 2.8eV. (5.12)

Proton transfer reactions occur between species with low proton affinity to species with high proton affinity. This difference in proton affinity is the source of the energy produced in the reaction. CHAPTER 5. ASTROCHEMISTRY 131

5.4 Chemistry in Molecular Clouds

Due to the low kinetic temperatures – and therefore energies - in molecular clouds, activation barriers of reactions cannot be overcome during collisions. This limits the types of reactions that can occur to radical-radical reactions and ion-molecule reactions, as neither of these have any barriers. In addition to this, the low densities make it unlikely that two molecules will collide, which is demonstrated by a low collision frequency. The collision frequency for a speciﬁc combination of molecules can be calculated using: 1 8k T 2 z = σ B n n , (5.13) c πµ A B where z is the number of collisions in a unit volume each second (the collision frequency), σc is the collision cross section, kB is the Boltzman constant, T is the temperature, µ is the reduced mass, and nA and nB are the number densities of the species (Shaw (2007)). As the values for z can be incredibly small, reactions in space can occur over large time frames. Whilst these time frames could potentially be problematic on Earth, giant molecular clouds can last 100 million years before being destroyed by stellar winds or heat from the stars forming inside them, meaning there is ample opportunity for reactions (Millar and Williams (1993)).

It is also important to consider the types of molecules that can be involved in these reactions. For example, on Earth carbon requires four bonds to become stable, but in interstellar clouds carbon can exist as a radical, molecular ion, subvalent species, or energetic isomer, allowing for a wider range of reactions that involve some form of carbon (Millar and Williams (1993)). CHAPTER 5. ASTROCHEMISTRY 132

5.5 Chemistry in Circumstellar Envelopes

Circumstellar envelopes found around evolved AGB stars are usually subjected to large amounts of UV radiation, both from the star they surround and from other nearby sources (Saberi et al. (2019b)). Whilst it is sus- pected that an internal UV source would increase the number of atomic and ionic species found in CSEs, internal sources are rarely included in models. Most standard models do include external UV radiation that causes photodestruction, and an internal UV source would aid this process (Millar and Williams (1993)). The internal source of UV radiation could come in many forms. It is most likely to arise due to activity in the chromosphere of the star contained within the CSE, but it may also be due to a hot binary companion, accretion between two stars in a binary, or a combination of factors (Saberi et al. (2019b)).

Within the CSE, photodissociation is the most common process, meaning it determines the abundances of CO, C and C+ throughout the CSE (Saberi et al. (2019a)). When an internal UV ﬁeld is added to CSE models, the number of dissociation reactions seen in CO in the inner CSE is expected to increase, which would lead to higher levels of C and C+, both of which are formed in dissociation reactions (Saberi et al. (2019a)). CHAPTER 5. ASTROCHEMISTRY 133

5.6 Astrochemical Modelling

The aim of the astrochemical modelling was to see if it was possible to ﬁnd a model that would produce the molecules found in the ALMA data sets. From this model, it would then be possible to make a rough prediction about the evolution of Sakurai’s Object, both in the near future and in far future.

The model would also be able to help confirm the line identifications made in Chapter 4, as if the model failed to produce the molecules seen in the ALMA data, it would be necessary to reevaluate the identifications.

5.6.1 Background to the UMIST Database for Astro-

chemistry

The UMIST Database for Astrochemistry (UDfA) is a chemical reaction network that details 617 gas-phase reactions that involve 467 species (McEl- roy et al. (2013)). The UDfA reaction network can be used to model dark clouds, circumstellar envelopes (CSEs), photodissociation regions (PDRs), hydrodynamic shock regions, and diﬀuse clouds without needing to edit the reactions that are included in the relevant codes (McElroy et al. (2013)). So far, the database has had 5 oﬃcial releases, Rate91, Rate95, Rate99, and Rate06 (McElroy et al. (2013)).

After the release of Rate06, a newer version with minor updates called Rate12 was released. The release of Rate12 was accompanied by an update to the UDfA website, which allows users to download the entire reactions network (McElroy et al. (2013)). The website also enables the user to search for reactions by species (McElroy et al. (2013)), with each species CHAPTER 5. ASTROCHEMISTRY 134 having a dedicated page. Here, the user can ﬁnd reactions that produce or destroy the species, alongside information on those reactions, including the values of α, β, and γ, as well as the maximum and minimum temperatures (McElroy et al. (2013)). Since the release of Rate12, some more minor improvements were made, and these were released as Rate13, which is the version used in this research.

5.6.2 Background to the Dark Cloud Chemical Model

In order to produce models, the dark cloud chemical model from UMIST was used. This consists of several ﬁles that are combined using the command ’make’, which compiles the model that is executed using the command ’./model’.

The species that are included in the model are listed in the ﬁle ’dc.specs’. This is split into four columns: the species number, species name, initial abundance relative to the number of hydrogen nuclei, and mass in atomic units.

The file ’rate13.rates’ lists the reactions that occur when the model is run. The first column gives the reaction number, the second gives the reaction type, columns 3 and 4 give the reactants, and columns 5 - 8 give the products (McElroy et al. (2013)). Column 9 gives the number of temperature fields, columns 10, 11, and 12 give the values of the constants α, β, and γ respectively which are used to calculate the reaction rate coefficient for each reaction (McElroy et al. (2013)). Columns 13 and 14 give the minimum and maximum temperatures for the reaction, column 15 gives the source type, column 16 gives the accuracy of the reaction, and column 17 CHAPTER 5. ASTROCHEMISTRY 135

provides references (McElroy et al. (2013)).

The ordinary differential equations (ODEs) used by the model can be found in the file ’dcodes.f’, which is a FORTRAN programme. These ODEs define the rate of change of abundance of a given species using the current abundance of the species and the previously calculated coefficients from the ’dcrates.f’ file.

The source code for the model is ’rate13main.f’, and it is here where the physical parameters of both the cloud and the grains can be defined. For the cloud, these parameters include the density and temperature of the cloud, cosmic ray ionisation, UV radiation field scaling factors, and visual extinction. For the grains, these parameters are the grain number density, radius, albedo, and the sticking coefficient for hydrogen atoms.

