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Astron. Astrophys. 327, 1230-1241 (1997)

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1. Introduction

The electron density and temperature are fundamental pieces of information needed to understand the physics of both cosmic and laboratory plasmas. In particular the study of the outer atmospheres of the Sun and the active stars requires the knowledge of density and temperature to model very different structures such as coronal holes, active loops, flares, and to evaluate radiative losses, a fundamental component of the energy budget, necessary to investigate the problem of coronal heating.

The soft x-ray and extreme ultraviolet region of solar and stellar spectra contain many bound-bound transitions of ions formed over a wide range of temperature and density regimes, and the line emission in this spectral region is an excellent tool to determine the physical conditions of the plasma.

While the temperature distribution of matter within the source is investigated by comparing the absolute intensity of a number of lines of ions formed in many very different temperature conditions, the most commonly used technique for measuring the electron density concerns the ratio of proper line pairs which originates from upper levels of the same ions with different density dependent populations. This technique has been extensively used to measure electron density in flares, active and quiet regions of the transition region and the corona of the Sun and the stars by means of soft x-rays and extreme ultraviolet lines. Comparison between the estimated density and the Emission Measure allows to evaluate the "true" volume of the source and to find whether the emitting volume completely fills the single pixels of the image, or filamentary structure is present.

Detailed and careful reviews of this method and of the most important results are available (Doschek 1990; Mason 1991; Dwivedi 1994).

However the line pairs ratio method assumes that the source of the two lines is strictly isothermal and the measured density is usually assigned to the region where the temperature equals the temperature of maximum abundance of the ion.

This is completely arbitrary and the simultaneous presence of spectral lines of very different ion stages is clear evidence of the contribution of different temperature regions along the line of sight. The Differential Emission Measure (d.e.m.) has been introduced to take into account the non isothermal nature of the radiation source in the solar corona and has proved to be very suitable for describing any type of source from coronal holes to flares.

The aim of this paper is to describe a improved method for evaluating the mean electron density of the region where the line is formed, without the isothermal hypothesis and using a proper definition of the effective temperature associated with the line radiation. Furthermore, no line pairs ratio are necessary since each line is considered independently. This helps to identify the "wrong" lines in the common situation when not all the lines of the same ion fit the same density solutions. Moreover, this method also allows the d.e.m. of the emitting region, to be evaluated.

In Sect. 2 the method is described and the procedures to evaluate density and d.e.m. are discussed. In Sect. 3 the method is applied to SERTS 89 observations, the data analysis is performed, and a detailed discussion of the results for many ions is given.

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998