SLIDE 1
Pulsating Stars
- Cepheid variables
- Standard candle
Image credit: European Science Agency, http://sci.esa.int/science-e- media/img/20/cepheid-variables.jpg
Solar-cycle variation of oscillation frequencies and surface - - PowerPoint PPT Presentation
Solar-cycle variation of oscillation frequencies and surface - - PowerPoint PPT Presentation
Solar-cycle variation of oscillation frequencies and surface magnetic field Shao Min Tan Carleton College Mentors: Michael Thompson, Rebecca Centeno-Elliot (HAO) Pulsating Stars Image credit: European Science Agency,
SLIDE 2
SLIDE 3
Closer to Home…
- 2000 2000
Velocity (m/s)
- 2000 2000
Velocity (m/s)
Image credit: Christensen-Dalsgaard, 2002 [1]
SLIDE 4
Instruments
- Michelson Doppler Interferometer (MDI) on
SOHO spacecraft
- Global Oscillation Network Group (GONG)
Image credit: GONG, http://gong.nso.edu/
SLIDE 5
Solar Oscillations
- Oscillation period ~ 5 minutes
- Data averaged over 72 days (SOHO) or 36 days
(GONG) to find frequencies
- p-modes and g-modes
SLIDE 6
Motivation
nspot number Measure of sun
Image credit: Broomhall et al., 2009 [2]
SLIDE 7
Oscillation Modes
Radial direction:
- Radial order, n
Surface:
- Degree, l
- Azimuthal order, m
- Image credit: GONG, http://gong.nso.edu/
SLIDE 8
Spherical Harmonics
l = 1, m = 0 l = 1, m = 1 l = 1, m = 0 l = 1, m = 1 l = 2, m = 0 l = 2, m = 1 l = 2, m = 2
Image credit: Christensen-Dalsgaard, 2003 [3]
SLIDE 9
Frequency Splitting
- Fourier analysis
- Legendre decomposition
SLIDE 10
ak Coefficients over the Solar Cycle
SLIDE 11
a2 a4
ak Coefficients over the Solar Cycle
a6 a8
SLIDE 12
Surface Magnetic Field
itude Lat Longitude Sine latit titude
Image credit: Solar Oscillations Investigation, http://soi.stanford.edu/magnetic/index6.html
SLIDE 13
Surface Magnetic Field
La ude Magnetic flux (G) Longitude titude Sine latitu
SLIDE 14
Legendre Decomposition of B-field
Scaled Pk for: k = 0 k = 1 k = 2 k = 3 k = 4
Sum (40 components)
= cos θ
SLIDE 15
B2 B4
Bk Coefficients over the Solar Cycle
B6 B8
SLIDE 16
Bk Coefficients over the Solar Cycle
B2 B4
Image credit: David Hathaway, http://solarscience.msfc.nasa.gov
SLIDE 17
ak vs. Bk
a2 B2
SLIDE 18
ak vs. Bk
a4 B4
SLIDE 19
ak vs. Bk – Linear Correlation
a2 vs. B2 a4 vs. B4 SOHO GONG
SLIDE 20
Rising phase Declining phase
R = -.995 R = -.990 R = -.998 R = -.984
ak vs. Bk over the Solar Cycle
SOHO GONG
SLIDE 21
ak vs. Bk
ak
a2 B2
Bk(scaled)
(SOHO data)
a4 B4
SLIDE 22
Absolute slope of the linear fit
My data lope (nHz/G)
GONG data
Antia et al. (2001) [4] Index number, k Absolute slo
SLIDE 23
Legendre decomposition at the poles
Rising edges (similar to Antia et al.) Flattened edges
SLIDE 24
Legendre decomposition at the poles
Rising edges (similar to Antia et al.) Flattened edges
SLIDE 25
Legendre decomposition at the poles
Rising edges (similar to Antia et al.) Flattened edges
SLIDE 26
a2 vs. B2 a4 vs. B4
Legendre decomposition at the poles
Flattened edges Rising edges
SLIDE 27
Conclusion
- Linear correlation between ak and Bk –
corroboration of Antia’s result
- Correlation strength is similar for rising and
declining phases of solar cycle – what does this mean for subsurface effects?
– Further work: separating modes with different penetration depths
- Slope varies nonmonotonically with k, regardless
- f handling of decomposition at poles
SLIDE 28