Calculating Exoplanet Habitability using Stefan-Boltzmann Law | Habitable Zones

[|Glitch|]

I have read several methods for calculating the habitable zones of exoplanets, but every single one of them includes assumptions about the planet that are yet unknown. Such as whether or not the planet has an atmosphere, or the atmospheric composition, or the exoplanet's albedo, etc.

Granted, to have liquid water on the surface of any exoplanet requires a specific range of atmospheric pressure and temperature. But they are determining whether or not an exoplanet falls in the habitable zone based upon data they do not yet have.

Would not a better approach be to use the Stefan–Boltzmann law to first determine whether or not an exoplanet falls in the right temperature range? Then when we learn more information, adjust the habitable zone for that specific exoplanet accordingly.

If we use our sun and Earth as an example, and calculate the distance Earth must be (as a "black body") from the sun to have surface temperatures between 0°C and 100°C, we get:

SQRT(((695,500,000² x 5,778⁴) / 374.15⁴) / 4) = 83,378,738,826 meters (0.56 AU)
SQRT(((695,500,000² x 5,778⁴) / 274.15⁴) / 4) = 155,603,658,580 meters (1.04 AU)​

If we knew nothing about the conditions on Earth, then 0.56 AU to 1.04 AU seems like a reasonable first estimate. Once we learn of Earth's albedo (32.5% ± 2.5%), for example, we can adjust the habitable zone accordingly:

(5,778 x SQRT( 695,500,000 / (2 x 149,597,870,700))) x 0.675^0.25 = (5,778 x 0.04821) x 0.906412 = 252.5°K (-20.65°C)​

Again, the -20.65°C mean surface temperature only takes into account Earth's albedo, and does not include Earth's atmospheric composition and pressure. Since the current mean surface temperature of Earth is actually +14.8°C, then the 35.45°C difference must be the result of radiative forcing in the atmosphere due to greenhouse gases.

Furthermore, the actual mean surface temperature of an exoplanet could tell us about its atmospheric pressure, once we learn about the exoplanet's atmospheric composition.

It just bothers me when they make assumptions about whether or not exoplanets fall in the habitable zone of its star when they have no data about the exoplanet, other that it's orbit. They should be determining habitable zones based upon the information they actually have, until more is known, and leave out all the assumptions.

What do you think? Or am I way out in left field?

 

[Simon Bridge]

Calculating a "goldilocks zone" about a primary is used as a first guess.
By definition, only the orbit is needed for this calculation... your own "reasonable first estimate" uses a few assumptions - what makes you decide that these are reasonable assumptions: how did you decide? How do you know the "unreasonable" assumptions of others are unfounded?

eg. http://phl.upr.edu/projects/habitable-exoplanets-catalog/methods
... the definitions are so provide a guideline for where to concentrate resources so they tend to err on the inclusive side.
As more is known about exoplanets, and techniques get better, the searches can get narrower.
Basically nobody wants to reject a habitable planets that happens ot be on the fringes of what is currently thought possible - we just don't know enough to make a restricted list.

Some papers are better than others: your argument will be clearer if you provide references so we know better what you are talking about.

 

[Matterwave]

I have read several methods for calculating the habitable zones of exoplanets, but every single one of them includes assumptions about the planet that are yet unknown. Such as whether or not the planet has an atmosphere, or the atmospheric composition, or the exoplanet's albedo, etc.

Granted, to have liquid water on the surface of any exoplanet requires a specific range of atmospheric pressure and temperature. But they are determining whether or not an exoplanet falls in the habitable zone based upon data they do not yet have.

Would not a better approach be to use the Stefan–Boltzmann law to first determine whether or not an exoplanet falls in the right temperature range? Then when we learn more information, adjust the habitable zone for that specific exoplanet accordingly.

