Black Hole Spin Research Articles

On dark energy effects on the accretion physics around a Kiselev spinning black hole

Kiselev metric in the static and rotating form is widely used to test different aspects of the dark energy (DE) effects. We consider a DE Kiselev spacetime, predicting the reduction to the Kerr black hole (BH) solution under suitable conditions on the DE parameters and in this frame we study the effects of the dark energy on BHs and disks accretion. Elaborating a close comparison with the limiting vacuum Kerr spacetime, we focus on thick accretion disks around the central BH in the Kiselev solution, both co-rotating and counter-rotating with respect the central BH. We examine different aspects of BH accretion energetics by focusing on quantities related to the accretion rates and cusp luminosity, when considered the DE presence, related to the pure Kerr central BH. Our findings show that in these conditions heavy divergences with respect to the vacuum case are expected for the DE metrics. A known effect of the Kiselev metric is to lead to a false estimation the BH spin, we confirm this characteristic from the fluids dynamics analysis. Remarkably our results show that DE is affecting differently the accretion physics, and particularly the accretion rate, according to the fluid rotation orientation with respect to the central spinning attractor, leading in some cases to an under-estimation of the BH spin mass ratio. These contrasting aspects emerging in dependence on the fluids rotational orientation can be a distinguishing general DE feature which could lead to a revised observational paradigm where DE existence is considered.

Perturbations of spinning black holes in dynamical Chern-Simons gravity: Slow rotation equations

The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the Ψ0 and Ψ4 Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for Ψ0 and Ψ4, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society 2024

Quenching massive galaxies across cosmic time with the semi-analytic model shark v2.0

ABSTRACT We introduce version 2.0 of the shark semi-analytic model of galaxy formation after many improvements to the physics included. The most significant being (i) a model describing the exchange of angular momentum (AM) between the interstellar medium and stars; (ii) a new active galactic nuclei feedback model which has two modes, a wind and a jet mode, with the jet mode tied to the jet energy production; (iii) a model tracking the development of black hole (BH) spins; (iv) more sophisticated modelling of environmental effects on satellite galaxies; and (v) automatic parameter exploration using Particle Swarm Optimization. We focus on two timely research topics: the structural properties of galaxies and the quenching of massive galaxies. For the former, sharkv2.0 is capable of producing a more realistic stellar size–mass relation with a plateau marking the transition from disc- to bulge-dominated galaxies, and scaling relations between specific AM and mass that agree well with observations. For the quenching of massive galaxies, sharkv2.0 produces massive galaxies that are more quenched than the previous version, reproducing well the observed relations between star formation rate (SFR) and stellar mass, and specific SFR and BH mass at z = 0. shark v2.0 produces a number density of massive-quiescent galaxies >1 dex higher than the previous version, in good agreement with JWST observations at z ≤ 5; predicts a stellar mass function of passive galaxies in reasonably good agreement with observations at 0.5 < z < 5; and environmental quenching to already be effective at z = 5.

The electric charge of black holes within galaxies

We present improved estimates of the electric charge that black holes could hold when these are embedded in the ionised plasma within galaxies. We have implemented the spontaneous emission of charges of opposite sign to that of the black hole via athermal Hawking evaporation, including its dependence on black hole spin, and we have estimated the equilibrium charge that arises as this charge loss is balanced by the continuous accretion of charges from the surrounding plasma. The resulting charge can be several orders of magnitude lower than previously estimated upper limits, but it can surpass the pair production limit noted by Gibbons (1974) by a margin that increases with the amplitude of the black hole spin and the density of the plasma. We also implement a calculation for the net charge of galaxies due to their stellar black holes and to primordial black holes in the case these make up a fraction of the dark matter. We find that these charges lie within the range that would produce adequate magnetic field seeds at the onset of galaxy formation.

What Is the Black Hole Spin in Cyg X-1?

