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The sunspot cycle length - Modulated by planets?

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The Schwabe frequency band of the sunspot record since 1700 has an average period of 11.06 years and contains four major cycles, with periods of 9.97, 10.66, 11.01 and 11.83 years. Analysis of the O-C residuals of the timing of solar cycle minima reveals that the solar cycle length is modulated by a secular period of about 190 years and the Gleissberg period of about 86 years. Based on a simple harmonic model with these periods, we predict that the solar cycle length will in average be longer during the 21st century. Cycle 24 may be about 12 years long, while cycles 25 and 26 are estimated to be about 9 and 11 years long. The following cycle are estimated to be 14 years long. In all periods during the last 1000 years, when the solar cycle length has increased due to the 190-year cycle, a deep minimum of solar activity has occurred. This is expected to re-occur in the first part of this century. The coherent modulation of the solar cycle length over a period of 400 years, is a strong argument for an external tidal forcing by the planets Venus, Earth, Jupiter and Saturn, as expressed in a spin-orbit coupling model.
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Pattern Recogn. Phys., 1, 159–164, 2013
www.pattern-recogn-phys.net/1/159/2013/
doi:10.5194/prp-1-159-2013
©Author(s) 2013. CC Attribution 3.0 License.
Open Access
Pattern Recognition
in Physics
The sunspot cycle length – modulated by planets?
J.-E. Solheim
formerly at: Department of Physics and Technology, Universtity of Tromsø, Norway
Correspondence to: J.-E. Solheim (janesol@online.no)
Received: 1 October 2013 – Revised: 8 November 2013 – Accepted: 12 November 2013 – Published: 4 December 2013
Abstract. The Schwabe frequency band of the sunspot record since 1700 has an average period of 11.06yr
and contains four major cycles, with periods of 9.97, 10.66, 11.01 and 11.83yr. Analysis of the O–C residuals
of the timing of solar cycle minima reveals that the solar cycle length is modulated by a secular period of about
190yr and the Gleissberg period of about 86 yr.
Based on a simple harmonic model with these periods, we predict that the solar cycle length will in average
be longer during the 21st century. Cycle 24 may be about 12yr long, while cycles 25 and 26 are estimated
to be about 9 and 11yr long. The following cycle is estimated to be 14yr long. In all periods during the last
1000yr, when the solar cycle length has increased due to the 190yr cycle, a deep minimum of solar activity
has occurred. This is expected to re-occur in the first part of this century.
The coherent modulation of the solar cycle length over a period of 400yr is a strong argument for an external
tidal forcing by the planets Venus, Earth, Jupiter and Saturn, as expressed in a spin-orbit coupling model.
1 Introduction
A possible relation between solar activity as manifested by
sunspots and the Earth’s climate has been discussed many
times since William Herschel (1801) speculated on a possi-
ble connection. In recent times Reid (1987) showed, based
on data on globally averaged sea surface temperature (SST),
that the solar irradiance may have varied in phase with the
80–90yr cycle represented by an envelope of the 11yr solar
activity cycle, called the Gleissberg cycle.
Friis-Christensen and Lassen (1991) investigated the re-
lation between the sunspot numbers and Northern Hemi-
sphere land temperature, and found similar variations, but
with the temperature variations leading the sunspot numbers.
They then discovered that using the solar cycle length (SCL)
as an indicator of solar activity in the sense that a shorter
cycle means higher activity, they could much better corre-
late with the NH land temperature variations. It was also
demonstrated (Friis-Christensen and Lassen, 1991; Hoyt and
Schatten, 1993; Larssen and Friis-Christensen, 1995) that the
correlation between SCL and climate has probably been in
operation for centuries. A statistical study of 69 tree ring
sets, covering more than 594yr, demonstrated that wider tree
rings (better growth conditions) were associated with shorter
sunspot cycles (Zhou and Butler, 1998).
In their study, Friis-Christensen and Lassen (1991) used
a smoothed mean value for the SCL with the length of five
solar cycles weighted 1-2-2-2-1. In a follow-up paper, Re-
ichel et al. (2001) concluded that the right cause-and-eect
ordering, in the sense of Granger causality, is present be-
tween the smoothed SCL and the cycle mean temperature
anomaly for the Northern Hemisphere land air temperature
in the 20th century at the 99% significance level. This sug-
gests that there may exist a physical mechanism linking so-
lar activity to climate variations. However, at the turn of the
century, a discrepancy between the SCL and NH land series
developed (Thejll and Lassen, 2000; Thejll, 2009), because
the short cycle 22 was followed by a much longer cycle 23,
without sign of cooling.
Recognizing that averaged temperature series from dier-
ent meteorological stations of variable quality and changing
locations may contain errors and partially unknown phenom-
ena derived from the averaging procedure, Butler (1994) pro-
posed instead to use long series of high quality from sin-
gle stations. He showed that this improved the correlation
when used for temperature series for Armagh, which corre-
lates strongly with the NH land temperature.
Archibald (2008) was the first to realize that the length of
the previous sunspot cycle (PSCL) has a predictive power
Published by Copernicus Publications.
160 J.-E. Solheim: The sunspot cycle length – modulated by planets?
for the temperature in the next sunspot cycle for certain lo-
cations, if the raw (unsmoothed) value for the SCL is used.
