by Shcherbakov, Roman V. and Penna, Robert F. and McKinney, Jonathan C.
17 pages, 13 figures, submitted to ApJ

The constraints on Sgr A* black hole (BH) and accretion flow parameters are found by fitting polarized sub-mm observations. The observations from 29 papers are averaged into a quasi-quiescent set. We run three-dimensional general relativistic magnetohydrodynamical (3D GRMHD) simulations for dimensionless spins a=0,0.5,0.7,0.9,0.98 till 20000M, construct an averaged dynamical model, perform GR polarized radiative transfer, and explore the parameter space of spin $latex a$, inclination angle \theta, position angle (PA), accretion rate \dot{M}, and electron temperature $latex T_e$ at 6M radius. The best-fitting model for spin a=0.9 gives \chi^2=0.99 with \theta=59deg, \dot{M}=1.3*10^{-8}M_sun/year, T_e=3.2*10^{10}K at 6M, the best-fitting model for spin a=0.5 gives \chi^2=0.84 with \theta=70deg, \dot{M}=7.0*10^{-8}M_sun/year, and T_p/T_e=22 at 6M with T_e=3.50*10^{10}K. We identify the physical phenomena leading to the matched linear polarization (LP), circular polarization (CP), and electric vector position angle (EVPA). Our statistical analysis reveals the most probable spin is a=0.9. The spin a=0.5 solutions are 10 times less probable despite giving lower minimum \chi^2 and spin a=0 is excluded as having probability P(a)<1%. Polarized data allows us to tightly constrain some quantities. Inclination angle, electron temperature, and position angle have ranges \theta=59+/-9deg, T_e=(3.4+1.2/-0.9)*10^{10}K, and PA=96+/-30deg with 90% confidence. The total range of accretion rate is large, but assuming spin a=0.9 we get \dot{M}(0.9)=(13+4/-3)*10^{-9}M_sun/year interval with 90% confidence. The emission region sizes at 230GHz of the best-fitting models are found to be marginally consistent with the observed by VLBI technique.

by Hannam, Mark and Husa, Sascha and Ohme, Frank and Mueller, Doreen and Bruegmann, Bernd
20 pages, 9 figures, 6 tables

We present gravitational waveforms for the last orbits and merger of black-hole-binary (BBH) systems along two branches of the BBH parameter space: equal-mass binaries with equal non-precessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein’s equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each BH is $latex \chi_i = S_i/M_i^2 \in [-0.85,0.85]$, and along the unequal-mass branch the mass ratio is $latex q =M_2/M_1 \in [1,4]$. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged BH, and compare the last 8-10 GW cycles up to $latex M\omega = 0.1$ with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins $latex \chi_i > -0.75$. When high-order amplitude corrections are included, the PN amplitude of the $latex (\ell=2,m=\pm2)$ modes is larger than the NR amplitude by between 2-4%.

by Galley, Chad R. and Herrmann, Frank and Silberholz, John and Tiglio, Manuel and Guerberoff, Gustavo

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.

by Porto, Rafael A.
25 pages, 4 figures, revtex4

Using effective field theory (EFT) techniques we calculate the next-to-leading order (NLO) spin-orbit contributions to the gravitational potential of inspiralling compact binaries. We use the covariant spin supplementarity condition (SSC), and explicitly prove the equivalence with previous results by Faye et al. in arXiv:gr-qc/0605139. We also show that the direct application of the Newton-Wigner SSC at the level of the action leads to the correct dynamics using a canonical (Dirac) algebra. This paper then completes the calculation of the necessary spin dynamics within the EFT formalism that will be used in a separate paper to compute the spin contributions to the energy flux and phase evolution to NLO.

by Hergt, Steven and Steinhoff, Jan and Schaefer, Gerhard
11 pages, submitted to CQG

Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein’s field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made.

by Lubich, Christian and Walther, Benny and Bruegmann, Bernd
9 pages, 6 figures

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In the context of the splitting, it is possible to integrate the individual terms of the spin-orbit and spin-spin Hamiltonians analytically, exploiting the special structure of the underlying equations of motion. The outcome is a symplectic, time-reversible integrator, which can be raised to arbitrary order by composition. A fourth-order version is shown to give excellent behavior concerning error growth and conservation of energy and angular momentum in long-term simulations. Favorable properties of the integrator are retained in the presence of weak dissipative forces due to radiation damping in the full post-Newtonian equations.

by Rothe, Tilman J. and Schäfer, Gerhard
18 pages, no figures

The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are in accordance with the relation between the total linear momentum and the center-of-mass velocity as demanded by global Lorentz invariance. The various generating functions for the center-of-mass and rest-frame canonical variables are explicitly given in terms of the single-particle canonical variables. The no-interaction theorem does not apply because the world-line condition of Lorentz covariant position variables is not imposed.

by Volonteri, Marta
10 pages. To appear in the proceedings of the conference “Accretion and ejection in AGN: a global view” (Como, 22-26 June 2009)

Black hole spins affect the efficiency of the “classical” accretion processes, hence the radiative output from quasars. Spins also determine how much energy is extractable from the hole itself. Recently it became clear that massive black hole spins also affect the retention of black holes in galaxies, be cause of the impulsive “gravitational recoil”, up to thousands km/s, due to anisotropic emission of gravitational waves at merger. I discuss here the evolution of massive black hole spins along the cosmic history, due to the combination of mergers and accretion events. I describe recent simulations of accreting black holes in merger remnants, and discuss the implication for the spins of black holes in quasars.

by Kesden, Michael and Sperhake, Ulrich and Berti, Emanuele
20 pages, 16 figures, revtex

