Supermassive Kerr Black Hole Research Articles

Prospects for determining the nature of the secondaries of extreme mass-ratio inspirals using the spin-induced quadrupole deformation

The measurement of multipole moments of astrophysical objects through gravitational wave (GW) observations provides a novel way to distinguish black holes from other astrophysical objects. This paper studies the gravitational wave radiation from an extreme mass ratio inspiral (EMRI) system consisting of a supermassive Kerr black hole (the primary object) and a spinning stellar-mass compact object (the secondary object). The quadrupolar deformation induced by the spin of the secondary is different for different astrophysical objects. We compute the effect of the quadrupolar deformation on the GW phase and provide an order of magnitude estimate of whether LISA can distinguish different astrophysical objects through GW phase measurement. We find that although LISA cannot distinguish between a black hole and a neutron star, it can distinguish black holes from a large variety of highly spinning astrophysical objects like superspinars and highly deformable exotic compact objects like boson stars for EMRI systems with relatively large mass ratio ($q\ensuremath{\sim}{10}^{\ensuremath{-}4}$). Furthermore, we show that the effect of spin-induced quadrupolar deformation on the GW phase for white dwarf and brown dwarf-EMRI systems can be quite significant even for small values of mass ratio ($q\ensuremath{\lesssim}{10}^{\ensuremath{-}6}$).

No Gravitational Wave from Orbiting Supermassive Kerr Black Hole—a model of matter distribution and propagation of gravitational waves inside the event horizon

The matter distribution of the extremely high-energy and dense plasma inside a supermassive rotating black hole has been theoretically investigated, starting from Einstein’s equation with the source term, in the coordinate close to the free-falling frame along the geodesics of interior matter, where the state of the force balance can be described with the formalism of modified Newtonian dynamics. For a model of equal-rotation velocity of matter, where the main component of plasma is rotating around a common axis with the same velocity close to the light velocity, with a high Lorentz factor (gamma rate), it is concluded that the matter distribution is condensed to a region with a much smaller radius than that of the event horizon of the Kerr spacetime. The gravitational waves that are generated from the condensed matter region due to the orbital motion of the binary, return towards the source, after ceasing at the critical sphere in the vacuum region of spinning Kerr spacetime. At the stage where returning waves encounter with foreword waves, the gravitational waves are deformed to standing waves that carry no energy outside of the event horizon. We conclude that no gravitational wave is radiated from the supermassive black hole binary

Detection of scalar fields by extreme mass ratio inspirals with a Kerr black hole

We study extreme mass ratio inspirals occurring in modified gravity, for which the system is modeled by a small compact object with scalar charge spiraling into a supermassive Kerr black hole. Besides the tensorial gravitational waves arising from the metric perturbations, radiations are also induced by the scalar field. The relevant metric and scalar perturbations are triggered by the orbital motion of the small object, which give rise to a system of inhomogeneous differential equations under the adiabatic approximation. Such a system of equations is then solved numerically using Green's function furnished by the solutions of the corresponding homogeneous equations. To explore the present scenario from an observational perspective, we investigate how the pertinent observables are dependent on specific spacetime configurations. In this regard, the energy fluxes and the gravitational wave dephasing accumulated during the process are evaluated, as functions of the scalar charge, mass ratio, and spin of the central supermassive black hole. In particular, the presence of additional scalar emission leads to a more significant rate of overall energy loss, which, in turn, decreases the total number of orbital cycles before the small object plunges into the central black hole. Moreover, for a central black hole with a higher spin, the imprints of the scalar charge on the resultant gravitational radiations are found to be more significant, which indicates the possibility of detecting the scalar charge.

Pair Drizzle around Sub-Eddington Supermassive Black Holes

Abstract Electron–positron pair creation near sub-Eddington accretion rate black holes is believed to be dominated by the Breit–Wheeler process (photon–photon collisions). The interacting high-energy photons are produced when unscreened electric fields accelerate leptons either in coherent, macroscopic gaps, or in incoherent structures embedded in the turbulent plasma flow. The latter type of acceleration results in a drizzle of pair production sourced by photons from the background radiation field whose energies are near the pair-production threshold. In this work, we use radiation general relativistic magnetohydrodynamic simulations to extend an earlier study of pair drizzle by Mościbrodzka et al. We focus on low-magnetization (standard and normal evolution) accretion onto supermassive Kerr black holes and consider radiation due to synchrotron, bremsstrahlung, and Compton upscattering processes. We confirm that pair drizzle in M87 is sufficient to keep the magnetospheric charge density orders of magnitude above the Goldreich–Julian density. We also find that pair production peaks along the jet–disk boundary.

