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.