The inspiral of binary black holes is governed by gravitational radiation reaction at binary separations r 10 M. Fortunately, binary evolution between these separations is well described by post-Newtonian equations of motion. We examine how this post-Newtonian evolution affects the distribution of spin orientations at separations r near 10 M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r =1000 M remain isotropic at r = 10 M, distributions that are initially partially aligned with the orbital angular momentum can be significantly distorted during the post-Newtonian inspiral. Spin-orbit resonances tend to align (anti-align) the binary black hole spins with each other if the spins were initially partially aligned (anti-aligned) with respect to the orbital angular momentum, thus increasing (decreasing) the average final spin. Resonant effects are stronger for comparable-mass binaries, and they could produce significant spin alignment in massive black hole mergers at high redshifts and in stellar-mass black hole binaries. We also point out that precession induces an intrinsic accuracy limitation of 0.03 in the dimensionless spin magnitude, and about 20 degrees in the direction in predicting the final spin resulting from widely separated binary configurations.

by King, Andrew
invited review, IAU Symposium 267, Co-Evolution of Central Black Holes and Galaxies, B.M. Peterson, R.S. Somerville, and T. Storchi-Bergmann, eds typos in eq (2.2) corrected

I review accretion and outflow in active galactic nuclei. Accretion appears to occur in a series of very small–scale, chaotic events, whose gas flows have no correlation with the large–scale structure of the galaxy or with each other. The accreting gas has extremely low specific angular momentum and probably represents only a small fraction of the gas involved in a galaxy merger, which may be the underlying driver.

Eddington accretion episodes in AGN must be common in order for the supermassive black holes to grow. I show that they produce winds with velocities $latex v \sim 0.1c$ and ionization parameters implying the presence of resonance lines of helium– and hydrogenlike iron. The wind creates a strong cooling shock as it interacts with the interstellar medium of the host galaxy, and this cooling region may be observable in an inverse Compton continuum and lower–excitation emission lines associated with lower velocities. The shell of matter swept up by the shocked wind stalls unless the black hole mass has reached the value $latex M_{\sigma}$ implied by the $latex M – \sigma$ relation. Once this mass is reached, further black hole growth is prevented. If the shocked gas did not cool as asserted above, the resulting (`energy-driven’) outflow would imply a far smaller SMBH mass than actually observed. Minor accretion events with small gas fractions can produce galaxy-wide outflows, including fossil outflows in galaxies where there is little current AGN activity.

by Moscibrodzka, M. and Gammie, C. F. and Dolence, J. and Shiokawa, H. and Leung, P. K.
To appear in “The Galactic Center: A Window on the Nuclear Environment of Disk Galaxies”, ed. Mark Morris, Daniel Q. Wang and Feng Yuan

We review results from general relativistic axisymmetric magnetohydrodynamic simulations of accretion in Sgr A*. We use general relativistic radiative transfer methods and to produce a broad band (from millimeter to gamma-rays) spectrum. Using a ray tracing scheme we also model images of Sgr A* and compare the size of image to the VLBI observations at 230 GHz. We perform a parameter survey and study radiative properties of the flow models for various black hole spins, ion to electron temperature ratios, and inclinations. We scale our models to reconstruct the flux and the spectral slope around 230 GHz. The combination of Monte Carlo spectral energy distribution calculations and 230 GHz image modeling constrains the parameter space of the numerical models. Our models suggest rather high black hole spin ($latex a_*\approx 0.9$), electron temperatures close to the ion temperature ($latex T_i/T_e \sim 3$) and high inclination angles ($latex i \approx 90 \deg$).

by Dutan, Ioana
12 pages, 10 figures, submitted to MNRAS

We present an alternative model for launching relativistic jets in active galactic nuclei (AGN) from an accreting Kerr black hole (BH) by converting the accretion disc energy into jet energy, when the rotational energy of the BH is transferred to the inner disc by closed magnetic field lines which connects the BH to the disc (BH-disc magnetic connection). In this way, the available disc energy is increased by the BH rotational energy. We assume that the BH may undergo recurring episodes of its activity with: (i) a first phase when accretion power dominates, and (ii) a second phase when BH spin-down power dominates. In both cases the jet is driven by a low-luminosity, (geometrically) thin accretion disc, as the disc energy is used to launch the jet. We use the general relativistic conservation laws to calculate the mass flow rate into the jets, the launching power of the jets, and the angular momentum transported by the jets. We consider BHs with a spin parameter $latex a_* \geqslant 0.95$, so that the jets are launched from the region inside of the BH ergosphere. The angular momentum removed from the accretion disc is carried away by the disc particles that ultimately form the jets. As far as the BH is concerned, it can (i) spin up by accreting matter and (ii) spin down due to the magnetic counter-acting torque on the BH. We found that a stationary state of the BH ($latex a_* = $ const) can be reached if the mass accretion rate is larger than $latex \dot{m} \sim 0.001$. The maximum value of the BH spin parameter depends on $latex \dot{m}$ being less but close to 0.9982 (Thorne’s model). In addition, the maximum AGN lifetime can be much longer than $latex \sim 10^{7}$ yr when using the BH spin-down power. This result is consistent with the estimation of the maximum AGN lifetime when the AGN output power is provided by the Blandford–Znajek mechanism.

by Petiteau, Antoine and Shang, Yu and Babak, Stanislav and Feroz, Farhan
25 pages, 9 figures

Coalescing massive Black Hole binaries are the strongest and probably the most important gravitational wave sources in the LISA band. The spin and orbital precessions bring complexity in the waveform and make the likelihood surface richer in structure as compared to the non-spinning case. We introduce an extended multimodal genetic algorithm which utilizes the properties of the signal and the detector response function to analyze the data from the third round of mock LISA data challenge (MLDC 3.2). The performance of this method is comparable, if not better, to already existing algorithms. We have found all five sources present in MLDC 3.2 and recovered the coalescence time, chirp mass, mass ratio and sky location with reasonable accuracy. As for the orbital angular momentum and two spins of the Black Holes, we have found a large number of widely separated modes in the parameter space with similar maximum likelihood values.