Based on the estimated longer SC23 than SC22, he predicted
cooling during SC24 for some selected locations. A system-
atic study of the correlation for locations around the North
Atlantic was published by Solheim et al. (2012). They found
that maximum correlation was obtained with an 8–12yr lag
for locations around and in the North Atlantic, and found that
a correlation with a lag of one solar cycle could explain 25 to
72 per cent of the temperature variance in that region. This
one cycle lag could therefore be used for forecasting the tem-
perature in the next solar cycle. Based on SC23 being consid-
erably longer than SC22, they forecast a temperature decline
during SC24 for the sites investigated.
In order to forecast the development of SCL for longer pe-
riods, it is necessary to investigate the long-term variability
of the SCLs. This was done for the first time by Fairbridge
and Hameed (1983), who found that the phase dierences re-
peated after 16 sunspot cycles, or 178 yr, if they used minima
as the start time for a cycle.
This was followed up by Richards et al. (2009), who used
median trace analyses of the SCL and power spectrum anal-
ysis of the O–C residuals (as explained in Eq. 1). They found
that the solar cycle length is controlled by periods of 188
and 87yr. They concluded that the length of the solar cycle
should increase gradually the next 75yr. They did not dis-
cuss the origin of their determined periods.
Regarding the 11yr sunspot period, many scientists have
noticed the bimodal structure of the distribution of solar cy-
cle length. According to analysis by Scafetta (2012), the
sunspot length probability distribution consists of three pe-
riods of about 9.98, 10.9 and 11.86yr. The side periods ap-
pear to be closely related to the spring period of Jupiter and
Saturn, which has a range between 9.5 and 10.5yr with a
median length of 9.93yr, and the sidereal period of Jupiter
(about 11.86yr). Scafetta (2012) proposed that the central
cycle period is associated with a quasi 11yr solar dynamo
cycle, which is forced by the two cyclical side attractors with
periods of 9.93 and 11.86 yr. He also suggested that the secu-
lar variations of the solar cycle amplitude and length are beat
periods of the three solar cycle periods, and that it is possible
to describe the secular variations of the sunspot cycle with
these beat periods.
Scafetta’s analysis covered the period 1755–2008 (solar
cycles 1–23). In the following we will investigate the solar
cycles for the longer period 1700–2010, and we will also in-
vestigate the O–C residuals all the way back to 1610 to search
for period combinations or harmonics. Based on a simple
harmonic model we will estimate the length of the next solar
cycles. Finally we will discuss if the modulation of the SCL
may be controlled by the planets, as proposed by Scafetta
(2012) and Wilson et al. (2008).
2 Data and methods
Yearly average sunspot numbers were downloaded
from the Solar Influences Data Center (SIDC). The
length and time of solar cycles were downloaded
from http://www.ngdc.noaa.gov/stp/space-weather/
solar-data/solar-indices/sunspot-numbers/cycle-data/table_
cycle-dates_maximum-minimum.txt.
For the analysis of the sunspot number time series I have
used the Period04 analysis package (Lenz and Breger, 2005),
downloaded from the Period04 website at http://www.astro.
univie.ac.at/dsn/dsn/Period04/. This program performs least
square fitting of a number of frequencies, where initial fre-
quencies may be determined by Fourier transform (FT) or
given as input. Error analysis is done by an analytical for-
mula (Breger et al., 1999) assuming an ideal case, or with
a least square error calculation. The largest of the obtained
errors is used.
The O–C technique for investigation of secular modulation
of the SCL is described in detail in Richards et al. (2009).
We follow their description and use the downloaded set of
SCLs determined between the minima, and construct the O–
C residuals cycle by cycle using the formula:
(OC)i=(tit0)(Ni×P0),(1)
where tiis the end time of cycle no. Ni,P0is the reference
period investigated, andCi=t0+Ni×P0.
3 Results
3.1 The 11yr cycle
The solar cycle length variation with time since 1610 is
shown in Fig. 1. We notice large variations in the 17th and
18th centuries, but with a generally shorter length from about
1850. The data set covers a total of 36 cycles, and the mean
length is 11.06±1.5 yr. In Fig. 2 we show the distribution of
the SCL between solar minima. The median value is between
10.7 and 11.0yr, but there are no observations in this range.
This clearly indicates a double or multiple bell distribution.
The resulting periodogram of the sunspot numbers from
1700–2010 is shown in Fig. 3. We find, as did Scafetta
(2012), a dominating band with periods 10–12yr, where
we identify four peaks: P1=9.97 ±0.02, P2=10.66±0.02,
P3=11.010±0.001 and P4=11.83±0.02 yr. The errors are
determined by an analytical formula (Breger et al., 1999).
There is also a triplet of periods in an 8.5 yr band, and a triplet
around 5.5yr. The latter is most likely higher harmonics of
three peaks in the 11yr band.
The long period of 53±0.6 yr is best explained as a 4th
subharmonics of P2(5 ×10.66 =53.3), and the long period
of 100±15 yr may be related to the known Gleissberg period
of 87yr.
