Welcome, Guest

Author Topic: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER  (Read 2102 times)


smjjames

  • *****
  • Posts: 1013
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #1 on: February 02, 2012, 09:09:19 AM »
Cool, its an M class star though and the tidal locking issue is an unanswered question, possibly unanswerable until we go there or develop powerful enough simulations to model 3+ body dynamics with tidal forces.

Also, if we're finding so many planets around red dwarfs so close to our system, shouldn't we try taking a closer look at the Alpha Centauri system? Proxima centauri in particular. It's far enough away from the other two to not worry about planetary instability.

Omnigeek6

  • *****
  • Posts: 111
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #2 on: February 05, 2012, 06:14:57 PM »
Quote
The two brightest components, Gl 667 A and Gl 667 B, are separated by an average distance of about 12.6 AU, but have an eccentric orbit, which takes them as close as about 5 AU, or as far as 20 AU. The orbit takes approximately 42.15 years to complete. The orbital distance translates to an average separation of 1.8".

Gl 667 C orbits further out, between about 56 and 215 AU, equating to an angular separation of about 30".

and the sma of GJ 667Cc is about 1/8 AU.

Yeah, I'm pretty sure it will be tidally locked. Of course, this is no reason to rule it out as a candidate for habitability.


smjjames

  • *****
  • Posts: 1013
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #3 on: February 05, 2012, 07:24:42 PM »
Regarding components GJ A and B, I looked on wikipedia since the article doesn't say what type they are, and those two are K class. I wonder whether any habitable planets are around those? The system itself resembles the Alpha Centauri system in many ways.

I know there was an article that was mentioned in another thread on here about tidal locking for K classes (while I agree that tidal locking would be an issue for M class red dwarfs, I'm skeptical about it on K class), but I'm wondering if a planet orbiting one of those two would be tidally affected by the companion star? I have no idea if it would, the effect might even be negligible, but it's a thought.

Omnigeek6

  • *****
  • Posts: 111
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #4 on: February 06, 2012, 12:31:07 AM »
EDIT:

Quote
I know there was an article that was mentioned in another thread on here about tidal locking for K classes (while I agree that tidal locking would be an issue for M class red dwarfs, I'm skeptical about it on K class), but I'm wondering if a planet orbiting one of those two would be tidally affected by the companion star? I have no idea if it would, the effect might even be negligible, but it's a thought.

Basically, tidal locking time turns out to involve a ridiculous number of variables which can drastically affect the results if not perfectly accurate.

I have found one formula which may work, from:
http://solar-flux.forumandco.com/t704-rotation-period-for-fictional-and-real-planets
Quote
D = 0.0483((AM²)/d)^(1/6)
where D is the distance required for a planet to tidally lock (AU), d is the density of the planet (kg/m^3), A is the age of the system (y), and M is the mass of the star (suns). The original link says density should be measured in tons per cubic decimeter (t/dm^3). Do not use this: it will not give you the right numbers.

For our solar system and a density of 5500 (about the density of Earth), this can be calculated to be 0.475 AU. At the tidal locking distance, a planet of the given density takes about 5 Gy to be locked.
Note: denser planets will take longer to become locked. For a planet with the density of Saturn the tidal lock distance is about 0.67 AU.

In general, we can set A to equal 10^10 years. (planets older than that may become uninhabitable due to stellar evolution, loss of internal heat, or loss of atmosphere). We will set d to equal 2500 kg/m^3, which is equivalent to an ocean planet with water as a major component of the mass. Habitable planets won't likely get much less dense than this, and denser planets will be stable a bit further out. Thus, we get the equation:

D = 0.0483 (4*10^6 M^2)^(1/6). Given the mass of a star, this tells us the tidal locking distance. What this doesn't tell us is where the tidal locking distance is relative to the habitable zone.

