Black Hole Spin Research Articles

Tidal Spin-up of Black Hole Progenitor Stars

Gravitational wave observations indicate the existence of merging black holes (BHs) with high spin (a ≳ 0.3), whose formation pathways are still an open question. A possible way to form those binaries is through the tidal spin-up of a Wolf–Rayet (WR) star by its BH companion. In this work, we investigate this scenario by directly calculating the tidal excitation of oscillation modes in WR star models, determining the tidal spin-up rate, and integrating the coupled spin–orbit evolution for WR–BH binaries. We find that, for short-period orbits and massive WR stars, the tidal interaction is mostly contributed by standing gravity modes, in contrast to Zahn’s model of traveling waves, which is frequently assumed in the literature. The standing modes are less efficiently damped than traveling waves, meaning that prior estimates of tidal spin-up may be overestimated. We show that tidal synchronization is rarely reached in WR–BH binaries, and the resulting BH spins have a ≲ 0.4 for all but the shortest-period (P orb ≲ 0.5 day) binaries. Tidal spin-up in lower-mass systems is more efficient, providing an anticorrelation between the mass and spin of the BHs, which could be tested in future gravitational wave data. Nonlinear damping processes are poorly understood but may allow for more efficient tidal spin-up. We also discuss a new class of gravito-thermal modes that appear in our calculations.

How Supermassive Black Holes Shape Galaxies

We often think of black holes as mysterious objects that swallow everything that passes by them—from dust to entire stars. In reality, black holes “eat” in a messy way, while spinning around super quickly. They do not swallow their whole “meal” (such as interstellar gas and dust) in a mouthful. Part of it rotates around the spinning black hole, like a merry-go-round, and is eventually thrown outward as very bright, energetic streams of particles called jets. Supermassive black holes the centers of galaxies can create jets that travel very far and affect the birth of baby stars! In this article, we will describe some of the things we know about black holes, including how astronomers found out about black hole jets using powerful telescopes. We will also mention some of the things we still do not understand about black holes and their jets.

The SOUX AGN sample: optical/UV/X-ray SEDs and the nature of the disc

ABSTRACT We use the SOUX sample of ∼700 active galactic nucleus (AGN) to form average optical-ultraviolet (UV)-X-rays spectral energy distributions (SEDs) on a two-dimensional (2D) grid of MBH and L2500. We compare these with the predictions of a new AGN SED model, qsosed, which includes prescriptions for both hot and warm Comptonization regions as well as an outer standard disc. This predicts the overall SED fairly well for 7.5 < log(MBH/M⊙) < 9.0 over a wide range in L/LEdd, but at higher masses the outer disc spectra in the model are far too cool to match the data. We create optical-UV composites from the entire Sloan Digital Sky Survey sample and use these to show that the mismatch is due to there being no significant change in spectral shape of the optical-UV continuum across several decades of MBH at constant luminosity. We show for the first time that this cannot be matched by standard disc models with high black hole spin. These apparently fit, but are not self-consistent as they do not include the General Relativistic effects for the emission to reach the observer. At high spin, increased gravitational redshift compensates for almost all of the higher temperature emission from the smaller inner disc radii. The data do not match the predictions made by any current accretion flow model. Either the disc is completely covered by a warm Comptonization layer whose properties change systematically with L/LEdd, or the accretion flow structure is fundamentally different to that of the standard disc models.

The Spin Measurement of MAXI J0637-430: a Black Hole Candidate with High Disk Density

The Galactic black hole candidate MAXI J0637-430 was first discovered by MAXI/GSC on 2019 November 2. We study the spectral properties of MAXI J0637-430 by using the archived NuSTAR data and Swift/XRT data. After fitting the eight spectra by using a disk component and a powerlaw component model with absorption, we select the spectra with relatively strong reflection components for detailed X-ray reflection spectroscopy. Using the most state-of-art reflection model, relxillCp, the spectral fitting measures a black hole spin a * > 0.72 and the inclination angle of the accretion disk i = degrees, at a 90% confidence level. In addition, the fitting results show an extreme supersolar iron abundance. Combined with the fitting results of reflection model reflionx_hd, we consider that this unphysical iron abundance may be caused by a very high-density accretion disk (n e > 2.34 × 1021 cm−3) or a strong Fe Kα emission line. The soft excess is found in the soft state spectral fitting results, which may be an extra free–free heating effect caused by high density of the accretion disk. Finally, we discuss the robustness of black hole spin obtained by X-ray reflection spectroscopy. The result of relatively high spin is self-consistent with broadened Fe Kα line. Iron abundance and disk density have no effect on the spin results.

