THE SEISMOLOGY OF SUNSPOTS - A COMPARISON OF TIME-DISTANCE AND FREQUENCY-WAVE-NUMBER METHODS

A pair of formulae are developed that relate the absorption coefficien t and partial-wave phase shift concepts of frequency-wavenumber local helioseismology to the center-annulus cross-correlation function of ti me-distance helioseismology, under the general circumstances that both induced and spontaneous sunspot oscillations may be present. These fo rmulae show that spontaneous emission of p-modes by magnetic and Reyno lds stresses within the spot and the mode mixing between incoming and outgoing p-modes affect only the outgoing center-annulus cross-correla tion time tau(+), and they caution that real or spurious phase lags of the umbral oscillation signal lead to differences in the incoming and outgoing correlation times, resulting in tau(-)not equal tau(+). The application of these methods to actual helioseismic data obtained by t he Global Oscillation Network Group (GONG) project is carried out in o rder to provide a tangible illustration of how time-distance and frequ ency-wavenumber ideas can profitably be combined to yield deeper insig ht into the seismic probing of sunspots. By using the helioseismic GON G data in conjunction with concurrent observations of Doppler velociti es and vector magnetic fields obtained by the High Altitude Observator y/National Solar Observatory (HAO/NSO) Advanced Stokes Polarimeter (AS P) for the 1995 October disk passage of active region NOAA 7912, we de monstrate that the inferred GONG umbral signal actually originates fro m the umbra-penumbra boundary about 6 Mm distant from the center of th e spot. Further, the ASP observations show that the 5 minute oscillati ons at the umbra-penumbra boundary lag behind those in the center of t he umbra by approximately 1 minute, which is precisely the difference between the incoming and outgoing correlation times for NOAA 7912 rece ntly determined by Braun. This remarkable result underscores the peril s of using umbral oscillations in time-distance helioseismology, and i t calls into question previous claims that correlation time difference s constitute direct evidence for the existence of a steady downflow in and around sunspots. Taken together, the observational and theoretica l evidence suggest that the p-mode forcing of the spot leads to the ge neration of upwardly propagating slow magnetoatmospheric waves. These waves are in turn responsible for the decreased amplitudes of the outw ardly propagating p-modes in the surrounding quiet Sun, and the disper sion in their travel times between the hidden subsurface layer where t hey are forced and the overlying level where the Doppler signals origi nate leads to the observed phase lag between the umbral and penumbral oscillations and the corresponding correlation time differences.