Introduction to Helioseismology and Asteroseismology

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Presentation transcript:

Introduction to Helioseismology and Asteroseismology Meryem Berrada

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

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

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.

Relationship between Luminosity and Temperature; 𝐿= 𝑅 2 𝑇 4 (1) Mass-Luminosity relationship ; L L ⨀ = M M ⨀ 4 (2) Time wave at speed c takes to travel stellar medium; 𝑡 𝑑𝑦𝑛 = 𝑅 3 𝐺𝑀 (3)

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. n: radial order, the number of nodes in the radial direction l: angular degree, the number of nodal lines m: angular order, the number of nodal lines that cross the equator

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

𝐹 𝑣 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡∗ 𝑛=1 𝑁 𝑦 𝑛 ( 𝑡 𝑛 ) 𝑒 −𝑖𝑡𝑛(2𝜋𝑣) Fourier Transform Oscillations are detected as functions of position on the solar disk. Fourier Transform in time will filter the corresponding frequencies. 𝐹 𝑣 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡∗ 𝑛=1 𝑁 𝑦 𝑛 ( 𝑡 𝑛 ) 𝑒 −𝑖𝑡𝑛(2𝜋𝑣) Fundamental frequency: period-1h  n=0 Oscillation frequencies: period- 5 min  n= 20-30

Power Spectrum Plot of power (energy per unit time ) relative to frequency Filter noise by setting limits of energy per unit time that can be received from the observed object: 1) Analyze the signal to noise ratio 2) Maximum energy per unit time for a frequency 𝐴 𝐴 0 = 𝐿 𝑀 ( 𝑇 𝑇 𝑒𝑓𝑓 ) 𝑠

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

Simulation of spherical harmonics

Quality factor Q ↑𝑄 :Low energy loss = almost no damping ↓𝑄 : Great energy loss = damped oscillation 𝑄=Π 𝑀 𝑀 ⊙ 1 2 𝑅 𝑅 ⊙ − 3 2 𝜌 ~ 𝑀 𝑅 3 𝑔 ~ 𝑀 𝑅 2 𝜌 𝜌 ⨀ = 𝑔 𝑔 ⨀ 𝑅 𝑅 ⊙ = 𝑔 𝑔 ⨀ 𝐿 ⨀ 1/2 𝑇 2 𝐿 1/2 𝑇 ⨀ 2 Gives direct relationship between the observed values and the stellar density.

Asteroseismology O-C diagram (Tool to check model ) Observed parameters [O] - Calculated parameters [C] vs time Curvature= period is changing with time Quadratic O-C curve = constant rate of change in the period Upward parabolic curve = steadily increasing period Increasing slope = real period > that used in model The calculated part comes from forward and reverse modelling

Example of model analysis: variable star Tau V1370 Constellation of Taurus (401 ly) Decreasing slope = real period (0.295523 𝑑𝑎𝑦𝑠)< that used in model

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

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