Full Project Detail
Geometry-dependent line ratios (Supervisor Professor Steven Rose)
The ratio of intensity of two spectral lines resulting from ions in a plasma has been used as a diagnostic of the local conditions of temperature and density for many years1 in both laboratory and astrophysical plasmas. In the latter case the plasma is usually so distant that it is often not possible to determine its geometrical shape. The orientation of the plasma to the observer is also variable. The idea that line ratios could provide information on the geometry of a plasma where the observer is distant and canno t resolve the plasma spatially arose from an attempt to solve an outstanding puzzle in the astrophysical literature2. Previously it had been expected that if an emission line in a plasma becomes optically thick by increasing the plasma size (for the same density), then the ratio of that line’s intensity to the intensity of another line that remains optically thin would decrease. However published calculations3 had shown that in certain cases the ratio would increase. We discovered that this effect was due to the fact that an ion in the upper state of the transition is pumped in the optically thick case by photons traversing the plasma at many different angles, whereas the photons that leave the plasma are attenuated by absorption only along the line of sight. A beautiful theorem of geometry (the Cauchy mean chord theorem) states that the mean chord through any convex body is given by 4V/A (where V is the volume and A is the area of the body). Taking the example of a planar plasma that results in a mean chord length of twice the perpendicular distance from one side to the other. Such a mean chord would be at an angle of 600 to the normal. So, for an observation angle of 0the upper state is pumped by plasma which is longer, on average, than that through which it is interrogated. The effect is that the line intensity is greater than the optically thin value, but that it drops to the thin value as the observation angle increases to 600 and falls below it for greater angles. This suggests that an enhancement of optically thick to optically thin emission can be used to discriminate between different possible geometries of plasma and between different orientations of the plasma to the observer4. The work has been applied to spectral line ratios from several stars where we drew conclusions about the geometry of the emitting plasmas5,6. We are now at the stage where it is necessary to move from the simple geometries considered to date to consider radiation transport in more complex geometries. The project will involve a mixture of analytic and numerical solution of the radiation transport equations in different geometries coupled with analysis of spectra observed from a variety of laboratory and astrophysical objects with the aim of developing a new robust spectral diagnostic of the geometry of distant plasma sources.