Ep. 777: The Eddington Limit

Oh

Astronomy cast episode seven seven seven the Eddington limit welcome to astronomy cast from weekly facts based journey through the cosmos where you help you understand not only what we know but how we know what we know

I'm Chris McCain. I'm the publisher of university with me as always is dr. Pamela gay a senior scientist for the planetary science it's due and the director of cause request. Hey Pamela, he don't I am doing well the howling wind is tremendous if you hear if you hear what sounds like ghosts in the background that is the wind people that is the wind now as usual I can't hear it because we zoomed a record and the modern technologies made it so your dog when your dogs are barking I don't hear it and so I'm definitely not going to hear the wind

but yeah here we are now I'm going to do something kind of mean but for the it's for the best and that is I'm going to say nice things about you and you're just going to have to take it which is you know I think a lot of people when they reach out to us about astronomy cast and they talk about like our scripts and sort of how we prepare.

They don't realize that there is no script that this is entirely off of the top of our heads that that I go in and what's nice is for me I don't really even have to prepare at all I like I write the intro which is sort of like my token donation to the cause and I usually come up with the idea but you know often Pamela has ideas that she wants to express.

But then she has to prepare and she doesn't have to prepare just for whatever is going to be the script she literally has to prepare for anything that I might ask and and and I don't know what I'm going to ask so how can she know what I'm going to ask and so Pamela you are amazing for being able to gather and prepare so much information be ready.

Sort of on your toes nimble on your toes to handle whatever comes your way and and in this case there's going to be a lot of information about the Eddington limit and I don't know what I'm going to talk about you know what you're going to talk about and yet you were always poised and prepared so amazing job thank you thank you.

Thank you this is a favorite topic so hopefully I will not disappoint great okay how big can a star get.

This is a calculation made by one of the original pioneers of modern astronomy Sir Arthur Eddington and it's named after him the Eddington limit now astronomers are finding examples of giant black holes early in the universe calling into questions some of Eddington's assumptions let's explore this fascinating concept.

It's time for brick.

Tyler Reddick here from 2311 racing victory lane yeah it's even better with chamba by my side race to chamba casino dot com let's chamba don't purchase necessary VTW group boy we're prohibited by law CT and C's 21 plus sponsored by chamba casino.

And we're back.

Okay so the Eddington limit.

What is this like what is this calculation that Eddington came up with.

So back in like circa 1916 that's when the paper came out so he's he'd been working on it.

Yeah this is fairly modern but not so modern because at this point in the history of astronomy we didn't actually know how stars worked.

People had realized they weren't.

Or they hadn't figured out galaxies existed yet.

So yeah Eddington was trying like so many other people to figure out what it was that allowed stars to exist.

And we were at a point in geology and paleontology that we were also realizing planet is old.

And so that meant the star had to be old that when stars had to be burning for a long period of time.

And they still hadn't fully figured out all the ins and outs of nuclear fusion.

But Eddington started to propose okay so what if we have.

Nuclear something going on in the center of a star.

Not correct.

As people were perhaps assuming or yeah it wasn't any kind of chemical exothermic reaction.

They knew that much it had to be something else and we were starting to understand nuclear reactions at this point.

And so what he proposed was something was going on and we were really struggling to figure it out because electrons were like no we won't allow this.

And so they had to figure out like electron tunneling and quantum mechanics and stuff like that.

So before we even fully understood the quantum mechanics that would allow the center of a star to do the things it needs to do.

Eddington proposed what if stars are balanced between light pressure pushing outwards and gravity pushing inwards.

And like light pushing are you mad?

It was absolutely amazing and I mean it's more complicated than that.

We have to look at what are the electron pressures involved, what are all the other atomic reactions involved.

And we're still working to figure out the details of stars.

And in coming up with this idea it was realized well shoot if a star is producing too much light it's going to overcome gravity and just blow things apart.

If anything is producing too much light it's just going to blow things apart.

So there is some kind of a limit on how much energy can be presented while at the same time gravity is trying to hold things together.

