Advective Accretion Flow Research Articles

Magnetized advective accretion flows: formation of magnetic barriers in magnetically arrested discs

We discuss the importance of large scale strong magnetic field in the removal of angular momentum outward, as well as the possible origin of different kinds of magnetic barrier in advective, geometrically thick, sub-Keplerian accretion flows around black holes. The origin of this large scale strong magnetic field near the event horizon is due to the advection of the magnetic flux by the accreting gas from the environment, say, the interstellar medium or a companion star, because of flux freezing. In this simplest vertically averaged, 1.5-dimensional disc model, we choose the maximum upper limit of the magnetic field, which the disc around a black hole can sustain. In this so called magnetically arrested disc (MAD) model, the accreting gas either decelerates or faces the magnetic barrier near the event horizon by the accumulated magnetic field depending on the geometry. The magnetic barrier may knock the matter to infinity. We suggest that these types of flow are the building block to produce jets and outflows in the accreting system. We also find that in some cases, when matter is trying to go back to infinity after knocking the barrier, matter is prevented being escaped by the cumulative action of strong gravity and the magnetic tension, hence by another barrier. In this way, magnetic field can lock the matter in between these two barriers and it might be a possible explanation for the formation of episodic jet.

Correlating non-linear properties with spectral states of RXTE data: possible observational evidences for four different accretion modes around compact objects

By analyzing the time series of RXTE/PCA data, the nonlinear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different nonlinear features. Sometimes they show low correlation/fractal dimension, but in other classes or intervals of time they exhibit stochastic nature. This could be because the accretion flow around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. However, the more conventional way of addressing a compact source is the analysis of its spectral state. Therefore, the question arises: What is the connection of nonlinearity to the underlying spectral properties of the flow when the nonlinear properties are related to the associated transport mechanisms describing the geometry of the flow? The present work is aimed at addressing this question. Based on the connection between observed spectral and nonlinear (time series) properties of two X-ray binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying accretion modes of the sources in terms of known accretion classes, namely, Keplerian disc, slim disc, advection dominated accretion flow (ADAF) and general advective accretion flow (GAAF). We explore the possible transition of the sources from one accretion mode to others with time. We further argue that the accretion rate must play an important role in transition between these modes.

Advective accretion flow properties around rotating black holes – application to GRO J1655-40

We examine the properties of the viscous dissipative accretion flow around rotating black holes in presence of mass loss. Considering thin disc approximation, we self-consistently calculate the inflow-outflow solutions and observe that the mass outflow rates decreases with the increase of viscosity parameter ($\alpha$). Further, we carry out the model calculation of Quasi-periodic Oscillation frequency ($\nu_{\rm QPO}$) that is frequently observed in black hole sources and observe that $\nu^{\rm max}_{\rm QPO}$ increases with the increase of black hole spin ($a_k$). Then, we employ our model in order to explain the High Frequency Quasi-periodic Oscillations (HFQPOs) observed in black hole source GRO J1655-40. While doing this, we attempt to constrain the range of $a_k$ based on observed HFQPOs ($\sim$ 300 Hz and $\sim$ 450 Hz) for the black hole source GRO J1655-40.

Transition of accretion flow from Keplerian phase to advective phase as a dynamical system

A model for the transition of Keplerian accretion flow to advective phase is proposed. The advective fluid particle in the Keplerian accretion background is modelled using two-phase hydrodynamics. The hydrodynamic equations for the advective phase is reduced to a non-linear dynamical system. For small fluctuation of advective nature for sufficiently small time, a linearized dynamical system in density and radial velocity is obtained. The fluctuation is found to be linearly growing for suitable choice of the values of free parameters. The linear growth is studied as a function of the angular Mach number of the background Keplerian accretion flow. The other parameters of the dynamical system are the radial Mach number of the Keplerian accretion flow, viscosity parameters and gas constants of the Keplerian phase as well as the advective phase and the angular velocity profile of the advective fluid particle. The location of the transition region between Keplerian accretion flow and advective accretion flow is parametrized by the radial Mach number and the angular Mach number of the Keplerian accretion flow. The Keplerian accretion flow is found to be linearly unstable against transition to advective phase only if the radial Mach number greater than or of the order of 10−3. Since radial velocity has no dynamical relevance in Keplerian accretion flow (radial Mach number is very small, and the radial velocity comes only as a drift velocity in the equation of continuity), this means that such a transition is possible only at much inner part of the accretion disc. Appreciable linear growth of the advective fluctuation is possible only if the viscosity parameter of the advective phase has high or intermediate value. This could severely restrict the plausible branches of global solution of the inner advective accretion disc.

