Innumerable as the Starrs of Night,
Or Starrs of Morning,
Dew-drops, which the Sun
Impearls
on every leaf and every flouer
Milton
Impearls
NGC3132 ©
Beauty is truth, truth beauty,
— that is all
Ye know on earth, and all
ye need to know.
Keats

E = M
Einstein

Energy is eternal delight.
William Blake

Impearls: The Earths of Alpha Centauri

Item page — this may be a chapter or subsection of a larger work.  Click on     link to access entire piece.

Earthdate 2009-07-20

The Earths of Alpha Centauri

Fig. 1. Schema of Alpha Centauri planetary systems

Figure 1.  Schema of the Alpha Centauri system


As a Board member of the Friends of the U.C. Santa Cruz Library, I was invited this year to assist in judging UCSC's annual Graduate Research Symposium, in which the university's graduate students present personal or poster presentations concerning their thesis research for prestige, prizes, and trophies.  The winner of this year's entire event was a female graduate student, Javiera Guedes of the Astronomy and Astrophysics department at UCSC, who presented a talk on “The Earths of Alpha Centauri,” concerning the likelihood that both principal stars of the binary Alpha Centauri system possess planets, which we should be able to start discovering (as detection technology has steadily improved, and given a determined search) within the next several years.  I wrote up a brief report on Guedes' talk for a mailing list, only to be subsequently invited by editor Kevin Langdon (also endorsed by Javiera) to expand that piece for the Mega Society's online journal Noesis's upcoming special issue on Astronomy and Space.

University of California at Santa Cruz astronomy and astrophysics graduate student Javiera Guedes (first author), together with her coauthors, have published a fascinating piece in The Astrophysical Journal titled the “Formation and Detection of Terrestrial Planets around α [Alpha] Centauri B” 1 — which in my view deserves far wider audience and consideration than it can receive in that journal, however prestigious and renowned a scientific journal it assuredly is.

The subject of that paper, the binary Alpha Centauri star system (also known as Rigil Kentaurus or Toliman), at some 4.4 light years (or about 1.3 parsecs) distant from the Sun, is the closest extrasolar stellar system to our own Solar System and Earth.  The brightest star in that system Alpha Centauri A is quite similar to our Sun in mass (at ∼1.105 solar masses), and extremely similar in color and thus temperature (classed like the Sun as a spectral type G2 V, a so-called “yellow dwarf”), whilst its companion Alpha Centauri B is only slightly smaller (∼0.934 times the Sun's mass) and a bit redder and therefore cooler (spectral type K1 V) than the Sun.  One might note that the Alpha Centauri system (at about 5.6–5.9 Gyr) is between 1 and 1.3 billion years older than our Sun and Solar System, while it's about half again as rich in “metals” (as astronomers regard them: i.e., elements heavier than hydrogen and helium) as our own system.

Though it has a third, much smaller (∼0.1 solar mass) spectral type M “red dwarf” companion star known as Proxima Centauri — swinging at an enormous distance (perhaps a fifth of a light year) away from its principals — however ignoring Proxima, Alpha Centauri is essentially a close binary star system; and thus one might imagine that Alpha Centauri's two principal stars A and B's gravitational interference on each other would forestall prospects for any stable planets circling either star.  As it happens, however, those primary components of Alpha Centauri are not actually all that close, orbiting each other some 23 astronomical units (23 times the distance between the Earth and the Sun, abbreviated AU) apart from each other — equivalent to B (or A) circling between the orbits of Uranus and Neptune (in our Solar System) with regard to the other — and as a result planets orbiting beyond what would be the orbit of Mars here, up to some 3 AU away from its primary (or well into our asteroid belt) are not ruled out around either star; moreover any planets (if they exist) are computed with high probability to be stable for the requisite billions of years time.  Moreover, planets have already been discovered orbiting other roughly similar binary stars (e.g., γ [Gamma] Cephei, HD 41004, and Gliese 86) having basically equivalent separations from each other.

Indeed, Alpha Centauri A and B would probably even have performed a positive perturbative role with regard each other's incipient planetary systems, similar to that which the gas giants Jupiter, Saturn, and beyond are thought to have played in planetary evolution here in our Solar System, to wit providing “perturbations allow[ing] for the accretion of a large number of planetary embryos into a final configuration containing 3–4 bodies.”  (Note that we omit end-note references in all quotes from The Astrophysical Journal article.)

