Black Hole Spin Parameter Research Articles

Giant Metrewave Radio Telescope Monitoring of the Black Hole X-Ray Binary, V404 Cygni during Its 2015 June Outburst

Abstract We report results from a Giant Metrewave Radio Telescope (GMRT) monitoring campaign of the black hole X-ray binary V404 Cygni during its 2015 June outburst. The GMRT observations were carried out at observing frequencies of 1280, 610, 325, and 235 MHz, and extended from June 26.89 UT (a day after the strongest radio/X-ray outburst) to July 12.93 UT. We find the low-frequency radio emission of V404 Cygni to be extremely bright and fast-decaying in the outburst phase, with an inverted spectrum below 1.5 GHz and an intermediate X-ray state. The radio emission settles to a weak, quiescent state ≈11 days after the outburst, with a flat radio spectrum and a soft X-ray state. Combining the GMRT measurements with flux density estimates from the literature, we identify a spectral turnover in the radio spectrum at ≈1.5 GHz on ≈ June 26.9 UT, indicating the presence of a synchrotron self-absorbed emitting region. We use the measured flux density at the turnover frequency with the assumption of equipartition of energy between the particles and the magnetic field to infer the jet radius (≈4.0 × 1013 cm), magnetic field (≈0.5 G), minimum total energy (≈7 × 1039 erg), and transient jet power (≈8 × 1034 erg s−1). The relatively low value of the jet power, despite V404 Cygni’s high black hole spin parameter, suggests that the radio jet power does not correlate with the spin parameter.

Disk–Jet Connection in Active Supermassive Black Holes in the Standard Accretion Disk Regime

Abstract We study the disk–jet connection in supermassive black holes by investigating the properties of their optical and radio emissions utilizing the SDSS DR7 and the NVSS catalogs. Our sample contains 7017 radio-loud quasars with detection both at 1.4 GHz and SDSS optical spectra. Using this radio-loud quasar sample, we investigate the correlation among the jet power ( P jet ), the bolometric disk luminosity ( L disk ), and the black hole mass ( M BH ) in the standard accretion disk regime. We find that the jet powers correlate with the bolometric disk luminosities as log P jet = ( 0.96 ± 0.012 ) log L disk + ( 0.79 ± 0.55 ) . This suggests the jet production efficiency of η jet ≃ 1.1 − 0.76 + 2.6 × 10 − 2 assuming the disk radiative efficiency of 0.1, implying low black hole spin parameters and/or low magnetic flux for radio-loud quasars. But it can be also due to the dependence of this efficiency on the geometrical thickness of the accretion flow, which is expected to be small for quasars accreting at the disk Eddington ratios 0.01 ≲ λ ≲ 0.3 . This low jet production efficiency does not significantly increase even if we set the disk radiative efficiency to be 0.3. We also investigate the fundamental plane in our samples among P jet , L disk , and M BH . We could not find a statistically significant fundamental plane for radio-loud quasars in the standard accretion regime.

A jet acceleration mechanism for the black hole disk system

A jet acceleration mechanism of extracting energy from the disk-corona surrounding a rotating black hole is proposed. In this disk-corona scenario, the central object is a rotating Kerr black hole, and a geometrically thin and optically thick disk is sandwiched by a slab corona. The large-scaled magnetic field plays an important role in jet acceleration mechanism. So we obtain the value of the magnetic field in such a disk-corona system by solving the disk dynamic equations in the context of general relativity. The results show that the value of magnetic field decreases with the increase of disk radius, while increases with the increase of black hole spin parameter a*. Then the analytical expression of the jet power is derived based on the electronic circuit theory of the magnetosphere. It is found that the jet power increases obviously with increasing black hole spin parameter a* and magnetic stress parameter . Furthermore, the calculation results also show that the jet power is mainly from the inner region of the disk-corona system, which is consistent with the observations of the jet. Finally, a sample composed of the 23 Fermi blazars with high jet power is used to explore our jet production mechanism. The conclusion suggests that our jet acceleration mechanism can simulate all sources with high power jet. By comparing with the observational data, we find that these high jet power sources cannot be explained by the Blandford-Znajek mechanism, even if the central object is extreme Kerr black hole.

