Black Hole Spin Parameter Research Articles

Estimating the possible QPOs of [formula omitted] from the parameters of a hairy Kerr black hole

In this paper, we study the dynamics of the shock cone formed around a hairy Kerr black hole due to Bondi-Hoyle-Lyttleton (BHL) accretion and investigate the quasi-periodic oscillations (QPO) behaviors resulting from the black hole-cone interaction, aiming to predict the QPO frequencies that may occur around the M87∗ black hole. To achieve this, we use the hairy Kerr black hole parameters consistent with the observed shadow parameters of M87∗ as initial conditions in numerical simulations, revealing the structure of the resulting shock cone and QPOs in a strong gravitational field. Numerical calculations show that the deviation of the hairy Kerr black hole from the Kerr metric and the hair parameters significantly influence the complex behavior of the resulting QPOs. It is found that the Lense-Thirring effect and the pressure modes trapped within the cone lead to the excitation of QPOs. The hair parameter has been observed to suppress the resulting QPO frequencies. The Lense-Thirring effect, in a strong gravitational field with a black hole spin parameter of a/M>0.7, also suppresses other modes and generates high-frequency QPOs. It is predicted that the QPO frequencies observed around the M87∗ black hole could span a wide range from nHz to mHz. Using both Kerr and hairy Kerr gravities, the QPO frequencies formed around the M87∗ black hole can be explained. Especially in cases where the black hole is spinning rapidly, power spectrum density (PSD) analyses have shown very distinct low-frequency QPOs and resonance conditions in both gravities. By comparing the results obtained from numerical calculations with observational and analytical results, we discuss the observability of the QPO frequencies that may occur around the M87∗ black hole.

Perturbing the Stable Accretion Disk in Kerr and 4D Einstein–Gauss–Bonnet Gravities: Comprehensive Analysis of Instabilities and Dynamics

The study of a disturbed accretion disk holds great significance in the realm of astrophysics, as such events play a crucial role in revealing the nature of disk structure, the release of energy, and the generation of shock waves. Consequently, they can help explain the causes of X-ray emissions observed in black hole accretion disk systems. In this paper, we perturb the stable disk formed by spherical accretion around Kerr and Einstein–Gauss–Bonnet (EGB) black holes. This perturbation reveals one- and two-armed spiral shock waves around the black hole. We find a strong connection between these waves and the black hole spin parameter (a/M) and the EGB coupling constant (α). Specifically, we find that as α increases in the negative direction, the dynamics of the disk and the waves become more chaotic. Additionally, we observe that the angular momentum of the perturbing matter significantly affects mass accretion and the oscillation of the arising shock waves. This allows us to observe changes in QPO frequencies, particularly, perturbations with angular momentum matching the observed C−type low-frequency QPOs of the GRS 1915+105 source. Thus, we conclude that the possibility of the occurrence of shock waves within the vicinity of GRS 1915+105 is substantial.

The 2018 Outburst of MAXI J1820+070 as Seen by Insight-HXMT

We present an analysis of the whole 2018 outburst of the black hole X-ray binary MAXI J1820+070 with Insight-HXMT data. We focus our study on the temporal evolution of the parameters of the source. We employ two different models to fit the disk’s thermal spectrum: the Newtonian model diskbb and the relativistic model nkbb. These two models provide different pictures of the source in the soft state. With diskbb, we find that the inner edge of the disk is close to the innermost stable circular orbit of a fast-rotating black hole and the corona changes geometry from the hard to the soft state. With nkbb, we find that the disk is truncated in the soft state and that the coronal geometry does not change significantly during the whole outburst. However, the model with nkbb can predict an untruncated disk around a fast-rotating black hole if we assume that the disk inclination angle is around 30° (instead of ∼60°, which is the inclination angle of the jet and is usually adopted as the disk inclination angle in the literature) and we employ a high-density reflection model. In such a case, we measure a high value of the black hole spin parameter with observations in the soft state, in agreement with the high spin value found from the analysis of the reflection features and in disagreement with the low spin value found by previous continuum-fitting method measurements with the disk inclination angle set to the value of the jet inclination angle.

