The influence of turbulence on the solar p‐mode frequencies I. Free‐mode approximation

Abstract

The influence of turbulence on the frequencies of free acoustic modes in convection zones is considered. The frequencies are modified via the speed of sound by the turbulence-induced alterations of the effective pressure: (i) by the correlated fluctuations of temperature and density and (ii) the pressure part of the Reynolds stress. The two effects shift the frequency of low 1 gmodes in opposite directions. In addition, the correlation of the density fluctuations with the random velocitythe eddy-mass flow -is also relevant. It is, in a steady state, balanced by a vertical mean velocity. The balance results in a rather small net effect completely disappearing for highly nonradial oscillations. Both effects of the density fluctuations produce a redshiJl of the low 1 p-mode frequencies. The Reynolds stress, however, makes a blueshijt of the frequencies relative to that computed for a laminar gas. This effect dominates for subsonic turbulences. The applied second-order correlation-approximation, however, only holds for the lowest frequencies, where the KORONAS (solar minimum) data are indicating a blueshift. Of part.icular importance for t,he present concept is the expected cycle-variations of the lineshifts, i.e. the consideration of the rnagnet.ic modification of the various contributions. Observations may show whether the suggested modifications of the solar oscillation theory are correct.

The effect of time-dependent random mass density field on frequencies of solar sound waves

“…Stein & Nordlund 1998), and different properties of the random perturbations (e.g. Rüdiger et al 1997). It is noteworthy here that a random density field is not the only effect which can account for the departure of the observational data from the theoretical data.…”

“…In most cases the frequency shifts were negative, although for the spherical degrees l = 1200 and l = 1400 these shifts were positive for the modes p 1 , p 2 , and p 3 . On the other hand, Rüdiger et al (1997) showed that the Reynolds stress shifts up the frequencies while the density fluctuations lead to frequency decrease. These two competitive effects shift up low frequencies and reduce high frequencies.…”

On the effect of convection on solarpmodes

“…Small discrepancies do exist, however, and have been attributed to the imperfect manner of modeling the convection in the layer immediately below the surface. Diverse improvements have been proposed, including modifications of the mean structure of the solar model (Christensen-Dalsgaard & Thompson 1997), and a contribution to the mean pressure caused by the turbulence (Rüdiger et al 1997;Baturin & Mironova 1998;Rosenthal et al 1999).…”