Thin Accretion Flows Research Articles

Electron Heating in the Transrelativistic Perpendicular Shocks of Tilted Accretion Flows

General relativistic magnetohydrodynamic (GRMHD) simulations of black hole tilted disks—where the angular momentum of the accretion flow at large distances is misaligned with respect to the black hole spin—commonly display standing shocks within a few to tens of gravitational radii from the black hole. In GRMHD simulations of geometrically thick, optically thin accretion flows, applicable to low-luminosity sources like Sgr A* and M87*, the shocks have transrelativistic speed, moderate plasma beta (the ratio of ion thermal pressure to magnetic pressure is β pi1 ∼ 1–8), and low sonic Mach number (the ratio of shock speed to sound speed is M s ∼ 1–6). We study such shocks with 2D particle-in-cell simulations, and we quantify the efficiency and mechanisms of electron heating for the special case of preshock magnetic fields perpendicular to the shock direction of propagation. We find that the postshock electron temperature T e2 exceeds the adiabatic expectation T e2,ad by an amount Te2/Te2,ad−1≃0.0016Ms3.6 , nearly independent of the plasma beta and of the preshock electron-to-ion temperature ratio T e1/T i1, which we vary from 0.1 to unity. We investigate the heating physics for M s ∼ 5–6 and find that electron superadiabatic heating is governed by magnetic pumping at T e1/T i1 = 1, whereas heating by B-parallel electric fields (i.e., parallel to the local magnetic field) dominates at T e1/T i1 = 0.1. Our results provide physically motivated subgrid prescriptions for electron heating at the collisionless shocks seen in GRMHD simulations of black hole accretion flows.

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.

Investigating shadow images and rings of the charged Horndeski black hole illuminated by various thin accretions

In this paper, we investigate the shadows and rings of the charged Horndeski black hole illuminated by accretion flow that is both geometrically and optically thin. We consider two types of accretion models: spherical and thin-disk accretion flow. We find that in both types of models, the size of the charged Horndeski black hole shadow decreases with the increase of the charge, and it decreases more slowly for the Reissner–Nordström (RN) black hole. In the spherical accretion flow model, we find that the increase of the charge of Horndeski black hole brightens the light ring around it, and it brightens more significantly in comparison with RN black hole. Due to the Doppler effect, the charged Horndeski black holes with accretion flow of radial motion have darker shadows than those with the static accretion flow, but the size of the shadow is not affected by accretion flow motion. In the thin disk-shaped accretion flow model, we find that the brightness of the light ring around the charged Horndeski black hole is dominated by the direct emission from the accretion flow, and the contribution from lensed rings is relatively small, and that from the photon rings is negligible. We also find that the ring brightness decreases as the charge of Horndeski black hole increases, and the decrease is more significant than that in the RN black hole case. Moreover, the radiation position of the accretion flow can affect the shadow size and the ring brightness of the charged Horndeski black hole.

Kinematics and Collimation of the Two-sided Jets in NGC 4261: VLBI Study on Subparsec Scales

We report multifrequency VLBI studies of the subparsec scale structure of the two-sided jets in the nearby radio galaxy NGC 4261. Our analyses include new observations using the source frequency phase referencing technique with the Very Long Baseline Array at 44 and 88 GHz, as well as archival data at 15 and 43 GHz. Our results show an extended double-sided structure at 43/44 GHz and provide a clear image of the nuclear region at 88 GHz, showing a core size of ∼0.09 mas and a brightness temperature of ∼1.3 × 109 K. Proper motions are measured for the first time in the two-sided jets, with apparent speeds ranging from 0.31 ± 0.14 c to 0.59 ± 0.40 c in the approaching jet and 0.32 ± 0.14 c in the receding jet. The jet-to-counterjet brightness ratio allows us to constrain the viewing angle to between ∼54° and 84° and the intrinsic speed to between ∼0.30 c and 0.55 c. We confirm the parabolic shape of the upstream jet on both sides of the central engine, with a power-law index of 0.56 ± 0.07. Notably, the jet collimation is found to be already completed at subparsec scales, with a transition location of about 0.61 pc, which is significantly smaller than the Bondi radius of 99.2 pc. This behavior can be interpreted as the initial confinement of the jet by external pressure from either the geometrically thick, optically thin advection-dominated accretion flows or the disk wind launched from it. Alternatively, the shape transition may also be explained by the internal flow transition from a magnetically dominated to a particle-dominated regime.