Alpha Centauri B, as a cooler, “quieter,” less variable and flare-prone star than Alpha Centauri A (or the Sun for that matter), as a result is somewhat easier than A to detect any planets circling round.  Thus it is on B that the authors concentrate their attention, estimating that after only about three years of “high cadence” observations (watching B on basically every night that there's good seeing, which could be close to 300 days a year), one could detect (using the so-called Doppler or radial-shift detection method) a planet of only some 1.8 Earth-masses circling within B's so-called “habitable zone,” while somewhat smaller worlds ought to become apparent in only a couple of years more.

Whilst it's also sometimes possible to detect extrasolar planets by observing their transit (or eclipse) across the disk of their primary star as seen from Earth, that method requires that the plane of any planets' orbits be closely aligned with the direction of our Sun with respect to that system — which is obviously extremely unlikely when attempting to locate worlds circling any particular star — and thus such an approach is suitable only for statistical surveys of a great many stars, not for finding the planets of any specific suns.

In addition to evaluating how Alpha Centaurian planets could be observed from the perspective of Earth, the authors conducted a number of computed simulations (eight in all) of possible routes to planetary system formation, starting from initial circumstances “mimic[ing] conditions at the onset of the chaotic growth phase of terrestrial planet formation in which collisions of isolated embryos, protoplanets of approximately lunar mass, dominate the evolution of the disk.  During this phase, gravitational interactions among planetary embryos serve to form the final planetary system around the star and clear out the remaining material in the disk.  At the start of this phase, several hundred protoplanets were presumed to orbit the star on nearly circular orbits.”  Each run of the simulation “populate[d] the disk with N = 400 to N = 900 embryos of lunar mass […].”

Simulation number 7 (see Figure 3), specially exemplified herein and in The Astrophysical Journal article (known as r600_1 there), started with 600 embryos.

All bodies in the simulations interact only through gravity and the evolution of their positions and velocities with time were calculated using the MERCURY code, designed for the presence of a binary companion and allowing planetary embryos to collide and stick together to form larger planets.

The investigators “focus[ed] on terrestrial planet formation around α Cen B […].”  As they note, “[P]lanet formation around α Cen A is expected to be qualitatively similar.”

Figure 2 illustrates how simulations of the evolution of a planetary system surrounding Alpha Centauri B typically progressed (using simulation 7):

Fig. 2. Simulated evolution of a planetary system (simulation 7) for Alpha Centauri B

Figure 2.  Simulated evolution of a planetary system (simulation 7) for Alpha Centauri B

The authors describe the foregoing figure thusly:

Figure [2] shows the late evolutionary stage of a protoplanetary disk initially containing 600 moon-mass embryos ([appearing in Figure 3 as simulation number 7]).  The radius of each circle is proportional to the radius of the object.  Bodies in the outer parts of the disk ([orbital semimajor axis] a > 3 AU) are immediately launched into highly eccentric orbits and either migrate inward to be accreted by inner bodies, collide with the central star, or are ejected from the system […].  In this simulation, ∼65% of the total initial mass is cleared within the first 70 Myr.  By the end of simulation [7], four planets have formed.  One planet has approximately the mass of Mercury and is located at a = 0.2 AU, two 0.6 [Earth mass] planets form at a = 0.7 and a = 1.8 AU, and a 1.8 [Earth mass] planet forms at a = 1.09 AU.

[…]  All of our simulations result in the formation of 1–4 planets with semimajor axes in the range 0.7 < a < 1.9 AU […].  We find that 42% of all planets formed with masses in the range 1–2 [Earth masses] reside in the star's habitable zone (Fig. [3]), taken to be 0.5 < ahab < 0.9 [AU].  […].  All of our disks form systems with one or two planets in the 1–2 [Earth] mass range.

Figure 3 illustrates the results of all eight Alpha Centauri B system evolution simulations that the authors performed.  The especially illustrated simulation used herein appears as number seven near the bottom, whilst for comparison our Solar System is shown to scale at top.

Fig. 3. Simulated planetary systems of Alpha Centauri B

Figure 3.  Simulated planetary systems of Alpha Centauri B

We see that realistic astrophysical simulations predict that planets surrounding Alpha Centauri B (as well as a similar system circling A) are quite likely. What will it take to actually find such worlds, if they do exist?

