# Encasing a star in a perfect insulator

Suppose that I have come into possession of a substance, technology, or spell that functions as a perfect insulator and reflector. No energy can pass through it, and is instead reflected back the way it came.

Now suppose that I completely encase a star in this stuff, cutting off any radiation of heat or magnetic fields from the star. This should have the effect of preventing the star from releasing heat by radiation, leaving the heat to build up indefinitely.

Theoretically, then, what would be the effect of this on the star itself? Does removing the ability to release heat change the behaviour of the star in any way?

• Well, supposedly, less energy would be lost so the star would simply last longer? Nov 11, 2016 at 17:00
• This is a cool hypothetical question...if you disallow an explosion...would it go out like a candle under a cup? Nov 11, 2016 at 17:02
• A candle is dependent upon external oxygen, a sun is not. Nov 11, 2016 at 17:09
• How close is the shield to the star? Stars don't have a well-defined surface, by the way, so you're going to have a region where there is a density dropoff but not a perfect vacuum. Radiation will still be emitted. Nov 11, 2016 at 17:39
• Extremely similar, if not the same: physics.stackexchange.com/q/20567/56299, physics.stackexchange.com/q/177991/56299. Nov 11, 2016 at 17:45

What you describe looks like a border case for a Dyson sphere. Its effects would depend on what the sphere is capable of.

# Simple reflection

I think that nothing much would happen (but I'm definitely not an astrophysicist). A star is a large fusion explosion happening, and it exists in hydrostatic equilibrium between its gravitational force (that tends to pull it inwards) and the thermal energy release (that tends to have it balloon into a nebula).

Reflecting back the whole radiative output of the star would lead to a negligible rise in temperature (where it counts, temperature is on the order of millions of K), and the star would proceed slightly along the main sequence - it would "age" a little faster, and probably its evolution would be skewed, so that in a couple billion years a borderline yellow dwarf might behave like an orange dwarf. Also, incredible as it may seem, a star is actually quite opaque and already not as good a thermal conductor as you might think, so upping the opacity to 100% isn't so radical a change.

Actually, something sort of like that already happens in some stars - the so-called Cepheid variables. In those stars, mass and temperature combine in such a way that a whole layer of the star finds itself in a condition with some properties of your handwavium sphere; namely, its radiative opacity is markedly lower than normal, and some energy is reflected back into the core. This makes the star age faster and burn hotter, but the raised temperature converts the handwavium layer back into transparency; the extra energy is radiated away and the star appears more luminous for a while. Then, the energy loss cools the star a bit, and the handwavium layer re-forms, and the cycle begins anew. This is called the Kappa mechanism.

Partially reflecting the output (e.g. leaving an exhaust nozzle, or using a Dyson semisphere) would result in thrust being applied to the whole assembly.

# Simple reflection, with unstable star

If the star were exactly in the right and unlikely condition - a hot, blue star with recent massive low-metallicity mass influx (typically from a binary companion or passer-by star), which by the way would be probably enough to trigger a star explosion - then the handwavium sphere could induce a runaway fusion process in a much-larger-than-normal volume of the star. Normally the star would get rid of the excess energy by massive flaring or further expanding, followed by cooling, and all you would get is a planetary nebula. This might be, roughly, what is now happening with the star Eta Carinae.

# Reflection and containment

If the handwavium is able to sustain the pressure increase as well as the radiation, then the star might undergo photodisintegration, or the instability might reflect inwards, lead to a core collapse, and we get to see whether the handwavium can withstand a supernova explosion. If it can't, the braking effect should be enough to trasform it into a hypernova explosion (roughly the same bang, but much more luminous).

# Reflection and indestructible containment

Otherwise, a supernova-proof reflecting enclosure would be a sure-fire method to guarantee that any star above the Landau limit - we should probably factor in some higher-than-normal neutrino loss - would ultimately collapse into a black hole. It couldn't happen to the Sun, since this limit is about 1.5 solar masses. "Ultimately", because the time to do so could well be of the order of magnitude of a normal star lifespan, especially if the star isn't too big and energetic to start with.

