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Astron. Astrophys. 355, 769-780 (2000)

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6. Plasma filling factor at the top of the PFL system

The results obtained from CDS electron density and emission measure analysis were used to estimate the geometrical filling factor of the examined PFL system in the Fe XIV line. If we assume that the plasma is isothermal and concentrated in filaments with a typical electron density [FORMULA], we can rewrite the formula for emission measure in this way:




In this integral we calculate the total thickness of the radiating elements along the line of sight. Using these quantities we can define the geometrical filling factor as


The density [FORMULA] in Eq. 8 has been derived from the density sensitive line ratio Fe XIV 334.2/353.8. This ratio measures the real electron density. The value of [FORMULA] has been derived by dividing the emission measure EM, calculated from the allowed line intensity, by the apparent size of the system along the line of sight, [FORMULA].

The quantities [FORMULA] and [FORMULA] are identical only in the case of homogeneous distribution of plasma along the line of sight. In this case the filling factor would be equal to one. If plasma is not distributed uniformly, the electron density obtained from line ratio is greater than the density obtained from the emission measure and the filling factor is less than one.

Using this method we determined the filling factor in pixels 26 - 30 (x axis) which correspond to the brightest parts of the Fe XIV loop-like structure. The uncertainties in [FORMULA] and [FORMULA] obtained in previous subsections were used to calculate the uncertainty of the geometrical filling factor. The results are summarized in Table 3. From our measurements it follows that the geometrical filling factor at the top of the examined PFL system in the regions with maximum electron density in Fe XIV line (formation temperature [FORMULA] MK) lies in the interval from [FORMULA] to [FORMULA]. The great range of its possible values reflects the realistic uncertainties in our knowledge of elemental abundance, integrated intensities and [FORMULA].


Table 3. Geometrical filling factor across the top of the loop system determined using the Fe XIV 334.2 and 353.8 lines.

The value of the geometrical filling factor in flare loops has an important consequence. The majority of flare loops observations have been made by Yohkoh/SXT. However, SXT can measure only the emission measure and not the electron density in observed regions. An approximation which assumes a homogeneous and isothermal plasma [FORMULA] is often used to derive the electron density. This approximation does not take into account the possibility that the spatial plasma distribution can be filamentary. If we assume that the typical electron density in such filaments is approximately the same for all of them and the electron density outside the filaments is much smaller than inside, knowing the filling factor we can estimate the real electron density [FORMULA] of emitting elements with a much better accuracy.

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000