If we use our sun and Earth as an example, and calculate the distance Earth must be (as a "black body") from the sun to have surface temperatures between 0°C and 100°C, we get:

SQRT(((695,500,000² x 5,778⁴) / 374.15⁴) / 4) = 83,378,738,826 meters (0.56 AU)
SQRT(((695,500,000² x 5,778⁴) / 274.15⁴) / 4) = 155,603,658,580 meters (1.04 AU)​

If we knew nothing about the conditions on Earth, then 0.56 AU to 1.04 AU seems like a reasonable first estimate. Once we learn of Earth's albedo (32.5% ± 2.5%), for example, we can adjust the habitable zone accordingly:

(5,778 x SQRT( 695,500,000 / (2 x 149,597,870,700))) x 0.675^0.25 = (5,778 x 0.04821) x 0.906412 = 252.5°K (-20.65°C)​

Again, the -20.65°C mean surface temperature only takes into account Earth's albedo, and does not include Earth's atmospheric composition and pressure. Since the current mean surface temperature of Earth is actually +14.8°C, then the 35.45°C difference must be the result of radiative forcing in the atmosphere due to greenhouse gases.

Furthermore, the actual mean surface temperature of an exoplanet could tell us about its atmospheric pressure, once we learn about the exoplanet's atmospheric composition.

It just bothers me when they make assumptions about whether or not exoplanets fall in the habitable zone of its star when they have no data about the exoplanet, other that it's orbit. They should be determining habitable zones based upon the information they actually have, until more is known, and leave out all the assumptions.

What do you think? Or am I way out in left field?

Well, if you "don't assume an albedo" like you suggest here (i.e. work with black bodies), really what you're doing is "assume an albedo of 0". If that's the assumption you prefer, then go ahead and use it, nobody stops you. But materials of albedo 0 are rare, even black asphalt has an albedo of .05 to .1 or something like that. I suppose most scientists would prefer to use a perhaps more likely assumption for the albedo based on current knowledge of planetary make up.

Again, if you "don't assume anything about the atmospheric pressure", what you're really saying is "assume 0 atmospheric pressure". Of course, with 0 atmospheric pressure, water would certainly not exist on the surface of such planets, so perhaps assuming a moderate atmosphere is not such a bad problem when it comes to considering habitability.

But of course, what assumptions you want to make is entirely up to the scientist writing the report.

 

[|Glitch|]

Calculating a "goldilocks zone" about a primary is used as a first guess.
By definition, only the orbit is needed for this calculation... your own "reasonable first estimate" uses a few assumptions - what makes you decide that these are reasonable assumptions: how did you decide? How do you know the "unreasonable" assumptions of others are unfounded?

eg. http://phl.upr.edu/projects/habitable-exoplanets-catalog/methods
... the definitions are so provide a guideline for where to concentrate resources so they tend to err on the inclusive side.
As more is known about exoplanets, and techniques get better, the searches can get narrower.
Basically nobody wants to reject a habitable planets that happens ot be on the fringes of what is currently thought possible - we just don't know enough to make a restricted list.

Some papers are better than others: your argument will be clearer if you provide references so we know better what you are talking about.

The only assumption being made using just the Stefan–Boltzmann law is that the exoplanet is a black body object. Unless that exoplanet is a black hole, I will grant you that there are no exoplanets that are a true black body objects. But when we know absolutely nothing about the exoplanet, except its orbit, should we be making assumptions about the exoplanet's albedo, atmospheric content and pressure? If it is wrong to start with the assumption that albedo, atmospheric content and pressure are zero until we learn otherwise, then it is not equally wrong to plug in values for albedo, atmospheric content and pressure when we really have no idea what those values are for the given exoplanet?

I can understand their desire to err on the side of being more inclusive, and an exoplanet with the right atmospheric content and pressure can certainly increase the outer range of the habitable zone significantly. However, that very same ideal atmospheric content and pressure that pushed the outer range of the habitable zone away from its parent star also pushes the inner range of the habitable zone further away from its parent state. So they really are not being more inclusive, they are merely changing the habitable zone range to be further away from the star. To be more inclusive would mean that the distance between the inner habitable zone and outer habitable zone should be expanded.

 

[|Glitch|]

Well, if you "don't assume an albedo" like you suggest here (i.e. work with black bodies), really what you're doing is "assume an albedo of 0". If that's the assumption you prefer, then go ahead and use it, nobody stops you. But materials of albedo 0 are rare, even black asphalt has an albedo of .05 to .1 or something like that. I suppose most scientists would prefer to use a perhaps more likely assumption for the albedo based on current knowledge of planetary make up.

