1

Con

sens

us H

elio

sphe

ric

Mag

netic

Fie

ld

duri

ng th

e la

st ~

120

year

s

L. S

valg

aard

Ea

sy T

oolk

it, In

c.

6927

Law

ler R

idge

, Hou

ston

, TX

770

55, U

SA.

(leif@

leif.

org)

A

bstr

act:

Geo

mag

netic

act

ivity

has

bee

n us

ed to

infe

r the

HM

F [o

r the

�op

en�

sola

r m

agne

tic fl

ux] b

efor

e th

e Sp

ace

Age

. Ear

lier,

thes

e in

fere

nces

wer

e di

scor

dant

and

co

ntro

vers

ial.

In th

e la

st c

oupl

e of

yea

rs, t

he so

urce

s of t

hese

dis

agre

emen

ts h

ave

been

un

cove

red

and

corr

ecte

d an

d a

rem

arka

ble

cons

ensu

s is n

ow e

mer

ging

, with

the

resu

lt th

at

the

helio

sphe

ric m

agne

tic fi

eld

and

the

sola

r win

d sp

eed

can

now

be

cons

ider

ed to

be

wel

l co

nstra

ined

to a

leve

l of ~

10%

or b

ette

r. W

e de

scrib

e th

e w

ork

that

has

led

to th

is

cons

ensu

s and

dis

cuss

the

impl

icat

ions

of t

he c

onse

nsus

for s

ever

al a

reas

of r

esea

rch,

in

clud

ing

estim

ates

of T

otal

Sol

ar Ir

radi

ance

and

Cos

mic

Ray

mod

ulat

ion.

2

A

= k

q(a,

f (V)

) (B

V) (n

V 2 )1/

3 ~ B

V 2

3

4

IH

V =

sum

of u

nsig

ned

diffe

renc

es b

etw

een

7 ho

urly

mea

ns c

ente

red

at m

idni

ght

5

020406080

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972

IHV

IHV

15N

NG

K-F

UR

-WN

G-W

IT-R

SV

-CLF

-HA

D

10

10

0

10

00

-90

-75

-60

-45

-30

-15

01

53

04

56

07

59

0

Co

rre

cte

d G

eo

ma

gn

eti

c L

ati

tud

e

IHV (log-scale)

NS

<IH

V>

19

96

-20

03

IHV

-inde

x is

wel

l-det

erm

ined

be

low

55

degr

ees g

eom

agne

tic

latit

ude.

For

thes

e m

id-la

titud

e st

atio

ns th

e in

dex

is n

ot v

ery

sens

itive

to se

cula

r cha

nges

in

the

geom

agne

tic fi

eld,

e.g

. the

po

sitio

n of

the

pole

s.

6

BV

o2 =

4.3

4 (

IHV

- 6

.5)

R2 =

0.7

6

0

10

0

20

0

30

0

40

0

02

04

06

08

01

00

IHV

BV

o2

Ro

tati

on

Me

an

s

050100

150

200

250 19

6519

7019

7519

8019

8519

9019

9520

0020

0

BVo2 (I

HV)

BVo2 (O

bs)

R-C

Effe

ct

The

IHV

-inde

x is

stro

ngly

co

rrel

ated

with

BV

2 on

a 27

-da

y ro

tatio

n ba

sis.

Ther

e ar

e so

me

seco

nd-o

rder

ef

fect

s tha

t we

can

eith

er

igno

re (t

hey

are

smal

l) or

co

rrec

t for

. Not

e hi

gh-s

peed

st

ream

s in

1974

and

200

3.

7

NH P

ower

(GW

) = 0

.680

7 IH

VR2 =

0.8

582

010203040506070

020

4060

8010

0

1978

-200

6

0102030405060

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

PO

ES (G

W) N

our

cal

ibra

tion

0.68

* IH

V N

Hem

isph

eric

Pow

er In

put (

PO

ES) a

nd IH

V G

eom

agne

tic A

ctiv

ity

Phys

ical

mea

ning

of t

he IH

V-in

dex

= En

ergy

inpu

t to

uppe

r atm

osph

ere

8

IDV

= A

vera

ge u

nsig

ned

diff

eren

ce b

etw

een

the

mid

nigh

t hou

rly m

eans

from

one

day

to th

e ne

xt.

