Alexander V. Koldoba

The paper proposes a computational algorithm for the numerical simulation of two-dimensional magnetohydrodynamic (MHD) flows, using a symmetry analyzer as an element of the numerical method. The algorithm is based on a finite-volume Godunov-type scheme with an approximate solution of the Riemann problem for calculating flows. A polar mesh is used, but the momentum and magnetic induction equations are approximated in a Cartesian coordinate system. It is assumed that the flows are either predominantly homogeneous plane-symmetric, or predominantly axisymmetric with respect to the grid’s axis. To reconstruct vector variables in the computational cells, a symmetry analyzer is used, which makes it possible to locally classify the flow as one of the indicated types. Depending on the type of the vector field, the corresponding components are used for its reconstruction.

The paper proposes a symmetry analyzer as an element of the computational algorithm for the numerical integration of two-dimensional equations of ideal gas dynamics. A symmetry analyzer is an algorithm that allows using grid data to give a preference to a component (in the present work, Cartesian or polar) of a vector field for its reconstruction on the cell interfaces of a computational grid and subsequent calculation of fluxes of conservative variables. A computational algorithm is constructed using a polar-type computational grid and including a symmetry analyzer. The algorithm is easily transferred to the three-dimensional cylindrical type of computational grids.

We consider numerical aspects of the mathematical modeling of composite flows (relativistic and nonrelativistic) on adaptive computational grids applied to a double pulsar–optical star...

We investigate the properties of magnetized stars in the propeller regime using axisymmetric numerical simulations. We modelled the propeller regime for stars with realistically large magnetospheres (5-7 stellar radii), so that our results could be applied to different types of magnetized stars, including Classical T Tauri stars, cataclysmic variables, and accreting millisecond pulsars. A wide range of propeller strengths has been studied, from very strong propellers (where the magnetosphere rotates much more rapidly than the inner disk) to very weak propellers (where the magnetosphere rotates only slightly faster than the inner disc. In both propellers, matter is accumulated at the inner disc for the majority of the time, while episodes of accretion onto the star and ejection into the wind are relatively brief. The efficiency of the propeller, which characterizes the part of inner disk matter flowing into the wind, strongly depends on the fastness parameter omega_s: propeller efficiency increases with omega_s. The properties of the winds are different in strong and weak propellers. In the strong propellers, matter is accelerated rapidly above the escape velocity and flows at a relatively small opening angle of 40-45 degrees. In the weak propellers, matter may flow faster or slower than the escape velocity and at a large opening angle of 60-70 degrees. A star-disk system loses energy and angular momentum. A part of the rotational energy of the star is ejected to the magnetically-dominated (Poynting flux) jet, which is only present in the strong propellers. The other part of the energy flows from the inner disk into a propeller-driven wind. A star spins down partly due to the flow of angular momentum from the star to the corona or to the Poynting flux jet along the open field lines, and partly due to the flow of angular momentum to the inner disk along the closed field lines.

We describe a Godunov-type magnetohydrodynamic (MHD) code based on the Miyoshi and Kusano (2005) solver which can be used to solve various astrophysical hydrodynamic and MHD problems. The energy equation is in the form of entropy conservation. The code has been implemented on several different coordinate systems: 2.5D axisymmetric cylindrical coordinates, 2D Cartesian coordinates, 2D plane polar coordinates, and fully 3D cylindrical coordinates. Viscosity and diffusivity are implemented in the code to control the accretion rate in the disk and the rate of penetration of the disk matter through the magnetic field lines. The code has been utilized for the numerical investigations of a number of different astrophysical problems, several examples of which are shown.

The deceleration of matter in a radioactive shock wave has been mathematically simulated. This problem is relevant to the variable radiancy of T Tauri stars. We assume that an ordered magnetic field at the surface of a star is not too great, i.e., B ≤ 100 G. In this case, the initial deceleration and plasma heating (at the entrance to the cooling zone) occur in a fast magnetohydrodynamic (MHD) shock wave. To calculate the intensity of radiation losses, we use real and power radiative functions. The stability/instability of a radiative shock wave is considered as a function of the incoming flow’s parameters: velocity, strength of the magnetic field, and its inclination to the surface of the star. In a series of calculations with the real radiative function, a simple criterion for stability at an accretion velocity of 1.3 × 10⁷ cm/s has been found. The results of modeling with the real and power radiative functions are compared.

We outline recent progress in understanding the accretion of plasma to rotating magnetized stars obtained from global axisymmetric (2D) and 3D magnetohydrodynamic (MHD) simulations in three main areas: (1.) Formation of jets from disk accretion onto rotating magnetized stars: From simulations where the viscosity and magnetic diffusivity within the disk are described by alpha models, we find long-lasting conical outflows/jets from the disk/magnetosphere boundary in both the case where the star is slowly rotating and where it is rapidly rotating (the “propeller regime”). Most of the mass flux in the outflows is in a hollow cone but inside this cone there is a low-density high-velocity magnetically dominated flow along the open polar field lines of the star. The outflows occur under conditions where the poloidal magnetic flux of the star is bunched up by the accretion disk near the disk/magnetosphere boundary. Recent simulations show that the conical outflows become well-collimated for axial distances of ≲ 20 times the inner disk radius. Exploratory 3D simulations show that conical winds are axisymmetric about the rotational axis (of the star and the disk), even when the dipole field of the star is significantly misaligned. (2.) Formation of intrinsically one-sided jets from disk accretion to rotating magnetized stars: There is strong observational evidence for an asymmetry between the approaching and receding jets from a number of young stars. We discuss the first MHD simulations of the formation asymmetric or one-sided jets arising from disk accretion to a rotating star with an asymmetric (dipole plus quadrupole) magnetic field. (3.) Global axisymmetric and 3D simulations of the magnetorotational instability (MRI) in disk accretion onto magnetized stars: In the axisymmetric simulations we observe cases where there is episodic or quasi-periodic burst of accretion similar to that observed in one X ray source. In 3D MHD simulations of accretion onto stars with tilted dipole fields using our Godunov-type code based on the “cubed sphere” grid we find that the density distribution is much less smooth than in the case of the laminar accretion flow described by α–viscosity. Instead, large turbulent cells dominate the flows and are strongly elongated in the azimuthal direction.