When the model is executed it produces 4 output files. The ’rates.txt’ file details the chemical reactions that occurred. The file ’analyse.out’ shows the reactions that destroy and produce each atom and molecule, and how much of the destruction or production the reaction is responsible for as a percentage. The file ’rate13steady.state’ contains the initial conditions and fractional abundances when the model reaches a steady state. This will occur at the final time step, which is 108 years. The main output file is ’dc.out’, which provides a table detailing the fractional abundance of each species at each time step. The abundance is relative to that of H2. For the

column detailing H2, the values listed are instead the number density per cm3. CHAPTER 5. ASTROCHEMISTRY 136

5.6.3 Using the Dark Cloud Chemical Model

Before any models were run, it was necessary to decide on a range of hydrogen to carbon ratios that would be used to cover a range of environments that were both hydrogen rich and hydrogen poor. This would enable us to determine the limits of the code, as it was found to fail when given extreme initial conditions. The ratios chosen were: 5H:C, 2.5H:C, 2H:C, H:C, H:2C, H:2.5C, and H:5C.

In order to achieve the ratios listed above, the initial abundances were changed in the ’dc.specs’ ﬁle. The values inputted into ’dc.specs’ are detailed in Table 5.1. It is important to note that this code prints output values when executed, and these are twice as large as the input values.

This is because the output values are given with respect to H2, whereas the input values are given with respect to the total amount of hydrogen nuclei.

For all models, the H2 input value is kept at 1, and the input values for all other species is set to 0 automatically by the code. To maintain a constant number of atoms in each model, the He abundance was varied in line with the abundance of C. This made the models more comparable, and ensured that a diﬀerence in the total number of atoms could not be responsible for any diﬀerences between the models.

Table 5.1: Input abundances for the ﬁrst test models

Atom or Molecule Abundance Relative to H Nuclei ——- 5H:C 2.5H:C 2H:C H:C H:2C H:2.5C H:5C H 1.00 1.00 1.00 1.00 1.00 1.00 1.00 He 28.60 28.20 28.00 27.00 25.00 24.00 19.00 C 0.40 0.80 1.00 2.00 4.00 5.00 10.00 N 2.00 2.00 2.00 2.00 2.00 2.00 2.00 O 2.00 2.00 2.00 2.00 2.00 2.00 2.00 H2 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CHAPTER 5. ASTROCHEMISTRY 137

These models did not take into consideration that the density in ’rate13main.f’ is relative to hydrogen, which means that in order to keep the density constant between models, the density would need to be multiplied by:

H k = tot , (5.14) ntot

where Htot is the number of atoms making up the H2 molecules and atomic hydrogen, and ntot is the total number of particles in the model. This means that the models are not fully comparable with each other, but they do provide an insight as to the appropriateness of the selected ratios, and whether they will produce the molecules previous identiﬁed. As all 7 models were successfully computed and produced the molecules predicted by ALMA, it could be concluded that these ratios were appropriate for further use.

Another factor that must be kept constant is the carbon to oxygen ratio, as changing this makes the models less comparable. As Sakurai’s Object is carbon rich, the initial C:O ratio was set at 2.5:1, allowing for minor changes at a later stage if needed.

The next stage was to include the number density alteration (Equation 5.14) in the models whilst keeping carbon constant to allow for comparisons between the models. This required the atomic hydrogen abundance to change for each model instead of the carbon. The abundance of helium was also changed to ensure each model had the same number of atoms. The parameters used are shown in the Table 5.2. The initial values for carbon, nitrogen, and oxygen were selected as an estimate that could be changed later. However, as many of the lines identiﬁed contained at least CHAPTER 5. ASTROCHEMISTRY 138 one carbon atom, more carbon was included.

Table 5.2: Input values for test models with a constant C:O ratio

Atom or Molecule Abundance Relative to H Nuclei ——- H:5C H:2.5C H:2C H:C 2H:C 2.5H:C 5H:C H 0.00 1.00 1.50 4.00 9.00 11.50 24.00 He 25.00 24.00 23.50 21.00 16.00 14.00 1.00 C 5.00 5.00 5.00 5.00 5.00 5.00 5.00 N 2.00 2.00 2.00 2.00 2.00 2.00 2.00 O 2.00 2.00 2.00 2.00 2.00 2.00 2.00 H2 1.00 1.00 1.00 1.00 1.00 1.00 1.00

The cosmic ray ionisation rate scaling and UV radiation ﬁeld scaling were both set at 1.00 throughout, and visual extinction was set as 10.00, as these were number predetermined by the code. The temperature was 100K, as this is a reasonable estimation for the temperature of the nebula, and the density was 2 ×104 × k, where k is given by equation 5.14. The only models that converged were those for H:5C, H:2.5C, and H:2C.

Upon examining the output ﬁles from the models more closely, an instability was found to occur just after 10,000 years. This causes the fractional abundances beyond this time step to be unreliable.

As Sakurai’s Object was discovered in 1996, it is likely that the VLTP occured a few years previously, causing the mass to be ejected between 1996 and 1998. As this likely means that Sakurai’s Object is less than 30 years old (Duerbeck et al. (1996)), it is possible for the model to be stopped at a time of 10,000 years and still give valid output abundances. The time evolution of the abundances will be discussed using Figures 5.1 and 5.2. By stopping the model at this point, long carbon chain molecules were prevented from forming. As Evans et al. (2006) did not ﬁnd these chains, it is unlikely that these exist in Sakurai’s Object, further justifying CHAPTER 5. ASTROCHEMISTRY 139 the decision to terminate the model early.

In order to determine which of these models was the best, it was necessary to look at the fractional abundances of both HC3N and HC5N at the new ﬁnal time step of 10,000 years. Ideally, the model used would have more

HC3N than HC5N, as this is what was seen in the ALMA data. However, this was not true for any of the models. Therefore, the decision was made to use the model with the smallest HC5N to HC3N ratio. From Table 5.3, this can be seen to be the model for H:2C, so this model was used going forwards. Whilst this may suggest that a model with additional hydrogen could be better, the decision was taken to ﬁrst test other properties, such as the type of carbon and the UV and visual extinction values.

Table 5.3: Fractional Output Abundances for HC3N and HC5N Molecule Fractional Abundance — H:2C H:2.5C H:5C −11 −11 −11 HC3N 3.059×10 3.787×10 2.547× 10 −10 −10 −10 HC5N 1.686×10 2.262×10 1.832× 10

It is important to note that Sakurai’s Object is likely to have regions with diﬀerent conditions, such as lobes. However, for the purposes of this research it was decided to try and ﬁnd a set of conditions that worked well for some of the molecules detected by ALMA, even if it did not work for all molecules.

5.6.4 Testing Molecular Carbon

After establishing which model was best, it was decided to see if the initial presence of molecular carbon (C2) would alter the output of the model. Initially, variations of the model were run that included molecular carbon CHAPTER 5. ASTROCHEMISTRY 140

in place of atomic carbon, and the input values are shown in Table 5.4.