Proposing a physical mechanism to explain various observed sources of QPOs by simulating the dynamics of accretion disks around the black holes

We propose a mechanism to explain the low-frequency QPOs observed in X-ray binary systems and AGNs. To achieve this, we perturbed stable accretion disks around Kerr and EGB black holes at different angular velocities, revealing characteristics of shock waves and oscillations on the disk. By applying this perturbation to scenarios with varying alpha values for EGB black holes and different spin parameters for Kerr black holes, we numerically observed changes in the disk dynamic structure and its oscillations. Through various numerical models, we found that the formation of one- and two-armed spiral shock waves on the disk serves as a mechanism for generating QPOs. We compared the QPOs obtained from numerical calculations with the low-frequency QPOs observed in X-ray binary systems and AGN sources, finding high consistency with observations. We observed that the shock mechanism, leading to QPOs, explains the X-ray binaries and AGNs studied in this article. Our numerical findings indicate that QPOs are more strongly dependent on the EGB constant than on the black hole spin parameter. However, we highlighted that the primary impact on oscillations and QPOs is driven by the perturbation angular velocity. The results from the models showed that the perturbation asymptotic speed at V∞=0.2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{\\infty }=0.2$$\\end{document} independently generates QPO frequencies, regardless of the black hole spin parameter and the EGB coupling constant. Therefore, for the moderate value of V∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{\\infty }$$\\end{document}, a two-armed spiral shock wave formed around the black hole is suggested as a decisive mechanism in explaining low-frequency QPOs.

Kinematic Model Yields Two Geo-Synchronous Orbits of E-M System and M-P-D System Validated by Total Energy Analysis

In Black Holes (BH) studies , a well-tested method of total energy analysis is used by which the radius of Innermost Stable Circular Orbit (ISCO) around the central BH is analyzed and the dimensionless spin parameter of BH is extracted. The same total energy analysis is utilized in case of E-M and M-P planet-satellite pairs and their extremum points are obtained. The energy maxima happens to be the inner unstable co-rotational orbit (aG1) and the energy minima happens to be outer stable corotational orbit(aG2) in case of E-M and M-P systems and their values from KM correspond to those obtained from Energy Analysis. This vindicates KM of binary pairs

Toward More Accurate Synthetic Reflection Spectra: Improving the Calculations of Returning Radiation

We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation. Assuming a lamppost coronal geometry, we simulate simultaneous observations of NICER and NuSTAR of bright Galactic black holes and we fit the simulated data with the latest version of relxill (modified to read the table of reflionx, which is the nonrelativistic reflection model used in our calculations). We find that relxill with returning radiation cannot fit well the simulated data when the black hole spin parameter is very high and the coronal height and disk’s ionization parameter are low, and some parameters can be significantly overestimated or underestimated. We can find better fits and recover the correct input parameters as the value of the black hole spin parameter decreases and the value of the coronal height increases.

A Multiwavelength Study of the Hard and Soft States of MAXI J1820+070 During Its 2018 Outburst

We present a comprehensive multiwavelength spectral analysis of the black hole (BH) X-ray binary MAXI J1820+070 during its 2018 outburst, utilizing AstroSat far-UV, soft X-ray, and hard X-ray data, along with (quasi-)simultaneous optical and X-ray data from the Las Cumbres Observatory and NICER, respectively. In the soft state, we detect soft X-ray and UV/optical excess components over and above the intrinsic accretion disk emission (kT in ∼ 0.58 keV) and a steep X-ray power-law component. The soft X-ray excess is consistent with a high-temperature blackbody (kT ∼ 0.79 keV), while the UV/optical excess is described by UV emission lines and two low-temperature blackbody components (kT ∼ 3.87 and ∼0.75 eV). Employing continuum spectral fitting, we determine the BH spin parameter (a = 0.77 ± 0.21), using the jet inclination angle of 64° ± 5° and a mass spanning 5–10 M ☉. In the hard state (HS), we observe a significantly enhanced optical/UV excess component, indicating a stronger reprocessed emission in the outer disk. Broadband X-ray spectroscopy in the HS reveals a two-component corona, each associated with its reflection component, in addition to the disk emission (kT in ∼ 0.19 keV). The softer coronal component dominates the bolometric X-ray luminosity and produces broader relativistic reflection features, while the harder component gets reflected far from the inner disk, yielding narrow reflection features. Furthermore, our analysis in the HS suggests a substantial truncation of the inner disk (≳51 gravitational radii) and a high disk density (∼1020 cm−3).

