Wednesday, May 30, 2012

Earth-Like Planets in the Habitable Zone

Updated 16/06/2012

The most probable Earth-like planets to host complex
life are those that are located at just the right distance
from high metallicity G and K type main-sequence
stars that allow the bulk of their surface water to
remain in the liquid state.

The volume of the spherical shell that encompasses 
the orbital distances that make liquid surface water 
possible on these planets is known as the Habitable 
Zone. 


The Sun's [current] Habitable Zone extends from
0.95 A.U. to about 1.37 A.U. (i.e. from just outside
the orbit of Venus at 0.72 A.U. to just inside the orbit
of Mars at 1.52 A.U.).

As a general rule, the mean distance of the centre of
the Habitable Zone from a main-sequence star [in
Astronomical Units or A.U.] is given by
[1. Wikipedia Habitable Zone 2012]:

= SQRT (Lstar / Lsun)

where Lstar = luminosity of the parent star
_____Lsun = luminosity of the Sun

This information can be used to place approximate
limits on the MK spectral type of potential candidate
stars.

First, main sequence stars with masses above ~ 1.5
solar masses [i.e. MK spectral types of F5 or earlier]
have lifetimes that are shorter than about 5 billion years.
Hence, these type of main sequence stars are unlikely
to remain stable over the billions of years that are needed
to support the development of advanced civilizations.
In addition, these type of stars have convective cores
and radiative outer envelopes and so the type of solar
activity that they support will not be the same as that in
lower mass stars which have convective outer envelopes.
     
Second, the following table shows that as the luminosity
[and mass] of stars decrease along the main sequence,
the distance to the centre of the Habitable Zone (shown
in column 3), moves closer into the parent star. This
means that for late K spectral types stars [i.e. K6, K7,
K8,..etc.], any earth-like planet that is in the Habitable
Zone will be tidally-locked with their parent star, markedly
reducing its chances of producing advanced life-forms.

MK_____Luminosity____HZ_____Tidal-Locking
Spectral___(Solar_____Distance____Distance
Type____Luminosities)__(A.U.)[2]__(A.U.)[3]

F0________6.0________2.45______0.55
F5________2.5________1.58______0.53
G0_______1.10________1.05______0.51
G5_______0.79________0.89______0.49
K0_______0.40________0.63______0.47
K5_______0.16________0.40______0.43
M0_______0.063_______0.25______0.39

[2. Zombeck 1990]
[3. Kasting et al. 1993]

Hence, searches for advanced civilizations 
should be restricted to single, high metallicity, 
old [> 5 billion years] main sequence stars that 
have MK spectral types between F8/F9V and 
K5V.

Recent studies of solar systems outside of our own
indicate that the probability of finding Earth-like
planets in the Habitable Zone is maximized if the 
Jovian-like planets in that system move in relatively
large (i.e. greater than or equal to ~ 3 to 5 A.U)
stable orbits of low eccentricity. 

If the Jovian-like planets are located in these 
near-circular long-term stable orbits, they allow the 
smaller Terrestrial-like (rocky) worlds that are closer
into the star [i.e. in the Habitable Zone between 0.5
and 1.5 A.U.], to remain in the near-circular long-
term stable orbits. This latter outcome is essential
if we want have Earth-like planets to remain resident 
in the Habitable Zone of the parent star for the billions 
of years that are necessary for complex life to evolve.

In our 2008 paper:

Does a Spin–Orbit Coupling Between the Sun
and the Jovian Planets Govern the Solar Cycle?
[4. Wilson et al. 2008]

we concluded that;
...another important consequence the synodic (phase locked)
resonance model is that any solar type main sequence
stars that exhibits solar cycles similar to the Sun must have
at least two Jovian planets orbiting the star, such that their
synodic period is comparable to the star’s solar cycle
length. This opens up the possibility that long term HK
observations of magnetic activity in solar type stars could
be used as an effective method for detecting Jovian
planets orbiting these stars.
In light of the recent development of the V-E-J Tidal
torquing model as a replacement for the synodic 
(phase-locked) resonance model, what we are proposing 
is that the presence of cyclical solar sunspot activity in 
the convective layer of solar-like main sequence stars
is indicative of the fact that these stars have at least one
Jovian-like planet revolving around them in a near-circular
stable orbit, with orbital periods ranging from a few years
to a couple of decades.