In the tables, CA represents atomic carbon, and CM represents molecular carbon.

Table 5.4: Input values for the molecular carbon models

Model Abundance Relative to H Nuclei —— H He CA CM NO 1 1.50 23.5 5.00 0.00 2.00 2.00 2 1.50 23.5 4.50 0.25 2.00 2.00 3 1.50 23.5 4.00 0.50 2.00 2.00 4 1.50 23.5 3.50 0.75 2.00 2.00 5 1.50 23.5 3.00 1.00 2.00 2.00 6 1.50 23.5 2.50 1.25 2.00 2.00 7 1.50 23.5 2.00 1.50 2.00 2.00 8 1.50 23.5 1.50 1.75 2.00 2.00 9 1.50 23.5 1.00 2.00 2.00 2.00 10 1.50 23.5 0.50 2.25 2.00 2.00 11 1.50 23.5 0.00 2.50 2.00 2.00

To ensure that the models were comparable, the number of carbon atoms was kept constant. As molecular carbon contains 2 atoms, the input values were such that the equation:

CA + 2CM = 5, (5.15) always held true.

Again, an ideal model would have more HC3N than HC5N, so the output ﬁles for each model were checked and the fractional abundance for each at 1×105 years was noted. This data is shown in Table 5.5. CHAPTER 5. ASTROCHEMISTRY 141

Table 5.5: Output Fractional Abundances for Molecular Models

Model HC3N HC5N HC7N HC9N

1 3.059×10−11 1.686×10−10

2 3.696×10−11 2.083×10−10

3 4.561×10−11 2.636×10−10

4 5.778×10−11 3.432×10−10

5 7.572×10−11 4.638×10−10

6 1.040×10−10 6.597×10−10

7 1.539×10−10 1.015×10−9

8 2.632×10−10 1.817×10−9

9 7.670×10−10 5.640×10−9

10 9.497×10−6 3.051×10−7 4.027×10−4 8.703×10−5

11 4.008×10−5 1.078×10−6 1.348×10−3 2.938×10−4

Initially, these results suggest that models 10 and 11 could be ideal candidates for further use in this research. However, upon further examination of the output ﬁles, both models were found to have high fractional abundances of both HC7N and HC9N. As these molecules are not seen in the

ALMA data, they are expected to have lower abundances than both HC3N and HC5N. These high abundances are therefore unexpected, and both models were excluded from any further research.

The increase in model 10 is due to an instability that appears somewhere between the penultimate 2 time steps, meaning it is predicted to appear between 63000 and 79500 years into the evolution of Sakurai’s Object. In

Figure 5.1, the sharp increase in both the HC7N and HC9N lines show where CHAPTER 5. ASTROCHEMISTRY 142 the instability occurs. There is also a less noticeable dip in the abundance of HC5N, which is likely to be due to the same instability. In both Figure 5.1 and 5.2, the black dashed lines indicate the current time.

Figure 5.1: Time Evolution of Sakurai’s Object as Predicted by Model 10

Figure 5.2 shows the predicted evolution based on model 11. As with model

10, there is a sharp increase in the abundances of both HC7N and HC9N, along with smaller dips in both HC3N and HC5N. CHAPTER 5. ASTROCHEMISTRY 143

Figure 5.2: Time Evolution of Sakurai’s Object as Predicted by Model 11

For both models there is an obvious abrupt change in the plots at approximately 180 years. At this point, the abundances of both HC7N and HC9N begin to increase relatively quickly, most likely due to reactions involving another molecule. These large abundances mean that it is best to remove both models from this research.

As Sakurai’s Object likely underwent its VLTP approximately 25 to 30 years ago (Miller Bertolami et al. (2006); Duerbeck et al. (1997)), only the ﬁrst few time steps of the models can be compared with current data. However, the rest of the model acts as an interesting prediction into the possible evolution of Sakurai’s Object, and may also act as the foundation of future predictions.

5.6.5 Testing Ionic Carbon

The model was then altered again to replace atomic carbon with ionic carbon. As with molecular carbon, the amount of ionic carbon was gradually CHAPTER 5. ASTROCHEMISTRY 144 increased, but the input values of atomic and ionic carbon always combined to make 5. The input values are shown in Table 5.6. The ﬁrst model again outlines the input values for the fully atomic model. Table 5.6: Input values for the ionic carbon models

Atom or Molecule Abundance Relative to H Nuclei —— H He C C+ NO 1 1.50 23.5 5.00 0.00 2.00 2.00 2 1.50 23.5 4.50 0.50 2.00 2.00 3 1.50 23.5 4.00 1.00 2.00 2.00 4 1.50 23.5 3.50 1.50 2.00 2.00 5 1.50 23.5 3.00 2.00 2.00 2.00 6 1.50 23.5 2.50 2.50 2.00 2.00 7 1.50 23.5 2.00 3.00 2.00 2.00 8 1.50 23.5 1.50 3.50 2.00 2.00 9 1.50 23.5 1.00 4.00 2.00 2.00 10 1.50 23.5 0.50 4.50 2.00 2.00 11 1.50 23.5 0.00 5.00 2.00 2.00

After running these models, the output ﬁles were examined to ﬁnd the fractional abundances of HC3N and HC5N, which are shown in Table 5.7.

Table 5.7: HC3N and HC5N output abundances for ionic models

Model HC3N Fractional Abundance HC5N Fractional Abundance 1 3.059×10−11 1.686×10−10 2 3.947×10−11 2.210×10−10 3 3.986×10−11 2.244×10−10 4 3.989×10−11 2.246×10−10 5 3.989×10−11 2.247×10−10 6 3.990×10−11 2.247×10−10 7 3.990×10−11 2.247×10−10 8 3.990×10−11 2.247×10−10 9 3.990×10−11 2.247×10−10 10 3.989×10−11 2.247×10−10 11 3.989×10−11 2.247×10−10

These models show that the addition of ionic carbon does not improve the ratio of HC3N abundance to HC5N abundance. As the best ratio is that CHAPTER 5. ASTROCHEMISTRY 145

from the original model, the atomic carbon model will be used in the rest of this research.

5.6.6 Testing the Visual Extinction and UV Radia-

tion Field Scaling Factor

In order to see if the UV radiation ﬁeld scaling factor and visual extinction have any impact on the output values, more models were run with changes made to these variables.

