EXCITATION OF SOLAR P-MODES

We investigate the rates at which energy is supplied to individual p-m odes as a function of their frequencies nu and angular degrees l. The observationally determined rates are compared with those calculated on the hypothesis that the modes are stochastically excited by turbulent convection. The observationally determined excitation rate is assumed to be equal to the product of the mode's energy E and its (radian) li ne width GAMMA. We obtain E from the mode's mean square surface veloci ty with the aid of its velocity eigenfunction. We assume that GAMMA me asures the mode's energy decay rate, even though quasi-elastic scatter ing may dominate true absorption. At fixed l, EF rises as nu7 at low n u, reaches a peak at nu almost-equal-to 3.5 mHz, and then declines as nu-4.4 at higher nu. At fixed nu, EF exhibits a slow decline with incr easing l. To calculate energy input rates, P(alpha), we rely on the mi xing-length model of turbulent convection. We find entropy fluctuation s to be about an order of magnitude more effective than the Reynolds s tress in exciting p-modes. The calculated P(alpha) mimic the nu7 depen dence of EGAMMA at low nu and the nu-4.4 dependence at high nu. The br eak of 11.4 powers in the nu-dependence of EGAMMA across its peak is a ttributed to a combination of (1) the reflection of high-frequency aco ustic waves just below the photosphere where the scale height drops pr ecipitously and (2) the absence of energy-bearing eddies with short en ough correlation times to excite high-frequency modes. Two parameters associated with the eddy correlation time are required to match the lo cation and shape of the break. The appropriate values of these paramet ers, while not unnatural, are poorly constrained by theory. The calcul ated P(alpha) can also be made to fit the magnitude of EF with a reaso nable value for the eddy aspect ratio. Our results suggest a possible explanation for the decline of mode energy with increasing l at fixed nu. Entropy fluctuations couple to changes in volume associated with t he oscillation mode. These decrease with decreasing n at fixed nu, bec oming almost zero for the f-mode.