Massive black hole binaries: dynamical evolution and observational signatures

The study of the dynamical evolution of massive black hole pairs in mergers is crucial in the context of a hierarchical galaxy formation scenario. The timescales for the formation and the coalescence of black hole binaries are still poorly constrained, resulting in large uncertainties in the expected rate of massive black hole binaries detectable in the electromagnetic and gravitational wave spectra. Here we review the current theoretical understanding of the black hole pairing in galaxy mergers, with a particular attention to recent developments and open issues. We conclude with a review of the expected observational signatures of massive binaries, and of the candidates discussed in literature to date.Comment: 4 Figures. Accepted for publication in Advances in Astronom

The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1 wave equation with a potential $V$, on a field $\Psi_z$. For smooth metric perturbations $\Psi_z$ is singular at $r_s=-6M/(\ell-1)(\ell+2)$, $\ell$ the mode harmonic number, and $V$ has a second order pole at $r_s$. This is irrelevant to the black hole exterior stability problem, where $r>2M>0$, and $r_s <0$, but it introduces a non trivial problem in the naked singular case where $M0$, and the singularity appears in the relevant range of $r$. We solve this problem by developing a new approach to the evolution of the even mode, based on a {\em new gauge invariant function}, $\hat \Psi$ -related to $\Psi_z$ by an intertwiner operator- that is a regular function of the metric perturbation {\em for any value of $M$}. This allows to address the issue of evolution of gravitational perturbations in this non globally hyperbolic background, and to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.Comment: typos corrected, references adde

Unstable fields in Kerr spacetimes

We show that both the interior region $r<M-\sqrt{M^2-a^2}$ of a Kerr black hole and the $a^2>M^2$ Kerr naked singularity admit unstable solutions of the Teukolsky equation for any value of the spin weight. For every harmonic number there is at least one axially symmetric mode that grows exponentially in time and decays properly in the radial directions. These can be used as Debye potentials to generate solutions for the scalar, Weyl spinor, Maxwell and linearized gravity field equations on these backgrounds, satisfying appropriate spatial boundary conditions and growing exponentially in time, as shown in detail for the Maxwell case. It is suggested that the existence of the unstable modes is related to the so called "time machine" region, where the axial Killing vector field is time-like, and the Teukolsky equation, restricted to axially symmetric fields, changes its character from hyperbolic to elliptic

Growing massive black holes through super-critical accretion of stellar-mass seeds

The rapid assembly of the massive black holes that power the luminous quasars observed at $z \sim 6-7$ remains a puzzle. Various direct collapse models have been proposed to head-start black hole growth from initial seeds with masses $\sim 10^5\,\rm M_\odot$, which can then reach a billion solar mass while accreting at the Eddington limit. Here we propose an alternative scenario based on radiatively inefficient super-critical accretion of stellar-mass holes embedded in the gaseous circum-nuclear discs (CNDs) expected to exist in the cores of high redshift galaxies. Our sub-pc resolution hydrodynamical simulations show that stellar-mass holes orbiting within the central 100 pc of the CND bind to very high density gas clumps that arise from the fragmentation of the surrounding gas. Owing to the large reservoir of dense cold gas available, a stellar-mass black hole allowed to grow at super-Eddington rates according to the "slim disc" solution can increase its mass by 3 orders of magnitudes within a few million years. These findings are supported by simulations run with two different hydro codes, RAMSES based on the Adaptive Mesh Refinement technique and GIZMO based on a new Lagrangian Godunov-type method, and with similar, but not identical, sub-grid recipes for star formation, supernova feedback, black hole accretion and feedback. The low radiative efficiency of super-critical accretion flows are instrumental to the rapid mass growth of our black holes, as they imply modest radiative heating of the surrounding nuclear environment.Comment: 12 pages, 8 figures, 2 tables. Accepted for publication in MNRA

A model for the interaction of high-energy particles in straight and bent crystals implemented in Geant4

A model for the simulation of orientational effects in straight and bent periodic atomic structures is presented. The continuum potential approximation has been adopted.The model allows the manipulation of particle trajectories by means of straight and bent crystals and the scaling of the cross sections of hadronic and electromagnetic processes for channeled particles. Based on such a model, an extension of the Geant4 toolkit has been developed. The code has been validated against data from channeling experiments carried out at CERN

Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations

We analyze the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension $D > 4$. We show that the evolution equations for this type of perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schr\"odinger-like stability equation. As an immediate application we prove that for $D \neq 6$ and $\alpha >0$, the sign choice for the Gauss-Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case $D =6$, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for $\alpha < 0$.Comment: 7 pages, 1 figure, minor corrections, references adde

Gravitational instabilities in Kerr space-times

In this paper we consider the possible existence of unstable axisymmetric modes in Kerr space times, resulting from exponentially growing solutions of the Teukolsky equation. We describe a transformation that casts the radial equation that results upon separation of variables in the Teukolsky equation, in the form of a Schr\"odinger equation, and combine the properties of the solutions of this equations with some recent results on the asymptotic behaviour of spin weighted spheroidal harmonics to prove the existence of an infinite family of unstable modes. Thus we prove that the stationary region beyond a Kerr black hole inner horizon is unstable under gravitational linear perturbations. We also prove that Kerr space-time with angular momentum larger than its square mass, which has a naked singularity, is unstable.Comment: 9 pages, 4 figures, comments, references and calculation details added, asymptotic expansion typos fixe

On the orientation and magnitude of the black hole spin in galactic nuclei

Massive black holes in galactic nuclei vary their mass M and spin vector J due to accretion. In this study we relax, for the first time, the assumption that accretion can be either chaotic, i.e. when the accretion episodes are randomly and isotropically oriented, or coherent, i.e. when they occur all in a preferred plane. Instead, we consider different degrees of anisotropy in the fueling, never confining to accretion events on a fixed direction. We follow the black hole growth evolving contemporarily mass, spin modulus a and spin direction. We discover the occurrence of two regimes. An early phase (M <~ 10 million solar masses) in which rapid alignment of the black hole spin direction to the disk angular momentum in each single episode leads to erratic changes in the black hole spin orientation and at the same time to large spins (a ~ 0.8). A second phase starts when the black hole mass increases above >~ 10 million solar masses and the accretion disks carry less mass and angular momentum relatively to the hole. In the absence of a preferential direction the black holes tend to spin-down in this phase. However, when a modest degree of anisotropy in the fueling process (still far from being coherent) is present, the black hole spin can increase up to a ~ 1 for very massive black holes (M >~ 100 million solar masses), and its direction is stable over the many accretion cycles. We discuss the implications that our results have in the realm of the observations of black hole spin and jet orientations.Comment: 14 pages, 7 figures, accepted for publication in Ap