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Adventures in Theoretical Astrophysics Adventures in Theoretical Astrophysics Thesis by Alison Jane Farmer In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2005 (Defended May 13, 2005) ii c 2005 Alison Jane Farmer All Rights Reserved iii Acknowledgements Thanks... To everyone who made my PhD more than just an academic experience. To my Caltech officemates, who have all managed to be successful despite my constant inane chatter: To Dawn Erb and Naveen “Dalek” Reddy for the best-decorated office in Robinson, to Margaret Pan for eating as many meringues as I did, and to Mike Santos for being as good at listening as he is at talking.1 To my big brothers at the IAS, for all the teasing. To all the men I have wronged. To everyone who beat me at sports. To everyone who is in more than one of the above categories. To California for my accent. To New Jersey for the cicadas. To db for feeding me like royalty while I wrote up this thesis.2 To Mr. Higgins of James Gillespie’s High School in Edinburgh for giving up his lunchtimes to talk physics. To Sterl Phinney for converting me to theory. To Asantha Cooray and Eric Agol for their collaboration. To Re’em Sari for making me behave better, and for lunch. To Peter Goldreich — my advisor, father-figure, grandfather-figure, personal trainer, chauffeur and friend — for everything. To Susan Goldreich for looking after him. To my parents, Ann and John Farmer, for believing in me. 1Marill! 2Rat vit rˆot, rˆot tenta rat, rat mit patte `arˆot, rˆot brˆula patte `arat. iv Abstract This thesis is a tour of topics in theoretical astrophysics, unified by their diversity and their pursuit of physical understanding of astrophysical phenomena. In the first chapter, we raise the possibility of the detection of white dwarfs in transit surveys for extrasolar Earths, and discuss the peculiarities of detecting these more massive objects. A population synthesis calculation of the gravitational wave background from extragalactic bi- nary stars is then presented. In this study, we establish a firm understanding of the uncertainties in such a calculation and provide a valuable reference for planning the Laser Interferometer Space Antenna mission. The long-established problem of cosmic ray confinement to the Galaxy is addressed in another chapter. We introduce a new wave damping mechanism, due to the presence of background turbu- lence, that prevents the confinement of cosmic rays by the resonant streaming instability. We also investigate the spokes in Saturn’s B ring, an electrodynamic mystery that is being illuminated by new data sent back from the Cassini spacecraft. In particular, we present assessments of the presence of charged dust near the rings, and the size of currents and electric fields in the ring system. We make inferences from the Cassini discovery of oxygen ions above the rings. In addition, the previous leading theory for spoke formation is demonstrated to be unphysical. In the final chapter, we explain the wayward motions of Prometheus and Pandora, two small moons of Saturn. Previously found to be chaotic as a result of mutual interactions, we account for their behavior by analogy with a parametric pendulum. We caution that this behavior may soon enter a new regime. v Contents Acknowledgements iii Abstract iv 1 Introduction and Executive Summary 1 2 Finding White Dwarfs with Transit Searches 8 Abstract 9 2.1 Introduction.................................... ..... 10 2.2 Whitedwarfbinaryvariations. ......... 11 2.3 Whitedwarfsinbinaries. ....... 13 2.3.1 EvolutiontotheWD–MSstage. .... 13 2.3.2 Populationsynthesis . ..... 14 2.4 Detectingwhitedwarfs. ....... 15 2.4.1 Stellarvariability. ...... 17 2.5 Discussion...................................... .... 20 2.6 Conclusions ..................................... .... 22 3 The Gravitational Wave Background from Cosmological Compact Binaries 26 Abstract 27 3.1 Introduction.................................... ..... 28 3.2 Gravitationalwavesfromabinarysystem . ........... 31 vi 3.3 EvolutiontotheDDstage. ...... 32 3.3.1 CEE+CEE ..................................... 33 3.3.2 StableRLOF+CEE ................................ 34 3.4 Analyticargumentsaboutspectralshape . ........... 35 3.5 Modelconstruction............................... ...... 39 3.5.1 The BSE codeandpopulationsynthesis . 39 3.5.2 Thestateofobservations . ..... 41 3.5.3 Candidatemodels ............................... .. 42 3.5.4 Interacting DDs and modifications made to the BSE code........... 46 3.6 Cosmologicalequations . ....... 48 3.6.1 Basicequations................................ ... 49 3.6.2 Computationalequations . ..... 50 3.6.3 Quantitiesused................................ ... 52 3.6.4 Cosmicstarformationhistory. ....... 53 3.7 Basicresults.................................... ..... 