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Measurements of oscillation frequencies of the Sun and stars can provideimportant independent constraints on their internal structure and dynamics.Seismic models of these oscillations are used to connect structure and rotationof the star to its resonant frequencies, which are then compared withobservations, the goal being that of minimizing the difference between the two.Even in the case of the Sun, for which structure models are highly tuned,observed frequencies show systematic deviations from modeled frequencies, aphenomenon referred to as the "surface term." The dominant source of thissystematic effect is thought to be vigorous near-surface convection, which isnot well accounted for in both stellar modeling and mode-oscillation physics.Here we bring to bear the method of homogenization, applicable in theasymptotic limit of large wavelengths (in comparison to the correlation scaleof convection), to characterize the effect of small-scale surface convection onresonant-mode frequencies in the Sun. We show that the full oscillationequations, in the presence of temporally stationary 3-D flows, can be reducedto an effective "quiet-Sun" wave equation with altered sound speed,Br\"{u}nt--V\"{a}is\"{a}la frequency and Lamb frequency. We derive the modifiedequation and relations for the appropriate averaging of three dimensional flowsand thermal quantities to obtain the properties of this effective medium. Usingflows obtained from three dimensional numerical simulations of near-surfaceconvection, we quantify their effect on solar oscillation frequencies, and findthat they are shifted systematically and substantially. We argue therefore thatconsistent interpretations of resonant frequencies must include modificationsto the wave equation that effectively capture the impact of vigoroushydrodynamic convection.

Frequency shifts of resonant modes of the Sun due to near-surface convective scattering