Kinsuk Giri

Hydrodynamic simulation of two-component advective flows around black holes

We carry out a series of numerical simulations of viscous accretion flows having a reasonable spatial distribution of the viscosity parameter. We add the power-law cooling throughout the flow. We show that, in agreement with the theoretical solutions of viscous transonic flows, matter having the viscosity parameter above a critical value becomes a Keplerian disk while matter having lesser viscosity remains a low angular momentum, sub-Keplerian flow. The latter component produces centrifugal pressure supported shock waves. Thus, for instance, a flow having sufficiently high viscosity on the equatorial plane and low viscosity above and below, would produce a Two Component Advective Flow (TCAF) where a Keplerian disk is surrounded by a rapidly infalling sub-Keplerian halo. We find that the post- shock region of the relatively cooler Keplerian disk is evaporated and the overall configuration is quite stable. This agrees with the theoretical model with two components which attempt to explain the spectral and timing properties of black hole candidates.

Hydrodynamic simulations of oscillating shock waves in a sub-Keplerian accretion flow around black holes

We study the accretion processes on a black hole by a numerical simulation. We use a grid-based finite difference code for this purpose. We scan the parameter space spanned by the specific energy and the angular momentum and compare the time-dependent solutions with those obtained from theoretical considerations. We found several important results. (a) The time-dependent flow behaves close to a constant height model flow in the pre-shock region and a flow with vertical equilibrium in the post-shock region. (c) The infall time-scale in the post-shock region is several times higher than the free-fall time-scale. (b) There are two discontinuities in the flow, one being just outside of the inner sonic point. Turbulence plays a major role in determining the locations of these discontinuities. (d) The two discontinuities oscillate with two different frequencies and behave as a coupled harmonic oscillator. A Fourier analysis of the variation of the outer shock location indicates higher power at the lower frequency and lower power at the higher frequency. The opposite is true when the analysis of the inner shock is made. These behaviours will have implications in the spectral and timing properties of black hole candidates.

Effects of Compton cooling on the hydrodynamic and the spectral properties of a two-component accretion flow around a black hole

We carry out a time-dependent numerical simulation where both the hydrodynamics and the radiative transfer are coupled together. We consider a two-component accretion flow in which the Keplerian disc is immersed inside an accreting low angular momentum flow (halo) around a black hole. The injected soft photons from the Keplerian disc are reprocessed by the electrons in the halo. We show that in presence of an axisymmetric soft-photon source the spherically symmetric Bondi flow loses its symmetry and becomes axisymmetric. The low angular momentum flow was observed to slow down close to the axis and formed a centrifugal barrier which added new features into the spectrum. Using the Monte Carlo method, we generated the radiated spectra as functions of the accretion rates. We find that the transitions from a hard state to a soft state is determined by the mass accretion rates of the disc and the halo. We separate out the signature of the bulk motion Comptonization and discuss its significance. We study how the net spectrum is contributed by photons suffering different number of scatterings and spending different amounts of time inside the Compton cloud. We study the directional dependence of the emitted spectrum as well.

Hydrodynamic simulations of viscous accretion flows around black holes

We study the time evolution of a rotating, axisymmetric, viscous accretion flow around black holes using a grid-based finite difference method. We use the Shakura–Sunyaev viscosity prescription. However, we compare with the results obtained when all the three independent components of the viscous stress are kept. We show that the centrifugal pressure supported shocks became weaker with the inclusion of viscosity. The shock is formed farther out when the viscosity is increased. When the viscosity is above a critical value, the shock disappears altogether and the flow becomes subsonic and Keplerian everywhere except in a region close to the horizon, where it remains supersonic. We also find that as the viscosity is increased, the amount of outflowing matter in the wind is decreased to less than a percentage of the inflow matter. Since the post-shock region could act as a reservoir of hot electrons or the so-called ‘Compton cloud’, the size of which changes with viscosity, the spectral properties are expected to depend on viscosity strongly: the harder states are dominated by low angular momentum and the low-viscosity flow with significant outflows while the softer states are dominated by the high-viscosity Keplerian flow having very few outflows.

