Retaining Black Holes with Very Large Recoil Velocities

Recent numerical simulations of binary black hole mergers show the possibility of producing very large recoil velocities (> 3000 km/s). Kicks of this magnitude should be sufficient to eject the final black hole from virtually any galactic potential. This result has been seen as a potential contradiction with observations of supermassive black holes residing in the centers of most galaxies in the local universe. Using an extremely simplified merger tree model, we show that, even in the limit of very large ejection probability, after a small number of merger generations there should still be an appreciable fraction (>50%) of galaxies with supermassive black holes today. We go on to argue that the inclusion of more realistic physics ingredients in the merger model should systematically increase this retention fraction, helping to resolve a potential conflict between theory and observation. Lastly, we develop a more realistic Monte Carlo model to confirm the qualitative arguments and estimate occupation fractions as a function of the central galactic velocity dispersion.Comment: 6 pages, 3 figures; Comments welcom

Electromagnetic Chirps from Neutron Star-Black Hole Mergers

We calculate the electromagnetic signal of a gamma-ray flare coming from the surface of a neutron star shortly before merger with a black hole companion. Using a new version of the Monte Carlo radiation transport code Pandurata that incorporates dynamic spacetimes, we integrate photon geodesics from the neutron star surface until they reach a distant observer or are captured by the black hole. The gamma-ray light curve is modulated by a number of relativistic effects, including Doppler beaming and gravitational lensing. Because the photons originate from the inspiraling neutron star, the light curve closely resembles the corresponding gravitational waveform: a chirp signal characterized by a steadily increasing frequency and amplitude. We propose to search for these electromagnetic chirps using matched filtering algorithms similar to those used in LIGO data analysis.Comment: 13 pages, 5 figures, submitted to Ap

Prompt Electromagnetic Transients from Binary Black Hole Mergers

Binary black hole (BBH) mergers provide a prime source for current and future interferometric GW observatories. Massive BBH mergers may often take place in plasma-rich environments, leading to the exciting possibility of a concurrent electromagnetic (EM) signal observable by traditional astronomical facilities. However, many critical questions about the generation of such counterparts remain unanswered. We explore mechanisms that may drive EM counterparts with magnetohydrodynamic simulations treating a range of scenarios involving equal-mass black-hole binaries immersed in an initially homogeneous fluid with uniform, orbitally aligned magnetic fields. We find that the time development of Poynting luminosity, which may drive jet-like emissions, is relatively insensitive to aspects of the initial configuration. In particular, over a significant range of initial values, the central magnetic field strength is effectively regulated by the gas flow to yield a Poynting luminosity of $10^{45}-10^{46} \rho_{-13} M_8^2 \, {\rm erg}\,{\rm s}^{-1}$, with BBH mass scaled to $M_8 \equiv M/(10^8 M_{\odot})$ and ambient density $\rho_{-13} \equiv \rho/(10^{-13} \, {\rm g} \, {\rm cm}^{-3})$. We also calculate the direct plasma synchrotron emissions processed through geodesic ray-tracing. Despite lensing effects and dynamics, we find the observed synchrotron flux varies little leading up to merger.Comment: 22 pages, 21 figures; additional reference + clarifying text added to match published versio

Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the ray-tracing calculations presented in Schnittman & Bertschinger (2004a): the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more detailed numerical calculations. Four primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, Poisson sampling of the detected photons, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.Comment: 30 pages, 5 figures, submitted to Ap

The Infrared Afterglow of Supermassive Black Hole Mergers

We model the spectra and light curves of circumbinary accretion disks during the time after the central black holes merge. The most immediate effect of this merger is the dissipation of energy in the outer regions of the disk due to the gravitational wave energy and linear momentum flux released at merger. This has the effect of perturbing the gas in the disk, which then radiates the dissipated energy over a cooling timescale, giving a characteristic infrared signal for tens of thousands of years when the total black hole mass is M~10^8 M_sun. On the basis of a simple cosmological merger model in which a typical supermassive black hole undergoes a few major mergers during its lifetime, we predict that ~10^4-10^5 of these IR sources should be observable today and discuss the possibility of identifying them with multi-wavelength surveys such as SWIRE/XMM-LSS/XBootes and COSMOS.Comment: v2: expanded discussion of optical depth calculations; ApJ in pres

Adjustment Method of S-λ Curves and Bezier Curves with 2 Shape Parameters

Fan和Zeng在[1]中提出了S-λ基函数和S-λ曲线的概念，并指出可以通过扰动生成函 数系数来对S-λ曲线形状进行调整。本文在此基础上进一步给出了当对生成函数单一系 数进行扰动时，扰动后的曲线与原曲线之间的相应关系以及两者到控制顶点的距离之 间的关系。对两类特殊控制多边形结构的三次Bezier曲线受到扰动后曲线变化情况做了 相应的分析，并给出了曲线变化的趋势。 另一方面，针对经典的Bezier曲线在控制顶点给定，曲线就唯一固定，缺乏进一步 调整曲线形状能力的这一状况，本文给出了一种带两个形状参数的Bezier曲线。这种带 形状参数的Bezier曲线保留了经典Bezier曲线的...In [1], Fan and Zeng introduced S-λ bases and S-λ curves, they also pointed out that we can adjust the shape of S-λ curves through disturbing the coefficients of generating function. In this paper, we do a further research on this method and give some conclusions about the relationships between the after-disturbing curve and the normal curve and the function of distance between the two curve and a...学位：理学硕士院系专业：数学科学学院_概率论与数理统计学号：1902010115250

Anatomy of the binary black hole recoil: A multipolar analysis

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.Comment: 28 pages, 20 figures, submitted to PRD; v2: minor revisions from referee repor

Anatomy of the binary black hole recoil: A multipolar analysis

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes

Self Organization and a Dynamical Transition in Traffic Flow Models

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.Comment: 6 pages, 4 figure

Twin-peak quasiperiodic oscillations as an internal resonance

Two inter-related peaks occur in high-frequency power spectra of X-ray lightcurves of several black-hole candidates. We further explore the idea that a non-linear resonance mechanism, operating in strong-gravity regime, is responsible for these quasi-periodic oscillations (QPOs). By extending the multiple-scales analysis of Rebusco, we construct two-dimensional phase-space sections, which enable us to identify different topologies governing the system and to follow evolutionary tracks of the twin peaks. This suggests that the original (Abramowicz and Kluzniak) parametric-resonance scheme can be viewed as an ingenuous account of the QPOs model with an internal resonance. We show an example of internal resonance in a system with up to two critical points, and we describe a general technique that permits to treat other cases in a systematical manner. A separatrix divides the phase-space sections into regions of different topology: inside the libration region the evolutionary tracks bring the observed twin-peak frequencies to an exact rational ratio, whereas in the circulation region the observed frequencies remain off resonance. Our scheme predicts the power should cyclically be exchanged between the two oscillations. Likewise the high-frequency QPOs in neutron-star binaries, also in black-hole sources one expects, as a general property of the non-linear model, that slight detuning pushes the twin-peak frequencies out of sharp resonance.Comment: Accepted for publication in A&A; 11 pages, 6 figure