At the Sun, the strongest magnetic fields are routinely detected at dark sunspots. The magnitude of the field is typically about 3000 G, with only a few exceptions that reported the magnetic field in excess of 5000 G. Given that the magnetic field decreases with height in the solar atmosphere, no coronal magnetic field above ∼2000 G was ever reported. Here, we present imaging microwave observations of anomalously strong magnetic field of about 4000 G at the base of the corona in solar active region NOAA 12673 on 06 September 2017. Combining the photospheric vector measurements of the magnetic field and the coronal probing, we created and validated a nonlinear force-free field coronal model, with which we quantify the record-breaking coronal magnetic field at various coronal heights.
The X-class solar flare of October 23, 2012, generated continuum photospheric emission and a strong helioseismic wave ("sunquake") that points to an intensive energy release in the dense part of the solar atmosphere. We study properties of the energy release with high temporal and spatial resolutions, using photospheric data from the Helioseismic Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO), and hard X-ray observations made by the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). For this analysis we use level-1 HMI data (filtergrams), obtained by scanning the Fe I line (6731Å) with the time cadence of ∼ 3.6 s and spatial resolution of ∼ 0.5 ′′ per pixel. It is found that the photospheric disturbances caused by the flare spatially coincide with the region of hard X-ray emission, but are delayed by 4 seconds. This delay is consistent with predictions of the flare hydrodynamics RADYN models. However, the models fail to explain the magnitude of variations observed by the HMI.The data indicate that the photospheric impact and helioseismic wave might be caused by the electron energy flux substantially higher than that in the current flare radiative hydrodynamic models.
Quantifying coronal magnetic field remains a central problem in solar physics. Nowadays the coronal magnetic field is often modelled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as π-disambiguation, photospheric field preprocessing, and volume reconstruction methods using a 3D snapshot of the publicly available fullfledged radiative MHD model. Specifically, from the MHD model we know the magnetic field vector in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored and the true magnetic field in the 3D model volume. Our tests show that the available π-disambiguation methods often fail at the quiet sun areas dominated by small-scale magnetic elements, while they work well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective 'elevation' of the magnetic field components. This 'elevation' height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from actual AR photospheric magnetogram are free from this systematic error, while have other metrics comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results, than those from the photospheric boundary.
We focus on quantitative evaluation of several methods for the reconstruction of force-free magnetic fields in the solar corona. We have studied two topics. The first is to carry out a comparison test of two approaches to implement the optimization method: (1) using a boundary layer with a weighting function and (2) involving an optimization algorithm for unknown boundary field vector values. The second approach is shown to provide a better approximation to a desired true solution that is finite in an unlimited semispace. The approximation obtained by the second approach is reasonably close to the true solution up to the boundaries of the reconstruction region. Among the applications of the optimization method to real data, we demonstrate its ability to obtain accurate enough energy estimates and find that the pre-to post-flare energy difference is sufficient in powering the flare.
An algorithm for calculating the gauge-invariant helicity of a magnetic field specified in a rectangular box is described. The algorithm has been tested and confirmed on a well-known semi-analytic force-free-field model of Low and Lou (Astrophys. J. 352, 343, 1990) which we have re-formulated in terms of the vector potential.
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