A Comment on the Relationship between the Modal and Time-Distance Formulations of Local Helioseismology

Details A Comment on the Relationship between the Modal and Time-Distance Formulations of Local Helioseismology A Comment on the Relationship between the Modal and Time-Distance Formulations of Local Helioseismology

Mar 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997apj...477..475b&link_type=abstract

Astrophysical Journal v.477, p.475

Astronomy and Astrophysics

Astronomy

45

Sun: Magnetic Fields, Sun: Oscillations, Sun: Activity, Waves

Scientific paper

The relationship between the time-distance and modal-decomposition approaches to solar active region seismology is clarified through the consideration of the oscillations of a plane-parallel, isentropic polytrope. It is demonstrated by direct construction that a wave packet formed through the superposition of neighboring p-modes interferes constructively along a ray bundle that follows the appropriate WKBJ ray path obtained by using the eikonal approximation. Because the actual power envelope of the solar 5 minute oscillations restricts the excited p-modes to rather low radial orders, the ray bundles are diffuse and sample portions of the solar envelope that are some ~10--30 Mm distant from the nominal WKBJ ray path. This behavior is consistent with the fact that the eikonal approximation becomes valid only in the limiting case of large radial orders (n >> 1). The p-mode wave packets that are isolated by employing the time-distance methods must therefore be described either as a superposition of individual p-modes (a wave packet), or as a sum of ray paths (a ray bundle), depending upon which representation proves to be optimal for the given circumstances.

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