Radial displacement eigenfunction, = r: Oscillations modes are described in terms of three quantum munbers: n (order or overtone, number of radial number), l (degree, number of surface nodes), m (azimuthal order, number of surface that are lines in the longitudinal)
Driving/Excitation mechanism The pulsation can only continue if energy is fed into the pulsation via a driving mechanism. -mechanism: opacity -mechanism: energy generation rate in the stellar core Stochastic driving: Convective zone To see if the star can sustain pulsations one need to evaluate work ontegral, W, which is defined as an increase of the total energy over one period.
Examples of pulsations in stars Cepheids pulsate in fundamental radial modes but some also pulsate in the first overtone. Solar-like oscillators and roAp: high-order pmodes White dwarfs: high-order g-modes Why? What selects the modes of pulsations in stars?
Taunenbaum & Howard (1969) Deubner (1975) http://solar-center.stanford.edu/images/lu2-sm.gif
Where did Helioseismology led us? Helioseismology is currently the best method for verifying stellar evolution modelling theories and for understanding the structure and interior processes within the sun. It was able to rule out the possibility that the solar neutrino problem was due to incorrect models. The sun speed is known to few parts per thounds over 90% of its radius. Features revealed by helioseismology include that the outer convective zone and the inner radiative zone rotate at different speeds to generate the main magnetic field of the Sun the convective zone has jet streams of plasma thousands of kilometers below the surface. Helioseismology can also be used to detect sunspots on the far side of the Sun from Earth.
Are non radial excited to observed amplitudes in red giants? There are modes with inertia similar to that of a radial modes. In principle, this modes might be excited to an observable level throught stochastic excitation. Hekker at al. (2006) found evidence that the modes in Oph had l=2.
Ongoing projects and future work Space based: MOST, COROT, BRITE, Kepler Ground based: SONG Asteroseismology and Interferometry.
Asteroseismology as piece of the big astro puzzle Helio- and asteroseismology Sun: Formation of the solar system Solar Wind Solar magnetic cycle Atmosphere Life Clusters Galaxies Universe Cosmology Ages and Compositions Weather Stars: Nuclear Reactions Stellar evolution Synthesize elements
Last word....Our telescopes may probe farther and farther into the depths of space; but how can we ever obtain certain knowledge of that which is hidden behind substantila barriers? What appliance can pierce through the outer layers of a star and test the conditions within? Eddington (1926):