As noted earlier, due to the extreme unlikelihood of any specific stellar planetary system's equivalent of our “plane of the ecliptic” (the plane in which its planets' orbits generally circle) exactly lining up on edge as seen from Earth, the transit method for detecting extrasolar planets cannot be applied (other than by the remotest chance) for locating worlds orbiting specific suns — leaving only the “Doppler wobble” approach available for finding planets in more particular circumstances.  Even for that method to work, the plane of a given star's planetary orbits must not directly face the Sun (i.e., the axis of that plane mustn't be oriented directly toward or away from the Sun), as there has to be some planetary radial velocity toward or away from the Earth for us to detect.  Inasmuch as theoretical considerations imply that the orbital plane of planets circling either star of a close binary system should in general be aligned with the orbits of the stars themselves as they revolve about each other — and since in the case of the Alpha Centauri system, its two stars' orbital plane can be observed to be inclined to the line of view from here in the Sol System by a mere 11 degrees (the axis of that plane being almost perpendicular to the line of sight from the Earth) — thus planets circling either A or B are nearly ideal for detection from Earth using the radial-velocity technique.

Indeed, as the authors of this study conclude:  “α Cen B is overwhelmingly the best star in the sky for which one can contemplate mounting a high-cadence [nightly] search” for extant terrestrial worlds, among other things because “α Cen B is exceptionally quiet, both in terms of acoustic p-wave mode oscillations and chromospheric activity.”

They note that “[t]he radial velocity [Doppler] detection of Earth-mass planets near the habitable zones of solar-type stars requires cm s−1 [centimeter per second velocity] precision,” whereas Alpha Centauri A exhibits (rather Sun-like) oscillatory noise on the order of 1 to 3 m s−1 (meters per second), which would effectively swamp attempts to detect planets circling A using near-term technology.  Alpha Centauri B, on the other hand, as a fundamentally quieter star, displays peak amplitude noise on the order of 0.08 m s−1 (8 cm/second), which is also far higher in frequency than the periods of any potential terrestrial planets to be detected.  As a result, a “focused high cadence approach involving year-round, all-night observations would effectively average out the star's p-mode oscillations.”

Observations also reveal that Alpha Centauri B exhibits much less chromospheric variability associated with stellar flares than does A (the former modifying its x-ray brightness only within a factor of two over a couple of years time whilst A could be observably seen to vary by an order-of-magnitude factor of ten).

The paper further points out that:

α Cen B is remarkably similar in age, mass, and spectral type to HD 69830, the nearby K0 dwarf known to host three Neptune mass planets.  Both α Cen B and HD 69830 are slightly less massive than the Sun with masses 0.91 and 0.86 [solar masses] respectively.  Their estimated ages are 5.6–5.9 Gyr for α Cen B and 4–10 Gyr for HD 69830.  Both stars are slightly cooler than the Sun:  α Cen B is a K1 V with [an effective temperature] Teff = 5350 K, while HD 69830 is a type K0 V star with Teff = 5385 K.  The stars have also similar visual absolute magnitudes, MV = 5.8 for α Cen B and MV = 5.7 for HD 69830; however, due to its proximity to us, the former star appears much brighter (mV = +1.34), allowing for exposures that are ∼60 times shorter.  One can thus use a far smaller aperture telescope, or alternatively, entertain a far higher observational cadence.

Moreover, Alpha Centauri A and B being so close to each other in space as well as physically similar to one another allows parallel observations of the two stars to reveal concurrent variations which, seen in both, allow identification of systematic artifacts in the observational process, that can thus be filtered out of any meaningful results.  Furthermore, as the study notes, the position of Alpha Centauri at about −60° declination in our southern sky is nearly perfect for virtually continuous night-by-night (“high cadence”) observations from two existing vantage points, the Las Campanas Observatory together with the Cerro Tololo Inter-American Observatory, both in Chile, either of which ought to provide up to almost 300 viewing days a year (60 days a year being basically unavailable while Alpha Centauri annually passes behind the Sun, plus a few more days lost as a result of bad weather).

Inasmuch as the proportionate density of binary, roughly solar-mass component star systems in this part of the galaxy is only about 0.02 per cubic parsec (1 cubic parsec = ∼35 cubic light years), since at this time the Alpha Centauri system hovers a mere 1.33 parsecs away from us, we're very lucky here in the Solar System having α Cen proceeding so close nearby during this era for us to perform this highly desirable search upon.