(It has been pointed out to me that such an enclosure would already be a black hole unless examined from planetary distances. For it would be a zone from which "nothing can exit, not even light", and yet there would be a gravitational field associated with the mass of the enclosed star).

# Life outside the edge

A semi-permeable or locally-permeable handwavium enclosure with the appropriate radius (to ensure a suitable surface gravity) would also be habitable (a true Dyson sphere). The energy sources would be "wells" drilled in the enclosure, which could then spew out plasma at a temperature of several tens of thousands of K. Using high-altitude passive radiators with a temperature below 300 K, this would yield a thermal efficiency in excess of 97-99% with almost no other technology - a simple heat engine made of handwavium would do.

• Wouldn't any black hole capable star also have enough energy, that it would become gravitationally unbound by all the heat released in the nuclear reactions, which would necessarily happen before core collapse could happen? So no black hole, unless the enclosure is very big, to allow the core to cool enough to be able to collapse? ...or unless the star was big enough to just collapse to black hole directly and never become a real star, but I guess that is out of scope here.
– hyde
Nov 12, 2016 at 12:14
• It's not quite a black hole. An event horizon is a one-way door, not a wall. Nov 12, 2016 at 18:57
• The Sun can't become a black hole naturally. I suspect that if you enclosed it in a perfectly solid insulator, the pressure and heat would increase so much that it would form pockets with density high enough to form a black hole. After all, black holes don't really have a lower limit on mass - the "1.5 solar masses" thing is just the point where gravity is strong enough to cause the collapse. If you use something else, the limit doesn't apply. Nov 13, 2016 at 10:53
• @hyde, we are dealing with an "impossible" border condition, so anything might happen. For a not too massive star, I expect it to evolve to a "solid" nucleus of heavy elements up to iron, absorbing a lot of energy through endothermal reactions, and a hot "atmosphere" at relatively high pressures with temperatures on the order of 10<sup>7</sup> K. At that point, conditions for gravitational collapse might still hold, but I wouldn't dream of attempting to estimate them. Nov 13, 2016 at 12:08
• @chepner you're right, I expressed myself badly. I meant that from a sufficient distance, there would not be a significant difference between a handwavium-enclosed star and a black hole (except for the absence of a flaring accretion disk and a difference in gravitational lensing, both observable at stellar distances). Nov 13, 2016 at 12:10

I disagree with the "nothing much" answers, since what you are describing is the key (in much smaller scales) for "Star Lifting" and "Shkadov Thrusters"

One of the methods to initiate "Star Lifting" is to beam energy back at the star using an energetic laser or even a system of mirrors to concentrate and focus the starlight on a point on the star. The extra energy begins to heat the local area, which responds eventually by emitting plasma. The Shkadov Thruster takes this idea to a higher level and can actually move entire stars and solar systems (details here)

The insulating layer means the energy of the star has nowhere to go, and the local environment becomes hotter and more energetic. I suspect (although i don;t really know how to calculate this) that there will be a positive feedback loop, more energy trapped in the environment heats the solar plasma, generating more energy in the upper layers of the star, which then continues until either the pressure "blows off" the insulator (and the outer layers of the star), or the insulating properties of the insulator are overcome and it emits enough blackbody radiation to allow the system to reach equilibrium.

Now assuming the insulator is strong and "perfect" enough to let the heat and pressure bottle up to a very high level, this energy is going to bleed back into the stellar core. Now the cores of stars are running on the knife edge of dynamic stability, with the radiation pressure from the fusion reaction balancing the gravitational pressure of all the mass of the star. Increasing the temperature could destabilize the equation in either direction. The increase in temperature and pressure could act to "squeeze" the star's core and speed up the rate of fusion reactions. On the other hand, since the density of the solar plasma will be reduced because of the increasing temperature, the core could "go out" as pressure is reduced below the critical pressure for fusion reactions to continue.

The only material I could think of which might have properties like that would be a shell of neutronium, but that is unlikely since the extreme density of the material would make it a superconductor of heat rather than an insulator. Some sort of "unobtanium" could be hand waved into existence to make this happen, but certainly not anything known to physics as we currently understand it.