Fortunately, we have other useful formulas. The mass to luminosity relationship of a main-sequence star is L = M^3.9. The relationship between planet temperature, star luminosity, and planet distance is T = k/(D/L^0.5)^0.5. k is a constant which is related to the albedo of the planet and a bunch of other stuff we don't care about. For Earth, which has an equilibrium temperature of 255 K, k=255, so we get:

255 = 255/(D/L^0.5)^0.5.

multiplying both sides by the denominator of that fancy fraction:

255(D/L^0.5)^0.5 = 255.
(D/L^0.5)^0.5 = 1

squaring both sides:

D/L^0.5 = 1
D = L^0.5

D is now an orbital distance somewhere in the middle of the habitable zone. Substituting M^3.9 for L:

D = (M^3.9)^0.5
D = M^1.95

So, given the mass of the star, we now have an approximate habitable distance and a tidal locking distance. If the habitable distance is less than the tidal locking distance, any habitable planets of the star will be tidally locked. If the habitable distance is greater than the tidal locking distance, habitable planets may rotate as they please. Therefore, the minimum mass M of the star for a habitable planet to not be tidally locked is the value of M such that the habitable distance is equal to the tidally locking distance. Translating this into algebra:

kM^1.95 = 0.0483 (4*10^6 M^2)^(1/6)

this is a mess. However, we can get rid of the obnoxious fractional exponent by raising everything to the power of 6:

M^11.7 = 1.270*10^-8 * 4*10^6 M^2

Let's simplify the constant...

M^11.7 = 0.0508 M^2.

Dividing by M^2:

M^11.7 / M^2 = 0.0508
M^9.7 = 0.0508
M = 0.0508^(1/9.7)
M = 0.736

So, if a star has a mass smaller than 0.736 suns, its habitable planets will probably be tidally locked. But what spectral class is the star at the threshold? well...

This list: http://en.wikipedia.org/wiki/List_of_exoplanetary_host_stars can be sorted by mass, giving us an idea of some real stars of this mass. It turns out that these stars are in the range of K1V to K4V. So, in general, this formula tells us that stars of K3V or cooler will tidally lock their habitable planets. Denser planets can be closer in while being locked.

This doesn't bode well for habitable moons of gas giants... or does it? The density of the planet affects the tidal locking distance, but not much (the term with density in it is taken the the power of 1/6. This means that a planet 50% less dense than Earth will have a tidal locking distance only 1.6% larger. In addition, the combined mass of the moons of a gas giant is about 0.02% the mass of the planet. This means that for the moon of a gas giant to be large enough to retain an atmosphere and generate a magnetic field (lets' say 0.1 earth masses... don't forget that tidal heating will help keep the moon geologically active, and the planet's magnetic field may provide some shielding) the gas giant needs to be at least 500 earth masses. Gas giants of above this mass don't change much in radius (provided they aren't extremely hot and puffy, which rules them out as parents of habitable moons anyway) so they can be as dense or denser than terrestrial planets.

Note: this assumes a planet somewhere in the middle of its habitable zone, perhaps a little bit towards the inside edge. Planets on the outer edge of their habitable zones (including planets with thick atmospheres... and moons of gas giants if the parent provides enough tidal heating) can orbit somewhat smaller stars without becoming tidally locked. Planets with ammonia-based life, which would exist at colder temperatures (surface temperature 200-240 K, possibly hotter for planets with high atmospheric pressure) could due fine around even colder stars.

To determine the exact numbers, we just need to change the equilibrium temperature of the planet, and thus the distance. For mars, on the outer edge of the HZ, the distance is 1.5 AU for a sunlike star. For an ammonia planet, the distance may be 2 AU to 2.5 AU, depending on the strength of the greenhouse effect. We add this as a coefficient to our habitable distance formula:

Mid-range water planet: D = M^1.95.
Outer range water planet: D = 1.5 M^1.95
Inner range ammonia planet: D = 2 M^1.95
Outer range ammonia planet: D = 2.5 M^1.95.

we now get the equation
kM^1.95 = 0.0483 (4*10^6 M^2)^(1/6), where k is the coefficient based on the equilibrium temperature of the planet. From here, we can proceed as before, but dividing the "0.0483" constant by k.

We now get a more complete set of masses. HZa means habitable zone for liquid-ammonia-based-life.

