A Technique to Measure Coronal Electron Density, Temperature, and Velocity Above $2.5\ \mathrm{R}_{\odot}$ from Sun Center Using Polarized Brightness Spectrum

Abstract

The current model for the polarized brightness (pB) spectrum has a decades-long history of progressively incorporating its dependence on electron density $N_{\mathrm{e}}$, temperature $T_{\mathrm{e}}$, and flow velocity in the radial direction ${\boldsymbol{V}}_{\mathrm{e}}$. The $\mathrm{pB}_{\mathrm{N}_{\mathrm{e}}}$ spectrum follows the exact shape of the photosphere spectrum, which is not smooth, which is expected from the thermal Doppler broadening of the photosphere spectrum due to the high coronal $T_{\mathrm{e}}$; the $\mathrm{pB}_{\mathrm{N}_{\mathrm{e}}\mathrm{T}_{\mathrm{e}}}$ spectrum is smooth, but the free coronal electrons remain static and unaffected by solar wind, and the $\mathrm{pB}_{\mathrm{N}_{\mathrm{e}}\mathrm{T}_{\mathrm{e}}\mathrm{V}_{\mathrm{e}}}$ spectrum is red-shifted by electrons seeing a red-shifted photosphere spectrum as they flow away from the Sun as solar wind, which takes a radial direction above $2.5~\mathrm{R}_{\odot}$ from Sun center. In this article, we review the progress of the above three model pB spectra in describing the observations and highlight the differences, first by comparing the three model pB spectra against wavelength using a model for $N_{\mathrm{e}}$ and constant values for $T_{\mathrm{e}}$ and ${\boldsymbol{V}}_{\mathrm{e}}$, and second by generating three model 2D pB maps by integrating over a selected wavelength region in the three model pB spectra along lines of sight passing through the 14 July 2000 (“Bastille Day”) coronal mass ejection (CME) model, which contains 3D information on $N_{\mathrm{e}}$, $T_{\mathrm{e}}$, and ${\boldsymbol{V}}_{\mathrm{e}}$. In this regard, the COronal Diagnostic EXperiment (CODEX) on the International Space Station (ISS) in 2024 will measure $N_{\mathrm{e}}$, $T_{\mathrm{e}}$, and ${\boldsymbol{V}}_{\mathrm{e}}$ by matching the measured pB with modeled $\mathrm{pB}_{\mathrm{N}_{\mathrm{e}}\mathrm{T}_{\mathrm{e}}\mathrm{V}_{\mathrm{e}}}$ in selected wavelength regions using multiple filters.