Visual extinction is the sum of the absorption and the scattering of photons. When clouds of diﬀuse matter absorb incoming photons, they prevent them from reaching the observer, causing a reduced photon count. If the absorbed photons are re-emitted, they will be emitted at redder wavelengths. Both of these will cause a reduction in the ﬂux being observed. For the additional models that were run, the visual extinction values used were 1, 2, 3, 4, 5, 6, and 10 magnitudes.

The UV radiation ﬁeld scaling factor is a dimensionless parameter (Habing

−14 −3 (1968)). Habing estimated that νuν ' 4× 10 erg cm at λ = 1000 A.˚ It is usual to calculate other estimates based on this value, which is done using the equation: (νuν) ˚ χ = 1000A , (5.16) 4 × 10−14

which gives the dimensionless parameter χ. For this research, the values of χ used were 5, 10, 20, 30, 40, and 50. The models were run for 100 years, as Sakurai’s Object is expected to be in the ﬁrst 100 year’s of its evolution. CHAPTER 5. ASTROCHEMISTRY 146

When the visual extinction value was set to 1 magnitude or 2 magnitudes, the ﬁrst two time steps showed an error message indicating that the time steps were too small. These visual extinction values were therefore discounted.

A visual extinction of 10 magnitudes was then tested, and whilst there was no error message, all the outputs produced by each UV value (χ) were identical. This is because extinction in the visual range can be described by the equation: F A = −2.5 log , (5.17) F0

where A is the visual extinction, F is the flux, and F0 is the reduction in flux. This means that in increase in the visual extinction by a factor of 10 will cause a reduction in flux of the order of 10000. As extinction is more severe in the UV, the flux reduction will be even greater, meaning the increase in the UV flux will not be able to compensate for the extinction. This meant that it was possible to rule out 10 as a possible value for visual extinction.

When a visual extinction of 3 magnitudes and a UV value of 30, 40, or 50 was used, there are error messages for the first 2 steps, ruling these combinations out. For a UV value of 5, the final 3 steps have more HC5N than HC3N, and for UV values of 10 and 20 this extends to the final 6 steps. Therefore, no UV values for a visual extinction of 3 are viable, and this visual extinction value was removed. This justifies removing any smaller values of extinction for which the model failed.

For a visual extinction of 4 with a UV value of 50, the ﬁnal time step had more HC5N, so this was removed. All other UV values worked, but the CHAPTER 5. ASTROCHEMISTRY 147 most promising was a UV value of 40, which had the highest ratio at 15 of the 20 time steps.

For visual extinctions of 5 and 6 magnitudes, all the UV values produced viable models, but none of these were as good as UV 40 with a visual extinction of 4, so this model will be used for the rest of this research.

5.6.7 Limits of the Dark Cloud Chemical Model

Whilst the dark cloud chemical model provides a good environment to test input parameters for a model of Sakurai’s Object, it is not without its limitations.

One of the most obvious limitations is that the number of reactions that are included is limited, although it is possible to edit the code to add any extra reactions the user may require. A limited number of reactions is both expected and necessary, as too many reactions would increase the computational time required to such a level that the code would be rendered useless. For this research, the reactions included were suﬃcient.

Another limit is that Sakurai’s Object is exceptionally helium and carbon rich (Asplund et al. (1997)), but hydrogen poor. These extreme conditions are not well supported by the UDfA code, limiting what initial conditions can be tested using it.

It is also important to note that surface chemistry and gas-phase reactions are both analysed by calculating abundances via the rate equations included in the model (http://udfa.ajmarkwick.net/downloads). Whilst this CHAPTER 5. ASTROCHEMISTRY 148 approach can be valid in simple cases, there will be cases where more complicated routines are required (http://udfa.ajmarkwick.net/downloads). How- ever, as with the number of reactions, a more complicated routine will increase the time required for computation, so a balance between time and accuracy must be found. CHAPTER 5. ASTROCHEMISTRY 149

5.7 RADEX

RADEX is a piece of software that uses datafiles from the Leiden Atomic and Molecular Database (LAMDA) (van der Tak et al. (2007)). It consists of a statistical equilibrium radiative transfer code in one dimension, and uses the escape probability formulation for calculations (van der Tak et al. (2007)). This software assumes an isothermal and homogeneous medium without large-scale velocity fields (van der Tak et al. (2007)). There are two versions of RADEX: an online version that can be used for quick estimates, and a source code, which can be modified to suit the users needs (see section 5.9 for details).

The LAMDA database provides the data required for RADEX to run excitation calculations (Schöieret al. (2010)). Each of the 40 atomic or molecular species has it’s own data file, which contain information on the energy levels, collisional rate coefficients, Einstein A-coefficients, and statistical weights (Schöieret al. (2010)). Some species also have files that include hyperfine splitting, but these have not been used for this research.

RADEX will be used these ﬁles to determine if the chemical models created using the UDfA Dark Cloud code can recreate properties observed by ALMA, such as ﬂux. RADEX was chosen as the online version allows for easy and quick estimations to be run, providing some rough parameters. The source code could then be used to get more accurate calculations and tweak the parameters as necessary. CHAPTER 5. ASTROCHEMISTRY 150

5.8 The Online Version of RADEX

In Sakurai’s Object, the 12CO to 13CO ratio is expected to be approximately 4:1 (Pavlenko et al. (2004)). In order to try and establish if there were any parameters that would achieve this ratio, the online version of RADEX was used. This can be found at http://var.sron.nl/radex/radex.php.

This version of RADEX is quite basic in comparison to the source code. The user is ﬁrst required to select a molecule from a drop down menu, then specify the frequency range. The background temperature is initially set to 2.73K, but this can be changed by the user, along with the kinetic tempera-

−3 ture in Kelvin, and the H2 column density in cm . These 3 parameters are collectively called the ’Excitation Conditions’. Below these are 2 ’Radiative Transfer Parameters’: the column density of the molecule in cm−2, and the thermal line width in km/s. The user does not have the option to select the geometry used, so the calculations are done using a uniform sphere model. The results provided after these calculations include the frequency (GHz), excitation temperature (K), tau, and radiation temperature (K) for each transition in the selected frequency range.

5.8.1 Calculating Input Values for the Online Version

of Radex

In order to find a set of guideline parameters, it was first necessary to establish the brightness temperatures of the lines detected by CASA, as these are the ideal output values that would be produced. The temperatures can be calculated by fitting a Gaussian to the images produced in CASA to get the peak flux in Jy/beam from an integrated emission map. This will CHAPTER 5. ASTROCHEMISTRY 151 measure the line flux in the central part of the nebula. This can then be converted into a brightness temperature using the equation:

2 Sνc TB = 2 , (5.18) 2ν kbΩ

where Sν is the peak ﬂux in Jy/beam of the image, ν is the frequency of the line in Hz, and Ω is the beam size, which is calculated using:

πθ θ Ω = a b , (5.19) 4 ln(2)

where θa and θb are the major and minor components of the restoring beam in radians.

