Emission Measures Demystified

Abstract

We review the terms spectral radiance and spectral irradiance, and show how their precise definitions are crucial for interpreting observations made with different instruments covering widely different energy or wavelength ranges. We show how the use of column and volume emission measures in different solar physics and astrophysics communities has led to confusion in relating measured extreme-ultraviolet and soft-X-ray spectra with theoretical spectra generated, in particular, using CHIANTI. We describe a method for obtaining spatially integrated X-ray line and continuum spectra using CHIANTI that requires a column emission measure when only the plasma temperature and volume emission measure, but not the source area, are known from observations.

Appendices

Appendix A: CHIANTI

CHIANTI is a package of Interactive Data Language (IDL) procedures that uses an extensive data base to compute the expected line and continuum emission (free–free, free–bound, and two-photon) from ionized astrophysical plasmas. The emission spectrum can be computed for an isothermal plasma or a plasma with a specified differential emission measure. Temperatures ranging from $10^{4}$ K to 100 MK can be used with a selection of compositions, densities, and ionization states. The latest version (10.1), used for this paper, is described by Del Zanna et al. (2021) and Dere et al. (2023). An IDL GUI is available (ch_ss.pro) to make setting the input parameters, calculating a spectrum, and generating a plot or an output data file (.genx) relatively straightforward. The User Guide for CHIANTI Version 9 is available on Solar Software (SSW) at /ssw/packages/chianti/doc/cug.pdf. It gives details on using the GUI and on the individual IDL commands when not using the GUI. The main input parameters for an isothermal plasma are log$_{10}\,T$(K) and the column emission measure ($EM_{h}$) in units of cm⁻⁵.

Note that CHIANTI uses $N_{H}$ rather than $N_{i}$ in the calculation of column emission measures, where $N_{H}$ is the density of hydrogen. Since $N_{H}/N_{i}{\sim 0.83}$ in a plasma with typical solar compositions, the column emission measures are smaller by this factor compared with those calculated using the density of all ions. While this approximate ratio is correct for high-temperature sources observed with RHESSI where both H and He are completely ionized, it is not correct for sources with temperatures below ∼100 000 K where He, at least, is not completely ionized.

The generated spectrum of the spectral radiance ($I_{E}$) provided by CHIANTI is in units of photons cm⁻² s⁻¹ sr⁻¹ keV⁻¹. Here, the $cm^{-2}$ refers to the area of the detector and the $sr^{-1}$ refers to the solid angle into which the photons are emitted (see Figure 1). All of the input and output data are stored in an IDL structure that can be saved in a .genx file and read back into an IDL procedure with the command, regen, for further customized display and analysis.

Appendix B: Object Spectral Executive – OSPEX

OSPEX⁴ is an IDL object-oriented interface for X-ray spectral analysis of solar X-ray and gamma-ray observations (Tolbert and Schwartz, 2020; Schwartz, 2020). Typically, it uses as input the measured count-rate spectra from one of many different spectrometers and fits them to predicted photon spectra based on many different thermal and nonthermal models. It covers the photon energy range from 1.1 keV to 100 MeV and temperatures from $\sim 5$ to $>100$ MK.

Generally, limited spatial information is available in this energy range, and consequently the dimensions of the source are not generally known. Hence, OSPEX determines the spectral irradiance in units of photons ${ \mathrm{cm}}^{-2}~{\mathrm{s}}^{-1}~{\mathrm{keV}}^{-1}$ rather than the spectral radiance provided by CHIANTI in units of photons ${\mathrm{cm}}^{-2}~{\mathrm{s}}^{-1}~{\mathrm{keV}}^{-1}~{\mathrm{sr}}^{-1}$, i.e., there is no “per steradians” in the flux units. The $cm^{-2}$ refers to the area of the detector, as illustrated in Figure 1. Also, for thermal spectra, OSPEX provides the volume emission measure ($EM_{V}$) rather than the column emission measure ($EM_{h}$) used by CHIANTI.