Measurements of absorption of acoustic waves in sunspots with direction filters and cross correlation

Observations show that the power of solar acoustic waves is reduced inside magnetic regions. Several mechanisms, including absorption, emissivity reduction, and local suppression, may contribute to the observed power reduction in magnetic regions. So far there is no way to distinguish absorption from emissivity reduction in a magnetic region. In this study, we use the property that the waves emitted along the wave path between two points have no correlation with the signal at the starting point to separate absorption from emissivity reduction in a sunspot, and measure the absorption coefficient in the sunspot. This method uses the direction filter, phase-velocity filter, and cross correlation. We apply this method to an active region, NOAA 9062. The absorption coefficient of the leading sunspot of NOAA 9062 is 0.23 ± 0.01 determined from the wave packet traveling northward with a phase velocity of 6.98 × 10^-5 rad s^-1, corresponding to l=300 at 3.33 mHz. The absorption coefficient is 0.17 ± 0.03 determined from the wave packet traveling southward. The corresponding contribution of absorption to the power deficit in the sunspot is 0.15 ± 0.01, in units of power in the quiet Sun, for the northward waves, and 0.11 ± 0.02 for the southward waves.