by Yuan, Feng and Bu, Defu
9 pages, 9 figures; submitted to MNRAS

The most important finding of two-dimensional hydrodynamical simulations of hot accretion flows is that the flow is convectively unstable, because of its inward increase of entropy. As a result, the profile of the mass accretion rate is a function of radius, i.e., only a small fraction of accretion gas available at the outer boundary can finally fall onto the black hole, while the rest is lost in the convective outflows. Radiation is usually neglected in these simulations. When the radiative cooling becomes more and more important, the entropy will increase slower inward. The entropy can even decrease when the radiation becomes stronger than the viscous heating, i.e, the flow enters into the luminous hot accretion flow regime. In the present paper, we investigate the convective instability and correspondingly the profile of accretion rate in the presence of strong radiative cooling by performing two-dimensional hydrodynamical numerical simulation. This problem is important because the profile of the mass accretion rate determines the observational appearance of accretion flows, the growth of black hole, and the evolution of black hole spin. We find that the flow is still strongly convectively unstable, and the radial profile of accretion rate changes little compared to the case of non-radiative flow. This is because the gradient of entropy in the gravitational direction still increases inward although the gradient of entropy decreases.

by Valtonen, M. and Mikkola, S. and Lehto, H. J. and Hyvönen, T. and Nilsson, K. and Merritt, D. and Gopakumar, A. and Rampadarath, H. and Hudec, R. and Basta, M. and Saunders, R.
12 pages, 4 figures, IAU261

We model the binary black hole system OJ287 as a spinning primary and a non-spinning secondary. It is assumed that the primary has an accretion disk which is impacted by the secondary at specific times. These times are identified as major outbursts in the light curve of OJ287. This identification allows an exact solution of the orbit, with very tight error limits. Nine outbursts from both the historical photographic records as well as from recent photometric measurements have been used as fixed points of the solution: 1913, 1947, 1957, 1973, 1983, 1984, 1995, 2005 and 2007 outbursts. This allows the determination of eight parameters of the orbit. Most interesting of these are the primary mass of $latex 1.84\cdot 10^{10} M_\odot$, the secondary mass $latex 1.46\cdot 10^{8} M_\odot$, major axis precession rate $latex 39^\circ.1$ per period, and the eccentricity of the orbit 0.70. The dimensionless spin parameter is $latex 0.28\:\pm\:0.01$ (1 sigma). The last parameter will be more tightly constrained in 2015 when the next outburst is due. The outburst should begin on 15 December 2015 if the spin value is in the middle of this range, on 3 January 2016 if the spin is 0.25, and on 26 November 2015 if the spin is 0.31. We have also tested the possibility that the quadrupole term in the Post Newtonian equations of motion does not exactly follow Einstein’s theory: a parameter $latex q$ is introduced as one of the 8 parameters. Its value is within 30% (1 sigma) of the Einstein’s value $latex q = 1$. This supports the $latex no-hair theorem$ of black holes within the achievable precision. We have also measured the loss of orbital energy due to gravitational waves. The loss rate is found to agree with Einstein’s value with the accuracy of 2% (1 sigma).

by Barausse, Enrico and Buonanno, Alessandra
22 pages, 9 figures

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle’s spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

by Pan, Yi and Buonanno, Alessandra and Buchman, Luisa T. and Chu, Tony and Kidder, Lawrence E. and Pfeiffer, Harald P. and Scheel, Mark A.
15 pages, 8 figures

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200Ms. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.

by Gergely, László Árpád
12 pages, 2 figures

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including spin and mass quadrupolar effects, for generic (noncircular, nonspherical) orbits. Then we analyze the conservative spin dynamics in terms of these variables. We prove that the only precessing and spinning black hole or neutron star binary configuration which is preserved by the post-Newtonian evolution with spin-spin and quadrupole-monopole contributions included is the equal mass, equal and identically oriented spin configuration. This analytic result puts severe limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.

by Valtonen, M. J. and Mikkola, S. and Merritt, D. and Gopakumar, A. and Lehto, H. J. and Hyvönen, T. and Rampadarath, H. and Saunders, R. and Basta, M. and Hudec, R.
12 pages, 6 figures

The compact binary system in OJ287 is modelled to contain a spinning primary black hole with an accretion disk and a non-spinning secondary black hole. Using Post Newtonian (PN) accurate equations that include 2.5PN accurate non-spinning contributions, the leading order general relativistic and classical spin-orbit terms, the orbit of the binary black hole in OJ287 is calculated and as expected it depends on the spin of the primary black hole. Using the orbital solution, the specific times when the orbit of the secondary crosses the accretion disk of the primary are evaluated such that the record of observed outbursts from 1913 up to 2007 is reproduced. The timings of the outbursts are quite sensitive to the spin value. In order to reproduce all the known outbursts, including a newly discovered one in 1957, the Kerr parameter of the primary has to be $latex 0.28 \pm 0.08$. The quadrupole-moment contributions to the equations of motion allow us to constrain the `no-hair’ parameter to be $latex 1.0\:\pm\:0.3$ where 0.3 is the one sigma error. This supports the `black hole no-hair theorem’ within the achievable precision.

