Habitable Zones?
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Topic authorEvil Dr Ganymede
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Habitable Zones?
Does anyone know how the distances of habitable zones around stars are calculated (eg in the star descriptions on SolStation? There seems to be some kind of formula used - the only one I know (which admittedly is from a scifi RPG) says that the habitable zone distance is at a distance in AU equal to the square root of the luminosity in Sols (and ranges between 0.95 and 1.35 times that value). Is that right?
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granthutchison
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Topic authorEvil Dr Ganymede
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. Is there any kind of proof for it?-
granthutchison
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Well, it's just the old inverse square law at work. Multiply the Sun's luminosity by 4, and you'd need to move the Earth outwards by a factor of root(4)=2 to get the insolation back to Earth-normal. So the equation is simply using the inverse square law to calculate the orbital radius at which an Earth-sized world would intercept the same amount of energy from its star as the Earth does from the Sun. If the energy intercepted by a planet is the same as Earth's, and if it is Earth-like in size, albedo, atmosphere and rotation, then it'll achieve the same equilibrium temperature as Earth.
The inner and outer limits are just lifted from theory relating to the solar system - they're the orbital radii corresponding to the critical minimum and maximum insolations before you greenhouse out, or freeze out, all the water. Applying these proportions to the Goldilocks orbit computed above gives you the corresponding radii for the same critical levels of insolation in the star system you're currently investigating.
Grant
The inner and outer limits are just lifted from theory relating to the solar system - they're the orbital radii corresponding to the critical minimum and maximum insolations before you greenhouse out, or freeze out, all the water. Applying these proportions to the Goldilocks orbit computed above gives you the corresponding radii for the same critical levels of insolation in the star system you're currently investigating.
Grant
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Topic authorEvil Dr Ganymede
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While on this topic...
Let's say you're on a planet in Proxima's habitable zone (which I'll assume is about 0.012 AU from the star, since according to SolStation the luminosity is apparently 0.000138 Sols). Now, Proxima's angular diameter is about 4 degrees in the sky from there according to Celestia, so it's about the size of 8 full moons in the sky, and the apparent magnitude from there would be -26 - about the same as the Sun.
So what does the scene on the planet's surface look like? Does Proxima look like a brilliant ball of bright white light like the Sun? Is there a reddish tinge to the light? Do things look like they're lit up by a red light?
What would it look like if Proxima flared (it's a flare star, after all)? Would the flares really have a drastic effect on the planet and its atmosphere or any life on it? (I'm thinking X-Ray flares can't be that healthy, though surely the Sun has those?).
Let's say you're on a planet in Proxima's habitable zone (which I'll assume is about 0.012 AU from the star, since according to SolStation the luminosity is apparently 0.000138 Sols). Now, Proxima's angular diameter is about 4 degrees in the sky from there according to Celestia, so it's about the size of 8 full moons in the sky, and the apparent magnitude from there would be -26 - about the same as the Sun.
So what does the scene on the planet's surface look like? Does Proxima look like a brilliant ball of bright white light like the Sun? Is there a reddish tinge to the light? Do things look like they're lit up by a red light?
What would it look like if Proxima flared (it's a flare star, after all)? Would the flares really have a drastic effect on the planet and its atmosphere or any life on it? (I'm thinking X-Ray flares can't be that healthy, though surely the Sun has those?).
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Guest
If I might offer my interpretation of this scene;
John Dollan and others have suggested that palnets around red dwarfs inside their comfort zone might be tidally locked, with a frozen side and a habitable side; in this case the red sun would be more or less fixed in position in the sky.
The sun would be 8 times as big as the full moon (is that area or diameter, by the way, Doctor?) and would be about as yellow as a house lightbulb- but too big and too bright to look at directly, as it would be perhaps half as bright as the Sun as seen from Earth in the visible wavelengths...
(I am sure Grant would know exactly how bright)
I don't myself believe that such a planet could evolve naturally, but it could almost certainly be created artificially with a lot of expended energy and effort.
All that energy would be wasted when the star flared, as this would ruin the ecosphere at such a close distance...
unless some way is found of controlling flares in red dwarfs, they will be uninhabitable by humans.
