Numerical studies of shock oscillations and MRI turbulence in accretion

Abstract

In this thesis, we study two different aspects of accretion flows- (i) quasi-periodic oscillations (QPOs) seen in the light curves of X-ray binaries as a possible consequence of shock oscillations, (ii) global 3D ideal MHD simulations of radiatively inefficient accretion flows (RIAFs). Spherically symmetric adiabatic accretion on to a BH is described by the accretion branch of Bondi solutions (Bondi 1952), because the BH acts like a mass sink. On the other hand, stars like NSs and white dwarfs (WDs), have surface and hence the infalling matter has to slow down at the surface. Due to the presence of the surface, a standing shock forms in the accretion flow for certain boundary conditions at the inner boundary (namely steady shock boundary condition, for details see Chapter 2). The standing shock is stable in 1D, but becomes unstable under non-radial perturbations and oscillates in the vertical direction about the equatorial plane. This phenomenon is known as standing accretion shock instability (SASI). We investigate the mechanism behind SASI using axisymmetric HD and MHD simulations. By comparing different wave propagation times and vertical oscillation period of the post shock cavity, we conclude that an ‘advective acoustic’ mechanism (Foglizzo et al. 2007) is the more likely cause of SASI, instead of a ‘purely acoustic’ (Blondin & Mezzacappa 2006) one. In our MHD simulations we observe, a moderately strong (but subthermal such that thermal pressure > magnetic pressure) large-scale magnetic field adds complicated features to the shock oscillation pattern, giving rise to a low-frequency modulation in the computed light curve. We propose that this low-frequency modulation may be responsible for ∼ 100 Hz QPOs (known as hHz QPOs) (for details see Chapter 3). Finally, we study the magnetorotational instability (MRI; Balbus & Hawley 1991) in geometrically thick (H/R ∼ 0.5) RIAFs using 3D global ideal MHD simulations in spherical polar coordinates (r,θ,φ) and a pseudo-Newtonian gravity. We find that 42 grid points per scale height in the meridional direction are adequate to resolve the MRI. The condition for convergence is given by the product of quality factors ⟨⟨Qθ ⟩⟩⟨⟨Qφ ⟩⟩ ≥ 300 and magnetic tilt angle θB ∼ 13◦−14◦. Because of the huge computational costs of the global simulations, it is desirable to reduce the azimuthal domain size Φ0 to a small fraction of 2π, provided that the outcomes (in particular, the level of transport and mean/fluctuating quantities) are similar to the ones with the full extent. We find stronger mean magnetic fields for the runs with restricted azimuthal domains. This is because, for runs with smaller azimuthal extent, the large-scale turbulent fields manifest themselves as mean fields as the magnetic fields tend to be at large scales and we use periodic boundary conditions at the azimuthal boundaries. On the other hand, steady state flow profiles (for example, radial velocity, sound speed) are very similar for the runs with Φ0 ≥ π/2. We conclude that the computational domain with Φ0 ≥ π/2 is sufficient to study the structure of RIAFs. On the other hand, for the study of turbulence and dynamo in RIAFs Φ0 = 2π is necessary. We also observe the generation of large scale magnetic fields with an intermittent dynamo cycle. The irregularity is due to the sub-Keplerian nature of the angular velocity (for which the shear parameter q = 1.7). We find signatures of two kinds of dynamos– i) a direct dynamo close to the mid-plane, and ii) a Parker-type dynamo away from the mid-plane. Away from the mid-plane, back reaction of the Lorentz force plays an important role in causing the suppression of kinematic helicity (αdyn kin ) by the small scale current helicity (−αdyn mag) of a similar magnitude. The effects of dynamical quenching are shown explicitly for the first time in global simulations of accretion flows.