As the CO line has a rest frequency of 230.538 GHz, a peak flux of 0.0198 ± 0.0029 Jy/beam, and a beam measuring 0.30” by 0.24”, it was calculated to have a brightness temperature of 6.3 ± 0.93K. The 13CO line has a rest frequency of 330.588 GHz, a peak flux of 0.0191 ± 0.0044 Jy/beam, and beam components of 0.30” and 0.17”, giving a brightness temperature of 4.2 ± 0.97K. Finally, the brightness temperature of the HC3N line was calculated using the rest frequency of 227.4189 GHz, the peak flux of 0.0102 ± 0.0011 Jy/beam, and beam components of 0.27” and 0.24”, giving a brightness temperature of 3.7 ± 0.6 K.

To ﬁnd the background temperatures for each of the three lines, Equations

5.18 and 5.19 can be used, but Sν will be the peak ﬂux of the continuum image for the band, and Ω will be the size of the beam used for the continuum image. The peak ﬂux for the 2014 data was 0.022 ± 9.6 × 10−4 Jy/beam for band 6, and 0.022 ± 1.59 × 10−3 Jy/beam for band 7. The CHAPTER 5. ASTROCHEMISTRY 152 line frequencies used are the same as those above. For band 6, which is where the CO and HC3N lines were found, the beam is 0.22” × 0.18”. For band 7 the beam is 0.18” × 0.14”. Using these numbers gives a background temperature of 12.8 ± 0.6 K for CO, 13.1 ± 0.5 K for HC3N, and 9.75 ± 0.7 K for 13CO.

5.8.2 Using the Online Version of RADEX

After ﬁnding the line and background temperatures, it was possible to set a frequency range for examination. As there was only 1 line each of CO and 13CO, it was decided to only use these lines in the exploratory research using the online version of RADEX. This is because these lines had been more convincingly identiﬁed, and, unlike the HC3N line, both came from spectral windows with no other features that could potentially interfere.

When setting the frequency range, it was convenient to use a range that would cover both lines at all times, so a range of 230 GHz - 331 GHz was used. The line width was then set to 1km. Through trial and error, the kinetic temperature was altered between 10-600K in an attempt to ﬁnd a kinetic temperature that produced lines with the calculated temperatures.

3 4 The H2 density was set at 1×10 or 1×10 each time, and the column density was set between 1×1016 - 1×1018 for 13CO, and between 4×1016 - 4×1018 for CO. CHAPTER 5. ASTROCHEMISTRY 153

5.8.3 Results from the Online Model

When the parameters for CO were set so that the kinetic temperature

4 −3 was 20.3K, the H2 density was 1×10 cm , and the column density was 4×1016 cm−2, a line with a temperature of 6.281K and a tau of 5.262 was found. Whilst this line does have a high optical depth, the temperature is very close to 6.3K which was calculated to be the temperature of this line using equations 5.18 and 5.19. If this combination of parameters is ideal, it should be possible to alter the background temperature to 9.76K and set the column density to 1×1016 cm−2 and RADEX would ﬁnd a 13CO line with a temperature of approximately 4.2K. When these parameters were used, the line found had a temperature of 4.047K and a tau of 1.699. As these were both close to the calculated values, the decision was made to use the same kinetic and background temperatures in the RADEX source code to try and ﬁnd a similar result. CHAPTER 5. ASTROCHEMISTRY 154

5.9 The RADEX Source Code

The RADEX source code is more complicated than the online version of RADEX. To use the RADEX source code, the user must first make any edits necessary to the ’radex.inc’ file. This includes adding the path to the data files that will be used in the calculations, and deciding on the geometry used. The user may select from a uniform sphere, an expanding sphere, or a parallel plane slab. As a parallel plane slab is the model most applicable to shocks, this was used for this research. After editing, the user must use the ’make’ command to produce an executable programme.

This programme can then be run in one of three ways: from the command line in the terminal, from a script, or from an input file. Whilst input files had been made during this research, it was decided that entering the data in these input files via the command line would enable any minor edits to be made for experimental purposes, so the method outlined below is for using the command line.

Upon using the command ’./radex’ to begin the programme, the user will first be asked for the name of the LAMDA data file to be used in the calculations. These will usually have names such as ’co.dat’, but these can be changed by the user if they so wish. Next, a name for the output file must be provided. Again, it is common to use the molecule name followed by the extension ’.rdx’, but this is down to personal preference. The third piece of information required is the output frequency range in GHz. For this research, this was set at 84 to 950 GHz, as this covers bands 3 to 10 of ALMA in full. An unlimited range an be used by inputting 0. The kinetic temperature in Kelvin is then inputted, followed by the number CHAPTER 5. ASTROCHEMISTRY 155 of collision partners. For each collision partner, the name and density in cm−3 is required. The background temperature is then inputted, followed by the molecular column density in cm−2, and the thermal line width in km/s. After this, the calculations will be run and an output file will be written. The user is then asked if another calculation for the same molecule is required. If the answer is yes, the user must input ’1’, otherwise they must input ’0’.

RADEX output files begin with a brief overview of the parameters used, including the version of RADEX, the geometry, the path to the molecular data file, the kinetic and background temperatures (K), the density of H2 (cm−3), the densities of the collision partners (cm−3), the column density (cm−2), and the thermal line width (km/s). This is followed by a table detailing all the lines within the frequency range that was specified. Each line then has data for its upper state energy (K), frequency (GHz), and wavelength (µm), which are found in the LAMDA data files (van der Tak et al. (2007)). This is followed by the excitation temperature (K), the optical depth, and the line intensity (K). The flux is given in both K km/s, and then again in erg cm−2 s−1.

RADEX begins the calculations by assuming that all lines are optically thin and then solving equations for statistical equilibrium to provide an estimate of the populations of the energy levels (van der Tak et al. (2007)). These estimates are then used to calculate the optical depths of the lines, which are in turn used to recalculate the populations (van der Tak et al. (2007)). This process is repeated until lines with τ > 10−2 have optical depths that are stable between 2 iterations, although there is a tolerance of 10−6 for this stage (van der Tak et al. (2007)). At this point, the program CHAPTER 5. ASTROCHEMISTRY 156 will write an output to the ﬁle speciﬁed, and then terminate. If this does not occur within 9999 iterations, the program will terminate and produce an error message.