Dragging of inertial frames in the composed Kerr-Newman-orbiting-ring system

The dragging of inertial frames by an orbiting object, a well known phenomenon in general relativity, implies that the horizon angular velocity ΩHBH-ring of a central black hole in a composed black-hole-orbiting-ring system is no longer related to its angular-momentum JH by the familiar vacuum functional relation ΩH(JH)=JH/Mα (here {M,α} are respectively the mass and normalized area of the central spinning black hole). Using a continuity argument, according to which the black-hole angular velocity changes smoothly during an adiabatic assimilation process of an orbiting ring, it has recently been revealed that the composed Kerr-ring system is characterized by the universal (that is, spin-independent) relation ΔΩH≡ΩHBH-ring(JH,JR,R→RH+)−ΩHKerr(JH)=JR/4M3, where {R,JR} are respectively the radius of the ring and its orbital angular momentum and RH is the horizon radius of the central Kerr black hole. This intriguing observation naturally raises the following physically interesting question: Does the physical quantity ΔΩH in a composed black-hole-orbiting-ring system is always characterized by the near-horizon functional relation ΔΩH=JR/4M3 which is independent of the spin (angular momentum) JH of the central black hole? In order to address this important question, in the present compact paper we explore the physical phenomenon of dragging of inertial frames by an orbiting ring in the composed Kerr-Newman-black-hole-orbiting-ring system. In particular, using analytical techniques, we reveal the fact that in this composed two-body (black-hole-ring) system the quantity ΔΩH has an explicit non-trivial functional dependence on the angular momentum JH of the central spinning black hole.

Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3

ABSTRACT The mass, spin, and merger rate distribution of the binary black holes (BBHs) across cosmic redshifts provide a unique way to shed light on their formation channel. Along with the redshift dependence of the BBH merger rate, the mass distribution of BBHs can also exhibit redshift dependence due to different formation channels and dependence on the metallicity of the parent stars. We explore the redshift dependence of the BBH mass distribution jointly with the merger rate evolution from the third gravitational wave (GW) catalogue GWTC-3 of the LIGO–Virgo–KAGRA collaboration. We study possible connections between peak-like features in the mass spectrum of BBHs and processes related to supernovae physics and time delay distributions. We obtain a preference for short-time delays between star formation and BBH mergers. Using a power-law form for the time delay distribution ($(t^{\rm min}_d)^{d}$), we find d < −0.7 credible at 90 per cent interval. The mass distribution of the BBHs could be fitted with a power-law form with a redshift-dependent peak feature that can be linked to the pair instability supernovae (PISN) mass-scale MPISN(Z*) at a stellar metallicity Z*. For a fiducial value of the stellar metallicity Z* = 10−4, we find the $\rm M_{\rm PISN}(Z_*)=44.4^{+7.9}_{-6.3}$$\rm M_\odot$. This is in accordance with the theoretical prediction of the lower edge of the PISN mass-scale and differs from previous analyses. Although we find a strong dependence of the PISN value on metallicity, the model that we explored is not strongly favoured over those that do not account for metallicity as the Bayes factors are inconclusive. In the future with more data, evidence towards metallicity dependence of the PISN will have a significant impact on our understanding of stellar physics.

Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation

This paper extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation (Science China, 65, 100411, (2022)) to the case of a binary system for the spinning black holes. An effective rotating metric and an improved Hamiltonian for the spinning black hole binaries were constructed. The decoupled equation for the null tetrad component of the gravitational perturbed Weyl tensor $\psi^B_{4}$ in the effective rotating spacetime is found with the help of the gauge transform characteristics of the Weyl tensors. The decoupled equation is then separated between radial and angular variables in the slowly rotating background spacetime, and a formal solution of $\psi^B_{4}$ is obtained. On this basis, the formal expressions of the radiation reaction force and the waveform for the ``plus'' and ``cross'' modes of the gravitational wave are presented. These results, obtained in the same effective spacetime, constitute a self-consistent effective-one-body theory for the spinning black hole binaries based on the post-Minkowskian approximation.