We perform a detailed study of the black hole spin of Cyg X-1, using accurate broadband X-ray data obtained in the soft spectral state by simultaneous NICER and NuSTAR observations, supplemented at high energies by INTEGRAL data. We use the relativistic disk model kerrbb together with different models of the Comptonization high-energy tail and the relativistically broadened reflection features. Unlike most previous studies, we tie the spin parameters of the disk and relativistic broadening models, thus combining the continuum and reflection methods of spin determination. We also consider a likely increase of the disk color correction due to a partial support of the disk by large-scale magnetic fields. We find that such models yield a spin parameter of a*=0.87−0.03+0.04 if the disk inclination is allowed to be free, with i=39°−1+1 . Assuming i = 27.°5, as determined by optical studies of the binary, worsens the fit but leads to similar values of the spin, a*=0.90−0.01+0.01 . In addition, we consider the presence of a warm Comptonization layer on top of the disk, motivated by successful modeling of soft X-ray excesses in other sources with such a model. This dramatically lowers the spin, to a * ≲ 0.1, consistent with the spin measurements from black hole mergers. On the other hand, if the natal spin of Cyg X-1 was low but now a * ≈ 0.9, a period of effective supercritical accretion had to take place in the past. Such accretion could be facilitated by photon advection, as proposed for ultraluminous X-ray sources.

Black Hole–Disk Interactions in Magnetically Arrested Active Galactic Nuclei: General Relativistic Magnetohydrodynamic Simulations Using a Time-dependent, Binary Metric

Perturber objects interacting with supermassive black hole accretion disks are often invoked to explain observed quasiperiodic behavior in active galactic nuclei (AGN). We present global, 3D general relativistic magnetohydrodynamic (GRMHD) simulations of black holes on inclined orbits colliding with magnetically arrested thick AGN disks using a binary black hole spacetime with mass ratio 0.1. We do this by implementing an approximate time-dependent binary black hole metric into the GRMHD Athena++ code. The secondary enhances the unbound mass outflow rate 2–4 times above that provided by the disk in quasiperiodic outbursts, eventually merging into a more continuous outflow at larger distances. We present a simple analytic model that qualitatively agrees well with this result and can be used to extrapolate to unexplored regions of parameter space. We show self-consistently for the first time that spin–orbit coupling between the primary black hole spin and the binary orbital angular momentum causes the accretion disk and jet directions to precess significantly (by 60°–80°) on long timescales (e.g., ∼20 times the binary orbital period). Because this effect may be the only way for thick AGN disks to consistently precess, it could provide strong evidence of a secondary black hole companion if observed in such a system. Besides this new phenomenology, the time-average properties of the disk and accretion rates onto the primary are only marginally altered by the presence of the secondary, consistent with our estimate for a perturbed thick disk. This situation might drastically change in cooled thin disks.

Magnetically driven relativistic jet in the high-redshift blazar OH 471

Context. Understanding the mechanisms that launch and shape powerful relativistic jets from supermassive black holes (SMBHs) in high-redshift active galactic nuclei (AGNs) is crucial for probing the co-evolution of SMBHs and galaxies over cosmic time. Aims. We focus on the high-redshift (z = 3.396) blazar OH 471 to explore the jet launching mechanism in the early Universe. Methods. Using multi-frequency radio monitoring observations and high-resolution Very Long Baseline Interferometry (VLBI) imaging over three decades, we studied the milliarcsecond structure and long-term variability of OH 471. Results. Our spectral modeling of the radio flux densities revealed a synchrotron self-absorbed spectrum, indicating strong magnetic fields within the compact core. By applying the flux freezing approximation, we estimated the magnetic flux carried by the jet. We found that it reaches or exceeds theoretical predictions for jets powered by black hole spin energy via the Blandford-Znajek mechanism. This implies that OH 471 is in a magnetically arrested disk (MAD) state, where the magnetic flux accumulated near the horizon regulates the accretion flow, allowing for an efficient extraction of black hole rotational energy. Conclusions. Our study demonstrates the dominance of MAD accretion in powering the prominent radio flares and relativistic jets observed in the radio-loud AGN named OH 471. Statistical studies of larger samples of high-redshift AGNs will shed light on the role of MAD accretion in launching and accelerating the earliest relativistic jets.

The Dependence of Gamma-Ray Burst Jet Collimation on Black Hole Spin

Gamma-ray bursts (GRBs) are the most luminous events in the Universe and are excellent laboratories to study extreme physical phenomena in the cosmos. Despite a long trajectory of progress in understanding these highly energetic events, there are still many observed features that are yet to be fully explained. Observations of the jet opening angle of long gamma-ray bursts (LGRBs) suggest that LGRB jets are narrower for those GRBs at higher redshift. This phenomenon has been explained in the context of collimation by the stellar envelope, with denser (lower metallicity) stars at higher redshifts able to collimate the jet more effectively. However, until now, the dependence of the jet opening angle on the properties of the central engine has not been explored. We investigate the effect of black hole spin on the jet collimation angle for a magnetically launched jet, using the general relativistic radiation magnetohydrodynamical code ν bhlight. We present 3D results for a range of spin values. The simulations show that higher-spinning black holes tend to create narrower jets. If indeed LGRB progenitors in the early Universe are able to produce black hole central engines with higher spin, this could account for at least some of the observed jet opening angle-redshift correlation.

