Abstracts
Amaro-Seoane, Pau
The gravitational capture of compact objects by Kerr supermassive black holes - Video
| TBA |
Antonini, Fabio
Black hole mergers in nuclear star clusters - Video
| Massive stellar clusters are often found at the photometric and kinematic centers of galaxies. Such nuclear clusters are the densest stellar systems observed in the local universe, representing a natural environment where compact object binaries can dynamically form, harden and merge. I will discuss the dynamical processes that lead to the merger of black hole binaries in nuclear clusters in connection to the origin of the gravitational wave sources detected by Advanced LIGO. I will show that nuclear clusters can produce a significant population of black hole binaries that merge in the local universe, and that these binaries have clear differences in the statistical distributions of their properties (e.g., mass, eccentricity) when compared to those formed either in globular clusters or through isolated binary evolution. |
Berczik, Peter
Galaxy collision simulations with central Post Newtonian Supermassive Binary Black Holes - Video
| Generally accepted that one of the most strong sources of the long time ago predicted gravitational waves (GW) are a merging Supermassive Binary Black Holes (SMBBH). In our high order Post Newtonian (PN) N-body simulations we try to study this process with the maximum possible today numerical resolution. For the simulations we use the largest astrophysical Graphical Processing Unit (GPU) accelerated clusters, including the Piz Daint GPU supercomputer in Switzerland which hold the third place in the recent top500 list (November 2017). The central SMBBH are simulated as a special particles with the PN force corrections (up to 1/c**7 terms) implemented for the BH's gravitational interactions. We prove that the SMBBH merging time scale shows a quite strong dependency from the merging galaxies mass ratios. For some particular SMBBH observational galaxy pairs candidates we obtain from our simulations the upper time limits for final GW merging. |
Chavanis, Pierre-Henri
Kinetic theory of stellar systems - Video
| The collisional evolution of stellar systems is usually described by the Fokker-Planck equation introduced by Chandrasekhar, or by the Landau equation. These equations rely on a local approximation (as if the system were spatially homogeneous) and neglect collective effects (i.e. the dressing of the stars by their polarization cloud). In this talk, I will present a more general kinetic equation that takes into account spatial inhomogeneity through the use of angle-action variables (inhomogeneous Landau equation) and collective effects through a response matrix (inhomogeneous Lenard-Balescu equation). Previously introduced kinetic equations are recovered in particular limits. I will also make a short historical review of the development of kinetic theories in plasma physics, stellar dynamics, and two-dimensional hydrodynamics. |
Davies, Melvyn
The Ecology of the Galactic Center - Video
| I review the many processes at play in the very centers of galaxies in particular those which may produce the various exotic objects seen in the center of our own Galaxy. I consider how collisions between various different stellar species, star-disk interactions and the assembly history of the galactic center may play a role in explaining the flattened surface density profile of red giants within 0.4 pc or so of the supermassive black hole. Such studies may help us to understand the assembly history of the central cluster and the growth of the supermassive black hole. |
Do, Tuan
Observational Constraints on the Formation and Evolution of the Milky Nuclear Star Cluster - Video
| Due to its proximity, the Milky Way nuclear star cluster provides us with a wealth of data not available in other galactic nuclei. In particular, we can observe the properties of individual stars. These properties include the position in two dimension and the velocity in three dimensions. With the rapid advances integral field and multi-object spectroscopy, we can also derive the physical properties of individual stars, such as the effective temperature, abundances, and surface gravity. I will discuss how the pass decade of adaptive optics measurements from HST, Keck, and Gemini have been used to derive physical properties of the cluster. While these analyses have been very successful at helping us understand its structure and star formation, there is still enormous untapped potential in these data sets. I will discuss new work on the physical properties of the stars, such as their metallicity, and how they will help us understand the origin and evolution of the nuclear star cluster. |
Dosopoulou, Fani
Dynamical friction and the evolution of Supermassive Black hole Binaries: the final hundred-parsec problem - Video
| Dynamical friction is a fundamental process in astrophysics and its understanding is arguably the most important contribution of Chandrasekhar to stellar dynamics. In this talk I will discuss the results of analytical models and N-body simulations that describe the evolution of a massive black hole binary due to dynamical friction. I will show that the standard Chandrasekhar's theory leads to erroneous conclusions about the evolution of the massive binary because the usual simplifying assumptions that lead to neglect the contribution of stars with large velocities appear to break down. I will discuss the implications of our results for a number of observational puzzles, which include the presence of multiple nuclei in bright ellipticals, off-center AGNs and eccentric nuclear disks. |
