RosenbergColeman rule in ES data

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Rosenberg-Coleman rule in ES data
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The ES data set (black) follows very closely the
observed (OMNI) HMF polarity (blue). The black
sinusoid is the least square fit to the full ES
data set. Red lines denote the solar cycle
minima. Plus and minus signs show the polarity
of the Suns dipole field.
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• The Rosenberg-Coleman rule is clearly valid in
  the ES data set both in Fall (top panel) and
  Spring (bottom panel).

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Annual (T-A)/(TA) ratio in ES data set

• HCS is southward shifted also during cycles
  16-18, i.e., during all observed cycles except
  for cycle 19 !
• In 1926-1955 sinusoid amplitude is 0.075
  (significance level 91)
• In 1967-2003 sinusoid amplitude of 0.053
  (significance level 93).
• OMNI data for the latter period has sinusoid
  amplitude of 0.077 (significance level 97).

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Southward shifted HCS
So rather than symmetric, the HCS is southward
shifted or coned and may look like this (Smith et
al., 2000)
During its first fast-latitude scan in 1994-95
Ulysses observed a conical, southward shifted HCS
(Simpson et al., 1996 Crooker et al., 1997).
The OMNI HMF results verified that HCS asymmetry
is a systematic feature, repeating around all the
solar minima covered by in situ IMF
measurements. Also The IMF strength is 5
stronger in the south (Forsyth et al., 1996
McComas et al., 2000 Smith et al., 2000)
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WSO solar magnetic observations
HMF results were confirmed by WSO source surface
field observations (photospheric magnetic field
PFSS). Top Mean field in the south stronger
than in the north. Middle The dipole (black)
and quadrupole (green) terms are indeed
opposite. Bottom HCS has a systematic southward
shift for 3 years. At this time the quadrupole
term has a definite sign. Zhao et al. (JGR,
2005)
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Coronal structure 2 Equator

• Note the extension of the northern polarity past
  the equator in 1984-1987, 1992-1994 and
  2003-2005. This is the Bashful Ballerina.

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Radial profile of the radial field

• Effective n has a strong solar cycle variation
• During the Ballerina times n is larger at the
  north because magnetic equator is shifted south
  and PFSS model gives larger values to northern
  footpoints.
• During the current minima n is large in general,
  because of the large dipole tilt.

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Source latitudes high resolution

• Despite large variability, high resolution data
  depicts the well known polarity cycle of the
  solar magnetic field.
• The field at 1 AU comes typically from 20-30
  latitude in minimum times and from any latitude
  at maximum times.
• Note the rather high latitudes of the present
  cycle!

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HMF at 1 AU

• All components of the HMF at 1 AU are now (since
  2007) weaker than ever since the start of in situ
  HMF measurements. So, the present minimum is
  indeed very exceptional. However, HMF at maximum
  of SC 23 was not weaker than in SC 20.

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HMF polarity at 1 AU

• The Rosenberg-Coleman rule is valid better in
  Fall (north) than Spring (south), leading to the
  Bashful ballerina shift (Mursula-Hiltula, 2003).
• Note that RC rule in SC 23 is established in
  North only very recently (in 2008) and NOT YET in
  South, indicating that the minimum is after 2008.

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Long-term evolution of solar N-S asymmetry from GA

• Size of asymmetry is related to overall solar
  activity, suggesting that the stronger the solar
  dynamo is, the more asymmetric it is.
• GA suggests that the streamer belt (maybe also
  HCS) asymmetry is oscillating with a period of
  about 200 years.

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Conclusions SC 23

• WSO PFSS model and direct HMF observations
  verify the exceptionally weak solar coronal and
  HMF field intensity in the late declining phase
  of SC 23.
• Present radial coronal, photospheric and HMF
  fields are weaker than ever since the
  measurements started in 1970s.
• HCS tilt did not reach the typical value for
  solar minima until the end of 2008, although
  sunspot numbers depict typical minimum values.
• The Bashful Ballerina was seen in WSO and n
  value in 2003-2005 but less strongly than in
  earlier minima.
• The Rosenberg-Coleman rule for SC 23 is
  established in the Northern hemisphere only very
  recently (in 2008) but not yet in the South,
  indicating that the minimum is after 2008.

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Aim of the study

• We compare the open solar magnetic field in the
  corona obtained by the PFSS model with the
  heliospheric magnetic field (HMF) measured in the
  inner heliosphere..

• Trace the observed 9-hour averaged HMF field to
  the corona using the observed solar wind speed
  and its theoretical evolution between PFSS and
  observation site.

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Photospheric structure

• Rotational averages of the photospheric field
  shows the butterfly structure of the magnetic
  field

• Polar field changes its polarity from one
  minimum to another.

• Note that during the current minimum the field
  is exceptionally weak.