It should be possible to test the present estimate in 2015 when the next outburst is due. The timing of the 2015 outburst is a strong function of the spin: if the spin is 0.36 of the maximal value allowed in general relativity, the outburst begins in early November 2015, while the same event starts in the end of January 2016 if the spin is 0.2

by Bhattacharya, Debbijoy and Ghosh, Shubhrangshu and Mukhopadhyay, Banibrata
26 pages including 7 figures; submitted in ApJ

The mechanism by which outflows and plausible jets are driven from black hole systems, still remains observationally elusive. Notwithstanding, several observational evidences and deeper theoretical insights reveal that accretion and outflow/jet are strongly correlated. Here, we model an advective disk-outflow coupled dynamics, incorporating explicitly the vertical flux. Inter-connecting dynamics of outflow and accretion essentially upholds the conservation laws. We investigate the properties of the disk-outflow surface and its strong dependence on the rotation parameter of the black hole. The energetics of disk-outflow strongly depend on mass, accretion rate and spin of the black holes. The model clearly shows that the outflow power extracted from the disk increases strongly with the spin of the black hole, inferring that the power of the observed astrophysical jets has a proportional correspondence with the spin of the central object. In case of blazars (BL Lacs and Flat Spectrum Radio Quasars), most of their emission are believed to be originated from their jets. It is observed that BL Lacs are relatively low luminous than Flat Spectrum Radio Quasars (FSRQs). The luminosity might be linked to the power of the jet, which in turn reflects that the nuclear regions of the BL Lac objects have a relatively low spinning black hole compared to that in the case of FSRQ. If the extreme gravity is the source to power strong outflows and jets, then spin of the black hole, perhaps, might be the fundamental parameter to account for the observed astrophysical processes in an accretion powered system.

by Tchekhovskoy, Alexander and Narayan, Ramesh and McKinney, Jonathan C.
15 pages, 7 figures, submitted to ApJ. Uses emulateapj format

The inferred power of radio loud active galactic nuclei (AGN) on average exceeds the power of similar radio quiet AGN by a factor of 1000. We investigate whether this dichotomy can be due to differences in the spin of the central black holes that power the radio-emitting jets in these sources. Using general relativistic magnetohydrodynamic simulations, we construct steady state axisymmetric numerical models of such systems for a wide range of spins (dimensionless spin parameter 0.1<= a <= 0.9999) and a variety of magnetic field geometries. We assume that the total magnetic flux through the hole horizon r=r_H(a) is held constant. We find that, if the black hole is surrounded by a thin accretion disk, the total black hole power output depends approximately quadratically on the hole angular frequency, P \propto \Omega_H^2 \propto (a/r_H)^2, and we conclude that in this scenario the spin alone can produce power variations of only a few tens at most. However, if the disk is thick, such that the jet subtends a narrow solid angle around the polar axis, then the power dependence can become much steeper, P \propto \Omega_H^4 or even \propto \Omega_H^6, and does produce power variations of 1000 for realistic black hole spin distributions. We derive an analytic solution that accurately reproduces this steeper scaling of power, and we provide a numerical fitting formula that accurately reproduces all our simulated results. We discuss other physical effects that might contribute to the observed radio loud/quiet dichotomy of AGN.

by Barausse, Enrico
5 pages, 3 figures. Submitted as proceeding of the 8th Amaldi International Conference on Gravitational Waves, NYC, 21-26 June 2009

The prediction of the spin of the black hole resulting from the merger of a generic black-hole binary system is of great importance to study the cosmological evolution of supermassive black holes. Several attempts have been recently made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. Here I compare the results of all the simulations appeared so far in the literature with various formulas for the final spin magnitude and direction. I show that although all the formulas give reasonable results for the final spin magnitude, only the formula that I recently proposed in (Barausse & Rezzolla, Apj 704 L40) accurately predicts the final spin direction when applied to binaries with separations of hundred or thousands of gravitational radii. This makes my formula particularly suitable for cosmological merger-trees and N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii, and happens because my formula takes into account the post-Newtonian precession of the spins in a consistent manner.

by Tessmer, Manuel
13 pages, 2 figures, submitted to PRD on 11 Sep. 2009

The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\”onigsd\”orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasi-circular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.

by Dotti, M. and Volonteri, M. and Perego, A. and Colpi, M. and Ruszkowski, M. and Haardt, F.
11 pages, 3 figures. Accepted for publication in MNRAS

Using high resolution hydrodynamical simulations, we explore the spin evolution of massive dual black holes orbiting inside a circumnuclear disc, relic of a gas-rich galaxy merger. The black holes spiral inwards from initially eccentric co or counter-rotating coplanar orbits relative to the disc’s rotation, and accrete gas that is carrying a net angular momentum. As the black hole mass grows, its spin changes in strength and direction due to its gravito-magnetic coupling with the small-scale accretion disc. We find that the black hole spins loose memory of their initial orientation, as accretion torques suffice to align the spins with the angular momentum of their orbit on a short timescale (<1-2 Myr). A residual off-set in the spin direction relative to the orbital angular momentum remains, at the level of <10 degrees for the case of a cold disc, and <30 degrees for a warmer disc. Alignment in a cooler disc is more effective due to the higher coherence of the accretion flow near each black hole that reflects the large-scale coherence of the disc’s rotation. If the massive black holes coalesce preserving the spin directions set after formation of a Keplerian binary, the relic black hole resulting from their coalescence receives a relatively small gravitational recoil. The distribution of recoil velocities inferred from a simulated sample of massive black hole binaries has median <70 km/s much smaller than the median resulting from an isotropic distribution of spins.

by Fragile, P. Chris
5 pages, 4 figures, accepted to ApJ Letters

One of the primary means of determining the spin of an astrophysical black hole is by actually measuring the inner radius of a surrounding accretion disk and using that to infer the spin. By comparing a number of different estimates of the inner radius from simulations of tilted accretion disks with differing black-hole spins, we show that such a procedure can give quite wrong answers. Over the range 0 <= a/M <= 0.9, we find that, for moderately thick disks (H/r ~ 0.2) with modest tilt (15 degrees), the inner radius is nearly independent of spin. This result is likely dependent on tilt, such that for larger tilts, it may even be that the inner radius would increase with increasing spin. In the opposite limit, we confirm through numerical simulations of untilted disks that, in the limit of zero tilt, the inner radius recovers approximately the expected dependence on spin.