Pattern Recogn. Phys., 1, 159–164, 2013 www.pattern-recogn-phys.net/1/159/2013/
J.-E. Solheim: The sunspot cycle length – modulated by planets? 161
8
10
12
14
16
Length(yr)
8
10
12
14
16
1650 1700 1750 1800 1850 1900 1950 2000
Yea r
Solar Cycle length
Figure 1. The solar cycle length (SCL) from 1610 as downloaded
from the National Geophysical Data Center (NGDC). We observe
that the SCL was longer than the mean of 11.06yr in most of the
19th century and shorter than the mean in most in the 20th century.
0
1
2
3
4
5
6
7
8
No
78910111213141516
Length (Year)
Sunspot Cycle Length between minima
Figure 2. The distribution of the solar cycle lengths in bins of 0.5 yr
width. The distribution covers 36 cycles from 1610 to 2008.
3.2 Long-term modulation of the length of the solar
cycle
We use the average period P=11.06yr as our reference pe-
riod and obtain the O–C residuals as shown in Fig. 4, where
the O–C residuals are given as a function of the cycle no.
As the starting point for cycle 13 we use 1610.8 with an
O–C=0.95. The residuals give us a picture of the long-
term trends in SCL. We observe that the residuals increase
most of the time between SC4 and SC14 (1775–1900), be-
cause the SCL is then nearly always longer than 11yr (see
also Fig. 1). Then we enter a period with shorter periods, and
a warming Earth. The question is now if that will continue.
To investigate what controls the length of the solar cycle,
we calculate a periodogram of the residual O–C data string,
and get the amplitude spectrum shown in Fig. 5.
The spectrum consists of two dominating periods: 190±9
and 85.6±2yr. Periods shorter than 50 years are harmonics
of the two main periods. There is also a period of the order
440yr, which explains why the peak around 1900 is higher
5
10
15
20
25
30
35
Amplitude
5
10
15
20
25
30
35
0.05 0.1 0.15 0.2 0.25
Frequency (Year-1)
Periodogram of Sunspot Numbers 1700-2010
100
53
21.3
11. 83
11. 01
10.66
9.97
8.47
5.5
Figure 3. Amplitude spectrum of the yearly average sunspot num-
bers 1700–2010.
-4
-2
0
2
4
O-C (yrs)
-4
-2
0
2
4
-15 -10 -5 0 5 10 15 20 25
Sunspot Cycle No
O-C for Sunspot Cycle Minima P = 11.06 yrs
1610 1712 1810 1900 2015
Figure 4. O–C residuals for the length of the solar cycle compared
with the average period of 11.06yr. The curve is increasing for
SCL>11.06 yr.
than the peak around 1700. A similar result was obtained by
Richards et al. (2009), who identified a Gleissberg period of
86.5±12.5 yr and a secular period of 188±38 yr. In their anal-
ysis they use SCLs based on both solar maxima and minima.
In Fig. 6 we show the O–C residuals with the strongest
controlling period 190yr and its subharmonic at 440 yr.
This dominant cycle is the reason for an increasing period
length in the 19th century and a decreasing length in the 20th
century. We can therefore expect increasing SCLs in the 21st
century.
Adding the Gleissberg cycle and three of the harmonics
gives the fit shown in Fig. 7, where we may also obtain an
estimate of near future SCLs. Times of minima can be esti-
mated from the following equation:
tmin =1755.5+11.06×Ni+(OC)est,(2)
where (O–C)est is the estimated O–C value determined with
the harmonic model as shown in Fig. 7 (red curve). For the
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162 J.-E. Solheim: The sunspot cycle length – modulated by planets?
Figure 5. Amplitude spectrum of O–C residuals of the SCL mea-
sured between minima.
-4
-2
0
2
4
O-C (yrs)
-4
-2
0
2
4
-15 -10 -5 0 5 10 15 20 25 30
Sunspot Cycle No
O-C for Sunspot Cycle Minima P = 11.06 yrs
Figure 6. O–C residuals for SCL minima, with a simulation based
on the dominating periods of 190 and 440 yr.
next minimum after SC24, Eq. (2) gives 2020.9, since the
(O–C)est then is close to zero.
4 Discussion
We have shown that the solar cycle length since 1600 is con-
trolled by stable oscillations, which provide an average cycle
length of 11.06yr. The cycle length is modulated by 3 long
periods of 440, 190 and 86yr, and some of their har-
monics. If the dominating period of 190 yr is followed back
in time, it is found (Richards et al., 2009) that all known solar
deep minima during the last 1000yr (the Oort, Wolf, Spörer,
Maunder and Dalton minima) are close to the minimum or on
the rising branch of this oscillation. We can therefore expect
another grand minimum during the first part of this century.
Looking more closely at the model simulations in Fig. 7,
we estimate the length of SC24 12 yr, SCL25 9yr, SCL26
11yr and SCL27 14 yr. The forecast for the time of the
next minimum (2020.9) can be compared with the forecast
-4
-2
0
2
4
O-C (yrs)
-4
-2
0
2
4
-15 -10 -5 0 5 10 15 20 25 30
Sunspot Cycle No
O-C for Sunspot Cycle Minima P = 11.06 yrs
Figure 7. O–C residuals for SCL minima, with a simulation based
on 6 harmonics with periods 440, 190, 86, 48, 43, and 38 yr.
based on a mathematical model (Salvador, 2013), which es-
timates the end of solar cycle 24 in 2018.