John Dollan and others have suggested that palnets around red dwarfs inside their comfort zone might be tidally locked, with a frozen side and a habitable side; in this case the red sun would be more or less fixed in position in the sky.
The sun would be 8 times as big as the full moon (is that area or diameter, by the way, Doctor?) and would be about as yellow as a house lightbulb- but too big and too bright to look at directly, as it would be perhaps half as bright as the Sun as seen from Earth in the visible wavelengths...
(I am sure Grant would know exactly how bright)
I don't myself believe that such a planet could evolve naturally, but it could almost certainly be created artificially with a lot of expended energy and effort.
All that energy would be wasted when the star flared, as this would ruin the ecosphere at such a close distance...
unless some way is found of controlling flares in red dwarfs, they will be uninhabitable by humans.
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eburacum45
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Topic authorEvil Dr Ganymede
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I can't see why a planet like that wouldn't form naturally around a red dwarf... yes, it'll be tidelocked, but they're not THAT uninhabitable (see papers by Joshi and others). But I guess we know little about how planets can form around low mass stars (I'd be surprised if nobody's written any papers on it though, considering they're the most common type of star around).
I'm not sure what the exact effect of flares would be, hence my question
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I'm not sure what the exact effect of flares would be, hence my question
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granthutchison
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There's a correction factor of root(2) required for your habitable zone calculations when the planet is synchronously rotating - such a planet radiates most of its heat from just the sunward side, and so achieves a higher equilibrium temperature than a body that rotates quickly and so radiates significantly from its nightside, too. So you need to nudge that habitable orbit out to root(2)*root(0.000138) = 0.017AU.
Celestia's radius estimate for cool stars is always low, because it doesn't take into account things like limb darkening and the massing of spectral lines in the visible part of the spectrum - so it's best to use another source for Proxima's radius; SolStation say 0.145 solar. That'd make the apparent diameter from the habitable zone equal to 4.55 degrees, or 83 times the angular area of the Sun in Earth's sky.
We know Proxima's absolute visual magnitude, 15.53, which makes it just 0.000052 times as luminous as the Sun in the visual range. From 0.017AU, that's 0.18 times the illumination received on Earth. Spread over 83 times the angular area, that means the surface brightness of Proxima's disc would be just 0.002 times the Sun's - through an atmosphere, that comes to 3000000 cd/m?, right in the ballpark of the filament of an incandescent light bulb (no surprise there, since the surface temperatures are about the same). So you would be able to look directly at Proxima without blinding yourself, but it would feel uncomfortable and it would leave you with a doozy of an afterimage when you looked away.
That light filament, as eburacum45 pointed out, is also about the same colour as a red dwarf star. But its light only looks yellow when you compare it to daylight or fluorescent lighting. Indoors at night, when incandescent light is all you have, it looks white. The filament itself always looks entirely white, to my eyes. So I think you'd see a white star shedding white light, and then you'd be astonished at how blue flourescent lighting looked when you went indoors.
Proxima flares irregularly, on average twice a year, and doubles its brightness over a few minutes. Because the flare temperature is around 30 million K, a close-in planet receives a massive dose of X-rays - hundreds of thousands of times the level associated with a solar flare on Earth.
Grant
Celestia's radius estimate for cool stars is always low, because it doesn't take into account things like limb darkening and the massing of spectral lines in the visible part of the spectrum - so it's best to use another source for Proxima's radius; SolStation say 0.145 solar. That'd make the apparent diameter from the habitable zone equal to 4.55 degrees, or 83 times the angular area of the Sun in Earth's sky.
We know Proxima's absolute visual magnitude, 15.53, which makes it just 0.000052 times as luminous as the Sun in the visual range. From 0.017AU, that's 0.18 times the illumination received on Earth. Spread over 83 times the angular area, that means the surface brightness of Proxima's disc would be just 0.002 times the Sun's - through an atmosphere, that comes to 3000000 cd/m?, right in the ballpark of the filament of an incandescent light bulb (no surprise there, since the surface temperatures are about the same). So you would be able to look directly at Proxima without blinding yourself, but it would feel uncomfortable and it would leave you with a doozy of an afterimage when you looked away.
