Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop

Aims. A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to infer sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density. Methods. Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and centroid positions of hard X-ray sources with sub-arcsecond resolution (∼ 0.2) for a solar limb flare. We show that the height variations of the chromospheric density and the magnetic flux densities can be found with unprecedented vertical resolution of ∼ 150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Results. Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140 ± 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tube in the chromosphere with height. The magnetic scale height B(z) (dB/dz) is found to be of the order of 300 km and strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of ∼ 900 km.