MONTE-CARLO SIMULATIONS OF COMPTONIZATION PROCESS IN A TWO COMPONENT ACCRETION FLOW AROUND A BLACK HOLE IN PRESENCE OF AN OUTFLOW

A black hole accretion may have both the Keplerian and the sub-Keplerian component. In the so-called Chakrabarti–Titarchuk scenario, the Keplerian component supplies low-energy (soft) photons while the sub-Keplerian component supplies hot electrons which exchange their energy with the soft photons through Comptonization or inverse Comptonization processes. In the sub-Keplerian component, a shock is generally produced due to the centrifugal force. The postshock region is known as the CENtrifugal pressure–supported BOundary Layer (CENBOL). In this paper, we compute the effects of the thermal and the bulk motion Comptonization on the soft photons emitted from a Keplerian disk by the CENBOL, the preshock sub-Keplerian disk and the outflowing jet. We study the emerging spectrum when the converging inflow and the diverging outflow (generated from the CENBOL) are simultaneously present. From the strength of the shock, we calculate the percentage of matter being carried away by the outflow and determine how the emerging spectrum depends on the outflow rate. The preshock sub-Keplerian flow is also found to Comptonize the soft photons significantly. The interplay between the up-scattering and down-scattering effects determines the effective shape of the emerging spectrum. By simulating several cases with various inflow parameters, we conclude that whether the preshock flow, or the postshock CENBOL or the emerging jet is dominant in shaping the emerging spectrum depends strongly on the geometry of the flow and the strength of the shock in the sub-Keplerian flow.

Numerical simulation of vertical oscillations in an axisymmetric thick accretion flow around a black hole

We study time evolution of rotating, axisymmetric, two dimensional inviscid accretion flows around black holes using a grid based finite difference method. We do not use reflection symmetry on the equatorial plane in order to inspect if the disk along with the centrifugal barrier oscillated vertically. In the inviscid limit, we find that the CENtrifugal pressure supported BOundary Layer (CENBOL) is oscillating vertically, more so, when the specific angular momentum is higher. As a result, the rate of outflow produced from the CENBOL, also oscillates. Indeed, the outflow rates in the upper half and the lower half are found to be anti-correlated. We repeat the exercise for a series of specific angular momentum {\lambda} of the flow in order to demonstrate effects of the centrifugal force on this interesting behaviour. We find that, as predicted in theoretical models of disks in vertical equilibrium, the CENBOL is produced only when the centrifugal force is significant and more specifically, when {\lambda} > 1.5. Outflow rate itself is found to increase with {\lambda} as well and so is the oscillation amplitude. The cause of oscillation appears to be due to the interaction among the back flow from the centrifugal barrier, the outflowing winds and the inflow. For low angular momentum, the back flow as well as the oscillation are missing. To our knowledge, this is the first time that such an oscillating solution is found with an well-tested grid based finite difference code and such a solution could be yet another reason of why Quasi-Periodic Oscillations should be observed in black hole candidates which are accreting low angular momentum transonic flows.

Dynamics of magnetic flux tubes in an advective flow around a black hole

Observational studies in the two spectral regions of the electromagnetic spectrum, in the domain of the hard X-rays on one hand, and in the domain of radio wavelengths on the other hand, revealed the existence of new stellar sources of relativistic jets known as micro-quasars (Mirabel et al. Nature 358(6383):215–217, 1992; Mirabel and Rodriguez, Nature 371(6492):46–48, 1994). It is seen that the relativistic jets with significant matter content are produced when the inner part of the disk is destroyed and evacuated (Chakrabarti and D’Silva, ApJ 424:138, 1994; Nandi et al. Astron. Astrophys. 380:245–250, 2001). Clearly, magnetic field has to play a major role in origin, acceleration and collimation of these relativistic jets. Due to predominantly rotating accretion flows close to the inner edge of a disk, entangled magnetic fields advected through the flow would be toroidal. This is particularly true for weakly viscous, low angular momentum transonic or advective discs. We focus our study to the trajectories of toroidal flux tubes inside a geometrically thick flow which undergoes a centrifugal force supported shock and also the effects of these flux tubes on the dynamics of the inflow and the outflow. Finite difference method (Total Variation Diminishing) is used for this purpose and specifically focussing on whether these flux tubes significantly affect the properties of the outflows such as its collimation and the rate. It is seen that depending upon the cross-sectional radius of the flux tubes which control the drag force, these field lines may move towards the central object or oscillate vertically before eventually escaping out of the funnel wall (pressure zero surfaces) along the vertical direction. A comparison of results obtained with and without flux tubes show these flux tubes indeed could play pivotal role in collimation and acceleration of jets and outflows.

NUMERICAL SIMULATIONS OF A TWO COMPONENT ADVECTIVE FLOW FOR THE STUDY OF THE SPECTRAL AND TIMING PROPERTIES OF BLACK HOLES

Two component advective flows are the most physical accretion disks which arise from theoretical consideration. Since viscosity is the determining factor, we investigate the effects of viscous stresses on accretion flows around a nonrotating black hole. As a consequence of angular momentum transfer by viscosity in an accretion flow, the angular momentum distribution is modified. We include cooling effects and found that a Keplerian disk is produced on the equatorial plane and the flow above and below remains sub Keplerian. This gives a complete picture to date, of the formation of a Two component advective flow around a black hole.