INTERSTELLAR SILICATE DUST: MODELING AND GRAIN ALIGNMENT by Indrajit Das A Dissertation Submitted to the Graduate Faculty of George Mason University In Partial fulfillment of The Requirements for the Degree of Doctor of Philosophy Physics Committee: Dr. Joseph Weingartner, Dissertation Director Dr. Shobita Satyapal, Committee Member Dr. Mario Gliozzi, Committee Member Dr. PadmanabhanSeshaiyer,CommitteeMember Dr. Michael Summers, Director, School of Physics, Astronomy and Computational Sciences Dr. Richard Diecchio, Interim Associate Dean for Student and Academic Affairs, College of Science Dr. Peggy Agouris, Interim Dean, College of Science Date: Fall Semester 2013 George Mason University Fairfax, VA Interstellar Silicate Dust: Modeling and Grain Alignment A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at George Mason University By Indrajit Das Master of Science George Mason University, 2008 Bachelor of Engineering Bengal Engineering and Science University, 1997 Director: Dr. Joseph Weingartner, Associate Professor School of Physics, Astronomy and Computational Sciences (SPACS) Fall Semester 2013 George Mason University Fairfax, VA Copyright c 2013 by Indrajit Das (cid:13) All Rights Reserved ii Dedication I dedicate this dissertation to my parents and sisters. iii Acknowledgments First and foremost, I would like to thank Dr. Joseph Weingartner for his wonderful and immense company on my side. He has always been there for me not only as an academic mentor but also as a great friend. Can’t thank him more. I would also like to thank my dissertation committee members - Dr. Shobita Satyapal, Dr. Mario Gliozzi and Dr. Padmanabhan Seshaiyer for their guidance and helpful comments. iv Table of Contents Page List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Dust, Polarization, and Magnetic Fields . . . . . . . . . . . . . . . . . . . 1 1.2 Constraints on Silicate Dust Models with 10 µm Feature . . . . . . . . . 3 1.2.1 Motivation from Min et al (2007) . . . . . . . . . . . . . . . . . . 4 1.3 Gaussian Random Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Grain Alignment Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Interstellar Silicate Dust Modeling - Constraints on shape and mineralogy . . . 12 2.1 Replicating Min et al (2007) results . . . . . . . . . . . . . . . . . . . . . . 12 2.1.1 Convergence calculations with DDA method . . . . . . . . . . . . 12 2.1.2 Running DDSCAT for 10 µm feature . . . . . . . . . . . . . . . . 14 2.1.3 Codes and data files used . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Material Compositions and their optical properties . . . . . . . . . . . . . 16 2.2.1 10 µm feature for different compositions . . . . . . . . . . . . . . . 16 2.3 Observed Data and Fitting Algorithm . . . . . . . . . . . . . . . . . . . . 32 2.4 Beyond Min et al (2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5 Densities used for materials . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6 Abundance constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.7 Stoichiometric Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.8 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.8.1 Fitting 10 µm extinction feature . . . . . . . . . . . . . . . . . . . 44 2.8.2 Varying Mg/Si abundance ratio . . . . . . . . . . . . . . . . . . . . 49 2.8.3 With Fe-oxide inclusions . . . . . . . . . . . . . . . . . . . . . . . . 52 2.8.4 Fitting with 10 µm Polarization feature . . . . . . . . . . . . . . . 54 2.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3 Mechanical Torques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 v 3.1 Physical properties of a GRS grain . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Collisions of Gas Particles with the Grain . . . . . . . . . . . . . . . . . . 63 3.3 Torque Due to Incoming and Reflected Atoms . . . . . . . . . . . . . . . . 65 3.4 Mechanical Torque Due to Outgoing Atoms/Molecules . . . . . . . . . . 69 3.5 Total Mechanical Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.6 Rotational Averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.7 Drag Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.8 Extreme Subsonic Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.9 Extreme Supersonic Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.10 Mechanical Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.11 Computational Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.11.1 Defining and Characterizing the GRS . . . . . . . . . . . . . . . . 86 3.11.2 Incoming Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.11.3 Arrival at the Grain Surface and Reflection . . . . . . . . . . . . . 88 3.11.4 Integrals over the Reduced Speed . . . . . . . . . . . . . . . . . . . 89 3.11.5 Characterization of the Grain Surface . . . . . . . . . . . . . . . . 89 3.11.6 Torque Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.11.7 Code Verification: Spherical Grains. . . . . . . . . . . . . . . . . . 91 3.12 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.12.1 Grain Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.12.2 Arrival Rate and Torques . . . . . . . . . . . . . . . . . . . . . . . 94 4 Grain Dynamics and Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.2 Stationary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.3 Crossover Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 122 A An Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 A.1 Details of solid GRS# 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 A.2 Details of solid GRS# 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 A.3 Details of vacuum included GRS# 1 . . . . . . . . . . . . . . . . . . . . . 132 A.4 Details of vacuum/Fe-oxide included GRS# 2 . . . . . . . . . . . . . . . . 132 B An Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 B.1 Torque Due to Incoming Atoms . . . . . . . . . . . . . . . . . . . . . . . 145 B.2 Torque Due to Outgoing Particles . . . . . . . . . . . . . . . . . . . . . . 146 vi B.3 Extreme Subsonic Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 B.4 Drag Force in the Extreme Subsonic Limit . . . . . . . . . . . . . . . . . 148 vii List of Tables Table Page 2.1 Sets of grain material mass densities (gcm−3) . . . . . . . . . . . . . . . 39 2.2 Mass percentages of different compositions used for the best χ2 fits for four different shapes fitted with extinction feature for Mg/Si = 1.22. . . . 44 2.3 Mass percentages of different compositions used for the best χ2 fits for four different shapes fitted with polarization feature. Mg/Si = 1.2. . . . . 59 3.1 GRS Expansion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.2 GRS Derived Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.1 Adopted Parameter Values for Grain Rotational Dynamics . . . . . . . . 115 A.1 Spherical Harmonic Coefficients for solid GRS# 1 . . . . . . . . . . . . . 128 A.2 Spherical Harmonic Coefficients for solid GRS# 2 . . . . . . . . . . . . . 130 A.3 Spherical Harmonic Coefficients for vacuum/Oxide included GRS# 1 . . . 131 A.4 Spherical Harmonic Coefficients for inclusion#1 for vacuum/Oxide in- cluded GRS# 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.5 Spherical Harmonic Coefficients for inclusion# 2 for vacuum/Oxide in- cluded GRS# 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.6 Spherical Harmonic Coefficients for inclusion# 3 for vacuum/Oxide in- cluded GRS# 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.7 Spherical Harmonic Coefficients for inclusion # 4 for vacuum/oxide in- cluded GRS# 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.8 Spherical Harmonic Coefficients for inclusion # 5 for vacuum/Oxide in- cluded GRS# 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 A.9 Spherical Harmonic Coefficients for vacuum/Oxide included GRS# 2 . . . 139 A.10 Spherical Harmonic Coefficients for inclusion#1 for vacuum/Oxide in- cluded GRS# 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 A.11 Spherical Harmonic Coefficients for inclusion# 2 for vacuum/Oxide in- cluded GRS# 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 viii A.12 Spherical Harmonic Coefficients for inclusion# 3 for vacuum/Oxide in- cluded GRS# 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 A.13 Spherical Harmonic Coefficients for inclusion # 4 for vacuum/oxide in- cluded GRS# 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 A.14 Spherical Harmonic Coefficients for inclusion # 5 for vacuum/Oxide in- cluded GRS# 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 ix