Solar rotation stereoscopy in microwaves

We present here the first stereoscopic altitude measurements of active region sources observed at microwave frequencies (10-14 GHz). The active region NOAA 7128 was observed with the Owens Valley Radio Observatory (OVRO) on 1992 April 13, 14, 15, and 16 as it passed through the central meridian. From white-light data of the underlying sunspot we determined the rotation rate of the active region, which was found to have a relative motion of dL/dt = +0°.240 day^-1 with respect to the standard photospheric differential rotation rate. Based on this rotation rate we determine for the microwave sources stereoscopic altitudes of 3.3-11.0 Mm above the photosphere. The altitude spectrum h(vν) of the right circular polarization (RCP) main source shows a discontinuity at 12 GHz and can be satisfactorily fitted with a dipole model with a transition from the second to the third harmonic level at 12 GHz. The dominance of the third harmonic for frequencies above 12 GHz occurs because the second harmonic level drops below the transition region, at a height of 2.6 ± 0.6 Mm according to the microwave data. The altitude spectrum h(ν) serves also to invert the temperature profile T(h) from the optically thick parts of the radio brightness temperature spectrum T_B(ν[h]). The microwave emission in both circular polarizations can be modeled with gyroresonance emission, with x-mode for RCP and o-mode in LCP, with the same harmonics at each frequency, but different emission angles in both modes. The contributions from free-free emission are negligible in both polarizations, based on the peak emission measure of EM ≈ 6 × 10²⁸ cm^-5 observed in soft X-rays by Yohkoh/SXT. This study demonstrates that the height dependence of the coronal magnetic field B(h) and the plasma temperature T(h) in an active region can be inverted from the stereoscopic altitude spectra h(ν) and the observed brightness temperature spectra T_B(V).