Neutron stars

Sir Cumference

Mar 19, 2016 17:24

Question...

anyone know about neutron stars and degenerate gases?

ACuriousMind

...what do you want to know about them?

Sir Cumference

Well, when a neutron star compresses and the Fermi energy rises, will all the neutrons rise to a higher energy level?

Physics Meta

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ACuriousMind

@SirCumference Are you asking whether the energy of the lowest lying state rises or stays the same? (I think it stays the same, but I don't know about neutron stars)

Sir Cumference

Yep

Really?

Then how can all the energy levels be filled to the Fermi energy when a star compresses?

If the Fermi energy rises

ACuriousMind

Mar 19, 2016 17:31

The Fermi energy is just the difference between the lowest and the highest occupied state at zero temperature. Isn't saying "the Fermi energy rises" the same as saying "the Fermi gas compresses", since more fermions distributed on the same states means higher states must get occupied?

Sir Cumference

Sorry if I'm misunderstanding it, but when the Fermi energy rises, doesn't that mean that most of the fermions will gain energy?

If the Fermi energy rises, then the highest occupied state would probably be higher, right?

Or the lowest state would be lower...any way, the difference in highest and lowest must be greater, right?

ACuriousMind

@SirCumference No. It just means the difference between the lowest and the highest occupied state changes. But a priori you can't say whether that is because the individual levels shifted or because you just have more fermions occuping states whose spacing is still the same.

Sir Cumference

But there aren't necessarily more fermions in the star, right? So why would more fermions be distributed on the same states?

Sorry if I'm not understanding you

Slereah

Doesn't pressure just generally change the energy levels of a system

Sir Cumference

It does

ACuriousMind

Mar 19, 2016 17:37

@SirCumference The density of states of a Fermi gas is constant. If you increase the density of the fermions, then you get a rising Fermi energy simply because you need to distribute more fermions on the same states.

@Slereah What? The states know nothing of pressure, pressure is a thermodynamic quantity.

Slereah

Well states know of the volume in which they are constrained!

Sir Cumference

Alright, idiot question here, but why would you need to distribute more fermions on the same states if you increase the density of the fermions?

I need to read more into this

ACuriousMind

@SirCumference Just look at the computation of the Fermi energy for a 3D fermi gas in a box. The number density of the fermions appears very straightforwardly.

0celo7

Mar 19, 2016 17:54

@Slereah everyone else does quantum BS

Sir Cumference

All right, and with a rising Fermi energy, higher energy levels will be occupied, and pressure increases?

Since the neutrons now move more?

Slereah

Let's talk about quantum states in GR

0celo7

We're the only people who care about the only physics that actually matters

No.

Sir Cumference

@0celo7 Cough neutron stars cough

Pretty important

ACuriousMind

@SirCumference Ehhhhh, I'd say that the pressure comes from elsewhere (gravitational attraction), I don't see what it has to do with neutrons "moving" more (don't say that, quantum objects don't really move about). And "particles moving" would be temperature, not pressure, anyway

Sir Cumference

Mar 19, 2016 17:57

Fuck it, my source sucks then

It's feeding me lies

Doesn't pressure cause gravitational attraction?

ACuriousMind

...what?

Sir Cumference

sigh...

I heard in GR, pressure can be a source of gravitational curvature in spacetime

ACuriousMind

Oh, that

Sir Cumference

I don't know what to think now...

ACuriousMind

Yes, pressure is a part of the stress-energy

Sir Cumference

Mar 19, 2016 17:59

Oh thank god

Alright, so gravity is causing the pressure, which causes gravity, which...

ACuriousMind

But I mean that the pressure on the neutrons in the star is because they attract each other (and that attraction has nothing to do with the gravitation the pressure itself might generate)

Sir Cumference

Then why do they attract?

ACuriousMind

...because they have mass?

Sir Cumference

Shoot...

Well what about the strong force?

Does it affect their attraction?

Excuse my ignorance here, honestly trying to understand it all

ACuriousMind

Not in the model you're looking at, I think.

Sir Cumference

Mar 19, 2016 18:01

Er...why not?

ACuriousMind

Because you talk about "Fermi energy" and such - that's characteristic of a Fermi gas, and that doesn't have the strong force in it, usually

Sir Cumference

Er...why not?

ACuriousMind

Also, the strong force is...not really a force, so you can't talk about it "causing attraction"

Sir Cumference

strong interaction

Excuse me

user54412

@BernardMeurer ::mumble:: asynchronous communication ::mumble:: protocol

ACuriousMind

Mar 19, 2016 18:04

@SirCumference When you model the neutron star as a bunch of neutrons, you can't easily include the strong force, as that would either require a quark-gluon model, or the effective treatment with pions mediating it.