024681012141618

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

10u

IDV

(H)

Yea

rly a

vera

ges

B =

0.46

IDV

+ 2.

09R2 =

0.8

7

V/10

0 =

0.03

IDV

+ 4.

14R2 =

0.0

4

B =

0.38

IDV

+ 2.

78R2 =

0.7

9

R2 = 0

.87

024681012

05

1015

20

1965

-200

6

IDV

012345678910

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

012345678910

B st

d.de

v

Cove

rage

100%

=>

B ob

sB

calc

from

IDV

B ob

s m

edia

n

9

IDV

is c

lose

ly re

late

d to

neg

ativ

e va

lues

of D

st:

J. Lo

ve h

as c

alcu

late

d D

st b

ack

to 1

905.

024681012141618

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

1909

IDV

IDV

cal

c. fr

om D

st(<

0)

IDV

= -0

.40

Dst

(<0)

+ 2

.85

R2 = 0

.89

024681012141618

-40

-30

-20

-10

0

1905

-200

4

IDV

Dst

(<0)

Year

ly a

vera

ges

The

diffe

renc

e in

geo

mag

netic

ef

fect

from

one

larg

e st

orm

to th

e ne

xt is

larg

ely

due

to d

iffer

ent I

MF

stre

ngth

(as t

he so

lar w

ind

spee

d of

ten

follo

ws a

lmos

t the

sam

e pa

ttern

from

stor

m to

stor

m).

So it

is

not a

surp

rise

that

IDV

is a

lmos

t �b

lind�

to th

e so

lar w

ind

spee

d.

10

012345678910

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

B n

T

B =

2.78

+ 0

.38

IDV

B =

3.93

- 0.

1546

(Dst

<0)

B IM

F ob

s

IMF

B in

ferr

ed fr

om ID

V an

d Ds

t

024681012

1870

1890

1910

1930

1950

1970

1990

2010

B n

T

Yea

r

IMF

B in

ferre

d fro

m ID

V

B =

0.4

45 ID

V +

2.21

R2 =

0.8

9

Usi

ng u

-mea

sure

and

IDV

we

can

infe

r IM

F B

dire

ctly

bac

k to

187

2.Th

ere

seem

s to

be a

�G

leis

sber

g�-

type

wav

e in

IMF

B. T

his i

s not

a

surp

rise

beca

use

the

suns

pots

show

a

sim

ilar w

ave.

The

IMF

at so

lar

min

imum

var

ies b

etw

een

4.5

nT

and

5.5

nT. N

ote

that

at p

rese

nt th

e IM

F is

clo

se to

wha

t it w

as 1

00

year

s ago

.

11

012345678910

1830

1840

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Infe

rred

IMF

B s

ince

183

6B

nT

Year

From

Bar

tels

u-m

easu

reIM

F B

obs

S/C

From

IDV

From

sqr

t(Rz)

B =

0.28

82 s

qrt(R

z) +

4.4

856

R2 = 0

.713

9

012345678910

05

1015

B nT

sqrt(

Rz)

1872

-200

6

The

mai

n so

urce

s of t

he e

quat

oria

l co

mpo

nent

s of t

he S

un�s

larg

e-sc

ale

mag

netic

fiel

d ar

e la

rge

activ

e re

gion

s. If

thes

e ac

tive

regi

ons e

mer

ge a

t ran

dom

lo

ngitu

des,

thei

r net

equ

ator

ial d

ipol

e m

omen

t will

scal

e as

the

squa

re ro

ot o

f th

eir n

umbe

r. Th

us th

eir c

ontri

butio

n to

th

e av

erag

e IM

F st

reng

th w

ill te

nd to

in

crea

se a

s SSN

1/2 w

hich

is p

reci

sely

as

obse

rved

.

12

Po

lar C

ap C

urre

nt S

heet

13

VB

= 5

0.14

6 R

ES

R2 =

0.8

594

VB

= 5

0.59

7 TH

LR

2 = 0

.885

6

0

1000

2000

3000

4000

5000

020

4060

8010

0

Ampl

itude

(nT)

VB (k

m/s

* nT

)

1965

-200

4

1883

-80

-60

-40

-20020406080100

-100

-80

-60

-40

-20

020

4060

80

BLC

CB

B

ALE

RE

S

THL

Ve

cto

r V

aria

tio

n o

f H

ori

zon

tal C

om

po

ne

nts

198

0-20

04

The

Pola

r Cap

Cur

rent

is

driv

en b

y th

e Po

lar C

ap

Elec

tric

Pote

ntia

l whi

ch in

tu

rn is

giv

en b

y th

e pr

oduc

t of

the

sola

r win

d sp

eed

V

and

the

IMF

B. T

here

is a

ve

ry d

irect

rela

tions

hip.

