Viewpoint: The First Sounds of Merging Black Holes
Gravitational waves emitted by the merger of two black holes have been detected, setting the course for a new era of observational astrophysics.
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arXiv subjects
Emanuele Berti
Publications and source records attributed to Emanuele Berti.
Distinguishing black-hole spin-orbit resonances by their gravitational wave signatures. II: Full parameter estimation
Gravitational waves from coalescing binary black holes encode the evolution of their spins prior to merger. In the post-Newtonian regime and on the precession timescale, this evolution has one of three morphologies, with the spins either librating around one of two fixed points ("resonances") or circulating freely. In this work we perform full parameter estimation on resonant binaries with fixed masses and spin magnitudes, changing three parameters: a conserved "projected effective spin" $ξ$ and resonant family $ΔΦ=0,π$ (which uniquely label the source), the inclination $θ_{JN}$ of the binary's total angular momentum with respect to the line of sight (which determines the strength of precessional effects in the waveform), and the signal amplitude. We demonstrate that resonances can be distinguished for a wide range of binaries, except for highly symmetric configurations where precessional effects are suppressed. Motivated by new insight into double-spin evolution, we introduce new variables to characterize precessing black hole binaries which naturally reflects the timescale separation of the system and therefore better encode the dynamical information carried by gravitational waves.
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Science with the space-based interferometer eLISA. I: Supermassive black hole binaries
We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parameter estimation accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only waveforms. We quantify the information present in the merger and ringdown by rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms, and from a reduced set of precessing numerical relativity/post-Newtonian hybrid waveforms. We find that all of the eLISA configurations considered in our study should detect some massive black hole binaries. However, configurations with six links and better low-frequency noise will provide much more information on the origin of black holes at high redshifts and on their accretion history, and they may allow the identification of electromagnetic counterparts to massive black hole mergers.
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Testing General Relativity with Present and Future Astrophysical Observations
One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.
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Slowly rotating black hole solutions in Horndeski gravity
We study black hole solutions at first order in the Hartle-Thorne slow-rotation approximation in Horndeski gravity theories. We derive the equations of motion including also cases where the scalar depends linearly on time. In the Hartle-Thorne formalism, all first-order rotational corrections are described by a single frame-dragging function. We show that the frame-dragging function is exactly the same as in general relativity for all known black hole solutions in shift symmetric Horndeski theories, with the exception of theories with a linear coupling to the Gauss-Bonnet invariant. Our results extend previous no-hair theorems for a broad class of Horndeski gravity theories.
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Gravity-dominated unequal-mass black hole collisions
We continue our series of studies of high-energy collisions of black holes investigating unequal-mass, boosted head-on collisions in four dimensions. We show that the fraction of the center-of-mass energy radiated as gravitational waves becomes independent of mass ratio and approximately equal to $13\%$ at large energies. We support this conclusion with calculations using black hole perturbation theory and Smarr's zero-frequency limit approximation. These results lend strong support to the conjecture that the detailed structure of the colliding objects is irrelevant at high energies.
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Reply to "On the branching of quasinormal resonances of near-extremal Kerr black holes" by Shahar Hod
In a study of the quasinormal mode frequencies of nearly extremal black holes, we pointed out a bifurcation of the mode spectrum into modes with finite decay and modes with vanishing decay in the extremal limit. We provided analytic and semi-analytic results identifying which families of modes bifurcated, and when modes with finite decay rates exist when approaching the extremal limit. In a recent note (arXiv:1510.05604), Hod suggests that additional modes asymptote to finite decay at extremely high spin parameter, based on past work by Detweiler. We search for these suggested modes and find no evidence of their existence. In addition, we point out an inconsistency in the derivation of the proposed modes, which further indicates that these damped modes do not exist.
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Precessional instability in binary black holes with aligned spins
Binary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been testbeds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is anti-aligned. Spins in these configurations are unstable to precession to large misalignment when the binary separation $r$ is between the values $r_{\rm ud\pm}= (\sqrt{χ_1} \pm \sqrt{q χ_2})^4 (1-q)^{-2} M$, where $M$ is the total mass, $q \equiv m_2/m_1$ is the mass ratio, and $χ_1$ ($χ_2$) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.
