Transcript Validation of One-point Inversion Solution of the Elliptic

Absence of a Long Lasting
Southward Displacement of the
HCS Near the Minimum
Preceding Solar Cycle 24
X. P. Zhao, J. T. Hoeksema and P. H.
Scherrer
Stanford University
D24 P110, July 15, 2008
37th COSPAR Scientific Assembly, Montreal
July 13-20, 2008
Abstract
Definitive observational evidence of a ~10 degres
southward displacement of the heliospheric current sheet
(HCS) from the heliographic equator was obtained from
Ulysses observations near the minimum phase preceding
Solar Cycle 23. The HCS southward displacement near the
minimum phase has been suggested to be a persistent
phenomenon. We found from the PFSS model prediction
that there are 3-year lasting southward displacement of
the HCS near the minimum preceding solar cycle 22
and 23 [Zhao et al., 2005]. This work shows, however, the
absence of similar interval of HCS southward
displacement between 2004 and 2008. Is the absence of
the 3-year interval an abnormal phenomena?
1. Introduction
• The heliospheric current sheet (HCS) separates the
heliosphere into two magnetic hemispheres with
opposite magnetic polarity.
• Definitive observational evidence of a ~10 deg
southward displacement of the HCS from the
heliographic equator was obtained from Ulysses
observations in the rapid transit from the south to
north solar poles between September 1994 and May
1995 [Simpson et al., 1996; Smith et al., 2000]. A
similar southward displacement in the green-line
corona was observed during solar minima of cycles
21 and 22; statistical analysis of the IMF sector
duration also shows a southward displacement of
the average HCS around the minimum phase of
cycles 20, 21 & 22.
• The positive-negative and north-south HCS
displacements computed using a potential
field - source surface model applied to Wilcox
Solar Observatory (WSO) observations
between 1976 and 2001 revealed the existence
of ~3-year lasting HCS southward
displacement near the minimum phase of solar
cycles 21 and 22, consistent with the greenline corona observations and the statistical
results of HMP polarity [Zhao et al., 2005]. We
extend the study to April 2008 to see if the
similar long lasting HCS southward
displacement occurs between 2003 and 2008
and discuss whether the absence is a normal
or abnormal phenomenon.
2. Prediction of the hemispheric
asymmetry of the heliomagnetosphere
• By defining the magnetic hemisphere with the same
polarity as the dominant polarity in north (south)
polar region as the north (south) heliomagnetic
hemisphere (HH), and using the PFSS model, the
effective displacement of the HCS from the Sun’s
dipole equator, λm, and from the heliographic
equator, λ, can be calculated
λm = arcsin (1 – In δΩ / 2π )
λ = λm |cos ψ|
(1)
(2)
Here ‘In’ denotes the number of solid angle element
(δΩ=4π/2160 for WSO) in the north HH; ψ, tilt angle.
Fig. 1 Evolution of Sun’s tilt angle ψ calculated using WSO data from
June 1976 to April 2008. The positive (negative) magnetic polarity is
in the north polar region when ψ = 0 (180).
Fig 2. The difference between positive and negative solid angles
corresponding to positive and negative heliomagnetic hemisphere.
In 1980s, south positive area is less than north negative area; in
1990s, north positive area is greater than south negative area. Both
show that the north hemisphere is more strongly developed and
greater than the south hemisphere.
Fig. 3 Calculated λm (dotted line) and λ (solid line). There are two 3-year
intervals of southward displacement of the HCS (between 1983:03 &
1986:07 and between1992:04 & 1995:05) preceding Cycle 22 and 23.
There is no such 3-year interval preceding Cycle 24 !?
Fig. 4 Predicted IMF radial component Br in the positive (away) and
negative (toward) heliomagnetic hemisphere. Between 83:03 & 86:07,
south positive Br is greater than north negative Br; between 92:04 &
95:05, south negative Br is greater than north positive Br, consistent
with the HCS southward displacement. There is no such systematicly
N-S asymmetry between 2005 and 2008.
3. Photospheric field in north
and south polar regions
The southward displacement of the HCS near the minimum has
been attributed to the north-south asymmetry in the Sun’s polar
magnetic field. The HMF is composed mainly of lower multipole
components: the dipole, the quadrupole, and the hexapole.