Unraveling Twisty Linear Polarization Morphologies in Black Hole Images

We investigate general relativistic magnetohydrodynamic simulations to determine the physical origin of the twisty patterns of linear polarization seen in spatially resolved black hole images and explain their morphological dependence on black hole spin. By characterizing the observed emission with a simple analytic ring model, we find that the twisty morphology is determined by the magnetic field structure in the emitting region. Moreover, the dependence of this twisty pattern on spin can be attributed to changes in the magnetic field geometry that occur due to the frame dragging. By studying an analytic ring model, we find that the roles of Doppler boosting and lensing are subdominant. Faraday rotation may cause a systematic shift in the linear polarization pattern, but we find that its impact is subdominant for models with strong magnetic fields and modest ion-to-electron temperature ratios. Models with weaker magnetic fields are much more strongly affected by Faraday rotation and have more complicated emission geometries than can be captured by a ring model. However, these models are currently disfavoured by the recent EHT observations of M87*. Our results suggest that linear polarization maps can provide a probe of the underlying magnetic field structure around a black hole, which may then be usable to indirectly infer black hole spins. The generality of these results should be tested with alternative codes, initial conditions, and plasma physics prescriptions.

Study of Spectral State Transitions in Black Hole Binaries

The aim of our work is to study the origin of the spectral transitions of transient black hole binaries. In this work, we find signatures of spectral state transition (hard to soft state) while studying the radiative shock for the accretion flow. The gradient of the energy dissipation curve shows a sudden break for certain critical flow parameters when the post-shock dissipation is maximum. This particular feature is common to all spins, and the transitions are well observed. We have identified all the critical flow parameters for different black hole spins. With the dissipation, the inner edge of the disk or the geometry of the post-shock corona reduces progressively and attains a minimum for maximum dissipation. The spin enhances the maximum dissipation further. Using the exact general relativistic framework, we therefore systematically study the various dynamical properties of radiative/dissipative shocks in accretion flows to understand the observed phenomena, namely, the variation of the hard intensity emitted from the evolving Comptonizing medium, the spectral transitions, and their entanglement with the inner edge of the disk, etc. The results presented here might be useful in finding the variation of the hardness ratio and could be a first step to procuring the “q” diagram theoretically.

Detecting vector charge with extreme mass ratio inspirals onto Kerr black holes

Extreme mass ratio inspirals (EMRIs) are excellent sources for space-based observatories to explore the properties of black holes and test no-hair theorems. We consider EMRIs with a charged compact object inspiralling onto a Kerr black hole in quasi-circular orbits. Using the Teukolsky and generalized Sasaki-Nakamura formalisms for the gravitational and vector perturbations about a Kerr black hole, we numerically calculate the energy fluxes for both gravitational and vector perturbations induced by a charged particle moving in equatorial circular orbits. With one-year observations of EMRIs, we apply the Fisher information matrix method to estimate the charge uncertainty detected by space-based gravitational wave detectors such as the Laser Interferometer Space Antenna, TianQin, and Taiji, and we find that it is possible to detect vector charges as small as q ∼ 0.0049. The results show that EMRIs composed of a Kerr black hole with a higher spin a and lighter mass M, and a secondary charged object with more vector charge give smaller relative error on the charge, thus constrain the charge better. The positive spin of the Kerr black hole can decrease the charge uncertainty by about one or two orders of magnitude.

The Hard-to-soft Transition of GX 339–4 as Seen by Insight–HXMT

We present an analysis of the relativistic reflection spectra of GX 339–4 during the hard-to-soft transition of its 2021 outburst observed by Insight–HXMT. The strong relativistic reflection signatures in the data suggest a high black hole spin (a * > 0.86) and an intermediate disk inclination angle (i ≈ 35°–43°) of the system. The transition is accompanied by an increasing temperature of the disk and a softening of the corona emission, while the inner disk radius remains stable. Assuming a lamppost geometry, the corona height is also found to stay close to the black hole across the state transition. If we include the Comptonization of the reflection spectrum, the scattering fraction parameter is found to decrease during the state transition. We also perform an analysis with a reflection model designed for hot accretion disks of stellar mass black holes where the surface of the innermost accretion disk is illuminated by emission from the corona and the thermal disk below. Our results support the scenario in which the state transition is associated with variations in the corona properties.

