Using line intensity ratios to determine the geometry of plasma in stars.

The I(15.01Å)/I(16.78Å) Fe XVII emission line intensity ratio deviates from its theoretical value in both solar and stellar X-ray Spectra, and this can be attributed to opacity in the 15.01Å emission line, causing a reduced intensity. Previous work conducted using the data set of line ratios from a variety of stars, was to analyse the ratios, and star EV Lac during the quiescent period was identified as having a significant variation from the theoretical line intensity ratio. This point is markedly above the theoretical line ratio and has relatively small error bars. It however shows pronounced enhancement of the optically thick line intensity ratio, which is counterintuitive.

During our time at Imperial we took this data further, using it to assess if the geometry of the plasma can be determined from spectral data using line intensity ratios. In order to do this a theoretical probability distribution of the probability of all the possible angles of observation was required. This long calculation eventually worked out to be a remarkably simple solution of P(θ) =sin θ. The mean and standard deviation of the probability distribution were also calculated by integrating between 0 and π/2, ∫ θ sinθ dθ and ∫ θ2 sinθ dθ respectively, giving values of m=1 and σ = 0.376. This provided the necessary framework for comparing the distribution of the actual data with the expected distribution.

It had been suggested that these enhancement/reduction ratios can be linked to the angle of observation of the particular bit of plasma which emitted this line. In a plasma there are two competing processes which determine the 15.01Å /16.78Å line intensity ratio. The first is the reabsorption of a photon which has been born, which causes a reduction in the 15.01 line and so a reduction in the ratio. The second is that of pumping by the absorption process above which populates the upper state of the thick (15.01) line, and therefore increases the thick/thin ratio. These two processes are determined by two distances in the plasma. The first is the line of sight distance and the second is the average distance across the plasma (the mean chord). If both distances are the same then the enhancement reduction ratio remains at one. If the mean chord length is greater then the ratio will be above one as there is greater intensity of the thick line as there is more pumping than absorption. The reverse is true if the line of sight distance is greater. Which is the case, depends on the geometry of the plasma, and therefore in principal it is possible to gain information about the geometry.

We applied these ratios from the satellite data to two different models, one of which modelled the star corona as a large number of plane slabs, the other of which considered the surface as numerous tubular loops, which extend from the surface and are very hot, suggesting that these are the parts of the corona that emit. These models converted a ratio into an angle of observation of the plasma, from the normal.

Neither of the two models fitted the distribution well, perhaps due to the limited number of values from the satellite (just 14). However some of the data points were from periods of flare activity at the particular star, and some were from quiescent periods. We decided to apply the quiescent points to the plane slab model to obtain angles for those values, and apply the flare points to the cylindrical tube model to get angles for those points too. The distribution of these angles was then compared to the probability distribution, and they were much more similar than the other models had shown suggesting that the models do have some success. However we had to conclude that the limited number of data points and the large error bars in the case of some of the points made the comparisons unreliable. Although the combined model showed the best correlation to the theoretical distribution, it is not an altogether satisfactory solution as it makes assumptions about things we are unsure about in the corona of stars. In addition the fact that 3 of the ratios didn�t even fit onto the models creates doubt in the reliability of the findings.