the open flux has been constant since at least 1840s - leif€¦ · the open flux has been constant...

1

The

Ope

n Fl

ux H

as B

een

Con

stan

t Sin

ce a

t Lea

st 1

840s

Leif

Sval

gaar

d

Invi

ted

pape

r in

SHIN

E 20

07 w

orki

ng g

roup

: Is

the

Ope

n Fl

ux in

the

Hel

iosp

here

Con

serv

ed?

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 n

T, 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

app

roac

hes

the

sam

e co

nsta

nt v

alue

of

4.5

[±0.

5] n

T (p

lus

a sm

all

SSN

-rel

ated

res

idua

l if

the

SSN

did

n't

go a

ll th

e w

ay t

o ze

ro),

corr

espo

ndin

g to

a n

early

con

stan

t ope

n flu

x of

~4x

1014

Wb.

We

revi

ew th

e ev

iden

ce (

and

the

grow

ing

cons

ensu

s) fo

r thi

s sta

rtlin

g co

nclu

sion

. As t

he su

n's p

olar

fiel

ds v

ary

cons

ider

ably

from

cycl

e m

inim

um to

cyc

le m

inim

um, i

t see

ms

that

the

Hel

iosp

heric

fiel

d is

not

det

erm

ined

by

the

pola

r fie

lds,

cont

rary

to w

hat i

s co

mm

only

hel

d. A

s th

e op

en fl

ux a

ppar

ently

has

sta

yed

clos

e to

cons

tant

ove

r th

e pa

st ~

175

year

s, it

mea

ns th

at it

, in

parti

cula

r, di

d no

t dou

ble

durin

g th

e pa

stce

ntur

y. I

n fa

ct, t

he I

MF

durin

g th

e cu

rren

t cyc

le 2

3 is

ver

y m

uch

the

sam

e as

it w

as d

urin

gcy

cle

13 a

cen

tury

ago

. The

abo

ve c

oncl

usio

ns a

re c

onsi

sten

t with

GC

R-b

ased

det

erm

inat

ions

of

B un

der

the

assu

mpt

ion

that

tra

nsie

nts

play

a m

ajor

rol

e in

GC

R m

odul

atio

n, a

lthou

ghin

cons

iste

nt w

ith o

ne re

cent

GC

R re

-cal

ibra

tion

of p

re-1

950

ioni

zatio

n-ch

ambe

r dat

a.

2

Wha

t is �

Ope

n Fl

ux�?

Som

e op

en, s

ome

clos

ed (e

.g. R

iley)

: A

ll op

en fl

ux (e

.g. 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

s R 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

of th

e so

lar w

ind

impi

ngin

gup

on it

. The

resu

lting

con

tinua

l adj

ustm

ent t

o th

e ev

er-c

hang

ing

sola

rwin

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

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 med

ian

y =

1.33

98x0.

6911

R2 = 0

.883

5

y =

0.43

91x

+ 2.

1645

R2 = 0

.866

2

012345678910

05

1015

20

IDV

IMF

B as

a F

unct

ion

of ID

V

B nT

1963

-200

7

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 an

d V,

we

can

infe

r bo

th B

and

V in

the

past

. Bel

ow is

the

IDV

-inde

x an

d ho

w it

can

be

used

to in

fer I

MF

B (y

early

ave

rage

s):

6

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

Her

e is

how

ver

y w

ell t

he IH

V-in

dex

repr

oduc

es th

e pr

oduc

t B V

2 :

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

7

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

Her

e ar

e B

and

V as

infe

rred

from

IDV

and

IHV

sinc

e 18

83:

01234567 1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Sola

r W

ind

Spee

d In

ferr

ed fr

om IH

V an

d ID

V

V o 1

00 k

m/s

V o o

bsV o

= 1

.6 [(

IHV

- 5) /

IDV

0.6

] 1/2

Floo

r

8

Rec

ently

Loc

kwoo

d et

al.

