On the Hydrodynamic Stability and Wave Interactions of Ionization-Shock Fronts.
Abstract
Disturbances appropriate to ionization-shock fronts in planar, expanding H II regions are studied from two points of view. In the first case the hydrodynamic stability of such fronts is investigated under the assumption of small amplitude perturbations allowing linearization of the equations. The evolving, unperturbed state is described by a similarity solution for simplicity. A technique is developed which reduces the stability problem from a system of partial differential equations and associated boundary conditions to a coupled set of ordinary differential equations with time dependent coefficients. This approach is shown to be valid as long as the transverse perturbation wavelength is much greater than the thickness of the ionization-shock front. Perturbations are considered to arise from density inhomogeneities in the ambient medium. Numerical results along with an approximate analytic solution are given and describe a new instability whereby all wavelengths greater than several recombination lengths grow without bound in an oscillatory manner. However, the wavelength with the fastest growth rate increases as the system evolves, due to the time dependence of the base state. A short discussion on the physical mechanism involved and several observational aspects, including a comparison with the morphology of the California nebula, is presented. The results suggest that this instability can produce irregular structures similar to the bright rims and elephant trunks seen in many diffuse nebulae. In addition, the gravitational and hydrodynamic instabilities of ionization-shock fronts are contrasted and lead to the conclusion that present theories on star formation in such fronts are incomplete. In the second case we drop the assumption of linearization and develop a semi-analytic method to solve for the flow configuration resulting from a one-dimensional interaction between an ionization front and a shock, rarefaction wave or contact discontinuity. This approach complements the linear stability analysis of finite wavelength perturbations since it can deal with strong disturbances, but it sacrifices the two-dimensionality of the previous study. Basically, the technique employs the jump conditions across discontinuities and rarefaction waves to obtain a set of relations which describe the associated changes in pressure and velocity. These results can be given a graphical interpretation which allows qualitative insight into the nature of the interaction. With the addition of a radiation condition, linking the flux of ionizing photons to the wave configuration, unique solutions can be determined. An essential criterion for applying this technique is that the flux of photons from the stars increases linearly with time. The method is extended to interactions involving ionization-shock fronts by reasonable assumptions on the gas flow and applied to two specific examples. The first example involves an interaction with a contact discontinuity which results show that the rocket effect can accelerate clouds only up to (DBLTURN)25 km s('-1) as long as the cloud is broad enough to alter the gas dynamics of the H II region. In the second example we show that the overtaking of an ionization-shock front by a strong shock is an ideal mechanism for explaining the high velocity ( > 30 km s('-1)) features observed in many H II regions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1980
- Bibcode:
- 1980PhDT.........2G
- Keywords:
-
- Physics: Astronomy and Astrophysics;
- Boundary Value Problems;
- Flow Stability;
- Ionization;
- Shock Wave Interaction;
- Stellar Evolution;
- Boundary Conditions;
- Electromagnetic Radiation;
- Magellanic Clouds;
- Nebulae;
- Plasma Waves;
- Wave Propagation;
- Astrophysics