Impact of multiple modes on the evolution of self-interacting axion condensate around rotating black holes

Ultra-light particles, such as axions, form a macroscopic condensate around a highly spinning black hole by the superradiant instability. Due to its macroscopic nature, the condensate opens the possibility of detecting the axion through gravitational wave observations. However, the precise evolution of the condensate must be known for the actual detection. For future observation, we numerically study the influence of the self-interaction, especially interaction between different modes, on the evolution of the condensate in detail. First, we focus on the case when condensate starts with the smallest possible angular quantum number. For this case, we perform the non-linear calculation and show that the dissipation induced by the mode interaction is strong enough to saturate the superradiant instability, even if the secondary cloud starts with quantum fluctuations. Our result indicates that explosive phenomena such as bosenova do not occur in this case. We also show that the condensate settles to a quasi-stationary state mainly composed of two modes, one with the smallest angular quantum number for which the superradiant instability occurs and the other with the adjacent higher angular quantum number. We also study the case when the condensate starts with the dominance of the higher angular quantum number. We show that the dissipation process induced by the mode coupling does not occur for small gravitational coupling. Therefore, bosenova might occur in this case.

Stellar-mass black hole spinning and its relation to transient jets

Despite the vast research on spinning black holes and jets, little is known about details of jet formation. This paper is aimed to study whether Penroses prediction that black hole spin power jets can be verified. Once proved, a deeper understanding of energy/momentum transfer near event horizon is to be achieved. This paper compares two dominant spin measuring methods. Thermal continuum fitting method makes use of thermal emission to measure the spin, where a theoretical flux profile is created by inputting parameters (inclination of X-ray binaries, distance of X-ray binaries from the earth, mass of black hole, etc). X-ray reflection method uses broadened Fe-line to measure the spin, and that corona geometry is often required. This paper also compares various definitions of jet power and spin-jets relation. In conclusion, transient jets are highly possible to be powered by black hole spin, but more evidence is required to confirm this. Steady jets remain in a vague relation with spin. It has also been found that different measuring methods of both spin and jets can affect the spin-jets relation.

Extending the theory of propagating fluctuations: the first fully relativistic treatment and analytical Fourier–Green’s functions

ABSTRACT The aperiodic variability ubiquitously observed from accreting black hole X-ray binary systems is generally analysed within the framework of the so-called ‘theory of propagating fluctuations’. In this paper we derive the Fourier transforms of the Green’s function solutions of the thin disc equations. These solutions suffice to describe all possible solutions through standard convolution techniques. Solutions are found for both Newtonian discs and general relativistic solutions with a vanishing ISCO stress. We use this new relativistic theory to highlight the Kerr black hole spin dependence of a number of observable variability properties of black hole discs. The phase lags, coherence, and power density spectra of Kerr discs are shown to be strong functions of black hole spin. Observations of the aperiodic variability of black hole accretion sources may now, at least in principle, offer a new avenue to directly constrain black hole spins.

Ringdown frequencies in black holes formed from precessing black-hole binaries

We present a simple formula for the effective ringdown frequencies of the gravitational-wave signal of a precessing black-hole binary in the co-precessing frame. This formula requires only knowledge of the quasi-normal mode frequencies of the system and the value of the precession angle $\beta$ during ringdown. Such a formula will be useful in modelling precessing systems. We also provide a comprehensive description of the oscillations in the ringdown frequency in an inertial frame where the spin of the final black hole is in the $z$-direction. These oscillations arise due to the superposition of the prograde and retrograde frequencies. Our understanding of these oscillations can be used to extract the ratio of the amplitudes of the prograde and retrograde frequencies from numerical data. Alternatively, knowledge of this ratio of the amplitudes can be used to produce a simple model of the time domain oscillations in the ringdown frequency.

Testing AGN outflow and accretion models with C iv and He ii emission line demographics in z ≈ 2 quasars

ABSTRACT Using ≈190 000 spectra from the 17th data release of the Sloan Digital Sky Survey (SDSS), we investigate the ultraviolet emission line properties in z ≈ 2 quasars. Specifically, we quantify how the shape of C iv λ1549 and the equivalent width (EW) of He ii λ1640 depend on the black hole mass and Eddington ratio inferred from Mg ii λ2800. Above L/LEdd ≳ 0.2, there is a strong mass dependence in both C iv blueshift and He ii EW. Large C iv blueshifts are observed only in regions with both high mass and high accretion rate. Including X-ray measurements for a subsample of 5000 objects, we interpret our observations in the context of AGN accretion and outflow mechanisms. The observed trends in He ii and 2 keV strength are broadly consistent with theoretical qsosed models of AGN spectral energy distributions (SEDs) for low spin black holes, where the ionizing SED depends on the accretion disc temperature and the strength of the soft excess. High spin models are not consistent with observations, suggesting SDSS quasars at z ≈ 2 may in general have low spins. We find a dramatic switch in behaviour at L/LEdd ≲ 0.1: the ultraviolet emission properties show much weaker trends, and no longer agree with qsosed predictions, hinting at changes in the structure of the broad line region. Overall, the observed emission line trends are generally consistent with predictions for radiation line driving where quasar outflows are governed by the SED, which itself results from the accretion flow and hence depends on both the SMBH mass and accretion rate.