ARTPOL: Analytical ray-tracing method for spectro-polarimetric properties of accretion disks around Kerr black holes

Spectro-polarimetric signatures of accretion disks in X-ray binaries and active galactic nuclei contain information on the masses and spins of their central black holes, as well as the geometry of matter in proximity to the compact objects. This information can be extracted by means of X-ray polarimetry. In this work, we present a fast analytical ray-tracing technique for polarized light (ARTPOL) that helps us to obtain the spinning black hole parameters from the observed properties. This technique can replace the otherwise time-consuming numerical ray-tracing calculations for any optically thick or geometrically thin accretion flow. For the purposes of illustration, we considered a standard optically thick, geometrically thin accretion disk in the equatorial plane of the Kerr black hole. We show that ARTPOL proves accurate for dimensionless spin parameter a ≤ 0.94 with a speed that is over four orders of magnitude faster than direct ray-tracing calculations. This approach opens up broader prospects for direct fittings of the spectro-polarimetric data from the Imaging X-ray Polarimetry Explorer.

Magnetic flux eruptions at the root of time lags in low-luminosity active galactic nuclei

Sagittarius A$^ is a compact radio source at the center of the Milky Way that has not conclusively shown evidence to support the presence of a relativistic jet. Nevertheless, indirect methods at radio frequencies do indicate consistent outflow signatures. Temporal shifts between features in frequency bands are known as time lags, associated with flares or outflows of the accretion system. It is possible to gain information on the emission and outflow mechanics by interpreting these time lags. By means of a combined general-relativistic magnetrohydrodynamical and radiative transfer modeling approach, we studied the origin of the time lags for magnetically arrested disk models with three black hole spins ($a_ $). We exclusively modeled the emission from the source across a frequency range of $ GHz. Our study also includes a targeted ``slow light'' investigation for one of the best-fitting ``fast light'' windows. We were able to recover the observational time-lag relations in various windows of our simulated light curves. The theoretical interpretation of these most promising time-lag windows is threefold: i) a magnetic flux eruption perturbs the jet-disk boundary and creates a flux tube; ii) the flux tube orbits and creates a clear emission feature; and iii) the flux tube interacts with the jet-disk boundary. The best-fitting windows have an intermediate (i=30$^ inclination and zero black hole spin. The targeted slow light study did not produce better-fitting time lag results, which indicates that the fast versus slow light paradigm is often not intuitively understood and is likely to be influential in timing-sensitive black hole accretion studies. While previous studies have sought to interpret time-lag properties with spherical or jetted expansion models, we show that this picture is too simplistic. Sophisticated general-relativistic magnetrohydrodynamical models consistently capture the observational time-lag behavior, which is rooted in the complex dynamic interplay between the flux tube and coupled disk-jet system.

Photon Rings and Shadow Size for General Axisymmetric and Stationary Integrable Spacetimes

There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and higher-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but do directly probe the free function that defines the event horizon. Based on those expressions, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.

Spin Doctors: How to Diagnose a Hierarchical Merger Origin

Gravitational-wave observations provide the unique opportunity of studying black hole formation channels and histories—but only if we can identify their origin. One such formation mechanism is the dynamical synthesis of black hole binaries in dense stellar systems. Given the expected isotropic distribution of component spins of binary black holes in gas-free dynamical environments, the presence of antialigned or in-plane spins with respect to the orbital angular momentum is considered a tell-tale sign of a merger’s dynamical origin. Even in the scenario where birth spins of black holes are low, hierarchical mergers attain large component spins due to the orbital angular momentum of the prior merger. However, measuring such spin configurations is difficult. Here, we quantify the efficacy of the spin parameters encoding aligned-spin (χ eff) and in-plane spin (χ p ) at classifying such hierarchical systems. Using Monte Carlo cluster simulations to generate a realistic distribution of hierarchical merger parameters from globular clusters, we can infer mergers’ χ eff and χ p . The cluster populations are simulated using Advanced LIGO-Virgo sensitivity during the detector network’s third observing period and projections for design sensitivity. Using a “likelihood-ratio”-based statistic, we find that ∼2% of the recovered population by the current gravitational-wave detector network has a statistically significant χ p measurement, whereas no χ eff measurement was capable of confidently determining a system to be antialigned with the orbital angular momentum at current detector sensitivities. These results indicate that measuring spin-precession through χ p is a more detectable signature of hierarchical mergers and dynamical formation than antialigned spins.