Accretion within the innermost stable circular orbit: analytical thermodynamic solutions in the adiabatic limit

ABSTRACT We present analytical solutions for the thermodynamic (temperature, pressure, density, etc.) properties of thin accretion flows in the region within the innermost stable circular orbit (ISCO) of a Kerr black hole, the first analytical solutions of their kind. These solutions are constructed in the adiabatic limit and neglect radiative losses, an idealization valid for a restricted region of parameter space. We highlight a number of remarkable properties of these solutions, including that these solutions cool for radii rI/2 < r < rI, before increasing in temperature for 0 < r < rI/2, independent of black hole spin and assumptions regarding the equation of state of the accretion flow. The radiative temperature of these solutions can, for some values of the free parameters of the theory, peak within the ISCO and not in the main body of the disc. These solutions represent a fundamentally new class of analytical accretion solutions, which are both non-circular and non-radial in character.

Prospects for Ray-tracing Light Intensity and Polarization in Models of Accreting Compact Objects Using a GPU

The Event Horizon Telescope (EHT) has recently released high-resolution images of accretion flows onto two supermassive black holes. Our physical understanding of these images depends on the accuracy and precision of numerical models of plasma and radiation around compact objects. The goal of this work is to speed up radiative-transfer simulations used to create mock images of black holes for comparison with the EHT observations. A ray-tracing code for general relativistic and fully polarized radiative transfer through plasma in strong gravity is ported onto a graphics processing unit (GPU). We describe our GPU implementation and carry out speedup tests using models of optically thin advection-dominated accretion flow onto a black hole realized semianalytically and in 3D general relativistic magnetohydrodynamic simulations, low and very high image pixel resolutions, and two different sets of CPU+GPUs. We show that a GPU with high double precision computing capability can significantly reduce the image production computational time, with a speedup factor of up to approximately 1200. The significant speedup facilitates, e.g., dynamic model fitting to the EHT data, including polarimetric data. The method extension may enable studies of emission from plasma with nonthermal particle distribution functions for which accurate approximate synchrotron emissivities are not available. The significant speedup reduces the carbon footprint of the generation of the EHT image libraries by at least an order of magnitude.

Measuring Photon Rings with the ngEHT

General relativity predicts that images of optically thin accretion flows around black holes should generically have a “photon ring”, composed of a series of increasingly sharp subrings that correspond to increasingly strongly lensed emission near the black hole. Because the effects of lensing are determined by the spacetime curvature, the photon ring provides a pathway to precise measurements of the black hole properties and tests of the Kerr metric. We explore the prospects for detecting and measuring the photon ring using very long baseline interferometry (VLBI) with the Event Horizon Telescope (EHT) and the next-generation EHT (ngEHT). We present a series of tests using idealized self-fits to simple geometrical models and show that the EHT observations in 2017 and 2022 lack the angular resolution and sensitivity to detect the photon ring, while the improved coverage and angular resolution of ngEHT at 230 GHz and 345 GHz is sufficient for these models. We then analyze detection prospects using more realistic images from general relativistic magnetohydrodynamic simulations by applying “hybrid imaging”, which simultaneously models two components: a flexible raster image (to capture the direct emission) and a ring component. Using the Bayesian VLBI modeling package Comrade.jl, we show that the results of hybrid imaging must be interpreted with extreme caution for both photon ring detection and measurement—hybrid imaging readily produces false positives for a photon ring, and its ring measurements do not directly correspond to the properties of the photon ring.

