Dynamics and Evolution of Supermassive Black Holes in Merging Galaxies Fazeel Mahmood Khan Astronomisches Rechen-Institut Zentrum f¨urAstronomie der Universit¨atHeidelberg Heidelberg 2011 Cover picture: Gemini image of NGC 5426-27 (Arp 271). Dissertation submitted to the Combined Faculties for the Natural Sciences and for Mathematics of the Ruperto-Carola University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Fazeel Mahmood Khan Born in: Azad Kashmir, Pakistan Oral examination: January 25, 2012 Dynamics and Evolution of Supermassive Black Holes in Merging Galaxies Referees: PD Dr. Andreas Just Prof. Dr. Volker Springel Abstract Supermassive black holes (SMBHs) are ubiquitous in galaxy centers and are correlated with their hosts in fundamental ways, suggesting an intimate link between SMBH and galaxy evolution. In the paradigm of hierarchical galaxy formation this correlation demands prompt coalescence of SMBH binaries, presumably due to dynamical friction, interaction of stars and gas with the binary and finally due to gravitational wave emission. If they are able to coalesce in less than a Hubble time, SMBH binaries will be a promising source of gravitational waves for gravitational wave detectors. However, it has been suggested that SMBH binaries may stall at a separation of 1 parsec. This stalling is sometimes referred to as the \Final Parsec Problem (FPP)". This study uses N-body simulations to test an improved formula for the orbital decay of SMBHs due to dynamical friction. Using a large set of N-body simulations, we show that the FPP does not occur in galaxies formed via mergers. The non spherical shape of the merger remnants ensures a constant supply of stars for the binary to interact with. On its way to coalescence, the SMBH binary ejects several times its total mass in stars and leads to the formation of the cores observed at the center of giant ellipticals. The results of this study also support a cosmological scenario where the prompt coalescence of SMBHs following galaxy mergers is common and where SMBH binaries are promising sources of gravitational waves at low and high redshifts. Zusammenfassung In vielen Galaxienzentren werden Supermassive Schwarze L¨ocher (SMBHs) detektiert. Ihre Massen korrelieren mit unterschiedlichen Eigenschaften dieser Galaxien, was als enge Verbindung in der Entwicklung der SMBHs und Galaxien interpretiert werden kann. Im Bild der hierarchi- schen Galaxienentstehung erfordert diese enge evolution¨areKoppelung ein schnelles Verschmelzen von Doppel-SMBHs, vermutlich verursacht durch dynamische Reibung, die Wechselwirkungen des Doppelsystems mit Sternen bzw. Gas und im finalen Stadium durch Abstrahlung von Gravita- tionswellen. W¨urdendie Doppel-SMBHs schneller als in einer Hubble-Zeit verschmelzen, w¨arensie eine vielversprechende Quelle von Gravitationswellen f¨urdie entsprechenden Detektoren. Jedoch wird vermutet, dass die Entwicklung der Doppel-SMBHs bei Abst¨andenvon ungef¨ahreinem Par- sec zum Erliegen kommt. Dieser Effekt wird manchmal auch als \Finales Parsec Problem" (FPP) bezeichnet. In dieser Arbeit nutzen wir N-K¨orper-Simulationen f¨ureine erweiterte Beschreibung des Herabsinkens von SMBHs als Folge dynamischer Reibung. Mit einer Vielzahl von N-K¨orper- Simulationen zeigen wir, dass das FPP in Galaxien, die durch Verschmelzungen entstehen, nicht auftritt. Die Abweichung von der Kugelsymmetrie der aus der Verschmelzung neu gebildeten Galaxie sorgt f¨ureinen kontinuierlichen Nachschub an Sternen, die mit dem SMBH-Doppelsystem wechselwirken. Auf dem Weg zu ihrer eigenen Verschmelzung schleudern die Doppel-SMBHs Sterne mit einem Vielfachen ihrer eigenen Masse aus der Galaxie heraus, wodurch sich flache Dichteprofile bilden, wie sie h¨aufigin elliptischen Galaxien beobachtet werden. Die Ergebnisse dieser Arbeit unterst¨utzenkosmologische Szenarien, in welchen das rasche Verschmelzen von SMBHs ¨ublicherweise sowohl bei niedrigen als auch bei hohen Rotverschiebungen nach einer Galaxienverschmelzung eintritt und in denen Doppel-SMBHs eine vielversprechende Quelle von Gravitationswellen sind. To my parents Contents 1 Introduction 1 2 Supermassive Black Holes in Galaxy Centers 7 2.1 Observational Evidence for Binary Supermassive Black Holes . 9 2.1.1 Direct Evidence for Dual SMBHs: Spatially Resolved Systems . 11 2.1.2 Indirect Evidence for BBHs: Spatially Unresolved Binary Systems . 13 2.2 Supermassive Black Hole Binary Evolution . 15 2.3 The Final Parsec Problem . 19 2.3.1 Numerical Studies of Final Parsec Problem . 19 2.3.2 Avoiding Final Parsec Problem . 22 3 Galaxy Models and N-body Simulations 27 3.1 Models for Spherical System . 28 3.1.1 The Plummer Model . 28 3.1.2 The Hernquist Model . 29 3.1.3 The Dehnen/Tremaine Model . 29 3.1.4 η-Models With a Central Black Hole . 30 3.2 Initial Setup . 