Research
Stability of particle orbits in a combined gravitational and electromagnetic field
Stability diagram for equatorial orbits in a rotating magnetosphere. The shaded regions represent equilibrium circular orbit solutions. Regions in dark gray represent the parameter space where stable circular orbits exist. Regions in light gray represent unstable orbits. The region in the intermediate shade of gray represents orbits that may be gyroscopically stabilized due to a toroidal magnetic field. This same region may be rendered unstable due to dissipation.
The problem of charged particle dynamics and stability in a gravitational and electromagnetic potential is a fundamental one with applications in plasma physics and astrophysics. In the space plasma physics community, this sometimes goes by the name of the general Störmer problem and concerns the orbital dynamics of charged particles (ions, electrons and charged dust grains) in a planetary magnetosphere.
Using a dynamical systems approach, we have analyzed the linear and nonlinear stability of charged particles in circular orbit in a combined axisymmetric gravitational and electromagnetic field. We have extended previous results on the subject by studying the possibility of stabilization of an otherwise unstable circular orbit due to a toroidal magnetic field component. We find that such gyroscopic stabilization is indeed possible in certain particle orbits in the equatorial plane. Furthermore, we find that gyroscopic stability is lost in the presence of even the slightest dissipation forces resulting in instability. This is a new case in the astrophysical literature of what is generally known as a dissipation induced instability.
Collaborators: Tobias Heinemann (NBIA), Martin Pessah (NBIA)
Magnetohydrodynamic instabilities in differentially rotating disks
Disks of ionized gas abound the universe we inhabit. Central to understanding the way in which these gigantic reservoirs of gas operate is to identify how matter is transported within them. A popular mechanism that enables most of the gas in these disks to accrete in towards the central stellar object is the magneto-rotational instability (MRI). This vigorous magnetohydrodynamic instability requires for its operation: a weak magnetic field tied to the gas and a decreasing angular velocity profile with radius.
In protoplanetary disks, wherein planets are born, the gas in large parts of the disk is weakly ionized causing the magnetic field to diffuse through it. The non-ideal effects that give rise to field slippage through the gas are namely, ohmic, Hall and ambipolar diffusion. We have performed a comprehensive examination of the effect of such diffusive terms on the MRI using a local linear analysis and shearing box simulations with special focus on the Hall effect. We have elucidated their characteristic signatures brought about by the non-ideal diffusivities such as the polarization of the Hall-MRI linear modes. We have also analyzed the nature of the kinetic and magnetic stresses and derived analytical relationships between them. We find that the relative strengths of the stresses can depend upon the length scales resolved suggesting the need for greater resolution in numerical simulations of these effects.
Collaborators: Martin Pessah (NBIA, Copenhagen)
A map of the three different regions where the Hall-MRI region behaves distinctly. In region I, the net vertical magnetic field and angular velocity are parallel; the Hall-MRI has a maximum growth rate at a unique wavenumber and finite wavenumber range. In regions II and III, the net vertical magnetic field and angular velocity are anti-parallel. In region II, the Hall-MRI has a maximum growth rate at a unique wavenumber but infinite wavenumber range. In region III, the Hall-MRI has maximum growth rate for infinite wavenumbers and has an infinite wavenumber range. We have found that while the magnetic stress is greater than the kinetic stress in region I, in regions II and III, the kinetic stress is greater than the magnetic stress. This is contrary to expectations derived from ideal and dissipative MRI and may hint at a different character of the ensuing turbulence.
Analytical Thermal Profiles for Exoplanetary Atmospheres
The past two decades have unleashed a flurry of discoveries leading to routine additions to the known catalog of extra-solar planets. Presently they number in the thousands and the consensus is that there are billions more undetected in our galaxy alone. Radial velocity, transits, gravitational microlensing and direct imaging are the means currently at our disposal to detect and characterize these distant worlds. Never failing to surprise, many of the planets that nature has revealed are unlike any of those found in our solar system. A lot of the observations come from tightly orbiting giant planets. Astronomers have now succeeded in peering into the atmospheres of these hot worlds and have begun to glean information about their mean temperatures and composition.
While powerful numerical techniques are available to compute the thermal profiles of planets, valuable physical intuition is most easily gained through simplified analytical treatments. A technique that goes by the name of the picket-fence model originally used to model the effect of spectral lines for stellar atmospheres was recently adapted to account for non-gray effects in irradiated planetary atmospheres. However, previous work only included pure absorption effects. We have performed a general analysis that accommodates for coherent isotropic scattering effects in both the line and continuum. We find that the resulting thermal profiles depend sensitively on coherent scattering in the shortwave (associated with external irradiation) and longwave (associated with internal flux) radiation components. Our model thus provides a better analytical approximation to the thermal structure of irradiated atmospheres.
Collaborators: Kevin Heng (CSH, Bern), Martin Pessah (NBIA)
The Temperature profile of an irradiated atmosphere. The picket fence model is used to represent uniformly spaced lines of constant width and strength. β is a measure of the line width and η is a measure of the line strength. ε is a measure of the contribution due to absorption in the line such that ε=1 designates the limit where the line is due entirely to absorption and ε=0 marks the opposite limit where the line is purely due to coherent isotropic scattering. γ is a measure of the strength of the absorption of the external irradiation. The top of the atmosphere is at low optical depth and bottom of the atmosphere at large optical depth. The black dashed line is the gray model in the dual-band approximation. The orange curves are relatively cooler in the upper atmosphere because the spectral lines are due to pure absorption while the blue curves are due to pure scattering. Both the orange and blue curves are warmer in the deeper layers regardless of the nature of line formation.