Outer disc edge: properties of low-frequency aperiodic variability in ultracompact interacting binaries

ABSTRACT Flickering, and more specifically aperiodic broad-band variability, is an important phenomenon used in understanding the geometry and dynamics of accretion flows. Although the inner regions of accretion flows are known to generate variability on relatively fast time-scales, the broad-band variability generated in the outer regions has mostly remained elusive due to its long intrinsic variability time-scales. Ultracompact AM CVn systems are relatively small when compared to other accreting binaries and are well suited to search and characterize low-frequency variability. Here, we present the first low-frequency power spectral analysis of the ultracompact accreting white dwarf system SDSS J1908+3940. The analysis reveals a low-frequency break at ∼6.8 × 10−7 Hz in the time-averaged power spectrum as well as a second higher frequency component with characteristic frequency of ∼1.3 × 10−4 Hz. We associate both components with the viscous time-scales within the disc through empirical fits to the power spectrum as well as analytical fits using the fluctuating accretion disc model. Our results show that the low-frequency break can be associated with the outer disc regions of a geometrically thin accretion flow. The detection of the low-frequency break in SDSS J1908+3940 provides a precedent for further detection of similar features in other ultracompact accreting systems. More importantly, it provides a new observable that can help constrain simulations of accretion flows.

How narrow is the M87* ring – II. A new geometric model

ABSTRACTThe 2017 Event Horizon Telescope (EHT) observations of M87* detected a ring-shaped feature ∼40 μas in diameter, consistent with the event horizon scale of a black hole of the expected mass. The thickness of this ring, however, proved difficult to measure, despite being an important parameter for constraining the observational appearance. In the first paper of this series, we asked whether the width of the ring was sensitive to the choice of likelihood function used to compare observed closure phases and closure amplitudes to model predictions. In this paper, we investigate whether the ring width is robust to changes in the model itself. We construct a more realistic geometric model with two new features: an adjustable radial falloff in brightness, and a secondary ‘photon ring’ component in addition to the primary annulus. This thin, secondary ring is predicted by gravitational lensing for any black hole with an optically thin accretion flow. Analysing the data using the new model, we find that the primary annulus remains narrow (fractional width ≤ 0.25) even with the added model freedom. This provides further evidence in favour of a narrow ring for the true sky appearance of M87*, a surprising feature that, if confirmed, would demand theoretical explanation. Comparing the Bayesian evidence for models with and without a secondary ring, we find no evidence for the presence of a lensed photon ring in the 2017 observations. However, the techniques we introduce may prove useful for future observations with a larger and more sensitive array.

QED and accretion flow models effect on optical appearance of Euler–Heisenberg black holes

Taking the quantum electrodynamics (QED) effect into account, we investigate the geometrical-optics appearance of the Euler–Heisenberg (EH) black hole (BH) under the different accretion flows context, which depends on the BH space-time structure and different sources of light. The more significant magnetic charge leads to the smaller shadow radius for the EH BH, while the different values of the EH parameter do not ruin it. Different features of the corresponding two-dimensional shadow images are derived for the three optically thin accretion flow models. It is shown that the total observed intensity in the static spherical accretion flow scenario leads than that of the infalling spherical accretion flow under same parameters, but the size and position of the EH BH shadows do not change in both of these accretions flows, implying that the BH shadow size depends on the geometric space-time and the shadows luminosities rely on the accretion flow morphology. Of particular interest is that a thin disk accretion model illuminated the BH, we found that the contribution of the lensing ring to the total observed flux is less than 5%, and the photon ring is less than 2%, indicating that the direct emission dominates the optical appearance of the EH BH. It is also believed that the optical appearance of the BH image depends on the accretion disk radiation position in this scenario, which can serve as a probe for the disk structure around the active galactic nucleus (AGN) of M87^{*} like.

