Gravitational Wave Driven Mergers and Coalescence Time of Supermassive Black Holes

The evolution of Supermassive Black Holes (SMBHs) initially embedded in the centres of merging galaxies realised with a stellar mass function (SMF) is studied from the onset of galaxy mergers till coalescence. We performed a large set of direct N-body simulations with three different slopes of the central stellar cusp and different random seeds. Post Newtonian terms up to order 3.5 are used to drive the SMBH binary evolution in the relativistic regime. The impact of a SMF on the hardening rate and the coalescence time is investigated. We find that SMBH binaries coalesce well within one billion years when our models are scaled to galaxies with a steep cusp at low redshift. Here higher central densities provide larger supply of stars to efficiently extract energy from the SMBH binary orbit and shrink it to the phase where gravitational wave (GW) emission becomes dominant leading to the coalescence of the SMBHs. Mergers of models with shallow cusps that are representative for giant elliptical galaxies having central cores result in less efficient extraction of binary orbital energy due to the lower stellar densities in the centre. However, high values of eccentricity witnessed for SMBH binaries in such galaxy mergers ensure that the GW emission dominated phase sets in earlier at larger values of the semi-major axis. This helps to compensate for the less efficient energy extraction during the phase dominated by stellar encounters resulting in mergers of SMBHs in about one Gyr after the formation of the binary. Additionally, we witness mass segregation in the merger remnant resulting in enhanced SMBH binary hardening rates. We show that at least the final phase of the merger in cuspy low mass galaxies would be observable with the GW detector eLISA.Comment: Accepted for publication in Astronomy & Astrophysic

Dynamics and Evolution of Supermassive Black Holes in Merging Galaxies

In vielen Galaxienzentren werden Supermassive Schwarze Löcher (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 hierarchischen Galaxienentstehung erfordert diese enge evolutionäre Koppelung 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 Gravitationswellen. Würden die Doppel-SMBHs schneller als in einer Hubble-Zeit verschmelzen, wären sie eine vielversprechende Quelle von Gravitationswellen für die entsprechenden Detektoren. Jedoch wird vermutet, dass die Entwicklung der Doppel-SMBHs bei Abständen von ungefähr einem Parsec zum Erliegen kommt. Dieser Effekt wird manchmal auch als "Finales Parsec Problem" (FPP) bezeichnet. In dieser Arbeit nutzen wir N-Körper-Simulationen für eine erweiterte Beschreibung des Herabsinkens von SMBHs als Folge dynamischer Reibung. Mit einer Vielzahl von N-Körper-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 für einen 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 häufig in elliptischen Galaxien beobachtet werden. Die Ergebnisse dieser Arbeit unterstützen kosmologische Szenarien, in welchen das rasche Verschmelzen von SMBHs üblicherweise sowohl bei niedrigen als auch bei hohen Rotverschiebungen nach einer Galaxienverschmelzung eintritt und in denen Doppel-SMBHs eine vielversprechende Quelle von Gravitationswellen sind

The Stellar Orbital Structure in Axisymmetric Galaxy Models with Supermassive Black Hole Binaries

It has been well-established that particular centrophilic orbital families in non-spherical galaxies can, in principle, drive a black hole binary to shrink its orbit through three-body scattering until the black holes are close enough to strongly emit gravitational waves. Most of these studies rely on orbital analysis of a static SMBH-embedded galaxy potential to support this view; it is not clear, however, how these orbits transform as the second SMBH enters the center, so our understanding of which orbits actually interact with a SMBH binary is not ironclad. Here, we analyze two flattened galaxy models, one with a single SMBH and one with a binary, to determine which orbits actually do interact with the SMBH binary and how they compare with the set predicted in single SMBH-embedded models. We find close correspondence between the centrophilic orbits predicted to interact with the binary and those that are actually scattered by the binary, in terms of energy and Lz distribution, where Lz is the z component of a stellar particle's angular momentum. Of minor note: because of the larger mass, the binary SMBH has a radius of influence about 4 times larger than in the single SMBH model, which allows the binary to draw from a larger reservoir of orbits to scatter. Of the prediction particles and scattered particles, nearly half have chaotic orbits, 40% have fx:fy=1:1 orbits, 10% have other resonant orbits

Formation and hardening of supermassive black hole binaries in minor mergers of disk galaxies