(Rou

illar

d, L

ockw

ood,

& F

inch

, JG

R,

112,

A05

103,

200

7) h

ave

real

ized

that

thei

r 199

9 (N

atur

e, 3

99, 4

37, 1

999)

ana

lysi

s w

as in

accu

rate

bec

ause

of r

elia

nce

onth

e in

corr

ectly

cal

ibra

ted

geom

agne

tic a

a-in

dex

and

brea

kdow

n of

an

ad h

ocre

latio

nshi

p be

twee

n so

lar

win

d sp

eed

and

the

Sarg

ent

recu

rren

ce i

ndex

. C

ombi

ning

sev

eral

ind

ices

(incl

udin

g th

eir n

ew m

-inde

x), t

heir

revi

sed

calc

ulat

ion

of IM

F B

is sh

own

here

(dot

s):

0246810

1965

1970

1975

1980

1985

1990

1995

2000

2005

0246810

S&

C

R,L

&F

(B

LS,ID

V,m

,aa c

)

IMF

obs

Mag

nitu

de o

f In

terp

lan

etar

y M

agn

etic

Fie

ld a

t E

arth

nT

Yea

r

Thei

r rev

ised

val

ues

(dot

s) a

gree

reas

onab

ly w

ell w

ith th

e ob

serv

ed IM

F an

d w

ith o

ur in

ferre

dB

from

IDV

, alth

ough

thei

r val

ues t

end

to o

vers

hoot

(low

val

ues t

oo lo

w; h

igh

valu

es to

o hi

gh).

Her

e is

a c

ompa

rison

bac

k to

189

5:

9

0246810

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

0246810

S&

CR

,L&

F (

BLS

,IDV

,m,a

a c)

IMF

obs

Mag

nitu

de o

f Int

erpl

anet

ary

Mag

netic

Fie

ld a

t E

arth

nT

Yea

r

Cyc

le 2

3

Apa

rt fro

m th

e ov

ersh

oots

, the

long

-term

tren

ds a

re in

goo

d ag

reem

ent (

4th-o

rder

pol

ynom

ial f

it sh

own)

. The

sin

gle

year

190

1 st

ands

out

as

an o

bvio

us o

utlie

r (e

xtre

me

over

shoo

t: ap

plyi

ng a

rela

tion

outs

ide

of th

e do

mai

n on

whi

ch it

was

def

ined

). It

does

not

see

m r

easo

nabl

e th

at th

eIM

F sh

ould

dro

p by

a f

acto

r of

tw

o in

a s

ingl

e so

lar

min

imum

yea

r an

d th

en i

mm

edia

tely

reco

ver (

whe

re d

id it

go?

And

whe

re d

id th

e re

cove

ry fl

ux c

ome

from

?).

Not

e th

at if

we

shift

cyc

le 2

3 to

107

year

s ea

rlier

to m

ake

it co

inci

de w

ith c

ycle

13,

we

see

that

the

IMF

was

the

sam

e th

en a

s now

. The

re d

oes n

ot se

em to

any

secu

lar t

rend

ove

r the

mor

e th

an10

0 ye

ars.

Ther

e do

es se

em b

e a

�Gle

issb

erg�

-type

osc

illat

ion,

just

like

in th

e su

nspo

t num

ber:

10

024681012

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

050100

150

200

250

300

350

400

B (ID

V)B

(SSN

)nT

o B

(RL&

F, m

-aac

-BLS

)

Rz

B =

(4.4

9±-0

.12)

+ (0

.277

±0.0

16)S

SN1/

2

R2 =

0.7

142

012345678910

01

23

45

67

89

1011

1213

14

IMF

B nT

SQR

T(SS

N)

IMF

B (Y

early

Avg

s) a

s a

Func

tion

of S

QR

T(SS

N)In

fac

t, it

seem

s th

at m

ost

of t

heva

riatio

n of

the

IMF

stre

ngth

ca n

be a

ccou

nted

for

(re

d cu

rve)

by

a(s

quar

e ro

ot o

f) s

unsp

ot n

umbe

rde

pend

ent

cont

ribut

ion:

rid

ing

ona

cons

tant

�flo

or�

of ~

4.5

nT. W

ein

terp

ret

this

flo

or a

s th

e�o

pen

flux�

, re

gard

ing

the

SSN

-rela

ted

part

to b

e la

rgel

y �c

lose

d� f

lux.