That light filament, as eburacum45 pointed out, is also about the same colour as a red dwarf star. But its light only looks yellow when you compare it to daylight or fluorescent lighting. Indoors at night, when incandescent light is all you have, it looks white. The filament itself always looks entirely white, to my eyes. So I think you'd see a white star shedding white light, and then you'd be astonished at how blue flourescent lighting looked when you went indoors.
Proxima flares irregularly, on average twice a year, and doubles its brightness over a few minutes. Because the flare temperature is around 30 million K, a close-in planet receives a massive dose of X-rays - hundreds of thousands of times the level associated with a solar flare on Earth.
Grant
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Topic authorEvil Dr Ganymede
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granthutchison
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I guess the detail depends on the energy and frequency of the flares. But since the X-rays and UV are largely absorbed by atmospheric gases, the whole evolution of the atmosphere would take place against a background of repeated dumps of fierce photodissociation. That would make water difficult to hold on to, since it would be photodissociated even in the low atmosphere, and the hydrogen would escape. The remaining oxygen would oxidize anything available, including photodissociated nitrogen. No ozone, since these nitrogen oxides remove it very efficiently.
A dry world with an atmosphere consisting of carbon dioxide and photochemical smog?
Grant
A dry world with an atmosphere consisting of carbon dioxide and photochemical smog?
Grant
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eburacum45
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I am trying to put together an imaginary technological defence against stellar wind events, for use on terraformed worlds without magnetic fields.
Basically it is a rotating network of superconducting wires, something like the technology imagined for a bussard ramscoop or a magsail;
rather than put this net in orbit around the planet concerned, I suggest placing it at the L1 lagrange point...
it would then be in a position to shield the planet from the stellar wind.
If placed at Mars L1 point, for example, it would be about a million km closer to the Sun than Mars; the net could form a disk, and rotate to maintain its shape...
around the outside of the net several million square kilometers of photovoltaic cells could be placed, framing the Sun as seen from Mars, and providing enough energy to produce up to a petawatt of magnetic shielding- similar in intensity to the Earth's magnetic field, as far as I can discover.
This Lagrangian Magshield, as I call it, might be effective enough to protect against charged particles from a flare star-
crazy, or what?
Basically it is a rotating network of superconducting wires, something like the technology imagined for a bussard ramscoop or a magsail;
rather than put this net in orbit around the planet concerned, I suggest placing it at the L1 lagrange point...
it would then be in a position to shield the planet from the stellar wind.
If placed at Mars L1 point, for example, it would be about a million km closer to the Sun than Mars; the net could form a disk, and rotate to maintain its shape...
around the outside of the net several million square kilometers of photovoltaic cells could be placed, framing the Sun as seen from Mars, and providing enough energy to produce up to a petawatt of magnetic shielding- similar in intensity to the Earth's magnetic field, as far as I can discover.
This Lagrangian Magshield, as I call it, might be effective enough to protect against charged particles from a flare star-
crazy, or what?
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Topic authorEvil Dr Ganymede
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I just noticed this post and I"d like to put in my two cents as this is something I've been working with for a while now. The information regarding habitable zones on SolStation.com, while technically correct, is not a good measure of where an "earthlike" planet should be placed, let me go back to my good standby star Wolf 359 to illustrate.
Solstation gives a figure of 0.005 AU for the habitable zone around Wolf 359. They also give an estimated luminosity of about 2/100,000 Suns. This isn't far from what you would expect to get when using the reported value of 16.55 for Absolute Magnitude that I found in the RECONS data sheet of the hundred nearest stars.
In my caculations, using the venerable and simple formula 2.512^(4.85-Mv) equation I find that Wolf 359's Visual Luminosity is around 0.0000208819 or about 1/50,000 that of Sol. To compute the actual luminosity in Watts you need the Equation L=4piR^2sT^4 where s = the stephan-boltzman constant.
From some old data tables I have, I found that the Radius of Wolf 359 is roughly 0.14 Sol, it's Mass around 0.10 Sol and its temperature about 2850K. Using these numbers I get a value for L of 4.45039*10^23 W.
Now I know from my own data that the Luminosity of the Sun, again in Watts to be 3.827*10^26. A simple Division of the Wolf 359 value by the Solar value (L/Lo) gives me a figure of 0.001163 Sols. Notice the difference, the Visual Luminosity is reported as being nearly 56 times less intense than the Luminosity ratio found using the real values. I'm sure you're wanting to know my point to all this yes? Well here it is.