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Methods

• The observed solar wind speed and the theoretical
  speed profile from corona to 1 AU (Cranmer, 2004)
  give the time delay between corona and
  observation site.

• Solar wind traveling time
• from corona to 1 AU is

• Now the current solar wind source Carrington
  longitude is

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Comparing the solar magnetic field in the corona
and in the inner heliosphere during solar cycles
21-23
Ilpo Virtanen, and Kalevi Mursula Department of
Physical Sciences, Space physics group University
of Oulu, Finland e-mail Ilpo.Virtanen_at_oulu.fi
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Data and models

• The solar magnetic field can be measured in the
  photosphere (Zeeman effect) and in the
  heliosphere (satellite in situ measurements of
  HMF).
• Coronal field is too weak for the Zeeman effect.
  Therefore one has to use photospheric field
  measurements and a model for the coronal magnetic
  field. Most often a PFSS model is used with PFSS
  at 2.5 Rs.
• The HMF at 1 AU has been measured by several
  satellites since 1963 (Omni data).
• Between 0.3 AU and 1 AU we have data from two
  Helios satellites in 1974-1981.

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Dipole tilt angle

• WSO rotational harmonic coefficients show that
  towards the current minimum the dipole tilt
  decrease very slowly and is still larger than it
  was during the three previous minima. So,
  according to tilt, SC 23 did no yet reach its
  minimum by the end of 2008.

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Coronal field strength

• WSO PFSS model results show a dramatically
  reduced polar field strength during SC 23. Note
  also that the field intensity tends to be larger
  below (than above) equator in the declining
  phase.

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Comparison between Omni and WSO at the same
latitude
Omni and WSO field variations match best during
solar maxima because the field values around HCS
are very weak and dominate in solar minima.
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Conclusions BaBa

• The radial component of the HMF does not decrease
  like

but the effective exponent is clearly smaller
esp. in solar minima. This is mainly due to the
equatorial proximity of the HCS, around which
very weak field values are located.

• During solar minimum times the effective n is
  larger in the north because the magnetic equator
  is shifted southward and the footpoint is further
  away from the (weak values of) HCS. This gives
  additional evidence for the Bashful ballerina
  (southward shifted HCS).
• WSO PFSS model shows that the magnetic field in
  the northern hemisphere is weaker but covers a
  larger area during roughly 3 years in each
  declining phase (Bashful ballerina). The
  extension of the northern polarity past the
  equator is seen in 1984-1987, 1992-1994 and
  2003-2005.

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Radial profile of radial field 1

• According to Maxwell equations, the radial
  magnetic field should behave like

with n 2.

• However, this relation is distorted by the fact
  that the field comes from different solar
  latitudes at different times of the solar cycle.
• During solar maxima, the field comes mainly from
  solar regions close to the line-of-sight location
  leading to better match between Omni and WSO
  fields, as observed.
• During minimum times, the field from large polar
  coronal holes fills even the equatorial
  heliosphere, raising the effective latitude of
  the observed Omni radial field, and filling the
  space between Sun and Earth with additional
  field, thus modifying the n2 rule!

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Coronal structure 1

• Rotational averages of the radial coronal field
  depict less structured field with with strong
  unipolar fields at solar poles around solar
  minima.

• The black line depicts the location of HCS
  according to the PFSS model, i.e., the minimum
  coronal field intensity.
• Yearly oscillation in HCS around solar minima is
  an artefact due to the varying heliographic
  latitude of the Earth, so called vantage point
  effect.

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WSO solar magnetic observations
WSO source surface field Large scale view.
Note the unusually weak polar fields of the soon
ending SC 23.
Yearly oscillation of contour lines, esp. during
solar minima is due to the varying heliographic
latitude of the Earth, the so called vantage
point effect.
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T/(TA) ratio in Fall and Spring (OMNI data)
A away sector magnetic north T toward
sector magnetic south
We have studied the occurrence fraction of one
HMF magnetic hemisphere separately in Fall and
Spring.
Despite some scatter, there is a clear dominance
in Fall of the magnetic hemisphere coming mainly
from the northern heliographic hemisphere. There
is a clear and systematic 22-year variation of
the baseline. Rosenberg-Coleman rule is very
well valid for the northern heliographic
hemisphere.
There is more scatter, and the average level of
dominance in Spring is lower than in Fall. Still,
clearly systematic 22-year variation of the
baseline.
Rosenberg-Coleman rule is valid for the southern
hemisphere, on an average, but less clearly than
in the northern hemisphere.
The difference in the level of the RC rule
between Fall and Spring leads to a systematic
shift of HCS.
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WSO solar magnetic observations Equatorial region
Note the extension of the northern polarity past
the equator in 1984-1987, 1992-1994 and 2003-
2004. This is the Bashful Ballerina.