Eckart, Andreas
Investigating the relativistic motion of the stars near the supermassive black hole in the galactic center - Video
| The S-star cluster in the Galactic center allows us to study the physics close to a supermassive black hole including distinctive dynamical tests of general relativity. Our best estimates for the mass of and the distance to Sgr A* using the three shortest period stars (S2, S38, and S55/S0-102) and Newtonian models are MBH = 4.15 ± 0.13 ± 0.57 × 10^6 Mo and Ro = 8.19 ± 0.11 ± 0.34 kpc. Additionally, we aim at a new and practical method to investigate the relativistic orbits of stars in the gravitational field near Sgr A*. We use a first-order post-Newtonian approximation to calculate the stellar orbits with a broad range of periapse distance rp . We present a method that employs the changes of orbital elements derived from elliptical fits to different sections of the orbit. These changes are correlated with the relativistic parameter defined as Υ ≡ rs /rp (with rs being the Schwarzschild radius) and can be used to derive Υ from observational data. For S2 we find a value of Υ = 0.00088 ± 0.00080 which is within the uncertainty consistent with the expected value of Υ = 0.00065 derived from MBH and the orbit of S2. We argue that the derived quantity is unlikely to be dominated by perturbing influences like noise on the derived stellar positions, field rotation, and black hole mass drifts. Accepting this result, S2 would be the first star on a spatially resolved orbit around a supermassive black hole for which a post-Newtonian effect has been measured. |
Eisenhauer, Frank
GRAVITY in the Galactic Center
| The GRAVITY interferometer will have finished its first semester of Galactic Center observations by the time of the workshop. With its unprecedented angular resolution and astrometric precision, GRAVITY allows the direct observations of the stellar dynamics at work in the very center of our Galaxy. We give an overview on what we already know from the past adaptive optics and integral field spectroscopy observations, present the results from the first GRAVITY observations, and give an outlook on which novel dynamic aspects we can address in the next years with a longer astrometric timeline. |
Ghez, Andrea
Review - Our Galactic Center: A Unique Laboratory for the Physics & Astrophysics of Black Holes - Video
| The proximity of our Galaxy's center presents a unique opportunity to study a galactic nucleus with orders of magnitude higher spatial resolution than can be brought to bear on any other galaxy. After more than a decade of diffraction-limited imaging on large ground-based telescopes, the case for a supermassive black hole at the Galactic center has gone from a possibility to a certainty, thanks to measurements of individual stellar orbits. The rapidity with which these stars move on small-scale orbits indicates a source of tremendous gravity and provides the best evidence that supermassive black holes, which confront and challenge our knowledge of fundamental physics, do exist in the Universe. This work was made possible through the use of speckle imaging techniques, which corrects for the blurring effects of the earth's atmosphere in post-processing and allowed the first diffraction-limited images to be produced with these large ground-based telescopes. Further progress in high-angular resolution imaging techniques on large, ground- based telescopes has resulted the more sophisticated technology of adaptive optics, which corrects for these effects in real time. This has increased the power of imaging by an order of magnitude and permitted spectroscopic study at high resolution on these telescopes for the first time. With adaptive optics, high resolution studies of the Galactic center have shown that what happens near a supermassive back hole is quite different than what theoretical models have predicted, which changes many of our notions on how galaxies form and evolve over time. By continuing to push on the cutting-edge of high-resolution technology, we will be able to capture the orbital motions of stars with sufficient precision to test Einstein’s General theory of Relativity as well as theories of galaxy formation and evolution - all in regimes that have never been probed before. |
Gillessen, Stefan
An Update on Monitoring Stellar Orbits in the Galactic Center - Video