It has for some time been discussed if the solar cycle length
is controlled by an internal or external clock. Dicke (1978)
argued that the phase of the solar cycle appears to be cou-
pled to an internal clock, because shorter cycles are usually
followed by longer cycles, as if the Sun remembers the cor-
rect phase. Another view (Huyong, 1996) is that the memory
eect can be explained by mean field theory, which predicts
coherent changes in frequency and amplitude of a dynamo
wave. However, it is admitted by solar physicists that present
solar dynamo theories, although able to describe the peri-
odicities and the polarity reversal of solar activity well, are
not yet able to quantitatively explain the 11 and 22yr cycles,
nor the other observed quasi-cycles (de Jager and Versteegh,
2005). The remarkable resemblance between planetary tidal
forcing periods and observed solar quasi-periods is a strong
argument for a planetary tidal forcing on the solar activity.
Regarding the splitting of the 11yr solar cycle band into
4 distinct peaks, the most remarkable is the strongest peak
P=11.010±0.001 yr. A period so close to 11 Earth years
has a great chance to be related to the Earth’s orbit. Wilson
(2013) explains that the Venus–Earth–Sun periodic align-
ments create a tidal bulge, which for a period of 11.07yr is
speeded up by Jupiter’s movement, and the next 11.07yr are
slowed down by the same. This is called the VEJ tidal-torque
coupling model, and explains both the average Schwabe and
Hales cycles. These tidal forces work to increase or decrease
the solar rotation rate in the convective layers where the solar
dynamo is situated (Wilson, 2013).
Among the other three periods in the 11yr band, 9.97 yr
is close to the Jupiter–Saturn spring tide period of 9.93yr,
which is half of the Jupiter–Saturn heliocentric conjunc-
tion period of 19.86yr. It should be noticed that the spring
tide period of Jupiter/Saturn varies between 9.5 and 10.5yr
(Scafetta, 2012). The period of 11.83yr is close to Jupiter’s
orbital period of 11.86yr. Scafetta (2012) proposes that the
solar cycle period 11.0yr is generated by the two side at-
tractors controlled by the two giant planets. We have found
another sunspot period at 10.66yr, which also may be a
Pattern Recogn. Phys., 1, 159–164, 2013 www.pattern-recogn-phys.net/1/159/2013/
J.-E. Solheim: The sunspot cycle length – modulated by planets? 163
dynamo period. Both these periods are strongly forced, since
they have higher harmonics of 5.5 and 5.25yr, and one sub-
harmonic of 21.3yr.
By our O–C analysis we find, as did Richards et al. (2009),
that the SCL is modulated by a secular period of 190±9 yr
in addition to a period of 86±2 yr, which most likely is the
Gleissberg period. The long period is close to the Jose cycle
of 178.7yr, which is the period of recurrent pattern of the
movement of the Sun around the barycenter of the solar sys-
tem (Jose, 1965). Fairbridge and Hameed (1985) found phase
coherence of solar cycle minima over two 176yr cycles, or
16 Schwabe periods. Our 190yr period is also close to a pe-
riod of 208 yr, which is found in cosmic ray observations and
in cosmogenic isotopes, and explained by tidal torque on the
Sun by the planets (Abreu et al., 2012).
However, a far better match with the 190 yr period is found
by introducing a so-called Gear Eect, which modulates the
tangential torque applied by the alignments of Venus and
Earth to the Jupiter–Sun–Saturn system as explained by Wil-
son (2013). He shows that prograde and retrograde torque os-
cillate in a quasi bidecadal period controlled by the 19.859 yr
synodic period of Jupiter and Saturn. Figure 13 in Wilson
(2013) shows the angel between the center of mass of the
Jupiter, Sun and Saturn system and Venus/Earth from 1013
to 2015. If we compare this with our Fig. 6, we find an excel-
lent match between periods and phases, indicating a strong
link between the modulation of the solar cycle length and
the torque eect proposed by Wilson (2013). The modula-
tion period can be calculated as the beat period between the
Hale-like period of 22.137yr and the Jupiter–Saturn synodic
period of 19.859 yr. The result is a beat period of 192.98 yr or
193±2 yr, when the orbital variations are included (Wilson,
2013). By also introducing the Gear Eect to the VEJ-tidal
torque model, he can also explain an 88.1yr Gleissberg cy-
cle.
Finally, it may be instructive to compare our predictions
of the next solar cycle lengths with a prediction made by de
Jager and Duhau (2009), based on the dynamo model that is
constructed from the relationship between the polodial and
torodial magnetic cycles. They conclude that the polar cycle
24 will be similar to polar cycle 12, which means that the
maxima of sunspot cycles 23 and 24 will be quite similar to
those of the cycle pair 11 and 12. They further conclude that
a short Dalton minimum will occur, lasting a maximum of 3
cycles (SC24-26), whereafter a grand minimum will follow,
starting with cycle 27. They predict the maximum sunspots
of SC24 to be 68±17 with a maximum at 2014.5±0.5, but
do not predict the length.
At the moment we are close to the solar maximum of
SC24, but have 7 more years to the next minimum, accord-
ing to our forecast. During that period we will observe if the
cooling forecast for the North Atlantic region will take place,
and if this will also keep the global temperature in hiatus, as
it has been since the start of SC23.
