Gravitational waves from coalescing massive black holes in young dense clusters

HST observations reveal that young massive star clusters form in gas-rich environments like the Antenn{\ae} galaxy which will merge in collisional processes to form larger structures. These clusters amalgamate and if some of these clusters harbour a massive black hole in their centres, they can become a strong source of gravitational waves when they coalesce. In order to understand the dynamical processes that are into play in such a scenario, one has to carefully study the evolution of the merger of two of such young massive star clusters and more specifically their respective massive black holes. This will be a promising source of gravitational waves for both, LISA and the proposed Big Bang Observer (BBO), whose first purpose is to search for an inflation-generated gravitational waves background in the frequency range of $10^{-1}-1$ Hz. We used high-resolution direct summation $N-$body simulations to study the orbital evolution of two colliding globular clusters with different initial conditions. Even if the final eccentricity is almost negligible when entering the bandwidth, it will suffice to provide us with detailed information about these astrophysical events

Intermediate-mass black holes in colliding clusters: Implications for lower-frequency gravitational-wave astronomy

Observations suggest that star clusters often form in binaries or larger bound groups. Therefore, mergers between two clusters are likely to occur. If these clusters both harbor an intermediate-mass black hole (IMBH; 10^{2-4} Msun) in their center, they can become a strong source of gravitational waves when the black holes merge with each other. In order to understand the dynamical processes that operate in such a scenario, one has to study the evolution of the merger of two such young massive star clusters, and more specifically, their respective IMBHs. We employ the direct-summation Nbody4 numerical tool on special-purpose GRAPE6 hardware to simulate a merger of two stellar clusters each containing 63,000 particles and a central IMBH. This allows us to study accurately the orbital evolution of the colliding clusters and the embedded massive black holes. Within ~7 Myr the clusters have merged and the IMBHs constitute a hard binary. The final coalescence happens in ~10^8 yrs. The implication of our analysis is that intermediate-mass black holes merging as the result of coalescence of young dense clusters could provide a source for the Laser Interferometer Space Antenna (LISA) space-based gravitational wave detector mission. We find that interactions with stars increase the eccentricity of the IMBH binary to about 0.8. Although the binary later circularizes by emission of gravitational waves, the residual eccentricity can be detectable through its influence on the phase of the waves if the last few years of inspiral are observed

Sagittarius A* Rivaled the Sun in the Ancient X-ray Sky

Sagittarius A*, lying the Galactic Center $8$ kpc from Earth, hosts the closest supermassive black hole known to us. It is now inactive, but there are evidences indicating that about six million years ago it underwent a powerful outburst where the luminosity could have approached the Eddington limit. Motivated by the fact that in extragalaxies the supermassive black holes with similar masses and near-Eddington luminosities are usually strong X-ray emitters, we calculate here the X-ray luminosity of Sagittarius A*, assuming that the outburst was due to accretion of gas or tidal disruption of stars, both scenarios having been considered to trigger the previous outburst. We show that in both cases Sagittarius A* could precipitate on Earth an X-ray ($h\nu>2$ keV) irradiance comparable to that from the current quiescent sun. The irradiance in harder energy band $20~{\rm keV}<h\nu<100~{\rm keV}$, however, surpasses that from an X-class solar flare, and the irradiation timescale is also much longer, ranging from weeks to $10^5$ years depending on the outburst scenario. This level of radiation would disturb the ozone and ionosphere around the ancient earth, and affect the abundance of organic molecules in dense interstellar environments around the solar neighbourhood, but these prospects have not been adequately explored so far. Our results indicate that the activity of supermassive black hole and the origin and evolution of life may be more closely linked than previously has been thought

Relativistic encounters in dense stellar systems

Two coalescing black holes (BHs) represent a conspicuous source of gravitational waves (GWs). The merger involves 17 parameters in the general case of Kerr BHs, so that a successful identification and parameter extraction of the information encoded in the waves will provide us with a detailed description of the physics of BHs. A search based on matched-filtering for characterization and parameter extraction requires the development of some $10^{15}$ waveforms. If a third additional BH perturbed the system, the waveforms would not be applicable, and we would need to increase the number of templates required for a valid detection. In this letter, we calculate the probability that more than two BHs interact in the regime of strong relativity in a dense stellar cluster. We determine the physical properties necessary in a stellar system for three black holes to have a close encounter in this regime and also for an existing binary of two BHs to have a strong interaction with a third hole. In both cases the event rate is negligible. While dense stellar systems such as galactic nuclei, globular clusters and nuclear stellar clusters are the breeding grounds for the sources of gravitational waves that ground-based detectors like Advanced LIGO and Advanced VIRGO will be exploring, the analysis of the waveforms in full general relativity needs only to evaluate the two-body problem. This reduces the number of templates of waveforms to create by orders of magnitude

