Seismic discrimination of thermal and magnetic anomalies in sunspot umbrae

Efforts to model sunspots based on helioseismic signatures need to discriminate between the effects of (1) a strong magnetic field that introduces time-irreversible, vantage-dependent phase shifts, apparently connected to fast- and slow-mode coupling and wave absorption and (2) a thermal anomaly that includes cool gas extending an indefinite depth beneath the photosphere. Helioseismic observations of sunspots show travel times considerably reduced with respect to equivalent quiet-Sun signatures.

Simulations by Moradi & Cally of waves skipping across sunspots with photospheric magnetic fields of order 3 kG show travel times that respond strongly to the magnetic field and relatively weakly to the thermal anomaly by itself. We note that waves propagating vertically in a vertical magnetic field are relatively insensitive to the magnetic field, while remaining highly responsive to the attendant thermal anomaly. Travel-time measurements for waves with large skip distances into the centers of axially symmetric sunspots are therefore a crucial resource for discrimination of the thermal anomaly beneath sunspot umbrae from the magnetic anomaly.