The h Bar

0celo7

2:00 AM

I don't think stars are interesting at all

user218912

it sounds too advanced for me right now and I'm in graduate qft and stat mech.

Sir Cumference

But this concept is tripping me up

@bloo The paper is surprisingly intuitive...mostly.

Obliv

@sirC honestly I'm not sure either. I could follow the lane-embden derivation but the eddington approx. is pretty whack

Sir Cumference

Basically it's a hypothetical star back in the early universe. The star has a black hole in its center, and that black hole is growing by eating the star inside out. That would explain the origins of supermassive black holes.

user218912

I returned my iPad btw. I bought a wacom drawing tablet and I take notes on my laptop with it.

user218912

2:01 AM

saved $1000.

Sir Cumference

To get an idea of how big quasi stars are, look here

Obliv

@bloo wow good job. what made you come to your senses though

user218912

@Obliv I wanted a blue iPad, so instead I bought a blue drawing tablet since blue ipads don't exist.

user218912

@SirCumference I like the first 3 stars.

Sir Cumference

@bloo You know UY Scuti is the biggest star we've ever found, right?

And quasi-stars would dwarf it.

user218912

2:03 AM

@SirCumference wait...

user218912

so quasi-stars are some theoretical star?

Sir Cumference

@bloo Hypothetical.

user218912

what makes them so big?

Sir Cumference

2 mins ago, by Sir Cumference

Basically it's a hypothetical star back in the early universe. The star has a black hole in its center, and that black hole is growing by eating the star inside out. That would explain the origins of supermassive black holes.

user218912

@SirCumference wow so it's like starception.

Sir Cumference

2:04 AM

@bloo Actually, the core is so compressed by its gravity that a black hole forms

@bloo Well, first of all they're thousands of times more massive than the Sun. Second, the radiation pressure from the black hole's accretion disk is immense.

Obliv

@bloo you know.. I'm not sure if I should be worried for your sanity or glad that you saved money and got what you wanted.

Sir Cumference

Like, accretion disks nowadays are what give way to quasars.

user218912

@SirCumference quasars are cool.

Sir Cumference

So the radiation pressure from the disk is what keeps the quasi-star alive.

Now, the problem I'm having is it keeps referring to polytropes

user218912

I decided to study black holes from a condensed matter point of view so that's why I added GR to my list of things to learn.

Sir Cumference

2:06 AM

And I have no idea how to use them

Obliv

okay @sirC you will understand this equation now. $$P = (\frac{k}{\mu m_H})^{4/3} (\frac{3(1-\beta)}{a\beta^4})^{1/3}\rho^{4/3}$$ here $\beta$ is the ratio between the gas pressure and the total pressure of the star. It is constant throughout the star. It doesn't really state the variables but I'm pretty sure P is pressure, $\rho$ is density, uh...

the rest is up to you my friend.

Sir Cumference

What...

Where is $n$ in that equation?

That doesn't seem to involve polytropes at all.

Obliv

$(4/3)$ is $\gamma = (n+1)/n$

so 3+1/3

Sir Cumference

Goddammit

user218912

@SirCumference why don't you learn stat mech? a good book is statistical physics of particles and fields by kardar.

Obliv

2:08 AM

it's the polytrope of a star with n = 3

Sir Cumference

I'm just as confused as before.

user218912

I am also lacking in stat mech that is why I am learning it now.

Sir Cumference

@bloo Because as of now, I'm already lacking in regular physics.

My high school was full of idiots.

user218912

@SirCumference read tong's notes.

user218912

damtp.cam.ac.uk/user/tong/teaching.html

user218912

2:09 AM

that should get you up to speed.

Sir Cumference

Oh boy...

None of that has Newtonian mechanics.

user218912

start from dynamics and relativity, you should be able to understand all of it.

user218912

yes it does.

user218912

the first one.

Sir Cumference

And how much mathematics should I know?

user218912

2:10 AM

basic calculus.

user218912

some basic linear algebra.

Obliv

@SirCumference that's a general solution to the lane-embden equation I think. If you look at the solution for n=3 it resembles it right

the constant followed by $\rho^{n+1/n}$

Sir Cumference

@Obliv GRAAAAAHHHHH

Obliv

anyway the thing to take away from this is: the pressure is related to the density with that equation

Sir Cumference

This is one thing after another!

All right, fine. Now what about a neutron star, with a polytrope of 0.5?

user218912

2:12 AM

@SirCumference forget this and start reading dynamics and relativity by tong.

Sir Cumference

@bloo I've got to finish this paper.

I'm too interested.

@bloo It's got partial derivatives in it.

