A thesis for the degree of Doctor of Philosophy defended July, 2018.
The PhD School of Science, Faculty of Science, Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen
Dr. Martin E. Pessah, Professor MSO, University of Copenhagen
Dr. Tobias Heinemann, Associate Professor, University of Copenhagen
On the dynamics of dust, magnetohydrodynamics of disks, and atmospheric radiation of planets
This thesis is an anthology of three theoretical problems in astrophysics with applications to planetary atmospheres, their immediate external environment, and their birthplaces.
The first problem concerns the linear and nonlinear stability of a charged particle in a circular orbit subject to axisymmetric gravitational and electromagnetic forces. We extend previous work on this problem by including a toroidal magnetic field. We show that the toroidal field acts as a gyroscopic force and can stabilize otherwise unstable particle orbits for a range of physical parameters. We also show that gyroscopic stability so attained is only temporary and that the slightest dissipative forces can render the system unstable again, albeit at a slower rate. Our results may apply to dust grains orbiting within a rotating planetary magnetosphere.
The second problem looks at how magnetic diffusion alters the character of the magnetorotational instability (MRI). The MRI is generally regarded as the foremost contender for driving turbulence in differentially rotating astrophysical disks. In disks that are poorly ionized, the three non-ideal effects of ohmic, Hall and ambipolar diffusion take hold. We conduct a systematic analysis of the non-ideal MRI and elucidate the character of the eigenmodes. We uncover a new characteristic scale when the net magnetic field and angular velocity are anti-parallel. This scale may possibly signal a change in the nature of the ensuing turbulence provided dissipative effects are relatively weak. Non-ideal effects pervade disks around young stars and our results may be relevant to the dynamical evolution of certain parts of such disks.
The third problem deals with modeling irradiated atmospheres. Using the methods of radiative transfer, we derive a plane-parallel equilibrium analytical model of an atmosphere that receives radiant energy from above and below. By using the picket-fence technique for modeling spectral lines, we are able to derive exact analytical solutions and thereby obtain thermal profiles of an atmosphere that receives strong collimated high frequency radiation from above in addition to thermally emitted radiant energy from below. Our model also includes the effects of coherent scattering in the lines and the continuum. An obvious application of our analysis is to modeling planetary atmospheres, in particular, those outside of our own solar system that are presently being discovered in the thousands.