| Using 25 years of data from uninterrupted monitoring of stellar orbits in the Galactic Center, we present an update of the main results from this unique data set: a measurement of mass and distance to Sgr A*. Our progress is not only due to the eight-year increase in time base, but also to the improved definition of the coordinate system. The star S2 continues to yield the best constraints on the mass of and distance to Sgr A* the statistical errors of 0.13×10^6 M_sun and 0.12 kpc have halved compared to the previous study. The S2 orbit fit is robust and does not need any prior information. Using coordinate system priors, the star S1 also yields tight constraints on mass and distance. For a combined orbit fit, we use 17 stars, which yields our current best estimates for mass and distance: M=4.28+/-0.10{stat.}+/-0.21{sys}×10^6 M_sun and R0=8.32+/-0.07{stat.}+/-0.14{sys} kpc. These numbers are in agreement with the recent determination of R0 from the statistical cluster parallax. The positions of the mass, of the near-infrared flares from Sgr A*, and of the radio source Sgr A* agree to within 1 mas. In total, we have determined orbits for 40 stars so far, a sample which consists of 32 stars with randomly oriented orbits and a thermal eccentricity distribution, plus eight stars that we can explicitly show are members of the clockwise disk of young stars, and which have lower-eccentricity orbits. |
Kocsis, Bence
Review - Gravitational Wave Sources in Galactic Nuclei - Video
| With the detections of the gravitational waves emitted during black hole and neutron star mergers, LIGO has recently opened the field of gravitational wave astrophysics. In this talk I will review some of the astrophysical processes that may be responsible for the observed events. Although less than 0.5% of the stellar mass is in dense stellar systems, I will argue that a large fraction of the black hole mergers may originate in these environments. In particular, I will review black hole mergers in galactic nuclei, including gravitational wave capture events, LIGO mergers driven by the central supermassive black holes, and those which are accelerated by gaseous disks. The event rate distribution may be used to understand the astrophysical origin of the observed gravitational wave events. I will argue that the eccentricity, mass, and spin distributions may be key to discriminate different processes that lead to black hole mergers. |
Leigh, Nathan
On the Rate of Black Hole Binary Mergers in Galactic Nuclei due to Dynamical Hardening - Video
| We consider the dynamical hardening of stellar-mass black hole binaries (BHBs) in galactic nuclei due to direct three-body scattering interactions. This is to assess the contribution of dynamical hardening to the rate of BHB mergers in galactic nuclei. We present an analytic model for the single-binary encounter rate in a two- component (spherical and disk) nucleus hosting a super-massive black hole (SMBH). We derive an equation for the total number of encounters NGW needed to harden a BHB to the point that the timescale for inspiral due to gravitational wave (GW) emission is shorter than the time for a subsequent three-body scattering event. This is done independently for both the spherical and disk components. Using a Monte Carlo approach, we refine our calculations for NGW to include GW emission between scattering events. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low velocity dispersions and no significant Keplerian component; and (2) migration traps in disks around SMBHs but lacking any significant spherical stellar component in the vicinity of the migration trap. We find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion v/σ in galactic nuclei and the rate of BHB mergers (∼ (v/σ)0.2), where the ratio v/σ is a proxy for the ratio between the rotation- and dispersion-supported components. In the limit of no spherical component, disks are efficient locations for BHB hardening, and could contribute significantly to the rate of BHB mergers detected by aLIGO. |
Levin, Yuri
Secular dynamics and systematic eccentricity changes of inspiraling IMBHs - Video
| Most theories for dynamical friction are derived using second-order perturbation theory. I will instead focus on the regime, explored in Madigan & Levin 2012, where IMBH experiences strong secular-dynamical encounters with the stars in the cusp. I will describe imprecise, qualitative arguments for how the eccentricity of an inspiraling IMBH ought to change in this case, and show evidence from numerical experiments in support of these arguments. |
Li, Gongjie
Implications of the eccentric Kozai-Lidov mechanism for stars surrounding supermassive black hole binaries - Video
| An enhanced rate of stellar tidal disruption events (TDEs) may be an important characteristic of supermassive black hole (SMBH) binaries at close separations. I will discuss the evolution of the distribution of stars around an SMBH binary due to the eccentric Kozai-Lidov (EKL) mechanism, including octupole effects and apsidal precession caused by the stellar mass distribution and general relativity. We identified a region around one of the SMBHs in the binary where the EKL mechanism drives stars to high eccentricities, which ultimately causes the stars to either scatter off the second SMBH or get disrupted. For SMBH masses 10^7 and 10^8 M⊙, the TDE rate can reach ~10^-2 yr-1 and deplete a region of the stellar cusp around the secondary SMBH in ~0.5 Myr. As a result, the final geometry of the stellar distribution between 0.01 and 0.1 pc around the secondary SMBH is a torus. These effects may be even more prominent in nuclear stellar clusters hosting a supermassive and an intermediate mass black hole. |
Lin, Doug
Seed binary black hole production and coalescence in disks around AGN's - Video
