Determination of the Height-Temperature Profile Above a Solar Active Region from Multi-Frequency Radio Observations

Abstract

An iterative method is presented for reconstructing the height-temperature profile of the solar atmosphere above a sunspot using multi-frequency spectro-polarimetric microwave observations. It is assumed that the emission is formed predominantly under gyroresonance conditions at harmonics of the electron gyrofrequency, and that the contribution at each frequency is associated with a layer of optical depth of order unity. The frequency-height correspondence is determined from extrapolation of the photospheric magnetic field into the corona. The reconstruction of the profile is reduced to solving an overdetermined system of linear equations with regularization, ensuring noise stability and physical smoothness of the solution. The method is tested on synthetic data for a dipole sunspot model and applied to observations of active region NOAA 11312 obtained with the RATAN-600 radio telescope. The derived temperature profiles are consistent with contemporary models of active regions and reproduce the observed spectra in the 3-18~GHz range with an accuracy of a few percent.

Figures (7)

• Figure 1: Top panel: surfaces of the gyrolevels corresponding to the second and third harmonics; pixels of layer $h_i$ where $\tau \approx 1$ are highlighted in red. Bottom panel: intensity surface. The summation in Equation (\ref{['eq:summa_tau_1']}) is performed over the pixels marked in red.
• Figure 2: Top: calculated radio maps of the active region for the dipole magnetic-field model ($B_{\max}=3000$ G, $f=8$ GHz) in right- and left-circular polarizations. Bottom: one-dimensional scans obtained by convolving the radio maps with the RATAN-600 beam pattern.
• Figure 3: Results of testing the iterative algorithm for reconstructing the height--temperature profile for a dipole model of an active region. The upper panels show the result for an initial temperature profile close to the model profile, while the lower panels correspond to an initial profile with an artificially elevated transition-region height. In each case, the height--temperature profile, the dependence of the residual on iteration number, and the microwave spectra in right- and left-circular polarizations are shown.
• Figure 4: Testing the sensitivity of the iterative method to additive noise in the input spectra. The reference and reconstructed height--temperature profiles are shown, together with the quality of spectral reproduction in right- and left-circular polarizations. (a) additive noise with a level of $5\%$; (b) additive noise with a level of $10\%$.
• Figure 5: Testing the robustness of the iterative method to multiplicative noise and the effect of enhanced regularization. The reference and reconstructed height--temperature profiles are shown, together with the reproduced spectra in right- and left-circular polarizations. (a) multiplicative noise with a level of $10\%$; (b) the same noise level with the weights of the regularization (temperature) equations increased by a factor of 100.