Thick Accretion Disk Research Articles

A Tutorial on the Strong Gravity Effects in Black Hole X-Ray Spectra

This is a tutorial on the strong gravity effects (motion of massive and massless particles in a curved spacetime, evaluation of redshift factors, estimate of physical quantities in different reference frames, etc.) necessary to calculate the electromagnetic spectra of geometrically thin and optically thick accretion disks around black holes. The presentation is intentionally pedagogical, and most calculations are reported step by step. In the disk–corona model, the spectrum of a source has three components: a thermal component from the disk, a Comptonized component from the corona, and a reflection component from the disk. This tutorial reviews only the strong gravity effects, which can be decoupled from the physical processes involving the interaction between matter and radiation. The formulas presented here are valid for stationary, axisymmetric, asymptotically flat, circular spacetimes, so they can be potentially used for a large class of black hole solutions.

Discovery of a Bow-shock Nebula Around the Z Cam-type Cataclysmic Variable SY Cancri

We report the serendipitous discovery of a bow-shock nebula around the cataclysmic variable (CV) SY Cancri. In addition, SY Cnc lies near the edge of a faint Hα-emitting nebula with a diameter of about 15′ . The orientation of the bow shock is consistent with the direction of SY Cnc’s proper motion. Nebulae are extremely rare around CVs, apart from those known to have undergone classical-nova (CN) outbursts; bow shocks and off-center nebulae are even more unusual. Nevertheless, the properties of SY Cnc and its nebulosity are strikingly similar to those of V341 Ara, another CV that is also associated with a bow shock and is likewise off-center with respect to its faint Hα nebula. Both stars are binaries with optically thick accretion disks, belonging to the classes of Z Cam CVs or nova-like variables. We discuss three scenarios to explain their properties. They may have resulted from chance encounters with interstellar gas clouds, with the stars leaving in their wakes material that is recombining after being photoionized by ultraviolet radiation from the CVs. Alternatively, the large nebulae could be ejecta from unobserved CN outbursts in the recent past, which have been decelerated through collisions with the interstellar medium (ISM), while the stars continue to snowplow through the gas. Or the faint Hα nebulae may be ambient ISM that was flash-ionized by a CN outburst in the past and is now recombining.

Direct Collapse Accretion Disks within Dark Matter Halos: Saturation of the Magnetorotational Instability and the Field Expulsion

We have used high-resolution zoom-in simulations of direct collapse to supermassive black hole (SMBH) seeds within dark mater halos in the presence of magnetic fields generated during the collapse, down to 10−5 pc or 2 au. We confirm an efficient amplification of magnetic field during collapse, the formation of a geometrically thick self-gravitating accretion disk inside 0.1 pc, and damping of fragmentation in the disk by the field. This disk differs profoundly from SMBH accretion disks. We find the following: (1) The accretion disk is subject to the magnetorotational instability, which further amplifies the field to near equipartition. No artificial seeding of the disk field has been used. (2) The equipartition toroidal field changes its polarity in the midplane. (3) The nonlinear Parker instability develops, accompanied by the vertical buckling of the field lines, which injects material above the disk, leading to an increase in the disk scale height. (4) With the Coriolis force producing a coherent helicity above the disk, the vertical poloidal field has been generated and amplified. (5) We estimate that the associated outflow will be most probably squashed by accretion. The resulting configuration consists of a magnetized disk with β ≳ 0.1 and its magnetosphere with β ≪ 1, where β = P th/P B is the ratio of thermal to magnetic energy density. (6) The disk is highly variable, due to feeding by variable accretion flow, and strong vortical motions are present. (7) Finally, the negative gradient of the total vertical stress drives an equatorial outflow sandwiched by an inward accretion flow.