For a planet of about Earthlike distance, M = 0.736 suns, or about K3V star.
For an outer HZ water planet, M = 0.572 suns, or about a K9V star.
For an inner HZa planet , M = 0.479 suns, or about an M0V star
For an outer HZa planet, M= 0.417 sun, or about an M1V star.

Conclusion: If your star is G class, the habitable planets won't be tidally locked. If the star is M class, they will. If the star is K class, check the tidal locking distance with this: D = 0.0483((AM²)/d)^(1/6).
Use the actual density and age of your planet.


« Last Edit: February 06, 2012, 02:51:08 AM by Omnigeek6 »

FiahOwl

  • *****
  • Posts: 1193
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #5 on: February 06, 2012, 07:55:46 AM »
WOW! IVE BEEN LOOKING FOR FORMULAS LIKE THIS!

Thanks omnigeek!

smjjames

  • *****
  • Posts: 1013
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #6 on: February 06, 2012, 08:13:24 AM »
Wow.

Anyways, what about the affects from other bodies in the system? Should we consider that? Tidal locking doesn't neccesarily rule out life and yea the current HZ assumes Terran-like lifeforms. Someplace much colder with liquid of some other kind such as Titan for example could very well evolve complex life forms.

Omnigeek6

  • *****
  • Posts: 111
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #7 on: February 06, 2012, 03:43:33 PM »
Wow.

Anyways, what about the affects from other bodies in the system? Should we consider that? Tidal locking doesn't neccesarily rule out life and yea the current HZ assumes Terran-like lifeforms. Someplace much colder with liquid of some other kind such as Titan for example could very well evolve complex life forms.

We don't really need to consider the gravity of other planets or stars when calculating rotation. In a nutshell, the gravity of other objects affects orbital parameters much more strongly than rotational parameters. If a star or other planet exerted enough gravitational force to prevent a planet from being tidally locked it would destabilize the planet's orbit.

However, some types of orbital resonance (like the one between Pluto and Neptune) may force one object into a fairly eccentric orbit, allowing for a spin-orbit resonance like Mercury's. Planets in such spin-orbit resonances would not be tidally locked, but life would have to cope with long periods of light and long periods of darkness. Such planets would have little or not axis tilt, but would undergo seasonal temperature variation due to orbital eccentricity.

The second major case is a resonance which causes one of the objects to have a fairly eccentric orbit

smjjames

  • *****
  • Posts: 1013
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #8 on: February 06, 2012, 04:22:46 PM »
Okay, how about a sufficiently large moon or possibly for SuperEarths, two or more moons that are big enough to have a significant impact? Or would that just accelerate tidal locking rather than keep it at bay? I'm not real sure on the mechanics of that.

Given the effect that our moon had on the Earth, logic would be that it would accelerate the process, but I don't know if it would keep it bay somehow.

Anyways, we've been talking about tidal locking in single star planetary systems, what about binaries in a close orbit of hours or days? I don't know if anybody has tried simulating tidal locking in that situation and the article I mentioned earlier didn't say anything about binaries. Given that many binaries would be of differing mass stars (as in the system mentioned here, although this one isn't a close binary), the differing amount of tidal force might be enough to not tidally lock a planet in the habitable zone.

Omnigeek6

  • *****
  • Posts: 111
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #9 on: February 06, 2012, 04:43:17 PM »
Okay, how about a sufficiently large moon or possibly for SuperEarths, two or more moons that are big enough to have a significant impact? Or would that just accelerate tidal locking rather than keep it at bay? I'm not real sure on the mechanics of that.

Given the effect that our moon had on the Earth, logic would be that it would accelerate the process, but I don't know if it would keep it bay somehow.

Anyways, we've been talking about tidal locking in single star planetary systems, what about binaries in a close orbit of hours or days? I don't know if anybody has tried simulating tidal locking in that situation and the article I mentioned earlier didn't say anything about binaries. Given that many binaries would be of differing mass stars (as in the system mentioned here, although this one isn't a close binary), the differing amount of tidal force might be enough to not tidally lock a planet in the habitable zone.

