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Tuesday, June 19, 2012

The difficult childhood of Tatooine-like planets

Most of what we know about the size of stars comes from pairs of stars that are oriented toward Earth in such a way that they are seen to eclipse each other. These star pairs are called eclipsing binaries. In addition, virtually all that we know about the size of planets around other stars comes from their transits across their stars. The Kepler-16 system combines the best of both worlds with planetary transits across an eclipsing binary system. This makes Kepler-16b one of the best-measured planets outside our solar system.

NASA's Kepler mission discovered in 2011 a world where two suns set over the horizon instead of just one. The planet, called Kepler-16b, is the most "Tatooine-like" planet yet found in our galaxy and is depicted here in this artist's concept with its two stars. Tatooine is the name of Luke Skywalker's home world in the science fiction movie Star Wars. In this case, the planet is not thought to be habitable. It is a cold world, with a gaseous surface, but like Tatooine, it circles two stars. The largest of the two stars, a slowly rotating K dwarf, very active with numerous star spots, is about 69 percent the mass of our sun, and the smallest, a red dwarf, is about 20 percent the sun's mass. The planetary orbital plane is aligned within half a degree of the stellar binary orbital plane. All these features combine to make Kepler-16 of major interest to studies of planet formation as well as astrophysics. Credit: NASA/JPL-Caltech/R. Hurt
According to data analyzed by researchers, Kepler-16b is an inhospitable, cold world about the size of Saturn and thought to be made up of about half rock and half gas. The parent stars are smaller than our sun. One is 69 percent the mass of the sun and the other only 20 percent. Kepler-16b orbits around both stars every 229 days, similar to Venus’ 225-day orbit, but lies outside the system’s habitable zone, where liquid water could exist on the surface, because the stars are cooler than our sun.

Now a new research published on June 15, 2012 on arXiv.org points out that Tatooine-like planets cannot form too close to their parent stars, because of gravitational perturbations due to the companion star. The formation of planetesimals and protoplanets can be hindered in these perturbed environments.

With regard to the formation of circumbinary planets, Sijme-Jan Paardekooper, lead author of the study, and his colleagues write:
The existence of planets in these systems baffles planet formation theory. A crucial step in the process of building a planet, namely growing gravitationally bound protoplanets from km-sized planetesimals, can be hindered or stopped in these perturbed environments for planetesimals on circumprimary orbits. The coupling between gravitational perturbations of the companion star and gas drag stirs up the eccentricities of planetesimals, which leads to high encounter velocities. This makes accretion towards larger bodies difficult. Similar problems haunt planetesimals on circumbinary orbits. … In this work, we investigate the effect of collisions on the evolution of the system. … Notably, if collisions are mostly destructive, any surviving planetesimals are embedded in a sea of small debris. If they can pick up some of this debris, planetesimals can grow despite the hostile environment. In this Letter, we aim to explore this possibility in the newly found planet-harbouring systems of Kepler 16, 34 and 35.
Then the authors describe the theoretical model used in their simulations:
In our simulations we consider a system of two stars with a coplanar circumbinary disk. The gas component of the disk is assumed to be circular and orbiting the binary centre of mass. The solid component of the disk consists of planetesimals ≥ 1 km, which we model as particles, and small dust, on the same orbits as the gas. Planetesimals can form from small dust, accrete small dust on their surface, and be returned to dust in catastrophic collisions. ... In the simulations presented here ... planetesimals form continuously with half of the total (local) dust mass converted into planetesimals in 105 local orbits. 
This artist's concept illustrates Kepler-16b, the first planet known to definitively orbit two stars – what's called a circumbinary planet. The two orbiting stars regularly eclipse each other, as seen from our point of view on Earth. The planet also eclipses, or transits, each star, and Kepler data from these planetary transits allowed the size, density and mass of the planet to be extremely well determined. The fact that the orbits of the stars and the planet align within a degree of each other indicate that the planet formed within the same circumbinary disk that the stars formed within, rather than being captured later by the two stars. Credit: NASA/JPL-Caltech/T. Pyle
Tatooine dune sea (from material produced for Star Wars). Credit: Aaron Canaday / Lucasfilm Entertainment Company
Planetesimal eccentricity and semi-major axis for binary parameters of Kepler 16AB. Top panel: no dust accretion, t = 250,000 binary orbits. Bottom panel: full dust accretion, t = 80,000 binary orbits. Colour indicates the size of the planetesimal in km. All darker-coloured particles have accreted mass since the start of the simulation. The vertical dashed line indicates the position of Kepler 16b. The vertical dotted line the inner boundary of the accretion-friendly zone. Credit: Sijme-Jan Paardekooper, Zoe M. Leinhardt, Philippe Thebault, Clement Baruteau (2012)
The top panel of the image shows the results of simulations without dust accretion, the bottom panel with dust accretion (the most favorable case). In both cases, the accretion-friendly zone, that is the region in which planets can grow, begins far outside the location where Kepler 16b resides. 

These are the authors' conclusions: 
We have studied planetesimal collisions in circumbinary gas disks, focusing on the planet-harbouring systems Kepler 16, 34 and 35. We have shown that in addition to secular forcing, planetesimals experience eccentricity forcing on a dynamical timescale, which leads to eccentricity oscillations and orbital crossings that can not be prevented by gas drag. This makes the current location of the planets Kepler 16b, 34b and 35b very hostile for planetesimal accretion. 

... Even in the most favourable case of 100% efficient dust accretion, we have been unable to grow planetesimals from initially 1 km at the current location of the planets. Since dust accretion is likely to be less than 100% efficient, for example because not all the small dust will be concentrated in the midplane of the disk, we conclude that in situ planetesimal accretion is difficult for the planets Kepler 16b, 34b and 35b.

... A formation mechanism which can leapfrog the problematic km-size range, such as gravitational collapse aided by streaming instabilities, may overcome the problems of planetesimal accretion. It remains to be seen, however, if such a mechanism can operate in close binary systems. Preliminary calculations show that in the current model, we would need to start with planetesimals of at least 10 km in order for in situ accretion of the Kepler circumbinary planets to become possible.

The most straightforward solution is that the three circumbinary planets were assembled further out in an accretion-friendly region, and migrated in towards their current location at a later stage. This can be achieved at a relatively early stage, in the 10-100 km size range, by radial drift due to a pressure gradient in the gas, or at a later stage when the planet is more or less fully grown, by Type I or Type II planetary migration. 

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