14

W

e ca

n ev

en d

o th

is o

n a

27-d

ay ro

tatio

nal b

asis

:

0

1000

2000

3000

4000

5000 1

965

1970

1975

1980

1985

1990

1995

2000

2005

VB

(km

/s *

nT

)

Ob

serv

ed

S/C

RE

S (

Re

solu

te B

ay)

TH

L (

Th

ule

)

012345678910

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

B f

rom

IDV

Vo f

rom

IHV

Ob

serv

ed in

sit

u

01020304050

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

BV

o c

alc.

fro

m ID

V a

nd

IHV

BV

o c

alc.

fro

m P

ola

r C

ap

BV

o o

bse

rved

IDV

giv

es u

s B,

and

IHV

giv

es u

s B

V2 , h

ence

we

can

com

pute

V, t

hen

BV

and

com

pare

w

ith p

olar

cap

BV

.

15

02468101214

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

IMF

B In

ferr

ed fr

om ID

V-In

dex

(Rot

atio

n Av

g.)

B o

bsB

= 1

.67

IDV

0.6

nT

Floo

r

01234567 1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Sola

r Win

d Sp

eed

Infe

rred

from

IHV

and

IDV

V o 1

00 k

m/s

V o o

bsV o

= 1

.6 [(

IHV

- 5) /

IDV

0.6] 1

/2

2313

16

Bac

k in

197

8 I p

ropo

sed

that

the

Sun�

s �op

en�

flux

had

doub

led

since

the

1900

s. Lo

ckw

ood

et a

l. in

a fa

mou

s 199

9 pa

per e

xten

ded

the

anal

ysis

to 1

995

and

infe

rred

an

incr

ease

by

a fa

ctor

of 2

.3 in

depe

nden

t of t

he su

nspo

t num

ber:

The

anal

ysis

was

bas

ed o

n th

e ge

omag

netic

aa-

inde

x.

Subs

eque

nt w

ork

by se

vera

l gr

oups

has

show

n th

at th

e ca

libra

tion

of a

a is

too

low

be

fore

195

7. In

add

ition

, the

re

is a

n in

hom

ogen

eity

in a

bout

19

37. B

efor

e th

at ti

me

May

aud

[who

con

stru

cted

the

aa-in

dex]

ha

d hi

mse

lf sc

aled

all

the

geom

agne

tic re

cord

s, af

ter t

hat

he u

sed

exis

ting

scal

ings

by

othe

rs.

The

mos

t diff

icul

t K-v

alue

to sc

ale

is K

= 0

[no

activ

ity a

t all]

bec

ause

it re

quire

s th

e co

rrec

t rem

oval

of t

he [e

ver c

hang

ing]

dai

ly v

aria

tion

due

to so

lar F

UV

ge

nera

ted

curr

ents

. May

aud

was

the

grea

t exp

ert a

t thi

s and

dar

ed c

lass

ify m

any

inte

rval

s as K

= 0

whe

re o

ther

peo

ple

cons

erva

tivel

y op

ted

for K

= 1

:

17

Seve

ral n

ew in

dice

s of g

eom

agne

tic a

ctiv

ity h

ave

rece

ntly

bee

n in

trodu

ced.

G

eom

agne

tic in

dex

Func

tion

of

B V

α

Prop

onen

ts

IDV

, [D

st<0

]; u

B α

= 0

Sval

gaar

d &

Cliv

er; B

arte

ls

m

B V

0.5

α =

0.5

Lock

woo

d et

al.

PCP

B V

α =

1 Le

Sag

er &

Sva

lgaa

rd

IHV

B

V 2

α =

2 Sv

alga

ard

& C

liver

aa

, am

; ap

B V

2 α

= 2

May

aud;

Bar

tels

B

ecau

se th

ese

depe

nd o

n di

ffer

ent f

unct

ions

of B

and

V, w

e ca

n in

fer b

oth

B an

d V

in th

e pa

st.