Impacts of nonthermal emission on the images of a black hole shadow and extended jets in two-temperature GRMHD simulations

The recent 230\,GHz observations from the Event Horizon Telescope (EHT) collaboration are able to image the innermost structure of the M87 galaxy showing the shadow of the black hole, a photon ring, and a ring-like structure that agrees with thermal synchrotron emission from the accretion disc. However, at lower frequencies, M87 is characterized by a large-scale jet with clear signatures of nonthermal emission. It is necessary to explore the impacts of nonthermal emission on black hole shadow images and extended jets, especially at lower frequencies. In this study, we aim to compare models with different electron heating prescriptions to one another and to investigate how these prescriptions and nonthermal electron distributions may affect black hole shadow images and the broadband spectrum energy distribution (SED) function. We performed general relativistic radiative transfer (GRRT) calculations in various two-temperature general relativistic magnetohydrodynamic (GRMHD) models utilizing different black hole spins and different electron heating prescriptions coupled with different electron distribution functions (eDFs). Through a comparison with GRRT images and SEDs, we found that when considering a variable kappa eDF, the parameterized prescription of the $R- electron temperature model with h $ = 1 is similar to the model with electron heating in the morphology of images, and the SEDs at a high frequency. This is consistent with previous studies using the thermal eDF. However, the nuance between them could be differentiated through the diffuse extended structure seen in GRRT images, especially at a lower frequency, and the behavior of SEDs at low frequency. The emission from the nearside jet region is enhanced in the case of electron heating provided by magnetic reconnection and it will increase if the contribution from the regions with stronger magnetization is included or if the magnetic energy contribution to kappa eDF mainly in the magnetized regions is considered. Compared with the thermal eDF, the peaks of the SEDs shift to a lower frequency when we consider nonthermal eDF.

Vortex Effects in Merging Black Holes and Saturons.

Vorticity has recently been suggested to be a property of highly spinning black holes. The connection between vorticity and limiting spin represents a universal feature shared by objects of maximal microstate entropy, so-called saturons. Using Q-ball-like saturons as a laboratory for black holes, we study the collision of two such objects and find that vorticity can have a large impact on the emitted radiation as well as on the charge and angular momentum of the final configuration. As black holes belong to the class of saturons, we expect that the formation of vortices can cause similar effects in black hole mergers, leading to macroscopic deviations in gravitational radiation. This could leave unique signatures detectable with upcoming gravitational-wave searches, which can thereby serve as a portal to macroscopic quantum effects in black holes.

Parameter-Free Tour of the Binary Black Hole Population

The continued operation of the Advanced LIGO and Advanced Virgo gravitational-wave detectors is enabling the first detailed measurements of the mass, spin, and redshift distributions of the merging binary black hole population. Our present knowledge of these distributions, however, is based largely on strongly parametric models. Such models typically assume the distributions of binary parameters to be superpositions of “building block” features like power laws, peaks, dips, and breaks. Although this approach has yielded great progress in the initial characterization of the compact binary population, the strong assumptions entailed often leave it unclear which physical conclusions are driven by observation and which by the specific choice of model. In this paper, we instead model the merger rate of binary black holes as an unknown autoregressive process over the space of binary parameters, allowing us to measure the distributions of binary black hole masses, redshifts, component spins, and effective spins with near-complete agnosticism. We find the primary mass spectrum of binary black holes to be doubly peaked, with a fairly flat continuum that steepens at high masses. We identify signs of unexpected structure in the redshift distribution of binary black holes: a uniform-in-comoving volume merger rate at low redshift followed by an increase in the merger rate beyond redshift z≈0.5. Finally, we find that the distribution of black hole spin magnitudes is unimodal and concentrated at small but nonzero values, and that spin orientations span a wide range of spin-orbit misalignment angles but are also moderately unlikely to be truly isotropic. Published by the American Physical Society 2024

The relationship between simulated sub-millimeter and near-infrared images of sagittarius A* from a magnetically arrested black hole accretion flow