Interestingly, these are the exact type of solar systems
we should be looking for to maximize our chances of
finding Earth-like planets in a star's Habitable Zone.


[N.B. This means that the solar systems of stars that 
do not exhibit long term cyclical solar sunspot activity
most likely do not contain a Jovian-like planet revolving
around them in large (greater than or equal to ~ 3 to 5
A.U) near-circular stable orbit.]

Hence, we are proposing that following main
sequence stars [listed in the table below] that
show regular stellar activity cycles should have a
Jovian-like planet(s) moving in a near circular
obit(s) at distances exceeding 3 to 5 A.U.

We request that searches be carried out to confirm
if these systems do indeed contain these Jovian-like
planets.

In addition, we are proposing that if:

a) Jovian-like planets are found to exist in these
systems in near circular orbits with distances
exceeding 3 to 5 A.U.

b) the stellar system's age is greater than 3 - 5
billion years


c) the parent star in the stellar system has a high
    solar-like metallicity



[update: it appears that sub-Neptune size planets
 may be equally likely to form around metal poor stars 
 (i.e. 25 % of the Sun's metallicity), unlike Jupiter-size
 gas giants which tend to favor metal rich stars.]

http://www.sciencedaily.com/releases/2012/06/120613141606.htm

d) the parent star is not producing dangerous long-term
    flaring activity that produces condition that are not
    suitable for life

then these systems should be considered as prime
candidates to search for planets in the Habitable 

Zone that could potentially support advanced 
extra-terrestrial life.

STAR______MK____STELLAR ACTIVITY__DISTANCE
________SPECTRAL__CYCLE LENGTH____(Light Years)
__________TYPE_[5]____(YEARS)_[5]________[6]

HD81809___G2V__________8.17____________102
HD152391__G7V__________10.9____________55.2
HD3651____K0V__________13.8____________36.2
HD26965___K1V__________10.1____________16.4
HD10476___K1V___________9.6____________24.3
HD219834B_K2V__________10.0____________67.8
HD160346__K3V___________7.0____________34.9
HD16160___K3V__________13.2____________23.5
HD4628____K4V__________8.37____________24.3
HD32147___K5V__________11.1____________28.7
HD201091__K5V___________7.3____________11.4 A.

Possible:
HD22049___K2V___________4.9____________10.5*
Epsilon Eri
*[Buccino & Mauas 2008]

N.B. Stellar systems that are too metal poor or too young need
to eliminated from the list above using the following information.


STAR_________AGE_____ROTATION____METALICITY
_____________(G yrs)_____PERIOD_______(solar = 0.0)
______________(**)_______(days)_(***)______(**)____

HD81809______4.57^_______40.2___________-0.34 a.
HD152391_____2.0_________11.43__________0.00 b.
HD3651_______6.4_________44____________-0.15
HD26965______5.6_________43_____________0.19 c.
HD10476______6.3_________35.2___________-0.04
HD219834B___3.24^________43______________?  d.
HD160346______?_________36.4_____________?
HD16160_____4.8-6.6______48.0____________-0.07 e.
HD4628_______5.4________38.5____________-0.22 f.
HD32147______4.5________48.0_____________0.28
HD201091_____6.1_________7.3____________-0.20 g.

** Wikipedia - accessed 04/06/2012.
*** [Lorente R. and Montesinos B., 2005, Ap. J., 624, p. 1104]
^

a. HD 81809 is a close visual binary with a separation
at apoastron of about 0.4 arcsec and a period of about
35 yr (Pourbaix 2000). The masses of the two
components are M1 = 1.7±0.64 M⊙ and M2 =
1.0±0.25 M⊙, with spectral types G2 and G9,
respectively. Both components are slow rotators, with
v sin i = 3 km/s (Soderblom 1982).

b. HD 152391 - chromospherically active but kinematically
old. Lithium age 2.0 G yrs. [Rocha-Pinto H.J., 2002, A&A,
384, p. 912]


c. HD26965 (40 Eridani = Keid) There is a DA4 white
dwarf + M5.4eV located at 400 A.U. (8000 year orbit)
from this star.

d. HD219834B=94 Aquarii B = G5

e. HD 16160 - companion B 1200 A.U. and companion C
24 A.U. with a period of 61.0 years.

f. An unconfirmed planet may exist at 4.29 A.U. with
a mass > 1.18 M(Jupiter) in a near circular orbit with a
period ~ 10.1 years.


g. 61 Cygni A


Supportive Evidence for the Proposition that Jovian
Planetary Systems May Be Responsible for Enhanced 
Stellar Activity.