32 3.3 Numerical Codes . 33 3.3.1 φ-GRAPE . 33 3.3.2 Φ-GPU . 34 3.3.3 SUPERBOX . 34 3.3.4 Semi-analytic Code - INTGC . 35 4 Dynamical Friction Force 37 4.1 Power Law Profiles . 38 4.1.1 Distribution Functions . 39 4.2 Physical Models . 42 4.3 Coulomb Logarithm . 43 4.4 Cumulative Distribution Functions . 44 4.5 Dynamical Friction in Gaseous Medium . 48 5 Orbital Decay of SMBHs in Galactic Centers 51 5.1 Kepler Potential . 57 5.1.1 Bahcall-Wolf cusp . 57 5.1.2 Hernquist Cusp . 58 5.1.3 The Outskirts of a Plummer Sphere . 58 5.1.4 The Outskirts of Dehnen Models . 60 5.2 Applications . 60 5.2.1 The Galactic Center . 60 5.2.2 Minor Merger . 61 i CONTENTS 6 Numerical Tests of Dynamical Friction Formula 63 6.1 Bahcall-Wolf Cusp . 64 6.1.1 Cusp Stability Analysis . 64 6.1.2 Circular Runs . 64 6.1.3 Eccentric Runs . 66 6.2 Hernquist Cusp . 70 6.3 Outskirts of the Plummer Sphere . 70 6.4 Outskirts of Dehnen Models . 71 6.5 Self Gravitating Cusps . 72 6.5.1 Dehnen-1.5 Model . 72 6.5.2 Hernquist Model . 74 6.6 Velocity Distribution Functions . 74 7 SMBH Binaries in Equal Mass Galaxy Mergers 79 7.1 Numerical Methods and Initial Conditions . 79 7.2 Isolated Models . 81 7.3 Galaxy Mergers . 83 7.4 SMBH Binary Evolution in Galaxy Mergers . 84 7.5 Estimates of Coalescence Time for SMBHs . 89 8 Unequal Mass Galaxy Mergers and SMBH Binaries 93 8.1 Initial Conditions and Numerical Methods . 94 8.1.1 The Host Galaxies and Their SMBHs . 94 8.1.2 Galaxy Merger Setup . 95 8.1.3 Numerical Methods and Hardware . 96 8.2 Evolution of SMBH Binaries . 96 8.3 Mass Deficits . 101 8.4 Coalescence Times for SMBH Binaries . 105 8.4.1 Post-Newtonian Simulations . 106 9 SMBH Binary Evolution in a Late Type Galaxy Merger 111 9.1 Initial Conditions . 111 9.2 Numerical Methods . 112 9.3 SMBH Binary Evolution . 112 9.4 Time for the Coalescence of SMBH Binary . 118 9.5 Discussion . 120 10 Conclusion 123 ii List of Acronyms AGN Active Galactic Nuclei BH Black Hole DF Distribution Function FPP Final Parsec Problem GW Gravitational Wave HST Hubble Space Telescope IMBH Intermediate Mass Black Hole IMF Initial Mass Function Λ CDM Lambda Cold Dark Matter PDF Probability Distribution Function POPIII Population III PTA Pulsar Timing Array SMBH Super Massive Black Holes VLBA Very Long Base-line Array Chapter 1 Introduction Black holes are one of the most exotic predictions of physics described by Einstein's Theory of General Relativity (GR). In GR matter and energy cause spacetime curvature and the black holes which are the densest masses in the Universe are the objects of spacetime wrapped around themselves. Indirect astronomical observational evidence support that the astrophysical black holes exist in three mass ranges: stellar mass black holes (BH), having masses of 4-15 M , are formed as the end product of stellar evolution of massive stars for a wide range of stellar masses and 2 4 metallicities. Intermediate mass black holes (IMBH), with masses ∼ 10 − 10 M , are suggested to have been formed by the collapse of population III (PopIII) stars (Rees 1984, Madau & Rees 2001) or by runaway mergers of very massive stars in the center of dense stellar clusters (Portegies Zwart & McMillan 2002, Portegies Zwart et al. 2004, G¨urkan et al. 2004). Supermassive black 5 9 holes (SMBH), with masses ranging from 10 − 10 M reside at the center of massive galaxies. SMBH are suggested to grow to these enormous masses by starting as a seed black hole of few hundred solar masses as a remnant of a PopIII star and then accretion plays vital role in the growth of supermassive black hole. In another scenario a SMBH can form as the end product of dynamical instabilities setting in massive gaseous protogalactic disks (Koushiappas et al. 2004, Begelman et al. 2006, Volonteri & Begelman 2010) or in the mergers of gas rich disk galaxies (Mayer et al. 2010). Mergers between SMBHs can also assist the mass growth of black holes. The idea of supermassive black holes was proposed in 1960s to explain the enormous luminosi- ties of quasars (Salpeter 1964, Zel'Dovich & Novikov 1964). Quasars, the most powerful sources of energy in the universe, are believed to be powered by accretion of gas and stars onto SMBHs. This idea has also been generally accepted for the explanation of radiation and jets emission from all active galactic nuclei (AGN). The existence of SMBHs is now firmly established by measurements of velocities of stars and gas which have Keplarian rise near the centers of galaxies. Observations of distant quasars (redshift greater than 6) suggest that SMBHs with masses of up to a billion solar masses were already in place at the centers of galaxies in the first billion years after the Big Bang (Fan 2006). The presence of the SMBH at the center of a galaxy is correlated with the dynamics of its stellar component.