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) 1/(Lifetime) Heat engine mode 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 wnl

Approximated equations High radial order Cowling approximation

Mode trapping Eigenfunction oscillates as function of r when 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

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