5.9.1 Making RADEX Input Files

In order to make RADEX input files from the chemical models produced by the UDfA code, a python script was used. The script, dc2rad.py, is available at http://udfa.ajmarkwick.net, and was originally written in 2015 by Paul Woods. For the purposes of this research, small edits were made to enable the script to be run in python 3 as oppose to python 2. As this python script required data files as an input, the decision was made to use those that have been made publicly available on LAMDA (Schöieret al. (2005)).

13 As carbon monoxide has been regularly studied and CO, CO, and HC3N have been detected in Sakurai’s Object, it was decided that these molecules would be focused on initially.

When running the script, the user may either specify a particular molecule or allow all molecules to be analysed (Woods, 2015, http://udfa.ajmarkwick.net). They must then include the path to their RADEX download, and the path to the LAMDA data ﬁles. The user can then deﬁne the thermal line width of the cloud in km/s, the diameter of the cloud in parsecs, and the age in years at which outputs should be produced (Woods, 2015, http://udfa.ajmarkwick.net). As the UDfA code has been edited to end at an age of 1× 105 years, this value was used. Based on estimates of the expansion rate of the cloud and the time since the material was expelled CHAPTER 5. ASTROCHEMISTRY 157

(van Hoof et al. (2015)), the cloud diameter was calculated to be approximately 0.004 pc for this research. The background temperature can also be edited if it is not 2.728K, which is the background due to the Cosmic Microwave Background. For this research, the background temperature was calculated and changed, and this process is detailed in section 5.7 using equations 5.18 and 5.19. Finally, the user must specify which ’dc.out’ ﬁle and which ’rate13steady.state’ ﬁle are being used under the variables ’dataFilename’ and ’ssDataFilename’ respectively.

When the code is executed, a RADEX input file is created. This file contains the frequency range (GHz), the kinetic temperature (K), the number of collision partners, the background temperature (K), the molecular column density (cm−2), and the thermal line width (km/s). For each collision partner, the name and density (cm−3) is listed. The data from these input files is then used to run RADEX.

5.9.2 Determining Parameters for Carbon Monoxide

Input Files

As these RADEX input files were based on the parameters used in the online version of RADEX, very little has changed. The background temperatures for CO and 13CO are the same as in section 5.7, and the thermal line width was fixed at 1 km/s. 1 km/s was used as this is a good approxi- mation for the thermal line width of CO when microturbulence is accounted for. As the best kinetic temperature found when using the online version of RADEX was 20.3K, this was used in the input files. Three different input files were created for CO and 13CO: one that terminated at 50.12 years, CHAPTER 5. ASTROCHEMISTRY 158 another that terminated at 100 years, and one that terminated at 1000 years. This was done to allow for the evolution of Sakurai’s Object to be analysed, and to establish if there was an approximate time step beyond which the RADEX model diverged from what was expected.

The method in section 5.9.1 was used to create all six input ﬁles.

5.9.3 Determining Parameters for HC3N Input Files

Cyanoacetylene (HC3N) can be found in spectral windows 2, 5, 10, and 16 of the band 6 data, spectral window 1 from the band 7 data, and spectral window 31 from the 2017 data. However, the spectral window 16 band 6 had one of the most prominent peaks that showed little noise distortion, so this window was used.

As with the carbon monoxide models, the background temperature was calculated using equations 5.18 and 5.19. Again, the kinetic temperature used was 20.3K, and the thermal line width was 1 km/s. As with carbon monoxide, three input ﬁles terminating at diﬀerent time steps were made for HC3N.

5.9.4 Using the RADEX Source Code

Each of the three input files for each molecule was run through RADEX using the method described in section 5.8. From the output files produced, the flux (K km/s), the tau value, and the radiation temperature (K) of the line in question was noted for comparison with the results from the online version of RADEX. Table 5.8 shows the output values at each different termination time. CHAPTER 5. ASTROCHEMISTRY 159

Table 5.8: Details of the Output Values at Diﬀerent Times

Formula Flux (K km/s) Tau TR (K) TB (K) 50 Years CO 1.45×10−1 2.90×10−1 1.36×10−1 6.3 ± 0.93 13CO 9.10×10−2 2.49×10−1 8.55×10−2 5.0 ± 0.97 −12 −10 −12 HC3N 6.34×10 6.15×10 5.98×10 3.7 ± 0.6 100 Years CO 3.88×10−1 6.29×10−1 3.65×10−1 6.3 ± 0.93 13CO 2.48×10−1 5.61×10−1 2.33×10−1 5.0 ± 0.97 −11 −9 −11 HC3N 1.51×10 1.46×10 1.42×10 3.7 ± 0.6 1000 Years CO 5.92 1.41×101 5.57 6.3 ± 0.93 13CO 6.10 1.65×101 5.73 5.0 ± 0.97 −9 −7 −9 HC3N 7.21×10 6.97×10 6.78×10 3.7 ± 0.6

In Table 5.8, the previously measured TB values are equivalent to the TR values taken from RADEX. From this table it is apparent that the model that most closely reproduces the temperatures found using the online version of RADEX is the model that terminates at 1000 years. However, it should be noted that whilst CO is only around 0.7K too faint, 13CO is around 0.7K too bright, making 13CO hotter than 12CO, which is unexpected. However, these diﬀerences are not signiﬁcant given the errors in the measurements. The results also show that this model has high tau values, suggesting optically thick lines. Whilst this is unexpected, it is not impossible.

In the ALMA data, HC3N has a similar brightness temperature to both

13 CO and CO, meaning that the low HC3N flux shown in these models does not agree with the data. As this model had been run with a thermal line width of 1 km/s, the expected flux for HC3N is approximately 3.7K km/s, meaning that this model is returning a flux approximately 5.1×108 times lower than the expected value. To address this, different column densities CHAPTER 5. ASTROCHEMISTRY 160

for HC3N were trialled in RADEX. The value suggested by the RADEX input file created from the UDfA chemical model was 3.940×1010 cm−2, but in order to see a flux of the order of 3.7 K km/s, a colum density of 3.940×1018 cm−2 had to be used. This is a possible, but not hugely realistic value, but it may be possible under some circumstances, such as a shock. This gave a flux of 4.852K km/s and a tau of 1.137×103, making the line optically thick.

Another method that was briefly trialled was to increase the carbon to oxygen ratio. The values trialled were 4:1 and 5:3, but neither made a significant difference to the fractional abundance of HC3N, and would therefore make little difference to the flux.