(Sva

lgaa

rd &

Cliv

er,

ApJ

Lette

rs,

661,

L20

3, 2

007)

.

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)

Ther

e is

sui

tabl

e ge

omag

netic

dat

a ba

ck to

183

6 al

low

ing

estim

atio

n of

IM

F B

indi

catin

g th

esa

me

basi

c re

sult:

that

IMF

Bst

ill th

at fa

r bac

k ca

n be

rega

rded

as

a co

mbi

natio

n of

a c

onst

ant

open

�flo

or�

and

the

clos

ed S

SN-r

elat

ed p

art:

The

trans

port

in th

e H

elio

sphe

re o

f Gal

actic

Cos

mic

Ray

s of e

nerg

y <

10 G

eV is

gov

erne

d by

the

stre

ngth

, sp

atia

l st

ruct

ure,

and

tur

bule

nce

of t

he I

MF

(or

may

be b

ette

r: th

e �H

MF�

), an

dco

nseq

uent

ly t

he i

nten

sity

of

the

radi

atio

n is

stro

ngly

mod

ulat

ed b

y ch

ange

s in

the

IM

Fas

soci

ated

with

sol

ar a

ctiv

ity.

Whe

n en

terin

g th

e Ea

rth�s

atm

osph

ere,

the

GC

R g

ener

ates

seco

ndar

y pa

rticl

es t

hat

then

pro

duce

the

cos

mog

enic

nuc

lides

(e.

g. 10

Be

and

14C

) th

at a

re

subs

eque

ntly

dep

osite

d in

ice

core

s an

d tre

e rin

gs f

rom

whi

ch th

e G

CR

flu

x in

the

past

may

be

estim

ated

. Ass

umin

g a

suita

ble

mod

el (c

alib

rate

d w

ith m

oder

n da

ta) o

f the

influ

ence

of B

on th

e di

ffusi

on a

nd m

odul

atio

n of

GC

Rs,

B in

the

past

may

then

be

infe

rred

.

12

A m

ajor

unk

now

n is

how

the

diff

usio

n co

effic

ient

, κ d

epen

ds o

n B.

Cab

alle

ro-L

opez

et a

l.(J

GR

,10

9, A

1210

2, 2

004)

con

side

r th

ree

case

s of

dep

ende

nce

of κ

on

corr

elat

ion

leng

th a

nd f

iel d

varia

nce

varia

tion

with

sol

ar a

ctiv

ity: l

ow (κ

~ B

-1),

mod

erat

e (κ

~ B

-2) o

r stro

ng (κ

~ B

-3).

The

latte

r cas

e w

ould

occ

ur if

larg

e-sc

ale,

tran

sien

t stru

ctur

es, s

uch

as IC

MEs

pla

y an

impo

rtant

role

durin

g pe

riods

of

high

sol

ar a

ctiv

ity. W

e ca

n co

mpa

re th

e re

sult

of th

e C

abal

lero

-Lop

ez e

t al.

inve

rsio

n un

der

the

assu

mpt

ion

that

κ ~

B-3

with

B in

ferr

ed f

rom

ID

V a

nd S

SN a

nd n

ote

good

agre

emen

t [al

so w

ith th

e �m

iddl

e� 14

C in

vers

ion

by M

üsch

eler

et a

l. (N

atur

e, 4

36, 3

, 200

5)]:

012345678910 1

500

1550

1600

1650

1700

175

01800

18

50

1900

1950

2000

B n

T

SS

N14

C10

Be

IDV

Cyc

le A

vera

ges

of

Infe

rred

IMF

Mag

nit

ud

e

13

The

IMF

infe

rred

from

GC

Rs i

s ver

y se

nsiti

ve to

the

depe

nden

ce o

f the

diff

usio

n co

effic

ient

on

B, a

s can

be

seen

in th

e fo

llow

ing

Figu

re fr

om C

abal

lero

-Lop

ez e

t al.:

Our

bes

t mat

ch c

urve

McC

rack

en (

e.g.