SolStations figures are based entirely on visual luminosity, meaning that for large stars planets are placed too far away and for small stars they are placed too close. Just because a star appears to be mag -26.72 in the sky doesn't mean the conditions will remain Earthlike. Consider this, using Wolf 359's visual luminosity of 0.0000208819 Sols I use a simple method of root(L) to find a suitable place to put a planet, in this case it would be at 0.00456967 AUs. At this extremely close orbit, one does not find an Earthlike world I'm affraid.
Certainly Wolf 359 appears as a sunlike -26.72 magnitude object, but, its disc coveres nearly 16 degrees in the sky. A planet the size of Earth at this distance would complete a revolution in just 0.296247 days, thats about 8 hours. Not only would said planet have a ridiculously small year, it would also be bathed in intense radiation. The solar flux from Wolf 359 at this distance would be about 75804.51 W/m^2, rendering an ambient temperature of 760.35Kelvins (over 900 degrees Fahreinheit). This is an unacceptable situation when it comes to finding a habitable planet.
Er-go, I do not recomend using visual magnitude when placing habitable planets or determining the size and or width of the Comfort Zone. It's better to find the actual Luminosity and use the Ratio of (L/Lo) where L = Luminosity of your star and Lo = Luminosity of the Sun. If you go by my method you can place a habitable planet at 0.031743 AUs, the period comes out to be 5.424927 Days, with an ambient temp at an earthlike 288.47 K, a flux of 1570.51 W/m^2 and in general better results, of course the planet is still tidally locked, but its not in a roasted-oven orbit either. Phew glad I could finally get this done, hope you found it informative. Cheers.
Solstation gives a figure of 0.005 AU for the habitable zone around Wolf 359. They also give an estimated luminosity of about 2/100,000 Suns. This isn't far from what you would expect to get when using the reported value of 16.55 for Absolute Magnitude that I found in the RECONS data sheet of the hundred nearest stars.
In my caculations, using the venerable and simple formula 2.512^(4.85-Mv) equation I find that Wolf 359's Visual Luminosity is around 0.0000208819 or about 1/50,000 that of Sol. To compute the actual luminosity in Watts you need the Equation L=4piR^2sT^4 where s = the stephan-boltzman constant.
From some old data tables I have, I found that the Radius of Wolf 359 is roughly 0.14 Sol, it's Mass around 0.10 Sol and its temperature about 2850K. Using these numbers I get a value for L of 4.45039*10^23 W.
Now I know from my own data that the Luminosity of the Sun, again in Watts to be 3.827*10^26. A simple Division of the Wolf 359 value by the Solar value (L/Lo) gives me a figure of 0.001163 Sols. Notice the difference, the Visual Luminosity is reported as being nearly 56 times less intense than the Luminosity ratio found using the real values. I'm sure you're wanting to know my point to all this yes? Well here it is.
SolStations figures are based entirely on visual luminosity, meaning that for large stars planets are placed too far away and for small stars they are placed too close. Just because a star appears to be mag -26.72 in the sky doesn't mean the conditions will remain Earthlike. Consider this, using Wolf 359's visual luminosity of 0.0000208819 Sols I use a simple method of root(L) to find a suitable place to put a planet, in this case it would be at 0.00456967 AUs. At this extremely close orbit, one does not find an Earthlike world I'm affraid.
Certainly Wolf 359 appears as a sunlike -26.72 magnitude object, but, its disc coveres nearly 16 degrees in the sky. A planet the size of Earth at this distance would complete a revolution in just 0.296247 days, thats about 8 hours. Not only would said planet have a ridiculously small year, it would also be bathed in intense radiation. The solar flux from Wolf 359 at this distance would be about 75804.51 W/m^2, rendering an ambient temperature of 760.35Kelvins (over 900 degrees Fahreinheit). This is an unacceptable situation when it comes to finding a habitable planet.
