°Master of Science Evolving Galactic Dynamos and Fits to the Reversing Rotation Measures in Edge-On Galaxies by Alex Woodfinden A thesis submitted to the Department of Physics, Engineering Physics & Astronomy in conformity with the requirements for the degree of Master of Science Queen's University Kingston, Ontario, Canada April 2019 Copyright © Alex Woodfinden, 2019 Abstract Rotation measure (RM) synthesis maps of NGC 4631 by Mora-Partiarroyo et al. (2018) show remarkable sign reversals on kpc scales as the distance from the minor axis increases in the northern halo of the galaxy. RM maps for edge-on galaxies observed in the CHANG-ES sample were searched through and show that regular reversals in the sign of the RM seen in galaxies appears to be a common phenomenon. These sign reversals can be naturally explained by a regular halo magnetic field that is alternating its azimuthal direction on kpc scales in the galaxy. This is a brand new phenomenon that has never before been observed in a galactic halo. Evidence of magnetic fields showing both axisymmetric and bisymmetric symmetry is found in the data. To explain this new phenomenon the dynamo equations are solved under the as- sumption of scale invariance and rotating logarithmic spiral solutions are searched for. The model solutions are then compared to the observational RM map of NGC 4631 in order to draw conclusions on the type of field geometry likely found in the galactic halo. Solutions for velocity fields that represent accretion onto the disk, outflow from the disk, and rotation-only in the disk are found that produce RM maps with reversing signs viewed edge-on. Model RM maps are created for a variety of input parameters using a Faraday screen technique and are then scaled to match the amplitude of the i observational maps. Residual images are then made and compared with one another in order to determine the models that provide the best fit to the data. Solutions for rotation-only, i.e. relative to a pattern uniform rotation, did in general, not fit the observational map of NGC 4631 well. Outflow models provided a reasonable fit to the magnetic field. However, the best results for the region modelled in the northern halo are found using accretion models. As there is abundant evidence for both winds and accretion in NGC 4631, this modelling technique has the potential to be able to distinguish between the dominant flows in galaxies. ii Statement of Co-Authorship The research presented in this thesis was done under the supervision of Judith Irwin (Queen's University) and Richard Henriksen (Queen's University). All the work pre- sented here was done by the author (Alex Woodfinden) except where explicitly stated otherwise. Chapter 3 contains a version of a manuscript submitted to the Monthly Notices of the Royal Astronomical Society as: "Evolving Galactic Dynamos and Fits to the Reversing Rotation Measures in the Halo of NGC 4631". A. Woodfinden, R.N. Hen- riksen, J. Irwin, and S.C. Mora-Partiarroyo. I am the lead author of this work. The theoretical basis of this manuscript presented in Sect. 3.3 & 3.4 was developed by Richard Henriksen who wrote these sections of the submitted manuscript. Fig- ures included in these sections (Figs. 3.3, 3.4, 3.5, 3.6, 3.7 & 3.8) were produced by Richard Henriksen with the exception of the rotation measure images in Figures 3.3, 3.5, 3.6 & 3.8 which were produced by myself. Judith Irwin and Richard Henriksen edited the submitted manuscript. Observational data for this manuscript, as seen in Figure 3.1, was provided by coauthor S.C. Mora-Partiattoyo. All other sections of this manuscript are my own work. Chapter 3 discusses fitting solutions to the dynamo equations with real observa- tional images. The actual fitting for this analysis was performed by myself while the iii solutions to the dynamo equations were provided by Richard Henriksen in the form of MAPLE1 worksheets that were subsequently modified by myself. See Sect. 2.3 for more details on this. Code used to convert image formats as well as perform the data analysis (see App. D & E) was written by the author. Chapter 4 discusses the rotation measure images of other galaxies in the CHANG- ES sample. The rotation measure data was provided by Phillip Schmidt, a member of the CHANG-ES collaboration. All images made and subsequent analysis of this data was performed by the author. 