INTRODUCTION TO HELIOSEISMOLOGY AND ASTEROSEISMOLOGY Meryem Berrada 1

Introduction • Helioseismology is the study of the sun’s structure • Asteroseismology is the study of other stellar bodies • Identify the internal structure • Variations of brightness oscillations within the structure • Convection occurring in the deep interior of a star • Observe Doppler shifts in spectrum lines • Standing sound waves Boundaries : beginning of the convection zone to the surface of the sun 2

Three different types of sound waves 1) Acoustic waves • p-modes • adiabatic process 2) Internal gravity waves • g-modes • Complex: imply a pressure gradient • adiabatic as one of the possible solution 3) Surface gravity waves • f-modes • Incompressible liquid • Constant density 3

Technique • Earthquake is recorded by different stations all around the earth’s surface • In Helioseismology, the source is estimated to any point of the surface • Assume that this point aligns on some great circle • Gives displacement function of the oscillations on that particular great circle. 4

Spherical harmonics • Model the oscillations • Two types of modes : radial & non radial • Sun modes are non-radial: the shape of the star is not preserved during oscillation • Defined by three wavenumbers. 1) n: radial order, the number of nodes in the radial direction 2) l: angular degree, the number of nodal lines 3) m: angular order, the number of nodal lines that cross the equator 6

Doppler shift • Many combinations of wavenumbers that can lead to a similar oscillation • From the Doppler shift analysis, approximate the complexity of the oscillations 7

Fourier Transform • 8

Power Spectrum • 9

Assumptions • Adiabatic process is occurring • Pressure caused by the dynamics of convection is neglected • No transition zone between the convection zone and the interior • Acoustic waves have specific boundary conditions • Effects of magnetic field are also neglected 10

Simulation of spherical harmonics 11

Quality factor Q • 12

Asteroseismology • 13

Example of model analysis: variable star Tau V 1370 • V 1370 Tau - O-C Diagr. -0, 045 O-C (days) -0, 055 -0, 065 -0, 075 14000 15000 16000 17000 18000 Cycle IBVS Nelson S 3 S 4 S 5 S 6 Misc Lin Fit 14

Conclusion • Data: luminosity, temperature, intensity, period and velocity of the sun’s oscillations. • Fourier time transforms : the wavenumbers’ corresponding frequencies • Power spectrum : Oscillation modes • Forward modelling : spherical harmonics, parameters estimation • Inverse modelling : more precise values for parameters • Perspective: diffusion, angular momentum, magnetic fields, transition zone, perturbations 15

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