| During the active phase of galactic nuclei, a fraction of nearby field stars are trapped into disks around massive black holes. They accrete gas, evolve into massive stars analogous to the young stellar population around the Galactic Center, and undergo supernova explosion which enriches the disk gas. Their black hole byproducts gain mass, capture companions, undergo binary contraction, coalescence, and radiate gravitational waves with occurrence rates consistent with the observed LIGO events. |
Luetzgendorf, Nora
Stellar winds near massive black holes: The case of the S-stars - Video
| The Galactic center provides a unique laboratory to study the interaction of a super- massive black hole (SMBH) with its gaseous and stellar environment. Simulations to determine the accretion of stellar winds from the surrounding O-stars onto the black hole have been performed earlier, but in those the presence of the S-star system was ignored. The S-stars are a group of young massive B-stars in relatively close orbits around the black hole. Here we simulate those stars in order to study their contribution to the accretion rate, without taking the more distant and massive O-stars into account. We use the Astrophysical Multi-purpose Software Environment (AMUSE) to combine gravitational physics, stellar evolution and hydrodynamics in a single simulation of the S-stars orbiting the supermassive black hole, and use this framework to determine the amount of gas that is accreted onto the black hole. |
Madigan, Ann-Marie
Tidal disruption events from eccentric nuclear disks - Video
| Eccentric nuclear disks, like the one in the Andromeda galaxy, are made up of stars on apsidally-aligned eccentric orbits. In this talk I will show how secular gravitational torques between the orbits not only maintains the stability of the nucleus but dramatically enhances the rates of tidal disruption events. As eccentric nuclear disks form during gas-rich major mergers, this can explain the preference for TDEs in recent- and post-merger galaxies. |
Magorrian, John
Modelling the eccentric disc of M31 - Video
| The innermost few parsecs of M31 are dominated by a double nucleus, which is most naturally explained by Tremaine's (1995) model of an eccentric disc of old stars around a supermassive black hole. A more recent surprise is the discovery of a very compact cluster of young stars around the black hole. I describe ongoing work on the construction of a coherent picture of this system, with particular emphasis on constraining the stellar phase-space density. |
Naoz, Smadar
Binary dynamics within galactic nuclei - Video
| Nuclear star clusters around massive black holes are likely the most collisional stellar systems in the Universe and are also embedded in extremely deep gravitational potential wells. Consequently, unique stellar dynamical processes and interactions are expected to take place. For example collisions and mergers between stars and compact objects, are likely to happen in this environment. I will explore these collisions and mergers and their product and will connect between them and some of the observed puzzles in galactic nuclei in general and our own Galactic Center in particular. For example, I’ll draw a connection between those merger products and (1) the perplexing population of young stars that are isotropically distributed (S-stars) in a region that is hostile to star formation, (2) the new class of cold stars in this same region that are two orders of magnitude larger than typical stars (e.g., the “gas-like cloud” G2), (3) stellar black hole-black hole binaries and LIGO sources. |
Ostriker, Jeremiah
Tidal Capture Runaway and the Formation of Seed Massive Black Holes - Video
| The physical processes leading to the development of massive black holes at the centers of normal galaxies remain uncertain despite much ingenious effort. Clues include the rough proportionality between the BH mass and the mass in the spheroidal component of the galaxy, with indications of a falloff from that proportionality for BHs less than ~ 10^5 M_sun. Nuclear star clusters (NSCs) provide a quite specific environment conducive to appropriate dynamical processes. One such process is tidal capture (which has a cross-section larger than other processes) whereby a stellar mass BH can capture a normal low mass star (m*) into a tight orbit leading to accretion of the captured star and growth of the BH. In a paper with Nicholas Stone and Andreas Kupper, it is shown that given the observed properties of NSCs a runaway can easily occur when the velocity dispersion of the NSC exceeds ~ 40 km/s leading to BH masses - MBH ~ σ^(3/2) \sqrt(m*t/G) ~ 10^(6.4) M_sun (σ/50km/s)^(3/2) (t/10^10 yrs)^(1/2). This mechanism, based on standard dynamical processes occurring in systems with observationally appropriate parameters, predicts the BH stellar mass relation in good accord with current data provided the NSCs form at an early enough epoch. |
Panamarev, Taras
Direct Million-body Simulation of the Galactic Center - Video
| We study the dynamics and evolution of nuclear star cluster of the Milky Way galaxy performing direct N-body simulations. We focus on interaction of the stellar system with the supermassive black hole. We obtain stellar density profiles for different stellar species, rate of tidal disruption events and detection of gravitational waves emitted by accretion of compact objects onto the central black hole. We discuss possible presence of millisecond pulsars in the galactic center. |
