Wednesday, April 17, 2013

A Confirmation of the VEJ Tidal-Torquing Model

                       UPDATED 30/04/2013
See the following newer post for the updates this post:

The diagram below shows the solar sunspot number 
(SSN) for solar cycles 13 through  to 23, plotted against 
the net tangential torque of Jupiter acting upon the V-E tidal 
bulge. The net tangential torque was obtained by adding
Jupiter's tangential torque at one V-E inferior conjunction 
to Jupiter's tangential torque at the next V-E superior 
conjunction. In this diagram, a positive net torque means 
that the rotational speed of the Sun's equatorial convective 
layer is sped-up and a negative net torque means that the 
equatorial convective layer is slowed-down.

[N.B. The net torque curve has been smoother with a 
5th and 7th order binomial filter to isolate low frequency 

This diagram clearly shows that:

a) The net torque of Jupiter acting on the V-E tidal bulge
     has a natural 22.4 year periodicity which matches the 22.1
     year period of the solar Hale (magnetic) cycle.

b) the equatorial convective layers of the Sun are 
     sped-up during ODD solar cycles and slowed-down 
     during EVEN solar cycles. 

Support for point b) is provided by the following 
figure which was kindly sent to me as a private
communication by Paul Vaughan. Paul has allowed 
me to use his graph here to support this post.

In this plot, Paul Vaughan has superposed the 22.1 year 
JEV cycle onto Tlatov & Makarov's (2005) Figure 3. 

Tlatov, A.G.; & Makarov, V.I. (2005). 22-year variations 
of the solar rotation, Large-scale Structures and their 
Role in Solar Activity, ASP Conference Series,  Ed: K. 
Sankarasubramanian, Matt Penn & Alexei Pevtsov, 
Vol. 346,

The underlying figure from Tlatov & Makarov (2005) shows 
the deviation of the surface rotation velocity of the Sun from 
its average value at corresponding latitudes. These 
measurements have been obtained from H-alpha observations 
of the Sun.  In this diagram, the regions where rotation is 
slower than normal are painted dark and the velocity is 
averaged over the northern and southern hemispheres 
(Note: The window for the spectral analysis was set to 
12 years).

Paul Vaughan's graph clearly shows the 22.1 year 
JEV cycle is almost perfectly synchronized in phase 
with the changes in rotational velocity on the 
surface of the Sun over a period of 100 years.

This is a remarkable result! 

Further confirmation of point b) is given by the following figure
which compares the deviation of the surface rotation velocity
plot of Tlatov & Makarov (2005) with the monthly solar sunspot 
number for cycles 13 through 23.

This plot  clearly shows that for all 11 solar cycles, the 
deviation of the rotation velocity of the surface of the 
Sun from its average value at corresponding latitudes, 
speeds up during ODD solar cycles and slows down 
during EVEN solar cycles.

This is a wonderful confirmation of my earlier results 
published in  the blog post of November 23rd 2012.

It also indirectly confirms the result obtained in our 2008 solar paper:

Does a Spin–Orbit Coupling Between the Sun and the Jovian Planets Govern the Solar Cycle? 

I. R. G. Wilson, B. D. Carter, and I. A. Waite
Publications of the Astronomical Society of 
Australia, 2008, 25, 85–93.

This graph from Wilson et al. 2008 (above) shows 
the moment arm of the torque for the quadrature 
Jupiter and Saturn nearest the maximum for a given 
solar cycle, plotted against the change in the average 
equatorial (spin) angular velocity of the Sun since 
the previous solar cycle (measured in μrad s−1). 
The equatorial (≤±15 deg) angular velocities published 
by Javaraiah (2003) for cycles 12 to 23 have been 
used to determine the changes in the Sun’s angular 
velocity (since the previous cycle) for cycles 13 to 23.

What these graphs clearly show is that the Sun's equatorial
angular velocity increases in ODD solar cycles and decreases
in EVEN solar cycles, in a manner that is predicted by the 
V-E-J Tidal-Torquing model.

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