And this idea I mean I think even now you know we look at stars we know they're in hydrostatic equilibrium and say well yeah it's the light pressure that is keeping the star from folding in on itself.

Explain that idea of just like even the light pressure.

It's I love this and if you ever want to see beautifully cleanly done maths on this.

Chandra Sekar put together a stellar evolution book that was published I want to say in the 1930s or 40s.

And there's copies of it still floating around it's a little penguin book penguin publishers.

And the maths for this is entirely straightforward it is all algebra.

And so the idea is light has it doesn't have mass but it has energy and energy in motion has momentum.

And so when photons hit things they transfer momentum.

And so every time you zot something with with a photon it can absorb the photon and it also has a transfer of momentum in the process.

And so in the core of a star we have all of these nuclear reactions taking place.

And in the process photons are being produced.

These photons work their way outwards and they random walk they're transferring energy in all directions as they go.

Which is good because that random walk without any specific direction supports a sphere quite nicely.

And because they can escape outward you end up with the bulk of the motion on average being outwards balanced against gravity.

So in the center you have this radiation pressure it goes out then you have convective zones that are supported through the old fashioned pressure laws.

And all these different things you can just work through the math for each area of the star figuring out where do these different pressures end up dominating.

And this is actually like an undergraduate homework assignment that I still remember both hating doing and really enjoying the fact that I was capable of doing it without getting help.

But that idea I mean I think when you think about say steam rising or filling up a balloon and you sort of think about the sort of thermodynamic movement of the molecules bouncing into each other.

That would probably and people were probably examining this at the time and that was probably their first incentive.

Well it's a giant blob of gas and the gas is hot and here's how much sort of you know entropy is going on.

We use that to calculate the star but no I didn't can say no it's the light it's the photons not just particles bouncing into each other in the way we experience this in steam engines and things like that.

And what's wild is it takes all of these things working together so the light is heating the gas there's gas pressure added.

So you have light pressure you have light transferring heat creating gas pressure you have different atomic reactions going on which are ionizing things and creating an electron pressure.

And the classical Eddington didn't include all the electrons properly and so we've had to modify the equations over the years to better and better represent what's going on in stars.

It's super complicated but Eddington was the first person to really realize what was going on and this is where having Chandrasekhar coming and being his graduate student made so much sense between the two of them they were able to figure out.

And Chandrasekhar did surpass his advisor and this did lead to a great deal of chaos that we talked about in our episode about Chandrasekhar years ago.

But the two of them together were able to explain all the different phases in a star's life and what keeps stars going the way they're going.

All right we're going to continue this conversation but it's time for another break.

Tyler Reddick here from 2311 Racing victory Lane yeah it's even better with Jamba by my side race to jump a casino dot com let's jump.

No purchase necessary VTW group boy we're prohibited by law CT and C's 21 plus sponsored by Jamba Casino.

And we're back so okay so this is kind of the limit is hydrostatic equilibrium but it also sort of defines how quickly a star can create mass.

Grow so sort of help me understand this.

So what you end up with is as stars get more and more massive it puts more and more pressure on the center of the star which accelerates the rate at which light is being produced.

At a certain point the light pressure exceeds the gravitational force holding the star together.

And so the light pushing outwards starts to push it a rate greater than what gravity can pull inwards it's this balancing of forces.

That that allows a star to start to blow things apart it's right the slow mode version of what happens in supernova in a supernova.

The stars core stops producing light you run out of balance it collapses violently in the collapse you end up with new nuclear reactions going on releasing energy and that blasts what's falling inwards outwards.

It's a much slower process or at least a much less violent process that goes on in young stars in massive stars as material tries to fall into them.

But it's the exact same physics and I love the fact that we're dealing with the same equations just implemented in different limits for all these different cases.

So then where does this kind of get us in the limits of how big stars can get?

This is where we keep being like oh shoot our observations don't match our equations so we keep finding new ways that stars find to produce things that generate pressure and don't create pressure.

So we think that the limits are somewhere below 200 solar masses and I'm going to put it that vaguely because the universe likes to keep going no you were wrong I'm going to be a bigger star.