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Gravitational-wave cutoff frequencies of tidally disruptive neutron star-black hole binary mergers
Tidal disruption has a dramatic impact on the outcome of neutron star-black hole mergers. The phenomenology of these systems can be divided in three classes: nondisruptive, mildly disruptive or disruptive. The cutoff frequency of the gravitational radiation produced during the merger (which is potentially measurable by interferometric detectors) is very different in each regime, and when the merger is disuptive it carries information on the neutron star equation of state. Here we use semianalytical tools to derive a formula for the critical binary mass ratio $Q=M_{\rm BH}/M_{\rm NS}$ below which mergers are disruptive as a function of the stellar compactness $\mathcal{C}=M_{\rm NS}/R_{\rm NS}$ and the dimensionless black hole spin $χ$. We then employ a new gravitational waveform amplitude model, calibrated to $134$ general relativistic numerical simulations of binaries with black hole spin (anti-)aligned with the orbital angular momentum, to obtain a fit to the gravitational-wave cutoff frequency in the disruptive regime as a function of $\mathcal{C}$, $Q$ and $χ$. Our findings are important to build gravitational wave template banks, to determine whether neutron star-black hole mergers can emit electromagnetic radiation (thus helping multimessenger searches), and to improve event rate calculations for these systems.
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Multi-timescale analysis of phase transitions in precessing black-hole binaries
The dynamics of precessing binary black holes (BBHs) in the post-Newtonian regime has a strong timescale hierarchy: the orbital timescale is very short compared to the spin-precession timescale which, in turn, is much shorter than the radiation-reaction timescale on which the orbit is shrinking due to gravitational-wave emission. We exploit this timescale hierarchy to develop a multi-scale analysis of BBH dynamics elaborating on the analysis of Kesden et al. (2015). We solve the spin-precession equations analytically on the precession time and then implement a quasi-adiabatic approach to evolve these solutions on the longer radiation-reaction time. This procedure leads to an innovative "precession-averaged" post-Newtonian approach to studying precessing BBHs. We use our new solutions to classify BBH spin precession into three distinct morphologies, then investigate phase transitions between these morphologies as BBHs inspiral. These precession-averaged post-Newtonian inspirals can be efficiently calculated from arbitrarily large separations, thus making progress towards bridging the gap between astrophysics and numerical relativity.
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Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the $N$-tuple of scalar fields takes values in a coordinate patch of an $N$-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In preparation for numerical relativity simulations, we also write down the $3+1$ decomposition of the field equations for generic tensor-multi-scalar theories.
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Aligned spin neutron star-black hole mergers: a gravitational waveform amplitude model
The gravitational radiation emitted during the merger of a black hole with a neutron star is rather similar to the radiation from the merger of two black holes when the neutron star is not tidally disrupted. When tidal disruption occurs, gravitational waveforms can be broadly classified in two groups, depending on the spatial extent of the disrupted material. Extending previous work by some of us, here we present a phenomenological model for the gravitational waveform amplitude in the frequency domain encompassing the three possible outcomes of the merger: no tidal disruption, "mild" and "strong" tidal disruption. The model is calibrated to 134 general-relativistic numerical simulations of binaries where the black hole spin is either aligned or antialigned with the orbital angular momentum. All simulations were produced using the SACRA code and piecewise polytropic neutron star equations of state. The present model can be used to determine when black-hole binary waveforms are sufficient for gravitational-wave detection, to extract information on the equation of state from future gravitational-wave observations, to obtain more accurate estimates of black hole-neutron star merger event rates, and to determine the conditions under which these systems are plausible candidates as central engines of gamma-ray bursts, macronovae and kilonovae.
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Post-Tolman-Oppenheimer-Volkoff formalism for relativistic stars
Besides their astrophysical interest, compact stars also provide an arena for understanding the properties of theories of gravity that differ from Einstein's general relativity. Numerous studies have shown that different modified theories of gravity can modify the bulk properties (such as mass and radius) of neutron stars for given assumptions on the microphysics. What is not usually stressed though is the strong degeneracy in the predictions of these theories for the stellar mass and radius. Motivated by this observation, in this paper we take an alternative route and construct a stellar structure formalism which, without adhering to any particular theory of gravity, describes in a simple parametrized form the departure from compact stars in general relativity. This "post-Tolman-Oppenheimer-Volkoff (TOV)" formalism for spherical static stars is inspired by the well-known parametrized post-Newtonian theory, extended to second post-Newtonian order by adding suitable correction terms to the fully relativistic TOV equations. We show how neutron star properties are modified within our formalism, paying special attention to the effect of each correction term. We also show that the formalism is equivalent to general relativity with an "effective" (gravity-modified) equation of state.
