The V-E-J Tidal-Torquing Model & Solar Maxima

Please read these posts if you are not familiar with the V-E-J Tidal Torquing model:


http://astroclimateconnection.blogspot.com.au/2012/03/planetary-spin-orbit-coupling-model-for.html
http://astroclimateconnection.blogspot.com.au/2012/03/short-comings-of-planetary-spin-orbit.html
http://astroclimateconnection.blogspot.com.au/2012/04/why-does-solar-cycle-keep-re.html
http://astroclimateconnection.blogspot.com.au/2012/04/v-e-j-tidal-torquing-model-maunder.html

Figures 1a and 1b show cumulative acceleration that would 
occur tangentially to the surface of the Sun, if the gravitational 
force of Jupiter were to tug upon the combined tidal bulge 
that is induced in the convective layer of the Sun by the 
periodic alignments of Venus and the Earth (every 1.599 
years). In essence, whenever the cumulative acceleration
is increasing (i.e its slope is positive), the tugging gravitational
force of Jupiter increase the rotation rate of a layer of plasma
in the Sun's convective layer [assumed to be a dynamically
decoupled layer ~ 0.02 % of the mass of the Sun]. Similarly, 
whenever the cumulative acceleration is decreasing (i.e its 
slope is negative), the tugging gravitational force of Jupiter 
decrease the rotation rate of a layer of plasma in the Sun's 
convective layer.


N.B. It is reasonable to assume that the dynamically
decoupled layer in the Sun's convection region is likely 
to be at the base of the convective zone near the 
Tachocline, since this is where most solar scientists 
believe that the solar dynamo is formed.


Figure 1a shows this cumulative acceleration between the 
years 1880 and 1960, while figure 1b shows the corresponding
plot between the years 1950 and 2030.


Superimposed on each of these figures are the times of solar 
maximum for solar sunspot cycles 13 through 23.

Figure 1a

Figure 1b

What these two figures show is that:

Whenever the Sun's sunspot cycles were weak, as in 

the later parts of the 19 th century and the first 40 years 

of the 20 th century (i.e. cycles 13 through 17), the 

rotation velocity of the layer in the convective region of 

the Sun changed direction PRIOR TO the date of solar 

sunspot maximum.

Whenever the Sun's sunspot cycles were strong, as in 

the last 60 years of the 20 th century (i.e. cycles 18 

through 23), the rotation velocity of the layer in the 

convective region of the Sun changed direction AFTER 

the date of solar sunspot maximum.

What this suggests is that there could be a correlation

between the relative timing of the change in rotation 

velocity of the layer in the convective region that is being

spun up and spun down by Jupiter's gravitational force.

Figure 2a shows the peak Solar sunspot number for cycles

-4 through 23 [covering the period from 1698 to 2009]

plotted against the number of years that the Jupiter

induced change in direction of rotation of the layer in
the convective zone, occurs BEHIND the year of solar 
maximum [i.e. Solar maximum minus peak cumulative 
acceleration in years]. 

The data in figure 2a clearly shows that there is indeed 

a moderately good correlation between these two 

variables (R = 0.678).

Figure 2a

One thing that immediately becomes apparent from figure 2a,

is that there are three solar sunspot cycles associated with 

the Dalton Minimum (i.e cycles 4, 5 and 6 which are 

labelled in the diagram) that are systematically shifted towards 

lower left of the figure. This raises the possibility that during 

periods of low solar activity like that in the Dalton Minimum, 

the Sun may respond differently to the tidal-torquing of Jupiter 

than at times of "normal" solar sunspot activity.

   

Figure 2b below, shows that if these three unusual solar cycles 

are excluded from the data set, the quality of the correlation 

greatly improves, with the new linear correlation co-efficient

being R = 0.784.     

Figure 2b

This is comparable to the level of correlation that exists between

the peak sunspot number for a solar cycle and the time it takes

[in years] for that sunspot cycle to reach maximum.

Figure 3 shows the relationship between the peak solar sunspot 

number and the time required for that sunspot cycle to reach its

maximum for solar cycles -4 through 23. As you can see, there

is a very good correlation between these two parameters with 

the correlation coefficient being R = 0.810.

