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Midas

White Dwarfs

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Calling upon the massed HERO wisdom:

 

What is the habitable zone of a white dwarf?

 

What would be the surface area of a Dyson Sphere (the solid kind) around a White Dwarf, at said habitable zone?

 

Assuming a depth large enough that tree roots wouldn't stick out the other side, (say 1/2 mile) what is the volume, in earths, of such a sphere?

 

Is there enough debris around a WD to consider such a project?

 

What is the life expantancy of a stable white dwarf?

 

Any other things I need consider without calling upon Clark's Maxim?

 

Thanks in advance,

Midas

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Re: White Dwarfs

 

If you're wanting to build a habitable structure which could (theoretically) last for the life expectancy of a stable white dwarf, there is one more thing to take into account.

 

White Dwarfs cool over the course of their lifetime, starting out extremely hot (150,000 K or more) eventually cooling to thermal equilibrium and becoming a 'black dwarf.' The 'habitable zone' will gradually migrate inwards as the white dwarf cools, so building a permanent structure in the habitable zone could be a problem.

 

However, the cooling process slows down after a while, so once a white dwarf is a few billion years old, it may be stable enough for a dyson sphere in its habitable zone to remain habitable for a few billion more.

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Re: White Dwarfs

 

If you're wanting to build a habitable structure which could (theoretically) last for the life expectancy of a stable white dwarf, there is one more thing to take into account.

 

White Dwarfs cool over the course of their lifetime, starting out extremely hot (150,000 K or more) eventually cooling to thermal equilibrium and becoming a 'black dwarf.' The 'habitable zone' will gradually migrate inwards as the white dwarf cools, so building a permanent structure in the habitable zone could be a problem.

 

However, the cooling process slows down after a while, so once a white dwarf is a few billion years old, it may be stable enough for a dyson sphere in its habitable zone to remain habitable for a few billion more.

 

 

How fast does it cool down? Because it seems to me all you have to do is build big spires pointing inwards and keep "raising" part of the surface inwards to compensate for the warming. You would need two layers, the outer one being a full sphere and the inner one consisting of raised blocks and "walls" which seal off the area under the raised blocks from the blocks that haven't been raised yet. When the new surface is completed the old outer surface is cannibalised and the new surface becomes the outer shell. If we're talking millions of years of cooling time per move I think doable with the energy from a white dwarf. The spires would double as things to move large masses in and out to cope with the inherent instability of a Dyson sphere.

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Re: White Dwarfs

 

How fast does it cool down? Because it seems to me all you have to do is build big spires pointing inwards and keep "raising" part of the surface inwards to compensate for the warming. You would need two layers' date=' the outer one being a full sphere and the inner one consisting of raised blocks and "walls" which seal off the area under the raised blocks from the blocks that haven't been raised yet. When the new surface is completed the old outer surface is cannibalised and the new surface becomes the outer shell. If we're talking millions of years of cooling time per move I think doable with the energy from a white dwarf. The spires would double as things to move large masses in and out to cope with the inherent instability of a Dyson sphere.[/quote']

 

Assuming the tech existed to build a dyson sphere to begin with, this solution should work. The cooling process actually takes billions of years.

 

Bergeron, Ruiz, and Leggett, for example, estimate that after a carbon white dwarf of 0.59 solar mass with a hydrogen atmosphere has cooled to a surface temperature of 7,140 K, taking approximately 1.5 billion years, cooling approximately 500 more kelvins to 6,590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6,030 K and 5,550 K) take first 0.4 and then 1.1 billion years.[62], Table 2.

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Re: White Dwarfs

 

Calling upon the massed HERO wisdom:

 

What is the habitable zone of a white dwarf?

 

What would be the surface area of a Dyson Sphere (the solid kind) around a White Dwarf, at said habitable zone?

 

Assuming a depth large enough that tree roots wouldn't stick out the other side, (say 1/2 mile) what is the volume, in earths, of such a sphere?

 

Is there enough debris around a WD to consider such a project?

 

What is the life expantancy of a stable white dwarf?

 

Any other things I need consider without calling upon Clark's Maxim?

