A Possible Reason for the 1.3 year Solar Oscillations near the Sun's Tachocline

Back in 2006, I was investigating the possibility that variations 

in planetary gravitational/tidal forces might be linked with the 

newly discovered 1.3 year oscillations seen near the Sun's

Tachocline boundary.

Howe et al. Science 31 March 2000: Vol. 287 no. 5462 pp. 2456-2460  

Dynamic Variations at the Base of the Solar Convection Zone


ABSTRACT 

We have detected changes in the rotation of the sun near the base 

of its convective envelope, including a prominent variation with a 

period of 1.3 years at low latitudes. Such helioseismic probing of

 the deep solar interior has been enabled by nearly continuous 

observation of its oscillation modes with two complementary 

experiments. Inversion of the global-mode frequency splittings 

reveals that the largest temporal changes in the angular velocity 

Ω are of the order of 6 nanohertz and occur above and below the

 tachocline that separates the sun's differentially rotating convection 

zone (outer 30% by radius) from the nearly uniformly rotating deeper 

radiative interior beneath. Such changes are most pronounced near 

the equator and at high latitudes and are a substantial fraction of the

 average 30-nanohertz difference in Ω with radius across the 

tachocline at the equator. The results indicate variations of rotation 

close to the presumed site of the solar dynamo, which may generate 

the 22-year cycles of magnetic activity.

The plot below shows a Fast Fourier Transform (FFT) Spectra 
of the Solar Motion about the Barycentre of the Solar System 
caused by the Terrestrial planets.

 The Solar Baycentric motion due to the Terrestrial planets is 

dominated by the Synodic periods of Venus/Earth (= 1.5593 yrs)

and Earth/Mars (=2.13 years). Also evident in this plot is the 

~ 6.4 year beat period between these two synodic periods

(i.e. Venus/Earth and Earth/Mars).

Now, I knew that Jovian planets act like a large washing 

machine, stirring the inner terrestrial planets with a 

gravitational force that varies with a frequency that is 

determined by the beat period between two main competing 

Jovian planetary alignments.

The first is that produced by the the retrograde tri-synodic 

period of Jupiter/Saturn ( = 59.577 yrs) and the second is 

the pro-grade synodic period of Uranus/Neptune (171.41 yrs):

(59.577 x 171.41) / (171.41 + 59.577) = 44.21 yrs

This driving period of the Jovian planets closley matched 

the synodic periods of the three largest Terrestrial planets 

with Jupiter: 

69 × SVJ = 44.770 yrs    SVJ = synodic period Venus/Jupiter

41 × SEJ = 44.774 yrs    SEJ = synodic period Earth/Jupiter

20 × SMJ = 44.704 yrs    SMJ = synodic period Mars/Jupiter

The 44. 7 year period for the three largest Terrestrial planets 

to realign with Jupiter appears to link Jupiter's orbital period 

directly into the time it takes for the three largest terrestrial 

planets to return to their same (relative) orbital configuration, 

which just happens to be 6.40 years:

4 x SVE = 6.3946 yrs  SVE = synodic period Venus/Earth

3 x SEM = 6.4059 yrs SEM = synodic period Earth/Mars

7 x SVM = 6.3995 yrs SVM = synodic period Venus/Mars

28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs   

This lead me to propose that resonances in the relative 

motion of the Jovian planets had effectively molded and 

shaped the orbital periods of the three main terrestrial 

planets, producing the 6.4 year period for their orbital 

realignment. 

In addition, I proposed that the gravitational/tidal pumping 

action of the Jovian planets would lead to a 6.4 amplitude 

modulation of the dominant 1.6 year frequency of the Sun's 

Barycentric motion [See the graph above], producing two 

side-lobes, one at 1.28 years and the other at 2.13 years. 

I speculated that it was this ~ 1.3 year side lobe that was 
driving the fundamental solar oscillation that Howe et al. 
2000 had observed near the Tachocline boundary. 


This "discovery" lead me to think that the relative orbital
configurations of the Jovian planets were not directly 
responsible for modulating/driving the level of solar activity 
on the Sun. Instead, I began to realize that it was more likely 
that the motion of the Jovian planets had molded the orbital
periods of the terrestrial planets and it was the tidal effects
of the latter (i.e. mostly due to tidal alignments of Venus
and the Earth) that were directly responsible for 
driving/modulating the Sun's activity, especially when they 
were coupled with the effects of Jupiter's dominant 
gravitational force acting upon the convective layers of the
Sun.