I'm not totally sure what happens to a planet with a huge moon in the tidal locking zone. Theoretically if the tides from the moon overpowered those from the star the planet would be tidally locked to its moon instead of its star. However, tides from the star would still slightly slow down the planet's rotation. The moon would now have an orbital period shorter than its' parent's rotational period. At this point, tidal effects from the planet would slow down the moon, causing it to fall into a closer-in orbit. This would strengthen the tides between moon and planet, and potentially speed up the planet's rotation.

I'm not sure whether there is a possible equilibrium, or whether the moon will eventually cross the roche limit and be destroyed. I'm also not sure whether it would be possible for a moon to survive for 10 Gy or longer in the second case.

smjjames

  • *****
  • Posts: 1013
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #10 on: February 06, 2012, 05:02:09 PM »
Gy? Do you mean billion years?

Given the vast variety of planetary orbits, combinations, etc, it could be possible for such planet-moon systems to exist for periods long enough for life to evove, even if they are very rare.

What about the close in binaries? The increased amount of energy could push back the HZ, making tidal locking less of an issue and the mass difference or even just the wobble could have an effect on tidal locking.

I tested with a red dwarf pair (actually one was more of an orange color, but they were both M class), so I don't really know for sure the effects on the HZ of K or G class close orbiting binaries.

Omnigeek6

  • *****
  • Posts: 111
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #11 on: February 06, 2012, 08:52:21 PM »
Gy? Do you mean billion years?

Given the vast variety of planetary orbits, combinations, etc, it could be possible for such planet-moon systems to exist for periods long enough for life to evove, even if they are very rare.

What about the close in binaries? The increased amount of energy could push back the HZ, making tidal locking less of an issue and the mass difference or even just the wobble could have an effect on tidal locking.

I tested with a red dwarf pair (actually one was more of an orange color, but they were both M class), so I don't really know for sure the effects on the HZ of K or G class close orbiting binaries.

Yep. Gy = giga-year.

Anyway...

A binary of two 0.5 solar mass stars would have a combined mass of 1 solar mass... but their combined luminosity would only be 14% that of the sun. Since HZ distance varies with the square root of star luminosity, this puts the middle of the HZ out at 0.366 AU, or about the distance of mercury. This is well within the tidal locking distance for a single star with the mass of the sun (HZ distance = 77% of tidal locking distance).

For a single star with 0.5 solar masses, on the other hand, the HZ distance is 0.26 AU, and the tidal locking distance is 0.377 AU. (HZ distance = 68% of tidal locking distance).

In short, the extra energy put out by two stars is mostly offset by the tidal force from the increase in total stellar mass. The more of the system's mass is distributed to the larger star, the less intense this effect becomes, to a limit of a secondary star mass of 0 (at which point you just have a planet orbiting a star. This means that circumbinary planets may be MORE prone to tidal locking than planets of single stars for a given total stellar mass or luminosity. I'm not sure what the effects of the differing gravitational forces as the binary rotated would be, but again I'm guessing that they would perturb the planet's orbit more than its rotation.

smjjames

  • *****
  • Posts: 1013
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #12 on: February 06, 2012, 09:43:03 PM »
I was talking about binaries with different masses, most binaries have stars of unequal mass. The dynamics would be different there.

Omnigeek6

  • *****
  • Posts: 111
Re: GJ 667Cc - 22 Lightyears Away - Best Canidate For Life EVER
« Reply #13 on: February 07, 2012, 12:39:10 AM »
I was talking about binaries with different masses, most binaries have stars of unequal mass. The dynamics would be different there.

Well, basically, the closer the masses of the stars are given their combined mass, the farther in the habitable zone of the pair is. So, a 0.8 solar mass star and a 0.2 solar mass star could have a habitable planet that wasn't tidally locked (combined mass 1 solar mass, combined luminosity 0.42 suns), while a 0.6 and a 0.4 solar mass star (combined mass 1 solar mass, combined luminosity 0.16 suns) would be less likely to.