So the true answer would depend on what sort of properties the insulator has, and how quickly it reaches equilibrium.

• The concept of a perfect insulator always make me feel uncomfortable. What happens is depend on their unknown and, possibly. unknowable properties. My suspicion is the star will end up in equilibrium, as a stellar pressure bomb. Nov 12, 2016 at 4:04
• The top rated answer starts with "nothing much", but then goes on to explain how it would cause a supernova, and then if the supernova doesn't destroy the box, a black hole. Nov 12, 2016 at 11:59

As others have pointed, insulating an star would cause heat to build up and therefore it would raise its temperature with several consequences. However, the key point is how much would it raise temperature, because that's the difference between "nothing happens" and weird consequences.

Let's compute a rough approximation for the Sun.

According to Wikipedia, the Sun yields $3.8·10^{26} W$ and has a mass of $1.98855·10^{30} kg$. Supposing the Sun is made of monoatomic hydrogen it's specific heat would be 12.5 J/mol/K at constant pressure (which involves a lot of very rough approximations), and that is 12500 J/kg/K: $$\text{temperature increment}=\frac{3.8·10^{26} W}{1.98855·10^{30} kg·12500 J/kg/K}=1.53·10^{-8} K/s=0.482K/year$$

That is, if the Sun were insulated, its temperature would be increased in less than a degree per year. Since present Sun temperature is several thousand degrees at the surface and milions of degrees in the core, it would take thousands to millions of years for insulation have any sizeable effect on the Sun.

That could seem counterintuitive because we see the Sun producing a lot of enery, as anyone sunbathing in summer could tell, and it's very hot, but that's just because it's very big and well insulated by tens of thousands of kilometers of gas layers but the amount of heat produced by mass unit is tiny by everyday standards. For example, a one ounce bread slice in a toaster is getting tens of thousands times the energy produced by an average ounce of solar mass.

In case you want to check my maths they are in this Google spreadsheet.

• I agree with your math, but disagree with the implications. Millions of years is actually not all that unreasonable of a time frame for a star. I'd say that after a billion years, the effect of the increased temperature should become quite pronounced. Dec 17, 2017 at 6:28
• Yes, it happens a lot but in a very long timescale. The timescale is not clear in the question, but I assumed it to be less than OP's lifespan. However, I must admit that before doing the calculations I expected to get some kind of solar bomb in a short time. Getting that result was at first quite surprising for me and therefore I stressed slowness of change in my answer.
– Pere
Dec 17, 2017 at 23:03

In short - nothing exciting

The core of a star like the Sun is surrounded by a zone in which energy is transferred by photons. It's called the radiative zone, and it acts like a pretty good thermal insulator for the core. Photons in the radiative zone bounce from one atom to another in a random walk, so it takes a long time for a photon to escape from the core to the sun's surface: about half a million years.

The effect of the radiative zone is to act as a pretty effective insulator for the sun's core.

The sun is in a dynamic equilibrium. The internal temperature is regulated by the release of nuclear energy which balances the gravitational collapse of the core, preventing the core from heating any further. This equilibrium is not regulated by the escape of heat from the surface of the sun, and so this equilibrium would not be unbalanced by wrapping the sun in an insulating layer.

So, the sun's core already has a pretty good insulator, and even if it were "perfect", it wouldn't have much effect on the sun.

• This equilibrium is not regulated by the escape of heat from the surface of the sun, and so this equilibrium would not be unbalanced by wrapping the sun in an insulating layer. - statement is not correct. Second part is not result of first part. First part is also incorrect - it is regulated, as core is in equilibrium - no escape would mean inflating the core at some point before pressure of external energy will be equal to pressure of EM in core, then core may collapse as external EM pressure is equivalent to internal EM pressure. Nov 12, 2016 at 10:29

Any heat would not escape, so entire star would start to heat up. Size of the insulating shell would make a lot of difference, in the end result.

