Coronal Magnetic Field Measurement from EUV Images made by the Solar   Dynamics Observatory
  By measuring the geometrical properties of the coronal mass ejection (CME) flux rope and the leading shock observed on 2010 June 13 by the Solar Dynamics Observatory (SDO) mission's Atmospheric Imaging Assembly (AIA) we determine the Alfv\'en speed and the magnetic field strength in the inner corona at a heliocentric distance of ~ 1.4 Rs. The basic measurements are the shock standoff distance (deltaR) ahead of the CME flux rope, the radius of curvature of the flux rope (Rc), and the shock speed. We first derive the Alfv\'enic Mach number (M) using the relationship, deltaR/Rc = 0.81[(gamma-1) M^2 + 2]/[(gamma+1)(M^2-1)], where gamma is the only parameter that needed to be assumed. For gamma =4/3, the Mach number declined from 3.7 to 1.5 indicating shock weakening within the field of view of the imager. The shock formation coincided with the appearance of a type II radio burst at a frequency of ~300 MHz (harmonic component), providing an independent confirmation of the shock. The shock compression ratio derived from the radio dynamic spectrum was found to be consistent with that derived from the theory of fast mode MHD shocks. From the measured shock speed and the derived Mach number, we found the Alfv\'en speed to increase from ~140 km/s to 460 km/s over the distance range 1.2 to 1.5 Rs. By deriving the upstream plasma density from the emission frequency of the associated type II radio burst, we determined the coronal magnetic field to be in the range 1.3 to 1.5 G. The derived magnetic field values are consistent with other estimates in a similar distance range. This work demonstrates that the EUV imagers, in the presence of radio dynamic spectra, can be used as coronal magnetometers. 
Nat Gopalswamy, Nariaki Nitta, Sachiko Akiyama, Pertti M\"akel\"a, and   Seiji Yashiro
astro-ph.SR