This revelation lead me to propose the tidal-torquing
(spin-orbit coupling) model that I have outlined at: 


http://astroclimateconnection.blogspot.com.au/2012/03/planetary-spin-orbit-coupling-model-for.html 

Short Comings of the Planetary Spin-Orbit Coupling Model

SIMPLE TIDAL TORQUING MODEL

(UPDATED 20/03/2012)

Imagine that Venus and Earth are aligned directly above a point A that is on the surface of the Sun. The combined tidal force of Venus and Earth produced two tidal bulges upon the surface of the Sun located at A and B.

Jupiter is located at an angle θ to the line joining the two tidal 

bulges at A and B. Let Rs be the radius of the Sun = OA = OB.

Now by the cosine rule:

JB² = RJ² + Rs² – 2 × RJ × Rs × cos(θ)                         and

JA² = RJ² + Rs² – 2 ×RJ × Rs × cos(π - θ)

      = RJ² + Rs² + 2 ×RJ × Rs × cos(θ)                                                             

Let angle JAO = φ 

and angle JBO = ψ                                                                  

then by the sine rule:

RJ / sin (φ) = JA / sin (π – θ)                                           and

RJ / sin(ψ) = JB / sin (θ)

therefore:

sin (φ)  = (RJ / JA) × sin (π – θ)

sin (ψ) = (RJ / JB) × sin (θ)

 By Newtons Law of Universal Gravitation

Ff = G M_J M_S / JA² = const / JA²                 const = G M_J M_S

Fn = G M_J M_S / JB² = const / JB²

Now

Ffp  = Ff × sin(φ)

hence:

Ffp  = (const / JA²) × (RJ / JA) x sin (π  − θ) 

       = (const’ / JA³) × sin (θ)       

                                                                   const’= const × RJ

and

Fnp = Fn × cos (ψ – π/2) 

       = Fn × cos (-(π/2 – ψ)) 

       = Fn × cos (π/2 – ψ) 

       = Fn × sin (ψ))

hence:

Fnp = (const / JB²) × (RJ /JB) × sin (θ) 

      = (const’ / JB³) × sin (θ)

Finally:  ΔF = The net tangential force of Jupiter's 

gravitational on the Sun's tidal bulges 

ΔF = Fnp – Ffp 

     = const’ × [(1 / JB³) – (1 / JA³)]  × sin (θ)

ΔF = const’ × {(1 / [RJ² + Rs² – 2 × RJ × Rs × cos(θ)]^3/2) 

         − (1 / [RJ² + Rs² + 2 ×RJ × Rs × cos(θ)]^3/2)} × sin(θ)

The following graph shows the net tangential acceleration of the  

Sun's surface due to Jupiter's gravitational force acting upon the 
tidal bulges that are induced by Venus/Earth upon the Sun's surface 
as a function of Jupiter's angle θ (please refer to diagram above). 
Note: It is assumed that Jupiter's force only acts upon one percent 
of the mass of the convective zone of the Sun (=0.0002 % of the 
mass of the Sun). 

Even under these ideal assumptions, the maximum peak acceleration 

only reaches ~ 3.0 micro-metres per second^2. 

Assuming that half this peak acceleration is applied to 0.02 % of the 
Sun's mass for one full day at each of the roughly seven alignments 
of Venus and Earth over the 11.07 years it takes for θ to change from 
0 to 90, the net change to to the Sun's velocity should be 


acceleration x delta time ~1.5x10^(-6) x 7 x 24 x 3600 ~ 0.91 m/sec

Given these highly optimistic assumptions, it could be argued that 
if Jupiter's gravitational force only had to change the rotational
velocity of one % of the mass of the convective zone of the Sun 
(~ 0.02 % of the mass of the Sun) it would produce a significant
change rotational velocity of this small amount of mass.


Of course, the assumptions used in these calculation require 
that the one % of the Sun's convective layer mass that is affected 
by Jupiter's gravity is dynamically decoupled from the remaining 
0.998 % of the Sun's mass. At this stage, there is no region of 
the Sun's convective layer that is known to be effectively 
dynamically decoupled from the rest of the Sun. In addition, 
even if such a region did exist within the Sun's convective zone, 
we have no idea of its relative mass. 


Given these large uncertainties, all we can say is that the 
0.91 m/sec change in rotational velocity is most likely a 
loose upper bound to the real value.   