Sir Cumference

Alright

ACuriousMind

But that's okay since it doesn't really appear as a "force" anyway

Sir Cumference

Jesus christ...so let's see if I got this straight

Neutron stars form. Gain mass, compress, Fermi energy rises, pressure increases

More mass, more pressure, higher fermi energy

Eventually black hole forms when pressure is high enough?

Danu

@DanielSank But wolfram alpha doesn't really try

Slereah

try mathematica then?

ACuriousMind

Mar 19, 2016 18:11

@SirCumference I...guess so? (Although I don't know why you keep mentioning the Fermi energy. You could just say "Star compresses until density is high enough for ablack hole to form". And I have a feeling the actual process would have a quark-gluon plasma phase between the neutron and the BH, but I don't know)

Danu

Mathematica solves it just fine @DanielSank @ACuriousMind

Sir Cumference

I always thought the neutron degeneracy pressure increased because the Fermi energy increased...

user54412

@Danu I was just going to say the same!

Danu

I can't believe nobody tried this haha

There are some conditions though

ACuriousMind

@SirCumference The "degeneracy pressure" is the pressure the neutrons exert against being compressed, it's not what compresses them.

@Danu Haha, I don't have Mathematica :P

Sir Cumference

Mar 19, 2016 18:14

All right, and where does the pressure come from?

ACuriousMind

@SirCumference Gravitational attraction of the neutrons, didn't I already say that?

Danu

The integral only converges is $Re(z^2)<0$

I don't know what z is supposed to be

Sir Cumference

GRAAAH

All right, well could you at least read what Rob Jeffries told me a few days ago?

It seems to be contradicting you

7

A: How could a neutron star collapse into a black hole?

The scenario you describe may occur. On the other hand it may actually be that neutronisation in a white dwarf is the trigger for a thermonuclear type Ia supernova. You may be misunderstanding the Pauli Exclusion Principle (PEP).The PEP states that no two fermions can occupy the same quantum sta...

0celo7

@SirCumference What?

Danu

Also @DanielSank your question has a typo, since you wrote:

Sir Cumference

Mar 19, 2016 18:15

@0celo7 What what?

ACuriousMind

Uh-oh. If you think I'm contradicting Rob than either I'm wrong or you're misunderstanding one of us ;)

Danu

$$P_Z(z) = \int_{-\infty}^\infty P_X(x) P_Y(z/y) \frac{1}{|z|}dz \, .$$

Sir Cumference

I'm so confused right now...

Danu

But the right hand side doesn't depend on $z$, but on $y$

I hope you meant to write

Bernard Meurer

@ChrisWhite Wut

user54412

Mar 19, 2016 18:16

@DanielSank $$\int_0^\infty \exp\left(-\frac{r^2+(z/r)^2}{\sigma^2N}\right) \frac{\mathrm{d}r}{r} = K_0\left(\frac{2z}{\sigma^2N}\right)$$

Danu

$$P_Z(z) = \int_{-\infty}^\infty P_X(x) P_Y(z/y) \frac{1}{|y|}dy \, .$$

Bernard Meurer

@ChrisWhite YES you're around

Danu

@ChrisWhite Didn't you get teh condition on $z$ though?

Bernard Meurer

What' s a GOTO for?

user54412

@Danu That holds for $\sigma$, $N$, and $z$ all positive reals. Didn't check more generally.

Danu

Mar 19, 2016 18:17

@ChrisWhite I find that strange

FullSimplify[Integrate[Exp[(-x^2 + A^2/x^2)/B] x, {x, 0, Infinity}],
Assumptions -> B > 0 && A > 0]

user54412

@BernardMeurer Summoning Cthulhu

Danu

Undefined for me

Bernard Meurer

@ChrisWhite HAHAHAHA

I'm looking at this fortran code

and there's all these GOTOs everywhere

and I have no idea what I'm doing

halp, what's a goto

0celo7

It goes to a line, obviously.

user54412

@Danu it's 1/x, not x, outside the exponential

Danu

Mar 19, 2016 18:19

@ChrisWhite #epicfail

Thanks.

DanielSank

@BernardMeurer Hating your life, usually.

0celo7

lol

Bernard Meurer

@DanielSank lol

user54412

@BernardMeurer They literally redirect code execution to that line of the code

Sir Cumference

@0celo7 Would you happen to know about neutron stars and degenerate gases?

Bernard Meurer

Mar 19, 2016 18:20

fortran's some evil stuff

0celo7

@BernardMeurer Went to a Brazilian all you can eat steak place today

Danu

@ChrisWhite I still get undefined

ACuriousMind

@SirCumference He's just saying that there is a small window just before the star collapses where the increasing degeneracy pressure actually leads to compressing the star even quicker (due to the pressure being a part of stress-energy), so even if the degeneracy pressure somehow increased arbitrarily fast, it would not rescue the star.