INDICATION OF THE BLACK HOLE POWERED JET IN M87 BY VSOP OBSERVATIONS

ABSTRACT In order to study the collimation and acceleration mechanism of relativistic jets, the jet streamline of M87 at milliarcsecond scale is extensively investigated with images from VSOP observations at 1.6 and 5 GHz. Thanks to the higher angular resolution of VSOP, especially in the direction transverse to the jet, we resolved the jet streamline into three ridgelines at the scale of milli arcseconds. While the properties of the outer two ridgelines are in good agreement with those measured in previous observations and can be expressed by one power-law line with a power law index of 1.7, an inner ridgeline is clearly observed for the first time. We compared the measured size with the outermost streamline expected by Blandford & Znajek's parabolic solutions, which are anchored at the event horizon, with different black hole spin parameters. We revealed that the observed inner ridgeline is narrower than the prediction, suggesting the origin of the inner ridgeline to be part of a spine originating from the spinning black hole. The inner ridgeline becomes very dim at large distances from the central engine at 5 GHz. We considered two possible cases for this; Doppler beaming and/or radiative cooling. Either case seems to be reasonable for its explanation, and future multi-frequency observations will discriminate those two possibilities.

Shadow of the rotating black hole with quintessential energy in the presence of plasma

We study the shadow of the rotating black hole with quintessential energy (i) in vacuum, (ii) in the presence of plasma with radial power-law density. For the vacuum case, the quintessential field parameter of the rotating black hole significantly changes the shape of the shadow. With increasing quintessential field parameter, the radius of the shadow also increases. With the increase of the radius of the shadow of the rotating black hole, the quintessential field parameter causes decrease of the distortion of the shadow shape: in the presence of the quintessential field parameter, the shadow of the fast rotating black hole becomes too close to the circle. We assume the distant observer of the black hole shadow to be located near the so-called static radius where the gravitational attraction of the black hole is just balanced by the cosmic repulsion. The shape and size of the shadow of quintessential rotating black hole surrounded by plasma depends on (i) plasma parameters, (ii) black hole spin and (iii) quintessential field parameter. With the increase of the plasma refraction index, the apparent radius of the shadow increases. However, for the large values of the quintessential field parameter, the change of the black hole shadow shape due to the presence of plasma is not significant, i.e. the effect of the quintessential field parameter dominates over the plasma effect.

Estimate of the radius responsible for quasinormal modes in the extreme Kerr limit and asymptotic behavior of the Sasaki–Nakamura transformation

The Sasaki-Nakamura transformation gives a short-ranged potential and a convergent source term for the master equation of perturbations in the Kerr space-time. In this paper, we study the asymptotic behavior of the transformation, and present a new relaxed necessary and sufficient condition of the transformation to obtain the short-ranged potential in the assumption that the transformation converges in the far distance. Also, we discuss quasinormal mode frequencies which are determined by the information around the peak of the potential in the WKB analysis. Finally, in the extreme Kerr limit, $a/M \to 1$, where $M$ and $a$ denote the mass and spin parameter of a Kerr black hole, respectively, we find the peak location of the potential, $r_p/M \lesssim 1 + 1.8 \,(1-a/M)^{1/2}$ by using the new transformation. The uncertainty of the location is as large as that expected from the equivalence principle.

Active galactic nuclei atz ∼ 1.5 – III. Accretion discs and black hole spin

This is the third paper in a series describing the spectroscopic properties of a sample of 39 AGN at $z \sim 1.5$, selected to cover a large range in black hole mass ($M_{BH}$) and Eddington ratio ($L/L_{Edd}$). In this paper, we continue the analysis of the VLT/X-shooter observations of our sample with the addition of 9 new sources. We use an improved Bayesian procedure, which takes into account intrinsic reddening, and improved $M_{BH}$ estimates, to fit thin accretion disc (AD) models to the observed spectra and constrain the spin parameter ($a_*$) of the central black holes. We can fit 37 out of 39 AGN with the thin AD model, and for those with satisfactory fits, we obtain constraints on the spin parameter of the BHs, with the constraints becoming generally less well defined with decreasing BH mass. Our spin parameter estimates range from $\sim$$-$0.6 to maximum spin for our sample, and our results are consistent with the "spin-up" scenario of BH spin evolution. We also discuss how the results of our analysis vary with the inclusion of non-simultaneous GALEX photometry in our thin AD fitting. Simultaneous spectra covering the rest-frame optical through far-UV are necessary to definitively test the thin AD theory and obtain the best constraints on the spin parameter.