(N.B. All the arguments given above assume that there are 
no other induced asymmetries in the spherical shape of the Sun 
other than those produced by the combined tidal forces of 
Venus and Earth at the time of alignment).

CONCLUSION

The simple planetary spin-orbit coupling model does not

appear to produce a significant change in the velocity of 

rotation in the outer layers of the Sun.

Hence, in order for it to taken seriously, the planetary 
spin-orbit coupling model would require a considerable 
and as yet unknown amplification mechanism .     

One possible amplification mechanism is discussed here:

http://astroclimateconnection.blogspot.com.au/2010/05/mechanism-for-amplifying-planetary.html 

A Planetary Spin-Orbit Coupling Model for Solar Activity

Do Periodic Peaks in the Planetary Tidal 

Forces Acting Upon the Sun Influence the 

Sunspot Cycle?

A free download of the paper is available in the General 

Science Journal were it was published in 2010 

http://www.wbabin.net/Science-Journals/Essays/View/3812

The General Science Journal paper (above) was written in 

order to further investigate the main conclusion of the Wilson 

et al. (2008) paper that the Sun's level of solar activity is 

driven by a spin-orbit coupling mechanism between the Sun 

and the Jovian planets:  

Publications of the Astronomical Society of Australia, 2008, 

25, 85–93.

Does a Spin–Orbit Coupling Between the Sun and 

the Jovian Planets Govern the Solar Cycle?

http://www.publish.csiro.au/?act=view_file&file_id=AS06018.pdf

The spin-orbit coupling mechanism investigated in the 

General Science Journal paper is based on the idea that the 

planet that applies the most dominant gravitational force upon 

the Sun is Jupiter, and that after Jupiter, the planets that apply 

the most dominant tidal forces upon the Sun are Venus and 

the Earth.

The spin-orbit coupling mechanism is based upon the idea that 

periodic alignments of Venus and the Earth (once every 1.5993 

years) produce temporary tidal bulges along the Earth-Venus

-Sun line, on opposite sides of the Sun. When these temporary

tidal bulges occur, Jupiter's gravitational force tugs on these 

bulges and either slows down or speeds up the Sun's rotation.

What makes this particular spin-orbit coupling mechanism

intriguing, is the time period over which the Jupiter's

gravitational pull speeds up and slows down the Sun rotation 

as Jupiter tugs on the tidal bulges.

   

[N.B. In the above diagram the planets are revolving in a
clock-wise direction and the Sun is rotating in a clock-wise
direction. Also, when near-side and far-side tidal bulges on
the Sun's surface are referred to, it is with respect to the
aligned planets Earth and Venus.]

The diagram above shows Jupiter, Earth and Venus initially 

aligned on the same side of the Sun (position 0). In this 

configuration, Jupiter does not apply any lateral torque upon 

the tidal bulges (The position of the near side bulge is shown by 

the black 0 just above the Sun's surface).  

1.5993 years later, each of the planets move to their respective

position 1's. At this time, Jupiter has moved 13.000 degree 

ahead of the far-side tidal bulge (marked by the red 1 just 

above the Sun's surface) and the component of its 

gravitational force that is tangential to the Sun's surface tugs 

on the tidal bulges, slightly increasing the Sun's rotation rate. 

After a second 1.5993 years, each of the planets move to 

their respective position 2's. Now, Jupiter has moved 26.00 

degrees ahead of the near-side tidal bulge (marked by the 

black 2 just above the Sun's surface), increasing Sun's 

rotation rate by roughly twice the amount that occurred at 

the last alignment.

This pattern continues with Jupiter getting 13.000 degrees 

further ahead of the alternating near and far-side tidal bulges, 

every 1.5993 years. Eventually, Jupiter will get 90 degrees 

ahead of  the closest tidal bulge and it will no longer exert a 

net torque on these bulges that is tangential to the Sun's surface 

and so it will stop increasing the Sun's rotation rate.

Interestingly, the Jupiter's movement of 13.000 degrees per 

1.5993 years with respect to closest tidal bulge, means that 

Jupiter will get 90 degrees ahead of the closest tidal bulge in 

11.07 years. This is almost the same amount of time as to 

mean length of the Schwabe Sunspot cycle (11.1 +/- 1.2 years).