0celo7

@SirCumference I've looked at their GR a little bit, but not anything specific.

Bernard Meurer

@ChrisWhite NO, really? It's based on the bloody line of code?

Sir Cumference

Mar 19, 2016 18:20

@ACuriousMind I know, but how about the part with Fermi energy?

Bernard Meurer

That's such a bad idea

Sir Cumference

Doesn't it say that the pressure increases as Fermi energy rises?

Danu

@ChrisWhite FullSimplify[
Integrate[(Exp[(-x^2 + A^2/x^2)/B^2])/x, {x, 0, Infinity}],
Assumptions -> B > 0 && A > 0]

Gives me undefined

Bernard Meurer

@0celo7 Nice stuff, which one?

ACuriousMind

@SirCumference The degeneracy pressure.

Sir Cumference

Mar 19, 2016 18:21

Did I not specify I was talking about that?

user54412

0celo7

@BernardMeurer what?

user54412

Though maybe I'm also failing

Sir Cumference

The degeneracy pressure matters

DanielSank

@ChrisWhite Wow, the depths of badness in that idea is impressive :-)

Bernard Meurer

Mar 19, 2016 18:21

@0celo7 The name of the place

user54412

DS's integral is designed to fool us all

0celo7

Oh

Texas de Brazil

Sir Cumference

@ACuriousMind Isn't it what is mainly preventing the star from collapsing?

ACuriousMind

@SirCumference You talked about the star getting compressed and the pressure rising. When you talk about something being "compressed" I assume "pressure" refers to the thing compressing it, not to the thing trying to counteract the compression.

0celo7

All you can eat steakhouse. Only in America, baby.

Sir Cumference

Mar 19, 2016 18:22

Crap...I probably should've specified that...

Bernard Meurer

@0celo7 Dunno that one. Fogo de Chão is pretty damn good (there's one in Cali afaik)

Sir Cumference

All right, so Fermi energy DOES play a role in it?

Bernard Meurer

@ChrisWhite Why would anyone fill their code with GOTO like this? it's bloody unreadable

0celo7

@BernardMeurer probably had a 3000 calorie meal

Didn't even have a soda!

Bernard Meurer

@0celo7 No wonder you're a giant

ACuriousMind

Mar 19, 2016 18:23

@SirCumference It's what determines the degeneracy pressure, yes. But I'd say the degeneracy pressure plays more of a role in every case where a black hole doesn't form :P

Danu

@ChrisWhite ^

user54412

@BernardMeurer well if you don't have a notion of loops or else statements

Sir Cumference

@ACuriousMind That's just...

Yeah...

Danu

Weird...

Sir Cumference

So why does the Fermi energy increase the degeneracy pressure?

0celo7

Mar 19, 2016 18:24

@BernardMeurer No

Bernard Meurer

@ChrisWhite Papa bless programmers in the 60's

They were bloody warriors

user54412

@Danu So it's possible both are right, but yours in tacitly incomplete

user54412

whereas mine is explicitly ignoring complex z

Danu

@ChrisWhite No

When I input $z>0$ I get undefined, explicitly

user54412

@Danu wat

Danu

Mar 19, 2016 18:26

@ChrisWhite Seriously weird eh

0celo7

@BernardMeurer I think the lobster bisque was 1000 calories right there

ACuriousMind

@SirCumference The higher the highest occupied level lies, the more energy could be set free if the fermions leave that highest energy level by falling into the ground state outside the star, and force (and thus pressure) is just a gradient of energy after all.

Danu

^

DanielSank

@Danu I think I fixed it.

Bernard Meurer

@0celo7 That's how we do it down here

ACuriousMind

Mar 19, 2016 18:27

Actually, I think for a simple Fermi gas the pressure is just the total energy per volume.

Bernard Meurer

3000 Kcal meals and coup d'etats

Danu

@DanielSank Ah, yeah of course haha :)

Bernard Meurer

Hell of a life

Sir Cumference

@ACuriousMind Wait, so the fermions have to leave the star?

ACuriousMind

@SirCumference No, that was a hypothetical.

Danu

Mar 19, 2016 18:27

Any ideas @ChrisWhite?

Copy-paste your code pliz?

ACuriousMind

"could be set free" is not "is set free". Read more carefully.

Sir Cumference

Wait, so why would the fermion drop down in energy then?

ACuriousMind

@SirCumference It doesn't. Force is the gradient of potential energy, it exists even if something counteracts it such that the motion to the lower energy state doesn't actually happen

Bernard Meurer

@0celo7 Wanna play something? I'm back home

Sir Cumference

OOOOOOOOOOooooooh

The h Bar

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