We examine the effects of a vertical magnetic field on p-mode frequencies, line widths, and eigen-functions. We employ a simple solar model consisting of a neutrally stable polytropic interior matched to an isothermal chromosphere. The p-modes are produced by a spatially distributed driver. The atmosphere is threaded by a constant vertical magnetic field. The frequency shifts due to the vertical magnetic field are much smaller than the shifts caused by horizontal fields of similar strength. A large vertical field of 2000 G produces shifts on the order of 1 μHz while a weak field of 50 G produces very small shifts of several nanohertz. We find that the frequency shifts decrease with increasing frequency, and increase with field strength. The shifts are positive, except at high frequency and low field strength, where small negative shifts are possible. Coupling of the acoustic fast mode to escaping slow modes is extremely inefficient. Constant vertical magnetic field models are therefore incapable of explaining the high level of absorption observed in sun-spots and plage. The damping due to this mode conversion process produces very narrow line widths. For a 2000 G field the line widths are several microhertz and for a 50 G field the line widths are several nanohertz.
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