Snacktime for Hungry Black Holes: Theoretical Studies of the Tidal Disruption of Stars by Linda Elisabeth Strubbe A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Astrophysics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Eliot Quataert, Chair Professor Joshua Bloom Professor Steven Boggs Fall 2011 Snacktime for Hungry Black Holes: Theoretical Studies of the Tidal Disruption of Stars Copyright 2011 by Linda Elisabeth Strubbe 1 Abstract Snacktime for Hungry Black Holes: Theoretical Studies of the Tidal Disruption of Stars by Linda Elisabeth Strubbe Doctor of Philosophy in Astrophysics University of California, Berkeley Professor Eliot Quataert, Chair A star that wanders too close to the massive black hole (BH) in the center of a galaxy is headed for trouble: within a distance r r (M /M )1/3 (where r and M are the star’s T ∼ ⋆ BH ⋆ ⋆ ⋆ radius and mass, and MBH is the BH’s mass), the BH’s tidal gravity overcomes the binding gravity of the star, and the star is shredded into a stream of stellar debris. Studying this process of tidal disruption has the potential to give us insights into how central BHs and their surrounding stellar population grow and evolve. Motivated by new and upcoming rapid- cadence optical transient surveys, which should detect and allow study of tidal disruption events (TDEs) in unprecedented detail, I make theoretical predictions of the observable properties of these events to aid in their detection, identification, and interpretation. I find that stellar debris falling towards the BH is likely driven off again by radiation pressure at early times when the feeding rate is super-Eddington: this outflow has a large photosphere 43 44 1 and relatively cool temperature, producing a luminous ( 10 few 10 erg s− ) transient event at optical wavelengths. I predict that new transient∼ surveys− × such as the Palomar Transient Factory are likely to find tens to hundreds of these events. I further predict the spectroscopic signature of super-Eddington outflows—broad, blueshifted absorption lines in the ultraviolet—which should help confirm and teach us more about TDE candidates. Finding that the observable appearance of TDEs depends not only on BH mass but on pericenter radius of the star’s last fateful orbit, I derive a theoretical expression for the disruption rate as a function of pericenter and apply it to the galaxy NGC 4467 using real observational data, laying the groundwork for more extensive studies in the future. Finally, I also present my work on the debris disk surrounding the star AU Mic, in which I propose an explanation for the physical processes of dust dynamics that give rise to the observed disk profile. i For Mummy and Papa, who taught me to wonder about Nature, and who encourage me at every step. And for David, the best brother in the Universe. ii Contents List of Figures v List of Tables vii Acknowledgments viii 1 Introduction 1 1.1 Overview: for non-scientists and scientists . .......... 1 1.2 Astrophysicalcontext. ... 4 1.2.1 The presence and masses of central black holes . ...... 5 1.2.2 Theorbitsofstarsingalacticnuclei. ..... 6 1.2.3 Thegrowthofblackholes ........................ 8 1.3 Previousstudies................................. 11 1.3.1 Stellar dynamical studies . .. 12 1.3.2 Predicted observational appearance . ..... 15 1.3.3 Observations of tidal disruption candidates . ........ 17 1.4 Summaryofchapters ............................... 20 2 Optical Signatures of Tidally Disrupted Stars 23 2.1 Introduction.................................... 24 2.2 TheInitiallyBoundMaterial. .... 25 2.2.1 Super-EddingtonOutflows . 26 2.2.2 TheAccretionDisk............................ 28 2.3 TheEquatorialUnboundMaterial. .... 30 2.4 PredictedEmission ............................... 33 2.4.1 Super-EddingtonOutflows . 33 2.4.2 Disk and Photoionized Unbound Debris . ... 34 2.5 PredictedRates.................................. 39 2.5.1 DiskandPhotoionizedMaterial . .. 40 2.5.2 Current Observational Constraints . .... 41 2.5.3 Super-EddingtonOutflows . 43 2.6 Discussion..................................... 46 Contents iii 2.6.1 Super-EddingtonOutflows . 48 2.6.2 The Accretion Disk, Photoionized Gas, & Broad EmissionLines . 50 2.6.3 ObservationalConsiderations . ... 51 2.6.4 Astrophysical Applications . ... 52 3 Spectroscopic Signatures of the Tidal Disruption of Stars 54 3.1 Introduction.................................... 55 3.2 Super-EddingtonOutflows . .. 56 3.2.1 SummaryofBasicProperties . 56 3.2.2 The Applicability of Thermal Equilibrium . ..... 58 3.2.3 SpectroscopicCalculations . ... 60 3.3 PredictedSpectra................................ 64 3.3.1 Implications of an X-ray Power-law . ... 68 3.4 Supernova Rates in Galactic Nuclei . ..... 