Spa

ce W

eath

er, 5

, S07

004,

200

7) a

rgue

s th

at th

ere

has

been

ver

y la

rge

chan

ges

(of a

n or

der o

f mag

nitu

de) i

n th

e op

en fl

ux c

omm

ensu

rate

with

κ ~

B-1

or w

eake

r. Ev

iden

ce fo

r thi

sar

e Lo

ckw

ood�

s or

igin

al c

laim

(th

e �d

oubl

ing�

) an

d a

re-c

alib

ratio

n of

old

�io

niza

tion-

cham

ber�

cosm

ic ra

y re

cord

s:

14

McC

rack

en p

ostu

late

s ~4

�flo

ors�

of I

MF

stre

ngth

in th

e la

st 6

00 y

ears

, the

low

est (

and

earli

est)

bein

g on

ly o

ne-te

nth

of t

he �

mod

ern�

flo

or. T

he l

ast

�jum

p� (

from

3.5

nT

to 5

.2 n

T) i

n flo

orva

lue

took

pla

ce a

roun

d 19

49. T

hat y

ear i

s w

ell w

ithin

the

rang

e of

the

high

-qua

lity

geom

agne

ticre

cord

that

doe

s not

supp

ort s

uch

a ju

mp.

Ano

ther

reco

nstru

ctio

n in

corp

orat

ing

the

old

ioni

zatio

n-ch

ambe

r da

ta (

left)

by

Stoz

hkov

et

al.

[Pro

c. I

CR

C,

p.38

83, 2

001]

doe

s not

show

any

�ju

mp�

aro

und

1950

.

15

Her

e is

McC

rack

en�s

re-

calib

rate

d G

CR

-rec

ord

(dot

s =

ioni

zatio

n-ch

ambe

rs;

line

= ne

utro

nm

onito

rs).

Just

like

with

the

aa-in

dex

(and

the

suns

pot n

umbe

r) w

e ar

e fa

ced

with

the

prob

lem

of e

nsur

ing

the

long

-term

sta

bilit

y of

the

calib

ratio

n of

our

prim

ary

data

. Thi

s is a

than

kles

s (b

u tim

porta

nt) j

ob.

The

sola

r cyc

le m

odul

atio

n in

the

ioni

zatio

n-ch

ambe

r GC

R d

ata

seem

s di

stor

ted

com

pare

d w

ithth

e ne

utro

n m

onito

r dat

a an

d se

ems

to la

ck to

cha

ract

eris

tic �

shar

p-fla

t� a

ltern

atio

n of

the

peak

s. I�m

not

qua

lifie

d to

com

men

t muc

h fu

rther

on

the

GC

R m

easu

rem

ents

, exc

ept t

o no

te th

at th

e G

CR

inve

rsio

ns a

re v

ery

mod

el-d

epen

dent

.

16

-150

-100-50050100

150 19

9419

9519

9619

9719

9819

9920

0020

0120

0220

0320

0420

0520

0620

07-4-3-2-101234

uTPo

lar F

ield

s in

Pho

tosp

here

(cur

ves)

and

in H

elio

sphe

re a

t 1 A

U (s

ymbo

ls)

