University:
Boston University
Course:
CAS AS 311 | Planetary Physics
Academic year:

2022
Views:

375

Pages:

13
Author:

Emery Goodwin

Helioseismology “At first sight it would seem that the deep interior of the Sun and stars is less accessible to scientific investigation than any other region of the universe. Our telescopes may probe farther and farther into the depths of space; but how can we ever obtain certain knowledge of that which is being hidden behind substantial barriers? What appliance can pierce through the outer layers of a star and test the conditions within?” Sir Arthur Eddington in “The internal constitution of stars” (1926) The “appliance” is ASTEROSEISMOLOGY Aster: Classical Greek for star Seismos: Classical Greek for tremors logos: Classical Greek for reasoning or discourse Helioseismology is slightly different from geoseismology Helioseismology usually uses “normal” modes The Sun and the stars oscillates in normal modes. Normal modes in an oscillating system are special solutions where all the parts of the system are oscillating with the same frequency (called "normal frequencies" or "allowed frequencies"). Stellar oscillations are standing waves. A standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves travelling in opposite directions. How do we study stellar interiors? We probe it with sound Image courtesy D. Kutz The speed of sound • Air = 343 m/s (20 C) • Helium = 965 m/s • Hydrogen = 1284 m/s • Water = 1482 m/s (20 C) • Granite = 6000 m/s • Outer layers of the Sun = 10 km/s • Core of the Sun = 550 km/s What about the Sun It rumbles at 3/1000 Hz Strings: normal modes in 1D xö æ yn (x,t) = An sin ç np ÷ cos(w nt - fn ) è Lø Vibrating drum: normal modes in 2D (0,1) (1,1) (0,2) (0,3) (1,2) (2,1) 2D oscillations The Sun: 3D example of normal modes Need 3 numbers to specify mode.: One for mode in the theta (θ) direction, One for nodes in the phi (ϕ) direction, One for the nodes in the radial (r) direction. (Spherical harmonics can describe the θ and ϕ part). Normal modes in 3D