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From temporal spectra to stellar interiors (and back) Jørgen Christensen-Dalsgaard Institut for Fysik og Astronomi, Aarhus Universitet Dansk AsteroSeismologisk Center Overview Pulsating stars in the HR diagram Excitation mechanisms Heat engine (k mechanism, etc) • Critical layer in the star is heated at compression • Mode is intrinsically unstable and grows exponentially •???Amplitude limitation mechanism, mode selection ??? Stochastic excitation • Mode is intrinsically damped • Excitation through stochastic driving by convection (compare church bell in sandstorm) • Resulting amplitudes from balance between forcing and damping Pulsating stars in the HR diagram Observational differences 1/(Observing time) Heat engine mode 1/(Lifetime) Stochastically excited mode Separated equations Separation of time as exp(- i t) Spherical harmonics Frequency dependence on stellar structure Frequencies depend on dynamical quantities: However, from hydrostatic equilibrium and Poisson’s equation p and g can be determined from r Hence adiabatic oscillations are fully characterized by or, equivalently Characteristic frequencies Acoustic frequency Buoyancy frequency: Internal gravity waves In reality increased inertia owing to horizontal motion Boundary conditions At centre At surface Equations and boundary conditions determine frequencies nl Approximated equations Cowling approximation High radial order Mode trapping Model of present Sun Eigenfunction oscillates as function of r when (Kawaler, Lecture 3) Asymptotics of low-degree p modes Large frequency separation: Small frequency separations Frequency separations: Asteroseismic HR diagram Echelle diagram Structure of evolving star with convective core 2.2 M¯ (Scaling with tdyn to ZAMS) Evolution of (scaled) frequencies Evolution of frequencies and eigenfunctions