Quantifying the Magnetic Structure of a Coronal Shock Producing a Type II Radio Burst

Type II radio bursts are thought to be produced by shock waves in the solar atmosphere. However, what magnetic conditions are needed for the generation of type II radio bursts is still a puzzling issue. Here, we quantify the magnetic structure of a coronal shock associated with a type II radio burst. Based on the multi-perspective extreme-ultraviolet observations, we reconstruct the three-dimensional (3D) shock surface. By using a magnetic field extrapolation model, we then derive the orientation of the magnetic field relative to the normal of the shock front ($\theta_{\rm Bn}$) and Alfv\'{e}n Mach number ($M_A$) on the shock front. Combining the radio observations from Nancay Radio Heliograph, we obtain the source region of the type II radio burst on the shock front. It is found that the radio burst is generated by a shock with $M_A \gtrsim 1.5$ and a bimodal distribution of $\theta_{Bn}$. We also use the Rankine-Hugoniot relations to quantify the properties of the shock downstream. Our results provide a quantitative 3D magnetic structure condition of a coronal shock that produces a type II radio burst.