55 3.7.1 Contributors .................................. .. 58 3.7.1.1 Eccentricharmonics . 58 3.7.1.2 Interactingbinaries . .. 59 3.7.1.3 WDtypes,chirpmass,andmergerrates . ... 61 3.7.2 Progenitors ................................... .. 67 3.8 Outlook ......................................... .. 72 3.9 Comparisonwithpreviouswork. ........ 74 3.10Conclusions .................................... ..... 77 4 Wave Damping by MHD Turbulence and its Effect upon Cosmic Ray Propagation in the ISM 83 vii Abstract 84 4.1 Introduction.................................... ..... 85 4.2 TheMHDcascadeasadampingmechanism. ....... 86 4.2.1 Relevantpropertiesofthecascade . ........ 86 4.2.2 Theturbulentdampingrate. ..... 87 4.3 Competitionbetweengrowthanddamping. .......... 88 4.3.1 Resonantscatteringofcosmicrays . ........ 88 4.3.1.1 Parallellengthscale . .. 88 4.3.1.2 Perpendicularlengthscale . .... 89 4.3.2 Growthanddamping .............................. 90 4.4 Application to cosmic ray self-confinement in the ISM . .............. 91 4.4.1 Comparisonwithpreviouswork. ...... 93 4.5 Conclusions ..................................... .... 94 5 Ghosts of Saturn: Studies for the Ring Spokes 97 Abstract 98 5.1 Introduction.................................... ..... 98 5.2 Observationsofthespokes: theclues . ........... 99 5.2.1 Immediateinferences. ..... 102 5.3 Saturniansystemandrings . ....... 103 5.3.1 Saturn........................................ 103 5.3.2 Rings ........................................ 103 5.4 Photoelectronlayer.. .. .. .. .. .. .. .. .. .. .. .. .. ....... 105 5.4.1 Distributionofsurfacecharge . ........ 107 5.5 Dustaroundtherings .............................. ..... 108 5.5.1 Dustfromimpacts ............................... 108 5.6 Dustcharging.................................... .... 110 viii 5.6.1 Dustcharginginvacuum . .. 111 5.6.2 Dust charging within the Debye sheath . ....... 112 5.6.3 Levitationofdust .............................. .. 113 5.6.4 Dustcharginginaplasma. .... 115 5.7 Theringatmosphereandionosphere . ......... 115 5.7.0.1 Theobservations. .. .. .. .. .. .. .. .. .. .. .. .. 116 5.7.1 Conservativeinterpretation . ........ 117 5.7.2 Liberalinterpretation . ...... 120 5.7.2.1 Neutrallossrate ............................. 120 5.7.2.2 Loss processes for ions in the collisional atmosphere ......... 121 5.7.3 Debyesheathinpresenceofplasma . ...... 125 5.8 Electrodynamicsandcurrents . ......... 127 5.8.1 Conductivities in a magnetic field . ........ 130 5.8.2 Currentsintheringplane . ..... 132 5.8.2.1 ElectronsinDebyesheath. 132 5.8.2.2 Ionsinringatmosphere . 132 5.8.2.3 Dustgrains................................ 134 5.8.3 Nonvanishingcurrentsatcorotation . ......... 137 5.8.3.1 RingcurrentduetogradBdrift . 137 5.8.3.2 Ringcurrentdue tocorotationcharge . ..... 138 5.8.3.3 Field-alignedcurrents . .. 138 5.9 Theionosphere ................................... .... 140 5.9.1 Collisiontypes ................................ .. 140 5.9.2 Ionosphericwinds .............................. .. 142 5.10 Summary of environment: what have we learned and where dowegofromhere? . 143 5.11 2-streaminstability. ......... 144 5.12Previousattempts ............................... ...... 147 ix 5.13Conclusions .................................... ..... 147 5.14 Appendix: Velocity drifts in electric fields . ............... 152 5.14.1 Withneutralcollisions. ....... 152 5.14.2 IncludingCoulombcollisions . ........ 153 5.15 Appendix: the 2-stream instability . ............ 155 5.15.1 Thefluidequations. .... 155 5.15.2 Identicalfluids ............................... .... 156 5.15.3 Extremeplasmafrequencyratio . ....... 156 5.15.4 Includinglightfluids . ...... 157 5.15.5 Saturation of the instability . ......... 158 6 Spoke Formation under Moving Plasma Clouds 159 Abstract 160 6.1 Introduction.................................... ..... 160 6.2 Driftofaplasmacloud............................. ...... 162 6.2.1 Themodel ..................................... 163 6.2.2 Finding the drift velocity . ...... 163 6.3 WhereGMerred .................................... 166 6.4 Recalculationofdriftvelocity . ........... 167 6.5 Conclusions ..................................... .... 168 7 Understanding the Behavior of Prometheus and Pandora 170 Abstract 171 7.1 Introduction.................................... ..... 171 7.2 Resonantinteractions . ....... 172 7.3 Chaos—asimpleintroduction . ........ 174 7.4 Pendulumequations ............................... ..... 175 x 7.4.0.1 Integration ................................ 176 7.4.1 Systembehaviorandtheseparatrix . ....... 176 7.4.2 Action and locating separatrix crossings . ........... 177 7.4.3 Separation in phase space and Lyapunov exponent . .......... 179 7.4.4
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