5.9.5 Limits of the RADEX Source Code

As discussed by van der Tak et al. (2007), RADEX does not take into account that continuous radiation may contribute to the escape probability, which was proposed by Takahashi et al. (1983). Whilst this radiation can be treated as providing a negligible contribution at wavelengths >1mm, at shorter wavelengths (< 100 µm) the contribution may need to be considered.

RADEX is also limited as it can only treat one molecule at any given time (van der Tak et al. (2007). This can cause line overlaps to be neglected, which may mean that excitation that would aﬀect hyperﬁne structure is not accounted for (van der Tak et al. (2007). Whilst this isn’t important in this work, it may make the program unusable for other projects.

RADEX also assumes that the medium being examined does not have CHAPTER 5. ASTROCHEMISTRY 161 large velocity gradients (van der Tak et al. (2007)), but this is not true for Sakurai’s Object, which is still subject to the gradients produced due to the VLTPs that occurred previously. This can be demonstrated to be true due to the high velocity outﬂows detected by Hinkle and Joyce (2014), which would have been the result of a velocity gradient. CHAPTER 5. ASTROCHEMISTRY 162

5.10 The Final Model and the Time Evolu-

tion of Sakurai’s Object

Following this research, a ﬁnal model has been produced. This model suggests that Sakurai’s Object has a kinetic temperature of approximately 20K, a visual extinction of 4, and a UV radiation ﬁeld scaling factor of 40. The input values used in the UDfA model are shown in Table 5.9.

Table 5.9: Details of the Input Values for the Final Model

Atom Abundance Relative to H Nuclei H 1.50 He 23.5 C 5.00 N 2.00 O 2.00

Figure 5.3: Time Evolution of Sakurai’s Object as Predicted by the Final Model

The time evolution of this model is shown in Figures 5.3 and 5.4, where CHAPTER 5. ASTROCHEMISTRY 163 the black dashed lines indicate the current time. Figure 5.3 suggests that the fractional abundance of CO will increase at a reasonably constant rate.

For C2H2, there is a noticeable rise in the fractional abundance that begins at around 100 years into the evolution, and continues steadily. Despite starting with a low abundance, after 1000 years the model predicts that there will be more C6H2 than C2H2. This is thanks to a rapid increase in the formation of C6H2 after approximately 10 years. For the ﬁrst 30 years,

HC3N and HC5N are forming at a similar rate, but at around 60 years the rate of formation for HC5N begins to outpace that of HC3N.

Figure 5.4: Time Evolution of HCN, HNC, and CN

Figure 5.4 illustrates the slight diﬀerences in abundances and evolution between HCN and HNC. Whilst both HCN and HNC seem to show very similar changes in formation rates at the same time, there is always more HCN than HNC, suggesting that the formation rate of HCN is slightly higher. It can also be seen that HCN and HNC both have abundances CHAPTER 5. ASTROCHEMISTRY 164 that vary dramatically over time, with a peak abundance at approximately -6.5. This may suggest that the formation and destruction rates of these molecules is highly sensitive to a particular aspect of their environment, but this cannot be established from this work.

Figure 5.4 also shows a possible dramatic increase in abundance for both HCN and CN at approximately 560 years. However, as has been previously mentioned, the ﬁnal time steps of this model have had instabilities before, so it is possible that this is the cause of this change. However, it is also possible that a slower reaction is starting to speed up producing more HCN and CN, whilst having no eﬀect on the abundance of HNC. CHAPTER 5. ASTROCHEMISTRY 165

5.11 Discussion of the Model Results

From the ’analyse.out’ ﬁle produced by the model, it is possible to ﬁnd the reactions that produce and destroy each molecule, along with the overall destruction and production rates for each molecule. However, isotopologues are not accounted for, so these have not been included below.

The UDfA model shows that HNC is formed by the reaction:

HNC3 + C −→ C3 + HNC (5.20)

which has a production rate of 0.495 × 10−15 and produces 96% of the HNC seen.

HNC is destroyed at a rate of 0.495 × 10−15 by the reaction:

CN + HNC −→ NCCN + H (5.21) which accounts for 99% of the destruction.

CN is produced by the reaction:

N + C2 −→ CN + C (5.22) which has a production rate of 0.156 × 10−10.

There are 2 destruction reactions for CN, which are:

CN + γcr −→ N + C, (5.23)

and CHAPTER 5. ASTROCHEMISTRY 166

+ + CN + C2H2 −→ HC3N + H (5.24)

where γcr is a cosmic ray photon. The reaction shown in equation 5.23 destroys 75% of the CN, whilst the reaction in equation 5.24 destroys 7%. The overall destruction rate is 0.96 × 10−11.

CO is produced in the reaction:

O + C2 −→ CO + C (5.25)

which has a production rate of 0.198 × 10−10.

It is destroyed by the reaction:

CO + γ −→ O + C (5.26)

which has a destruction rate of 0.198 × 10−10.

HC3N is formed by the reactions:

− − H + C3N −→ HC3N + e , (5.27)

and

+ − HC3NH + e −→ HC3N + H. (5.28)

The reaction in equation 5.27 is responsible for producing the majority of

the HC3N seen. CHAPTER 5. ASTROCHEMISTRY 167

The destruction of HC3N is governed by three reactions:

+ + C + HC3N −→ C3H + CN, (5.29)

+ + C + HC3N −→ C4N + H, (5.30) and

HC3N + γ −→ CN + C2H. (5.31)

Equation 5.29 dominates the destruction, with the reactions in equations 5.30 and 5.31 contributing roughly equally. The destruction and production rates for HC3N are equal to 3 decimal places, with both being 0.209 × 10−12.

HC5N also has 2 reactions for production. These are:

− − H + C5N −→ HC5N + e (5.32) and

CN + HC4H −→ HC5N + H. (5.33)

Of these two reactions, that shown in equation 5.32 produces 92% of the HC5N, with the reaction in equation 5.33 producing the remaining 8%.

The destruction is again governed by three equations:

+ + C + HC5N −→ C5H + CN, (5.34)

HC5N + γ −→ C4H + CN, (5.35) CHAPTER 5. ASTROCHEMISTRY 168 and

HC5N + γ −→ C5N + H. (5.36)

Equation 5.34 is responsible for 84% of the destruction, with the remaining 2 reactions each responsible for 8%. The overall destruction rate for

−13 −13 HC5N is 0.222 × 10 , compared with a production rate of 0.223 × 10 , meaning there is a net production of HC5N.

