The Open Flux Has Been Constant Since at Least 1840s - Leif€¦ · The Open Flux Has Been Constant...
18
1 The Open Flux Has Been Constant Since at Least 1840s Leif Svalgaard Invited paper in SHINE 2007 working group: Is the Open Flux in the Heliosphere Conserved? 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, although inconsistent with one recent GCR re-calibration of pre-1950 ionization-chamber data.
Transcript of 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.
