On solar p - mode frequency shifts caused by near - surfacemodel

The eeect on p-mode frequencies of changing the near-surface structure of solar models is investigated. As is well known, changes connned to the near-surface region have little eeect on the low-frequency p modes: this is as one would expect from a simple asymp-totic 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 xed fractional radius (an Eulerian description), the small frequency shifts at low frequency come about through near-cancellation of diierent 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 xed fractional mass (a Lagrangian description) are connned much closer to the the surface, so that the small frequency shifts come about in a natural way.