Egg-shaped sections of fluid structures around black holes

Astrophysical fluids subjected to the strong gravity of black holes can form rotating toroidal-like structures known as thick accretion discs. In order to facilitate the study of such structures, we introduce approximate empirical formulae for a relatively simple analytical description of their poloidal cross-sections that are usually described only numerically. Our comparisons of the approximate and exact descriptions of the cross-sections of the structures rotating around Schwarzschild and Kerr central black holes, together with the determination of the associated total masses of these structure, indicate a high degree of accuracy for these introduced formulae.

Mass and spin measurements of black hole and neutron stars X-ray binaries through axisymmetric oscillation modes of thick torus

ABSTRACT This paper examines the oscillatory behaviour of relativistic, non-self-gravitating, charged-fluid toroidal structures within the context of the Kerr metric. The primary objective is to explore how thick accretion discs influence the mass and spin measurements of black holes and neutron stars in low-mass X-ray binaries (LMXBs) through quasi-periodic oscillations (QPOs) models. To achieve this, we conduct a local analysis within a general relativistic framework, determining the radial epicyclic and orbital frequencies in a perfect fluid disc. The tori are modelled using a non-Keplerian distribution of specific angular momentum, and we analyse how the oscillation properties depend on the model’s angular momentum distribution parameters. Subsequently, we connect these oscillatory frequencies to high-frequency QPOs observed in LMXBs, enabling us to calculate the optimal mass and spin values for each studied source.

Geometrically thick equilibrium tori around a Schwarzschild black hole in swirling universes

We study geometrically thick non-self gravitating equilibrium tori orbiting a Schwarzschild black hole immersed in swirling universes. This solution is axially symmetric and non-asymptotically flat, and its north and south hemispheres spin in opposite directions. Due to repulsive effects arising from the swirl of the background spacetime, the equilibrium torus exists only in the small swirling case. With the increase of the swirling parameter, the disk structure becomes small and the excretion of matter near the black hole becomes strong. Moreover, the odd Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_2$$\\end{document} symmetry of spacetimes originating from the swirling parameter yields that the orientation of closed equipotential surfaces deviates away from the horizontal axis and the corresponding disk does not longer possess the symmetry with respect to the equatorial plane. These significant features could help to further understand the equilibrium tori and geometrically thick accretion disks around black holes in swirling universes.

An Eddington-limited Accretion Disk Wind in the Narrow-line Seyfert 1 PG 1448+273

PG 1448+273 is a luminous, nearby (z = 0.0645), narrow-line Seyfert 1 galaxy, which likely accretes close to the Eddington limit. Previous X-ray observations of PG 1448+273 with XMM-Newton in 2017 and NuSTAR in 2022 revealed the presence of an ultrafast outflow, as seen through its blueshifted iron (Fe) K absorption profile, where the outflow velocity appeared to vary in the range 0.1−0.3c. In this work, new X-ray observations of PG 1448+273 are presented, in the form of four simultaneous XMM-Newton and NuSTAR observations performed in 2023 July and August. The X-ray spectra appeared at a similar flux in each observation, making it possible to analyze the mean 2023 X-ray spectrum at high signal-to-noise ratio. A broad (σ = 1 keV) and highly blueshifted (E = 9.8 ± 0.4 keV) Fe K absorption profile is revealed in the mean spectrum. The profile can be modeled by a fast, geometrically thick accretion disk wind, which reveals a maximum terminal velocity of v ∞ = −0.43 ± 0.03c, one of the fastest known winds in a nearby active galactic nucleus. As a result, the inferred mass outflow rate of the wind may reach a significant fraction of the Eddington accretion rate.