Again, if you "don't assume anything about the atmospheric pressure", what you're really saying is "assume 0 atmospheric pressure". Of course, with 0 atmospheric pressure, water would certainly not exist on the surface of such planets, so perhaps assuming a moderate atmosphere is not such a bad problem when it comes to considering habitability.

But of course, what assumptions you want to make is entirely up to the scientist writing the report.

You are absolutely right, of course, the Stefan–Boltzmann law assumes the exoplanet is a black body, with zero albedo, zero atmospheric content and zero atmospheric pressure. As unrealistic as that may be, is it any more realistic to imagine an ideal atmospheric content and pressure for the exoplanet when no information is known?

If all that is known about an exoplanet is the orbit, is it even possible to calculate a habitable zone for a given star without making assumptions about the exoplanet, one way or the other?

If the atmospheric pressure of an exoplanet were zero, then you are absolutely right, there could be no liquid water on the surface of the exoplanet. However, the habitable zones as they are being calculated today assumes an atmospheric pressure of one atmosphere at the surface of the exoplanet so that liquid water can exist within a temperature range between 0°C and 100°C. If the atmospheric pressure is less than one atmosphere, then the boiling point of liquid water on the exoplanet's surface would also have to be less. Conversely, the higher the atmospheric pressure, the higher the boiling point temperature will be.

What I am really trying to determine, I suppose, is how the habitable zone of a star can be calculated while making as few assumptions as possible about the exoplanet, until we learn more.

 

[Matterwave]

You are absolutely right, of course, the Stefan–Boltzmann law assumes the exoplanet is a black body, with zero albedo, zero atmospheric content and zero atmospheric pressure. As unrealistic as that may be, is it any more realistic to imagine an ideal atmospheric content and pressure for the exoplanet when no information is known?

If all that is known about an exoplanet is the orbit, is it even possible to calculate a habitable zone for a given star without making assumptions about the exoplanet, one way or the other?

What I am really trying to determine, I suppose, is how the habitable zone of a star can be calculated while making as few assumptions as possible about the exoplanet, until we learn more.

As you are quickly finding out, you really can't find a habitable zone without some assumptions being made. 0 atmospheric pressure means no liquid water period. Below the triple point of water, you can't have liquid, only ice and water vapor/steam. So if you are strict in enforcing "no atmosphere" then you must say the habitable zone around any star is non-existent.

Again if you want to assume a black body that's up to you. But I don't see that as any more or less of an assumption than A=.25, after all, you're simply choosing A=0.

The only thing you can do with certainty when it comes to habitable zones is you can rule out where the habitable zone can't be. For example, very close to the star, there can not be any liquid water on the surface of a planet, it will fizzle away no matter how much albedo your planet has (other than 100% I guess...but that's not reasonable). Too far from the star, no amount of green house heating will allow your planet to be hot enough to have liquid water. But this is really all we can do "with certainty".

All the rest requires some assumptions, some educated guessing.

 

[|Glitch|]

As you are quickly finding out, you really can't find a habitable zone without some assumptions being made. 0 atmospheric pressure means no liquid water period. Below the triple point of water, you can't have liquid, only ice and water vapor/steam. So if you are strict in enforcing "no atmosphere" then you must say the habitable zone around any star is non-existent.

Again if you want to assume a black body that's up to you. But I don't see that as any more or less of an assumption than A=.25, after all, you're simply choosing A=0.

The only thing you can do with certainty when it comes to habitable zones is you can rule out where the habitable zone can't be. For example, very close to the star, there can not be any liquid water on the surface of a planet, it will fizzle away no matter how much albedo your planet has (other than 100% I guess...but that's not reasonable). Too far from the star, no amount of green house heating will allow your planet to be hot enough to have liquid water. But this is really all we can do "with certainty".

All the rest requires some assumptions, some educated guessing.

It would appear that you are right. Apparently some assumptions must be made about the exoplanet, one way or the other, in order to calculate the habitable zone of a star. It just really bothers me to make any assumptions at all. Science is not about making assumptions.

I agree that assuming an exoplanet has an albedo of 1 is just as unreasonable as assuming an exoplanet has an albedo of 0.