Role of thermal conduction in an advective accretion with bipolar outflows

Steady-state advective accretion flows in the presence of thermal conduction are studied. All three components of velocity in a spherical coordinates are considered and the flow displays both inflowing and outflowing regions according to our similarity solutions. Thermal conductivity provides latitudinal energy transport and so, the flow rotates more slowly and becomes hotter with increasing thermal conductivity coefficient. We also show that opening angle of the outflow region decreases as thermal conduction becomes stronger.

Testing slim-disk models on the thermal spectra of LMC X-3

Slim-disk models describe advective accretion flows at high luminosities, while reducing to the standard thin disk form in the low luminosity limit. We have developed a new spectral model, slimbb, within the framework of XSPEC, which describes fully relativistic slim-disk accretion and includes photon ray-tracing that starts from the disk photosphere, rather than the equatorial plane. We demonstrate the features of this model by applying it to RXTE spectra of the persistent black-hole X-ray binary LMC X-3. LMC X-3 has the virtues of exhibiting large intensity variations while maintaining itself in soft spectral states which are well described using accretion-disk models, making it an ideal candidate to test the aptness of slimbb. Our results demonstrate consistency between the low-luminosity (thin-disk) and high luminosity (slim-disk) regimes. The results also illustrate that advection alone does not solve the problem of the origin of the surprisingly soft high-luminosity spectra in LMC X-3. We show that X-ray continuum-fitting in the high accretion rate regime can powerfully test black-hole accretion disk models.

QUASI-SPHERICAL, TIME-DEPENDENT VISCOUS ACCRETION FLOW: ONE-DIMENSIONAL RESULTS

We investigated the instability of advective accretion flow as a consequence of angular momentum transfer in one-dimensional, quasi-spherical transonic accretion flow around a non-rotating black hole. The code is designed to include the effects of viscosity; the hydrodynamics component preserves angular momentum strictly with Lagrangian and remap method in absence of viscosity, while the viscosity component updates viscous angular momentum transfer through the implicit method. We performed two tests to demonstrate the suitability of the code for accretion study. First, we simulated the inviscid, low angular momentum, transonic accretion flow with shocks around a black hole, and then the subsonic, self-similar ADAF solution around a Newtonian object. Both simulations fitted the corresponding analytical curves extremely well. We then simulated a rotating, viscous, transonic fluid with shocks. We showed that for low viscosity parameter, stable shocks at larger distance are possible. For higher viscosity parameter, more efficient angular momentum transfer in the post-shock disk makes the shock structure oscillatory. Moreover, as the shock drifts to larger distances, a secondary inner shock develops. We showed that the inner shock is the direct consequence of expansion of the outer shock, as well as creation of regions with $\partial l / \partial r < 0$ due to more efficient angular momentum transfer near the inner sonic point. We showed that all disk parameters, including emissivity, oscillate with the same period as that of the shock oscillation. Our simulation may have implication for low frequency QPOs, e.g., GRO J1655-40 and XTE J1550-564.

Studies of dissipative standing shock waves around black holes

We investigate the dynamical structure of advective accretion flow around stationary as well as rotating black holes. For a suitable choice of input parameters, such as, accretion rate ($\dot {\cal M}$) and angular momentum ($\lambda$), global accretion solution may include a shock wave. The post shock flow is located at few tens of Schwarzchild radius and it is generally very hot and dense. This successfully mimics the so called Compton cloud which is believed to be responsible for emitting hard radiations. Due to the radiative loss, a significant energy from the accreting matter is removed and the shock moves forward towards the black hole in order to maintain the pressure balance across it. We identify the effective area of the parameter space ($\dot {\cal M} - \lambda$) which allows accretion flows to have some energy dissipation at the shock $(\Delta {\cal E})$. As the dissipation is increased, the parameter space is reduced and finally disappears when the dissipation is reached its critical value. The dissipation has a profound effect on the dynamics of post-shock flow. By moving forward, an unstable shock whose oscillation causes Quasi-Periodic Oscillations (QPOs) in the emitted radiation, will produce oscillations of high frequency. Such an evolution of QPOs has been observed in several black hole candidates during their outbursts.

Transition from radiatively inefficient to cooling dominated phase in two temperature accretion disks around black holes

We investigate the transition of a radiatively inefficient phase of a viscous two temperature accreting flow to a cooling dominated phase and vice versa around black holes. Based on a global sub-Keplerian accretion disk model in steady state, including explicit cooling processes self-consistently, we show that general advective accretion flow passes through various phases during its infall towards a black hole. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. Hence the flow governs a much lower electron temperature ∼ 108 – 109.5 K compared to the hot protons of temperature ∼ 1010 2 – 1011.8 K in the range of the accretion rate in Eddington units 0.01 ≲ Ṁ ≲ 100. Therefore, the solutions may potentially explain the hard X-rays and the γ-rays emitted from AGNs and X-ray binaries. We finally compare the solutions for two different regimes of viscosity and conclude that a weakly viscous flow is expected to be cooling dominated compared to its highly viscous counterpart which is radiatively inefficient. The flow is successfully able to reproduce the observed luminosities of the under-fed AGNs and quasars (e.g. Sgr A*), ultra-luminous X-ray sources (e.g. SS433), as well as the highly luminous AGNs and ultra-luminous quasars (e.g. PKS 0743–67) at different combinations of the mass accretion rate and ratio of specific heats.