Constraints on black hole spins with a general relativistic accretion disk corona model

The peaks in the spectra of the accretion disks surrounding massive black holes in quasars are in the far-UV or soft X-ray band, which are usually not observed. However, in the disk corona model, soft photons from the disk are Comptonized to high energy in the hot corona, and the hard X-ray spectra (luminosity and spectral shape) contain information on the incident spectra from the disk. The values of black hole spin parameter a* are inferred from the spectral fitting, which are spread over a large range, ∼ −0.94 to 0.998. We find that the inclination angles and mass accretion rates are well determined by the spectral fitting, but the results are sensitive to the accuracy of black hole mass estimates. No tight constraints on the black hole spins are achieved, if the uncertainties in black hole mass measurements are a factor of four, which are typical for the single-epoch reverberation mapping method. Recently, the accuracy of black hole mass measurement has been significantly improved to 0.2 – 0.4 dex with the velocity resolved reverberation mapping method. The black hole spin can be well constrained if the mass measurement accuracy is ≲ 50%. In the accretion disk corona scenario, a fraction of power dissipated in the disk is transported into the corona, and therefore the accretion disk is thinner than a bare disk for the same mass accretion rate, because the radiation pressure in the disk is reduced. We find that the thin disk approximation, H/R ≲ 0.1, is still valid if 0.3 < ṁ < 0.5, provided half of the dissipated power is radiated in the corona above the disk.

Probing spacetime around Sagittarius A* using modeled VLBI closure phases

The emission region and black hole shadow of Sagittarius A*, the supermassive black hole at the Galactic Center, can be probed with millimeter Very Long Baseline Interferometry. Our goal is to probe the geometry of the emitting plasma around Sgr A* by using modeled mm-VLBI closure phase calculations at 1.3 mm and to constrain the observer's inclination angle and position angle of the black hole spin axis. We have simulated images for three different models of the emission of Sgr A*: an orbiting spot, a disk model, and a jet model. The orbiting spot model was used as a test case scenario, while the disk and jet models are physically driven scenarios based on standard three-dimensional general relativistic magnetohydrodynamic simulations of hot accretion flows. Our results are compared to currently available closure phase observational limits. Our results indicate that more models with closer to edge-on viewing angles are consistent with observational limits. In general, jet and disk geometries can reproduce similar closure phases for different sets of viewing and position angles. Consequently, the favored black hole spin orientation and its magnitude are strongly model dependent. We find that both the jet and the disk models can explain current VLBI limits. We conclude that new observations at 1.3 mm and possibly at longer wavelengths including other triangles of VLBI baselines are necessary to interpret Sgr A* emission and the putative black hole spin parameters.

Model dependence of the multi-transonic behaviour, stability properties and the corresponding acoustic geometry for accretion onto rotating black holes

Stationary, multi-transonic, integral solutions of hydrodynamic axisymmetric accretion onto a rotating black hole have been compared for different geometrical configurations of the associated accretion disc structures described using the polytropic as well as the isothermal equations of state. Such analysis is performed for accretion under the influence of generalised post Newtonian pseudo Kerr black hole potential. The variations of the stationary shock characteristics with black hole spin have been studied in details for all the disc models and are compared for the flow characterised by the two aforementioned equations of state. Using a novel linear perturbation technique it has been demonstrated that the aforementioned stationary solutions are stable, at least upto an astrophysically relevant time scale. It has been demonstrated that the emergence of the horizon related gravity like phenomena (the analogue gravity effects) is a natural consequence of such stability analysis, and the corresponding acoustic geometry embedded within the transonic accretion can be constructed for the propagation of the linear acoustic perturbation of the mass accretion rate. The analytical expression for the associated sonic surface gravity κ has been obtained self consistently. The variations of κ with the black hole spin parameter for all different geometric configurations of matter and for various thermodynamic equations of state have been demonstrated.

