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)

Then why do they attract?

...because they have mass?

Shoot...

Well what about the strong force?

Does it affect their attraction?

Excuse my ignorance here, honestly trying to understand it all

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

Er...why not?

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

Er...why not?

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

strong interaction

Excuse me

@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.

Alright

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

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?

@DanielSank But wolfram alpha doesn't really try

try mathematica then?

@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)

Mathematica solves it just fine @DanielSank @ACuriousMind

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

I can't believe nobody tried this haha

There are some conditions though

@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

All right, and where does the pressure come from?

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

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

I don't know what z is supposed to be

GRAAAH

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

It seems to be contradicting you

@SirCumference What?

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

@0celo7 What what?

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

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

I'm so confused right now...

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

I hope you meant to write

@ChrisWhite Wut

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

@ChrisWhite YES you're around

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

What' s a GOTO for?

@ChrisWhite I find that strange

Undefined for me

@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

It goes to a line, obviously.

@ChrisWhite #epicfail

Thanks.

@BernardMeurer Hating your life, usually.

lol

@DanielSank lol

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

fortran's some evil stuff

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

@ChrisWhite I still get undefined

@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.

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

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

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

That's such a bad idea

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

Gives me undefined

@0celo7 Nice stuff, which one?

@SirCumference The degeneracy pressure.

Did I not specify I was talking about that?

@BernardMeurer what?

The degeneracy pressure matters

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

@0celo7 The name of the place

Oh

Texas de Brazil

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

@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.

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

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

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

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

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

@BernardMeurer probably had a 3000 calorie meal

Didn't even have a soda!

@0celo7 No wonder you're a giant

@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

@ChrisWhite ^

@ACuriousMind That's just...

Yeah...

Weird...

So why does the Fermi energy increase the degeneracy pressure?

@BernardMeurer No

@ChrisWhite Papa bless programmers in the 60's

They were bloody warriors

@ChrisWhite No

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

@ChrisWhite Seriously weird eh

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

@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 I think I fixed it.

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

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

3000 Kcal meals and coup d'etats

@DanielSank Ah, yeah of course haha :)

Hell of a life

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

@SirCumference No, that was a hypothetical.

Any ideas @ChrisWhite?

Copy-paste your code pliz?

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

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

@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

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

OOOOOOOOOOooooooh

@BernardMeurer at the mall.

@ChrisWhite JK fixed it

@ACuriousMind Do you want to go to Sweden and get me a CD?

sign errors, every fucking time

Or you @Danu?

@DanielSank Wait, that was the error that I had alos seen and that I could find anymore when you asked me what it was :D

@BernardMeurer wat

(my sign was not in front of the fraction) @ChrisWhite

And now, of course, it only converges when $Re(z^2)>0$ :)

@ACuriousMind I NEED a CD that is only sold & shipped in/to Sweden. I need someone to get it for me

Okay so yeah, @DanielSank, both me and Chris agree that you get $K_0(2z/n\sigma^2)$

You could use some vacation in Stockholm, right?

Swedish folktronica is hard to get

@ChrisWhite wanna post an answer?

@BernardMeurer I don't plan on visisting Sweden anytime soon

@ACuriousMind So this source has been completely wrong...?

astronomynotes.com/evolutn/s10.htm

@ACuriousMind Oh you do now

Screw it...

@ChrisWhite eh?

I don't know whether to hate or love neutron stars

They've been giving me headaches

Moral of the story: Fucking Wolfram Alpha sucks.

Doesn't Google have Mathematica? Really?

Or some other thing to solve integrals for you?

Grad students?

@Danu They bought a @DanielSank instead of Mathematica

It was a limited edition product

@Danu : I suggest that you "buy" mathematica

wink wink

@0celo7 Russian ones from the 50's or what?

@Danu haha

@SirCumference I'm not going to read all that, but at a first glance, I don't see anything blatantly wrong about it, except for the unfortunate use of "speed" for the energy content of a quantum state.

Speed is just momentum over mass

All right, it states that "neutrons barely move in a neutron star"

IS IT

That more compression will make them move more

I will fite you over this

And that they occupy low energy states

@Danu Sweet. You guys are my way around having to pay for Wolfram Alpha Pro or whatever.

Not lowest, but rather the subject term low

@DanielSank Mathematica, but yeah. Any time, really.

@SirCumference I think it tells a lie-to-children because it doesn't assume the reader knows quantum mechanics.

Answer (CW) posted @DanielSank

@Danu "or whatever" = "Mathematica"

CV: I have friends that will let me use Mathematica for free

And since the energy of the particles in a Fermi gas really is "kinetic" energy in a certain sense, equating that with particles moving to get a picture across is wrong, but understandable.

I'd take that as a plus if I was hiring

@DanielSank Perhaps I can even get you a copy of your own.

@ACuriousMind Lovely...so I'm still left confused...

@Danu Doesn't Mathematica cost the same as a black market lung?