Study of accretion disk dynamics in presence of cooling

We examine the behaviour of accretion flow around a rotating black hole in presence of cooling. We obtain global flow solutions for various accretion parameters that govern the accreting flow. We show that standing isothermal shock wave may develop in such an advective accretion flow in presence of cooling. This shocked solution has observational consequences as it successfully provides the possible explanations of energy spectra as well as generation of outflows/jets of various galactic and extra-galactic black hole candidates. We study the properties of isothermal shock wave and find that it strongly depends on the cooling efficiency. We identify the region in the parameter space spanned by the specific energy and specific angular momentum of the flow for standing isothermal shock as a function of cooling efficiencies and find that parameter space gradually shrinks with the increase of cooling rates. Our results imply that accretion flow ceases to contain isothermal shocks when cooling is beyond its critical value.

Behaviour of dissipative accretion flows around black holes

We investigate the behaviour of dissipative accreting matter close to a black hole, as this provides important observational features of galactic and extragalactic black hole candidates. We find a complete set of global solutions in the presence of viscosity and synchrotron cooling. We show that advective accretion flow can have a standing shock wave and the dynamics of the shock is controlled by the dissipation parameters (both viscosity and cooling). We study the effective region of the parameter space for standing as well as oscillating shock. We find that the shock front always moves towards the black hole as the dissipation parameters are increased. However, viscosity and cooling have opposite effects in deciding the solution topologies. We obtain two critical cooling parameters that separate the nature of the accretion solution.

Role of Shocked Accretion Flows in Regulating the Quasi-periodic Oscillation of Galactic Black Hole Candidates

Using a generalized nonspherical, multitransonic accretion flow model, we analytically calculate the normalized quasi-periodic oscillation (QPO) frequency qpo of Galactic black hole candidates in terms of dynamical flow variables and self-consistently study the dependence of qpo on such variables. Our results are in fairly close agreement with the observed QPO frequencies of GRS 1915+105. We find that qpo is quite sensitive to various parameters describing the black hole accretion flow containing dissipative and nondissipative shock waves. Thus, the QPO phenomena is, indeed, regulated by shocked black hole accretion, and, for the first time, we establish a definitive connection between the QPO frequency and the properties of advective black hole accretion flows. This information may provide an explanation for some of the important observations of Galactic microquasars.

Multitransonic Black Hole Accretion Disks with Isothermal Standing Shocks

In this work we would like to address the issue of shock formation in black hole accretion discs. We provide a {\it generalized two parameter solution scheme} for multi-transonic, accretion and wind around Schwarzschild black holes, by mainly concentrating on accretion solutions which may contain steady, standing isothermal shocks. Such shocks conserve flow temperature by the dissipation of energy at the shock location.Unlike previous works in this field, our calculation is {\it not} restricted to any particular kind of post-Newtonian gravitational potentials, rather we use {\it all} available pseudo-Schwarzschild potentials to formulate and solve the equations governing the accretion and wind only in terms of flow temperature $T$ and specific angular momentum $\lambda$ of the flow. Our generalized formalism assures that the shock formation is not just an artifact of a particular type of gravitational potential, rather inclusion of all available black-hole potentials demonstrates a substantially extended zone of parameter space allowing for the possibility of shock formation. We thus arrive at the conclusion that the standing shocks are essential ingredients in rotating, advective accretion flows of isothermal fluid around a non-spinning astrophysical black hole. Types of shocks discussed in this paper may appear to be `bright' because of the huge amount of energy dissipation at shock, and the quick removal of such energy to maintain the isothermality may power the strong X-ray flares recently observed to be emerged from our Galactic centre. The results are discussed in connection to other astrophysical phenomena of related interest, such as the QPO behaviour of galactic black hole candidates. (Abridged).