5 Conclusions
We have shown that the Schwabe frequency band of the
sunspot record since 1700 has an average period of 11.06yr
and contains four major cycles, with periods of 9.97, 10.66,
11.01 and 11.83 yr. Analysis of the O–C residuals of the tim-
ing of solar cycle minima reveals that the solar cycle length is
modulated by a secular period of about 190yr and a Gleiss-
berg period of about 86yr. Our result is a confirmation of
earlier phase studies by Fairbridge and Hameed (1983) and
Richards et al. (2009).
Based on a simple harmonic model with these periods, we
predict that the solar cycle length will increase during the
21st century. Cycle 24 may be about 12yr long, while cycles
25 and 26 are estimated to be about 9 and 11yr long. The
following cycle 27 will be much longer. In all periods when
the solar cycle length has increased due to the 190yr cycle
during the last 1000yr, a deep minimum of solar activity has
occurred. This is also to be expected in the early part of this.
The coherent modulation of the solar cycle length over a
period of 400yr is a strong argument for an external forcing
by the planets Venus, Earth, Jupiter and Saturn, expressed in
the spin-orbit coupling model as proposed by Wilson (2013).
Excellent phase coherence with this model is a strong
added argument for this interpretation.
Acknowledgements. The author acknowledges the use of
sunspot numbers and times of minima from the National Geophys-
ical Data Center. He also thanks the Vienna astroseismological
group for the excellent Period04 program package, and two referees
with helpful advice for improving this publication.
Edited by: N.-A. Mörner
Reviewed by: H. Yndestad and H. Jelbring
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Sol.-Terr. Phy., 60, 1711–1718, 1998.
Pattern Recogn. Phys., 1, 159–164, 2013 www.pattern-recogn-phys.net/1/159/2013/
... Building on this phase stability of the Hale cycle, in [60,62] we exploited ideas of Wilson [87] and Solheim [90] to explain the mid-term Suess-de Vries cycle as a beat period between the 22.14-year Hale cycle and the 19.86-year synodic cycle of Jupiter and Saturn, which governs the motion of the Sun around the barycenter of the solar system. Note that, apart from first ideas [87,[90][91][92], the spin-orbit coupling that is necessary to translate the orbital motion of the Sun into some dynamo-relevant internal forcing, is yet far from understood. ...
... Building on this phase stability of the Hale cycle, in [60,62] we exploited ideas of Wilson [87] and Solheim [90] to explain the mid-term Suess-de Vries cycle as a beat period between the 22.14-year Hale cycle and the 19.86-year synodic cycle of Jupiter and Saturn, which governs the motion of the Sun around the barycenter of the solar system. Note that, apart from first ideas [87,[90][91][92], the spin-orbit coupling that is necessary to translate the orbital motion of the Sun into some dynamo-relevant internal forcing, is yet far from understood. In our model, the Suess-de Vries cycle acquires a clear (beat) period of 193 years, which is in the lower range of usual estimates (see [93]). ...
Article
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The paper aims to quantify solar and anthropogenic influences on climate change, and to make some tentative predictions for the next hundred years. By means of double regression, we evaluate linear combinations of the logarithm of the carbon dioxide concentration and the geomagnetic aa index as a proxy for solar activity. Thereby, we reproduce the sea surface temperature (HadSST) since the middle of the 19th century with an adjusted R2 value of around 87 percent for a climate sensitivity (of TCR type) in the range of 0.6 K until 1.6 K per doubling of CO2. The solution of the double regression is quite sensitive: when including data from the last decade, the simultaneous occurrence of a strong El Niño and of low aa values leads to a preponderance of solutions with relatively high climate sensitivities around 1.6 K. If these later data are excluded, the regression delivers a significantly higher weight of the aa index and, correspondingly, a lower climate sensitivity going down to 0.6 K. The plausibility of such low values is discussed in view of recent experimental and satellite-borne measurements. We argue that a further decade of data collection will be needed to allow for a reliable distinction between low and high sensitivity values. In the second part, which builds on recent ideas about a quasi-deterministic planetary synchronization of the solar dynamo, we make a first attempt to predict the aa index and the resulting temperature anomaly for various typical CO2 scenarios. Even for the highest climate sensitivities, and an unabated linear CO2 increase, we predict only a mild additional temperature rise of around 1 K until the end of the century, while for the lower values an imminent temperature drop in the near future, followed by a rather flat temperature curve, is prognosticated.
... The BIE movement north was rapid after the deep Maunder Minimum, but slow after the Dalton minimum, using more than a century to gather momentum. This may be explained by a "tired Sun" in the 1800s, after high activity in the 1700s, related to a bicentennial cycle [15]. ...
... It is observed that long solar cycles in general correspond to low BIE, and short cycles as 1700-1800 and after 1900 corresponds to high values of BIE (see Figure 2). It is shown [15] that SCL varies with periods 190 and 86 years. This International Journal of Astronomy and Astrophysics corresponds to planetary periods (Section 6). ...