Rest-frame Optical Spectroscopy of Ten z ∼ 2 Weak Emission-line Quasars

We present near-infrared spectroscopy of 10 weak emission-line quasars (WLQs) at redshifts of z ∼ 2, obtained with the Palomar 200 inch Hale Telescope. WLQs are an exceptional population of type 1 quasars that exhibit weak or no broad emission lines in the ultraviolet (e.g., the C iv λ1549 line), and they display remarkable X-ray properties. We derive Hβ-based single-epoch virial black hole masses (median value 1.7 × 109 M ⊙) and Eddington ratios (median value 0.5) for our sources. We confirm the previous finding that WLQ Hβ lines, as a major low-ionization line, are not significantly weak compared to typical quasars. The most prominent feature of the WLQ optical spectra is the universally weak/absent [O iii] λ5007 emission. They also display stronger optical Fe ii emission than typical quasars. Our results favor the super-Eddington accretion scenario for WLQs, where the weak lines are a result of a soft ionizing continuum; the geometrically thick inner accretion disk and/or its associated outflow is responsible for obscuring the nuclear high-energy radiation and producing the soft ionizing continuum. We also report candidate extreme [O iii] outflows (blueshifts of ≈500 and 4900 km s−1) in one object.

Images of Kerr-MOG black holes surrounded by geometrically thick magnetized equilibrium tori

We adopt general relativistic ray-tracing (GRRT) schemes to study images of Kerr-MOG black holes surrounded by geometrically thick magnetized equilibrium tori, which belong to steady-state solutions of thick accretion disks within the framework of general relativistic magnetohydrodynamics (GRMHD). The black hole possesses an extra dimensionless MOG parameter described its deviation from usual Kerr one. Our results show that the presence of the MOG parameter leads to smaller disks in size, but enhances the total flux density and peak brightness in their images. Combining with observation data of black hole M87* from the Event Horizon Telescope (EHT), we make a constraint on parameters of the Kerr-MOG black hole and find that the presence of the MOG parameter broadens the allowable range of black hole spin.

Misaligned precessing jets are choked by the accretion disc wind

ABSTRACT We analytically and numerically study the hydrodynamic propagation of a precessing jet in the context of tidal disruption events (TDEs) where the star’s angular momentum is misaligned with the black hole spin. We assume that a geometrically thick accretion disc undergoes Lense–Thirring precession around the black hole spin axis and that the jet is aligned with the instantaneous disc angular momentum. At large spin-orbit misalignment angles $\theta _{\it LS}$, the duty cycle along a given angle that the jet sweeps across is much smaller than unity. The faster jet and slower disc wind alternately fill a given angular region, which leads to strong shock interactions between the two. We show that precessing jets can only break out of the wind confinement if $\theta _{\it LS}$ is less than a few times the jet opening angle $\theta _{\rm j}$. The very small event rate of observed jetted TDEs is then explained by the condition of double alignment: both the stellar angular momentum and the observer’s line of sight are nearly aligned with the black hole spin. In most TDEs with $\theta _{\it LS}\gg \theta _{\rm j}$, the jets are initially choked by the disc wind and may only break out later when the disc eventually aligns itself with the spin axis due to the viscous damping of the precession. Such late-time jets may produce delayed radio rebrightening as seen in many optically bright TDEs. Our model is also applicable to jets associated with (stellar mass) black hole-neutron star mergers where the black hole’s spin is misaligned with the orbital angular momentum.

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.

Imaging thick accretion disks and jets surrounding black holes

Based on the horizon-scale magnetofluid model developed in [1], we investigate the millimeter-wave images of a geometrically thick accretion disk or a funnel wall, i.e., the magnetofluid that encloses the base of the jet region, around a Kerr black hole. By employing the numerical method to solve the null geodesic and radiative transfer equations, we obtain the optical appearances at various observational angles and frequencies, generated by the thermal synchrotron radiation within the magnetofluid. For the thick disk, we specifically examine the impact of emission anisotropy on images, concluding that anisotropic synchrotron radiation could play an important role in the observability of the photon ring. For the funnel wall, we find that both the outflow and inflow funnel walls exhibit annular structures on the imaging plane. The outflow funnel wall yields a brighter primary image than the photon ring, whereas the inflow one does not. Based on our investigation, the inflow funnel wall model can not be ruled out by current observations of M87*.