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Slowly Rotating Anisotropic Neutron Stars in General Relativity and Scalar-Tensor Theory
Some models (such as the Skyrme model, a low-energy effective field theory for QCD) suggest that the high-density matter prevailing in neutron star interiors may be significantly anisotropic. Anisotropy is known to affect the bulk properties of nonrotating neutron stars in General Relativity. In this paper we study the effects of anisotropy on slowly rotating stars in General Relativity. We also consider one of the most popular extensions of Einstein's theory, namely scalar-tensor theories allowing for spontaneous scalarization (a phase transition similar to spontaneous magnetization in ferromagnetic materials). Anisotropy affects the moment of inertia of neutron stars (a quantity that could potentially be measured in binary pulsar systems) in both theories. We find that the effects of scalarization increase (decrease) when the tangential pressure is bigger (smaller) than the radial pressure, and we present a simple criterion to determine the onset of scalarization by linearizing the scalar-field equation. Our calculations suggest that binary pulsar observations may constrain the degree of anisotropy or even, more optimistically, provide evidence for anisotropy in neutron star cores.
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Ultra-high-energy debris from the collisional Penrose process
Soon after the discovery of the Kerr metric, Penrose realized that superradiance can be exploited to extract energy from black holes. The original idea (involving the breakup of a single particle) yields only modest energy gains. A variant of the Penrose process consists of particle collisions in the ergoregion. The collisional Penrose process has been explored recently in the context of dark matter searches, with the conclusion that the ratio $η$ between the energy of post-collision particles detected at infinity and the energy of the colliding particles should be modest ($η\lesssim 1.5$). Schnittman has shown that these studies underestimated the maximum efficiency by about one order of magnitude (i.e., $η\lesssim 15$). In this work we show that particle collisions in the vicinity of rapidly rotating black holes can produce high-energy ejecta and result in high efficiencies under much more generic conditions. The astrophysical likelihood of these events deserves further scrutiny, but our study hints at the tantalizing possibility that the collisional Penrose process may power gamma rays and ultra-high-energy cosmic rays.
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Effective potentials and morphological transitions for binary black-hole spin precession
We derive an effective potential for binary black-hole (BBH) spin precession at second post-Newtonian order. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a fixed period the BBH spins return to their initial relative orientations and jointly precess about the total angular momentum by a fixed angle. Using these solutions, we classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. We also derive a precession-averaged evolution equation for the total angular momentum that can be integrated on the radiation-reaction time and identify a new class of spin-orbit resonances that can tilt the direction of the total angular momentum during the inspiral. Our new results will help efforts to model and interpret gravitational waves from generic BBH mergers and predict the distributions of final spins and gravitational recoils.
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Massive Black Hole Science with eLISA
The evolving Laser Interferometer Space Antenna (eLISA) will revolutionize our understanding of the formation and evolution of massive black holes along cosmic history by probing massive black hole binaries in the $10^3-10^7$ solar mass range out to redshift $z\gtrsim 10$. High signal-to-noise ratio detections of $\sim 10-100$ binary coalescences per year will allow accurate measurements of the parameters of individual binaries (such as their masses, spins and luminosity distance), and a deep understanding of the underlying cosmic massive black hole parent population. This wealth of unprecedented information can lead to breakthroughs in many areas of physics, including astrophysics, cosmology and fundamental physics. We review the current status of the field, recent progress and future challenges.
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A Black-Hole Primer: Particles, Waves, Critical Phenomena and Superradiant Instabilities
These notes were prepared for a lecture on black holes delivered at the DPG Physics School "General Relativity @ 99" (Physikzentrum Bad Honnef, Germany, September 2014). The common thread of the lecture is the relation between geodesic stability and black-hole perturbations in the geometric optics limit. Chapter 1 establishes notation and discusses a common misconception on Michell's "Newtonian black holes". Chapters 2 and 3 deal with particle dynamics and wave dynamics in black-hole spacetimes, respectively. All calculations should be simple enough that they can be done with pen and paper. Chapter 4 builds on this introduction to discuss two exciting topics in current research: critical phenomena in black-hole mergers and the black-hole bomb instability.
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