Hydromagnetic stability of a slim disc in a stationary geometry

The magnetorotational instability originates from the elastic coupling of fluid elements in orbit around a gravitational well. Since inertial accelerations play a fundamental dynamical role in the process, one may expect substantial modifications by strong gravity in the case of accretion on to a black hole. In this paper, we develop a fully covariant, Lagrangian displacement vector field formalism with the aim of addressing these issues for a disc embedded in a stationary geometry with negligible radial flow. This construction enables a transparent connection between particle dynamics and the ensuing dispersion relation for magnetohydrodynamic wave modes. The magnetorotational instability (MRI) — in its incompressible variant — is found to operate virtually unabated down to the marginally stable orbit; the putative inner boundary of standard accretion disc theory. To obtain a qualitative feel for the dynamical evolution of the flow below r_(ms), we assume a mildly advective accretion flow such that the angular velocity profile departs slowly from circular geodesic flow. This exercise suggests that turbulent eddies will occur at spatial scales approaching the radial distance while tracking the surfaces of null angular velocity gradients. The implied field topology, namely large-scale horizontal field domains, should yield strong mass segregation at the displacement nodes of the non-linear modes when radiation stress dominates the local disc structure (an expectation supported by quasi-linear arguments and by the non-linear behaviour of the MRI in a non-relativistic setting). Under this circumstance, baryon-poor flux in horizontal field domains will be subject to radial buoyancy and to the Parker instability, thereby promoting the growth of poloidal field.

A High‐Resolution X‐Ray Image of the Jet in M87

We present the first high-resolution X-ray image of the jet in M87 using the Chandra X-Ray Observatory. There is clear structure in the jet and almost all of the optically bright knots are detected individually. The unresolved core is the brightest X-ray feature but is only 2-3 times brighter than knot A (123 from the core) and the inner knot HST-1 (10 from the core). The X-ray and optical positions of the knots are consistent at the 01 level, but the X-ray emission from the brightest knot (A) is marginally upstream of the optical emission peak. Detailed Gaussian fits to the X-ray jet one-dimensional profile show distinct X-ray emission that is not associated with specific optical features. The X-ray/optical flux ratio decreases systematically from the core, and X-ray emission is not clearly detected beyond 20'' from the core. The X-ray spectra of the core and the two brightest knots, HST-1 and A, are consistent with a simple power law (Sν ∝ ν-α) with α = 1.46 ± 0.05, practically ruling out inverse Compton models as the dominant X-ray emission mechanism. The core flux is significantly larger than expected from an advective accretion flow, and the spectrum is much steeper, indicating that the core emission may be due to synchrotron emission from a small-scale jet. The spectral energy distributions of the knots are well fitted by synchrotron models. The spectral indices in the X-ray band, however, are comparable to that expected in the Kardashev-Pacholczyk synchrotron model but are much flatter than expected in the pitch-angle isotropization model of Jaffe and Perola. The break frequencies derived from both models drop by factors of 10-100 with distance from the core.

Analytic Model for Advection‐dominated Accretion Flows in a Global Magnetic Field

A model for advection-dominated accretion flows (ADAFs) in a global magnetic field is proposed. In contrast to the well known ADAF models in which the viscosity of a fluid determines both angular momentum transfer and energy dissipation in the flow, the magnetic field and the electric resistivity, respectively, control them in this model. A manageable set of analytic solutions for the flow and the magnetic field is obtained to vertically non-integrated basic equations. This set describes mathematically a fully advective accretion flow and, in physically plausible situations for most AGNs, it is also confirmed that the radiation cooling estimated on this solution is really negligible compared with the internal energy of the flow.

Numerical Simulations of Advective Flows Around Black Holes

Observational results of compact objects are best understood using advective accretion flows (Chakrabarti, 1996, 1997). We present here the results of numerical simulations of all possible types of such flows.Two parameter (specific energy ε and specific angular momentum λ) space of solutions of inviscid advective flow is classified into ‘SA’ (shocks in accretion), ‘NSA’ (no shock in accretion), ‘I’ (inner sonic point only), ‘O’ (outer sonic point only) etc. (Fig. 1 of Chakrabarti, 1997 and references therein). Fig. 1a shows examples of solutions (Molteni, Ryu &amp; Chakrabarti, 1996; Eggum, in preparation) from ‘SA’, ‘I’ and ‘O’ regions where we superpose analytical (solid) and numerical simulations (short dashed curve is with SPH code and medium dashed curve is with TVD code; very long dashed curve is with explicit/implicit code). The agreement is excellent. In presence of cooling effects, shocks from ‘SA’ oscillate (Fig. 1b) when the cooling timescale roughly agrees with postshock infall time scale (Molteni, Sponholz &amp; Chakrabarti, 1996). The solid, long dashed and short dashed curves are drawn for T1/2 (bremsstrahlung), T0.4 and T0.75 cooling laws respectively. In the absence of steady shock solutions, shocks for parameters from ‘NSA’ oscillate (Fig. 2) even in the absence of viscosity (Ryu et al. 1997). The oscillation frequency and amplitude roughly agree with those of quasi-periodic oscillation of black hole candidates. When the flow starts from a cool Keplerian disk, it simply becomes sub-Keplerian before it enters through the horizon. Fig. 3a shows this behaviour where the ratio of λ/λKeplerian is plotted. When the flow deviates from a hot Keplerian disk, it may develop a standing shock as well (Fig. 3b) (Molteni et al. 1996).