From these RADEX models it is apparent that the results gained do not fully reproduce the data gathered from ALMA. Whilst RADEX fits the strength of both CO and 13CO well and the difference is not significant within the errors, this is not the case for HC3N. RADEX suggests HC3N is very faint, producing a flux 5.1×108 lower than expected. As the RADEX models are based on input files created from the UDfA chemical models, it can be concluded that the UDfA chemical models drastically underestimate the abundance of HC3N in this case. However, it should be noted that

HC3N is not expected to form until later on in the evolution of Sakurai’s Object, meaning that running the models for longer may provide a better value. The RADEX models also suggest that all 3 lines are optically thick, and whilst this is unexpected, it is not impossible.

The RADEX results also show a degree of variation between the online version and the source code. In this case, this is likely due to the online version using geometry for a uniform sphere, but the source code was edited to use the geometry of a parallel plane slab as this model is most representative of a shock environment.

The RADEX models outlined in Table 5.8 predict that 13CO will have a higher flux than CO by the time Sakurai’s Object has evolved to 1000 CHAPTER 5. ASTROCHEMISTRY 169 years. Based on the ALMA data, this is unexpected, as CO currently has a higher flux. If this is true, it may be due to 13CO being formed in an environment with different characteristics, such as a higher temperature or column density.

A similar statement may also be true for HC3N, which may be produced in higher abundances in an environment with a diﬀerent temperature or more reactants. It is also possible that a code that better simulates a shock would change the chemistry, increasing the predicted abundance of HC3N.

From the time evolution plots, it can be seen that the evolution of Saku- rai’s Object is likely to be quick, with HCN and HNC changing very rapidly. Chapter 6

Conclusions

From the ALMA observations it can be concluded that Sakurai’s Object is a resolved source that may contain some unresolved features. From the continuum images, Sakurai’s Object is likely to be between 0.21”×0.16” to 0.35”×0.29” in size. The ALMA data ﬁnds that Sakurai’s Object is likely

13 13 to contain large amounts of HC3N, some CN, a CN line, a CO line, a CO line, and H13CN line, and a HNC line. Some of the most interesting data can be found in spectral window 16 band 6 of the 2014 data, which shows 2 emission features separated by an absorption feature. It is likely that the absorption feature and the left emission feature are cause by the same CN line that has an emission and absorption part. It is likely that Sakurai’s Object is cool, with the ﬁnal model giving an estimated dust temperature of around 20K, but with the incompleteness of this model, this can only be taken as an estimation. An estimation of the velocity was also made from the HNC line, giving a range of 50 km/s to 250 km/s.

The ﬁnal UDfA chemical model suggests there is a H:C ratio of 1:2, and

170 CHAPTER 6. CONCLUSIONS 171 a C:O ratio of 5:2, but this model does not produce the high fractional abundances of HC3N which were expected based on the ALMA data. In- creasing the C:O ratio to 5:3 and 4:1 was trialled, but neither provided the increases necessary. This suggests that there may be at least one reaction that is not eﬃcient enough at producing HC3N, or that there is a reaction that is destroying HC3N too quickly. Both of these could cause the low abundance predictions.

The RADEX source code model closely reproduced the expected fluxes for both CO and 13CO, but suggested that 13CO had a slightly higher flux than CO, which is contrary to the ALMA data. Both of these lines were found to be optically thick. The source code also returned a flux value for

8 HC3N that was 5.1×10 times lower than that predicted by ALMA. This could only be corrected when the column density increased from 3.940×1010 cm−2 to 3.940×1018 cm−2. However, it should be noted that these column density values are unlikely.

The differences in the input values required to produce HC3N with the correct flux indicates that this line may be from a area of Sakurai’s Ob- ject that has a slightly different environment to that of the CO and 13CO lines.

The time evolution of the ﬁnal model is discussed in section 5.9. Whilst the abundances predicted for the ﬁrst 60 or so years are as expected based on the ALMA data, beyond this point HC5N begins to unexpectedly dominate

HC3N. Whilst this is not supported by the current ALMA data, changes in the chemical input caused by properties such as stellar ﬂux and wind composition may allow for this in the future. Evans et al. (2006) found CHAPTER 6. CONCLUSIONS 172

evidence for C2H2 and C6H2 approximately 10 years after the discovery of Sakurai’s Object, and both of these molecules are seen in the ﬁnal chemical model. At a time of approximately 10 years, the production rate of C6H2 increases rapidly, possibly explaining the detection made by Evans et al. (2006). CHAPTER 6. CONCLUSIONS 173

6.1 Further Work

As mentioned in Section 4.1, the peak flux of Sakurai’s Object increased between 2014 and 2017, suggesting continued evolution. Further observations of the flux over a longer time period would enable this to be confirmed and allow for more investigation into other potential features of Sakurai’s Object that are not resolved. However, given how quickly Sakurai’s Object seems to be evolving, further observations may get different results is both the flux and the abundances. Therefore, continuous careful monitoring may allow for a detailed picture of the evolution to be constructed.

To improve upon this work, a more accurate UDfA input model that included elements such as silicon and sulphur would be highly useful. These molecules would be of particular interest as silicon can form the surfaces of dust grains where chemical reactions occur, and a small amount of sulphur was suggested by Asplund et al. (1997). These adaptations may produce ﬁnal abundances in the UDfA model that are closer to the true values in Sakurai’s Object, which may then be used to produce more accurate evolutionary models. If these models were more accurate, this would be seen in the RADEX outputs.

It may also be interesting to try and determine the differences in conditions in different parts of Sakurai’s Object. For example, it has been suggested that CN will be found in the lobes, so creating a model specifically for the lobes would then allow for a comparison to be made between factors such as temperature that may impact the chemistry.

This research could be expanded by running RADEX on other molecules that are predicted by the model. Of particular interest would be HC5N, CHAPTER 6. CONCLUSIONS 174

C2H2, and C6H2.C2H2, and C6H2 were both discussed by Evans et al.

(2006), and HC5N is a molecule that is predicted by the evolutionary models to occur with abundances similar to that of HC3N. However, there are currently no data ﬁles for these molecules on LAMDA, meaning they would need to be created. This could potentially provide an insight into the optical depths of these lines, which may be useful in providing an estimate of the optical depths of lines such as HC3N, which was found to be optically thick in this research.

It would also be beneficial to create source codes such as RADEX and that from the UDfA that are designed for hydrogen poor environments undergoing shocks. This may change the chemistry that occurs, providing a more accurate environment in which to model Sakurai’s Object, and may help with problems such as instabilities and the lack of HC3N formation. It would also be beneficial to include internal UV sources, as these may eliminate or reduce the differences seen between the models and the observations. Bibliography

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