As The Astrophysical Journal paper concludes:  “All these criteria make α Cen B the ideal host and candidate for the detection of a planetary system that contains one or more terrestrial planets.”  Indeed, “our current understanding of the process of terrestrial planet formation strongly suggests that both principal components of the α Cen system should have terrestrial planets.”

Given that extremely tantalizing possibility, what will it take to find at least those worlds orbiting Alpha Centauri B, if they exist?  As the authors make note:

A successful detection of terrestrial planets orbiting α Cen B can be made within a few years and with the modest investment of resources required to mount a dedicated radial-velocity campaign with a 1 m class telescope and high-resolution spectrograph.  The plan requires three things to go right.  First, the terrestrial planets need to have formed, and they need to have maintained dynamical stability over the past 5 Gyr.  Second, the radial velocity technique needs to be pushed (via unprecedentedly high cadence) to a degree where planets inducing radial velocity half-amplitudes of order cm s−1 [centimeter per second] can be discerned.  Third, the parent star must have a negligible degree of red noise on the ultralow frequency range occupied by the terrestrial planets.

In this paper, we have made the case that conditions 1 and 2 are highly likely to have been met.  In our view, the intrinsic noise spectrum of α Centauri B is likely all that stands between the present day and the imminent detection of extremely nearby, potentially habitable planets.  Because whole-Sun measurements of the solar noise are intrinsically difficult to obtain, our best opportunity to measure microvariability in radial velocities is to do the α Cen AB Doppler experiment.  The intrinsic luminosity of the stars, their sky location, and their close pairing will allow for a definitive test of the limits of the radial velocity technique.  If these limits can be pushed down to the cm s−1 level, then the prize, and the implications, may be very great indeed.

At this point well over three hundred planets have been discovered circling other stars beyond the Sun — all thus far found, due to hitherto operative technical limitations, necessarily being much larger than Earth and thus far from being really terrestrial in type.  The Alpha Centauri system offers the opportunity to refine those limits downward towards worlds much closer in size, and thus potentially in habitability, to the Earth.

Figures 4 and 5 below illustrate how such a high-cadence search over a period of several years could zero in closer and closer towards identifying any planets of Alpha Centauri B that are truly terrestrial in scale.

Fig. 4. How the detection “periodogram” for a simulated Alpha Centauri B planetary system (simulation 7) evolves over 5 years of observations

Figure 4.  How the detection “periodogram” for a simulated Alpha Centauri B planetary system (simulation 7) evolves over 5 years of observations

Fig. 5. How nightly observations over 5 years build that periodogram for a simulated Alpha Centauri B planetary system

Figure 5.  How nightly observations over 5 years build that periodogram for a simulated Alpha Centauri B planetary system

As the capability for detecting truly terrestrial-type planets circling round nearby stars approaches, we're on the cusp of an adventure grander by far than Columbus's voyages to the New World or other great discoveries of the age of exploration, not only for its tremendous scientific value (finding what variety of worlds so-called “terrestrial” planets can form, not to speak of the enormous significance of possibly discovering other independently evolved organisms inhabiting them), but also for the sake of the future history of mankind, along with the ultimate fate of all life dwelling on — but presently restricted to this single egg-basket of — our planet Earth.

In a discussion such as this of potential planets circling the component stars of the Alpha Centauri system, special recognition is due the late biochemist and most prolific science fiction and fact writer Isaac Asimov, for it was he who, just a half-century ago (in June, 1959), penned his far-sighted essay “The Planet of the Double Sun” 2 concerning the possibility of just such worlds existing.  A quarter-century later, in 1985 he wrote another essay on the subject of life near Alpha Centauri called “The Double Star&rdquo 3; whilst in 1976 Asimov published an entire book on Alpha Centauri, The Nearest Star4

In regard to the intrinsic value of such planets, it's worth noting the ending of Asimov's affecting science fiction novel The End of Eternity 5, which serves as the introduction to his famous Galactic Empire and Foundation series of stories.  In the context of this tale, when it is realized that ready access to the universe is at hand for humanity (provided they take a critical step, namely make a certain change to the past), the principal protagonist wonders aloud what good it would really do if they should indeed accomplish it:

“And what would have been gained?” asked Harlan doggedly.  “Would we be happier?”