... The arising 11.07-yr period of the helicity parameter ultimately leads to the 22.14 year period of the Hale cycle. Building on this phase coherence of the Hale cycle, later (Stefani et al., 2020a; we exploited ideas of Wilson (2013); Solheim (2013) to explain the mid-term Suess-de Vries cycle as a beat period between the 22.14-yr Hale cycle and the 19.86-yr synodic cy- cle of Jupiter and Saturn which governs the motion of the Sun around the barycenter of the solar system. Note that, apart from first ideas (Javaraiah, 2003;Sharp, 2013;Solheim, 2013;Wilson, 2013), the spin-orbit coupling that is necessary to translate the orbital motion of the Sun into some dynamo-relevant internal forcing, is yet far from understood. ...
... Building on this phase coherence of the Hale cycle, later (Stefani et al., 2020a; we exploited ideas of Wilson (2013); Solheim (2013) to explain the mid-term Suess-de Vries cycle as a beat period between the 22.14-yr Hale cycle and the 19.86-yr synodic cy- cle of Jupiter and Saturn which governs the motion of the Sun around the barycenter of the solar system. Note that, apart from first ideas (Javaraiah, 2003;Sharp, 2013;Solheim, 2013;Wilson, 2013), the spin-orbit coupling that is necessary to translate the orbital motion of the Sun into some dynamo-relevant internal forcing, is yet far from understood. In our model, the Suess-de Vries acquires a clear (beat) period of 193 years which is in the lower range of usual estimates (but see Ma and Vaquero (2020)). ...
Preprint
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The two main drivers of climate change on sub-Milankovic time scales are re-assessed by means of a multiple regression analysis. Evaluating linear combinations of the logarithm of carbon dioxide concentration and the geomagnetic aa-index as a proxy for solar activity, we reproduce the sea surface temperature (HadSST) since the middle of the 19th century with an adjusted $R^2$ value of around 87 per cent for a climate sensitivity (of TCR type) in the range of 0.6 K until 1.6 K per doubling of CO$_2$. The solution of the regression is quite sensitive: when including data from the last decade, the simultaneous occurrence of a strong El Ni\~no on one side and low aa-values on the other side lead to a preponderance of solutions with relatively high climate sensitivities around 1.6 K. If those later data are excluded, the regression leads to a significantly higher weight of the aa-index and a correspondingly lower climate sensitivity going down to 0.6 K. The plausibility of such low values is discussed in view of recent experimental and satellite-borne measurements. We argue that a further decade of data collection will be needed to allow for a reliable distinction between low and high sensitivity values. Based on recent ideas about a quasi-deterministic planetary synchronization of the solar dynamo, we make a first attempt to predict the aa-index and the resulting temperature anomaly for various typical CO$_2$ scenarios. Even for the highest climate sensitivities, and an unabated linear CO$_2$ increase, we predict only a mild additional temperature rise of around 1 K until the end of the century, while for the lower values an imminent temperature drop in the near future, followed by a rather flat temperature curve, is prognosticated.
... Statistical processing of these data yielded a mean solar cycle length of 11.06 ± 1.5 years and a medium of these values between 10.7 and 11.0 years. These data indicate pulsating, which we cannot explain by internal processes on the Sun (Solheim, 2013). The planets' rotations around the Sun, cause constantly movement planetary system's mass center, and consequently also the position of the Sun on it. ...
Article
The paper first introduces the sunspot cycles and discusses the relationship between the solar cycles and the 12?year Chinese calendar. The latter has a significant impact on the lives and thinking of some East Asian countries and the emigrants from those countries. Western civilization considers solar cycles and their impact on human life only as solar astronomy and geomagnetism. Through the established effects on life on Earth, the life span of an individual is the starting point through which the paper represents the long-term influence of the Sun on us.
... The current state of the theory has some problems. Some authors tried to explain solar cycles in terms of the complex arithmetic of the orbital periods of the planets Scafetta & Wilson, 2013;Solheim, 2013;Wilson, 2013). If the solar cycles would be really related to the opposition or conjunction of the planets, we have to find the orbital periods of the planets themselves in the spectrum of solar activity because the Fourier analysis decomposes an arbitrary signal into the linear series of the elementary sinusoidal cycles. ...
Preprint
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The question on the long-term solar cycles is still open. I choose the stable solar cycles in terms of the sampling and differencing stability in samplogram, the time stability or stationarity in wavelet scalogram and the modulation analysis. The short-term solar cycles are also little known due to the strong randomness of solar activity. I found the stable cycles near to the orbital cycles of all major planets upto the Saturn. This may imply a possible planetary forcing of solar activity.
... Still, it is the dominant 19.86-years cycle which has the capability to produce, in concert with the 22.14-years Hale cycle, a beat period of 19.86×22.14/(22.14−19.86) = 193 years, as worked out in the above mentioned paper by Wilson (2013) and also by Solheim (2013). This 193 years period is suspiciously close to the Suess-de Vries cycle. ...
Preprint
We argue that the most prominent temporal features of the solar dynamo, in particular the Hale cycle, the Suess-de Vries cycle (associated with variations of the Gnevyshev-Ohl rule), Gleissberg-type cycles, and grand minima can be self-consistently explained by double synchronization with the 11.07-years periodic tidal forcing of the Venus-Earth-Jupiter system and the (mainly) 19.86-years periodic motion of the Sun around the barycenter of the solar system. In our numerical simulation, grand minima, and clusters thereof, emerge as intermittent and non-periodic events on millennial time scales, very similar to the series of Bond events which were observed throughout the Holocene and the last glacial period. If confirmed, such an intermittent transition to chaos would prevent any long-term prediction of solar activity, notwithstanding the fact that the shorter-term Hale and Suess-de Vries cycles are clocked by planetary motion.
