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Long-term Variations of Open Flux in the Solar Corona (The ... · 400 300 200 100 0 BV 1990 1991...

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1 Long-term Variations of Open Flux in the Solar Corona (The Open Flux Has Been Constant Since at Least 1840s) Leif Svalgaard ETK, Houston, TX Abstract: The geomagnetic record allows us to infer the strength of the Interplanetary Magnetic Field, | B|, at Earth for the past ~175 years. We find B to be 4.5 + 0.28 (SSN) 1/2 nT, where SSN is the sunspot number. We interpret the SSN-dependent part to be closed flux related to CMEs and flare ejecta, effectively riding on top of a constant minimum of open B of 4.5 nT. At each solar minimum as SSN goes to near zero, the field strength B approaches the same constant value of 4.5 [–0.5] nT (plus a small SSN-related residual if the SSN didn’t go all the way to zero), corresponding to a nearly constant open flux of ~4x10 14 Wb. We review the evidence (and the growing consensus) for this startling conclusion. As the sun’s polar fields vary considerably from cycle minimum to cycle minimum, it seems that the Heliospheric field is not determined by the polar fields, contrary to what is commonly held. As the open flux apparently has stayed close to constant over the past ~175 years, it means that it, in particular, did not double during the past century. In fact, the IMF during the current cycle 23 is very much the same as it was during cycle 13 a century ago. The above conclusions are consistent with GCR-based determinations of B under the assumption that transients play a major role in GCR modulation.
Transcript

1

Lon

g-te

rm V

aria

tions

of O

pen

Flux

in th

e So

lar

Cor

ona

(The

Ope

n Fl

ux H

as B

een

Con

stan

t Sin

ce a

t Lea

st 1

840s

)

Leif

Sval

gaar

d ET

K, H

oust

on, T

X

Abs

tract

: The

geo

mag

netic

reco

rd a

llow

s us

to in

fer t

he s

treng

th o

f the

Inte

rpla

neta

ry M

agne

ticFi

eld,

|B|,

at E

arth

for t

he p

ast ~

175

year

s. W

e fin

d B

to b

e 4.

5 +

0.28

(SSN

)1/2

nT, w

here

SSN

is

the

suns

pot n

umbe

r. W

e in

terp

ret t

he S

SN-d

epen

dent

par

t to

be c

lose

d flu

x re

late

d to

CM

Es a

ndfla

re e

ject

a, e

ffect

ivel

y rid

ing

on to

p of

a c

onst

ant m

inim

um o

f ope

n B

of 4

.5 n

T. A

t eac

h so

lar

min

imum

as

SSN

goe

s to

nea

r zer

o, th

e fie

ld s

treng

th B

appr

oach

es th

e sa

me

cons

tant

val

ue o

f4.

5 [±

0.5]

nT

(plu

s a

smal

l SS

N-r

elat

ed r

esid

ual

if th

e SS

N d

idn'

t go

all

the

way

to

zero

),co

rres

pond

ing

to a

nea

rly c

onst

ant o

pen

flux

of ~

4x10

14W

b. W

e re

view

the

evid

ence

(an

d th

egr

owin

g co

nsen

sus)

for t

his s

tartl

ing

conc

lusi

on. A

s the

sun'

s pol

ar fi

elds

var

y co

nsid

erab

ly fr

omcy

cle

min

imum

to c

ycle

min

imum

, it s

eem

s th

at th

e H

elio

sphe

ric fi

eld

is n

ot d

eter

min

ed b

y th

epo

lar f

ield

s, co

ntra

ry to

wha

t is

com

mon

ly h

eld.

As

the

open

flux

app

aren

tlyha

s st

ayed

clo

se to

co

nsta

nt o

ver

the

past

~17

5 ye

ars,

it m

eans

that

it, i

n pa

rticu

lar,

did

not d

oubl

e du

ring

the

past

cent

ury.

