COROT planets Options

[djellison]

I think they just want to be 100% sure on REALLY interesting things with follow-up ground based obs with spectroscopy before going "WE FOUND AN EARTH"

Doug

[belleraphon1]

Yes, they certainly need to be prudent.

What I am reading sounds very promising as far as what COROT is capable of. Much to look forward to.

Thanks Again Doug.

[nprev]

Yeah...to quote Carl, "Extraordinary claims require extraordinary evidence." Seems that the COROT team is employing this invaluable heuristic, and should be commended for doing so...but, boy howdy, I sure hope that there's something extraordinary just around the corner...

[JRehling]

Well, the negative side of the COROT survey is that the search is limited to closely orbiting transiting planets so we get a very biased sample. Which is far better than nothing, of course.

Check my math in trying to characterize the bias.

Given two similar planets orbiting two similar stars, but with one planet N times farther from its star than the other, the ratio of likelihood of detection in a short time frame should be N^2.5. That is, the probability of appropriate geometry for a transit is decreased by N for the farther planet, whereas the probability of a transit taking place at the right time is a function of the orbital period, which introduces another factor of N^1.5.

For example, if Earth were orbiting at 5 AU, it would be precisely 1/5 as likely for its orbit to transit the Sun as seen from afar, and if it did, it would do so about 1/11th as often. So a factor of 5 in distance translates to a factor of 55 in transit observations. A factor of 10 in distance translates to a factor of 300 in transit observations.

The temporal factor is mitigated as the observations continue. Given a mission lasting Y years, we'd get one observation of every transiting planet with a period <=Y, two observations of every transiting planet with a period <=Y/2, and a probability Y/X of one observation of every transiting planet with a period X longer than Y.

The diameter of the planet is also a minor factor. Jupiter might graze the Sun's disk whereas a Pluto in the same location would just miss. As the planets get much smaller than the star, this factor almost vanishes.

COROT will survey a few different areas, none for more than 150 days or so, so repeat detections will be strictly limited to planets in close-in orbits. Single detections of planets farther out will (presumably!) take place, and could help us get an idea of the distribution of planets in different-sized orbits. But at some point out there, the data will be too sparse to make predictions significant.

So overall, I think it's going to be pretty sparing in telling us about the raw numbers of Venuses, Earths, and Neptunes. But a few data points would be a lot nicer than none.

[Greg Hullender]

I get the same result, JR.

A good question would be "how many transits do they need to see to confirm a discovery?" On the Kepler site, they say they'll only need one for Jovian planets (although obviously you need two to get the orbital period), but that for Earth-sized planets, they want to see three transits.

If COROT switches targets every few months, that'd mean it really wouldn't spot any Terrestrial planets with periods longer than a few weeks. That'd still be very interesting, but makes it seem unlikly they'll find anything that could fairly be described as "another Earth."

--Greg

[nprev]

Just out of curiosity, would the habitable zone of a fairly anemic red dwarf be close-in enough for a period of a few days to be possible for "another Earth?"

[stevesliva]

Just out of curiosity, would the habitable zone of a fairly anemic red dwarf be close-in enough for a period of a few days to be possible for "another Earth?"

Wouldn't something that close be tidally locked?

[Greg Hullender]

Tidal locking time is an interesting problem.

http://en.wikipedia.org/wiki/Tidal_locking

Considering the warning that these figures can be off by a factor of 10, I get the following for putting an Earth with a 12-hour day to start with around some familiar stars:

Sol: 365.25 day period, 5.4 billion years to tidally lock. (Ignoring the effect of the moon).
Alpha Centauri A: 524-day year, 16 billion years (Earth years) to lock.
Tau Ceti: 221-day year, 1.7 billion years
Alpha Centauri B: 207-day year, 800 million years
Epsilon Eridani: 134-day year, 170 million years
Gliese 581: 7.8-day year, 120,000 years.
Proxima Centauri: 3.9-hour year, 350 days.

The difference between Tau Ceti and Epsilon Eridani surprises me; I hadn't realized there was almost a factor of two luminosity difference, even though the latter is actually slightly more massive.

Anyway, even with all the caveats, it seems to be a cinch that any earthlike planet with a period under 100 days will be tidally-locked.

(Anyone want to check the math?)

--Greg

[belleraphon1]

Anyway, even with all the caveats, it seems to be a cinch that any earthlike planet with a period under 100 days will be tidally-locked.
--Greg

So what if it is tidally locked?

http://www.liebertonline.com/doi/abs/10.1089/ast.2006.0124

http://www.astrobio.net/news/article1694.html

Craig

[stevesliva]

So what if it is tidally locked?

Iiiiinteresting. I wonder what the climate models predict for temperature maps on the sun-facing side?

I also find it interesting that the earth would be tidally locked in a mere 5 billion years sans luna.

[Greg Hullender]

Remember that there's enough fudge in these numbers that it might really be 50 billion, not 5 billion. Thing is, the effect of radius (a SIXTH power!) is so strong and the ages of these systems is so great (billions of years, typically) that it doesn't really matter. Anything with an estimate under ten million years was almost certainly tidally locked long, long ago -- even those with estimates under 100 million.

It's interesting to note that Luna makes the moment of inertia of the system over 100 times larger, so that'd probably push that number up to 500 billion years, although that wouldn't rule out Earth being tidally locked to the moon well before that happened.

--Greg (The other major caveat is that this equation came from Wikipedia -- I didn't derive it myself.) :-)

[belleraphon1]

Iiiiinteresting. I wonder what the climate models predict for temperature maps on the sun-facing side?

I also find it interesting that the earth would be tidally locked in a mere 5 billion years sans luna.

"Simulations of the Atmospheres of Synchronously Rotating Terrestrial
Planets Orbiting M Dwarfs: Conditions for Atmospheric Collapse and
the Implications for Habitability"
http://www.seismo.unr.edu/ftp/pub/gillett/joshi.pdf

Also, ANY terrestrial planet around any star will probably lose the internal heat needed to keep plate techtonics going after 10 billion years or so. When that ends, the cycles that reprocess the geochemical needs of a biosphere will grind to a halt.

A lot of interesting studies going on ........................ what COROT and KEPLER may give us is a stat on
how prevalent the above fates are.

Craig

[nprev]

Gliese 581: 7.8-day year, 120,000 years.
Proxima Centauri: 3.9-hour year, 350 days.

So it seems that any true red dwarf exoEarths should blink rapidly enough for detection using mass sampling...sounds like a seed for a mission proposal, here, if the observable (key point; they're so damn faint that they'd have to be fairly nearby) number of dwarves is large enough to make it worthwhile.

[Greg Hullender]

It seems that at least four factors help here: As you say, there are more red dwarves in the first place and more transits per unit of time. As JR pointed out above, there's a greater chance of having transits in the first place. There should also be a greater difference in brightness transiting a smaller star than a larger one.

One would predict that if Corot finds any "Earth-like" planets, they'll be around red dwarves, but if they find any, they'll find lots of them.

--Greg

[JRehling]

So what if it is tidally locked?

Seems to me that possibility means two "habitable zones". One for the substellar point and one for the dark side.