Heating or Cooling: Study of Advective Heat Transport in the Inflow and the Outflow of Optically Thin Advection-dominated Accretion Flows

Advection is believed to be the dominant cooling mechanism in optically thin advection-dominated accretion flows (ADAFs). When outflow is considered, however, the first impression is that advection should be of opposite sign in the inflow and the outflow, due to the opposite direction of radial motion. Then how is the energy balance achieved simultaneously? We investigate the problem in this paper, analyzing the profiles of different components of advection with self-similar solutions of ADAFs in spherical coordinates (r θ ϕ). We find that for n < 3γ/2 − 1, where n is the density index in ρ ∝ r −n and γ is the heat capacity ratio, the radial advection is a heating mechanism in the inflow and a cooling mechanism in the outflow. It becomes 0 for n = 3γ/2 − 1, and turns to a cooling mechanism in the inflow and a heating mechanism in the outflow for n > 3γ/2 − 1. The energy conservation is only achieved when the latitudinal (θ direction) advection is considered, which takes an appropriate value to maintain energy balance, so that the overall effect of advection, no matter the parameter choices, is always a cooling mechanism that cancels out the viscous heating everywhere. For the extreme case of n = 3/2, latitudinal motion stops, viscous heating is balanced solely by radial advection, and no outflow is developed.

Influence of accretion flow and magnetic charge on the observed shadows and rings of the Hayward black hole

The feature of the observed shadows and rings of an astrophysical black hole (BH) may depend on its accretion flows and magnetic charge. We find that the shadow radii and critical impact parameters of the Hayward BH are decreased with the increase of the magnetic charge. Comparing the Schwarzschild BH with the Hayward BH using the ray-tracing method, we show that the density and deflection of lights increase with the magnetic charge, and the BH singularity does not affect the generation of the shadow. Based on three optically thin accretion flow models, the two-dimensional shadows in celestial coordinates are derived. It is found that the shadow and photon ring luminosities of a Hayward BH surrounded by infalling spherical accretion flow are dimmer than that of a static spherical accretion flow. Taking three kinds of inner radii at which the accretion flow stops radiating, we find that the observed luminosity of a Hayward BH surrounded by a thin disk accretion flow is dominated by the direct emission, and the photon ring emission has a weak influence on it. These results suggest that the size of the observed shadow is related to the space-time geometry, and the luminosities of both the shadows and rings are affected by the accretion flow property and the BH magnetic charge.

Tracking the evolution of the accretion flow in MAXI J1820+070 during its hard state with the JED-SAD model

Context. X-ray binaries in outburst typically show two canonical X-ray spectral states (i.e., hard and soft states), as well as different intermediate states, in which the physical properties of the accretion flow are known to change. However, the truncation of the optically thick disk and the geometry of the optically thin accretion flow (corona) in the hard state are still debated. Recently, the JED-SAD paradigm has been proposed for black hole X-ray binaries, aimed at addressing the topic of accretion and ejection and their interplay in these systems. According to this model, the accretion flow is composed of an outer standard Shakura-Sunyaev disk (SAD) and an inner hot jet emitting disk (JED). The JED produces both hard X-ray emission, effectively playing the role of the hot corona, and radio jets. The disruption of the JED at the transition to the soft state coincides with the quenching of the jet. Aims. In this paper we use the JED-SAD model to describe the evolution of the accretion flow in the black hole transient MAXI J1820+070 during its hard and hard-intermediate states. Unlike the previous applications of this model, the Compton reflection component has been taken into account. Methods. We use eight broadband X-ray spectra, including NuSTAR, NICER, and the Neil Gehrels Swift Observatory data, providing a total spectral coverage of 0.8–190 keV. The data were directly fitted with the JED-SAD model. We performed the procedure twice, considering two different values for the innermost stable circular orbit (ISCO): 4 RG (a* = 0.55) and 2 RG (a* = 0.95). Results. Our results suggest that the optically thick disk (the SAD) does not extend down to the ISCO in any of the considered epochs. In particular, assuming RISCO = 4 RG, as the system evolves toward the transitional hard-intermediate state, we find an inner radius within a range of ∼60 RG in the first observation down to ∼30 RG in the last one. The decrease of the inner edge of the SAD is accompanied by an increase in the mass-accretion rate. However, when we assume RISCO = 2 we find that the mass accretion rate remains constant and the evolution of the accretion flow is driven by the decrease in the sonic Mach number mS, which is unexpected. In all hard–intermediate state observations, two reflection components, characterized by different values of ionization, are required to adequately explain the data. These components likely originate from different regions of the SAD. Conclusions. The analysis performed provides a coherent physical evolution of the accretion flow in the hard and hard-intermediate states and supports a truncated disk scenario. We show that a flared outer disk could, in principle, explain the double reflection component. The odd results obtained for RISCO = 2 RG can also be considered as further evidence that MAXI J1820+070 harbors a moderately spinning black hole, as suggested in other works.