Figure 3

Hence, provided we exclude the unusual solar sunspot 

cycles associated with grand solar minima, there appears 

to be an excellent correlation between peak sunspot 

number of a solar-cycle and the timing of the Jupiter induced 

change in direction of the rotation rate [of a layer in the 

convective zone of the Sun] compared to the timing of 

solar maximum.

Peak SSN = -13.485 x (SOL MAX - PEAK of Cumulative Acceleration) + 116.05  

Unfortunately, this relationship cannot be used to predict the 

peak SN for the next two solar cycles, as there is a strong 

possibility that both cycles 24 and 25 will be very similar to 

cycles 5 and 6 in the Dalton Minimum. Evidence for this can 

be seen in figure 4.  

Figure 4 is a reproduction of figure 2a, with a box superimposed 

on the figure showing were we expect solar cycle 24 to be 

located if it reached a sunspot maximum some time between 

2013 and 2014, with a peak sunspot number between 65 

and 85. This places cycle 24 in similar part of the diagram as 

solar cycles 5 and 6.

N.B. The relation between peak SN and the rise time of a solar 

cycle [shown in figure 3] would point to a maximum for cycle 24 

that is either at or after 2014, tending to favor a location for cycle

24 that is at the right hand side of the box in figure 4.

    

Figure 4

Finally, it is important to note that unlike other models that 

link the level of solar sunspot activity to planetary motions, 

the simple V-E-J  Tidal-Torquing model [that has been 

presented in this blog] implicitly produces many of the 

observed properties of the Solar sunspot cycle without 

any need for a "phase-catastrophe" to realign the planetary

motions with the solar dynamo.

If you want to see how the V-E-J Tidal-Torquing model
implicitly produces many of the observed properties of the
Solar sunspot cycle then you can download the following
paper in the General Science Journal for free:

http://www.wbabin.net/Science-Journals/Research%20Papers-Astrophysics/Download/3812


Do Periodic Peaks in the Planetary Tidal Forces
Acting Upon the Sun Influence the Sunspot Cycle?
Ian R. G. Wilson 2010

The V-E-J Tidal-Torquing Model & the Maunder Minimum

Please read this post if you are not familiar with this topic
and the V-E-J Tidal Torquing model:


http://astroclimateconnection.blogspot.com.au/2012/04/why-does-solar-cycle-keep-re.html

Here is the abstract of a recent publication by 

Vaquero et al. (2011) The Astrophysical Journal 

Letters 731 (2011) L24

REVISITED SUNSPOT DATA: A NEW SCENARIO FOR 

THE ONSET OF THE MAUNDER MINIMUM

http://iopscience.iop.org/2041-8205/731/2/L24/fulltext/apjl_731_2_24.text.html#apjl386754r35

ABSTRACT
The Maunder minimum forms an archetype for the Grand
minima, and detailed knowledge of its temporal 
development has important consequences for the solar 
dynamo theory dealing with long-term solar activity 
evolution. Here, we reconsider the current paradigm of 
the Grand minimum general scenario by using newly 
recovered sunspot observations by G. Marcgraf and 
revising some earlier uncertain data for the period
1636-1642, i.e., one solar cycle before the beginning of
the Maunder minimum. The new and revised data
dramatically change the magnitude of the sunspot cycle
just before the Maunder minimum, from 60-70 down to
about 20, implying a possibly gradual onset of the 
minimum with reduced activity started two cycles 
before it. This revised scenario of the Maunder 
minimum changes, through the paradigm for Grand 
solar/stellar activity minima, the observational 
constraint on the solar/stellar dynamo theories 
focused on long-term studies and occurrence of 
Grand minima.

The main result of this paper is shown in the 
following figure from the paper, a summary of 
which is available at:

http://iopscience.iop.org/2041-8205/731/2/L24/fulltext/apjl_731_2_24.text.html#apjl386754r35

Figure 1

Figure 1 shows that Cycle -11 peaked with an annual sunspot

number in the mid 30's and lasted until at least ~ 1632 

(length ~ 15 years). 

In addition, it shows that with the the new results from Vaquero 

et al. (2011) that cycle -10 peaked with a sunspot number of only 

20 and ended in ~ 1645.

The 60 year hiatus in solar activity known as the Maunder 

Minimum is normally thought to have started in 1645. However, 

the paper by Vaquero et al. (2011), clearly shows that solar 

activity started  faltering two solar sunspot cycles earlier 

than this in about 1618. 