Whereupon his erstwhile enemy, more recent ally, and soon to be spouse replies:

“Whom do you mean by ‘we’?  Man would not be a world but a million worlds, a billion worlds.  We would have the infinite in our grasp.  Each world would have its own stretch of the Centuries, each its own values, a chance to seek happiness after ways of its own in an environment of its own.  There are many happinesses, many goods, infinite variety….  That is the Basic State of mankind.”

Now, on the cusp of the fortieth anniversary of mankind's (as representative of all life on Earth) first visit in all the billions of years history of Earthly life to another planet, it's time to get on with it.  Let's find those worlds!


Glossary

absolute magnitude intrinsic visual brightness of an object as it would be seen from a fixed distance — in the case of a star this is established as being 10 parsecs or 32.6 light years away
AU astronomical unit, abbreviated AU (sometimes symbolized ua): one AU is the average distance between Earth and the Sun — about 150 million km or 93 million miles
binary star system star system consisting of two stars orbiting each other about a common center of mass
chromosphere relatively thin (perhaps 2,000 km thick in the case of the Sun) semitransparent layer in a star which lies just above its opaque photosphere or visible “surface”
chromospheric variability activity or variability in a star which occurs within its chromosphere
Doppler wobble method for locating extrasolar planets by the radial velocity (as seen from Earth) perturbations they induce in the motions of the primary star they orbit
Earth mass mass of the Earth: some 6 × 1024 kg or about 0.31% the mass of Jupiter
dynamical stability long-term probabilistic stability of planets over gigayears time against perturbations that would eject them from the system, or throw them into their primary star or each other
eccentric orbit an orbital path that is a highly flattened ellipse rather than being approximately circular
ecliptic rough plane in which the planets of the Solar System (exception: Pluto) generally orbit
extrasolar body planet, star, or other body which orbits or moves outside the realm of the Solar System
gas-giant planet giant planet like Jupiter which is composed principally of the gases hydrogen and helium
Gyr gigayears: billions of years
habitable zone region surrounding a star where temperatures on an Earth-type planet circling within that zone are suitable for life as we know it — in our Solar System it is considered to lie between about 0.95 to 1.37 AU from the Sun
half-amplitude absolute (positive) value of maximum amplitude, as opposed to amplitudes varying in sign between positive and negative over a continuous approximately sine-wave cycle
high cadence astronomical observations conducted at a high frequency — e.g., nightly
Jupiter mass mass of Jupiter: around 2 × 1027 kg, or about 0.1% the mass of the Sun versus 318 times the mass of Earth
light year the distance that light travels in vacuum in a year: about 9 trillion km or 6 trillion miles
Mercury mass mass of the planet Mercury: about 3 × 1023 kg or around 5.5% the mass of Earth
metals metals as astronomers regard them: to wit, elements heavier than hydrogen and helium
microvariability small amplitude variability
Moon (or lunar) mass mass of the Moon: some 7 × 1022 kg or about 1.2% the mass of Earth
Neptune mass mass of Neptune: close to 1 × 1026 kg, or some 17 times the mass of Earth or 5.4% of Jupiter's mass
parsec the distance at which an extrasolar body's parallax with regard to Earth's orbit around the Sun subtends an angle of one second of arc — approximately 3.26 light years
periodogram measured periodic radial velocity variations in a star over time that might indicate the presence of planets
photosphere opaque layer of a star which constitutes its visible “surface”
protoplanet Moon-sized or larger planetary embryos orbiting a star within its protoplanetary disk
protoplanetary disk rotating disk of gas and dust surrounding a fledgling star which may accrete into planets
radial velocity velocity component of an extrasolar star or planet directed toward or away from Earth
red noise low-frequency random noise emitted by a star under observation
semimajor axis one-half of the length of the long axis of an elliptical orbit — equivalent to a body's average distance from its primary
spectral type classification system for stars based on a star's color and thus its surface temperature
spectrograph instrument measuring an object's light output across a spectrum of optical frequencies
stellar flare eruption of plasma from the surface of a star
Sun (or solar) mass mass of the Sun: about 2 × 1030 kg or some 333,000 times the mass of Earth
terrestrial planet planets consisting primarily of rocks (normally silicate rocks) at least near the surface; as opposed to gas-giant planets
transit method method for detecting an extrasolar planet by observing the dip in its primary star's light output as the planet passes directly in front of the star's disk as viewed from Earth


Acknowledgments and References

Many thanks to talented astronomy and astrophysics graduate student Javiera Guedes for her support and suggestions as well as permission to use the figures (indeed her own modifications to one of the figures) from her and her coauthors' article in The Astrophysical Journal.  One might note that Ms. Guedes herself will personally be conducting observations of Alpha Centauri later on this year.  Kudos to her and the other investigators in this study, and best wishes in the great search!