71 3.5 Discussion..................................... 74 3.5.1 ObservationalProspects . 75 3.5.2 Optically-selected candidates . ..... 78 4 Tidal Disruption Rate as a Function of Pericenter 79 4.1 Introduction.................................... 80 4.2 Tidaldisruptionratebasics . .... 81 4.3 Fokker-Planckformalism . ... 84 4.3.1 The distribution function and coordinate systems . ........ 84 4.3.2 Deriving the Fokker-Planck equation for (E, R; r)space........ 87 4.3.3 Diffusioncoefficients ........................... 89 4.3.4 The Fokker-Planck equation, continued . ..... 92 4.3.5 The distribution function outside the tidal disruptionzone ...... 93 4.3.6 The distribution function inside the tidal disruptionzone....... 94 4.3.7 Flowratesinphasespace ........................ 96 4.3.8 Calculating f(Rlc) ............................ 97 4.4 Tidal disruption rate as a function of pericenter . .......... 99 4.4.1 Keplerian potential with power-law density profile . ......... 101 4.4.2 Thenon-Keplerianpotential . 103 4.5 Results:NGC4467................................ 109 4.5.1 Implications for optical transient surveys . ........ 110 4.6 Discussion & directions for future work . ....... 111 5 Dust Dynamics, Surface Brightness Profiles, and Thermal Spectra of De- bris Disks: The Case of AU Mic 116 5.1 Introduction.................................... 117 5.2 Preliminaries ................................... 118 5.2.1 StellarProperties . .. .. 119 Contents iv 5.2.2 CollisionTimes .............................. 119 5.2.3 Blow-out by Stellar Wind and Radiation Pressure . ...... 120 5.2.4 Corpuscular and Poynting-Robertson Drag . ..... 122 5.3 Theory....................................... 123 5.3.1 Equilibrium Size Distribution . 124 5.3.2 Physical Implications of Optical Depth Profiles . ....... 129 5.3.3 Unbound Grains (β 1/2)........................ 133 ≥ 5.3.4 Unequilibrated Grains (sblow <s<sage) ................ 134 5.4 MonteCarloModelling............................. 135 5.4.1 Procedure ................................. 135 5.4.2 Products of the Monte Carlo Calculation . .... 137 5.4.3 Results................................... 138 5.5 SummaryandDirectionsforFutureWork . .... 140 6 Epilogue: Recent observational work 148 6.1 PTF10iya ..................................... 148 6.2 Swift1644+57................................... 152 Bibliography 153 v List of Figures 2.1 Spatialdiagramofthestellardebris. ......... 30 2.2 Predicted spectral energy distributions for super-Eddingtonoutflows . 31 2.3 Predicted optical light curves . ....... 32 2.4 Peak luminosities of the super-Eddington outflows . ............ 35 2.5 Predicted spectral energy distributions for the accretion disk & unbound debris 37 2.6 Predicted ultraviolet to near-infrared spectra for the accretion disk & unbound debris ......................................... 38 2.7 Predicted evolution of emission line strengths . ............ 38 2.8 Duration of maximum luminosity during the late-time accretion disk phase . 42 2.9 Predicted detection rates as a function of black hole mass for a survey like Pan- STARRS 3π ...................................... 43 2.10 Predicted detection rates as a function of pericenter distance for a survey like Pan-STARRS 3π ................................... 44 2.11 Duration of peak luminosity during the early super-Eddington outflow phase . 45 2.12 Predicted detection rates for emission from super-Eddington outflows by a survey like Pan-STARRS 3π ................................. 46 2.13 Predicted detection rates for emission from super-Eddington outflows for various opticaltransientsurveys . ... 47 3.1 Predicted spectra for our three fiducial tidal disruption flares at several different timesafterdisruption.. .. .. .. 65 3.2 Predicted spectra varying the mass-loss rate in the outflow, focusing on the wave- length region 1000 2000 A.............................˚ 66 − 3.3 Predicted spectra showing the effects of varying the mass-loss rate and outflow speedinthesuper-Eddingtonwind . ... 69 3.4 Predicted spectra including the presence of an X-ray power-lawtail . 70 3.5 Rates of supernovae close to the galactic nucleus . ............ 72 4.1 Normalized tidal disruption rate as a function of pericenter distance at various energies ........................................ 100 4.2 Tidal disruption rate as a function of pericenter distance at various energies inside theradiusofinfluence ................................ 103 List of Figures vi 4.3 Ratio q and distribution function f calculatedforNGC4467 . 109 4.4 Predicted tidal disruption rate as a function of pericenter distance for the galaxy NGC4467....................................... 110 4.5 Predicted optical detection rate incorporating dγ/d ln rp result .