The absolute minimum surface atmospheric pressure for liquid water to exist is 7 millibars at a temperature of 0.01°C. Anything less than 7 millibars and ice sublimates away as soon as the temperature is above 0°C. The critical point for liquid water is 218.3 atmospheres at 374.15°C, when water vapor and liquid water become indistinguishable. However, I would not consider either of those extremes to be "habitable", even though liquid water can exist.

"Habitable zone" is really a misnomer. What it should really be called is the "Stellar Liquid Water Zone."

 

[Matterwave]

Yes, "habitable zone" is kind of a misnomer.

 

[Simon Bridge]

When we talk about habitable planets we are really talking about habitable candidates ... the popular press just get a bit carried away.
So it is saying - provided the planet fits in a generous range for what we know about planets, then there is a fair chance that there would be liquid water on the surface. Once identified like that, more resources can be allocated to the particular system to, say, figure if there is any evidence for an atmosphere.

The initial assumption numbers are not picked out of a hat though - we know what sort of albedoes planets have and what sorts of atmospheres to expect ... assuming planets in our solar system are not fringe outliers in the scheme of things. Of course we may not have been making good assumptions about the kind of things that affected our own solar system. Further investigation will tell us about those assumptions and also about our own solar system as a result.

And that is kinda the point - investigating exoplanets, at this stage, is more about learning about our own solar system and the assumptions we have about it so far than it is about learning about the exoplanets for themselves.

The assumptions you choose should speak to the purpose of the investigation.

 

[|Glitch|]

I appreciate the feedback, it has given me a lot to think about.

As Simon advises, the purpose of the investigation is to determine whether or not complex life could exist on an exoplanet, given its distance from its parent star. That narrows down the criteria considerably from merely finding an exoplanet that can support liquid water. In order for H₂O to be in a liquid form it must have a minimum atmospheric pressure of 0.0069 atm at 0.01°C, and a maximum of 218.3 atm at 374.15°C. However, to be considered "habitable" (as in able to support complex life) the minimum atmospheric pressure should be greater than 0.306 atm and 0.01°C, and less than ~3 atm at 35°C.

The atmospheric pressure at the peak of Mount Everest is 0.306 atm, and to my knowledge there is no complex life form that evolved or ever lived in under such low pressure on Earth. With regard to the maximum atmospheric pressure, I came across this interesting article:

Through their modeling, Vladilo and colleagues saw that the habitable zone expanded in width as the atmospheric pressure increased. At a tenth of Earth’s atmospheric pressure, the outer edge of the habitable zone reached just two percent farther out than Earth; not a lot of wiggle room for a low-pressure, Earth-like world, in other words, when it comes to habitability. But as the atmospheric pressure increased to threefold that of Earth’s, the habitable zone extended out a farther 18 percent.

For the same pressure interval, low-to-high, the inner edge of the habitable zone ranged from 87 percent of the Earth-Sun distance to 77 percent. In this model, for a planet with Earth’s atmospheric pressure, cloudiness, and humidity, the inner edge of the habitable zone is smack dab in the middle of this range, at 82 percent of the Earth-Sun distance.

The results indicate that an exoplanet just like Earth in all other respects but with a higher atmospheric pressure could be considered habitable about five percent closer to its Sun-like star. Conversely, a low-pressure Earth would not be considered habitable unless placed in an orbit five percent farther out than a standard-pressure Earth.

Source: [/PLAIN]
Under Pressure: How the Density of Exoplanets' Atmospheres Weighs on the Odds for Alien Life - Astrobiology Magazine

The reason I chose a maximum temperature of 35°C is because of the Permian/Triassic extinction event. We know that the mean surface temperatures around the equator 250 million years ago ranged between 35°C and 40°C. We also know that there are no fossils in the rock layer that was formed at the equator at the Permian/Triassic boundary. Our observations suggest a "dead zone" existed between 15° north and south of the equator 250 million years ago, where no complex life existed in either the sea or on land. Therefore, a mean surface temperature no higher than 35°C seems like a good educated guess as to the upper limit for the temperature range of complex life forms.