1 J. M. Guedes, E. J. Rivera, E. Davis, and G. Laughlin (all at the University of California at Santa Cruz, Astronomy and Astrophysics department), E. V. Quintana (SETI Institute, Mountain View, CA), and D. A. Fischer (San Francisco State University, Physics and Astronomy department), “Formation and Detection of Terrestrial Planets around α Centauri B,” The Astrophysical Journal, Vol. 679, Issue No. 2 (2008), pp. 1581-1587; doi: 10.1086/587799.

2 Isaac Asimov, “The Planet of the Double Sun,” The Magazine of Fantasy and Science Fiction, 1959-06, Mercury Press, New York.  Collected in Fact and Fancy, Doubleday & Co., Garden City, NY, 1962; also in Asimov on Astronomy, Anchor Press, Garden City, NY, 1975.

3 Isaac Asimov, “The Double Star,” American Way, American Airlines, 1985-09-03.  Collected in The Dangers of Intelligence And Other Science Essays, Houghton Mifflin, Boston, 1986.

4 Isaac Asimov, Alpha Centauri, The Nearest Star, Lothrop, Lee & Shepard Co., New York, 1976.

5 Isaac Asimov, The End of Eternity, Doubleday & Co., Garden City, NY, 1955, p. 187.


UPDATE:  2009-07-19 19:40 UT:  Version 2:  Updated via suggestions from Javiera Guedes.

UPDATE:  2009-07-28 06:00 UT:  Version 3:  At the time of submission for publication in Noesis.

UPDATE:  2009-08-03 19:00 UT:  Version 4:  Further updates to the Noesis publication version, including adding the Glossary.

UPDATE:  2009-08-04 15:30 UT:  Version 5:  A few corrections.

UPDATE:  2009-08-05 03:40 UT:  Version 6:  Minor fix.


Labels: , , , , ,



0 comments:  (End Post a Comment


Links to this post:  Create a Link



Home

(Blank last screen)

Home

Are you an
Impearlist?

If you fancy
any piece
you may donate
to reprise!


 

Pajamas Media BlogRoll Member
 

[Powered by Blogger]
 
 

Impearls Archives

2002-11-03 2002-11-10 2002-11-17 2002-11-24 2002-12-01 2002-12-08 2002-12-15 2002-12-22 2002-12-29 2003-01-05 2003-01-12 2003-01-19 2003-01-26 2003-02-02 2003-02-16 2003-04-20 2003-04-27 2003-05-04 2003-05-11 2003-06-01 2003-06-15 2003-06-22 2003-06-29 2003-07-13 2003-07-20 2003-08-03 2003-08-10 2003-08-24 2003-08-31 2003-09-07 2003-09-28 2003-10-05 2003-10-26 2003-11-02 2003-11-16 2003-11-23 2003-11-30 2003-12-07 2003-12-14 2003-12-21 2003-12-28 2004-01-04 2004-01-11 2004-01-25 2004-02-01 2004-02-08 2004-02-29 2004-03-07 2004-03-14 2004-03-21 2004-03-28 2004-04-04 2004-04-11 2004-04-18 2004-04-25 2004-05-02 2004-05-16 2004-05-23 2004-05-30 2004-06-06 2004-06-13 2004-06-20 2004-07-11 2004-07-18 2004-07-25 2004-08-22 2004-09-05 2004-10-10 2005-06-12 2005-06-19 2005-06-26 2005-07-03 2005-07-10 2005-07-24 2005-08-07 2005-08-21 2005-08-28 2005-09-04 2005-09-11 2005-09-18 2005-10-02 2005-10-09 2005-10-16 2005-10-30 2005-11-06 2005-11-27 2006-04-02 2006-04-09 2006-07-02 2006-07-23 2006-07-30 2007-01-21 2007-02-04 2007-04-22 2007-05-13 2007-06-17 2007-09-09 2007-09-16 2007-09-23 2007-10-07 2007-10-21 2007-11-04 2009-06-28 2009-07-19 2009-08-23 2009-09-06 2009-09-20 2009-12-13 2011-03-27 2012-01-01 2012-02-05 2012-02-12