Determination of the lifetime of high-l solar p-modes from the interaction of p-mode waves with sunspots

We use the absorption of the solar p-mode waves in sunspots as a tool to determine the lifetime of the p-modes in the range l = 200-700. We measure the absorption coefficients of the p-modes of the sunspots with the helioseismology data taken by the Taiwan Oscillation Network and find that the absorption coefficients of all five sunspots decrease with the distance from the annular region, used to compute the absorption coefficients, to the central sunspot. This decrease of the absorption coefficients is interpreted as the effect of the finite p-mode lifetime. The measured absorption coefficients of the sunspot regions become negative when the distance from the annular region to the central sunspot is large. This phenomenon is also found in a quiet region. We interpret this phenomenon in two different ways: the effective acoustic emission and the observational center-to-limb effect. We set up two simple models to relate the p-mode lifetime and effective emission strength to the measured absorption coefficient. By fitting the measured absorption coefficient versus distance to the models, we obtain the lifetime and the strength of the effective acoustic emission for the modes in the range l = 200-700. The measured p-mode lifetimes decrease with l and the frequency.