The following graph [Gray et al. 2006] shows the level of
chromospheric activity, as measured by log [R'HK], plotted
against metallicity, for dwarf F, G, and K stars. The
histograms below this graph show that level of chromospheric
activity is bi-modal for high-metallicity stars (i.e. [M/H] > -0.2)
and single-peaked for low-metallicity stars (i.e. [M/H] < -0.2).
[Gray R.O. et al. 2006]

The most obvious explanation for lack of chromospherically
active stars amongst the low-metallicities stars is that they
are, on average, older than the high-metallicity stars. Hence,
the low activity is a direct consequence of the fact that older
stars are less chromospherically active because they are
rotating more slowly than the younger stars.

One problem with this explanation is that there is a very sharp
transition from bimodality to single-peak behavior in stellar
activity at [M/H] = -0.2.

             [N.B. Solar metal abundance is [M/H] = 0.0]



















Indeed, Gray et al. 2006 state that:

"This sharp transition from bimodality to single-peaked
 behavior at [M/H] = -0.2 suggests that the cause of this 
phenomenon is not primarily age-related but rather is 
associated with some parameter necessary for the 
generation of an active chromosphere that is switched 
off at this divide.We expect that this parameter 
has something to do with rotation or, more specifically, 
differential rotation, but we do not have sufficient data 
to speculate further."

Of course, another equally plausible explanation for the abrupt
onset of high stellar activity at [M/H] = -0.2 is the fact that the
likelihood of a stellar system containing a Jovian planet increases
as the square of the metallicity, with Fischer and Valenti 2005
finding that:

"From this subset of stars, we determine that fewer than 3% of 
stars with -0.5 < [Fe/H]  < 0.0 have Doppler-detected planets. 
Above solar metallicity, there is a smooth and rapid rise in the 
fraction of stars with planets. At [Fe/H ] > +0.3 dex, 25% of 
observed stars have detected gas giant planets. A power-law 
fit to these data relates the formation probability for gas giant 
planets to the square of the number of metal atoms." 
[Fischer and Valenti 2005]


Hence, it is possible that high stellar activity is a
direct consequence of Jovian planetary action and 
that the presence of differential rotation in the outer 
layers of a star is just an indication that this 
interaction is taking place.


CASE STUDIES:


A. 61 Cygni A/B = HD 201091/HD 201092


61 Cygni A/B forms a widely separated stellar binary system
located at a distance of 11.41 light years from the Sun. 
Component A is a K5V star of 0.70 Solar masses and 
component B is a K7V star of 0.63 Solar masses. The two
stars move about each other in an elliptical orbit with a
mean separation of 84 A.U. and an ellipticity of 0.49.
The ellipticity of the orbit produces a periapsis 44 A.U.
and a apoapsis of 124 A.U. with the two stars orbiting
each other once every ~ 660-680 years. 
[10. Wikipedia 61 Cygni 2012]  


A comparison with Alpha-Centauri A/B stellar system
can be used to give us an idea as to the likelihood that
planets in stable can be formed in the 61 Cygni A/B 
system.

Alpha Centauri A/B is a binary system located 4.366 light
years from the Sun. Component A is a G2V star of 1.10 
Solar masses and component B is a K1V star of 0.91 
Solar masses. The two stars move about each other in 
an elliptical orbit with a mean separation of 23.4 A.U. 
and an ellipticity of 0.5179. The ellipticity of the orbit produces 
a periapsis 11.2 A.U. and a apoapsis of 35.6 A.U. with 
the two stars orbiting each other once every 79.91 years. 
[11. Wikipedia Alpha centauri 2012]  

Computer simulations shows that planetary formation
may be possible around Centaurus B out to 1.1 A.U.
and a slightly larger radius around Centaurus A. This
distance is ~ 1/10 th of their periapsis distance of 11.2
A.U. [8. Wikipedia Alpha Centauri 2012]. This means 
that it would unlikely for Jovian planets to form in 
system like this and the best that could be hoped for 
would be some terrestrial-like planets somewhere near
the Habitable Zone. Given that the Habitable Zones of
Alpha Centauri A and B are located at 1.25 and 0.7
A.U., respectively, this might just be possible.