Investigating the hard state of MAXI J1820 + 070: a comprehensive Bayesian approach to black hole spin and accretion properties

ABSTRACT We analyse the X-ray spectrum of the black hole (BH) X-ray binary MAXI J1820 + 070 using observations from XMM-Newton and NuSTAR during ‘hard’ states of its 2018–2019 outburst. We take a fully Bayesian approach, and this is one of the first papers to present a fully Bayesian workflow for the analysis of an X-ray binary X-ray spectrum. This allows us to leverage the relatively well-understood distance and binary system properties (like inclination and BH mass), as well as information from the XMM-Newton RGS data to assess the foreground X-ray absorption. We employ a spectral model for a ‘vanilla’ disc-corona system: the disc is flat and in the plane perpendicular to the axis of the jet and the BH spin, the disc extends inwards to the innermost stable circular orbit around the BH, and the (non-thermal) hard X-ray photons are up-scattered soft X-ray photons originating from the disc thermal emission. Together, these provide tight constraints on the spectral model and, in combination with the strong prior information about the system, mean we can then constrain other parameters that are poorly understood such as the disc colour correction factor. By marginalizing over all the parameters, we calculate a posterior density for the BH spin parameter, a. Our modelling suggests a preference for low or negative spin values, although this could plausibly be reproduced by higher spins and a modest degree of disc truncation. This approach demonstrates the efficacy and some of the complexities of Bayesian methods for X-ray spectral analysis.

Black Hole Spin Measurements in LMC X-1 and Cyg X-1 Are Highly Model Dependent

The black hole spin parameter, a *, was measured to be close to its maximum value of 1 in many accreting X-ray binaries. In particular, a * ≳ 0.9 was found in a number of studies of LMC X-1. These measurements were claimed to take into account both statistical and systematic uncertainties. We perform new measurements using a recent simultaneous observation by NICER and NuSTAR, providing a data set of high quality. We use the disk continuum method together with improved models for coronal Comptonization. With the standard relativistic disk model and optically thin Comptonization, we obtain values of a * similar to those obtained before. We then consider modifications to the standard model. Using a color correction of 2, we find a * ≈ 0.64–0.84. We then consider disks with dissipation in surface layers. To account for that, we assume the standard disk is covered by a warm and optically thick Comptonizing layer. Our model with the lowest χ 2 then yields a*≈0.40−0.32+0.41 . In order to test the presence of such effects in other sources, we also study an X-ray observation of Cyg X-1 by Suzaku in the soft state. We confirm the previous findings of a * > 0.99 using the standard model, but then we find a weakly constrained a*≈0.82−0.74+0.16 when including an optically thick Comptonizing layer. We conclude that determinations of the spin using the continuum method can be highly sensitive to the assumptions about the disk structure.

