Estimating Electron Densities in the Middle Solar Corona using White-light and Radio Observations

The electron density of the solar corona is a fundamental parameter in many areas of solar physics. Traditionally, routine estimates of coronal density have relied exclusively on white-light observations. However, these density estimates, obtained by inverting the white-light data, require simplifying assumptions, which may affect the robustness of the measurements. Hence, to improve the reliability of coronal density measurements, it is highly desirable to explore other complementary methods. In this study, we estimate the coronal electron densities in the middle corona, between approximately $1.7-3.5R_\odot$, using low-frequency radio observations from the recently commissioned Long Wavelength Array at the Owens Valley Radio Observatory (OVRO-LWA). The results demonstrate consistency with those derived from white-light coronagraph data and predictions from theoretical models. We also derive a density model valid between 1.7–3.5 $r_\odot$ and is given by $ρ(r’)=1.27r’^{-2}+29.02r’^{-4}+71.18r’^{-6}$, where $r’=r/R_\odot$, and $r$ is the heliocentric distance. OVRO-LWA is a solar-dedicated radio interferometer that provides science-ready images with low latency, making it well-suited for generating regular and independent estimates of coronal densities to complement existing white-light techniques.

💡 Research Summary

The paper presents a comprehensive study of electron density in the middle solar corona (1.7–3.5 R☉) by combining low‑frequency radio observations from the Owens Valley Long Wavelength Array (OVRO‑LWA) with traditional white‑light polarized brightness (pB) measurements from the LASCO/C2 coronagraph. Historically, coronal density has been derived almost exclusively from white‑light Thomson‑scattered light, which requires assumptions of spherical symmetry and an unknown line‑of‑sight (LOS) depth, leading to potentially large uncertainties, especially in the observational gap between EUV imagers (≈1.2 R☉) and coronagraphs (≈2.2 R☉). The authors argue that low‑frequency radio emission, dominated by thermal free‑free (bremsstrahlung) radiation, provides an independent diagnostic that directly links observed brightness temperature (T_B) to electron density (n_e) through the absorption coefficient α ∝ n_e² f⁻² T_e⁻³⁄².

The methodology follows the approach of Mercier & Chambé (2015). First, an initial hydrostatic temperature (T_H ≈ 1.4 MK) and no‑refraction assumption are used to obtain a provisional n_e(r) profile from the measured T_B at each impact parameter r₁. This provisional profile yields a new estimate of T_H and, via Snell’s law in spherical geometry, a correction for ray bending, giving the true closest approach distance r_min (where most of the optical depth accumulates). The density at r_min is then assigned to the sky‑plane radius r₁, and the process iterates until the relative change in n_e at fixed radii falls below 5 %. The authors verify that varying the electron temperature between 0.8–1 MK has negligible effect, confirming the weak temperature dependence (∝ T_e⁰·²⁵) compared with the strong dependence on T_B and observing frequency f.

Parallel to the radio analysis, the authors perform a classic van de Hulst inversion of pB images, carefully selecting CME‑free intervals to minimize contamination. The inversion assumes spherical symmetry and integrates the Thomson scattering kernel to retrieve n_e(r). The resulting white‑light densities are compared with the radio‑derived densities and with several empirical models (Newkirk, Saito, Leblanc). The comparison shows that the radio and white‑light results agree within ~10 % across the entire 1.7–3.5 R☉ range, while the empirical models either over‑estimate (Newkirk) or under‑estimate (Saito, Leblanc) the density, sometimes by an order of magnitude.

To provide a theoretical benchmark, the authors use the data‑driven Magnetohydrodynamic Algorithm outside a Sphere (MAS) model for Carrington Rotation 2283. MAS incorporates synoptic photospheric magnetograms (e.g., SDO/HMI) and solves the steady‑state MHD equations to produce a 3‑D electron density distribution. Averaging MAS densities over latitude and longitude yields a radial profile that matches both the radio and white‑light results, especially between 2–3 R☉, reinforcing the validity of the observational techniques.

From the combined analysis, the authors derive an empirical density model valid for 1.7–3.5 R☉: \