Helioseismology: GONG/BiSON/SoHO
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1 Helioseismology: GONG/BiSON/SoHO
2 Asteroseismology: Solar-like oscillations in other stars Study stars of different Masses, Ages and Chemical Composition Stellar Structure and Evolution
3 Solar-like oscillations in other stars Amplitudes are very low; 20 cm/s in velocity, or m in displacement, a fraction of a degree in temperature, a few ppm in brightness Only see modes with few node-lines: surface unresolved Only possible in the brightest stars using the best telescopes
4 Observations of Pulsating Stars Time Series Photometry Time Series Spectroscopy
5 Solar-like oscillations in other stars Brightness variations are extremely difficult to observe from ground because of the low amplitudes and the effect of the atmosphere:
6 Time
7 Differential photometry Variable star: Constant star: Variable constant:
8 + 800 m/s: redshifted: 12 må m/s: blueshifted: 6 må Time-series Spectroscopy Doppler-shifts of Radial Velocities due to the oscillations
9 Solar-like oscillations in other stars Amplitudes are very low; 20 cm/s in velocity, or m in displacement, a fraction of a degree in temperature, a few ppm in brightness From ground: only possible with spectroscopy but thats anyway much better than photometry because the star itself is much more noisy in photometry
10
11 Measurement precision of Radial Velocities now below 1 m/s for a 1 min observation of bright stars:
12 5700 spectra of Procyon obtained with HARPS in January 2007:
13 + 800 m/s: redshifted: 12 må m/s: blueshifted: 6 må 20 cm/s: 3-6 µå (~ 80 Si-atoms on the CCD-detector)
14 ThAr reference
15 Stellar spectrum without iodine Stellar spectrum with Iodine
16 HARPS: High Accuracy Radial-velocity Planet Searcher
17
18 Example: µ Arae a solar-like star with 3 planets
19 M sin( i ) = 14 Planet M Earth An Exo-planet found from Asteroseismic observations
20 Example: µ Arae a solar-like star with 3 planets
21 From Time Series to Frequencies
22 Calculating the Power Spectrum Use Discrete Fourier Transform as our observations are unequally spaced in time + will use statistical weights The PS can be calculated as a least-squares fit of A ν + ϕ sin( i i i t ) to the time-series See, e.g., Lomb 1975, Ap&SS 39, 447 or Frandsen et al. 1995, A&A 301, 123
23 Calculating the Power Spectrum A set of N observations, ( x, t 1 ),...,( x N, t 1 N ) Set up a model of the observations at each frequency x ν β ν = α cos( t ) + sin( t j i i j i i j ) ν i
24 Calculating the Power Spectrum A set of N observations, ( x, t 1 ),...,( x N, t 1 N ) Set up a model of the observations at each frequency x ν β ν = α cos( t ) + sin( t j i i j i i j ) Minimize the Sum of Squares N ( ν ) { x [ cos( t ) + sin( t i j i i j i i j j 1 R α ν β ν = = ν i )]} 2
25 Calculating the Power Spectrum Then the Power Spectrum is calculated as ) ( ) ( ) ( ) ( ) ( sc cc ss sc s ss c sc cc ss sc c cc s A P i = = + = = ν β ν α ν β ν α ν = = = = = = = = = = N j j i j i N j j i N j j i N j j i j N j j i j t t sc t cc t ss t x c t x s ) cos( ) sin( ) ( cos ) ( sin ) cos( ) sin( ν ν ν ν ν ν See e.g., Frandsen et al. 1995, A&A 301, 123
26 DFT
27
28
29
30 White noise See, e.g., Kjeldsen & Frandsen 1992, PASP 104, 413 White noise is frequency independent noise 4 2 PS N σ TimeSeries π σ = σ = amp TimeSeries N σ
31 Resolution and The Nykvist Frequency The Frequency Resoluton: (Loumos and Deeming 1978) f 1.5 T The Nyquist Frequency: 1 f c 2 t The upper limit for meaningful frequency detections
32 The observations have to be sufficiently long in order to cover Beat Periods: Not even Fourier would help us here
33
34 Not planets
35
36
37
38 Non-white (red) noise Frequency dependent noise: Instrumental + Stellar Noise
39 Granulation Background
40
41
42 Activity Noise similar to the Sun
43 The Spectral Window Function Comes into play if the observations are non-continuous (e.g., from a single observing site) The representation of a single sinusoid in the Power Spectrum of a given set of observations
44 The Spectral Window Function
45 The Spectral Window Function
46 The Spectral Window Function
47 The Spectral Window Function
48 The Spectral Window Function
49
50
51 Multi-site Single-site
52 Multi-site Single-site
53
54 Binary with a period of 1.1 day
55 Multi-site Campaign on Procyon
56 Multi-site Campaign on Procyon Coverage during central 9 days: 89% (duty cycle)
57 Multi-site Campaign on Procyon
58
59
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61
62
63
64 27. december 2006
65 Convection, Rotation & planetary Transits CoRoT has two scientific objectives: - Stellar Seismology - Search for Exoplanets. Proteus platform - 27 cm telescope - 4 2kx4k frame transfer CCDs - Colors provided by a prism in front of two of the CCDs
66 CoRoT was launched with a Soyuz rocket from Baikonur on the 27th of December Measured precision for Asteroseismology: 0.74 ppm in 5 days.
67 Activity and Oscillations in a Solar-like star 27. december 2006
68 The First Exoplanet detected with CoRoT Corot-Exo-1b Period: 1.5 d Mass: 1.3 M J Radius: 1.78 R J
69 NASA Kepler mission Launch date: 1. November 2008
70
71
72 Try it yourself with Period98/Period04: Data can be found at
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