1www.maplesoft.com iv Acknowledgments First of all, I would like to thank my supervisors Judith Irwin and Richard Henriksen for providing me the opportunity to complete this project. I am thankful for all that I have learned from you both as well as the opportunity to travel and collaborate with others around the world. It has truly been a pleasure working with both of you and I greatly appreciate all the advice, support, and guidance given over the past two years. I would also like to thank my family for their constant support as well as always being there for me. Thank you for always taking the time to listen and your support has always been appreciated. Thank you to all my friends, in particular Alex for always being there as a source of support and encouragement. I would also like to thank my new friends I have met at Queens and all their advice, it has truly been helpful in completing this project. I am thankful for the support from the Queen Elizabeth II Scholarship and would like to thank the Queen's Physics Department faculty for all that I have learned over the last two years as well as the staff whose hard work is always appreciated. v Contents Abstract i Statement of Co-Authorship iii Acknowledgments v Contents vi List of Tables viii List of Figures ix Chapter 1: Introduction 1 1.1 CHANG-ES Project . 3 1.1.1 CHANG-ES Data Products . 7 1.2 FaradayRotation............................. 9 1.2.1 Derivation . 11 1.3 Rotation Measure Synthesis . 16 1.4 Organization of Thesis . 21 Chapter 2: Preparation For Fitting Dynamo Models 23 2.1 Dynamos.................................. 23 2.2 DynamoSolutions............................. 26 2.3 Implementation .............................. 29 Chapter 3: Evolving Galactic Dynamos and Fits to the Reversing Rotation Measures in the Halo of NGC 4631 34 3.1 Abstract.................................. 34 3.2 Introduction................................ 35 3.3 Scale Invariant, Evolving, Magnetic Dynamo Spiral fields . 41 3.3.1 Boundary conditions . 52 3.4 Generic Scale Invariant Dynamo Magnetic Field Modes . 53 vi 3.4.1 Outflow or Accretion in the Pattern Reference Frame . 54 3.4.2 RM Screen for Face-on Galaxies . 63 3.5 FittoNGC4631 ............................. 65 3.6 Comparison with Previous Models . 75 3.7 Conclusions ................................ 77 Chapter 4: Other Galaxies in the CHANG-ES Sample 78 4.0.1 General Trends . 80 4.0.2 Axisymmetric and Bisymmetric Signatures in the Data . 81 4.0.3 Serendipitous Results . 82 Chapter 5: Conclusions 84 Appendix A: General Results and Observational Expectations 100 A.1 Outflow or Accretion in the Pattern Reference Frame . 105 A.2 Rotation-Only in the Pattern Reference Frame . 109 Appendix B: Conversion From Maple Table to FITS Format 110 Appendix C: Rotation Measure Synthesis Images 112 Appendix D: Code: Maple Output to Fits File Conversion 133 Appendix E: Code: Automation of Analysis to Search a Large Pa- rameter Space 144 vii List of Tables 1.1 Summary of the technical specification of measurements from the EVLA 9 1.2 Limits of CHANG-ES measurements in Faraday space . 21 2.1 Physical interpretation of parameters used in dynamo equation solutions. 26 2.2 Self-similarity Class Identification . 27 3.1 Best fit dynamo solutions to NGC 4631 without combining spiral modes 70 3.2 Best fit dynamo solutions to NGC 4631 with combining spiral modes 71 C.1 RMS values for selected CHANG-ES galaxies in L-Band . 132 viii List of Figures 1.1 Gaseous Halo of a Galaxy . 4 1.2 Face-on galaxy NGC 5457 . 5 1.3 Edge-on galaxy NGC 4631 . 6 1.4 VLA.................................... 7 1.5 Visualization of a Data Cube . 10 1.6 Electric Field Vector of a Polarized Electromagnetic Wave . 11 1.7 Faraday Rotation along an axis. 15 2.1 Toroidal Vs Poloidal Schematic . 25 2.2 Effect of Varying the Spiral Mode Number . 28 2.3 Effect of varying the Spiral Pitch Angle . 30 2.4 Effect of Varying the Rotation Rate . 31 3.1 Rotation measure map for NGC 4631 . 38 3.2 Examples of axisymmetric and bisymmetric field geometry. 39 3.3 Field geometries and rotation measure map for an example dynamo solutionwithoutflow............................ 56 3.4 Magnetic field line loop for an example dynamo solution. 58 3.5 Field geometries and rotation measure map for an example dynamo solution with accretion. 59 ix 3.6 Rotation measure map and field geometry for an example dynamo so- lution with accretion and a higher order spiral mode number . 60 3.7 Magnetic field geometry of an example dynamo solution undergoing rotation with respect to the line of sight . 62 3.8 Rotation measure map for an example face-on dynamo solution . 66 3.9 Best fit outflow solution matched to NGC 4631 . 73 3.10 Best fit inflow solution matched to NGC 4631 . 74 A.1 Example rotation measure maps when varying the spiral mode number 102 A.2 Example rotation measure maps when varying the spiral pitch angle . 103 A.3 Example rotation measure maps when varying the rate of rotation of themagneticfield............................. 104 A.4 Example rotation measure maps of an accretion solution when varying the wind speed .