RADs energetics and constraints on emerging tori collisions around super-massive Kerr black holes

We provide constraints on possible configurations and interactions of two coplanar tori orbiting a central Kerr black hole (BH), in dependence on its dimensionless spin. The two-tori configurations can be directly linked to the current models featuring the obscuration of galactic BH X-ray emission. The emergence of each torus instability phases is discussed and tori collision has been also investigated. The first simple evaluation of the center-of-mass energy proves that collision-energy-efficiency increases with the dimensionless BH spin. We explore the phenomenological aspects of the corotating and counterrotating tori by analyzing properties of the orbiting toroidal configurations related to the fluid enthalpy flux, the mass-flux, the mass-accretion-rates, and the cusp luminosity in the two cases of corotating and counterrotating fluids in dependence on the SMBH spin. The analysis resulted ultimately in a comparative investigation of the properties of corotating versus counterrotating tori, demonstrating that two accretion tori can orbit around the central Kerr attractor only under very specific conditions. Our results also demonstrate that the dynamics of the unstable phases of these double tori systems is significant for the high energy phenomena which could be observable in the X-ray emission and extremely energetic phenomena in active galactic nuclei and quasar.

Proto-jet configurations in RADs orbiting a Kerr SMBH: symmetries and limiting surfaces

Ringed accretion disks (RADs) are agglomerations of perfect-fluid tori orbiting around a single central attractor that could arise during complex matter inflows in active galactic nuclei. We focus our analysis to axi-symmetric accretion tori orbiting in the equatorial plane of a supermassive Kerr black hole; equilibrium configurations, possible instabilities, and evolutionary sequences of RADs were discussed in our previous works. In the present work we discuss special instabilities related to open equipotential surfaces governing the material funnels emerging at various regions of the RADs, being located between two or more individual toroidal configurations of the agglomerate. These open structures could be associated to proto-jets. Boundary limiting surfaces are highlighted, connecting the emergency of the jet-like instabilities with the black hole dimensionless spin. These instabilities are observationally significant for active galactic nuclei, being related to outflows of matter in jets emerging from more than one torus of RADs orbiting around supermassive black holes.

Ringed Accretion Disks: Evolution of Double Toroidal Configurations

Abstract We investigate ringed accretion disks composed of two tori (rings) orbiting on the equatorial plane of a central supermassive Kerr black hole. We discuss the emergence of the instability phases of each ring of the macro-configuration (ringed disk) according to the Paczynski violation of mechanical equilibrium. In the full general relativistic treatment, we consider the effects of the geometry of the Kerr spacetimes relevant to the characterization of the evolution of these configurations. The discussion of ring stability in different spacetimes enables us to identify particular classes of central Kerr attractors depending on their dimensionless spin. As a result of this analysis, we set constraints on the evolutionary schemes of the ringed disks relative to the torus morphology and on their rotation relative to the central black hole and to each other. The dynamics of the unstable phases of this system is significant for the high-energy phenomena related to accretion onto supermassive black holes in active galactic nuclei and the extremely energetic phenomena in quasars, which could be observed in their X-ray emission.

RINGED ACCRETION DISKS: INSTABILITIES

ABSTRACT We analyze the possibility that several instability points may be formed, due to the Paczyński mechanism of violation of mechanical equilibrium, in the orbiting matter around a supermassive Kerr black hole. We consider a recently proposed model of a ringed accretion disk, made up by several tori (rings) that can be corotating or counter-rotating relative to the Kerr attractor due to the history of the accretion process. Each torus is governed by the general relativistic hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. We prove that the number of the instability points is generally limited and depends on the dimensionless spin of the rotating attractor.

Tidal and centripetal stress in a model human falling deep into a Kerr black hole

I calculate the tidal and centripetal stress in the Misner–Thorne–Wheeler model human—a rigid prism—falling into a high-spin supermassive Kerr black hole at a constant, near-equatorial latitude with high energy, enough to surmount the radial potential barrier near the throat of the black hole. The stress in the model human would be nonlethal.