Study of relativistic accretion flow in Kerr-Taub-NUT spacetime

We study the properties of the relativistic, steady, axisymmetric, low angular momentum, inviscid, advective, geometrically thin accretion flow in a Kerr-Taub-NUT (KTN) spacetime which is characterized by the Kerr parameter ($a_{\rm k}$) and NUT parameter ($n$). Depending on $a_{\rm k}$ and $n$ values, KTN spacetime represents either a black or a naked singularity. We solve the governing equations that describe the relativistic accretion flow in KTN spacetime and obtain all possible global transonic accretion solutions around KTN black hole in terms of the energy $({\cal E})$ and angular momentum $(\lambda)$ of the flow. We identify the region of the parameter space in $\lambda-{\cal E}$ plane that admits the flow to possess multiple critical points for KTN black hole. We examine the modification of the parameter space due to $a_{\rm k}$ and $n$ and find that the role of $a_{\rm k}$ and $n$ in determining the parameter space is opposite to each other. This clearly indicates that the NUT parameter $n$ effectively mitigates the effect of black hole rotation in deciding the accretion flow structure. Further, we calculate the maximum disc luminosity ($L_{\rm max}$) corresponding to the accretion solutions around the KTN black hole and for a given set of $a_{\rm k}$ and $n$. In addition, we also investigate all possible flow topologies around the naked singularity and find that there exists a region around the naked singularity which remains inaccessible to the flow. We study the critical point properties for naked singularities and find that the flow possesses maximum of four critical points. Finally, we obtain the parameter space for multiple critical points for naked singularity and find that parameter space is shrunk and shifted to lower $\lambda$ and higher ${\cal E}$ side as $a_{\rm k}$ is increased which ultimately disappears.

Physical conditions in thin laminar-convective accretion flows

The physical conditions of convection appearance in laminar accretion flows with microscopic transport coefficients are examined. Hot sparse ionised flow with periods below an hour found to be optically thin and have convective layer. Cold sparse molecular flow with period about a year found to be optically thin too and are fully convective. Ranges of temperature, density and period of optically thick laminar accretion flow are shown.

The absence of a thin disc in M81*

We present the results of simultaneous Suzaku and NuSTAR observations of the nearest Low-Luminosity Active Galactic Nucleus (LLAGN), M81*. The spectrum is well described by a cut-off power law plus narrow emission lines from Fe K$\alpha$, Fe XXV and Fe XXVI. There is no evidence of Compton reflection from an optically thick disc, and we obtain the strongest constraint on the reflection fraction in M81* to date, with a best-fit value of $R = 0.0$ with an upper limit of $R < 0.1$. The Fe K$\alpha$ line may be produced in optically thin, $N_H = 1 \times 10^{23}$ cm$^{-2}$, gas located in the equatorial plane that could be the broad line region. The ionized iron lines may originate in the hot, inner accretion flow. The X-ray continuum shows significant variability on $\sim 40$ ks timescales suggesting that the primary X-ray source is $\sim 100$s of gravitational radii in size. If this X-ray source illuminates any putative optically thick disc, the weakness of reflection implies that such a disc lies outside a few $\times 10^3$ gravitational radii. An optically thin accretion flow inside a truncated optically thick disc appears to be a common feature of LLAGN that are accreting at only a tiny fraction of the Eddington limit.

