## 3. Plasma diagnosticsWithout a knowledege of the density, temperature, and elemental
abundances in astrophysical plasmas, almost nothing can be said
regarding the physical processes taking place in them. Thus, a
considerable effort has been made in the past years in developing
diagnostic techniques to infer plasma temperature, density, and
elemental abundances for solar and other astrophysical plasmas,
especially by means of optically thin emission-line spectra (e.g.,
Dwivedi 1994; Mason & Monsignori-Fossi 1994, and references
therein). A fundamental property of hot solar plasmas is their
inhomogeneity. The emergent intensities of spectral lines from
optically thin plasmas are determined by integrals along the line of
sight through the plasma. Spectroscopic diagnostics of the temperature
and density structure of hot optically thin plasmas using
emission-line intensities is usually described in two ways. The
line-ratio method uses an observed line intensity ratio to determine
density or temperature from theoretical density or
temperature-sensitive line-ratio curves, calculated taking account of
physical processes for the formation of lines, in the assumption that
both lines are emitted by the same plasma volume. The line-ratio
method is stable, leading to well-defined values of T or
N However, since off-limb plasma outside active regions has been
found to be nearly isothermal (Feldman et al. 1998), the
The power P per unit volume (in energy units) emitted in an optically thin spectral line emanating from an upper level (j) to a lower level (i) is given by where is the transition
probability, is the population of
the upper level where is the relative upper level
population, Combining Eqs. (1) and (2), we can write where is evaluated at the plasma electron density and temperature, and is evaluated at the plasma temperature. In low-density plasmas, the collisional excitation processes are generally faster than ionization and recombination timescales, and therefore the collisional excitation is dominant over ionization and recombination in populating excited states. The low-lying level populations can then be treated separately from the ionization and recombination processes. The number density population of level j is calculated by solving the statistical equilibrium equations for a number of low-lying levels, taking account of all the important collisional and radiative excitation and deexcitation mechanisms. In order to obtain relative abundances of two elements X and Y, ratios of spectral line intensities from the two elements are used. The line intensity ratio R of two lines is given by If the intensities of the two lines have a similar temperature dependence, then the lines are presumably formed in the same plasma volume and at the same density. For determining the relative element abundance between X and Y, we can then compute a theoretical line intensity ratio assuming equal abundances for X and Y, and subsequently deduce from the observed line intensity ratio . Theoretical line ratios have been computed using the CHIANTI database (Dere et al. 1997; Landi et al. 1999) and the density and temperature values measured from the observations, assuming unity elemental abundances. Unless otherwise specified, ion fractions come from Mazzotta et al. (1998). © European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |