Transcript From temporal spectra to stellar interiors (and back)

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