Periodicities in Photospheric Magnetic Flux

Periodicities in Photospheric Magnetic Flux

Wenbin Song

National Astronomical Observatories, CAS, Beijing 100012

Outline

• Data

• Method

• Result

• Discussion

Two sequences of magnetic flux:

AreaFlux

• 360 equal steps in the longitude & 180 equal steps in the sine latitude

• line-of-sight component of flux density

• Pixel areas are the same• Carrington rotations

1666 – 2007 (1978 - 2003)

1. Active sun: In the latitude band S60˚- N60˚ & its flux density > 25 Gauss 2. Polar region: we think that due to its flux density being within

the measurement error

NSO/Kitt Peak synoptic magnetic chart

D a t a

1.1 How to calculate flux of active sun during one Carrington rotation?

2. Assume Btrue being along the vertical direction. Through projection, we have Btrue= Bobs /cos(θ), θ means the latitude;

3. One pixel flux: Φ = |Btrue | • s, s indicates the pixel area 4πR⊙

2/(360×180);

1. In a synoptic chart, seek out pixels with absolute values higher than 25 Gauss and in latitude band S60˚- N60˚;

4. Add up Φ values of all pixels we sought in the first step.

Flux sequence of active sun

Subtract one simple sine function from the flux sequence. This sine function is obtained using the Fourier filter method and its period is about 140 rotations.

1.2 How to identify polar regions in synoptic chart? Two criteria

During solar maximum, mainly according to the border of plage regions;

During solar minimum, mainly according to the border of unipolar regions.

Polar area (unit: 1=full disk)

In short time scale, polar areas of two hemisphere vary in opposite direction perhaps due to the movement of solar equator.

Polar area We also subtract one

simple sine wave which has opposite phase to solar activity cycle.

Method 2.1 Blackman-Tukey method0nx

Sample autocovariance:

For any sample

1

0, 1,,2,1,0

1)(

~ N

nnn Nxx

NR

Power density:

1

)1(

)2exp()(~

)(N

N

isRs

If the spectrum represents a random sample, the sample spectrum estimates at a given frequency are distributed about the corresponding population spectrum according to a distribution divided by the equivalent degree of freedom. We can use this character for evaluating the significance level.

2

Method 2.2 Wavelet transform

)6cos()( 2/2

tet t

Morlet wavelet:

Wavelet transform:

dt

s

tnnfsstW )()(),(

2/1

Wavelet transform can yield periodicity information in time and frequency domains simultaneously.

Result 3.1 flux of active sun

Five solid lines correspond to five periods obtained by B-T method.

Two dashed lines depicts periods around 1.6 yr and 6.0 yr.

Result 3.2 total polar area

Three dashed lines depicts periods around 154 d, 1.8 yr and 5.8 yr.

Two solid lines correspond to two periods obtained by B-T method.

Discussion

Common periods: ~5.9-, ~3.4-, ~1.7-yr, ~320- and ~150-d. The 320-d and 150-d periods are the most typical ones which can be found in many other solar variabilities and activities;

3.4 yr and 1.7 yr periods might be the harmonics: 1. length (2:1); 2. evolution (in WT spectra, similar including its power amplitude and its length).

~1.3- and ~2.6- yr periods occur in flux of active sun which is associated with the rotation period at the base of convective zone (1.3±0.2 yr, Howe et al., sci, 2000);

In real domain

Most periods are the same in the measurement error so that in frequency domain their correlation is good enough

We think that solar activity might origin from polar regions.

Open question: polar area during solar minimum VS flux sequence of active sun during the following solar maximum

1. Relative strength during cycles 22 and 23;

2. Two peak structure during cycle 22

In frequency domain

Thank you!