The

net r

esul

t was

th

at a

a w

as o

n th

e av

erag

e 3-

5 nT

too

low

dur

ing

the

early

ye

ars,

whi

ch fo

r the

so

lar m

inim

a ye

ars

1901

and

191

2 w

ould

am

ount

to a

bout

40%

, so

no

won

der w

e al

l m

isca

lcul

ated

the

IMF

B a

nd th

e op

en

flux.

18

Usi

ng th

eir n

ew �m

-inde

x� a

nd th

e co

rrec

ted

aa-in

dex,

the

Lock

woo

d gr

oup

(Rou

illar

d et

al

.) ha

s rec

ently

reca

lcul

ated

IMF

B a

nd o

btai

ned

resu

lts th

at a

re v

ery

clos

e to

our

s, al

thou

gh L

ockw

ood

still

mai

ntai

ns th

at th

e 19

99 re

sult

is v

alid

[c.f.

Sol

anki

at S

OR

CE,

20

08]�

The

poin

t for

190

1 is

in e

rror

(Rou

illar

d, P

ers.

Com

m.,

2007

) and

thei

r res

ult b

efor

e 19

10 is

ba

sed

on v

ery

few

sta

tions

with

resu

lting

larg

e er

ror b

ar. A

part

from

such

det

ails

, the

va

rious

gro

ups t

ryin

g to

reco

nstru

ct B

and

V a

re c

onve

rgin

g on

a c

omm

on p

ositi

on th

at

shou

ld b

e ta

ken

into

acc

ount

now

by

othe

r res

earc

hers

, rat

her t

han

rely

ing

on th

e su

perc

eded

ear

lier r

esul

ts.

This

re-a

sses

smen

t of t

he �

open

� flu

x ha

s im

plic

atio

ns fo

r rec

onst

ruct

ions

of v

ario

us so

lar

prox

ies t

hat p

ostu

late

a se

cula

r inc

reas

e of

the

�ope

n� fl

ux.

0246810

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Helio

sphe

ric M

agne

tic F

ield

Mag

nitu

de

Sval

gaar

d &

Cliv

er ID

V07

B nT

Roui

llard

et a

l. 20

07Le

Sage

r & S

valg

aard

200

4IM

F B

Obs

erve

dFl

oor

19

One

exa

mpl

e is

McC

rack

en [2

007]

who

inve

rted

the

cosm

ic ra

y flu

x (in

ferr

ed fr

om 10

Be

fitte

d to

the

secu

lar c

hang

e) to

cal

cula

te th

e IM

F B

(or t

he H

MF

as h

e ca

lls it

):

012345678 18

70

189

01

91

01

930

19

50

19

70

19

90

201

00123456781

1-y

r R

un

nin

g M

ean

of

Heli

osp

heri

c M

ag

ne

tic F

ield

Str

en

gth

B nT

Yea

r

Svalg

aa

rd &

Cliv

er

IDV

07

Ro

uill

ard

et

al. 2

00

7Le

Sa

ger

& S

valg

aard

20

04

Lo

ckw

ood

et

al.

19

99

McC

rack

en 2

007

o

ooooo

IM

F B

ob

serv

ed

012345678910 1

40

015

00

160

0170

018

00

19

00

200

001234567891

0

McC

racke

n 2

007

Sva

lga

ard

& C

liver

20

08

Heli

osp

he

ric

Mag

ne

tic

Fie

ld S

tre

ng

thB nT

Hekla

Mayon,

Ta

mbo

raK

rakato

a?

Ne

utr

on

Mu

on

20

Ano

ther

exa

mpl

e is

reco

nstru

ctio

ns o

f TSI

(Tot

al S

olar

Irra

dian

ce) w

hich

ofte

n re

ly o

n an

�o

pen

flux

back

grou

nd�:

With

out t

he b

ackg

roun

d �r

ise�

190

0-19

60, t

he T

SI se

ems t

o ha

ve v

arie

d le

ss th

an

com

mon

ly a

ssum

ed.

The

end

1362

1363

1364

1365

1366

1367

1700

1750

1800

1850

1900

1950

2000

Hoy

tLe

anW

ang

Sva

lgaa

rdP

rem

inge

rP

MO

DA

CR

IMTI

MD

IAR

AD

TSI R

econ

stru

ctio

ns &

Com

posi

tes

W/m

2

Kriv