 

Thanks in advance,

Midas

 

BTW a Dyson Shell (what you are calling a Dyson Sphere) is inherently unstable in orbit. It would require some sort of engine/thrust to remain in orbit and not go wonky and crash into the star. Apparently parts of the sphere are gravitationally neutral to the star and this could cause said instability. Orbital instability is a problem with a number of megastructures including NivenRings, and Klemperer rosettes.

 

What Dyson had envisioned was a set of satellites that orbited around the star which could include habitats and a bunch of power collectors. It idea being to collect a high percentage of the solar output. The problem comes when the orbits are close enough to interact with other orbits or there are still other bodies in the system that can interact gravitationally with the spheres/swarm/bubble elements.

 

The Wikipedia article on these megastructures can tell you more about them.

 

Niven's ring world was 250m thick that should be enough to keep roots from being a problem. Also any structure like a NivenRing or a Dyson Shell, would require a VERY VERY strong material. Also there might not be enough material available in a single system (and that assumes a system like ours, a WD probably has less mass than we do.) to create a Dyson shell (assuming that you could turn most of the matter into the unobtanium needed for the floor of the shell). I have heard that a good star type to build a mega structure around would be a Low mass Red Dwarf, since it would burn for a VERY long time and not balloon into something that would eat your megastructure.

 

http://en.wikipedia.org/wiki/Dyson_sphere

http://en.wikipedia.org/wiki/Niven_ring (The meaty stuff about ringworld engineering follows the books synopsis)

http://en.wikipedia.org/wiki/Klemperer_rosette

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Re: White Dwarfs

 

one proble with white dwarfs (until they have cooled A LOT) is that they put out hight levels of HHigh frequency stuff like Ultra Violet, x-ray and gamma, meaning you probably need an extra "strong" filter of an atmosphere

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Re: White Dwarfs

 

Calling upon the massed HERO wisdom:

 

What is the habitable zone of a white dwarf?

Depends on the luminosity (total power output) of the white dwarf, which depends on its radius and its surface temperature. I've found mass-radius relations for white dwarfs easily (there's one on Wikipedia), but I haven't found cooling curves (temperature as a function of time) at all. White dwarfs are simply cooling off forever, their nuclear energy sources exhausted.

 

HOWEVER... I did blunder across a time-luminosity relation (here) that indicates that luminosity goes roughly as time to the -5/7 power.

 

Wait long enough and the cooling rate gets pretty slow, but "long enough" is probably about a billion years.

 

The size of the habitable zone can be estimated crudely as (R / AU) = (L / Lsun)^1/2, where here R is the size of the orbit and AU is one astronomical unit, the size of Earth's orbit. So mash all those with some algebra, and you should be able to get a relation for the radius of the habitable zone as a function of time. And it MUST vary with time, getting smaller as time goes on, because the luminosity of white dwarfs decreases with time.

 

So I plugged in that billion years of cooling, got a luminosity, and estimated a habitable zone radius, and I get 0.0364 AU.

 

What would be the surface area of a Dyson Sphere (the solid kind) around a White Dwarf, at said habitable zone?

 

0.0166 square AUs. At 1.5e+8 km per AU, that's 3.75e+14 square kilometers, or about 736,000 times the surface area of Earth.

 

Assuming a depth large enough that tree roots wouldn't stick out the other side, (say 1/2 mile) what is the volume, in earths, of such a sphere?

Choosing one km thick, that's 3.75e+14 cubic kilometers, which is about 347 times Earth's volume.

 

Is there enough debris around a WD to consider such a project?

Depends on when you try making it. When a white dwarf forms, the envelope of a red giant star is detaching from its dying core; the latter becomes the white dwarf. Ejecting the envelope means pushing at least half a solar mass of envelope (and up to 7 or so solar masses of envelope) out into space, at first making a planetary nebula. That's more than enough material for this; one earth mass is about 3e-6 solar masses. Although only about 1% by mass of solar material is stuff other then hydrogen and helium (which aren't useful for making a solid sphere), there's plenty of matter there. Probably another factor of several (no more than 10) needs to be applied since lots of the most abundant heavy elements are things that are of limited utility in making such a sphere (oxygen is #1, and some but not all of it can be used; neon is useless; nitrogen isn't too useful, etc.).

