On solar p-mode frequency shifts caused by near-surface model changes

The effect on p-mode frequencies of changing the near-surface structure of solar models is investigated. As is well known, changes confined to the near-surface region have little effect on the low-frequency p modes: this is as one would expect from a simple asymptotic description which shows that these modes have upper turning points located well beneath the photosphere. However, some examples of structural changes show that, if the changes are viewed at fixed fractional radius (an Eulerian description), the small frequency shifts at low frequency come about through near-cancellation of different contributions which are individually much larger than the resultant shifts themselves; the reason is that even so-called near-surface changes extend substantially below the upper turning points of these modes. We demonstrate that the corresponding changes at fixed fractional mass (a Lagrangian description) are confined much closer to the surface, so that the small frequency shifts come about in a natural way.