In

fact

, the

IM

F du

ring

the

curr

ent c

ycle

23

is v

ery

muc

h th

e sa

me

as it

was

dur

ing

cycl

e 13

a c

entu

ry a

go. T

he a

bove

con

clus

ions

are

con

siste

nt w

ith G

CR

-bas

ed d

eter

min

atio

ns o

f B

unde

r the

ass

umpt

ion

that

tran

sien

ts p

lay

a m

ajor

role

in G

CR

mod

ulat

ion.

2

Wha

t is �

Ope

n Fl

ux�?

Som

e op

en, s

ome

clos

ed (e

.g. P

. Rile

y):

All

open

flux

(e.g

. M. L

ockw

ood)

: (m

ore

than

dou

blin

g in

100

yea

rs)

No

open

flux

(Max

wel

l):

The

(uns

igne

d, to

circ

umve

nt M

axw

ell)

mag

netic

flu

x, F

, in

the

Hel

iosp

here

is c

alcu

late

d by

inte

grat

ing

the

unsi

gned

rad

ial c

ompo

nent

, |B r

,| of

the

IMF

over

a s

urfa

ce (

�eff

ectiv

e� r

adiu

sR F

) en

clos

ing

the

Sun.

The

re a

re s

ome

disa

gree

men

ts o

ver

whe

ther

to

coun

t th

e flu

x tw

ice

(onc

e fo

r eac

h po

larit

y), s

o w

e w

rite

F

= |B

r| 4π

RF2 / k

whe

re k

= 1

or 2

.

3

0.0

0.1

0.2

0.3

0.4

0.5

0.6 19

6019

6519

7019

7519

8019

8519

9019

9520

0020

05

Obs

. |B r

|/B0.

53 -

R z/2

000

IMF

Radi

al C

ompo

nent

Br a

t Ear

th Firs

t Ave

rage

d ov

er 1

Day

Wea

k Fu

nctio

n of

SS

N

Frac

tion

of M

agni

tude

B o

f IM

F

Cal

cula

ting

the

radi

al c

ompo

nent

is tr

icky

as

the

IMF

varie

s co

nsid

erab

ly in

dire

ctio

n on

man

y tim

e sc

ales

and

Br

thus

dep

ends

on

the

aver

agin

g in

terv

al.

Ofte

n, a

s w

e ar

ein

tere

sted

in

the

larg

e-sc

ale

stru

ctur

e) o

ne d

ay i

s us

ed.

One

fin

ds t

hat

the

ratio

Br/B

isab

out

0.5

with

a s

mal

l (w

eak)

var

iatio

n w

ith t

he S

SN:

mor

e so

lar

activ

ity m

akes

the

dire

ctio

n va

ry m

ore

and

thus

low

ers

B r/B

slig

htly

. To

first

ord

er w

e ca

n th

us d

eter

min

e B r

from

B. F

rom

geo

mag

netic

act

ivity

we

can

dete

rmin

e B

and

thus

est

imat

e th

e lo

ng-te

rmbe

havi

or o

f the

flux

.

4

The

Earth

�s m

agne

tic f

ield

is

conf

ined

by

the

sola

r w

ind

to a

�m

agne

tosp

here

�, w

hich

is

sens

itive

to th

e in

terp

lane

tary

mag

netic

fiel

d an

d th

e ki

netic

ene

rgy

ofth

e so

lar w

ind

impi

ngin

g up

on it

. The

resu

lting

con

tinua

l adj

ustm

ent t

o th

e ev

er-c

hang

ing

sola

r win

d co

nditi

ons

is c

alle

d�g

eom

agne

tic a

ctiv

ity�.

Her

e is

a ty

pica

l exa

mpl

e (a

s mea

sure

d at

the

surf

ace

of th

e Ea

rth):

From

the

ampl

itude

of

the

varia

tion

of th

e fie

ld w

ithin

a c

erta

in in

terv

al (

thre

e ho

urs

in th

e ab

ove

exam

ple)

one

con

stru

cts

a ge

omag

netic

�in

dex�

that

cod

ifies

tha

t va

riatio

n an

d ca

n be

use

d as

apr

oxy

for s

olar

win

d co

nditi

ons d

urin

g th

e in

terv

al.

