FUNDAMENTAL LIMITATIONS OF EMISSION-LINE SPECTRA AS DIAGNOSTICS OF PLASMA TEMPERATURE AND DENSITY STRUCTURE

We discuss the problem, of determining plasma structure from optically thin emission lines whose emission coefficients and frequency-integra ted intensities are dependent on temperature T and electron density n. We cast the problem into the inverse form discussed by Hubeny & Judge (1995). Three properties of the kernels in the integral equations lea d to fundamental limitations in trying to determine the source term mu (T, n), the ''emission measure differential in temperature and density ,'' from a set of emission-line intensities. First, the kernels are ra ther weakly dependent on n. Second, they have asymptotically identical dependencies on n. The inverse problem is therefore very poorly condi tioned in the density dimension. Third, the kernels cannot (and may ne ver) be calculated with an accuracy better than +/- 10%. These propert ies set limits on the accuracy of all solutions, independent of the ac curacy of observed line intensities. This concurs with earlier but les s general work by Brown et al. (1991). We try to determine solutions f or mu(T, n), using specific target sources and numerical algorithms. U sing realistic uncertainties, calculations indicate that meaningful in verse solutions for mu(T, n) cannot be obtained owing to the severe pr opagation of kernel errors, irrespective of the quality of observation al data. Solutions for the ''emission measure differential in temperat ure'' xi(T) = integral mu(T, n)dn are more robust against instabilitie s driven by poor conditioning. Since traditional ''emission-line diagn ostic ratios'' can only be defined through mu(T, n) (or some generaliz ation thereof), our analysis casts doubt on the meaning of plasma prop erties derived from such line ratios, and illustrates the severe nonun iqueness of any equivalent ''inverse'' solution. This work may be impo rtant for studying a wide variety of atomic and ionic emission-line sp ectra, including work with instruments on SOHO and the Hubble Space Te lescope.