Now the question is, does the V-E-J tidal torquing model 

agree with this re-interpretation of the onset of the Maunder

Minimum?

The blue curve in figures 2a and 2b, shown below, is the 

time-rate of change of the gravitational force of Jupiter,
tangential to the Sun's surface, that acts upon the periodically
induced tidal bulge produced by the alignments of Venus and the
Earth every 1.599 years. The brown curve is simply the 1,2,1
binomial filtered version of the blue curve. Superimposed on
each of these figures are green vertical lines showing the dates
of solar minimum.


Figure 2a shows the period from 1590 to 1680 and figure 2b the
period from 1670 to 1750. The cycle number for each solar 
sunspot cycle is displayed in each of the figures.
Note: The vertical axis is the time-rate of change of the
gravitational force of Jupiter, acting tangential to the Sun's
surface, that pulls and pushes upon the periodically induced
tidal bulge produced by the alignments of Venus and the Earth.
The units are metres per second^(2) per 1.599 years and it is
assumed that Jupiter's gravitational force is acting upon one
percent of the mass of the convective layer of the Sun
(=0.02 % of the mass of the Sun).

Figure 2a

Figure 2b

What figures 2a and 2b clearly show is that there are only two
loss of synchronization events between 1600 and 1750. The first
occurs at the first minimum for cycle -11 in 1619 and the second 
occurs for the first minimum in cycle -4 in 1698.
(Note: Synchronization is regained at the next sunspot minimum
  in each case.)


Amazingly, these two dates mark the start of the descent into the
Maunder Minimum in 1618, according to the modified onset 
scenario of Vaquero et al. (2011), and the abrupt restart of 
solar activity in 1698 with the first minimum of cycle -4.


Thus, there are now FOUR [out of a total of four] loss of 
synchronization events that closely correspond to the four 
most important changes in the level of sunspot activity over 
the last ~ 410 years:


1618/19
First minimum of cycle -11 marking the start of the gradual
onset of the Maunder Minimum.
1698
First minimum of cycle -4 marking the end of the Maunder
Minimum or restart of the solar sunspot cycle after a
60 year hiatus.
1784.7
First minimum of cycle 4 marking the start of the Dalton
Minimum
1996.5
First minimum of cycle 23 marking the start of the next
"Dalton-like" Minimum.


This is absolutely amazing!


An interesting point to note:

The first solar minimum in the telescope era was the 
first minimum for Cycle -12 starting 1610.8.
The corresponding zero acceleration was in ~ 1611.5 
(a difference of 0.8 years, which is probably about the 
size of the errors involved in setting the date of this 
minimum)

This means that by ~ 2021 there have been 37 VEJ 
cycles each of 11.07 years length.

1611.5 + (37 x 11.07) = 2021.1

Hence, if solar cycle 25 has its first minimum in the start 
of 2021, it will show that solar cycle has re-synchronized 
itself to a 11.07 year period VEJ cycle over a ~ 410 year 
period.

If the first minimum of cycle 25 occurs in the start of 
2019, it will show that solar cycle has re-synchronized 
itself to a 11.02 year period VEJ cycle over a ~ 410 year 
period, since:

1611.5 + (37 x 11.02) = 2019.24

If the first minimum of cycle 25 occurs at the beginning 
of 2023, it will show that solar cycle has re-synchronized 
itself to a 11.12 year period VEJ cycle over a ~ 410 year 
period, since:

1611.5 + (37 x 11.12) = 2022.94

Thus, a first minimum for SC 25 that occurs
between 2019.24 and 2022.94 (i.e. ~ 2021 
+/- 2 years) will indicate a re-synchronization 
to a VEJ cycle length of 11.07 +/- 0.05 years 
over a 410 year period.

Why Does the Solar Cycle Keep Re-synchronizing Itself With the Gravitational Force of Jupiter That is Tangentially Pushing and Pulling Upon the Venus-Earth Tidal Bulge in the Sun's Convective Layer?