by Li, Guang-Xing and Yuan, Ye-Fei and Cao, Xinwu
15 pages, 13 figures

Based on a new estimation of their thickness, the global properties of relativistic slim accretion disks are investigated in this work. The resulting emergent spectra are calculated using relativistic ray-tracing method. The angular dependence of the disk luminosity, the effects of the heat advection and the effect of disk thickness on the estimation of the black hole spin and accretion rate are discussed. The improvements compared to previous works are that we use self-consistent disk equations and we consider the disk self-shadowing effect. We find that at moderate accretion rate, with inclusion of the heat advection effect, radiation trapped in the outer region of the accretion disks will escape in the inner region of the accretion disk and contribute to the emergent spectra. At high accretion rate, large inclination and large black hole spin, both the disk thickness and the heat advection have significant influence on the emergent spectra. Consequently, these effects will influence the measurement of the black hole spin based on the spectral fitting and influence the angular dependence of luminosity.

by Lousto, Carlos O. and Nakano, Hiroyuki and Zlochower, Yosef and Campanelli, Manuela
20 pages, 24 figures, abridged abstract

We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 and magnitudes S1=S2=0.97 for different mass ratios. Starting from a fiducial initial separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16^4 simulations for six mass ratios between q=1 and q=1/16 and compute the distribution of the angles between L and Delta and L and S, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products. To study the merger of black-hole binaries, we turn to full numerical techniques. We introduce empirical formulae to describe the final remnant black hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary’s mass ratio. We found that the magnitude of the recoil velocity distribution decays as P(v) \exp(-v/2500km/s), =630km/s, and sqrt{ – ^2}= 534km/s, leading to a 23% probability of recoils larger than 1000km/s, and a highly peaked angular distribution along the final orbital axis. The final black-hole spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and a 25 degrees misalignment with respect to the final orbital angular momentum.

by Schaefer, Gerhard
44 pages, to appear in the book “Mass and Motion in General Relativity”, proceedings of the CNRS School in Orleans/France, eds. L. Blanchet, A. Spallicci, and B. Whiting

A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the generalized isotropic ones of the canonical formalism of Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant Fock-de Donder approach. Conserved quantities of isolated systems are identified and the Poincar\’e algebra is introduced. Post-Newtonian expansions are performed in the near and far (radiation) zones. The natural fitting of multipole expansions to post-Newtonian schemes is emphasized. The treated matter models are ideal fluids, pure point masses, and point masses with spin and mass-quadrupole moments modelling rotating black holes. Various Hamiltonians of spinning binaries are presented in explicit forms to higher post-Newtonian orders. The delicate use of black holes in post-Newtonian expansion calculations and of the Dirac delta function in general relativity find discussions.

by Blum, J. L. and Miller, J. M. and Fabian, A. C. and Miller, M. C. and Homan, J. and van der Klis, M. and Cackett, E. M. and Reis, R. C.
Accepted for publication in ApJ

GRS 1915+105 harbors one of the most massive known stellar black holes in the Galaxy. In May 2007, we observed GRS 1915+105 for 117 ksec in the low/hard state using Suzaku. We collected and analyzed the data with the HXD/PIN and XIS cameras spanning the energy range from 2.3-55 keV. Fits to the spectra with simple models reveal strong disk reflection through an Fe K emission line and a Compton back-scattering hump. We report constraints on the spin parameter of the black hole in GRS 1915+105 using relativistic disk reflection models. The model for the soft X-ray spectrum (i.e. < 10 keV) suggests a/M = 0.56(2) and excludes zero spin at the 4 sigma level of confidence. The model for the full broadband spectrum suggests that the spin may be higher, a/M = 0.98(1) (1 sigma confidence), and again excludes zero spin at the 2 sigma level of confidence. We discuss these results in the context of other spin constraints and inner disk studies in GRS 1915+105.

by Ajith, P. and Hannam, M. and Husa, S. and Chen, Y. and Bruegmann, B. and Dorband, N. and Mueller, D. and Ohme, F. and Pollney, D. and Reisswig, C. and Santamaria, L. and Seiler, J.
4 pages, 5 figures

We present the first analytical inspiral-merger-ringdown gravitational waveforms from black-hole (BH) binaries with non-precessing spins. By matching a post-Newtonian description of the inspiral to a set of numerical calculations performed in full general relativity, we obtain a waveform family with a conveniently small number of physical parameters. The physical content of these waveforms includes the “orbital hang-up” effect, when BHs are spinning rapidly along the direction of the orbital angular momentum. These waveforms will allow us to detect a larger parameter space of BH binary coalescence, to explore various scientific questions related to GW astronomy, and could dramatically improve the expected detection rates of GW detectors.

by Chu, Tony and Pfeiffer, Harald P. and Scheel, Mark A.
14 pages, 15 figures

High-accuracy binary black hole simulations are presented for black holes with spins anti-aligned with the orbital angular momentum. The particular case studied represents an equal-mass binary with spins of equal magnitude S/m^2=0.43757 \pm 0.00001. The system has initial orbital eccentricity ~4e-5, and is evolved through 10.6 orbits plus merger and ringdown. The remnant mass and spin are M_f=(0.961109 \pm 0.000003)M and S_f/M_f^2=0.54781 \pm 0.00001, respectively, where M is the mass during early inspiral. The gravitational waveforms have accumulated numerical phase errors of <~ 0.1 radians without any time or phase shifts, and <~ 0.01 radians when the waveforms are aligned with suitable time and phase shifts. The waveform is extrapolated to infinity using a procedure accurate to <~ 0.01 radians in phase, and the extrapolated waveform differs by up to 0.13 radians in phase and about one percent in amplitude from the waveform extracted at finite radius r=350M. The simulations employ different choices for the constraint damping parameters in the wave zone; this greatly reduces the effects of junk radiation, allowing the extraction of a clean gravitational wave signal even very early in the simulation.