RINGED ACCRETION DISKS: EQUILIBRIUM CONFIGURATIONS

We investigate a model of ringed accretion disk, made up by several rings rotating around a supermassive Kerr black hole attractor. Each toroid of the ringed disk is governed by the General Relativity hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. Properties of the tori can be then determined by an appropriately defined effective potential reflecting the background Kerr geometry and the centrifugal effects. The ringed disks could be created in various regimes during the evolution of matter configurations around supermassive black holes. Therefore, both corotating and counterrotating rings have to be considered as being a constituent of the ringed disk. We provide constraints on the model parameters for the existence and stability of various ringed configurations and discuss occurrence of accretion onto the Kerr black hole and possible launching of jets from the ringed disk. We demonstrate that various ringed disks can be characterized by a maximum number of rings. We present also a perturbation analysis based on evolution of the oscillating components of the ringed disk. The dynamics of the unstable phases of the ringed disk evolution seems to be promising in relation to high energy phenomena demonstrated in active galactic nuclei.

Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals

We explore the ability of future low-frequency gravitational wave detectors to measure the spin of stellar mass and intermediate mass black holes that inspiral onto super-massive Kerr black holes (SMBHs). We develop a kludge waveform model based on the equations of motion derived by Saijo et al. [Phys Rev D 58, 064005, 1998] for spinning BH binaries, augmented with spin-orbit and spin-spin couplings taken from perturbative and post-Newtonian (PN) calculations, and the associated conservative self-force corrections, derived by comparison to PN results. We model the inspiral phase using accurate fluxes which include perturbative corrections for the spin of the inspiralling body, spin-spin couplings and higher-order fits to solutions of the Teukolsky equation. We present results of Monte Carlo simulations of parameter estimation errors and of the model errors that arise when we omit conservative corrections from the waveform template. For a source 5000+10^6 solar mass observed with an SNR of 1000, LISA will be able to determine the two masses to within a fractional error of ~0.001, measure the SMBH spin magnitude, q, and the spin magnitude of the inspiralling BH to 0.0001, 10%, respectively, and determine the location of the source in the sky and the SMBH spin orientation to within 0.0001 steradians. For a 10+10^6 solar mass system observed with SNR of 30, LISA will not be able to determine the spin magnitude of the inspiralling BH, although the measurement of the other waveform parameters is not significantly degraded by the presence of spin. The model errors which arise from ignoring conservative corrections become significant for mass-ratios above 0.0001, but including these corrections up to 2PN order may be sufficient to reduce these systematic errors to an acceptable level.

Gravitational radiation from a spinning compact object around a supermassive Kerr black hole in circular orbit

The gravitational waves and energy radiations from a spinning compact object with stellar mass in a circular orbit in the equatorial plane of a supermassive Kerr black hole are investigated in this paper. The effect how the spin acts on energy and angular moment fluxes is discussed in detail. The calculation results indicate that the spin of small body should be considered in waveform-template production for the upcoming gravitational wave detections. It is clear that when the direction of spin axes is the same as the orbitally angular momentum ("positive" spin), spin can decrease the energy fluxes which radiate to infinity. For antidirection spin ("negative"), the energy fluxes to infinity can be enlarged. And the relations between fluxes (both infinity and horizon) and spin look like quadratic functions. From frequency shift due to spin, we estimate the wave-phase accumulation during the inspiraling process of the particle. We find that the time of particle inspiral into the black hole is longer for positive spin and shorter for negative compared with the nonspinning particle. Especially, for extreme spin value, the energy radiation near the horizon of the extreme Kerr black hole is much more than that for the nonspinning one. And consequently, the maximum binging energy of the extreme spinning particle is much larger than that of the nonspinning particle.

Gravitational wave emission from a companion black hole in the presence of an accretion disc around a super-massive Kerr black hole

Gravitational wave signal characteristics from a binary black hole system in which the companion moves through the accretion disc of the primary are studied. We chose the primary to be a super-massive (M = 10 8 M ⊙ ) Kerr black hole and the companion to be a massive black hole (M = 10 5 M ⊙ ) to clearly demonstrate the effects. We show that the drag exerted on the companion by the disc is sufficient to reduce the coalescence time of the binary. The drag is primarily due to the fact that the accretion disc on a black hole deviates from a Keplerian disc and becomes sub-Keplerian due to inner boundary condition on the black hole horizon. We consider two types of accretion rates on to the companion. The companion is deeply immersed inside the disc and it can accrete at the Bondi rate which depends on the instantaneous density of the disc. However, an accretion disc can also form around the smaller black hole and it can accrete at its Eddington rate. Thus, this case is also studied and the results are compared. We find that the effect of the disc will be significant in reducing the coalescence time and one needs to incorporate this while interpreting gravitational wave signals emitted from such a binary system.