Er-go, I do not recomend using visual magnitude when placing habitable planets or determining the size and or width of the Comfort Zone. It's better to find the actual Luminosity and use the Ratio of (L/Lo) where L = Luminosity of your star and Lo = Luminosity of the Sun. If you go by my method you can place a habitable planet at 0.031743 AUs, the period comes out to be 5.424927 Days, with an ambient temp at an earthlike 288.47 K, a flux of 1570.51 W/m^2 and in general better results, of course the planet is still tidally locked, but its not in a roasted-oven orbit either. Phew glad I could finally get this done, hope you found it informative. Cheers.
"May Fortune Favor the Foolish" - James T. Kirk
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eburacum45
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Except, being tidally locked, it would not really be habitable.
Could it rotate harmonically, so that with an eight day year you get a day length of four Earth days or something? Probably not.
If not- well, imagine Earth with no rotation. The dayside would bake, the nightside freeze; there might be an atmospheric ciirculation something like that proposed for Hot Jupiters, but with a much thinner atmosphere it would be quite different. Also the cold side would collect all the water, I think, freeze drying the atmosphere so that the hot side is also dry.
How about moving the planet out a bit further? There might only be a small habitable zone somewhere near the terminator, but the circulation might not be so fierce, and the hot side might not be so inhospitable.
Could it rotate harmonically, so that with an eight day year you get a day length of four Earth days or something? Probably not.
If not- well, imagine Earth with no rotation. The dayside would bake, the nightside freeze; there might be an atmospheric ciirculation something like that proposed for Hot Jupiters, but with a much thinner atmosphere it would be quite different. Also the cold side would collect all the water, I think, freeze drying the atmosphere so that the hot side is also dry.
How about moving the planet out a bit further? There might only be a small habitable zone somewhere near the terminator, but the circulation might not be so fierce, and the hot side might not be so inhospitable.
It is possible to extend the planet out farther, by increasing the green house effectiveness, however with Red Dwarfs your limited by their exceedingly thin and close-to-the-star CZ. Also your limited, at least by our current level of understanding by going with a planet who has a thin enough and cool enough atmosphere to support life. Anytime you deal with Red Dwarf planets you get interesting results, frankly I'm not sure if I'd write off a habitable world there but I'm also not sure how you'd go about making one either.
Cheers!
Cheers!
"May Fortune Favor the Foolish" - James T. Kirk
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eburacum45
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I have been working on a few tidally locked habitable planets; here they are, briefly visible in the period before 50.megs realise that I am remote linking again...
the habitable zone is confined to the terminator, where the slowly circulating winds either heat up or cool down (both events causing precipitation)
Twilight, by Anders Sandberg (actually around Keid A, which is a K class orange dwarf)...
A new one, Dante, around Hip 85647
A comparison between Hip 85647 as seen from the habitable zone of Dante, forever motionless (more or less) in the perpetual evening, and the good old Sun as seen from Earth.
(some slight image editing here)
the habitable zone is confined to the terminator, where the slowly circulating winds either heat up or cool down (both events causing precipitation)
Twilight, by Anders Sandberg (actually around Keid A, which is a K class orange dwarf)...
A new one, Dante, around Hip 85647
A comparison between Hip 85647 as seen from the habitable zone of Dante, forever motionless (more or less) in the perpetual evening, and the good old Sun as seen from Earth.
(some slight image editing here)
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lazy chaos
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eburacum45
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Certainly more and more red dwarfs are being classified as flare stars;
I chose Hip 85647 as it is quite a bright red dwarf and so the planet can be at a relatively safe distance during a flare.
These people have the idea that flares might not be as bad as all that- the total amount of UV is the same as a sunlike star, if averaged out over time; and the atmosphere of an Earth-like world would protect against X-rays, while any magnetosphere would help deflect charged particles...
http://www.astrobiology.com/asc2002/abs ... ?ascid=352
I chose Hip 85647 as it is quite a bright red dwarf and so the planet can be at a relatively safe distance during a flare.
These people have the idea that flares might not be as bad as all that- the total amount of UV is the same as a sunlike star, if averaged out over time; and the atmosphere of an Earth-like world would protect against X-rays, while any magnetosphere would help deflect charged particles...
http://www.astrobiology.com/asc2002/abs ... ?ascid=352
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Guest
Ok, thanks for that. Interestingly 85647 is in the HabCat as available at http://www.projectrho.com/smap06.html, so flares weren't considered a problem when compiling the catalog.