Bandersnatch said:
@Glitch:
Whether the planet is habitable is indeed unknown, but it does lie within the HZ as defined by both Kasting 1993 and Kopparapu 2013.
Both define HZ as the region where liquid water can exist on a terrestial planet with N2-H2O-CO2 dominated atmosphere.
For a planet to be habitable while lying in the outer HZ region, it does indeed need to have maximum greenhouse effect provided by CO2. But it doesn't mean that you need a special planet with just the right amount of CO2 present to be habitable. There can be various feedback mechanisms that change the composition of the atmosphere as the planet changes its place in the HZ(due to stellar evolution increasing output of the central star and orbital migration). Kastings describes one of such feedback mechanisms - the Carbonate-Silicate cycle.
I've been reading Kasting's paper that you said you used to calculate the low HZ limits in post #23, and I can't find any reference to the calculation method(with numerical constants) presented on the Planetary Biology page that you linked to earlier in post #8(even though they cite the paper as the source). In fact, Kasting calculated HZ for an M0 star in that paper, and it's pretty close to what you get from Kopparapu's(outer is about 0.47 AU for a 3700K star).
If you know where to find it, give us a shout.
Kasting's paper is here:
http://adsabs.harvard.edu/abs/1993Icar..101..108K
It's behind the paywall, but googling the title and authors quickly nets a few places from which a free copy can be obtained.
All the complaints about the Kopparapu paper that you've voiced so far apply to this paper as well. I don't understand why you said in post #23 that it is somehow different. Both papers parametrise H2O cloud effects on the inner HZ without actually modelling cloud cover(which doesn't affect outer HZ, by the way, and that's where Kepler-186f lies). Both use the same definiton of HZ, both calculate the effects of atmospheric gasses on the surface temperature.
In fact, Kopparapu's is merely an update on Kasting's methods with more refined data.
I couldn't access the other source Planetary Biology used(Whitmire et al.) as it's from a textbook, I believe. Maybe that would shed some light on the reason for the calculations they used, but it seems odd that their other source doesn't appear to support them.
Thanks for the link, and I was able to find a free copy. I apologize for taking so long to respond to your post. I too was searching for the source of those two constants (1.1 and 0.53) on the Planetary Biology web page. This was the basis for my original calculations, and why I determined that Kepler-186f was not in the habitable zone. I was not able to find any references to such constants in Kasting (1993 or 1996) or anywhere else. Since I do not know how those constants were derived, I cannot use those equations on the Planetary Biology web page.
As far as the "habitable zone" is concerned, that is only the area where water can be in a liquid state on the surface of a planet. Which means that anywhere that the surface temperature is between 1°C (274°K) and 99°C (372°K) is considered to be in the "habitable zone."
As mfb mentioned in post #27, "
The habitable zone is the distance where a planet with liquid water could exist, it does not depend on the planet itself." I happen to agree, it should not depend on the planet at all. Everyone, including the Kasting and Kopparapu papers are fixated on liquid water actually being present instead of just the temperature range at which liquid water could be present.
For example, using a black-body object (absorbs 100% of the energy it receives) with no atmosphere, will still have a surface temperature in the range between 1°C (274°K) and 99°C (372°K) at some point for any given star. Using Sol as an example, and using the
Stefan–Boltzmann law, the inner "habitable zone" radius would be 0.5548 AU and the outer "habitable zone" radius would be 1.0337 AU. That assumes a black-body planet with no atmosphere.
As we both know, no planet is a perfect black-body. Even Mercury has an albedo of 0.06. However, now we are getting into the characteristics of the specific planet, which should not be a determining factor.
The habitable zone for any given star should be based solely on the surface temperature of the star and the star's radius, as follows:
TE = TS x √ RS / 2ao
Where:
TE = Black-Body Surface Temperature (Kelvin)
TS = Star Surface Temperature (Kelvin)
RS = Star Radius (Meters)
ao = Distance from Star (Meters)
Using Sol as an example:
5,778 x √ ( 695,500,000 / ( 2 x 83,000,180,000 )) = 372°K
5,778 x √ ( 695,500,000 / ( 2 x 154,639,700,000 )) = 274°K
In the case of the star Kepler-186, no radius is given. However, the Stefan–Boltzmann law can be used to approximate the radius, as follows:
R / R☉ ≈ ( T☉ / T )2 x √ ( L / L☉ )
( 5,778 / 3,788 )2 x √ ( 0.0412 / 1 ) ≈ 0.4723 x 695,500,000 ≈ 328,458,781 meters
This would put the inner habitable zone radius for Kepler-186 at ~0.1138 AU, and the outer habitable zone radius at ~0.2098 AU. Again, that assumes a perfect black-body planet with no atmosphere.
We should be determining the habitable zone for a given star, not for a given planet. A planet with a high albedo would have to be much closer to its star. A planet with a dense CO
2 atmosphere could be much further away and still be warm enough to support liquid water on its surface. However, until we know more about the planet in question, it is entirely conjecture.