2010-12-16 (2)工作汇报 1

Reconstruction of solar magnetic field since 1700 onwards

姜 杰

工作汇报（ 2）

In collaboration with Robert Cameron, Dieter Schmitt and Manfred Schuessler

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Initial condition

e-folding time of approximately 4000 years

Complements of Talk 1

Free parameter

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The way to deal with radial diffusion

Complements of Talk 1

1

( ) ( ) llm lma t a t e

2 2 10[ ]

l r lR k Decay time:

mlP

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Modeling cys. 15-21

Towards 300 yrs recon. –

Old result

Royal Greenwich Observatory (1874 -- 1976)USAF/NOAA (1976 onwards) Sunspot Data

Locations and areas of sunspots groups:

Tilt angles of sunspots groups:

Mount Wilson (1917 -- 1985) Kodaikanal (1906 -- 1987)

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Cycle variation of sunspot group tilts

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Modeling cys. 15-21: results

simulation

aa-index (Lockwood)

* Makarov et al. (2003)

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Modeling cys. 15-21: results

极区磁场和前一活动周的强度没有相关性，

而和其下一活动周的强度有很好的相关性

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About open flux

l = 1; m = 0 l = 1; m = 1

Axial dipole field Equatorial dipole field

～

Low order modes

Open fluxaxi. dip. (solar mini.)

equ. dip. (solar maxi.)

Lati. sep.

Long. sep.

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How can we go back further ?

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Sunspot number datasets

Characteristics of sunspot group emergence

Sunspot number

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Statistical properties of sunspot group emergence (latitude, longitude, area and tilt angle) as functions of the cycle strength and of time during the solar cycle defined by sunspot number.

Datasets (1874 — 1976, cy. 12-20) : Sunspot groups (RGO) sunspot number (RG)

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Latitude distribution

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Mean lati. vs. cycle strength

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A comparison of the mean lati. for cycles 12--20

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Width of the lati. distribution

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Longitude distribution

Eq. dipole (moment) of a sunspot group ( ) in direction in N. Hem.

Eq. dipole of all the SGs from both Hem. emerging between times t and

The magnitude of the observed sunspot dipole (moment)

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Longitude distribution

The difference betweenreflects the amount of nesting

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Area distribution

Area distribution function

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Cycle phase dependence of area distribution

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Tilt angle distribution

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Number of sunspot groups as a function of time

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Reconstruction of butterfly diagram (1)

Obs.

Sim.

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Reconstruction of butterfly diagram (2)

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Reconstruction of butterfly diagram (3)

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Flow chart

lati., area & tilt angle random longitudes (lowest eq. DM)

lati., area & tilt angle 2 active longitudes (highest eq. DM)

SFT (20

runs)solar surface field (1)

solar surface field (2)

SFT (20 runs)

Polar field (1)=(2)

20 runs average

CSSS extrapolation Zhao & Hoeksema (1995)

CSSS extrapolation Zhao & Hoeksema (1995)

source surface field source surface field

Open field 20 runs average

c% 1- c%

Input: sunspot number dataset

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Calibration of the parameter of active long.

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The case without radial diffusion

CJSS10

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The case with weak radial diffusion

Less reliable sunspot number

rms diff. 14% 20%

Polar field vs. solar cycle becomes weak

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Reconstruction

during 1700--2010

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Reconstruction

during 1700--2010

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Correlation between SN and polar field strength

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Relation between SN and total surface flux

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Relation between SN and open flux

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Comparison of open flux with other reconstructions

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Lost cycle?

Usoskin et al. (2009)

Cy.4: 1784.7 — 1798.3

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Results including the ‘lost cycle’

Against the ‘lost cycle’

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Focus on last 3 cycles(without radial diffusion)

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Possible cause of the weak polar field in cycle 23

40% decrease of sunspot number

28% decrease of the sunspot group tilt angle

55% increase of meridional flow

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Jiang et al., 2010, ApJ, 709, 301

Open flux & field strength near Earth

The disagreement during the minima: strong radial diffusion (100km2s-1) tilt angle

Maxima: amplitude; phase difference

Improved method

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Parameter

dependence