by Gergely, László Á. and Biermann, Peter L. and Mikóczi, Balázs and Keresztes, Zoltán
10 pages, to appear in Class. Quantum Grav. GWDAW13 Proceedings Special Issue, v2: no typos conjecture

We analyze galactic black hole mergers and their emitted gravitational waves. Such mergers have typically unequal masses with mass ratio of the order 1/10. The emitted gravitational waves carry the inprint of spins and mass quadrupoles of the binary components. Among these contributions, we consider here the quasi-precessional evolution of the spins. A method of taking into account these third post-Newtonian (3PN) effects by renormalizing (redefining) the 1.5 PN and 2PN accurate spin contributions to the accumulated orbital phase is developed.

by Comeau, Simon and Poisson, Eric
4 pages, 2 figures

The rates at which the mass and angular momentum of a small black hole change as a result of a tidal interaction with a much larger black hole are calculated to leading order in the small mass ratio. The small black hole is either rotating or nonrotating, and it moves on a circular orbit in the equatorial plane of the large Kerr black hole. The orbits are fully relativistic, and the rates are computed to all orders in the orbital velocity V < V_{isco}, which is limited only by the size of the innermost stable circular orbit. We show that as V \to V_{isco}, the rates take on a limiting value that depends only on V_{isco} and not on the spin parameter of the large black hole.

by Svoboda, J. and Dovciak, M. and Goosmann, R. W. and Karas, V.
18 pages, 18 figures, accepted to Astronomy and Astrophysics

Spin of an accreting black hole can be determined by spectroscopy of the emission and absorption features produced in the inner regions of an accretion disc. We discuss the method employing the relativistic line profiles of iron in the X-ray domain, where the emergent spectrum is blurred by general relativistic effects. Precision of spectra fitting procedure could be compromised by inappropriate account of the angular distribution of the disc emission. Often a unique profile is assumed, invariable over the entire range of radii in the disc and energy in the spectral band. We study how sensitive the spin determination is to the assumptions about the intrinsic angular distribution of the emitted photons. We find that the uncertainty of the directional emission distribution translates to 20% uncertainty in determination of the marginally stable orbit. By assuming a rotating black hole in the centre of an accretion disc, we perform radiation transfer computations of an X-ray irradiated disc atmosphere to determine the directionality of outgoing X-rays in the 2-10 keV energy band. We implemented the simulation results as a new extension to the KY software package for X-ray spectra fitting of relativistic accretion disc models. Although the parameter space is rather complex, leading to a rich variety of possible outcomes, we find that on average the isotropic directionality reproduces our model data to the best precision. Our results also suggest that an improper usage of limb darkening can partly mimic a steeper profile of radial emissivity. We demonstrate these results on the case of XMM-Newton observation of the Seyfert galaxy MCG-6-30-15, for which we construct confidence levels of chi squared statistics, and on the simulated data for the future X-ray IXO mission.

by Schmoll, S. and Miller, J. M. and Volonteri, M. and Cackett, E. and Reynolds, C. S. and Fabian, A. C. and Brenneman, L. W. and Miniutti, G. and Gallo, L. C.
Accepted for publication in ApJ

We report on the results of spectral fits made to data obtained from a 168 ksec Suzaku observation of the Seyfert-1 galaxy Fairall 9. The source is clearly detected out to 30 keV. The observed spectrum is fairly simple; it is well-described by a power-law with a soft excess and disk reflection. A broad iron line is detected, and easily separated from distinct narrow components owing to the resolution of the CCDs in the X-ray Imaging Spectrometer (XIS). The broad line is revealed to be asymmetric, consistent with a disk origin. We fit the XIS and Hard X-ray Detector (HXD) spectra with relativistically-blurred disk reflection models. With the assumption that the inner disk extends to the innermost stable circular orbit, the best-fit model implies a black hole spin parameter of a = 0.60(7) and excludes extremal values at a high level of confidence. We discuss this result in the context of Seyfert observations and models of the cosmic distribution of black hole spin.

by Martin, Rebecca G. and Pringle, J. E. and Tout, Christopher A.
Accepted for publication in MNRAS

We model the overall shape of an accretion disc in a semi-detached binary system in which mass is transfered on to a spinning black hole the spin axis of which is misaligned with the orbital rotation axis. We assume the disc is in a steady state. Its outer regions are subject to differential precession caused by tidal torques of the companion star. These tend to align the outer parts of the disc with the orbital plane. Its inner regions are subject to differential precession caused by the Lense-Thirring effect. These tend to align the inner parts of the disc with the spin of the black hole. We give full numerical solutions for the shape of the disc for some particular disc parameters. We then show how an analytic approximation to these solutions can be obtained for the case when the disc surface density varies as a power law with radius. These analytic solutions for the shape of the disc are reasonably accurate even for large misalignments and can be simply applied for general disc parameters. They are particularly useful when the numerical solutions would be slow.

by Perego, A. and Dotti, M. and Colpi, M. and Volonteri, M.
20 pages, 15 figures (jpg or png format), 3 tables; to be published in MNRAS

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass and spin parameter evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction. We develop an iterative scheme based on the adiabatic approximation to study the BH-disc coevolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen-Petterson effect) and interacts with the BH until the BH spin aligns with the outer angular momentum direction. For a BH aligning with a co-rotating disc, the fractional increase in mass is typically less than a few percent, while the spin modulus can increase up to a few tens of percent. The alignment timescale is between ~ 100 thousands and ~ 1 millions years for a maximally rotating BH accreting at the Eddington rate. BH-disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular co-rotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.