 

The problem is that this material is ejected "quickly", over a few hundred thousand years, when the newly formed white dwarf is still very hot and cooling very quickly. Much of that envelope is heated up to temperatures up to 100,000 Kelvin, and its density gets very, very low; the nebula disperses in about 100,000 years, but it's expanded to the extent that it's just interstellar gas at the end of it. Speaking strictly about the white dwarf itself, by the time its own cooling has slowed down to the point where the temperature (and hence habitable zone radius) is changing slowly enough to be useful, that matter is long, long gone.

 

What is the life expantancy of a stable white dwarf?
Effectively infinite; I expect this is a bit longer than the life of a proton. The cooling of the white dwarf will render your Dyson sphere uninhabitably cold first.

 

Any other things I need consider without calling upon Clark's Maxim?
Interesting idea, one I hadn't thought of before.

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Re: White Dwarfs

 

Calling upon the massed HERO wisdom:

 

What is the habitable zone of a white dwarf?

Depends on the last time he had a bath and if he has been eating chilli.

 

What would be the surface area of a Dyson Sphere (the solid kind) around a White Dwarf, at said habitable zone?

 

Assuming a depth large enough that tree roots wouldn't stick out the other side, (say 1/2 mile) what is the volume, in earths, of such a sphere?

about 100 square meters?

 

Is there enough debris around a WD to consider such a project?

Depends on if his wife has had time to clean after him.

 

What is the life expantancy of a stable white dwarf?

Well assuming you could find one who wasn't completely bonkers about 400yrs.

 

Any other things I need consider without calling upon Clark's Maxim?

I would think a elf would be better but to each his own I say:)

Thanks in advance,

Midas

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Re: White Dwarfs

 

Out of curiosity' date=' what is "Clark's Maxim"?[/quote']

 

I believe it is "any suitably advanced technology is indistinguishable from magic"

 

That's the one I was going for. Didn't Clark also promote "The universe is not only stranger than we imagine, it is stranger than we can imagine."? Apropo, but not as much as the tech=magic one.

 

Thanks to everyone for their thoughtful replies. I'll give a longer reply later when I've masticated the info.

 

Midas

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Re: White Dwarfs

 

What is the habitable zone of a white dwarf?

 

Depends on the last time he had a bath and if he has been eating chilli.

 

 

about 100 square meters?

 

For a WHITE dwarf, that is about right. One has to be wary of the superficially similar WIGHT dwarf, around whom a 100 square meter circle is completely uninhabitable.

 

Midas

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Re: White Dwarfs

 

more Dyson Sphere links:

 

http://www.alcyone.com/max/writing/essays/outside-dyson-shells.html (this link has some of the math you are looking for and talks about why one would want to use a red dwarf star)

 

where k is a constant of proportionality and nu is a constant somewhere between 3.5 and 4.0. (k naturally depends on the choice of nu, clearly.)

 

"Variables won't and constants aren't!"? :cool:

 

I'm working my way through the math and physics involved, slowly (Unsophisticated hick think MIT something to catch ball with, not something to assign for stellar volume computation - Should not have two "t's"?). :confused:

 

I tried answering post by post, but it's almost like trying to transcribe a chat session. :ugly::D I'll try to post my thoughts line by line, instead.

 

The reason I chose a white dwarf was because of the obvious problem with a DysonSHELL (thanx for that BTW, useful distinction :thumbup: ) around a main sequence star: The huge tonnage involved in making a sphere 1AU in radius. Drop the radius down to 0.035 and you get a reasonable volume, comparatively.

 

Midas

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Re: White Dwarfs

 

OK, re the debris available:

 

As I understand it, a white dwarf is the third stage of a large main sequence star. The main sequence star changes into a supergiant when it reaches a proportion of fuel. Then it collapses into a white dwarf at another tipping point. In the first event, the star expands out into the gas giant orbits, and absorbs anything within its diameter. Does it vaporise the rest of the planets out to the Kuyper belt and the comets in the Oort cloud?

 

If not, at the second "lifechange" when the nebular cloud is expanding, same question.

 

Where I'm coming from is whether our high tech aliens can harvest the outer plutoids and comets or have to go with the more difficult task of rounding up and condensing solid elements out of the expanding gas envelope.