Evolution of binary systems accompanying axion clouds in extreme mass ratio inspirals

Superradiant instability of rotating black holes (BHs) leads to the formation of a cloud of ultralight bosons, such as axions. When the BH with the cloud belongs to a binary system and is in an inspiraling orbit, the resonant transition between the axion's bound states can occur. We study the history of the evolution of the binary system accompanying the cloud composed of the fastest growing mode, and its impact on the observational signatures, especially for small mass ratio cases. In this case, the hyperfine resonance, which has a very small resonance frequency, is relevant. Therefore, due to the long timescale, we should take into account the decaying process of axions in the transition destination mode, the backreaction to the orbital motion and the central BH, and gravitational emission from the cloud. We present a formulation to examine the evolution of the system around the resonance and useful expressions for the analysis. As a result, we found the mass of the cloud that can remain after the resonance is, at most, about $10^{-5}$ of the central BH. The maximum remaining cloud mass is achieved when the mass ratio of the binary is $q\sim10^{-3}$. In addition, we show that the resonant transition hardly changes the BH mass and spin distribution, while the associated modification of the gravitational wave frequency evolution when the binary pass through the resonance can be a signature of the presence of the cloud.

Erratum: Constraining black-hole binary spin precession and nutation with sequential prior conditioning [Phys. Rev. D 106 , 024019 (2022)

1 MoreReceived 5 April 2023DOI:https://doi.org/10.1103/PhysRevD.107.109901© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitationGravitational wave sourcesGravitational wavesPhysical SystemsAstronomical black holesTechniquesBayesian methodsGravitation, Cosmology & Astrophysics

Black hole mergers as tracers of spinning massive black hole and galaxy populations in the OBELISK simulation

Massive black hole (BH) mergers will be key targets of future gravitational wave and electromagnetic observational facilities. In order to constrain BH evolution with the information extracted from BH mergers, one must take into account the complex relationship between the population of merging BHs and the global BH population. We analysed the high-resolution cosmological radiation-hydrodynamics simulation OBELISK, run to redshift z = 3.5, to study the properties of the merging BH population, and its differences with the underlying global BH population in terms of BH and galaxy properties. In post-processing, we calculated dynamical delays between the merger in the simulation at the resolution limit and the actual coalescence well below the resolution scale. We find that merging BHs are hosted in relatively massive galaxies with stellar mass M* ≳ 109 M⊙. Given that galaxy mass is correlated with other BH and galaxy properties, BH mergers tend to also have a higher total BH mass and higher BH accretion rates than the global population of main BHs. These differences generally disappear if the merger population is compared with a BH population sampled with the same galaxy mass distribution as merger hosts. Galaxy mergers can temporarily boost the BH accretion rate and the host’s star formation rate, which can remain active at the BH merger if sub-resolution delays are not taken into account. When dynamical delays are taken into account, the burst has generally faded by the time the BHs merge. BH spins are followed self-consistently in the simulation under the effect of accretion and BH mergers. We find that merging BHs have higher spins than the global population, but similar or somewhat lower spins compared to a mass-matched sample. For our sample, mergers tend to decrease the spin of the final BH remnant.

Geodesic structure of a rotating regular black hole

We examine the dynamics of particles around a rotating regular black hole. In particular we focus on the effects of the characteristic length parameter of the spinning black hole on the motion of the particles by solving the equation of orbital motion. We have found that there is a fourth constant of motion that determines the dynamics of orbits out the equatorial plane similar as in the Kerr black hole. Through detailed analyses of the corresponding effective potentials for massive particles the possible orbits are numerically simulated. A comparison with the trajectories in a Kerr spacetime shows that the differences appear when the black holes rotate slowly for large values of the characteristic length parameter.