Pichon, Christophe
Review - Kinetic Theory in Galactic Centers - Video
| I will review the formalism allowing for the description of the long-term evolution of a large set of particles orbiting a dominant massive object, such as in galactic nuclei. Because stars move in the quasi-Keplerian potential induced by the central black hole, their orbits can be approximated by ellipses whose orientations remain fixed over many dynamical times. Yet, on secular timescales, such a system will undergo a slow collisional relaxation driven by the remaining fluctuations in the system. When these fluctuations originate from the system intrinsic graininess (finite-N effects), the associated (scalar) resonant relaxation is captured by the (degenerate) inhomogeneous Balescu-Lenard equation. I will review in detail this kinetic formalism and emphasise the key physical mechanisms at play in this context. I will show in particular how one can account for the system's inhomogeneity (intricate trajectories), as well as the system's ability to amplify perturbations (self-gravity). I will finally show how such methods may be used to study the self-induced resonant relaxation of a discrete self-gravitating razor-thin axisymmetric disc orbiting a massive black hole, to recover for example the quenching of resonant diffusion in the vicinity of the black hole due to the divergence of the relativistic precessions. |
Polyachenko, Evgeny
Radial orbit and loss cone instabilities in spherical systems - Video
| Spherical stellar systems are considered to enjoy a certain degree of stability preventing them from forming structures like triaxial ellipsoids. However, a number of collective effects force them to evolve unexpectedly, in conflict with the standard relaxation based on star-star encounters. For example, there are instabilities leading to the quadrupole asymmetry of the density distribution both in radially and tangentially anisotropic systems. In my talk, I shall review our latest results of theoretical and numerical studies of the instabilities. |
Portegies Zwart, Simon
Ergodicity in Chaotic Self-Gravitating Systems - Video
| Numerical solutions to Newton's equations of motion for self-gravitating systems are commonly assumed to be irreversible due to the exponential growth of the errors introduced by the integration scheme and the numerical round-off in the least significant figure. This secular monotonic growth of error is then attributed to the increase in microscopic entropy of the system, even though Newton's equations of motion are strictly speaking time reversible. I will demonstrate how microscopic reversibility of numerical solutions is retrieved when numerical errors are reduced below the exponential growth of the non-linear response, and discuss the need for time reversible simulation of chaotic system to validate the common practice in which families of solutions are assumed to lead to the correct ensemble average. |
Rossi, Elena Maria
Hypervelocity stars in the GAIA era - Video
| In this talk I will review my group efforts to find hypervelocity stars in the Gaia catalogue with machine learning algorithms and model them to simultaneously constrain the Galactic Potential and the Galactic centre stellar population. |
Sari, Re'em
Dynamics in the galactic center - the effect of binaries - Video
| Binary stars dissolving in the tidal field of a super massive black hole are thought to produce hyper velocity stars. We show that the bound members of the dissolved binaries play a role in setting the stellar cusp around the central black hole. We use analytical arguments to show that this process (a) steepens the cusp, from rho~r^(-7/4) to rho~r^(-9/4) and (b) increases the rate of EMRIs as compared to that of TDEs. We show analytically that without binaries EMRIs are less frequent than TDEs by the square of the ratio of the tidal radius to the Schwarzschild radius (about 1% in our galaxy), while dissolving binaries could render EMRIs to be almost as frequent as TDEs. |
Schödel, Rainer
The stellar cusp around the Milky Way’s central black hole - Video
| The existence of stellar cusps in Milky-Way-like galaxies plays a key role in understanding stellar dynamics in such systems and in predicting the potential rates of observable events such as tidal disruptions or EMRIs. However, the existence of such a cusp around Sagittarius A* at the Galactic Center has been disputed. In my talk I will revisit the most recent evidence, discuss the observational problems and biases and argue that such a cusp does indeed exist around Sagittarius A*. |
Sesana, Alberto
Dynamics of massive black hole triplets: promising sources for LISA and pulsar timing - Video
| I will describe a large suite of numerical simulation of massive black hole (MBH) triplets forming by subsequent galaxy mergers. We model the evolution of triple systems including an external galactic potential, dynamical friction, stellar hardening, and post Newtonian dynamics. Triple interactions are a promising way of merging stalled MBH binaries and guarantees a minimal number of sources for LISA and pulsar timing, should any other dynamical process driving the binaries fail. I will discuss the implications for observations of MBHs with LISA and pulsar timing arrays. |
