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Thread: How does one calculate a star's habitable zone?

  1. #1
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    How does one calculate a star's habitable zone?

    What's the formula for how far away a planet must be from a star to attain Earthlike surface temperatures?

  2. #2
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    Got a copy of GURPS Space: Third Edition?

    Page 152 has a chart.

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    I think the concept of “habitable zone” is deeply flawed. Habitability is a much more complex phenomenon than just calculating temperatures at various distances from a star based on its luminosity.

    1. Luminosity changes. Our sun is probably about 50% more luminous today than it was when the Earth was formed, and that luminosity has changed throughout the history of Earth, and it will continue to increase.

    2. The temperature at the surface will depend in part on the atmospheric gases that are available over time. Even slight variations in the amount of methane available, for instance, would have effects much larger than those produced by the same variations in the amount of CO2. A planet with a lot of methane could be as warm as Earth even beyond a “habitable zone” based on little or no methane.

    3. Bodies heated by tidal friction could have substantial warm layers far outside any habitable zone—Europa in our solar system, for instance.

    4. Differences in albedo at the surface or which results from some atmospheric gas could heat or cool planets beyond a simple Earth type model.

    5. A body with more radioactive elements would have a greater heat flow to the surface than Earth.

    6. Highly elliptical orbital parameters could render habitable a planet with an average distance far beyond the “habitable zone” based on some means of storing heat and energy either physically or biologically or both.

    7. A planet beyond the “habitable zone” with a very slow rotation relative to its star could have one hemisphere with liquid water and an eco-system that would slowly migrate as the planet rotated over a period of tens of thousands of years.

    8. There are probably a lot of ways to have habitable bodies far inside or outside orbits equivalent to that of Earth. Anybody have any other clever ideas?

    There are lots of different types of habitable zones under lots of different circumstances. In the case of the Earth we don't have a very good grasp on how the Earth stayed habitable with a cool young sun. And some concern as to how it will stay habitable as the sun gets older and hotter.

    Bob

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    A crude approximation is to take the square root of the star's bolometric luminosity.

    For instance, Sirius A's bolometric luminosity is about 26 times greater than the Sun's. So, to get the same amount of overall radiation that we get on Earth, you would have to be:

    (26)^0.5 * 1 AU = 5.1 AU

    It's important that you take the star's bolometric--or total--luminosity into account, instead of merely its visual brightness relative to the Sun. Many stars radiate most of their energy in the invisible infrared or ultraviolet, and using only visual brightness will put the HZ too close to the star.

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    Using Sol as the stellar unit of measure and AU as the standard planetary distance...

    All assumptions are for planets that are large enough retain an atmosphere...
    At .7 AU, a greenhouse effect would boil away water. So, the minimum distance is somewhere between .7 and 1.0 AU.

    At 1.4 AU, the verdict is less certain since Mars is too small to retain an atmosphere. Considering that there is evidence of liquid water on Mars, it seems that 1.4 AU is close enough if atmospheric warming is present. Therefore, the maximum distance is somewhere greater than 1.4 AU.

    For main-sequence stars other than our own, we can estimate their luminosity based on age and mass. Now consider that for the effective temperature of a planet to remain unchanged, its distance from its star is proportional to the square root of its star's luminosity. The "Earth-distance" for a star 100 times as luminous as the sun would be 10 times further away.

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    Quote Originally Posted by Bobunf
    1. Luminosity changes. Our sun is probably about 50% more luminous today than it was when the Earth was formed, and that luminosity has changed throughout the history of Earth, and it will continue to increase.
    There is an idea spoken of on GLP and other "fringe" sites that claims the Sun is "brighter and hotter" now than in the past. Are you saying this is true?

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    To a certain extent it is true. The Sun is slowly increasing in luminosity, and by a billion years from now the Earth will probably be too warm to support a biosphere (althought the biosphere might adapt somehow).

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    Quote Originally Posted by Bobunf
    8. There are probably a lot of ways to have habitable bodies far inside or outside orbits equivalent to that of Earth. Anybody have any other clever ideas?
    Much higher air pressure than on Earth will allow water to remain liquid beyond 100 C -- and we already know there are organisms which thrive at such temperatures.

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    Yes; I'd imagine a large terrestrial, up to about two or three Earth masses, might have liquid water from Venus's orbit right out to two or three AU, what with increased atmospheric pressure and greater greenhouse effect.
    The environment on such a planet would be quite a bit different to Earth's but it might support life.

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    Imagine a solar system inside a nebula or surrounded by a big ring of dust. Some of the light emitted by the star will be reflected back. Then it will warm the planetes inside. And there will be no true night , sky shining from everywhere ! If people live on these planets they have never seen any stars ! and astronomy cannot develop !
    So the habitable zone will be farther from the sun.

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    Quote Originally Posted by Lance
    There is an idea spoken of on GLP and other "fringe" sites that claims the Sun is "brighter and hotter" now than in the past. Are you saying this is true?
    As I understand it, the energy producing processes of the Sun since shortly after its formation consist of three nuclear processes, which, in essence, involve the combining of four hydrogen nuclei to form one helium nucleus.