If the shell is small enough, then quite soon the heating star would fill it up with plasma, and pressure would begin to rise, increasing the rate of fusion, increasing temperature, eventually in exponentially accelerating reaction. So this would basically be a supernova explosion, except there would be nowhere for the matter and energy to escape to. So things wouldn't ever cool down, but instead an equilibrium would be reached, where the shell would be filled with iron plasma (because iron is where both fission and fusion stop producing energy). Energy could not escape (so it wouldn't collapse to neutron star or black hole), more energy would not be freed, things would be stable.

If insulating shell was really small, so that even the iron nuclei couldn't hold together due to energy density, then things would end up in conditions similar to what they were after the big bang, at the time when density was same. But I am not sure if the matter in a star can contain enough energy (as binding energy of the atom nuclei) for this. Of course if it was shrinking insulating shell, anything would be possible.

If shell was large enough, star would just probably burn up a bit quicker (larger core due to increased temperature), but the star wouldn't have enough potential fusion energy to heat up and pressurize entire shell internals. Eventual (after a long time, when the star exhausts its fuel) end state (after an explosion resembling a supernova) would be a white dwarf or neutron star core, with plasma atmosphere filling rest of the sphere, as there would be enough energy to keep it all from raining down to the core. With large enough star, it would be a black hole in the middle of dark , extreme vacuum (there would be brief single particles of Hawking radiation, but they would get sucked back in because there's no escape from the insulating shell).

• second paragraph is not bad Nov 12, 2016 at 10:34

Is your material invulnerable? Because in time, heat will build up, particles will get more and more energetic as they will be reflected back from the surface to other particles on the sun. As the particles get more energetic, their push to the sphere will increase. At one point your material will be cracked.

If it does not, this outward force will turn into to heat (through friction) and will be radiated away. The increased heat will cause sun to get larger and fill up the sphere, cooling down to an extent, being able to push the object even more and at some point, equilibrium will be met.

• The details of the material aren't really the point - obviously such a material could never exist, even theoretically, in the real world. If you prefer, think of the 'material' as pure handwavium; it doesn't really matter what it is. I'm trying to figure out what would happen with all that energy perfectly contained within the star. Nov 11, 2016 at 17:19
• So this material will not even get hot through expansion stress? If that would be the case, it will get hot, really hot, but after a temperature, it will probably stabilize. The sun doesn't have enough matter to turn into something interesting. Maybe it would end up being a ball of plasma but that would be it. Nov 11, 2016 at 18:31

You could create the most impressive spaceship ever.

If this star was encased in a Dyson sphere:

I thought of using a "cloaking" field but not in the sense of a military cloak.

Research is already being done to hide objects for things like x-rays etc.

Imagine inverting the cloaking field, so it covers the interior of the sphere. Then by bending the photons path you would create a sort of combustion chamber and exhaust port. Effectively a Class C Shkadov thruster.

In theory this would also reduce the heat because the "interior" is "cloaked" from certain wavelengths of photons as they would never touch the structure.

It may also be possible to "dial" a rate of fusion in the star. By reflecting energy back at the star you could increase the rate of fusion. By releasing the pressure you cool the star somewhat and reduce the fusion rate.

You could line the interior with "solar" panels and allow those wavelengths through the cloak that work best for energy generation.

How to create such a "cloak" is a matter of sci-fy wizardry.

Heat and pressure building up would soon create environment very similar to that close after Big Bang.

I don't think anyone could tell what would that mean in closed system, out physics breaks down for energies that extreme.

• Can you add something to support this claim? I'm a bit doubtful of it. Nov 11, 2016 at 17:39
• @HDE226868 not sure about big bang conditions, probably not, not enough energy in a star for that volume. but definitely equilibrium between thermonuclear reactions and energy. or just matter and energy if there is not enough energy for such equilibrium. Question to answer is how much is enough for that equilibrium, which density of electromagnetic waves is enough. Nov 11, 2016 at 17:47
• yhea 2 orders of magnitude is not enough if we talking about star like the Sun, not enough even for energy-thermonuclear reaction equilibrium. 100 times more massive in same volume and it could be interesting. Nov 11, 2016 at 18:08