PREDICTIONS FOR THE REVERBERATING SPECTRAL LINE FROM A NEWLY FORMED BLACK HOLE ACCRETION DISK: CASE OF TIDAL DISRUPTION FLARES

Tidal Disruption Events (TDEs) can be perfect probes of dormant SMBHs in normal galaxies. During the rising phase, the accretion luminosity can increase by orders of magnitude in several weeks and the emergent ionizing radiation illuminates the fresh accretion flow. In this paper, we simulated the evolution of the expected spectral line profile of iron due to such a flare by using a ray-tracing code with effects of general relativity (GR) taken into account. We found that the time-dependent profile changes significantly with black hole spin, inclination angle with respect to the black-hole equatorial plane, and the expansion velocity of the ionization front. At low values of spin, a "loop" feature appears in the line profile vs. time plot when the inclination is no less than $30^\circ$ and the expansion velocity $v_{\rm exp}$ is no less than half speed of light, due to a shadow in the emission of the truncated disk. In the light curve two peaks occur depending on the inclination angle. At large $v_{\rm exp}$, a shallow "nose" feature may develop ahead of the loop, its duration depends on the expansion velocity and the inclination angle. We explore the entire interval of black hole spin parameter ranging from extreme prograde to extreme retrograde rotation, $-1<a<1$. In the prograde case, a low-energy tail appears to be more pronounced in the evolving centroid energy of the line. Our results demonstrate the importance to search for X-ray spectral lines in the early phase of TDE flares in order to constrain black hole mass and spin, as well as properties of the innermost accretion flow.

JET LUMINOSITY OF GAMMA-RAY BURSTS: THE BLANDFORD–ZNAJEK MECHANISM VERSUS THE NEUTRINO ANNIHILATION PROCESS

A neutrino-dominated accretion flow (NDAF) around a rotating stellar-mass black hole (BH) is one of the plausible candidates for the central engine of gamma-ray bursts (GRBs). Two mechanisms, i.e., Blandford-Znajek (BZ) mechanism and neutrino annihilation process, are generally considered to power GRBs. Using the analytic solutions from Xue et al. (2013) and ignoring the effects of the magnetic field configuration, we estimate the BZ and neutrino annihilation luminosities as the functions of the disk masses and BH spin parameters to contrast the observational jet luminosities of GRBs. The results show that, although the neutrino annihilation processes could account for most of GRBs, the BZ mechanism is more effective, especially for long-duration GRBs. Actually, if the energy of afterglows and flares of GRBs is included, the distinction between these two mechanisms is more significant. Furthermore, massive disk mass and high BH spin are beneficial to power high luminosities of GRBs. Finally, we discuss possible physical mechanisms to enhance the disk mass or the neutrino emission rate of NDAFs and relevant difference between these two mechanisms.

Fourth-order split monopole perturbation solutions to the Blandford-Znajek mechanism

The Blandford-Znajek (BZ) mechanism describes a physical process for the energy extraction from a spinning black hole (BH), which is believed to power a great variety of astrophysical sources, such as active galactic nuclei and gamma ray bursts. The only known analytic solution to the BZ mechanism is a split monopole perturbation solution up to $O({a}^{2})$, where $a$ is the spin parameter of a Kerr black hole. In this paper, we extend the monopole solution to higher order $\ensuremath{\sim}O({a}^{4})$. We carefully investigate the structure of the BH magnetosphere, including the angular velocity of magnetic field lines $\mathrm{\ensuremath{\Omega}}$, the toroidal magnetic field ${B}^{\ensuremath{\phi}}$, as well as the poloidal electric current $I$. In addition, the relevant energy extraction rate $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{E}$ and the stability of this high-order monopole perturbation solution are also examined.

Shadow of a Kerr-like black hole

AbstractThe shadow of a Kerr-like black hole has been considered and it was shown that in addition to the specific angular momentum a, deformation parameter of Kerr-like space-time essentially deforms the shape of the black hole shadow. For a given value of the black hole spin parameter a, the presence of a deformation parameter ε reduces the shadow and enlarges its deformation with respect to the one in the Kerr space-time.