In addition, for the next 11.07 years, Jupiter will start to lag 

behind the closest tidal bulge by 13.000 degrees every 

1.5993 years, and so its gravitational force will pull on the 

tidal bulges in such a way as to slow the Sun's rotation rate 

down.

All together there will be four periods of 11.07 years, with 

the gravitational force of Jupiter, increasing the Sun's rotation 

rate over the first and third periods of 11.07 years, and 

decreasing the Sun's rotation rate over the second and fourth 

periods of 11.07 years.

Hence, the basic unit of change in the Sun's rotation rate (i.e. 

and increase followed by a decrease) is 2 x 11.07 years = 

22.14 years. This is essentially equal to the mean length of the 

Hale magnetic sunspot cycle of the Sun which is 22.1 +/- 2.0 yrs)

However, the complete planetary tidal cycle is actually 

(4 x11.07 years =) 44.28 years.   

    

Now the outer Jovian planets act like a large washing 

machine, stirring the inner terrestrial planets with a 

gravitational force that varies with a frequency that is the 

beat period between two main competing Jovian planetary 

alignments.

The first is that produced by the the retrograde tri-synodic 

period of Jupiter/Saturn ( = 59.577 yrs) and the second is 

the pro-grade synodic period of Uranus/Neptune (171.41 yrs):

(59.577 x 171.41) / (171.41 + 59.577) = 44.21 yrs

[N.B. This calculation assumes the following sidereal 

orbital period for the Jovian planets: Jupiter = 11.862 yrs; 

Saturn = 29.457 yrs; Uranus = 84.011 yrs; Neptune 

= 164.79 yrs.

http://nssdc.gsfc.nasa.gov/planetary/]

In addition, there is a remarkable near-resonance condition 

that exists between the orbital motions of the three largest 

terrestrial planets with:

4 x SVE = 6.3946 years  SVE = synodic period of Venus and Earth

3 x SEM = 6.4059 years SEM = synodic period of Earth and Mars

7 x SVM = 6.3995 years SVM = synodic period of Venus and Mars

28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs 

This means that these three planets return to the same 

relative orbital configuration once every 6.40 years, and 

that exactly 7.0 times this re-alignment period is 44.8 years, 

close to the 44.2 - 44.3 year period cited above for the 

gravitational forcing of the Jovian planets upon the terrestrial 

planets.

Further evidence for a link between the re-alignment period 

of the three largest Terrestrial planets and the period of Jupiter 

comes from the fact that: 

69 × SVJ = 44.770 yrs        SVJ = synodic period of Venus & Jupiter

41 × SEJ = 44.774 yrs         SEJ = synodic period of Earth & Jupiter

20 × SMJ = 44.704 yrs            S = synodic period of Mars & Jupiter

This means that Venus, Earth and Jupiter, in particular, form 

alignments at sub-multiples of Jose cycle 178.72 years i.e.

½ × 178.72 yrs = 89.36 yrs 

¼ × 178.72 yrs = 44.68 yrs

1/8 × 178.72 yrs = 22.34 yrs 

1/16 × 178.72 yrs = 11.17 yrs

These alignments only change slowly over hundreds of 

years and they closely match the well known Schwabe 

(~ 11.1 yrs), Hale (~ 22.2 yrs) and Gleissberg (~ 90 years) 

solar cycles.

CONCLUDING REMARKS

It would appear that a simple spin-orbit coupling mechanism

proposed in this posting would naturally produce a  link

between systematic changes in the rotation rate of the Sun 

that would be synchronized with the Bary-centric motion of 

the Sun about the centre-of-mass of the Solar System as 

suggested by Wilson et al. (2008). 

APPENDIX - Some additional matches between the
planetary orbital cycles and the long term periodicities
that are observed in the level of Solar activity.

DATA VALUES USED  

V = 224.70069 days E = 365.356363 days 

=>  VE = 583.920628  VE = 1.59866 years

J = 11.862 years S = 29.457 years; 

JS = 19.9590; 5 x VE = 7.993298 years

Hale cycle (22.1 years)

There is an 8:9 resonance between the Hale and JS cycles

178.73 x 19.859/ (178.73 – 19.859) = 22.341

178.73 = 9 x 19.859

178.73 = 8 x 22.341

Gleissberg Cycle (~ 90 years)

Hale cycle drifts out of phase with the JS cycle by ½ of 

JS cycle

4 x Hale = 4 x 22.341 = 89.364 yrs

4 ½ JS = 4 ½ x 19.859 = 89.366 yrs

DeVries Cycle (208 years)