We model for the first time the complete orbital evolution of a pair of supermassive black holes (SMBHs) in a 1:10 galaxy merger of two disk-dominated gas-rich galaxies, from the stage prior to the formation of the binary up to the onset of gravitational wave (GW) emission when the binary separation has shrunk to 1 mpc. The high-resolution smoothed particle hydrodynamics (SPH) simulations used for the first phase of the evolution include star formation, accretion onto the SMBHs as well as feedback from supernovae explosions, and radiative heating from the SMBHs themselves. Using the direct N-body code phi-GPU, we evolve the system further without including the effect of gas, which in the mean time has been mostly consumed by star formation. We start at the time when the separation between two SMBHs is ~700 pc and the two black holes are still embedded in their galaxy cusps. We use three million particles to study the formation and evolution of the SMBH binary until it becomes hard. After a hard binary is formed, we reduce (reselect) the particles to 1.15 million and follow the subsequent shrinking of the SMBH binary due to three-body encounters with the stars. We find approximately constant hardening rates and that the SMBH binary rapidly develops a high eccentricity. Similar hardening rates and eccentricity values were reported in earlier studies of SMBH binary evolution in the merging of dissipationless spherical galaxy models. The estimated coalescence time is ~5.5 Gyr, significantly smaller than a Hubble time. We discuss why this timescale should be regarded as an upper limit. Since 1:10 mergers are among the most common interaction events for galaxies at all cosmic epochs, we argue that several SMBH binaries should be detected with currently planned space-borne GW interferometers, whose sensitivity will be especially high for SMBHs in the mass range considered here

Efficient Merger of Binary Supermassive Black Holes in Merging Galaxies

In spherical galaxies, binary supermassive black holes (SMBHs) have difficulty reaching sub-parsec separations due to depletion of stars on orbits that intersect the massive binary - the final-parsec problem. Galaxies that form via major mergers are substantially nonspherical, and it has been argued that the centrophilic orbits in triaxial galaxies might provide stars to the massive binary at a high enough rate to avoid stalling. Here we test that idea by carrying out fully self-consistent merger simulations of galaxies containing central SMBHs. We find hardening rates of the massive binaries that are indeed much higher than in spherical models, and essentially independent of the number of particles used in the simulations. Binary eccentricities remain high throughout the simulations. Our results constitute a fully stellar-dynamical solution to the final-parsec problem and imply a potentially high rate of events for low-frequency gravitational wave detectors like LISA.Comment: 9 pages, 11 figures. Accepted for publication in The Astrophysical Journa

Mergers of Unequal Mass Galaxies: Supermassive Black Hole Binary Evolution and Structure of Merger Remnants

Galaxy centers are residing places for Super Massive Black Holes (SMBHs). Galaxy mergers bring SMBHs close together to form gravitationally bound binary systems which, if able to coalesce in less than a Hubble time, would be one of the most promising sources of gravitational waves for the Laser Interferometer Space Antenna (LISA). In spherical galaxy models, SMBH binaries stall at a separation of approximately one parsec, leading to the "final parsec problem" (FPP). On the other hand, it has been shown that merger-induced triaxiality of the remnant in equal-mass mergers is capable of supporting a constant supply of stars on so-called centrophilic orbits that interact with the binary and thus avoid the FPP. In this paper, using a set of direct N-body simulations of mergers of initially spherically symmetric galaxies with different mass ratios, we show that the merger-induced triaxiality is able to drive unequal-mass SMBH binaries to coalescence. The binary hardening rates are high and depend only weakly on the mass ratios of SMBHs for a wide range of mass ratios q. The hardening rates are significantly higher for galaxies having steep cusps in comparison with those having shallow cups at centers. The evolution of the binary SMBH leads to relatively shallower inner slopes at the centers of the merger remnants. The stellar mass displaced by the SMBH binary on its way to coalescence is ~ 1-5 times the combined mass of binary SMBHs. The coalescence times for SMBH binary with mass ~ million solar masses are less than 1 Gyr and for those at the upper end of SMBH masses (~ billion solar masses) are 1-2 Gyr for less eccentric binaries whereas less than 1 Gyr for highly eccentric binaries. SMBH binaries are thus expected to be promising sources of gravitational waves at low and high redshifts.Comment: Accepted for publication in the Astrophysical Journal (ApJ). 14 pages, 8 figure