Stochastic Excitation of Acoustic Modes in Stars

Abstract

Abstract. For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...).Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modelled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions.We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.

Turbulent eddy-time-correlation in the solar convective zone

“…Note that the absolute values of mode excitation rates are not reproduced by using a mixing-length description of convection, this is in agreement with Samadi (2009), and arises because that it underestimates the convective velocities as well as convective length-scales. It then explains the differences between the computation of mode excitation rates using the MLT and the 3D numerical simulations (Fig.…”

“…The formalism we used to compute excitation rates of radial modes was developed by and Samadi et al (2005) (see Samadi 2009, for a thorough discussion)…”

“…The equilibrium model also includes turbulent pressure; -a semi-analytical approach: calculation of the mode excitation rates is performed essentially in the manner of Samadi et al (2008a,b). All required quantities, except the eddy-time correlation function, the mode eigenfunctions (ξ r ) and mode inertia (I), are directly obtained from a 3D simulation of the outer layers of the Sun (see Samadi 2009, for details on the numerical simulation).…”

“…A direct computation from 3D numerical simulations is possible and was performed by Samadi et al (2008a). Nevertheless, Samadi (2009) pointed out that the results depend on the spatial resolution, and therefore dedicated high-resolution 3D numerical simulations are required. This then becomes an important limitation when computing mode amplitudes for a large number of stars, preventing us from applying statistical astereosismology.…”

“…In this case, low-frequency modes (ν < 2 mHz) are excited deep in the solar convective region by large-scale eddies that give a substantial fraction of the energy injected to the modes. Chaplin et al (2005) andSamadi (2009) then suggested that most contributing eddies situated deep in the Sun have a χ k more Gaussian than Lorentzian because at a fixed frequency, a Gaussian χ k decreases more rapidly with depth.…”