Abstract Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, undergoes large-amplitude near-infrared (NIR) flares that can coincide with the continuous rotation of the NIR emission region. One promising explanation for this observed NIR behavior is a magnetic flux eruption, which occurs in three-dimensional General Relativistic Magneto-Hydrodynamic (3D GRMHD) simulations of magnetically arrested accretion flows. After running two-temperature 3D GRMHD simulations, where the electron temperature is evolved self-consistently along with the gas temperature, it is possible to calculate ray-traced images of the synchotron emission from thermal electrons in the accretion flow. Changes in the gas dominated (σ = b2/2ρ < 1) regions of the accretion flow during a magnetic flux eruption reproduce the NIR flaring and NIR emission region rotation of Sgr A* with durations consistent with observation. In this paper, we demonstrate that these models also predict that large (1.5x - 2x) size increases of the sub-millimeter (sub-mm) and millimeter (mm) emission region follow most NIR flares by 20 - 50 minutes. These size increases occur across a wide parameter space of black hole spin (a = 0.3, 0.5, −0.5, 0.9375) and initial tilt angle between the accretion flow and black hole spin axes θ0 (θ0 = 0○, 16○, 30○). We also calculate the sub-mm polarization angle rotation and the shift of the sub-mm spectral index from zero to -0.8 during a prominent NIR flare in our high spin (a = 0.9375) simulation. We show that, during a magnetic flux eruption, a large (∼10rg), magnetically dominated (σ > 1), low density, and high temperature “bubble” forms in the accretion flow. The drop in density inside the bubble and additional electron heating in accretion flow between 15 rg- 25 rg leads to a sub-mm size increase in corresponding images.

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We study the optical properties of spacetime around a novel black hole in general relativity coupled to nonlinear electrodynamics, which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric black hole spacetime. Later, we obtain the rotating black hole solution using the Newman–Janis algorithm and determine the event horizon properties of the black hole. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating black hole. Also, we analyze the photon sphere around the novel black hole and its shadow using celestial coordinates. We obtain that an increase of the black hole spin and charge as well as nonlinear electrodynamics field nonlinearity parameters causes an increase in the distortion parameter of the black hole shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the black hole charge and the nonlinearity parameters using Event Horizon Telescope data from shadow sizes of supermassive black holes Sgr A* and M87*. Finally, the emission rate of black hole evaporation through Hawking radiation is also studied.

Ancestral spin information in gravitational waves from black hole mergers

The heaviest black holes discovered through gravitational waves have masses that are difficult to explain with current standard stellar models. This discrepancy may be due to a series of hierarchical mergers, where the observed black holes are themselves the products of previous mergers. Here we present a method to estimate the masses and spins of previous generations of black holes based on the masses and spins of black holes in a binary. Examining the merger GW190521, we find that assuming black hole spins that are consistent with those of merger remnants will alter the reconstructed ancestral spins when compared to results with uninformed priors. At the same time, the inclusion of black hole spins does not significantly affect the mass distributions of the ancestral black holes.

Rethinking the 67 Hz QPO in GRS 1915+105: Type C quasi-periodic oscillations at the innermost stable circular orbit

Context. We study quasi-periodic oscillations (QPO) at low and high frequency in the variability of the high-energy emission from black hole binaries and their physical interpretation in terms of signatures of General Relativity in the strong-field regime. Aims. We wish to understand the nature of the 67 Hz QPOs observed in the X-ray emission of the peculiar black hole binary GRS 1915+105 within the general classification of QPOs, and to determine the spin of the black hole in the system by applying the relativistic precession model (RPM). Methods. Within the RPM, the only relativistic frequency that is stable in time over a wide range of accretion rates and can be as low as 67 Hz (for a dynamically measured black hole mass) is the nodal frequency at the innermost stable circular orbit (ISCO). In the application of the model, this corresponds to type C QPOs. Under this assumption, it is possible to measure the spin of the black hole by using the mass of the black hole previously obtained via dynamical measurements. We re-analysed a large number of Rossi-XTE observations to determine whether other timing features confirm this hypothesis. Results. The identification of the 67 Hz QPO as the nodal frequency at ISCO yields a value of 0.706 ± 0.034 for the black hole spin. With this spin, the only two QPO detections at higher frequencies available in the literature are consistent with being orbital frequencies at a radius outside ISCO. The high-frequency bumps often observed at frequencies between 10 and 200 Hz follow the correlation expected for orbital and periastron-precession frequencies at even larger radii.

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.