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18 16 H2 O and H2 O Observations of Intermediate Mass Star Formation Regions by Mollie E. Conrad A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Science in Physics Waterloo, Ontario, Canada, 2018 © Mollie Conrad 2018 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract While the process of low mass (LM) star formation is a well studied area of astrophysics, the formation of high mass (HM) stars is much more complicated. The study of intermediate mass (IM) star formation is expected to shed some light on the clustered high mass regime. In this thesis, observations of 6 intermediate mass star formation regions were obtained with the Heterodyne Instrument for the Far Infrared (HIFI) aboard the Herschel Space Observatory (HSO) as part of the Water In Star-Forming regions with Herschel (WISH) project. Observations of all regions were decomposed into Gaussian components. NGC 7129 FIRS 2 is the main focus for this 18 thesis as water observations for this source also include H2 O. This isotopologue in conjunction 16 with H2 O allow for tighter constraints to be placed on the star formation regions. Modelling of the emission components corresponding to the IM YSO envelope was conducted with a radiative transfer program called RATRAN. This program allows for constraints to be placed on the chemical and physical parameters of the star formation region and the determination 18 16 of the abundance of H2 O and H2 O present. The best-fit RATRAN models assume a freeze-out temperature of 100 K and a free-fall infall velocity towards a central mass of 1.1M . Three different power-law density profiles are considered with indices of α = 1.4, α = 1.5, and a hybrid of the two. 1 18 The narrow 7:8 km s− component of the 547 GHz (110-101)H2 O ortho line was determined − 11 to have an outer envelope abundance of 3.5 0:3 10− with respect to H2 and an outer turbulent 1 ± × 18 velocity of 2.25 km s− for the α = 1:4 density profile. The inner envelope H2 O abundance and turbulent velocity could not be constrained due to a larger optical depth (greater than 1.0) in 18 this region. The higher energy state H2 O lines (995 GHz/202-111 and 1096 GHz/312-303) were 16 not detected; this was confirmed by RATRAN modelling. The H2 O ortho outer abundance was 8 determined to be Xout = 1.5 0:5 10− for the hybrid density profile, and the para outer ± × 9 16 abundance was determined to be Xout = 4.5 0:3 10− . This yields a total H2 O abundance 8 ± × of 1.95 1:0 10− . The water abundance value is consistent with that of the low-mass and ± × 8 high-mass WISH teams ( 10− ), and the turbulent velocity is consistent with that of the high- ∼ 1 mass WISH team (2.0{2.5 km s− ). The water abundances derived for the other density profiles are also consistent with this conclusion. This analysis determined an abundance ratio consistent with that of Herpin et al. (2016) (a HM study). The least useful molecular lines proved to be the 16 ortho and para H2 O ground state lines; these are not suggested as ideal probes of star formation 18 regions. That being said, the most useful lines proved to be the H2 O ground state ortho 547 16 GHz line and the H2 O para 988 GHz line. This study of water in intermediate mass star formation regions is to be considered alongside studies in the low and high mass regimes; this will allow for increased understanding of the overall star formation process. iii Acknowledgements I would like to extend my sincerest gratitude to my supervisor Dr. Michel Fich. This degree would not have been possible without his patience, mentoring, and wisdom. I would like to thank my graduate instructors; Dr. Mike Hudson, Dr. Niayesh Afshordi, and again Dr. Michel Fich, for their teaching excellence and patience with my after-lecture questions. Thank you Dr. Mike Hudson for offering me the best piece of advice, \Always remember the bigger picture". I want to thank my committee members; Dr. Michael Balogh and Dr. James Taylor for their continued support and motivation. Also, thank you to Dr. Avery Broderick for providing invaluable feedback during my defence. I would also like to thank all my peers and friends for their advice and support; George Bobotsis, Adrian Vantyghem, Nicole Drakos, Rufus Ni, Issac Spitzer, Paul Charlton and Saoussen Mbarek. Finally, I would like to thank my mother Penny Conrad for often volunteering to drive 3 hours just to clean my laundry and watch me obsess over RATRAN models. \You the real MVP". iv Dedication I can't even begin to decide who to dedicate well over two years of my life to. There are so many people responsible for getting me where I am today. I think I will leave it at this: I dedicate this thesis to my parents for raising me to value hard work, to Mike Fich for presenting me with the opportunity to strive for more, and to my partner Chris Praill for always being in my corner. In loving memory of my late Nanny and Poppy Dyer. v Table of Contents List of Tablesx List of Figures xiii List of Symbols xviii 1 Introduction1 1.1 Star Formation.................................3 1.1.1 Giant Molecular Cloud Substructure.................3 1.1.2 Turbulence...............................4 1.1.3 Ambipolar Diffusion..........................5 1.1.4 Collapse Criterion............................6 1.1.5 Heating & Cooling...........................9 1.1.6 From GMC to Protostar........................ 