Kinetic and radiative power from optically thin accretion flows

We perform a set of general relativistic, radiative, magneto-hydrodynamical simulations (GR-RMHD) to study the transition from radiatively inefficient to efficient state of accretion on a non-rotating black hole. We study ion to electron temperature ratios ranging from $T_{\rm i}/T_{\rm e}=10$ to $100$, and simulate flows corresponding to accretion rates as low as $10^{-6}\dot M_{\rm Edd}$, and as high as $10^{-2}\dot M_{\rm Edd}$. We have found that the radiative output of accretion flows increases with accretion rate, and that the transition occurs earlier for hotter electrons (lower $T_{\rm i}/T_{\rm e}$ ratio). At the same time, the mechanical efficiency hardly changes and accounts to ${\approx}\,3\%$ of the accreted rest mass energy flux, even at the highest simulated accretion rates. This is particularly important for the mechanical AGN feedback regulating massive galaxies, groups, and clusters. Comparison with recent observations of radiative and mechanical AGN luminosities suggests that the ion to electron temperature ratio in the inner, collisionless accretion flow should fall within $10<T_{\rm i}/T_{\rm e}<30$, i.e., the electron temperature should be several percent of the ion temperature.

A viscous instability in axially symmetric laminar shear flows

A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport coefficients, the instability arises when the viscous dissipation is taken into account in the energy equation. Using the local WKB approximation, we derive a third-order algebraic dispersion equation with two modes representing the modified Rayleigh modes R+ and R-, and the third X-mode. We show that in thin accretion flows the viscosity destabilizes one of the Rayleigh modes in a wide range of wavenumbers, while the X-mode always remains stable. In Keplerian flows, the instability increment is found to be a few Keplerian rotational periods at wavelengths with $kr\sim 10-50$. This instability may cause turbulence in astrophysical accretion discs even in the absence of magnetic field.

MECHANISM OF OUTFLOWS IN ACCRETION SYSTEM: ADVECTIVE COOLING CANNOT BALANCE VISCOUS HEATING?

Based on no-outflow assumption, we investigate steady state, axisymmetric, optically thin accretion flows in spherical coordinates. By comparing the vertically integrated advective cooling rate with the viscous heating rate, we find that the former is generally less than 30% of the latter, which indicates that the advective cooling itself cannot balance the viscous heating. As a consequence, for radiatively inefficient flows with low accretion rates such as $\dot M \la 10^{-3} \dot M_{Edd}$, where $\dot M_{Edd}$ is the Eddington accretion rate, the viscous heating rate will be larger than the sum of the advective cooling rate and the radiative cooling one. Thus, no thermal equilibrium can be established under the no-outflow assumption. We therefore argue that in such case outflows ought to occur and take away more than 70% of the thermal energy generated by viscous dissipation. Similarly, for optically thick flows with extremely large accretion rates such as $\dot M \ga 10 \dot M_{Edd}$, outflows should also occur due to the limited advection and the low efficiency of radiative cooling. Our results may help to understand the mechanism of outflows found in observations and numerical simulations.

Very fast X-ray spectral variability in Cygnus X-1: origin of the hard- and soft-state emission components

The way in which the X-ray photon index, {\Gamma}, varies as a function of count rate is a strong diagnostic of the emission processes and emission geometry around accreting compact objects. Here we present the results from a study using a new, and simple, method designed to improve sensitivity to the measurement of the variability of {\Gamma} on very short time-scales. We have measured {\Gamma} in ~2 million spectra, extracted from observations with a variety of different accretion rates and spectral states, on time-scales as short as 16 ms for the high mass X-ray binary Cygnus X-1, and have cross-correlated these measurements with the source count rate. In the soft-state cross-correlation functions (CCFs) we find a positive peak at zero lag, stronger and narrower in the softer observations. Assuming that the X-rays are produced by Compton scattering of soft seed photons by high energy electrons in a corona, these results are consistent with Compton cooling of the corona by seed photons from the inner edge of the accretion disc, the truncation radius of which increases with increasing hardness ratio. The CCFs produced from the hard-state observations, however, show an anti-correlation which is most easily explained by variation in the energy of the electrons in the corona rather than in variation of the seed photon flux. The hard-state CCFs can be decomposed into a narrow anti-correlation at zero lag, which we tentatively associate with the effects of self-Comptonisation of cyclo-synchrotron seed photons in either a hot, optically thin accretion flow or the base of the jet, and a second, asymmetric component which we suggest is produced as a consequence of a lag between the soft and hard X-ray emission. The lag may be caused by a radial temperature/energy gradient in the Comptonising electrons combined with the inward propagation of accretion rate perturbations.