Depends whether the person smoked?

@BernardMeurer Not if your university has a nice license

@Danu lol

@Danu, why is your answer "community wiki"?

My university doesn't have a nice license, though :(

@ACuriousMind Ooooh, I see

@ChrisWhite I ssh into a raspberry pi with overheating issues :c

> I end up using the gui over ssh

Heretic!

@Danu Yes, we have, but I don't have it on my laptop.

@ACuriousMind Uh, then I'm confused.

Down here everyone is super excited about Mathematica, they talk about it like it's the new messiah or something

Never had the pleasure tho

@BernardMeurer It's nice.

@DanielSank Ah, okay.

You can often get rid of your Russian table of integrals when you have Mathematica.

@DanielSank Because I feel I shouldn't really receive any points for this.

@DanielSank I wonder if they have them all

@DanielSank Can it repel Russian invaders tho?

Of course, since it runs on a computer, it's not as useful as Russian books when the power goes out and you throw an "integrals in the dark" party.

A more interesting question is the asymptotics.

@ChrisWhite I bet you use GO TO

"integrals in the dark": An engineer's call to sex

@Danu Well, figuring out (i.e. looking up) asymptotics of known functions is easy.

With his textbook of course

@BernardMeurer "Integrals 'n chill"?

@DanielSank OMG, you just gave me an idea!

@DanielSank Of integrals.

@DanielSank Remind me I owe you a burrito now, brb

@BernardMeurer ಠ_ಠ

@BernardMeurer wat?

@DanielSank $K_0$'s simple integral representation might lead you to the construction of a solution by hand.

@Danu You mean just massaging that integral until it's the definition of $K_0$?

Yes

@DanielSank You gave me a pickup line idea that I'm about to test

@Danu Right.

Btw @DanielSank ever made Ma Po Tofu?

@BernardMeurer Wait just a damn minute.

It's a really really really nice dish, imo.

@DanielSank Yeah?

@BernardMeurer You have a procedure by which you can test pickup lines, in a controlled way, at a moment's notice?

@Danu When made properly it's one of my favorites.

I have never attempted it.

@DanielSank Yeah? It's called a girl's phone number :p

I... see...

@DanielSank I made it twice now, the recipe I found online isn't very hard.

However, the second time was decidely less delicious as the first time

The consistency and/or water-to-contents ratio was off

@BernardMeurer tell me the pickup line

Also I'm using silken tofu for it, which is perhaps a bit too soft

@BernardMeurer So you called someone up and asked if she'd like to come over and find the area under your curves?

@0celo7 It's an internal joke

@Danu Gotta keep it low-water.

In my opinion Resnick & Halliday's book is too much school.

...internal?

@DanielSank Pretty much that's the message I sent hahaha

@0celo7 Yes, inside

Tsc, nevermind, I'm only making it sound worse

It sounds pretty stupid

@0celo7 Surprising since it didn't come from you

snap

@DanielSank I'm actually not sure whether the amount of water or just the amount of e.g. chili bean paste was off

@Danu Aya! Don't do that.

@DanielSank On the other hand, I've seen some sites say you should use silken tofu

@Danu Do you know what Ma Po refers to? :-)

@Danu It's entirely a matter of taste.

My bear?

@DanielSank No

@Danu Roughly, the pock marks in old grandma's face.

My butt

Lol

@DanielSank So what do you think of this recipe (skip down to the bottom for the actual recipe)

@DanielSank Ew.

@Danu That's a maths link?

It evokes the idea of your old grandmother, who's face is scarred, who makes the dish.

@Danu Are you cooking integrals?

D'oh

@Danu That's a bessel function page.

@DanielSank Fixed.

Was that an accident, or an attempt at the mathematical equivalent of rickrolling?

I never really didn't know anything about it and just bumped into it, so don't scold me if it's a bad recipe @DanielSank

@DanielSank I was at Canonical last week (the Ubuntu people) Told them you had managed to make iPython crash the whole system, they were quite impressed

@HDE226868 The former, sadly.

@Danu Damn, that looks tasty

Ah yes.

That was fun.

@Danu It looks ok but not great.

There's an issue with the sauce.

@DanielSank What?

Master Chef Physics SE edition

@Danu I'm trying to figure it out.

@DanielSank btw! Some friends of mine made your chili and they really liked it!

In the photos you can tell that the sauce is kind of thick.

@Danu YES!

(I sadly didn't make it yet, but I have this sharing folder where I share recipes with people)

@DanielSank Well when I made it the thickness just come from throwing in this starch-water mixture.

@DanielSank Gimme that recipe!

I need a proper chilli

(but mine were more watery than what you see on the page)

@ChrisWhite Cause they're German

Today I did myself a Finnish lunch

Reindeer meat and baked potatoes

@ChrisWhite You can be my friend! :p

@Slereah Meaning you ate alone?

Also yes

I didn't have any sour berries, though

Reindeer meat