The black hole spins of quasars

AbstractWe present the estimates of the black hole spins of five quasars. The peaks of the spectra of the accretion discs surrounding massive black holes in quasars are in the far-UV or soft X-ray band, which are usually not observed. However, in the disc corona model, the soft photons from the disc are Comptonized to high energy in the hot corona, and the hard X-ray spectra (luminosity and spectral shape) contain the information of the incident spectra from the disc. The values of black hole spin parameter a are inferred from the spectral fitting, which spread over a large range, ~ −0.94 to 0.998.

Possible imprints of cosmic strings in the shadows of galactic black holes

We examine the shadow cast by a Kerr black hole pierced by a cosmic string. The observable images depend not only on the black hole spin parameter and the angle of inclination, but also on the deficit angle yielded by the cosmic string. The dependence of the observable characteristics of the shadow on the deficit angle is explored. The imprints in the black hole shadow left by the presence of a cosmic string can serve in principle as a method for observational detection of such strings.

Measuring the Kerr spin parameter of regular black holes from their shadow

In a previous paper, one of us has showed that, at least in some cases,the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the ``shadow'' of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of the Kerr spin parameter of the Bardeen and Hayward regular black holes from their shadow, and we then compare the result with the estimate inferred from the Kα iron line and from the frequency of the innermost stable circular orbit. For non-rotating black holes, the shadow approach provides different values, and therefore the Kerr black hole hypothesis can potentially be tested. For near extremal objects, all the approaches give quite similar results, and therefore it is not possible to constrain deviations from theKerr solution. The present work confirms that it is definitively challenging to test this kind of metrics, even with future facilities. However, the detection of a source that looks like a fast-rotating Kerr black hole can put meaningful constraints on the nature of the compact object.

Shadow of rotating non-Kerr black hole

The shadow of a rotating non-Kerr black hole has been studied, and it was shown that in addition to the specific angular momentum $a$, the deformation parameter of non-Kerr spacetime essentially deforms the shape of the black hole shadow. For a given value of the black hole spin parameter $a$, the presence of a deformation parameter $ϵ$ reduces the shadow and enlarges its deformation with respect to the one in the Kerr spacetime. Optical features of the rotating non-Kerr black hole in terms of rotation of the polarization vector along null congruences have been studied. A comparison of the obtained theoretical results on the polarization angle with the observational data on Faraday rotation measurements provides the upper limit for the dimensionless deformation parameter as $ϵ\ensuremath{\le}19$.

Corotation resonance and overstable oscillations in black hole accretion discs: general relativistic calculations

We study the dynamics of spiral waves and oscillation modes in relativistic rotating discs around black holes. Generalizing the Newtonian theory, we show that wave absorption can take place at the corotation resonance, where the pattern frequency of the wave matches the background disc rotation rate. We derive the general relativistic expression for the disc vortensity (vorticity divided by surface density), which governs the behaviour of density perturbation near corotation. Depending on the gradient of the generalized disc vortensity, corotational wave absorption can lead to the amplification or damping of the spiral wave. We apply our general theory of relativistic wave dynamics to calculate the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the inner-most region of a black hole accretion disc. Because general relativity changes the profiles of the radial epicyclic frequency and disc vortensity near the inner disc edge close to the black hole, these p-modes can become overstable under appropriate conditions. We present the numerical results of the frequencies and growth rates of p-modes for various black hole spin and model disc parameters (the surface density profile and sound speed), and discuss their implications for understanding the enigmatic high-frequency quasi-periodic oscillations observed in black hole X-ray binaries.

Shadow of rotating Hořava-Lifshitz black hole

The shadow of rotating Hořava-Lifshitz black hole has been studied and it was shown that in addition to the specific angular momentum a, parameters of Hořava-Lifshitz spacetime essentially deform the shape of the black hole shadow. For a given value of the black hole spin parameter a, the presence of a parameter Λ W and KS parameter ω enlarges the shadow and reduces its deformation with respect to the one in the Kerr spacetime. We have found a dependence of radius of the shadow R s and distortion parameter δ s from parameter Λ W and KS parameter ω both. Optical features of the rotating Hořava-Lifshitz black hole solutions are treated as emphasizing the rotation of the polarization vector along null congruences. A comparison of the obtained theoretical results on polarization angle with the observational data on Faraday rotation measurements provides the upper limit for the δ parameter as δ≤2.1⋅10−3.