The Planetary Spin-Orbit Coupling Model:

http://astroclimateconnection.blogspot.com.au/2012/03/planetary-spin-orbit-coupling-model-for.html
http://astroclimateconnection.blogspot.com.au/2012/03/short-comings-of-planetary-spin-orbit.html
http://astroclimateconnection.blogspot.com.au/2010/05/mechanism-for-amplifying-planetary.html

is based upon the idea that the gravitational force of Jupiter
acts upon the Venus-Earth tidal bulge that periodically
forms in the convective layer of the Sun. The cumulative effects
of Jupiter's gravitational force (acting on the tidally induced
asymmetry) produces a tidal torquing that systematically
slows and then speeds up the rotation rate of a thin shell of the
Sun's convective zone. The model proposes that it is these
changes in rotation rate that modulate the level of activity of
the sunspot cycle and possibly produce the torsional oscillation
that are observed in the Sun's convective layer.

The blue curve in figures 1a, 1b, 1c, and 1d, shown below, is
the time-rate of change of the gravitational force of Jupiter,
tangential to the Sun's surface, that acts upon the periodically
induced tidal bulge produced by the alignments of Venus and the
Earth every 1.599 years. The brown curve is simply the 1,2,1
binomial filtered version of the blue curve. Superimposed on
each of these figures are green vertical lines showing the dates
of solar minimum.

Figure 1a shows the period from 1740 to 1820, figure 1b the
period from 1810 to 1890, figure 1c the period from 1880 to
1960, and figure 1d the period from 1950 to 2030. The cycle
number for each solar sunspot cycle is displayed in each of the
figures.

Note: The vertical axis is the time-rate of change of the
gravitational force of Jupiter, acting tangential to the Sun's
surface, that pulls and pushes upon the periodically induced
tidal bulge produced by the alignments of Venus and the Earth.
The units are metres per second^(2) per 1.599 years and it is
assumed that Jupiter's gravitational force is acting upon one
percent of the mass of the convective layer of the Sun
(=0.02 % of the mass of the Sun).

Figure 1a  

Figure 1b

Figure 1c

Figure 1d

Collectively, figures 1a  to 1d can be used to establish 

two very important rules:

RULE 1:

In all but two cases between 1750 and 2030, 

the time of a solar minimum is tightly synchronized 

with time that the change in the gravitational force 

of Jupiter, acting tangentially on the Venus-Earth 

tidal bulge, is a minimum.   

The two exceptions to this rule, are the minima at
the start of cycle 4 (see figure 1a) and cycle 23
(see figure 1d). In each case there is a clear loss
of synchronization between the rate of change of
Jupiter's tangential acceleration and the timing of
the first minimum for that solar cycle. The loss of
synchronization is in the sense that the sunspot
minimum takes place more than ~ 3 years earlier
than the zero point in the change in Jupiter's
tangential acceleration.

The thing that makes cycles 4 and 23 stand out
from all the other sunspot cycles is the fact that
they are amongst the longest sunspot cycles
between 1750 and 2012, with cycle 4 lasting 13.7
years and cycle 23 lasting 12.4 years. Additionally,
both of these cycles were long lasting because the
decay of each from their respective maximum
sunspot number was considerably longer than normal.

It also important to note that Cycle 4 was followed
by a two weak solar cycles (cycles 5 and 6) known
as the the Dalton Minimum. Many now believe that
the same thing is happening again with Cycles 24
and perhaps cycle 25 being historically weaker than
normal.

Note: There is a weak loss of synchronization for
the first minima of cycles 14, 15 and 16, with
re-synchronization occurring for the first minimum
of cycle 17. This corresponds with a series of
weak solar cycles which is sometimes called the
Victorian minimum.

RULE 2:

On the two occasions where synchronization is
significantly disrupted ( > 3 years - at the start 
of cycles 4 and 23), the timing of the first sunspot 
minimum of the next cycle immediately 
re-synchronizes with the timing of the minimum 
change in Jupiter's tangential force acting upon
Venus-Earth tidal bulge (NB There is a correction 
to this rule in comment 7 below).

This raises the important question:

Why does the Solar sunspot cycle re-synchronize itself
with the gravitational force of Jupiter that is tangentially
pushing and pulling upon the Venus-Earth tidal bulge in
the Sun's convective layer?

The simplest explanation is that tidal torquing of Jupiter
upon the Venus-Earth tidal bulge must play a role in
determining the long-term changes in the overall level of
activity of the sunspot cycle.

The 178 year Jose Cycle of the Jovian Planets

                                Updated 13/04/2012

There is some dispute about how long it takes for the four Jovian
planets to re-align. Some people claim that there is a ~ 178 year
re-alignment period (Jose, P.D., ApJ (1965)), while others say
that the long-term re-alignment period (as measured by
asymmetries in the Sun's angular momentum about the
Barycentre) is 171.4 years and the ~ 178 year Jose cycle does
not exist.