 

Midas

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Re: White Dwarfs

 

"Variables won't and constants aren't!"? :cool:

That "L = k M^nu" is an approximation of reality. Like all "scaling laws", it is a rule-of-thumb made up from the results of more detailed, more rigorous calculations; the rule of thumb is useful for quick & dirty calculations exactly like these that we're doing here. There's nothing fundamental about it.

 

It happens, that when you look at main sequence stars of around 1 solar mass, the luminosity at zero age [note luminosity increases with time, too, for any single main sequence star!] scales approximately like stellar mass to a power that is in the range 3.5 to 4. Stellar composition (whose effects are not included in that rule of thumb, but does vary from star to star) affects that exponent; so do some other factors. The value of k depends on what case you pick to be your fiducial case.

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Re: White Dwarfs

 

Welcome to ASTR 432, Stellar Interiors & Evolution. :straight:

 

As I understand it' date=' a white dwarf is the third stage of a large main sequence star. [/quote']

Not "large". Single stars less massive than 8 solar masses or so are believed to end up as white dwarfs. Stars more massive than 8 solar masses, which are high mass stars, do other things, like explode as Type II (or "core collapse") supernovae.

The main sequence star changes into a supergiant when it reaches a proportion of fuel.
Red giant, not supergiant. The term supergiant carries with it the implication of large mass, like 10 or more solar masses. Red giants are post-main-sequence stars, with extended envelopes (i.e., a large stellar diameter), no energy generation by means of fusion of hydrogen in the very center of the star, but perhaps several "shell sources", thin spherical shells around the core in which nuclear fusion is going on, generating energy. If there are any such shell sources, the outermost one of them will be a hydrogen fusion source.

Then it collapses into a white dwarf at another tipping point.

If it makes a white dwarf, the star never actually "collapses". The thing that becomes a white dwarf has been present in the core of the star for a long time. It has slowly contracted, but never "collapsed". That thing is "degenerate" (a condition that happens at very high densities; describing what that is is beyond our purposes here) and is not hot enough to initiate nuclear fusion of any of the nuclei in it. (In effect, any stuff that could be fused at the temperatures there has already been completely used up, leaving behind nuclei that need a higher temperature to get the reactions started.) Around that degenerate core -- which is physically small, about the size of Earth, but typically has a mass between half and 1 solar masses -- is a shell source where stuff is fusing, and the fusion products are adding to that core.

 

Shell sources are extremely hot, and in a manner of speaking, the presence of a high-temperature fusion source away from the center of the star causes the material above it to expand. This is what causes the "red giant" appearance of post-main-sequence stars.

 

If the addition of fusion products to that central core is enough to make it dense enough and hot enough to initiate fusion in the stuff that's in there, then it "flashes" -- lots of it fuses immediately in a thermal runaway -- causing a rapid, violent alteration in the stellar structure; the shell source(s) get extinguished; the envelope contracts some, though never all the way back to what it was like on the main sequence.

 

If it doesn't get hot/dense enough to start the next fusion reaction, then the envelope continues to expand. In a process that is not well understood, all or nearly all the envelope ends up expanding right off into space, detaching from the core in a nonviolent way. As the envelope thins out the envelope becomes exposed to the radiation from the core (which is still at temperatures well over 100 million kelvin) and is photoionized, making a lovely but temporary structure called a "planetary nebula". The term "planetary" refers to how it looks to the eye peering through a small telescope at one: they are round and sort of greenish in color, which is sort of similar to how planets of our Solar System look to people peering through small telescopes. The term "planetary" has nothing to do with planets otherwise.

 

When the envelope detaches, the old hot core that's been there all along is exposed to view for the first time, and while there's some interesting transient things that might happen right as this is going on, that exposed hot core is a white dwarf.

In the first event, the star expands out into the gas giant orbits, and absorbs anything within its diameter. Does it vaporise the rest of the planets out to the Kuyper belt and the comets in the Oort cloud?

 

If not, at the second "lifechange" when the nebular cloud is expanding, same question.

 

Where I'm coming from is whether our high tech aliens can harvest the outer plutoids and comets or have to go with the more difficult task of rounding up and condensing solid elements out of the expanding gas envelope.