First image of a jet launching from a black hole accretion system: Kinematics

Jets are endemic to both Galactic solar mass and extragalactic supermassive black holes. A recent 86 GHz image of M 87 shows a jet emerging from the accretion ring around a black hole, providing the first direct observational constraint on the kinematics of the jet-launching region in any black hole jetted system. The very wide (∼280 μas), highly collimated, limb-brightened cylindrical jet base is not predicted in current numerical simulations. The emission was shown to be consistent with that of a thick-walled cylindrical source that apparently feeds the flow that produces the bright limbs of the outer jet at an axial distance downstream of 0.4 mas < z < 0.65 mas. The analysis here applies the conservation laws of energy, angular momentum, and magnetic flux to the combined system of the outer jet, the cylindrical jet, and the launch region. It also uses the brightness asymmetries of the jet and counterjet to constrain the Doppler factor. The only global solutions have a source that is located < 34 μas from the event horizon. This includes the Event Horizon Telescope annulus of emission and the regions interior to this annulus. The axial jet begins as a magnetically dominated flow that spreads laterally from the launch radius (< 34 μas). It becomes super-magnetosonic before it reaches the base of the cylindrical jet. The flow is ostensibly redirected and collimated by a cylindrical nozzle formed in a thick accretion disk. The flow emerges from the nozzle as a mildly relativistic (0.3c < v < 0.4c) jet with a significant protonic kinetic energy flux.

The bright black hole X-ray binary 4U 1543–47 during the 2021 outburst: A thick accretion disk inflated by high luminosity

The black hole X-ray binary source 4U 1543–47 experienced a super-Eddington outburst in 2021, reaching a peak flux of up to ∼1.96 × 10−7 erg cm−2 s−1 (∼8.2 Crab) in the 2−10 keV band. Soon after the outburst began, it rapidly transitioned into the soft state. Our goal is to understand how the accretion disk structure deviates from a standard thin disk when the accretion rate is near Eddington. To do so, we analyzed spectra obtained from quasi-simultaneous observations conducted by the Hard X-ray Modulation Telescope (Insight-HXMT), the Nuclear Spectroscopic Telescope Array (NuSTAR), and the Neil Gehrels Swift Observatory (Swift). These spectra are well fitted by a model comprising a disk, a weak corona, and a reflection component. We suggest that the reflection component is caused by disk self-irradiation, that is by photons emitted from the inner disk that return to the accretion disk surface as their trajectories are bent by the strong gravity field. In this scenario, the best-fitting parameters imply that the reflected flux represents more than half of the total flux. Using general relativistic ray-tracing simulations, we show that this scenario is viable when the disk becomes geometrically thick, with a funnel-like shape, as the accretion rate is near or above the Eddington limit. In the specific case of 4U 1543–47, an angle ≳45 deg between the disk surface and the equatorial plane can explain the required amount of self-irradiation.

Magnetic field transport in geometrically thick discs: multidimensional effects on the field strength and inclination angle

ABSTRACT We theoretically investigate the magnetic flux transport in geometrically thick accretion discs which may form around black holes. We utilize a two-dimensional (2D) kinematic mean-field model for poloidal field transport which is governed by both inward advection and outward diffusion of the field. Assuming a steady state, we analytically show that the multidimensional effects prevent the field accumulation towards the centre and reduce the field inclination angle. We also numerically investigate the radial profile of the field strength and the inclination angle for two geometrically thick discs for which (quasi-)analytical solutions exist: radiatively inefficient accretion flows (RIAFs) and super-Eddington accretion flows. We develop a 2D kinematic mean-field code and perform simulations of flux transport to study the multidimensional effects. The numerical simulations are consistent with our analytical prediction. We also discuss a condition for the external field strength that RIAF can be a magnetically arrested disc. This study could be important for understanding the origin of a large-scale magnetic field that drives jets and disc winds around black holes.

