Solar-cycle variation of oscillation

frequencies and surface magnetic

field

Shao Min Tan

Carleton College

Mentors: Michael Thompson, Rebecca Centeno-Elliot (HAO)

Pulsating Stars

• Cepheid variables

• Standard candle

Image credit: European Science Agency, http://sci.esa.int/science-e-

media/img/20/cepheid-variables.jpg

Closer to Home…

-2000 2000

Velocity (m/s)

-2000 2000

Velocity (m/s)

Image credit: Christensen-Dalsgaard, 2002 [1]

Instruments

• Michelson Doppler Interferometer (MDI) on

SOHO spacecraft

• Global Oscillation Network Group (GONG)

Image credit: GONG, http://gong.nso.edu/

Solar Oscillations

• Oscillation period ~ 5 minutes

• Data averaged over 72 days (SOHO) or 36 days

(GONG) to find frequencies(GONG) to find frequencies

• p-modes and g-modes

Motivation

Me

asu

re o

f su

nsp

ot

nu

mb

er

Me

asu

re o

f su

nsp

ot

nu

mb

er

Image credit: Broomhall et al., 2009 [2]

Oscillation Modes

Radial direction:

• Radial order, n

Surface:

• Degree, l

• Azimuthal order, m

•

Image credit: GONG, http://gong.nso.edu/

Spherical Harmonics

l = 1, m = 0 l = 1, m = 1l = 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]

Frequency Splitting

• Fourier analysis

• Legendre decomposition

ak

Coefficients over the Solar Cycle

a2

a4

ak

Coefficients over the Solar Cycle

a6

a8

Surface Magnetic Field

Sin

e la

titu

de L

atitu

de

Longitude

Sin

e la

titu

de L

atitu

de

Image credit: Solar Oscillations Investigation,

http://soi.stanford.edu/magnetic/index6.html

Surface Magnetic Field

Latitu

de

Sin

e l

ati

tud

e

Magnetic flux (G)

Longitude

Latitu

de

Sin

e l

ati

tud

e

Legendre Decomposition of B-field

Scaled Pk

for:

k = 0

k = 1

k = 2

k = 3k = 3

k = 4Sum (40

components)

= cos θ

B2

B4

Bk

Coefficients over the Solar Cycle

B6

B8

Bk

Coefficients over the Solar Cycle

B2

B4

Image credit: David Hathaway, http://solarscience.msfc.nasa.gov

ak

vs. Bk

a2

B2

ak

vs. Bk

a4

B4

ak

vs. Bk

– Linear Correlation

a2

vs. B2

a4

vs. B4

SOHO

GONG

Rising phase Declining phase

R = -.995

R = -.990

R = -.998

R = -.984

ak

vs. Bk

over the Solar Cycle

SOHO

GONG

ak

vs. Bk

ak

B (scaled)

a2

B2

k

Bk(scaled)

(SOHO data)a4

B4

Absolute slope of the linear fit

My data

Ab

solu

te s

lop

e (

nH

z/G

)

GONG data

Antia et al.

(2001) [4]

Index number, k

Ab

solu

te s

lop

e (

Legendre decomposition at the poles

Rising edges (similar to Antia et al.) Flattened edges

Legendre decomposition at the poles

Rising edges (similar to Antia et al.) Flattened edges

Legendre decomposition at the poles

Rising edges (similar to Antia et al.) Flattened edges

a2

vs. B2

a4

vs. B4

Legendre decomposition at the poles

Flattened edges

Rising edges

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 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

of handling of decomposition at poles

References