Impact of the returning radiation in current tests of the Kerr black hole hypothesis using X-ray reflection spectroscopy

The past 10 years have seen remarkable progress in our capability of analyzing reflection features in the X-ray spectra of accreting black holes. Today X-ray reflection spectroscopy is a mature technique and a powerful tool for studying the accretion process around black holes, measuring black hole spins, and testing Einstein’s theory of General Relativity in the strong field regime. However, current reflection models still rely on a number of simplifications and caution is necessary when we derive very precise measurements. In this paper, we study the impact of the returning radiation on our capability of measuring the properties of black holes using X-ray reflection spectroscopy, and in particular on our capability of testing the Kerr black hole hypothesis. While the returning radiation alters the reflection spectrum of the disk, from the analysis of our simulations we find that models without returning radiation can normally recover well the correct black hole spin parameters and can test the Kerr metric.

An apparent positive relation between spin and orbital angular momentum in X-ray binaries

ABSTRACT The origin of current angular momentum (AM) of the black hole (BH) in X-ray binary (XRB) is still unclear, which is related with the birth and/or the growth of the BH. Here, we collect the spin parameters a* measured in BH XRBs and find an apparent bimodal distribution centered at ∼ 0.17 and 0.83. We find a positive relation between the spin parameter and the orbital period/orbital separation through combining distinct XRB categories, including neutron star (NS) low-mass X-ray binaries (LMXBs), Roche lobe overflow (RLOF) BH XRBs, and wind-fed BH XRBs. It seems that the AM of the compact star and the binary orbit correlates by combining the different XRB systems. These positive relations imply that accretion process is a common mechanism for spinning up the compact star in these diverse XRB systems. We infer that the low and high spin BH XRBs may experience different evolution and accretion history, which corresponds to the bimodal distribution of the BH spin parameters. The low spin BHs (a* < 0.3) are similar to the NS LMXBs, the compact star of which is spun-up by the low-level accretion, and the high spin BHs (a* > 0.5) had experienced a short hypercritical accretion ($\gg \dot{M}_\mathrm{Edd}$) period, during which, the BH spin dramatically increased.

Non‐Linear Electrodynamics in Blandford–Znajek Energy Extraction

AbstractNon‐linear electrodynamics (NLED) is a generalization of Maxwell's electrodynamics for strong fields. It has significant implications for the study of black holes and cosmology and has been extensively studied in the literature, extending from quantum to cosmological contexts. In this work, two new ways to investigate these non‐linear theories are investigated. First, the Blandford‐Znajek mechanism is analyzed in light of this promising theoretical context, providing the general form of the extracted power up to second order in the black hole spin parameter a. It is found that, depending on the NLED model, the emitted power can be extremely increased or decreased, and that the magnetic field lines around the black hole seem to become vertical quickly. Considering only separated solutions, it is found that no monopole solutions exist and this could have interesting astrophysical consequences (not considered here). Last but not least, it is attempted to confine the NLED parameters by inducing the amplification of primordial magnetic fields (“seeds”), thus admitting non‐linear theories already during the early stages of the Universe. However, the latter approach proves to be useful for NLED research only in certain models. These (analytical) results emphasize that the behavior of non‐linear electromagnetic phenomena strongly depends on the physical context and that only a power‐law model seems to have any chance to compete with Maxwell.

Shadow Cast of Rotating Charged Black Hole with Scalar Q-Hair

In this paper, we investigate the shadow cast by non-rotating and rotating charged black holes with scalar Q-hair. We find that in addition to the spin parameter of black hole and inclination angle of the observer, the charge parameter and the self-interaction parameters of the scalar hair also influence the shape of the black hole shadow. Our studies show that the charged black holes with scalar Q-hair always have smaller shadow size compared to those without hair. Moreover, it is found that the parameters significantly affect the shadow observables. In particular, for the fixed spin parameter and inclination angle, a larger charge parameter will increase the shadow size but decrease the shadow distortion, whilst stronger self-interaction parameters have the opposite influence. In short, the shadow of the charged black hole with scalar Q-hair can be distinguished from the Reissner–Nordstro¨m (RN) black hole or Kerr–Newmann (KN) black hole, and they indeed generate new templates with large deviations from general relativity those are invariably smaller in size.