10 1.1.7 Star Formation Overview........................ 11 1.1.8 Stellar Mass............................... 12 1.2 Herschel Space Observatory & HIFI...................... 14 1.3 WISH Team................................... 15 1.3.1 Spectral Line Profile.......................... 15 1.4 Water...................................... 18 1.5 Radiative Transfer............................... 22 vi 1.6 Modelling Overview............................... 24 1.7 Previous Studies: NGC 7129 FIRS 2..................... 25 1.8 Thesis Outline.................................. 30 2 Observations 31 2.1 Data Reduction................................. 34 2.1.1 HIPE.................................. 34 2.1.2 Spectral Smoothing........................... 39 2.1.3 Observations: Summary........................ 45 3 Overview of Model Techniques 47 3.1 Radiative Transfer Equations: Testing Model Results............................. 47 3.1.1 Determining Population: Overview.................. 48 3.1.2 Other Radiative Transfer Equations.................. 52 3.2 Results...................................... 56 4 RATRAN Modelling 59 4.1 How does RATRAN work?........................... 59 4.1.1 Foundation RATRAN Models..................... 62 4.1.2 DUSTY Model to RATRAN Model.................. 62 4.2 Limitations................................... 64 4.3 Modelling Approach: NGC 7129 FIRS 2................... 65 4.4 NGC 6334 I(N): a High-Mass Young Stellar Object............. 66 4.5 NGC 7129 FIRS 2: an Intermediate-Mass Young Stellar Object...... 81 4.5.1 Water Abundance............................ 82 4.5.2 Abundance Ratio Xratio ........................ 87 4.5.3 Radial Velocity vr ............................ 88 4.5.4 Doppler Broadening Parameter db ................... 96 vii 4.5.5 Gas and Dust Temperature...................... 108 4.5.6 Freeze-out Temperature........................ 110 4.5.7 ncell: Number of Spherical Shells................... 117 4.5.8 Ortho-to-Para Ratio.......................... 119 4.5.9 Collision Rates............................. 122 4.5.10 Beamsize................................ 127 4.5.11 RATRAN Physical Structure of NGC 7129 FIRS 2......... 128 5 RADEX Modelling 144 5.1 How does RADEX work?............................ 145 5.2 Limitations................................... 145 5.3 How does RADEX apply?........................... 146 5.4 Results...................................... 146 18 1 5.4.1 H2 O: Emission Components at 8.6 and 0.6 km s− ......... 146 5.4.2 RATRAN vs. RADEX......................... 153 5.4.3 Summary: Validation of RATRAN Results with RADEX...... 162 6 Discussion 168 6.1 Observations................................... 168 6.1.1 P-Cygni and Inverse P-Cygni Profiles................. 169 6.2 Gaussian Decomposition of Observed Spectral Lines............. 172 6.2.1 Other IM WISH Candidates...................... 172 6.3 Optical Depths................................. 176 6.4 Modelling Results................................ 185 7 Conclusions 191 8 Future Work 194 References 195 viii APPENDICES 209 A Other WISH IM Candidates 210 B RADEX Input & Output 233 C RATRAN Input & Output 235 D Constants 239 E NGC 7129 FIRS 2 RATRAN Model 240 ix List of Tables 2.1 Observation Identification Numbers...................... 32 2.2 WISH Target Information: Intermediate and High Mass YSOs........ 33 2.3 List of NGC 7129 FIRS 2 Observed Water Lines............... 33 2.4 Spectral Fits to Water Data: NGC 7129 FIRS 2............... 38 2.5 RMS Noise of NGC 7129 FIRS 2....................... 44 2.6 Comparing σRMS ................................ 44 3.1 State Population Equation: Matrix Determinant............... 49 3.2 2-State System - Molecules Entering & Exiting................ 49 3.3 3-State System - 2nd & 3rd Non-Interacting................. 50 3.4 3-State System - 2nd & 3rd Collisionally Interacting............. 51 3.5 Comparing 2 and 3 Level Radiative Transfer Systems............ 52 3.6 Beamwidths for Herschel HIFI......................... 57 3.7 RADEX Input.................................. 57 3.8 RADEX Output using Input from Table 3.7................. 58 3.9 RADEX: Output vs. Manual Calculations.................. 58 4.1 NGC 6334 I(N): Source Data......................... 66 4.2 NGC 6334 I(N): HIFI Observed Water Lines................. 68 4.3 NGC 6334 I(N): Gaussian Components.................... 68 4.4 NGC 6334 I(N): Envelope Model Parameters................. 71 x 4.5 NGC 6334 I(N): Envelope Model....................... 71 4.6 Herpin et al. (2016) RATRAN Spectral Fits - Intensities and Widths..

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