There's some complications here that aren't known. Late in the red giant stage, the star does start losing mass at a rate that can be important. One of the things that goes on when you lose mass is that you also lose gravitational binding energy for anything orbiting the star. The orbits of such things get bigger. Lose enough mass and the planets and other stuff can have their orbits become unbound. (If you remove 50% of the mass in the system in one sudden go, then everything goes unbound, but steal it away gently and then orbits change, perhaps without going unbound.) The exact history of such mass loss isn't known well enough to make strong statements how many planets escape, though certainly some do. OTOH, if the expanding stellar photosphere touches a planet, the gas drag on the planet "instantly" (i've seen a paper saying this happens in about 300 orbits, that is, about 300 years from first contact to complete destruction) decays its orbit and the planet is engulfed and destroyed.

 

I don't think there's enough energy in the nebula to destroy a non-engulfed planet, even a small one like Mars, and certainly not a jovian planet. The asteroids are more complicated and I don't know about them.

 

My guess is that the Kuiper Belt objects will escape as their orbits go unbound. These could be harvested, I guess, but there's not much matter there: the total mass in KBO's now is estimated to be only a tenth of an Earth mass. So harvesting them may be easy but it's a drop in the bucket for what you need to collect to make a Dyson sphere.

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Re: White Dwarfs

 

"Variables won't and constants aren't!"? :cool:

 

I'm working my way through the math and physics involved, slowly (Unsophisticated hick think MIT something to catch ball with, not something to assign for stellar volume computation - Should not have two "t's"?). :confused:

 

I tried answering post by post, but it's almost like trying to transcribe a chat session. :ugly::D I'll try to post my thoughts line by line, instead.

 

The reason I chose a white dwarf was because of the obvious problem with a DysonSHELL (thanx for that BTW, useful distinction :thumbup: ) around a main sequence star: The huge tonnage involved in making a sphere 1AU in radius. Drop the radius down to 0.035 and you get a reasonable volume, comparatively.

 

Midas

 

A couple of issues you have to deal with with a Dyson Shell, that you don't have to worry about with Dyson's original ideas.

 

1) How do you get enough solid materials to make the shell (this one you have to worry about a bit with the swarm, and other sphere ideas, but not as much)

2) Assuming that you are going to inhabit the inside of the shell, how do you keep the atmosphere from falling into the sun?

3) If you decide to spin the whole thing to give the structure fake gravity, then the thickness of the shell increases by a huge amount. Also the material the shell is made of must be unnaturally strong.

4) Again, the shell will be very unstable in it's orbit and anything that hits it or anything left that can interact with it gravitationally will quickly destabilize the structure catastrophically.

 

 

One strange idea that I read for using a Shell, was to inhabit the outer shell, and use the inner shell for energy generation. Apparently the shell would be warm enough to keep people alive and that the inner sun and structure of the Shell would generate enough gravity to keep a breathable atmosphere in place. Though to grow earthlike green photosynthesizing plants would require the generation of the correct kind of light. Which I guess could be done using all of that energy that you are trapping from the sun inside the shell.

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Re: White Dwarfs

 

If the white dwarf has a strong magnetic field, would it be possible to use the inner shell for power generation, and then use the power to keep the sphere stable by interacting with the magnetic field?

 

Magnetic force >>> gravity.

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Re: White Dwarfs

 

Does the shell have to be rigid? Could it be relatively thin and supported by radiation pressure and/or stellar wind pressure?

 

Stellar wind might be less effective coming off a white dwarf compared to other stars -- but IANAA. (I Am Not An Astrophysicist.)

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Re: White Dwarfs

 

Does the shell have to be rigid? Could it be relatively thin and supported by radiation pressure and/or stellar wind pressure?

 

It has to withstand people living somewhere on the shell. It also has to be strong enough to not break apart when things like the solar wind strike it's surface.

 

Questions like these are why Dyson never proposed a solid shell. He proposed a group of closely orbiting satellites (ie like orbiting habitats) that would be able to use a large percentage of the energy output of a sun. I am not an astrophysicist either, but I can read and google "Dyson Sphere, Dyson Shell, Ringworld". There are a ton of great sites out there that explain in plain english what is possible and what isn't and why.

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