Probing bumblebee gravity with black hole X-ray data

Bumblebee gravity is one of the simplest gravity theories with spontaneous Lorentz symmetry breaking. Since we know a rotating black hole solution in bumblebee gravity, we can potentially test this model with the available astrophysical observations of black holes. In this work, we construct a reflection model in bumblebee gravity and we use our model to analyze the reflection features of a NuSTAR spectrum of the Galactic black hole EXO 1846-031 in order to constrain the Lorentz-violating parameter ell . We find that the analysis of the reflection features in the spectrum of EXO 1846-031 cannot constrain the parameter ell because of a very strong degeneracy between the estimates of ell and of the black hole spin parameter a_*. Such a degeneracy may be broken by combining other observations.

Shadow of topologically charged rotating braneworld black hole

In this paper, we investigate the optical properties by a charged rotating braneworld black hole, in the Randall–Sundrum scenario. We study the horizon, the photon region, the shadow of the black hole and other observables. The results show that in addition to the black hole spin parameter [Formula: see text], the other two parameters, tidal charge [Formula: see text] and electric charge [Formula: see text], are found to affect the horizon, the photon region and the black hole shadow. We also have researched different observables and found that with the increase of the three parameters, the area and perimeter of the black hole shadow decrease, while the deformation of the shadow intensifies. Finally, through the observations of the oblateness [Formula: see text], the circularity deviation [Formula: see text] and the angular diameter [Formula: see text] and the latest M87[Formula: see text] and SgrA[Formula: see text] black hole shadows, the three parameters are analyzed to turn out that those observations give different constraints due to the three parameters.

New Constraints on the Spin of the Black Hole Cygnus X-1 and the Physical Properties of its Accretion Disk Corona

We present a new analysis of NuSTAR and Suzaku observations of the black hole Cygnus X-1 in the intermediate state. The analysis is performed using kerrC, a new model for analyzing spectral and spectropolarimetric X-ray observations of black holes. kerrC builds on a large library of simulated black holes in X-ray binaries. The model accounts for the X-ray emission from a geometrically thin, optically thick accretion disk, the propagation of the X-rays through the curved black hole spacetime, the reflection off the accretion disk, and the Comptonization of photons in coronae of different 3D shapes and physical properties before and after the reflection. We present the results from using kerrC for the analysis of archival NuSTAR and Suzaku observations taken on 2015 May 27–28. The best wedge-shaped corona gives a better fit than the cone-shaped corona. Although we included cone-shaped coronae in the funnel regions above and below the black hole to resemble to some degree the common assumption of a compact lamppost corona hovering above and/or below the black hole, the fit chooses a very large version of this corona that makes it possible to Comptonize a sufficiently large fraction of the accretion disk photons to explain the observed power-law emission. The analysis indicates a black hole spin parameter a (−1 ≤ a ≤ 1) between 0.861 and 0.921. The kerrC model provides new insights into the radial distribution of the energy flux of returning and coronal emission irradiating the accretion disk. kerrC furthermore predicts small polarization fractions around 1% in the 2–8 keV energy range of the recently launched Imaging X-ray Polarimetry Explorer.

Axion cloud evaporation during inspiral of black hole binaries: The effects of backreaction and radiation

Abstract Ultralight scalar fields such as axions can form clouds around rotating black holes (BHs) by the superradiant instability. It is important to consider the evolution of clouds associated with BH binaries for the detectability of the presence of clouds through gravitational wave signals and observations of the mass and spin parameters of BHs. The impact on the axion cloud due to the tidal perturbation from the companion in a binary system was first studied in D. Baumann et al., Phys. Rev. D, 101, 083019. Here, we re-examine this issue taking into account the following points. First, we study the influence of higher-multipole moments. Second, we consider the backreaction due to the angular momentum transfer between the cloud and the orbital motion. This angular momentum transfer further causes the backreaction to the hyperfine split through the change in geometry. Finally, we calculate the particle number flux to infinity induced by the tidal interaction. As a result, we find that the scalar field is not reabsorbed by the BH. Instead, the scalar particles are radiated away to evaporate during the inspiral, irrespective of the direction of the orbital motion, for almost equal mass binaries.