Around sunspot minimum these lower-order multipoles are
orientated basically parallel to the Sun’s rotation axis and can
be approximately represented by the zonal harmonic
coefficients g10, g20 and g40. The polar field represented by
g10 has opposite polarity in the north and south polar regions,
but the field described by g20 & g40 has the same polarity in
both polar regions, giving rise to an asymmetry in the field
strength. The absence of the 3-year southward displacement of
the HCS preceding the cycle 24 implies the absence of the
asymmetry in the field strength between the south and north
polar regions.
Fig. 5 The difference in WSO mean field amplitude between the north and south
polar caps above 55 degrees of north and south heliographic latitude. Each point
denotes the rotation-averaged value of the north polar field subtracted by the
rotation-averaged value of the south polar field. There are 3-year interval when
south polar field is stringer than north polar field. But there is no such asymmetry
in the polar field preceding cycle 24.
Fig 6. The evolution of the amplitude and sign of the zonal lower-order
multipole components, g10, g20 and g40 between June 1976 and April
2008. The opposite sign between g10 and g20 lasts near 3-year in the
earlier two intervals, but g20 shows small fluctuations around zero
preceding the cycle 24 , and g10 is significantly less than what in the
earlier two intervals.
4. Duration of two IMF sector
structures
The southward displacement of the HCS should affect the duration of two
sector structures observed near the Earth, but the effect may be
contaminated by the ICME, large-amplitude Alfvenic waves, and various
stream-stream interaction. As shown in Figure 3, the southward
displacement of the HCS is mostly less than 7.2 degrees, its effect may
be shown in the in situ observations made in Fall and Spring seasons
when the Earth reaches 7.2 degrees of solar latitude. Mursula and Hiltula
[2003] have calculated the Toward sector occurrence fractions T/(T+A )
using hourly IMF data between 1967 & 2001 (here T & A denote the total
number of Toward & Away sector hours for each 3-month season of
Spring=Feb--Apr and Fall=Aug—Oct). They found that the IMF sector in
the northern hemisphere is systematically more strongly developed,
suggesting the southward displacement of the HCS. We extend the
analysis to April, 2008 using IMF daily polarity of OMNI and Leif
Svalgaard ( http://omniweb.gsfc.nasa.gov/ and
http://www.leif.org/research/).
Figure 7. The same as Figure 1 of Mursula and Hiltula [2003], but
extending to April 2008 from 2001 and using daily IMF polarity. The
evolution of the toward sector occurrence fraction before 2002 is
basically the same as what Mursula and Hiltula obtained, showing that
the IMF sector in the northern hemisphere is systematically more
strongly developed, but there is no such asymmetry after 2003.
Figure 8. The same as Figure 7 but using the IMF daily polarity inferred
by Dr. Leif Svalgaard. The evolution of the toward sector occurrence
Fraction here is basically the same as Figure 7, implying the validation of
IMF polarity data inferred by Dr. Leif Svalgaard in analyzing latitudinal
Variation of dominate IMF polarity.
Figure 9. The same as Figure 8, but starting from the year of 1926,
increasing 4 more solar cycles. The evolution of the toward sector
occurrence fraction before the year of 1940 is the same as after 2003,
showing the absence of the asymmetry in the development of IMF
sector structures between the north and south hemisphere, i.e.,
the absence of the long lasting southward displacement of the HCS
near the minimum phase in solar cycles 16, 17, and 23.
Figure 10. The time variation of the sunspot number between
Janual1926 and April 2008, showing the normal evolution of the
solar activity in solar cycle 23.
6. Summary & Discussion
6.1 Using the algorithm developed for
quantitative estimate of the north-south
displacement of the HCS [Zhao et al., 2005]
and the WSO data observed until April 2008,
we find that, different from Solar cycles 21
and 22, there is no the ~3-year lasting HCS
southward displacement near the minimum
phase in solar cycle 23. In addition, there is
no N-S asymmetry of the polar field amplitude
between the two hemispheres between 2003
and 2008.
6.2 The occurrence fraction of the toward sector
calculated using the daily IMF polarity both observed
and inferred shows the same evolution, i.e. the
absence of the asymmetry of IMF sector development
between northern and southern hemisphere after the
year of 2003. It support our PFSS model prediction of
the absence of the long lasting southward
displacement of the HCS. By using the daily IMF
polarity inferred by Dr. Leif Svalgaard, it is found that
there is also no such asymmetry near the minimum
phase in solar cycles 16 and 17, suggesting that the
long lasting HCS southward displacement near the
minimum phase is not a persistent phenomenon and
thus, the absence of the long lasting southward
displacement of the HCS near the minimum phase of
solar cycle 23 is not an abnormal phenomenon.