    Hydrogen nuclei have an atomic mass of 1.008; helium an atomic mass of 4. The four hydrogen nuclei have a combined mass greater than the one helium nucleus; and the lost mass is converted mostly to energy. The one helium nucleus doesn’t exert as much resistance to compression as the four hydrogen nuclei, which results in a contraction of the Sun, and an increase in the pressure and temperature at its core, where the nuclear fusion occurs. The increasing pressure and temperature increase the rate of fusion, which increases the energy output; and the Sun gradually becomes more luminous.

    As I understand it, four and a half billion years ago, shortly after the Earth formed, the Sun was about 70% as luminous as it is today; 2.8 billion years ago the Sun was about 80% as luminous as today, and since then the Sun has, and will continue, to become hotter by about 1% per 100 million years. The rate of increase very gradually increases over time. The Earth has received more and more radiation from the Sun, and, all else being equal, it should have gradually become warmer and warmer.

    Fortunately for us, apparently, all else was not equal.

    Bob

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    Quote Originally Posted by Romanus
    A crude approximation is to take the square root of the star's bolometric luminosity.

    For instance, Sirius A's bolometric luminosity is about 26 times greater than the Sun's. So, to get the same amount of overall radiation that we get on Earth, you would have to be:

    (26)^0.5 * 1 AU = 5.1 AU

    It's important that you take the star's bolometric--or total--luminosity into account, instead of merely its visual brightness relative to the Sun. Many stars radiate most of their energy in the invisible infrared or ultraviolet, and using only visual brightness will put the HZ too close to the star.
    This approximation is for a distance from the star at one point in time. Since the luminosity of Sirus A changes at a different rate (much faster) than the luminosity of our sun, the distance would be different 100 million years ago than it is today.

    It seems to me this is a significant issue for long-lasting biological systems: How do they maintain themselves in the presence of stars with changing luminosity, and, presumably, shifting habitable zones?

    Bob

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    Quote Originally Posted by Bobunf
    This approximation is for a distance from the star at one point in time. Since the luminosity of Sirus A changes at a different rate (much faster) than the luminosity of our sun, the distance would be different 100 million years ago than it is today.
    Thanks, I was going to bring up a similar point. More massive stars evolve more quickly, so their luminosity changes more quickly. They also have a shorter lifetime - ~ a billion years in the case of Sirius A. Sirius also has a companion (Sirius B) that is now a white dwarf, and was substantially more massive than Sirius A while on the main sequence (probably around 5 solar masses), so was hotter and evolved quicker.

    There are other issues too: How long does it take for a protoplanetary system to settle down? It is suspected that large planets like Jupiter help clear the "junk" out of a solar system, reducing the rate of impact. However, it takes time for this to occur. Impacts are likely to be much higher in a young solar system. And then there is the spectrum of the star ...

    It wouldn't surprise me if it was occasionally possible to terraform a planet in the habitable zone of a star like Sirius A, but you may be unlikely to find life beyond something like bacteria on it naturally. Also, you would probably want to have a spaceguard handy to move the occasional asteroid out of the way.

    "The problem with quotes on the Internet is that it is hard to verify their authenticity." — Abraham Lincoln

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    Quote Originally Posted by Lance
    There is an idea spoken of on GLP and other "fringe" sites that claims the Sun is "brighter and hotter" now than in the past. Are you saying this is true?
    GLP woo-woos have a tendency to compress timeframes.

    It's true that the Sun is getting brighter, but not to a noticeable extent in our lifetimes.

    It's true that Yellowstone is going to blow up at some point, but probably not this year.

    It's true that Earth is going to be hit by a giant meteorite someday, but probably not in the year 2012.
    Everything I need to know I learned through Googling.

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    Does that mean that Mars will be warmer, too? Quite interesting.

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    Quote Originally Posted by Bobunf
    It seems to me this is a significant issue for long-lasting biological systems: How do they maintain themselves in the presence of stars with changing luminosity, and, presumably, shifting habitable zones?
    Hence the concept of the Continuously Habitable Zone (CHZ), which looks for regions that could maintain liquid water for billions of years despite the evolution of the parent star.
    This page provides some apparently sensible discussion and equations, though unreferenced. (Search down the page on "habitable zone", and you'll find the relevant section.)

    Grant Hutchison

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    Re Wolf S
    ^
    Yes. In fact, in a few billion years Mars will be as warm or warmer than the Earth is now. By the time the Sun reaches the subgiant branch, Mars will be positively hot.

    The good news about all this is that it means there will be a time when Mars has (even more) Earthlike weather for perhaps a couple of billion years. The bad news is that Mars won't have the regulatory mechanisms the Earth has to stably maintain favorable conditions. For instance, the carbon dioxide released will probably get quickly bound up within rocks, without volcanoes to replenish it, while the planet will lose water rapidly to photodissociation. Still, it will be the garden spot of the Solar System compared to Earth by then, let alone Venus.

  18. #18
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    Quote Originally Posted by Bobunf
    *snip*
    8. There are probably a lot of ways to have habitable bodies far inside or outside orbits equivalent to that of Earth. Anybody have any other clever ideas?
    *snip*
    I read an SF novel once that had a moon of a gas giant outside the habitable zone, which was warmed by the heat the gas giant gave off, so it was still habitable, if a bit on the cool side.

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