Gas giant equilibrium

Conversation started Apr 27, 2016 at 2:34.

Sir Cumference

Apr 27, 2016 02:34

@dmckee Dmckee, can I ask ya a question?

dmckee

Just did.

Sir Cumference

K thx bai

No seriously though.

I was thinking, main-sequence stars prevent collapse because they undergo nucleosynthesis, and their radiation pressure counters gravity.

Gas planets don't undergo nuclear fusion. Yet they are very massive, with little density.

Why don't their gravities compress them more?

I know their cores are supported by electron degeneracy pressure, but what about the rest?

dmckee

Virial theorem.

Sir Cumference

Er...what?

Explain

dmckee

The Virial theorem puts a limit on their compression. Potential energy increase must go into heating the gas in the short term, that holds it up.

Then they radiate and are able to compress a little more, but because they are pretty cool and small compared to starts that is a slow process.

It's actually the same thing that sets the size of stars.

Sir Cumference

Apr 27, 2016 02:38

Wouldn't an increase in heat lead to less density?

dmckee

But stars get into an equilibrium with the fusion process and hold the same size for longer.

@SirCumference Tries to. It's an equilibrium.

Sir Cumference

So...what prevents the further decrease in density?

Just gravity?

dmckee

@SirCumference Yeah. What else?

Sir Cumference

Maybe they release the heat as radiation?

dmckee

To lift some of the mass is to extract kinetic energy from it leading to a cooler average temperature which means it stops trying to expand. There is an equilibrium.

Sir Cumference

Apr 27, 2016 02:40

I'm just guessing here.

dmckee

@SirCumference They do, but that is a low process compared to finding the Virial equilibrium.

Sir Cumference

So where would they get the heat to expand?

dmckee

Radiation causes the Virial equilibrium to change slowly over time. But of course, the cooler and denser they get the more slowly that process proceeds.

@SirCumference They don't without some kind of input. But they can't contract too much because that would warm them. There is an equilibrium.

I know I sound like a broken record with the equilibrium thing, but that's because that is all of the physics.

Sir Cumference

All right. So compressing too much would cause them to heat up, allowing them to expand before cooling again?

Basically "contract > heat up > expand > cool down"?

And repeat

dmckee

@SirCumference Your trying to have there be steps that are followed in sequence, but an equilibrium is a state of constant balance with two processes evenly opposed.

Sir Cumference

Apr 27, 2016 02:43

Ah.

dmckee

So if you perturb the system you get some of that cycle, but it damps down right away.

Sir Cumference

Why wouldn't temperature alone be enough to prevent a star's collapse?

Because it also needs radiation pressure

dmckee

Like the equilibrium between ice and iced tea. There is a slow overall melting, but the system is buffered against small perturbation in temperature.

@SirCumference Stars start shining a considerable time before they start fusing. They start out of equilibrium, warm as they contract (shine when they get hot enough) and eventually halt the collapse with energy from fusion.

Near stars, find their equilibrium before they start fusing and never get hot enough.

I do a BOtE calculation in mechanics about the sun.

If you magically turned off fusion, no one but neutrino physicist would notice for thousands of years.

Sir Cumference

All right, so why wouldn't a star just remain in equilibrium?

dmckee

Because the Virial heating would compensate for a long time.

@SirCumference Well, eventually the core gets hydrogen depleted. Then it has to contract to warm up some gas further out enough to continue.

Sir Cumference

Apr 27, 2016 02:48

Yes, but that's late in a star's life cycle

dmckee

Eventually the center gets hot enough to burn hydrogen rapidly, and the dynamics change: red giant time.

Sir Cumference

I'm talking about early protostars.

dmckee

@SirCumference They warm up as they compress, and shrink as the radiate. Until the fusion input is enough to compensate for the radiative losses.

Sir Cumference

Shouldn't they just remain in equilibrium, like gas giants?

dmckee

@SirCumference They do. Meaning the collapse slows and is regulated by radiation.

But they're bigger than gas giants and get hotter, so they shrink faster.

Sir Cumference

Apr 27, 2016 02:51

Er...sorry, so protostars emit radiation, contract, and eventually begin nucleosynthesis?

Sorry if I'm not understanding it right away

dmckee

@SirCumference Everything hot radiates.

Sir Cumference

Yep.

dmckee

Blackbody, right?

Sir Cumference

Yeah.

dmckee

As the system loses energy, it tries to cool, but that lets it contract which keeps the temperature up.

Sir Cumference

Apr 27, 2016 02:52

So it will lose energy through radiation?

dmckee

That's what gas giants are doing, too. But the planets do it slowly, and proto-stars do it relatively fast. Very fast for very massive proto-stars.

When the core gets hot enough, fusion begins. The core of planets never get that hot, which is how we know they are not stars.

Sir Cumference

So protostars begin in equilibrium, emit radiation, lose energy, contract, and eventually become hot enough to begin nuclear fusion?

3075

why don't you read a book on it.

dmckee

They begin out of equilibrium, reach an initial equilibrium that is pretty hot, emit radiation (which is energy loss, they're not separate) ...

Sir Cumference

Yes. Yes.

All right, now it makes sense.

Thanks!

Conversation ended Apr 27, 2016 at 2:56.

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