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Commenting the 11-year sunspot cycle, Wolf (1859, MNRAS 19, 85–86) conjectured that “the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn.” The high synchronization of our planetary system is already nicely revealed by the fact that the ratios of the planetary orbital radii are closely related to each other through a scaling-mirror symmetry equation (Bank and Scafetta, Front. Astron. Space Sci. 8, 758184, 2022). Reviewing the many planetary harmonics and the orbital invariant inequalities that characterize the planetary motions of the solar system from the monthly to the millennial time scales, we show that they are not randomly distributed but clearly tend to cluster around some specific values that also match those of the main solar activity cycles. In some cases, planetary models have even been able to predict the time-phase of the solar oscillations including the Schwabe 11-year sunspot cycle. We also stress that solar models based on the hypothesis that solar activity is regulated by its internal dynamics alone have never been able to reproduce the variety of the observed cycles. Although planetary tidal forces are weak, we review a number of mechanisms that could explain how the solar structure and the solar dynamo could get tuned to the planetary motions. In particular, we discuss how the effects of the weak tidal forces could be significantly amplified in the solar core by an induced increase in the H-burning. Mechanisms modulating the electromagnetic and gravitational large-scale structure of the planetary system are also discussed.
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We argue that the most prominent temporal features of the solar dynamo, in particular the Hale cycle, the Suess–de Vries cycle (associated with variations of the Gnevyshev–Ohl rule), Gleissberg-type cycles, and grand minima can all be explained by combined synchronization with the 11.07-year periodic tidal forcing of the Venus–Earth–Jupiter system and the (mainly) 19.86-year periodic motion of the Sun around the barycenter of the solar system. We present model simulations where grand minima, and clusters thereof, emerge as intermittent and non-periodic events on millennial time scales, very similar to the series of Bond events which were observed throughout the Holocene and the last glacial period. If confirmed, such an intermittent transition to chaos would prevent any long-term prediction of solar activity, notwithstanding the fact that the shorter-term Hale and Suess–de Vries cycles are clocked by planetary motion.
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Guided by the working hypothesis that the Schwabe cycle of solar activity is synchronized by the 11.07‐year alignment cycle of the tidally dominant planets Venus, Earth, and Jupiter, we reconsider the phase diagrams of sediment accumulation rates in Lake Holzmaar and of methanesulfonate data in the Greenland ice core Greenland Ice Sheet Project 2 (GISP2), which are available for the period 10000–9000 cal. BP. As some half‐cycle phase jumps appearing in the output signals are, very likely, artifacts of applying a biologically substantiated transfer function, the underlying solar input signal with a dominant 11.04‐year periodicity can be considered to be mainly phase‐coherent over the 1,000‐year period in the early Holocene. For more recent times, we show that the reintroduction of a hypothesized “lost cycle” at the beginning of the Dalton minimum would lead to a real phase jump. Similarly, by analyzing various series of 14C and 10Be data and comparing them with Schove's historical cycle maxima, we support the existence of another “lost cycle” around 1565, also connected with a real phase jump. Viewed synoptically, our results lend greater plausibility to the starting hypothesis of a tidally synchronized solar cycle, which at times can undergo phase jumps, although the competing explanation in terms of a nonlinear solar dynamo with increased coherence cannot be completely ruled out.
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A Venus-Earth-Jupiter spin-orbit coupling model is constructed from a combination of the Venus-Earth-Jupiter tidal-torquing model and the gear effect. The new model produces net tangential torques that act upon the outer convective layers of the Sun with periodicities that match many of the long-term cycles that are found in the 10Be and 14C proxy records of solar activity.
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We present evidence to show that changes in the Sun's equatorial rotation rate are synchronized with changes in its orbital motion about the barycentre of the Solar System. We propose that this synchronization is indicative of a spin-orbit coupling mechanism operating between the Jovian planets and the Sun. However, we are unable to suggest a plausible underlying physical cause for the coupling. Some researchers have proposed that it is the period of the meridional flow in the convective zone of the Sun that controls both the duration and strength of the Solar cycle. We postulate that the overall period of the meridional flow is set by the level of disruption to the flow that is caused by changes in Sun's equatorial rotation speed. Based on our claim that changes in the Sun's equatorial rotation rate are synchronized with changes in the Sun's orbital motion about the barycentre, we propose that the mean period for the Sun's meridional flow is set by a Synodic resonance between the flow period (~22.3 yr), the overall 178.7-yr repetition period for the solar orbital motion, and the 19.86-yr synodic period of Jupiter and Saturn.