Hence, by analogy to the Centaurus A/B system, planetary
formation should be possible in the 61 Cygni system within
a distance equal to ~ 1/10th the periapsis distance of 44 A.U.
or about 4.5 A.U. This raises the possibility that a Jovian-like
planet could form about either 61 Cygni A or B between
about 3 to 5 A.U.

Unfortunately, no planets have been found in the 61 Cygni
A and B systems to date. All that we can do at this time
is place upper limits upon the masses of potential planets
in the 61 Cygni A and B systems. Wittenmyer et al. 2006 has
found the the following upper mass limits for planets with
orbital radii of 3.0 and 5.2 A.U. and ellipticities of 0.0 and
0.6:

61 Cygni A

Distance___Ellipticity____Mass Limits

3.0_A.U.____0.0_____>_0.85_MJ
3.0_A.U.____0.6_____>_1.60_MJ

5.2_A.U.____0.0_____>_0.98_MJ
5.2_A.U.____0.6_____>_2.10_MJ

61 Cygni B

Distance___Ellipticity____Mass Limits

3.0_A.U.____0.0_____>_0.66_MJ
3.0_A.U.____0.6_____>_1.12_MJ

5.2_A.U.____0.0_____>_0.80_MJ
5.2_A.U.____0.6_____>_1.48_MJ

[12. Wittenmyer et al. 2006]
  
These limits do not rule out the possibility that
a planet with a mass ~ 1 Jovian mass could exist
in a near circular orbit a radii between 3 to 5 A.U.

Indeed, a 1 Jovian mass planet at a distance of
3.8 A.U. would have an orbital period that would
closely match the 7.3 years period of the solar
activity cycle for 61 Cygni A.

References
2. Zombeck, M. V. 1990. Handbook of Space Astronomy
and Astrophysics (2nd Addition), Cambridge University Press.

3. Kasting J.F., Wirtmire D.P., and Reynolds R.T. 1993,
Habitable Zones Around Main-Sequence Stars,
Icarus, 101, pp. 108-128.

4. Wilson I. R. G., Carter B. D., and Waite I.A. 2008,
Does a Spin–Orbit Coupling Between the Sun
and the Jovian Planets Govern the Solar Cycle?
Publications of the Astronomical Society of Australia,
25, pp. 85–93

5. Baliunas, S.L. et al. 1995, Chromospheric Variations
in Main Sequence Stars, Ap. J., 438, pp. 269-287

6. http://server1.sky-map.org - accessed 30/05/2012

7. Buccino, A. P., & Mauas, P. J. D. 2008, Mg II h + k 
emission lines as stellar activity indicators of main 
sequence F-K stars, A&A, 483, 903

8. Gray R.O. et al. 2006, Ap. J., 132, pp. 161 - 170

9. Fischer D. A. and Valenti J., 2005, The 
Planetary-Metallicity Correlation,
Ap.J., 622, pp. 1102 - 1117

10. http://en.wikipedia.org/wiki/61_Cygni - accessed 31/05/2012

11. http://en.wikipedia.org/wiki/Alpha_Centauri
  - accessed 31/05/2012

12. Wittenmyer, R. A., Endl, M., Cochran, W. D., Hatzes, A. P.,
Walker, G. A. H.,Yang, S. L. S., & Paulson, D. B. 2006,
Detection Limits from the McDonald Observatory Planet Search
Program, AJ, 132, 177

Finally, here is the [CaII] emission H&K stellar activity
curve for HD 81809 from Baliunus et al. 1995 compared
to the Sun's activity cycle. We believe that both of these
plots are indicative of planetary-driven solar activity.




























Saturday, May 12, 2012

Here's an Old Favorite

WHICH CAME FIRST THE CHICKEN OR THE EGG?


















In case you are still not sure what the 
mysterious external factor is at the 
end of my Lavoisier Society 
power-point presentation, 
it's the long-term lunar tides!!

[And I thought my last PP slide would be a dead giveaway!]

Monday, April 30, 2012

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

Monday, April 23, 2012

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 (2011L24

REVISITED SUNSPOT DATA: A NEW SCENARIO FOR 
THE ONSET OF THE MAUNDER MINIMUM



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:

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.

Sunday, April 22, 2012

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.