The argument presented below investigates if there really is a
~ 178 year Jose Cycle for the re-alignment of the Jovian planets.

Using the following orbital periods of the Jovian planets:

Ju = 11.862 yrs Sa = 29.457 yrs
Ur = 84.01 yrs  Ne = 164.79 yrs

we get the following synodic periods between the Jovian planets:

A___B__Synodic Period______Orbits A_____Orbits B___dir_

Ju - Sa___19.858 yrs________1.6741_______0.6741__retro
Ju - Ur___13.812 yrs________1.1644_______0.1644__prog
Ju - Ne___12.782 yrs________1.0776_______0.0776__prog

Sa - Ur___45.363 yrs________1.53997______0.53997_retro
Sa - Ne___35.869 yrs________1.2177_______0.2177_prog

Ur- Ne___171.379 yrs_______2.03998______1.03998_prog

where columns 1 and 2 give the two planets (A and B) that are
being considered; column 3 gives the synodic period in years;
columns 4 and 5 the number of orbits completed by planets A
and B,respectively over one synodic period; and column 6 the
direction of movement of the alignments i.e. prog = prograde
and retro = retrograde.

This means that there are three possible alignments of the Jovian
planets:

1. Ju - Sa re-alignments will align with Ur - Ne re-alignments after
    a whole multiple of the following number of years:

i.e.   (19.858 x 171.379) / (171.379 + 19.858) = 17.7959 yrs

2.  Ju - Ur re-alignments will align with Sa - Ne re-alignments after
    a whole multiple of the following number of years:

i.e.   (13.812 x 35.869) / (35.869 - 13.812) = 22.461 yrs

3.  Ju - Ne re-alignments will align with Sa - Ur re-alignments after
    a whole multiple of the following number of years:

i.e.   (12.782 x 45.363) / (45.363 + 12.782) = 9.9721 yrs

Hence, these re-alignments of the four Jovian planets take place:

After one Gleissberg cycle of ~ 89 years:

Ju - Ne / Sa - Ur___9 x 9.9721 yrs___=  89.75 yrs
Ju - Sa / Ur - Ne___5 x 17.7959 yrs__=  88.98 yrs
Ju - Ur / Sa - Ne___4 x 22.461 yrs___=  89.84 yrs

and then again after one Jose cycle ~ 179 years:

Ju - Ne / Sa - Ur__18 x 9.9721 yrs___= 179.50 yrs
Ju - Sa / Ur - Ne__10 x 17.7959 yrs__= 177.96 yrs
Ju - Ur / Sa - Ne__8  x 22.461 yrs____= 179.69 yrs

Since the actual orbital periods of the four Jovian planets
slowly drift over the centuries you would expect these two
cycles to slowly drift in and out depending on the actual
orbital periods of the planets, however, the whole
re-alignment pattern seems to reset itself once every
4628 yrs.

The actual dates upon which the re-alignments of Uranus and
Neptune are re-synchronized with the re-alignments of Jupiter
and Saturn are:

_________= 7949 B.C.
5725 B.C.  = 7949 B.C. + 2224 yrs
3322 B.C.  = 5725 B.C. + 2403 yrs
1098  B.C.  = 3322 B.C. + 2224 yrs
1306 A.D.  = 1098 B.C. + 2405 yrs
3530 A.D.  = 1306 A.D. + 2224 yrs
5933 A.D.  = 3530 A.D. + 2403 yrs

As you can see, there is an oscillation between a period of 2224
years and 2403.7 yrs, giving a full repetition period (where all the
Jovian planets are lined up on the same side of the Sun) of ~4628
yrs. This means that the Jovian planets reset their alignments
roughly once every 26 Jose cycles = 26 x 178 yrs = 4628 yrs.

The actual repetition cycle is 18,512 (= 4 x 4628) yrs long,
as after each 4628 yrs, the four Jovian planets come back
into alignment along an axis that rotates through a quarter of
a full revolution around the Sun.

The ~ 18500 year repetition cycle for the gravitational influence
of the Jovian planets is responsible for the slow precession of the
line-of-Apsides of the Earth's orbit, causing perihelion (and
aphelion) to advance by roughly 1 day every 58 years.