This period is still a bit of a mystery but it is interesting to 
note that:

26 x PVE =  26 x 7.993 yrs = 207.826 yrs

10 1/2 JS =  208.509 yrs

3 1/2 TJS = 208.509 yrs


PVE = Penta-Synodic periods of Venus and the Earth
JS = Synodic period of Jupiter/Saturn
TJS = Tri-Synodic period of Jupiter/Saturn = 59.574 yrs 

Hallstatt Cycle (~ 2320 years)

A grand alignment of the Jovian planets (Jupiter, Saturn, 

Uranus, Neptune), with all of the planets arranged in a 

line on the same side of the Sun, occurs roughly every 

4628 year. 

This 26 x 178 years (Jose cycle) = 4628 years.

Half this realignment period is 2314 years which is close

to the long term solar cycle called the Hallstatt cycle.

cycle  

The Open Atmospheric Science Journal, 2012, 6, 49-60

Lunar Tides and the Long-Term Variation of the Peak Latitude Anomaly of the Summer Sub-Tropical High Pressure Ridge over Eastern Australia

by Ian R.G. Wilson

Download (Free) Bentham Open Atmospheric Science Paper

Abstract: This study looks for evidence of a correlation between long-term changes in the lunar tidal forces and the interannual to decadal variability of the peak latitude anomaly of the summer (DJF) subtropical high pressure ridge over Eastern Australia (LSA) between 1860 and 2010. A simple "resonance" model is proposed that assumes that if lunar tides play a role in influencing LSA, it is most likely one where the tidal forces act in "resonance" with the changes caused by the far more dominant solar-driven seasonal cycles. With this type of model, it is not so much in what years do the lunar tides reach their maximum strength, but whether or not there are peaks in the strength of the lunar tides that re-occur at the same time within the annual seasonal cycle. The “resonance” model predicts that if the seasonal peak lunar tides have a measurable effect upon LSA then there should be significant oscillatory signals in LSA that vary in-phase with the 9.31 year draconic spring tides, the 8.85 year perigean spring tides, and the 3.80 year peak spring tides. This study identifies significant peaks in the spectrum of LSA at 9.4 (+0.4/-0.3) and 3.78 (± 0.06) tropical years. In addition, it shows that the 9.4 year signal is in-phase with the draconic spring tidal cycle, while the phase of the 3.8 year signal is retarded by one year compared to the 3.8 year peak spring tidal cycle. Thus, this paper supports the conclusion that long-term changes in the lunar tides, in combination with the more dominant solar-driven seasonal cycles, play an important role in determining the observed inter-annual to decadal variations of LSA.

Important blog sites that are discussing this paper.

Jo Nova

Jennifer Marohasy

Tallbloke

The above graph shows that there is actually quite a good match between the number of days the nearest Full/New moon is from perihelion and the peaks in LSA (see the diagram below). In fact, the correspondence between the peaks in the data sets are (generally) so good, that it is possible identify peaks in LSA that are caused by large Plinarian [> 4] volcanic eruptions to the near north of Australia. (i.e. in the Indonesian Archipelago (e.g. Krakatoa in 1883) and New Britain).

A recently published paper that supports the assertion that atmospheric tides can have an influence upon regional weather patterns on times scales of ~ two weeks. 

Monthly lunar declination extremes’ influence on tropospheric circulation patterns

Daniel S. Krahenbuhl,1 Matthew B. Pace,1 Randall S. Cerveny,1 and Robert C. Balling Jr.1

Received 22 July 2011; revised 13 October 2011; accepted 13 October 2011; published 15 December 2011.

Short‐term tidal variations occurring every 27.3 days from southern (negative) to northern (positive) maximum lunar declinations (MLDs), and back to southern declination of the moon have been overlooked in weather studies. These short‐term MLD variations’ significance is that when lunar declination is greatest, tidal forces operating on the high latitudes of both hemispheres are maximized. We find that such tidal forces deform the high latitude Rossby longwaves. Using the NCEP/NCAR reanalysis data set, we identify that the 27.3 day MLD cycle’s influence on circulation is greatest in the upper troposphere of both hemispheres’ high latitudes. The effect is distinctly regional with high impact over central North America and the British Isles. Through this lunar variation, mid-latitude weather forecasting for two‐week forecast

periods may be significantly improved.

http://www.agu.org/pubs/crossref/2011/2011JD016598.shtml