a practical introduction to stellar nonradial oscillations (i)

A Practical Introduction to Stellar Nonradial Oscillations (i)

Rich TownsendUniversity of Delaware

ESO Chile ! November 2006

Overview

• Historical Perspective– Radial pulsators– Nonradial pulsators

• Waves in stars• Global oscillations• Surface variations• Rotation effects• Driving mechanisms

p-mode Surface Variations

g-mode Surface Variations

p modes vs. g modes

Carnot Cycle

Excitation Mechanisms

• Add heat when temperature is high• Remove heat when temperature is

low• Mechanisms:

– κ : opacity– ε : nuclear energy– δ : superadiabatic stratification– γ : ionization

OPAL / OP Opacities

5 M¯ model

WN model

Brown Dwarf model

Asteroseismology

• Compare observations against models– Frequencies– Multi-color light curve

• Amplitudes• Phases

– Spectroscopy• Line-profile variations• Mean profiles

Frequencies

Photometric Amplitudes

ℓ = 1

ℓ = 2ℓ = 3

Line-Profile Variations

lpv: Time-Series

Modeling

• Photometric– Semi-analytical

• Spectroscopic– Semi-analytical

• Moments• TVS

– Numerical• BRUCE/KYLIE• PULSTAR

Photometric Modeling

• Stamford & Watson (1981)• Semi-analytical formula for flux

changes

Photometry of SPB stars

Spectroscopic Modeling

• Represent stellar surface with mesh• Perturb mesh with pulsation(s)• Rasterize mesh• Synthesize spectra for each pixel• Combine spectra

Spectral Synthesis

• For each pixel:– Teff– log g– V–

• Interpolate spectrum in intensity grid

Pulsation & Rotation

• Coriolis force becomes significant when Ω/ω > 0.5

• Pulsation confined within equatorial waveguide

• New formula– Townsend (2003)– Extends Dziembowski

(1977)– Low-frequency (SPBs)

Effects of Rotation

Townsend (2003)