That's not basic calculus.

user218912

@SirCumference a partial derivative is just a regular derivative with respect to one variable but keeping the other variables treated as constants.

user218912

that's all you need to know.

Sir Cumference

So what's next? Partial integral?

user218912

no.

Sir Cumference

2:15 AM

I'm kidding.

user218912

there are no 2 or 3 dimensional integrals in those notes I think.

user218912

you just need to know basic integration so you'll be fine.

0celo7

@SirCumference Huh?

Sir Cumference

@0celo7 Oh no...

0celo7

That's elementary calculus by any measure

Sir Cumference

2:16 AM

Even you said it wasn't.

I asked if it were covered in Calc 1-3, you said it wasn't.

0celo7

When

It's in calc 3

user218912

@SirCumference he lied then xD

0celo7

I never lie

You misread

Sir Cumference

I have no idea how people like IceLord pull up year-old messages

But I know you said it

@0celo7 You troll.

You lied about Schwarzschild radii.

user218912

:32791215

user218912

2:17 AM

Oct 4 at 19:13, by 0celo7

I lied

Zacharee1

@SirCumference why is this flagged?

0celo7

@SirCumference Not Nice

Sir Cumference

@0celo7 Oh my god...

You flagged that?

You can't be serious.

Zacharee1

That is not how to use flags

Sir Cumference

@Zacharee1 He knows.

0celo7

2:18 AM

@bloo I'm pretty sure you misunderstood me there, actually.

tpg2114

Just in case you guys forgot:

Sep 29 at 9:47, by David Z

Don't use chat flags except for seriously inappropriate messages. We've had a problem with inappropriate chat flagging for a while, and more so recently.

Zacharee1

@SirCumference then why the flags?

Sir Cumference

@Zacharee1 Because he wants to mess with me.

Or something.

I don't know, ask him.

Obliv

@SirCumference right so .. I've got to go now but I will say this. I think it's fine if you use that simple equation $P = K\rho^{n+1/n}$ but you won't know what $K$ is and consequently how the pressure is related to the density. If you're interested then look at that derivation of eddington solution. I couldn't find a solution using $n = .5$ so i'm not sure what the polytrope is for that

and if you're interested then you can look it up or try finding the solution yourself lol

Sir Cumference

Lovely.

Zacharee1

2:21 AM

@0celo7 flags notify every mod and every user with 10k chat rep currently in a room. It's annoying to deal with invalid flags.

3

user218912

@SirCumference but yeah seriously you should read tong's notes in order...

0celo7

@Zacharee1 I think it was valid.

Sir Cumference

@Zacharee1 There's a difference between ignorance and apathy.

Zacharee1

I don't think it was very inappropriate, much less "seriously inappropriate"

@SirCumference ?

0celo7

I think it was.

Sir Cumference

2:22 AM

@Zacharee1 He knows. He doesn't care.

He's gotten me kicked before.

For no reason.

tpg2114

@0celo7 Well, then let's agree to disagree and move on with our lives

Zacharee1

hmm

tpg2114

@SirCumference And let's stop fanning the fires and also agree to disagree and move on with our lives

Sir Cumference

Regardless, I'm still back to trying to figure out what a polytrope is.

Or rather, how to use it.

0celo7

@SirCumference I'm sure if the 10k users validated the flag, there was a good reason.

Sir Cumference

2:24 AM

@0celo7 I was kicked by a bot.

Explain?

0celo7

It says that when the 10k users kick.

Sir Cumference

...

user218912

@SirCumference did you look at the wikipedia page for it?

Sir Cumference

@bloo Yes.

It gave me an equation but didn't tell me what the constant of proportionality was.

user218912

can I see the paper?

Sir Cumference

2:25 AM

@bloo Here ya go.

user218912

@SirCumference where?

Sir Cumference

@bloo Page 2, top right paragraph.

Also, just wondering. When it mentions $\dot M$ in the next paragraph, is that the time derivative of M, or something else?

user218912

are you sure the constant is important for this purpose, or if it is, is it well known for quasi-stars?

user218912

@SirCumference yes it's the time derivative because it says accretion rate before that.

Sir Cumference

@bloo K good

Polytrope

In astrophysics, a polytrope refers to a solution of the Lane–Emden equation in which the pressure depends upon the density in the form P = K ρ ( n + 1 ) / n , {\displaystyle P=K\rho ^{(n+1)/n},} where P is pressure, ρ is density and K is a constant of proportionality. The constant n is known as the polytropic index and is sometimes linked to the polytropic exponent γ ...