by Klein, Antoine and Jetzer, Philippe and Sereno, Mauro
20 pages, 20 figures. Submitted to Phys. Rev. D

Gravitational waves emitted by binary systems in the inspiral phase carry a complicated structure, consisting in a superposition of different harmonics of the orbital frequency, the amplitude of each of them taking the form of a Post-Newtonian series. In addition to that, spinning binaries experience couplings which induce a precession of the orbital angular momentum and of the individual spins. So far, all studies of the measurement accuracy of gravitational wave experiments for comparable-mass binary systems have considered either spinless binaries, or spinning binaries without subdominant harmonics in the waveform as well as no amplitude modulations. In this paper, we consider supermassive black hole binaries as expected to be observed with the planned space-based interferometer LISA, and study the measurement accuracy for several astrophysically interesting parameters obtainable taking into account the full 2PN waveform for spinning bodies, as well as spin-precession effects. We find that for binaries with a total mass in the range 10^5 M_Sun < M 10 for M < 10^7 M_Sun, 1.5 – 5 times higher than with the restricted waveform. We computed that the full waveform allows to use supermassive black hole binaries as standard sirens up to a redshift of z = 1.6, about 0.4 larger than what previous studies allowed.

by Steiner, James F. and McClintock, Jeffrey E. and Remillard, Ronald A. and Narayan, Ramesh and Gou, Lijun
5 pages, 3 figs, 1 table. Submitted to ApJL

All prior work on measuring the spins of stellar-mass black holes via the X-ray continuum-fitting method has relied on the use of weakly-Comptonized spectra obtained in the thermal dominant state. Using a self-consistent Comptonization model, we show that one can analyze spectra that exhibit strong power-law components and obtain values of the inner disk radius, and hence spin, that are consistent with those obtained in the thermal dominant state. Specifically, we analyze many RXTE spectra of two black hole transients, 1743-322 and XTE J1550-564, and we demonstrate that the radius of the inner edge of the accretion disk remains constant to within a few percent as the strength of the Comptonized component increases by an order of magnitude, i.e., as the fraction of the thermal seed photons that are scattered approaches 25%. We conclude that the continuum-fitting method can be applied to a much wider body of data than previously thought possible, and to sources that have never been observed to enter the thermal dominant state (e.g., Cyg X-1).

by Sperhake, U. and Cardoso, V. and Pretorius, F. and Berti, E. and Hinderer, T. and Yunes, N.
4 pages, 4 pages, revtex

We study the collision of two highly boosted equal mass, nonrotating black holes with generic impact parameter. We find such systems to exhibit zoom-whirl behavior when fine tuning the impact parameter. Near the threshold of immediate merger, these systems can produce black holes rotating close to the Kerr limit and generate radiated energies as large as ~35% of the center of mass energy.

by Lovelace, Geoffrey and Chen, Yanbei and Cohen, Michael and Kaplan, Jeffrey D. and Keppel, Drew and Matthews, Keith D. and Nichols, David A. and Scheel, Mark A. and Sperhake, Ulrich
Submitted to Phys. Rev. D

Research on extracting science from binary-black-hole (BBH) simulations has often adopted a “scattering matrix” perspective: given the binary’s initial parameters, what are the final hole’s parameters and the emitted gravitational waveform? In contrast, we are using BBH simulations to explore the nonlinear dynamics of curved spacetime. Focusing on the head-on plunge, merger, and ringdown of a BBH with transverse, antiparallel spins, we explore numerically the momentum flow between the holes and the surrounding spacetime. We use the Landau-Lifshitz field-theory-in-flat-spacetime formulation of general relativity to define and compute the density of field energy and field momentum outside horizons and the energy and momentum contained within horizons, and we define the effective velocity of each apparent and event horizon as the ratio of its enclosed momentum to its enclosed mass-energy. We find surprisingly good agreement between the horizons’ effective and coordinate velocities. To investigate the gauge dependence of our results, we compare pseudospectral and moving-puncture evolutions of physically similar initial data; although spectral and puncture simulations use different gauge conditions, we find remarkably good agreement for our results in these two cases. We also compare our simulations with the post-Newtonian trajectories and near-field energy-momentum. [Abstract abbreviated; full abstract also mentions additional results.]

by Kato, Y. and Miyoshi, M. and Takahashi, R. and Negoro, H. and Matsumoto, R.
5 pages, 3 figures, submitted to MNRAS LETTER

We determine the spin of a supermassive black hole in the context of discseismology by comparing newly detected quasi-periodic oscillations (QPOs) of radio emission in the Galactic centre, Sagittarius A* (Sgr A*), as well as infrared and X-ray emissions with those of the Galactic black holes. We find that the spin parameters of black holes in Sgr A* and in Galactic X-ray sources have a unique value of $latex \approx 0.44$ which is smaller than the generally accepted value for supermassive black holes, suggesting evidence for the angular momentum extraction of black holes during the growth of supermassive black holes. Our results demonstrate that the spin parameter approaches the equilibrium value where spin-up via accretion is balanced by spin-down via the Blandford-Znajek mechanism regardless of its initial spin. We anticipate that measuring the spin of black holes by using QPOs will open a new window for exploring the evolution of black holes in the Universe.

by Murphy, K. D. and Yaqoob, T. and Dovčiak, M. and Karas, V.
7 pages, 7 figures. Accepted for publication in ApJ

