Effects of horizontal magnetic fields on acoustic travel times

Local helioseismology techniques seek to probe the subsurface magnetic fields and flows by observing waves that emerge at the solar surface after passing through these inhomogeneities. Active regions on the surface of the Sun are distinguished by their strong magnetic fields, and techniques such as time-distance helioseismology can provide a useful diagnostic for probing these structures. Above the active regions, the fields fan out to create a horizontal magnetic canopy. We investigate the effect of a uniform horizontal magnetic field on the travel time of acoustic waves by considering vertical velocity in a simple plane-parallel adiabatically stratified polytrope. It is shown that such fields can lower the upper turning point of p-modes and hence influence their travel time. It is found that acoustic waves reflected from magnetically active regions have travel times up to a minute less than for waves similarly reflected in quiet regions. It is also found that sound speeds are increased below the active regions. These findings are consistent with time-distance measurements.