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The evolved delta Scuti variable 4 CVn was observed photometrically for 53 nights on three continents. We found a total of 34 significant and 1 probable simultaneously excited frequencies. Of these, 16 can be identified as linear combinations of other frequencies. All significant frequencies outside the 4.5 to 10 cd(-1) (52 to 116 mu Hz) range can be identified with frequency combinations, f_i +/- f_j, of other modes with generally high amplitudes. There exists a number of closely spaced frequencies with separations of ~ 0.06 cd(-1) . This cannot be explained in terms of amplitude variability. The results show that even for stars on and above the main sequence other than the Sun, a very large number of simultaneously excited nonradial oscillations can be detected by conventional means. Since all pulsation modes with photometric amplitudes of 1 mmag or larger have now been detected for this star, a presently unknown mode selection mechanism must exist to select between the 1000+ of low-degree modes predicted to be excited for this (and many other) stars. Phase differences and amplitude ratios between the y and v colors are determined for the ten main modes. The phase differences indicate p_1 to p_4 modes of l = 1 for four of these modes. The formulae to determine the uncertainties in the amplitudes and phases of sinusoidal fits to observational data are derived in the Appendix.
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Using many features of Ian Wilson's Tidal Torque theory, a mathematical model of the sunspot cycle has been created that reproduces changing sunspot cycle lengths and has an 85% correlation with the sunspot numbers from 1749 to 2013. The model makes a reasonable representation of the sunspot cycle for the past 1000 yr, placing all the solar minimums in their right time periods. More importantly, I believe the model can be used to forecast future solar cycles quantitatively for 30 yr and directionally for 100 yr. The forecast is for a solar minimum and quiet Sun for the next 30 to 100 yr. The model is a slowly changing chaotic system with patterns that are never repeated in exactly the same way. Inferences as to the causes of the sunspot cycle patterns can be made by looking at the model's terms and relating them to aspects of the Tidal Torque theory and, possibly, Jovian magnetic field interactions.
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Context. Understanding the Sun's magnetic activity is important because of its impact on the Earth's environment. Direct observations of the sunspots since 1610 reveal an irregular activity cycle with an average period of about 11 years, which is modulated on longer timescales. Proxies of solar activity such as 14C and 10Be show consistently longer cycles with well-defined periodicities and varying amplitudes. Current models of solar activity assume that the origin and modulation of solar activity lie within the Sun itself; however, correlations between direct solar activity indices and planetary configurations have been reported on many occasions. Since no successful physical mechanism was suggested to explain these correlations, the possible link between planetary motion and solar activity has been largely ignored. Aims: While energy considerations clearly show that the planets cannot be the direct cause of the solar activity, it remains an open question whether the planets can perturb the operation of the solar dynamo. Here we use a 9400 year solar activity reconstruction derived from cosmogenic radionuclides to test this hypothesis. Methods: We developed a simple physical model for describing the time-dependent torque exerted by the planets on a non-spherical tachocline and compared the corresponding power spectrum with that of the reconstructed solar activity record. Results: We find an excellent agreement between the long-term cycles in proxies of solar activity and the periodicities in the planetary torque and also that some periodicities remain phase-locked over 9400 years. Conclusions: Based on these observations we put forward the idea that the long-term solar magnetic activity is modulated by planetary effects. If correct, our hypothesis has important implications for solar physics and the solar-terrestrial connection.
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Solar data have been used as parameters in a great number of studies concerning variations of the physical conditions in the Earth's upper atmosphere. The varying solar activity is distinctly represented by the 11-yr cycle in the number of sunspots. The length of this sunspot period is not fixed. Actually, it varies with a period of 80–90 yr. Recently, this variation has been found to be strongly correlated with long-term variations in the global temperature. Information about northernhemisphere temperature based on proxy data is available back to the second half of the sixteenth century. Systematic monitoring of solar data did not take place prior to 1750. Therefore, a critical assessment of existing and proxy solar data prior to 1750 is reported and tables of epochs of sunspot minima as well as sunspot cycle lengths covering the interval 1500–1990 are presented. The tabulated cycle lengths are compared with reconstructed and instrumental temperature series through four centuries. The correlation between solar activity and northern hemisphere land surface temperature is confirmed.
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The principal object of this paper is to explore the causes or sym­ptoms of the variation we observe in the emission of light and heat from the sun. Considering the great influence of these agents on most of the concerns of life, it is scarcely necessary to point out the importance of the inquiry: not that any discoveries we may make on the subject will ever enable us to modify their operations, but that, by a due knowledge of them, we may be guided in our own proceedings, in the same manner as we frequently are by the meteorological instruments, on whose combined indications we have been taught to place a certain degree of confidence.
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We have determined the correlation coefficient between tree-ring index values and the sunspot cycle length for 69 tree-ring data sets from around the world of greater than 594 years duration. A matrix of correlation coefficients is formed with varying delay and smoothing parameters. Similar matrices, formed from the same data, but randomly scrambled, provide a control against which we can draw conclusions about the influence of the solar cycle length on climate with a reasonable degree of confidence. We find that the data confirm an association between the sunspot cycle length and climate with a negative maximum correlation coefficient for 80% of the data sets considered. This implies that wider tree-rings (i.e. more optimum growth conditions) are associated with shorter sunspot cycles. Secondly, we find that the climatic effect of the solar cycle length is smoothed by several decades and the degree of smoothing is dependent on the elevation and the geographical location of the trees employed. Thirdly, we find evidence for a cyclic variation of ∼200 years period in either solar cycle length or tree ring index. © 1999 Elsevier Science Ltd. All rights reserved.