Numerical Simulations of Fluid Flows Around Compact Objects

Abstract

This thesis presents the development of a new simulation code, accompanied by a relativistically correct equation of state (EoS), dedicated to correctly accounting for the thermodynamics of multispecies plasma composed of electrons, protons, and positrons. The EoS used in the code has a simple algebraic form, hence the incorporation of the EoS does not significantly increase the computational cost of the code. This allows us for a comprehensive exploration of plasma composition on the flow dynamics, even for long-term simulations. The code’s efficacy and accuracy are demonstrated in capturing the intricate flow patterns and discontinuities like shocks, contact discontinuities, and rarefaction waves by comparing the numerical solutions with the exact solutions of the Riemann problem. We have also developed a new methodology to obtain the solution of the Riemann problem for a general EoS. We have used our simulation code to investigate the dynamics of jets that are accelerated by the radiation field of the accretion disk around a black hole (BH). This area, which has seen limited exploration in terms of numerical simulations, has been the focus of our investigation. We investigated this problem in the non-relativistic hydrodynamic regime and found that radiation can accelerate the jets to a moderately relativistic speed. We also found out that depending on the geometry of the accretion disk, the radiation field can also generate shocks very close to the jet base. We have also shown how any change in the radiation field of the disk gets reflected in the jet solution. As any information regarding the change in disk configuration takes a finite time to reach the jet, different parts of the jet get influenced by the different disk configurations at the same epoch. This time-dependent behavior of the radiation field makes the jet time-dependent. As the jets are relativistic, we extended our analysis to a special relativistic regime. We were interested in the acceleration of the jets that originate very close to the BH the effect of gravity must be incorporated in the simulations. We included the gravity by modifying the special relativistic metric itself, similar to the weak field approximation. The major advantage of using this metric is since the space part of the metric is flat, one can avoid the computation of a curved photon propagation path and yet get the effect of the horizon and strong gravity as the curvature is through the time component in the metric. In this modified framework, our simulation results showed that the radiation field is an efficient accelerator for leptonic jets, which can attain ultra-relativistic Lorentz factor even through the radiation field of sub-Eddington luminous accretion disks. The electron-proton jet also attained Lorentz factors ∼ 3 for super-Eddington luminosities. Another key finding from these simulations is that the shocks generated by the radiation in the jet beam can collide and result in a shock cascade. We also performed two-dimensional axisymmetric simulations of these relativistic transonic jets to study the morphology and structures formed by these jets. These simulations show the morphology of radiatively driven jets that start with a subsonic boundary and propagate up to significantly large distances where these jets have become supersonic and start to form backflow and other features associated with low-density supersonic jets. The effect of plasma composition on the morphology of the jets and their long-term evolution was explored by performing axisymmetric special relativistic hydrodynamic simulations as well as through exact solutions. For one-dimensional studies, the narrow jet beam which consists of a forward shock, jet head, or contact discontinuity, and a reverse shock, resembles an initial value problem. Hence we extended the solution procedure of the Riemann problem to study one-dimensional jet dynamics. Results from these studies have shown that the leptonic jets turn out to be the slowest. In simulations, we found out that despite fixing the initial parameters, jets with different compositions evolved in a completely different fashion.