5

A

= k

q(a,

f (V)

) (B

V) (n

V 2 )1/

3 ~ B

V 2

6

7

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

8

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

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. 1

0

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

9

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.

10

0

100

200

300

400 19

9019

9119

9219

9319

9419

9519

9619

9719

9819

9920

0020

0120

02

BVo2 o

bs

BV o

2 cal

c

0

100

200

300

400 20

0020

0120

0220

0320

0420

0520

0620

0720

0820

0920

1020

1120

12

BVo2 o

bs

BVo2 c

alc

y =

4.24

81x

- 21.

156

R2 =

0.7

869

y =

2.55

22x1.

0975

R2 =

0.7

675

0

100

200

300

400

020

4060

8010

0

BV o

2R

otat

ion

Mea

ns

IHV

22-y

ear c

ycle

eff

ect

11

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

NH P

ower

(GW

) = 0

.680

7 IH

VR2 =

0.8

582

010203040506070

020

4060

8010

0

1978

-200

6

12

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

13

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.

14

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

07

year

s ago

.

15

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 w

hat w

e ob

serv

e (le

ft).

16

Yet

ano

ther

way

Po

lar C

ap C

urre

nt S

heet

17

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.

18

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

.

19

W

e ca

n ev

en d

o th

is o

n a

27-d

ay ro

tatio

nal b

asis

:

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

20

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

:

21

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

amou

nt to

abo

ut 4

0%,

so n

o w

onde

r we

all

mis

calc

ulat

ed th

e IM

F B

and

the

open

flu

x.

-10-8-6-4-20246810

18

901

900

19

10

19

20

19

30

19

40

19

50

19

60

19

70

19

80

19

90

20

00

Aa o

bs -

Aa c

alc

1957

.0

Diff

eren

ce b

etw

een

aa o

bser

ved

and

aa

calc

ulat

ed fr

om IH

V(fo

r 198

0-20

04):

Aa =

0.3

6 IH

V 1.1

856

R2 =

0.9

511

22

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

., 20

07) h

as re

cent

ly re

calc

ulat

ed IM

F B

and

obt

aine

d re

sults

that

are

ver

y cl

ose

to o

urs,

alth

ough

Loc

kwoo

d st

ill m

aint

ains

that

the

1999

resu

lt is

val

id [c

.f. S

olan

ki a

t SO

RC

E]�

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 b

ased

on

very

few

stat

ions

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 ca

lcul

ated

from

B h

as im

plic

atio

ns fo

r re

cons

truct

ions

of v

ario

us so

lar p

roxi

es th

at p

ostu

late

a se

cula

r inc

reas

e of

the

�ope

n�

flux.

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

23

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

va

lga

ard

20

04

Lo

ckw

ood

et

al. 1

99

9M

cC

racke

n 2

007

o

ooooo

IM

F B

ob

se

rved

012345678910 1

400

15

00

160

017

00

180

019

00

200

001234567891

0

McC

racke

n 2

007

Svalg

aa

rd &

Cliv

er

200

8

Heli

osp

he

ric M

ag

ne

tic F

ield

Str

en

gth

B nT

Hekla

Mayo

n,

Tam

bora

Kra

kato

a?

Neu

tron

Muo

n

24

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.

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

25

Con

clus

ion

Geo

mag

netic

act

ivity

has

bee

n us

ed t

o in

fer

the

HM

F [o

r th

e �o

pen�

sol

ar

mag

netic

flu

x] b

efor

e th

e Sp

ace

Age

. Ear

lier,

thes

e in

fere

nces

wer

e di

scor

dant

an

d co

ntro

vers

ial.

In th

e la

st c

oupl

e of

yea

rs, t

he s

ourc

es o

f the

se d

isag

reem

ents

ha

ve b

een

unco

vere

d an

d co

rrec

ted

and

a re

mar

kabl

e co

nsen

sus

is

now

em

ergi

ng, w

ith th

e re

sult

that

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 con

stra

ined

to a

leve

l of ~

10%

or b

ette

r.

The

end


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