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From temporal spectra to stellar interiors (and back)

From temporal spectra to stellar interiors (and back). J ørgen 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)

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From temporal spectra to stellar interiors (and back)

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  1. From temporal spectra to stellar interiors (and back) Jørgen Christensen-Dalsgaard Institut for Fysik og Astronomi, Aarhus Universitet Dansk AsteroSeismologisk Center

  2. Overview

  3. Pulsating stars in the HR diagram

  4. 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

  5. Pulsating stars in the HR diagram

  6. Observational differences 1/(Observing time) 1/(Lifetime) Heat engine mode Stochastically excited mode

  7. Separated equations Separation of time as exp(- i  t)

  8. Spherical harmonics

  9. 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 Frequency dependence on stellar structure Frequencies depend on dynamical quantities:

  10. Characteristic frequencies Acoustic frequency Buoyancy frequency:

  11. In reality increased inertia owing to horizontal motion Internal gravity waves

  12. Boundary conditions At centre At surface Equations and boundary conditions determine frequencies wnl

  13. Cowling approximation High radial order Approximated equations

  14. Model of present Sun Mode trapping Eigenfunction oscillates as function of r when

  15. (Kawaler, Lecture 3)

  16. Large frequency separation: Asymptotics of low-degree p modes

  17. Frequency separations: Small frequency separations

  18. Asteroseismic HR diagram

  19. Echelle diagram

  20. Structure of evolving star with convective core 2.2 M¯ (Scaling with tdyn to ZAMS)

  21. Evolution of (scaled) frequencies

  22. Evolution of frequencies and eigenfunctions

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