A Unified Shock-Front Framework for Type II Radio Burst Band-Splitting and Herringbone Fine Structure

Type II solar radio bursts show two kinds of spectral fine structure, band-splitting of the emission lanes and short, rapidly drifting herringbone bursts, whose origins remain debated and which are usually modelled separately. We propose that both follow from a single curved coronal shock front along which two local quantities, the shock obliquity and the Mach number, vary systematically. Using the oblique magnetohydrodynamic Rankine–Hugoniot relations, the band-split frequency ratio at quasi-perpendicular parts of the front is the square root of the density compression ratio, which we evaluate as a function of the sonic Mach number and plasma beta. We describe herringbone formation, which we associate with quasiparallel parts, with an injection-efficiency function that combines the first critical Mach number for ion reflection with a whistler-mediated electron-injection threshold; we leave its weighting function and steepness parameters free. A minimal expanding-shock model with standard coronal density and field profiles numerically yields the local obliquity and Mach number. For a shock speed of 800 km/s, the predicted band-split ratio lies within the observed metric range (fupper/flower ≈ 1.14–1.28) only at ≈ 1.4–1.7 𝑅⨀ and exceeds it at greater heights. The model qualitatively accounts for the super-critical nose and sub-critical flank of observed coronal mass ejection shocks and the increase in herringbone occurrence with burst intensity. It does not reproduce the nearly height-independent relative band-split width found statistically, and the electron-injection threshold lies far above the Mach numbers reached at realistic shock speeds. We state five falsifiable predictions and identify the band-splitting emission mechanism and the electron-injection channel as the main open issues.