Stone, Nicholas
Tidal Disruption Event Rates: Diagnostics of Stellar Dynamics Inside the Sphere of Influence - Video
| In recent years, dozens of powerful, multiwavelength transients have been seen from the photometric centers of inactive galactic nuclei. There is a growing consensus that this class of flares are due to tidal disruption events (TDEs), the accretion-powered death throes of stars that have been torn apart by supermassive black holes (SMBHs). I will discuss two interesting puzzles that have emerged from our current sample of TDEs. First, most observational estimates of the per-galaxy TDE rate are about an order of magnitude lower than even conservative theoretical rate predictions due to two-body relaxation. I will present theoretical (but empirically-calibrated) rates of tidal disruption, and argue that the resolution of this discrepancy is a broad TDE luminosity function. Second, observed TDEs occur preferentially in extremely rare post-starburst galaxies. I will present my recent observational and theoretical work to understand this post-starburst preference, which may be due to unusually dense central star clusters, radially anisotropic orbits, or (more speculatively) unresolved SMBH binaries. |
Touma, Jihad
Review - Whither Resonant Relaxation? - Video
| Two decades separate the foundational work on resonant relaxation (Rauch and Tremaine, NewA, 1996) from the first fundamental treatment of the process as it applies to stellar black hole nuclei (Sridhar and Touma, MNRAS, 2016-17). The resulting formalism provides practitioners in the field, ourselves included, with the requisite rigorous tools to address model problems which have hitherto been the subject of ad hoc and/or numerically expensive games. Through it, we learn that resonant relaxation is driven by apsidal and nodal resonances and that, in general, there is no real separation between `scalar’ and `vector’ resonant relaxation. While there is currently much to be resonantly excited about, it is also true that, in the intervening years, we learned enough about the dynamical (and observational) complexity of our systems to temper excitement about idealized equilibrium models (be they thermal or not). In this talk, I will provide an eccentric, and largely animated, overview of the rich topography over which the kinetics of galactic nuclei plays out. |
Varri, Anna Lisa
Equilibrium and stability of differentially rotating stellar systems - Video
| The analysis of the stability properties of self-gravitating, uniformly rotating equilibria is a classical fluid dynamics problem with a distinguished history, yet the stability of differentially rotating spheroidal stellar systems have rarely been explored, especially in terms of a full phase space description, and the connection with the corresponding fluid systems is only partially understood. I will investigate the emergence of such dynamical instabilities in spherical and axisymmetric differentially rotating equilibria, with emphasis on some tantalizing analogies with instabilities recently observed in 'low T/|W|' differentially rotating fluid polytropes. Such an analysis has the potential to enrich our fundamental understanding of the role of angular momentum in the dynamics of both collisional and collisionless stellar systems, and the implications for galactic nuclei, which are often characterized by a significant degree of differential rotation, will be discussed. |
Volonteri, Marta
Review - Supermassive BHs Mergers - Video
| Massive black holes inhabit the center of many galaxies, from the local Universe to high redshift. Over the cosmic evolution of structures, galaxy mergers imply massive black hole mergers. The physics governing the formation of a binary of massive black holes, and its subsequent merger, is however very complex, bridging a range of physical scales and processes. I will review the phases of massive black hole dynamical evolution during galaxy mergers, identifying the expected bottlenecks, and embed them in the cosmological context. Do black holes merge as often as galaxies do? |
Will, Clifford
Hierarchical triple systems: Effects of higher multipoles and general relativity - Video
| We analyze the secular evolution of hierarchical triple systems with the Newtonian third-body perturbation expanded to hexadecapole order. We also include the leading orbital effects of post-Newtonian theory, namely the pericenter precessions of the inner and outer orbits. Using the Lagrange planetary equations for the orbit elements of both binaries, we average over orbital timescales, obtain the equations for the secular evolution of the elements through hexadecapole order, and employ them to analyze cases of astrophysical interest. We find that, for the most part, orbital flips found at octupole order are robust against both relativistic and hexadecapole perturbations. We show that, for equal-mass inner binaries, where the octupole terms vanish, the hexadecapole contributions can alone generate orbital flips and excursions to very large eccentricities. |