The equation on that page is asking for a constant of proportionality

No idea where to find it

user218912

2:32 AM

why is it important in this case though?

Sir Cumference

Because stars like the Sun have polytropic indices of 3 as well

And if I know the Sun's density, I'd like to know it's pressure

user218912

page 2 www2.astro.psu.edu/users/rbc/a534/lec16.pdf @SirCumference

user218912

is this what you're looking for?

Sir Cumference

Uh, I guess.

But what if I were looking at a neutron star, whose polytropic index is 0.5?

user218912

the formula for $K$ is the one you need right?

Sir Cumference

2:36 AM

Yep.

user218912

@SirCumference replace 3 with 0.5?

user218912

in the equation.

Sir Cumference

Will that equation still work?

My god, it looks nightmarish.

What's $ξ$?

user218912

no. ignore what I said.

user218912

see $n$ in the equation?

user218912

2:38 AM

that's the polytropic index.

Sir Cumference

Yes

user218912

so just replace it with 0.5?

Sir Cumference

But what about all the other stuff in the equation?

What's $ξ$?

I see no function $\theta(ξ)$

Yet it's asking me to differentiate $\theta$ with respect to $ξ$

What the hell is all this?

;-;

user218912

yes it is.

Sir Cumference

Yes what is?

user218912

2:41 AM

$\xi$ is a dimensionless angle like I said. and $\theta$ is a function of it.

Sir Cumference

So what's the function?

I assume since it's dimensionless, I'd be using radians.

But where on Earth would I need an angle?

user218912

read this @SirCumference

user218912

it should answer all your questions.

Sir Cumference

Oh God...

More reading...

user218912

it has everything you need properly and clearly explained.

user218912

2:43 AM

that other pdf follows this one.

Sir Cumference

I'm so confused.

user218912

which part?

Sir Cumference

I thought relating densities with pressure was as easy as plugging $n$ into the equation

Now I gotta figure out what $P = Kρ^{1/(1−∇ad)}$ is.

> where $K$ is not a function of atomic physics, but instead depends on the star’s boundary conditions

The hell is a boundary condition?

user218912

I think you should learn differential equations first.

Sir Cumference

Yeah, I should. But I am determined to finish this goddamn paper.

0celo7

2:50 AM

I like your attitude, whoever you are @bloo

I won't help that Canadian kid any more when I think he should understand something from a previous class

Sir Cumference

@0celo7 "Canadian"?

0celo7

Ia that not the word for someone from Canadia?

Sir Cumference

You called HDE Canadian too

0celo7

Because he is.

Sir Cumference

@0celo7 Yes, but I speak American, so I'm from America.

0celo7

2:52 AM

I wasn't talking about you.

@Icelord

that guy

Sir Cumference

Oh.

0celo7

huh his name doesn't show up any more

Sir Cumference

Is he actually Canadian or...?

Oh.

Bloo is icelord

That's neat.

user218912

3 hours ago, by bloo

I changed my name to bloo (blue).

user218912

I already said that.

user218912

2:53 AM

so this whole time you thought I was some new guy? lol

Sir Cumference

@bloo Yep.

When I changed my name from Pies, I made it "Sir Cumference — Pies"

So people knew who I was.

Then after a while I just changed it to Sir Cumference.

user218912

@0celo7 uhm...

Sir Cumference

@bloo Then again, that doesn't say you were icelord.

No one knows who changed their name.

0celo7

@SirCumference Huh? Proof?

user218912

I don't remember you helping me on anything from a previous class. @0celo7

user218912

2:55 AM

@SirCumference look at the message under it.

Sir Cumference

bloo

88 2 7

That links to "icelord"

0celo7

@bloo I don't remember helping you at all

user218912

@0celo7 ikr...

Sir Cumference

It redirects to bloo.

user218912

I should change my name to BlooLord

Sir Cumference

2:56 AM

Or, never mind. Just after physics.stackexchange.com, put "users/122132/icelord"

It'll redirect to bloo.

user218912

@SirCumference because on stackexchange only the user number matters.

user218912

you can type that without any name at the end and get the same user.

Sir Cumference

Now anyways, what are we going to do about these goddamn polytyopes?

0celo7

yeah well I don't know who you are

user218912

@0celo7 if you helped me with basic stuff instead of making me figure it out myself I would have progressed a lot faster.

Sir Cumference

2:58 AM

@0celo7 When I changed my name you called me "The pun man who doesn't know calculus."

0celo7

stop talking to me, I don't know who you are

Sir Cumference

;-;

user218912

@0celo7

user218912

3 hours ago, by bloo

fuck do we have to go through this every time I change my name?

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