GraviDy, a GPU modular, parallel direct-summation N-body integrator: Dynamics with softening

A wide variety of outstanding problems in astrophysics involve the motion of a large number of particles ($N\gtrsim 10^{6}$) under the force of gravity. These include the global evolution of globular clusters, tidal disruptions of stars by a massive black hole, the formation of protoplanets and the detection of sources of gravitational radiation. The direct-summation of $N$ gravitational forces is a complex problem with no analytical solution and can only be tackled with approximations and numerical methods. To this end, the Hermite scheme is a widely used integration method. With different numerical techniques and special-purpose hardware, it can be used to speed up the calculations. But these methods tend to be computationally slow and cumbersome to work with. Here we present a new GPU, direct-summation $N-$body integrator written from scratch and based on this scheme. This code has high modularity, allowing users to readily introduce new physics, it exploits available high-performance computing resources and will be maintained by public, regular updates. The code can be used in parallel on multiple CPUs and GPUs, with a considerable speed-up benefit. The single GPU version runs about 200 times faster compared to the single CPU version. A test run using 4 GPUs in parallel shows a speed up factor of about 3 as compared to the single GPU version. The conception and design of this first release is aimed at users with access to traditional parallel CPU clusters or computational nodes with one or a few GPU cards

Hybrid methods in planetesimal dynamics (I) : Description of a new composite algorithm

The formation and evolution of protoplanetary systems, the breeding grounds of planet formation, is a complex dynamical problem that involves many orders of magnitudes. To serve this purpose, we present a new hybrid algorithm that combines a Fokker-Planck approach with the advantages of a pure direct-summation N-body scheme, with a very accurate integration of close encounters for the orbital evolution of the larger bodies with a statistical model, envisaged to simulate the very large number of smaller planetesimals in the disc. Direct-summation techniques have been historically developped for the study of dense stellar systems such as open and globular clusters and, within some limits imposed by the number of stars, of galactic nuclei. The number of modifications to adapt direct-summation N-body techniques to planetary dynamics is not undemanding and requires modifications. These include the way close encounters are treated, as well as the selection process for the "neighbour radius" of the particles and the extended Hermite scheme, used for the very first time in this work, as well as the implementation of a central potential, drag forces and the adjustment of the regularisation treatment. For the statistical description of the planetesimal disc we employ a Fokker-Planck approach. We include dynamical friction, high- and low-speed encounters, the role of distant encounters as well as gas and collisional damping and then generalise the model to inhomogenous discs. We then describe the combination of the two techniques to address the whole problem of planetesimal dynamics in a realistic way via a transition mass to integrate the evolution of the particles according to their masses

Blocking low-eccentricity EMRIs: A statistical direct-summation N-body study of the Schwarzschild barrier

The capture of a compact object in a galactic nucleus by a massive black hole (MBH), an extreme-mass ratio inspiral (EMRI), is the best way to map space and time around it. Recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on low-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called "Schwarzschild barrier" is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower-eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a statistical sample of 2,500 direct-summation N-body simulations using both a post-Newtonian and also for the first time in a direct-summation code a geodesic approximation for the relativistic orbits. The existence of the barrier prevents low-eccentricity EMRIs from approaching the central MBH, but high-eccentricity EMRIs, which have been wrongly classified as "direct plunges" until recently, ignore the presence of the barrier, because they are driven by two-body relaxation. Hence, since the rates are significantly affected in the case of low-eccentricity EMRIs, we predict that a LISA-like observatory such as eLISA will predominantly detect high-eccentricity EMRIs

Fake plunges are very eccentric real EMRIs in disguise ... they dominate the rates and are blissfully ignorant of angular momentum barriers

The capture of a compact object in a galactic nucleus by a massive black hole (MBH) is the best way to map space and time around it. Compact objects such as stellar black holes on a capture orbit with a very high eccentricity have been wrongly assumed to be lost for the system after an intense burst of radiation, which has been described as a "direct plunge". We prove that these very eccentric capture orbits spend actually a similar number of cycles in a LISA-like detector as those with lower eccentricities if the central MBH is spinning. Although the rates are higher for high-eccentricity EMRIs, the spin also enhances the rates of lower-eccentricity EMRIs. This last kind have received more attention because of the fact that high-eccentricity EMRIs were thought to be direct plunges and thus negligible. On the other hand, recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on these lower-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called "Schwarzschild barrier" is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower-eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a statitical sample of 2,500 direct-summation N-body simulations using both a post-Newtonian but also, and for the first time, a geodesic approximation for the relativistic orbits. The existence of the barrier prevents "traditional EMRIs" from approaching the central MBH, but if the central MBH is spinning the rate will be anyway dominated by highly-eccentric extreme-mass ratio inspirals, which insolently ignore the presence of the barrier, because they are driven by two-body relaxation