SUPERMASSIVE BLACK HOLES OR BOSON STARS? HAIR COUNTING WITH GRAVITATIONAL WAVE DETECTORS

The evidence for supermassive Kerr black holes in galactic centers is strong and growing, but only the detection of gravitational waves will convincingly rule out other possibilities to explain the observations. The Kerr space–time is completely specified by the first two multipole moments: mass and angular momentum. This is usually referred to as the "no-hair theorem," but it is really a "two-hair" theorem. If general relativity is the correct theory of gravity, the most plausible alternative to a supermassive Kerr black hole is a rotating boson star. Numerical calculations indicate that the space–time of rotating boson stars is determined by the first three multipole moments ("three-hair theorem"). The Laser Interferometer Space Antenna (LISA) could accurately measure the oscillation frequencies of these supermassive objects. We propose to use these measurements to "count their hair," unambiguously determining their nature and properties.

Relativistic cross sections of mass stripping and tidal disruption of a star by a super-massive rotating black hole

[abbreviated] We consider the problem of tidal disruption of a star by a super-massive Kerr black hole. Using a numerically fast Lagrangian model of the tidally disrupted star we survey the parameter space of the problem and find the regions in the parameter space where the total disruption of the star or a partial mass loss take place as a result of fly-by around the black hole. Our treatment is based on General Relativity, and we consider the range of the black hole masses where the tidal disruption competes with the relativistic effect of direct capture of the star by the black hole. We find that our results can be represented on the plane of specific orbital angular momenta of the star $(j_{\theta}, j_{\phi})$. We calculate the contours of a given mass loss of the star on this plane, referred to as the tidal cross sections, for a given black hole mass $M$, rotational parameter $a$ and inclination of the trajectory of the star with respect to the black hole equatorial plane. It is shown that the tidal cross sections can be approximated as circles symmetric above the axis $j_{\phi}=0$, and shifted with respect to the origin of the coordinates in direction of negative $j_{\theta}$. The radii and shifts of these circles are obtained numerically for the black hole masses in the range $5\cdot 10^{5}M_{\odot}-10^{9}M_{\odot}$ and different values of $a$. It is shown that when $a=0$ the tidal disruption takes place for $M < 5\cdot 10^{7}M_{\odot}$ and when $a\approx 1$ the tidal disruption is possible for $M < 10^{9}M_{\odot}$.

Transition from inspiral to plunge for eccentric equatorial Kerr orbits

Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near-exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively -- essentially randomly -- on initial conditions. Still, Ori and Thorne's zero-eccentricity results are essentially an upper bound on the length of eccentric transitions involving similar bodies (e.g., $a$ fixed). Hence the implications for observations are no better: if the massive body is $M=10^{6}M_{\odot}$, the captured body has mass $m$, and the process occurs at distance $d$ from LISA, then $S/N \lesssim (m/10 M_{\odot})(1\text{Gpc}/d)\times O(1)$, with the precise constant depending on the black hole spin. For low-mass bodies ($m \lesssim 7 M_\odot$) for which the event rate is at least vaguely understood, we expect little chance (probably [much] less than 10%, depending strongly on the astrophysical assumptions) of LISA detecting a transition event with $S/N>5$ during its run; however, even a small infusion of higher-mass bodies or a slight improvement in LISA's noise curve could potentially produce $S/N>5$ transition events during LISA's lifetime.

X-ray emission from accretion disks in active galactic nuclei

We constructed a grid of relativistic models for standard high-relative-luminosity accretion α-disks around supermassive Kerr black holes (BHs) and computed X-ray spectra for their hot, effectively optically thin inner parts by taking into account general-relativity effects. They are known to be heated to high (∼106–109 K) temperatures and to cool down through the Comptonization of intrinsic thermal radiation. Their spectra are power laws with an exponential cutoff at high energies; i.e., they have the same shape as those observed in active galactic nuclei (AGNs). Fitting the observed X-ray spectra of AGNs with computed spectra allowed us to estimate the fundamental parameters of BHs (their mass and Kerr parameter) and accretion disks (luminosity and inclination to the line of sight) in 28 AGNs. We show that the Kerr parameter for BHs in AGNs is close to unity and that the disk inclination correlates with the Seyfert type of AGN, in accordance with the unification model of activity. The estimated BH masses Mx are compared with the masses Mrev determined by the reverberation mapping technique. For AGNs with luminosities close to the Eddington limit, these masses agree and the model under consideration may be valid for them. For low-relative-luminosity AGNs, the differences in masses increase with decreasing relative luminosity and their X-ray emission cannot be explained by this model.

