Distribution of magnetic flux on the solar surface and low-degree p-modes

The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs bet ween the rising and falling phases of the solar cycle, leading to a hystere sis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree (l less than or eq ual to 3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of mo des with different order and degree as a function of time. The resulting cu rves are periodic functions (in simple cases just sine curves) shifted in t ime by different amounts for the different modes. We show how this may easi ly lead to hysteresis cycles comparable to those observed. Our models sugge st that high-latitude fields are necessary to produce a significant differe nce in hysteresis between odd- and even-degree modes. Only magnetic field d istributions within a small parameter range are consistent with the observa tions by Jimenez-Reyes et al. Observations of p-mode frequency shifts are t herefore capable of providing an additional diagnostic of the magnetic fiel d near the solar poles. The magnetic distribution that is consistent with t he p-mode observations also appears reasonable compared with direct measure ments of the magnetic field.