Future X-ray instrumentation is expected to allow us to significantly improve the constraints derivedfrom the Fe K lines in AGN, such as the black-hole angular momentum (spin) and the inclination angle of the putative accretion disk. We consider the possibility that measurements of the persistent, time-averaged Fe K line emission from the disk could be supplemented by the observation of a localized flare, or “hotspot”, orbiting close to the black hole. Although observationally challenging, such measurements would recover some of the information loss that is inherent to the radially-integrated line profiles. We present calculations for this scenario to assess the extent to which, in principle, black-hole spin may be measured. We quantify the feasibility of this approach using realistic assumptions about likely measurement uncertainties.

by Stavridis, Adamantios and Will, Clifford M.
10 pages, 5 figures

Observations of gravitational waves from massive binary black hole systems at cosmological distances can be used to search for a dependence of the speed of propagation of the waves on wavelength, and thereby to bound the mass of a hypothetical graviton. We study the effects of precessions of the spins of the black holes and of the orbital angular momentum on the process of parameter estimation using matched filtering of gravitational-wave signals vs. theoretical template waveforms. For the proposed space interferometer LISA, we show that precessions, and the accompanying modulations of the gravitational waveforms, are effective in breaking degeneracies among the parameters being estimated, and effectively restore the achievable graviton-mass bounds to levels obtainable from binary inspirals without spin. For spinning, precessing binary black hole systems of equal masses (10^6 solar masses) at 3 Gpc, the bounds on the graviton Compton wavelength achievable are of the order of 5 X 10^{16} km.

by Garofalo, David
Phys.RevD accepted

We study the spin dependence of accretion onto rotating Kerr black holes using analytic techniques. In its linear regime, angular momentum transport in MHD turbulent accretion flow involves the generation of radial magnetic field connecting plasma in a differentially rotating flow. We take a first principles approach, highlighting the constraint that limits the generation and amplification of radial magnetic fields, stemming from the transfer of energy from mechanical to magnetic form. Because the energy transferred in magnetic form is ultimately constrained by gravitational potential energy or Killing energy, the spin-dependence of the latter allows us to derive spin-dependent constraints on the success of the accreting plasma to expel its angular momentum and accrete. We find an inverse relationship between this ability and black hole spin. If this radial magnetic field generation forms the basis for angular momentum transfer in accretion flows, accretion rates involving Kerr black holes are expected to be lower as the black hole spin increases in the prograde sense.

by Garofalo, David
ApJL accepted

We explore the connection between black hole spin and AGN power by addressing the consequences underlying the assumption in the recent literature that the gap region between accretion disks and black holes is fundamental in producing strong, spin-dependent, horizon-threading magnetic fields. Under the additional assumption that jets and outflows in AGN are produced by the Blandford-Znajek and Blandford-Payne mechanisms, we show that maximum jet/outflow power is achieved for accretion onto black holes having highly retrograde spin parameter, an energetically excited yet unstable gravitomagnetic configuration.

by Petiteau, Antoine and Yu, Shang and Babak, Stanislav
10 pages, 4 figures, proceeding for GWDAW13 (Puerto Rico)

We use a genetic algorithm to analyze the data from the third round of the mock LISA data challenge. These data consist of gaussian stationary instrumental noise, a Galactic background and four to six signals from the inspiralling spinning BHs in quasi-circular orbits. We present a particular implementation of the genetic algorithm which uses properties of the signal and the response function. We discuss the results of a preliminary search for a single signal in the instrumental noise.

by Barausse, Enrico and Rezzolla, Luciano
4 pages, 2 figures

The knowledge of the spin of the black hole resulting from the merger of a generic binary system of black holes is of great importance to study the cosmological evolution of supermassive black holes. Several attempts have been recently made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. While these expressions are in good agreement with the simulations, they are intrinsically imprecise when predicting the final spin direction, especially if applied to binaries with separations of hundred or thousands of gravitational radii. This is due to neglecting the precession of the orbital plane of the binary, and is a clear drawback if the formulas are employed in cosmological merger-trees or N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii. We remove this problem by proposing an expression which is built on improved assumptions and that gives, for any separation, a very accurate prediction both for the norm of the final spin and for its direction. By comparing with the numerical data, we also show that the final spin direction is very accurately aligned with the total angular momentum of the binary at large separation. Hence, observations of the final spin direction (e.g. via a jet) can provide information on the orbital plane of the binary at large separations and could be relevant, for instance, to study X-shaped radio sources.

by Miller, M. Coleman and Alexander, Tal and Amaro-Seoane, Pau and Barth, Aaron J. and Cutler, Curt and Gair, Jonathan R. and Hopman, Clovis and Merritt, David and Phinney, E. Sterl and Richstone, Douglas O.
8 pages, Science white paper for the Astro2010 Decadal Survey

Electromagnetic observations over the last 15 years have yielded a growing appreciation for the importance of supermassive black holes (SMBH) to the evolution of galaxies, and for the intricacies of dynamical interactions in our own Galactic center. Here we show that future low-frequency gravitational wave observations, alone or in combination with electromagnetic data, will open up unique windows to these processes. In particular, gravitational wave detections in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to unprecedented precision and will provide clues to the properties of the otherwise undetectable stellar remnants expected to populate the centers of galaxies. Such observations are therefore keys to understanding the interplay between SMBHs and their environments.

by Madau, P. and Abel, T. and Bender, P. and Di Matteo, T. and Haiman, Z. and Hughes, S. and Loeb, A. and Phinney, E. and Primack, J. and Prince, T. and Rees, M. and Richstone, D. and Schutz, B. and Thorne, K. and Volonteri, M.
Science White Paper submitted to the Astro2010 Decadal Survey

This White Paper to the National Academy of Sciences Astro2010 Decadal Review Committee outlines some of the outstanding questions regarding the assembly history of Massive Black Holes in the nuclei of galaxies and the revolutionary contributions anticipated in this field from low-frequency gravitational wave astronomy.