Nor

th

Sou

th

nT

The

exis

tenc

e of

a F

loor

in th

e IM

F (o

ne th

roug

hout

or s

ever

al [M

cCra

cken

]) p

rese

nts

a pu

zzle

:O

ur u

nder

stan

ding

, cod

ified

in o

ur m

odel

s, of

the

orig

in o

f the

IMF

dict

ates

that

the

IMF

at s

olar

min

imum

is v

ery

sens

itive

to th

e so

lar p

olar

fiel

ds. �

As

the

pola

r fie

lds

go, s

o go

es th

e ca

lcul

ated

IMF�

(ope

n sy

mbo

ls =

mod

eled

Br p

er W

SA &

MA

S; fi

lled

sym

bols

= U

lyss

es B

r per

the

team

):

The

pola

r fie

lds

at d

iffer

ent m

inim

a ar

e ob

serv

ed to

var

y by

a fa

ctor

of t

wo

or m

ore;

eith

erpr

edic

ting

the

size

of

the

next

sol

ar c

ycle

(Sv

alga

ard

et a

l.) o

r, as

the

rem

nant

s of

the

prev

ious

cyc

le, r

efle

ctin

g th

e si

ze o

f th

at c

ycle

(D

ikpa

ti et

al.)

. We

wou

ld th

us e

xpec

t the

IM

F to

var

y by

the

sam

e fa

ctor

; the

puz

zle

is th

at it

doe

s not

:

17

For

the

two

min

ima

befo

re c

ycle

s 20

and

19,

res

pect

ivel

y, th

e po

lar

field

s ca

n on

ly b

e ro

ughl

yes

timat

ed. A

s a

mea

sure

of

the

Sun�

s di

pole

mom

ent,

DM

, we

take

the

abs

olut

e va

lue

of t

hedi

ffer

ence

bet

wee

n th

e N

orth

and

Sou

th p

olar

fiel

ds. D

M v

arie

s as

1.6

Rm

ax, s

o fo

r Rm

axva

ryin

g fr

om 6

4 (c

ycle

14)

to 1

90 (

cycl

e 19

), D

M s

houl

d va

ry f

rom

100

uT

to 3

00 u

T, a

nd I

MF

Bat

m

inim

um s

houl

d va

ry f

rom

4 n

T to

12

nT w

hich

it c

lear

ly d

oes

not.

Wha

t is

mis

sing

in o

ur

mod

els (

and

unde

rsta

ndin

g)?

DM

= 1

.6 R

max

(nex

t cyc

le)

0

100

200

300

400

025

5075

100

125

150

175

200

0246810121416

19

2023

24

21

22

DM

uT

Rm

ax

Sola

r 'D

ipol

e M

omen

t' as

a fu

nctio

n of

Siz

e of

Fol

low

ing

Suns

pot C

ycle

IMF

nT

B24

18

Con

clus

ions

1. T

he g

eom

agne

tic re

cord

bac

k to

~18

40 su

ppor

ts th

e no

tion

that

the

IMF

is t

he s

um o

f a

cons

tant

�flo

or�

at 4

.5 n

T (o

pen

flux)

and

ava

riabl

e co

ntrib

utio

n (m

ostly

clo

sed

flux)

fro

m C

MEs

and

oth

er

suns

pot-r

elat

ed fl

ux.

2. T

his

is c

onsi

sten

t with

the

IMF

stre

ngth

der

ived

from

cos

mog

enic

nucl

ides

und

er t

he a

ssum

ptio

n th

at l

arge

-sca

le, t

rans

ient

stru

ctur

es,

such

as

ICM

Es p

lay

an i

mpo

rtant

rol

e in

the

mod

ulat

ion

of G

CR

sdu

ring

perio

ds o

f hi

ghso

lar

activ

ity, a

lthou

gh th

ere

is (

unre

solv

ed)

disa

gree

men

t with

a r

ecen

t re-

calib

ratio

n of

GC

R f

lux

deriv

ed f

rom

ioni

zatio

n-ch

ambe

r dat

a be

fore

abo

ut 1

949.

3.

The

IM

F B

at s

olar

min

imum

doe

s no

t se

em t

o va

ry i

n co

ncer

tw

ith th

e so

lar p

olar

fiel

ds a

s our

mod

els s

ugge

st it

shou

ld.