Effect of Magnetic Seed Fields on Lyman Alpha Emission from Distant Quasars ASSAC INSTITUTE OFTECHNOLOGY by Sruthi Annapoorny Narayanan JUL 0 72016 LIBRARIES Submitted to the Department of Physics ARCHIVES in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2016 @ Massachusetts Institute of Technology 2016. All rights reserved. Author ... Signature redacted Department of Physics May 6, 2016 Signature redacted Certified by.... Mark Vogelsberger Assistant Professor of Physics Thesis Supervisor Accepted by......... Signature redacted Nergis Mavalvala Associate Department Head of Physics, Senior Thesis Coordinator 2 Effect of Magnetic Seed Fields on Lyman Alpha Emission from Distant Quasars by Sruthi Annapoorny Narayanan Submitted to the Department of Physics on May 6, 2016, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract There are indications that weak magnetic fields originating in the early Universe and magnified via magnetohydrodynamic (MHD) processes could cause perturba- tions in the thermodynamic state of the gas in the intergalactic medium which affect the Lyman-Alpha spectrum we observe. In this work we investigate to what extent the properties of the Lyman-Alpha forest are sensitive to the presence of large-scale cosmological magnetic fields as a function of the seed field intensity. To do so, we develop and use a series of numerical tools to analyze previously constructed cosmo- logical MHD simulations that include state-of-the-art implementation of the relevant physical processes for galaxy formation. The inclusion of these physical mechanisms is crucial to get the level of magnetic field amplification currently observed in the struc- tures that populate our Universe. With these tools we isolate characteristics, namely the Flux Probability Density Function and the Power Spectrum, of the Lyman-Alpha forest that are sensitive to the magnetic field strength. We then examine the impli- cations of our results. Thesis Supervisor: Mark Vogelsberger Title: Assistant Professor of Physics 3 4 Acknowledgments First and foremost I would like to acknowledge Federico Marinacci who has provided so much assistance in the writing of this thesis. I would like to thank him for patiently reading every draft and giving me thorough comments as well as helping me to learn and understand all the integral physics for this project. His help has been invaluable. I would also like to thank Professor Vogelsberger for his guidance and useful discussion. My overall experience at MIT has been shaped by my friends. In particular Elise Newman, Francisco Machado, Will Conway and Nick Rivera have made my time here especially fruitful. They have helped me a considerable amount in understanding this project. I would also like to thank Evan Zayas for his help and motivation when writing my thesis because everyone needs that one person who they can complain to all the time and who can also help them with physics. Lastly I want to express my gratitude and love to my parents who have been with me through countless endeavors over the past four years and constantly give me a reason to not give up. 5 6 Contents 1 Introduction 13 2 The Ly-a Forest 19 2.1 Proposed Effect of Magnetic Fields ...... ............ 23 3 Simulation Details 25 3.1 Analyzing Simulation Output ............ .......... 28 3.1.1 Choosing a Random Line of Sight ........... ..... 28 3.1.2 Interpolation along line of sight ................. 29 4 Computing Ly-a Spectrum 31 4.1 Error Estimation Methods ........................ 33 4.1.1 Bootstrap Method ...... .................. 33 4.1.2 Jackknife Method .. ....................... 34 5 Results and Discussion 36 5.1 Flux Probability Density Function .................... 42 5.2 Power Spectrum ..... ......................... 44 6 Conclusions and Summary 46 A Cosmology 48 A.1 ACDM Cosmology ............................ 48 A.1.1 A Simple Example ........................ 49 A.2 Adiabatic Heating and Cooling ............. ........ 50 7 B Astrophysics 52 B.1 Reionization ... ... .. .. .... .... ... .. 52 B.1.1 Ionization Fraction ...... .................. 53 8 List of Figures 1-1 The cosmological epochs .................... ..... 15 1-2 Visualization of the magnetic field strength in the simulation box at redshifts z = 4.1 and z = 0 ........................ 17 2-1 Example star absorption spectrum and quasar emission spectrum . 20 2-2 Toy model of quasar emission spectrum ................. 21 2-3 Variation in gas density with magnetic field .............. 23 3-1 Simulation box with random line of sight and interpolation cylinder 29 3-2 Example of tesselation of two dimensional simplices .......... 30 5-1 Spectra as a function of distance for B = 10-12 G and z = 2.0 ... 37 5-2 Column density of neutral hydrogen for B = 10-12 G ......... 37 5-3 Spectra as a function of distance for B = 10-12 G and z = 2.5,3.0 . 39 5-4 Spectra as a function of distance for B = 5 x 10-' G and z = 2.0 . 40 5-5 Column density of neutral hydrogen for B = 5 x 10-' G ....... 