When it concerns albedo we have objects in our solar system with an albedo as high as 0.99 (Saturn's moon Enceladus) and as low as 0.04 (some asteroids in the asteroid belt). If we look at only the planets, there is still a huge range between Mercury (0.068) and Venus (0.9). All the other planets range between 0.25 (Mars) and 0.343 (Jupiter). If you exclude Mercury and Venus as outliers, and average the albedo of the other six planets you get an average of 0.3052. While I grant you that six planets is not much of a sample to go by, an albedo of 0.30 is an educated "best guess" when applied to exoplanets.

Without having at least some idea about the composition of the atmosphere, it is impossible to even hazard an educated guess about how much heat is retained in the atmosphere. Can we make an educated guess as to the composition of an atmosphere in order for complex life to consider it habitable? Or can atmospheric composition vary considerably on exoplanets and still support complex life?

 

[Simon Bridge]

etc etc etc
You can ask, for eg, given the range of parameters for a planet to be a "habitable" - where should we look for one?
And: how good-a fit are any of the ones we know about?
... you get to pick what you like and write a paper on it and see if it gets published.

Hopefully you have a better idea about how such decisions get made now.

 

[Matterwave]

I think at this point we would be very excited if we even found microbial life on other planets, and we shouldn't limit ourselves to "complex life". SETI is looking for intelligent life, the search for habitable exoplanets is probably more focused towards any kind of life. In fact, here on Earth, the organisms that most affected its atmospheric composition are not very complex lifeforms (algae and cyanobacterial mostly, which gave us our oxygen rich atmosphere), and a particular "organic atmosphere" might be one of the key features we might look for in an exoplanet in terms of signs of life, since sending a spaceship there is probably not within the realm of feasibility in the near future.

 

[|Glitch|]

etc etc etc
You can ask, for eg, given the range of parameters for a planet to be a "habitable" - where should we look for one?
And: how good-a fit are any of the ones we know about?
... you get to pick what you like and write a paper on it and see if it gets published.

Hopefully you have a better idea about how such decisions get made now.

I still do not like all the assumptions that are being made in the absence of actual data, because we could be leaving out, or including, exoplanets that we should not. At the very least there should be a huge "fudge factor" where we should say that we do not know either way - yet. However, I completely agree with you that it depends on how one forms the question that determines the criteria.

 

[Simon Bridge]

still do not like all the assumptions that are being made in the absence of actual data,...

... you don't have to.
If you think you can do better, you are welcome to write the paper.

At the very least there should be a huge "fudge factor" where we should say that we do not know either way

That s what gets done ... it is implicit in the way the calculation is set up. Everyone in the field understands this.
What sources are you using?

 

[|Glitch|]

I think at this point we would be very excited if we even found microbial life on other planets, and we shouldn't limit ourselves to "complex life". SETI is looking for intelligent life, the search for habitable exoplanets is probably more focused towards any kind of life. In fact, here on Earth, the organisms that most affected its atmospheric composition are not very complex lifeforms (algae and cyanobacterial mostly, which gave us our oxygen rich atmosphere), and a particular "organic atmosphere" might be one of the key features we might look for in an exoplanet in terms of signs of life, since sending a spaceship there is probably not within the realm of feasibility in the near future.

At this point, I completely agree with you. Any form of extraterrestrial life would be a momentous discovery.

However, this exercise of trying to determine the habitable zone is part of a larger question concerning the Fermi Paradox, which I will not get into here since that would divert the purpose of this thread.

 

[|Glitch|]

... you don't have to.
If you think you can do better, you are welcome to write the paper.

That s what gets done ... it is implicit in the way the calculation is set up. Everyone in the field understands this.
What sources are you using?

I suppose that is what I am trying to determine - can I do better? I do not have an answer to that question - yet.

The source I have been using comes from:

[URL='http://arxiv.org/pdf/1301.6674v2.pdf']Habitable Zones Around Main-Sequence Stars: New Estimates[/url] --- arVix : 1301.6674v2 [PDF]​

However, the above source assumes carbon dioxide in the atmosphere. While carbon dioxide is certainly a greenhouse gas, there are other greenhouse gases with more radiative forcing, such as water vapor and methane.