The spins of the Galactic black holes in MAXI J1535–571 and 4U 1630–472 from Insight-HXMT

ABSTRACT Insight-HXMT is the first Chinese X-ray astronomical mission. With a 1–250 keV bandpass, an energy resolution of 150 eV at 6 keV, and without being subject to pile-up distortions, it is suitable to study bright X-ray sources like Galactic black holes. In this paper, we study Insight-HXMT observations of the X-ray binaries MAXI J1535–571 and 4U 1630–472 during their outbursts in 2017 and 2020, respectively. From the analysis of the reflection features, we are able to infer the black hole spin parameter in the two sources. For MAXI J1535–571, we find a spin parameter very close to 1, a* = 0.9916 ± 0.0012 (90 per cent C.L., statistical error), which is consistent with the previous NuSTAR measurement. For 4U 1630–472, we find a moderately high value of the black hole spin parameter, a* = 0.817 ± 0.014 (90 per cent C.L., statistical error), which is lower than the almost extremal value found with NuSTAR data.

Dynamical evolution of the shock cone around 4D Einstein-Gauss Bonnet rotating black hole

In this paper, a Bondi-Hoyle accretion onto the rotating black hole in Einstein-Gauss Bonnet gravity is studied. By injecting the gas from the upstream region of the computational domain, we have found the occurrence of the stable shock cones in the downstream region. The dynamical structures and oscillation properties of these shock cones strongly depend on the black hole spin parameter a and Gauss-Bonnet coupling constant α. It is found that the various values of α can lead the different amounts of matter to pile up close to the black hole horizon, higher α causes bigger oscillation amplitude in the mass accretion rate, and the required time to reach the steady state is getting smaller with the increase in α. Moreover, increasing α in the negative direction causes a decrease in the shock opening angle and this angle slightly increases with the increasing α in the positive direction. We found that the negative values of Gauss-Bonnet coupling constant are more favored to have interesting physical outcomes such as accretion rate and oscillation. In addition, the higher the black hole rotation parameter a emerges the higher the accretion rate. It is also confirmed that, for α→0, the black hole solution in EGB gravity converges to Kerr in general relativity. Furthermore, Gauss-Bonnet coupling constant could be used to constrain the size of the observed shadow of M87⁎ radius for various values of the black hole rotation parameter.

Jets in magnetically arrested hot accretion flows: geometry, power, and black hole spin-down

ABSTRACT We present the results of nine simulations of radiatively inefficient magnetically arrested discs (MADs) across different values of the black hole spin parameter a*: −0.9, −0.7, −0.5, −0.3, 0, 0.3, 0.5, 0.7, and 0.9. Each simulation was run up to $t \gtrsim 100\, 000\, GM/c^3$ to ensure disc inflow equilibrium out to large radii. We find that the saturated magnetic flux level, and consequently also jet power, of MAD discs depends strongly on the black hole spin, confirming previous results. Prograde discs saturate at a much higher relative magnetic flux and have more powerful jets than their retrograde counterparts. MADs with spinning black holes naturally launch jets with generalized parabolic profiles whose widths vary as a power of distance from the black hole. For distances up to 100GM/c2, the power-law index is k ≈ 0.27–0.42. There is a strong correlation between the disc–jet geometry and the dimensionless magnetic flux, resulting in prograde systems displaying thinner equatorial accretion flows near the black hole and wider jets, compared to retrograde systems. Prograde and retrograde MADs also exhibit different trends in disc variability: accretion rate variability increases with increasing spin for a* > 0 and remains almost constant for a* ≲ 0, while magnetic flux variability shows the opposite trend. Jets in the MAD state remove more angular momentum from black holes than is accreted, effectively spinning down the black hole. If powerful jets from MAD systems in Nature are persistent, this loss of angular momentum will notably reduce the black hole spin over cosmic time.