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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!]