Non‐LTE Models and Theoretical Spectra of Accretion Disks in Active Galactic Nuclei. II. Vertical Structure of the Disk

We have calculated several representative models of vertical structure of an accretion disk around a supermassive Kerr black hole. The interaction of radiation and matter is treated self-consistently, taking into account departures from LTE for calculating both the disk structure and the radiation field. The structural equations are described in detail, and various approximations are discussed. We have demonstrated that departures from LTE are very important for determining the disk structure, even at the midplane, as well as the emergent radiation, particularly for hot and electron-scattering-dominated disks. We have shown that at least for the disk parameters studied in this paper, non-LTE effects tend to reduce the value of the Lyman jump with respect to the LTE predictions, regardless whether LTE predicts an emission or absorption jump. We have studied the effects of various values of viscosity on the model structure and predicted spectral energy distribution. The viscosity is parameterized through a parameter α0 that describes the vertically averaged viscous stress, two power-law exponents, ζ0 and ζ1, and the division point md between these two forms. The disk structure and emergent radiation is sensitive mainly to the values of α0, while the other parameters influence the disk structure to a much lesser extent. However, although the detailed shape of the predicted spectrum is sensitive to adopted value of α0, the overall appearance of the spectrum is quite similar.

Non-LTE Models and Theoretical Spectra of Accretion Disks in Active Galactic Nuclei

We present self-consistent models of the vertical structure and emergent spectrum of AGN accretion disks. The central object is assumed to be a supermassive Kerr black hole. We demonstrate that NLTE effects and the effects of a self-consistent vertical structure of a disk play a very important role in determining the emergent radiation, and therefore should be taken into account. In particular, NLTE models exhibit a largely diminished H I Lyman discontinuity when compared to LTE models, and the He II discontinuity appears strongly in emission for NLTE models. Consequently, the number of ionizing photons in the He II Lyman continuum predicted by NLTE disk models is by 1 - 2 orders of magnitude higher than that following from the black-body approximation. This prediction has important implications for ionization models of AGN broad line regions, and for models of the intergalactic radiation field and the ionization of helium in the intergalactic medium.

Extracting x rays, gamma rays, and relativistic e-e+ pairs from supermassive Kerr black holes using the Penrose mechanism.

Monte Carlo computer simulations of Compton scattering and ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$${\mathit{e}}^{+}$ pair production processes, in the ergosphere of a supermassive (\ensuremath{\sim}${10}^{8}$${\mathit{M}}_{\mathrm{\ensuremath{\bigodot}}}$) rotating black hole, are presented. Particles from an accretion disk surrounding the black hole fall into the ergosphere and scatter off particles that are in bound orbits. In this paper, the equations that govern the orbital trajectory of a particle about a Kerr black hole (KBH) are used to derive analytical expressions for the conserved energy and angular momentum of material and massless particles that have orbits not confined to the equatorial plane. The escape conditions to determine whether or not a particle escapes from the potential well of the KBH are applied to the scattered particles. The Penrose mechanism, in general, allows rotational energy of a KBH to be extracted by scattered particles escaping from the ergosphere to large distances from the black hole. The results of these model calculations, presented in this paper, show that the Penrose mechanism is capable of producing the astronomically observed high energy particles (\ensuremath{\sim} GeV) emitted by quasars and other active galactic nuclei (AGN). This mechanism can extract hard x-ray and \ensuremath{\gamma}-ray photons, from Penrose Compton scatterings of initially low energy UV and soft x-ray photons by target orbiting electrons in the ergosphere; such low energy infalling photons, and high energy scattered escaping photons, are consistent with observations and popular theoretical accretion disk, black hole models. The Penrose pair production processes (\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$), presented here, allow relativistic ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$${\mathit{e}}^{+}$ pairs to escape with energies up to \ensuremath{\sim}2 GeV; these pairs are produced when infalling low energy photons collide with bound target, highly blueshifted photons at the photon orbit. This process may very well be the origin of the relativistic electrons inferred, from observations, to emerge from the cores of AGN. Overall, these Penrose processes can apply to any mass size black hole, more or less, and suggest a complete theory for the extraction of energy from a black hole.