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.
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).
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