40 5-6 Spectra as a function of distance for B = {10-12, 10-11, 10-10, 10-9, 5 x 10-9, 10-8} G and z = 2.0 . ....................... 41 5-7 Magnetic field variation of the Flux PDF for z = 2.0 ......... 43 5-8 Magnetic field variation of the power spectrum for z = 2.0 ...... 45 B-i Graphical representation of the history of the universe ........ 53 9 10 """ mr,'' I I "I I - -- ,"Mmm List of Tables 3.1 Properties of the performed simulations ...... ...... ..... 26 4.1 Comparison between bootstrap and jackknife methods .. ...... 35 11 12 Chapter 1 Introduction Magnetic fields are an essential component in many astrophysical phenomena at all mass and length scales ranging from stars to galaxy clusters and possibly extend- ing even to the intergalactic medium (Govoni and Feretti [2004]). The rotation of compact objects, like supermassive black holes, affects the magnetic fields lines by "twisting" and "tangling" them.' Twists and tangles can produce highly localized fields with the potential to generate relativistic jets that propagate into the intra- cluster medium (Blandford and Znajek [1977]) which can then affect the accretion on compact objects like neutron stars and supermassive black holes (Balbus [2003]). Additionally magnetic fields affect the propagation of relativistic particles like cosmic rays which then have an effect on other observable astrophysical processes (Kotera and Olinto [2011]). At the level of galaxies, the magnetic fields allow for the production of synchrotron radiation seen in disc galaxies (Beck and Krause [2005]) and in some active galactic nuclei (AGN) (Urry and Padovani [1995]). On smaller scales (smaller than galaxies and clusters) magnetic fields provide magnetic pressure that acts along with thermal pressure against gravity in the interstellar medium (ISM) and potentially the inter- galactic medium (IGM) (Boulares and Cox [1990]). The study of the origin and the 'For example, twisting and tangling of magnetic fields is what causes the polarity of the Earth's magnetic field to switch. 13 evolution of these fields is therefore a key aspect in our understanding of the Uni- verse. However, it is not yet clear from a theoretical perspective how magnetic fields were generated in the early Universe and whether these fields affected the structures that developed later on. There are indications that pre-existing magnetic fields were magnified by dynamical processes in our Universe but we still do not understand the origins of this supposed seed field (Widrow et al. [2011]). One proposed model suggests a cosmological origin of the seed, which means it was generated via inflationary processes. This could have occurred due to phase tran- sitions. It is postulated that in the early Universe, phase transitions were present that changed the nature of particles and fields. For example, electroweak symmetry breaking marked the transition from a high-energy regime in which the W and Z bosons and the photon were effectively massless and interchangeable to one in which the W and Z bosons were heavy while the photon remained massless. This transi- tion coincided with the increased relevance of electromagnetism and the weak nuclear force (Widrow et al. [2011]). Transitions like this one had potential to generate strong magnetic fields because they involved the release of a lot of energy. In Figure 1-1 we show a time table of the cosmological epochs in the early universe that could have contributed to the production of a seed field. A non-inflationary process that could have contributed to the production of a seed field is the Biermann battery mechanism proposed by L. Biermann in 1950 that can occur simultaneously with cosmological shocks (Ryu et al. [1998]) or during cosmic reionization (Gnedin [2000]). It is then proposed that these seed fields were amplified by turbulent processes or galactic dynamos (baryons collapse into dark matter haloes that assemble structures in our Universe.) Another class of models suggests that the magnetic fields were produced by stars in protogalaxies and then later ejected outwards, conceivably by the Biermann mech- anism mentioned above (Schoeffler et al. [2016]). Whereas we seem to have many 14 Time Since Major Events Big Bang Since Big Bang present Humans stars, observe Era of galaxies the cosmos. Gataxie! and clusters Galaie e (made of I billion sma years First galaxies oms and form. Era of Jstars Atoms bagin Atoms form; 500,000 form) photons fly free and become years plasma of microwave Er. - hydrogen and background, NuE0e helium nuclei Cie nplus electrons Fusion ceases; 3 minutes. normal matter is protons. neutrons 75% hydrogen. Era ol - ~ electrons. neutrinos 25% helium, by Nucleosynthesis (antimatter rare) mass. 0.001 seconds Matter annihilates Omentary partlcles antimatter. , ltmattor Particle Era e e * O 10 seconds ag common) El. ctromagnetic and weak ces become distinct. Electroweak Ern - ele Io 13- Pa'ticles Sti 10 seconds rong force becomes distinct, perhaps GUT Ern elementary ca using inflation of iverse.