Geometrically thick equilibrium tori around a dyonic black hole with quasi-topological electromagnetism

We study geometrically thick and non-self gravitating equilibrium tori orbiting a static spherically symmetric dyonic black hole with quasi-topological electromagnetism. Our results show that the electric and magnetic charges together with the coupling parameter in the quasi-topological electromagnetism lead to a much richer class of equilibrium tori. There are a range of parameters which allow for the existence of double tori. The properties of double equilibrium tori become far richer. There exist transitions between single torus and double tori solutions as we change the specific angular momentum of the fluid. These properties of equilibrium tori could help to understand the dyonic black hole and its thick accretion disk.

Impact of the Accretion Disk Thickness on the Polarization of the Thermal Emission from Stellar Mass Black Holes

The Imaging X-ray Polarimetry Explorer, launched in 2021 December, enables precision measurements of the energy-dependent polarization of the X-ray emission from stellar mass and supermassive black holes. In this paper, we study the impact of the accretion disk geometry on the polarization of the thermal emission of mass-accreting stellar-mass black holes. We present a ray-tracing code that allows us to predict how the X-ray polarization energy spectra change as we dial up the thickness of the accretion disk from a geometrically thin accretion disk to a torus-shaped geometrically thick accretion disk. The results show that thicker disks can produce higher polarization degrees as the thick disk geometries lead to a larger fraction of X-rays reflecting off portions of the disk. We study the observational degeneracies between the disk shape on the one hand and the black hole spin and disk inclination on the other hand. We conclude with a discussion of the implications of our studies for black hole spin measurements.

Thick accretion disk configurations around a compact object in the brane-world scenario

We have studied the equipotential surfaces of a thick accretion disk around a Casadio–Fabbri–Mazzacurati compact object in the brane-world scenario, which possesses a mass parameter together with a parameterized post-Newtonian (PPN) parameter. With the increase in the PPN parameter, the size of the thick accretion disk decreases, but the corresponding Roche lobe size increases. Thus, the larger PPN parameter yields the larger region of existing bound disk structures, where the fluid is not accreted into the central wormhole. Moreover, with the increase in the PPN parameter, the position of the Roche lobe gradually moves away from the central compact object, and the thickness of the region enclosed by the Roche lobe decreases near the compact object but increases in the region far from the compact object. Our results also show that the pressure gradient in the disk decreases with the PPN parameter. These effects of the PPN parameter on the thick accretion disk could help one to further understand compact objects in the brane-world scenario.

Neutrino spin oscillations in a magnetized Polish doughnut

We study the gravitational scattering of ultrarelativistic neutrinos off a rotating supermassive black hole (BH) surrounded by a thick magnetized accretion disk. Neutrinos interact electroweakly with background matter and with the magnetic field in the disk since neutrinos are supposed to possess nonzero magnetic moments. The interaction with external fields results in neutrino spin oscillations. We find that the toroidal magnetic field, inherent in the magnetized Polish doughnut, does not cause a significant spin-flip for any reasonable strengths of the toroidal component. The reduction of the observed neutrino flux, owing to neutrino spin oscillations, is predicted. A poloidal component of the magnetic field gives the main contribution to the modification of the observed flux. The neutrino interaction with matter, rotating with relativistic velocities, also changes the flux of neutrinos. We briefly discuss the idea of the neutrino tomography of magnetic field distributions in accretion disks near BHs.

Effects of Heat Conduction on Blocking off the Super-Eddington Growth of Black Holes at High Redshift

We investigate the effect of conductive heating of the gas surrounding a geometrically thick accretion disk on the growth of a black hole (BH) at high redshift. If a BH is accreting the surrounding gas at a super-Eddington rate, the X-ray radiation from the vicinity of the BH would be highly anisotropic due to the self-shielding of a geometrically thick accretion disk, and then the radiative feedback on the surrounding medium would be suppressed in the equatorial region, within which super-Eddington accretion can continue. However, if this region is sufficiently heated via thermal conduction from the adjacent region that is not shielded and heated by the X-ray irradiation, the surrounding gas becomes isotropically hot, and the Bondi accretion rate would be suppressed and become sub-Eddington. We evaluate the condition under which such isotropic heating is realized and derive new criteria required for super-Eddington accretion.