Yeah I'm going to start over here.

Yeah and quantum mechanics isn't complete we know this because particles don't do what we thought they were supposed to do.

We don't know the underlying physics to the standard model we just know the standard model is there may not even be underlying physics which is super annoying to think about.

But at some point below 200 solar masses you are adding material to a star and it just starts blasting light to the point that it clears the area around it.

And is that sort of separate like I sort of I think about the editing limit core first that you're imagining that you're adding material to the star the star is getting hotter both in its core and at its surface and like the level of heat is kind of ridiculous.

Yeah a star like our son 15 million at this Kelvin I think at the center while say 5,800 Kelvin at the at the surface but you take a star like the hottest star like one of those like 200 times solar masses and you're at millions of degrees even on the surface.

And so if you try to add more material then this thing is going to you know it's going to it's age will decrease and it's going to go through some of its phases of dying almost instantly right because it's just but then I think where you're getting at next is that not only that but then you have all of the incredibly intense solar wind that's coming out all of the radiation that's coming off of the star.

This is heating up the gas that's around it you need cold gas to get a star to form not hot gas but the bright stars heat up the gas they make ionized gas and then that doesn't want to add to the star so.

So in addition to sort of the internal limits of how big a star can get you also have it sort of interaction with its environment preventing additional material from falling in.

And and this is just one of the many super cool things that happens as we we literally live in the realm where we're looking at the quantum mechanics of how atoms change as a function of temperature pressure and everything is balanced between these things temperature and pressure defines all these characteristics.

And the pressure is coming both from gravity inwards and light outwards but some of the energy can go into ionization and and this starts to lead to really weird things and and I'm going to take a moment and say variable stars we have to remember the variable stars because one of the super cool things that

that Anakin realized while doing this work is in a star's atmosphere you have light going through all these different parts of the star that are different temperatures different pressures and because of this they have gases at different states and gases in different states have different optical properties and one of the weird ones is helium.

So helium one like us through it so neutral helium like us through it helium to helium with no electrons attached is like I shall not let light pass and an opacity means that when the photons hit a cloud of fully ionized hydrogen it it is more likely to cause pressure instead of to pass through it acts like a wall.

So in a star as it heats up it hits a point as it's heating up heating up heating up that the helium goes from singly ionized to doubly ionized and it becomes opaque and it's like I'm going to expand instead of getting hotter at this point and so you have a star's atmosphere starts expanding instead of heating up the same way.

Now as gas expands it cools so as the stars expanding it eventually hits the point where it's like I'm going to become singly ionized again and then the light can just pass right back through and so now you have a star that doesn't have the same amount of light pressure because it's now singly ionized helium.

And it's also cooler and so there's less light pressure in general and so it begins to collapse as it collapses it heats up and it eventually hits the point where it heats up enough where the it starts to expand because it's heating but it's also heating faster than it's expanding until it hits that doubly ionized helium again.

This is the capa mechanism and it's entirely driven by quantum mechanics playing an extra role with the ionization of helium so it's the little physics like this where things decide instead of cooling, expanding, heating they're going to ionize and just do something completely different with all that energy.

These are the kinds of things that we keep realizing we've left something out of our equations and this is why stars can be bigger and stuff like that.

You just chucked a mini episode about variable stars into this episode.

We're going to talk about the implications of all of this in a second but it's time for another break.

And we're back. So now I think we need to pull this all together which is when you take this law, this limit, and you use this to calculate how stars grow in the early universe and then you can kind of apply this to the growth of black holes, you get a certain sort of limit for how big a black hole should be.

And to be clear, the limit is not the feeding of the black hole, the limit is the accretion disk around the black hole, which actually gets star.

So you can sneak up on bigger and bigger black holes, but it's trickstery. So the situation that we're looking at is take black hole, this works for stellar mass black holes, this works for supermassive black holes, it does not matter what size black hole you have.

When the black hole is feeding because angular momentum is a insert naughty word here, as material attempts to fly in towards that black hole, the angular momentum is like no, you shall go spiraling around.

And so material builds up in a disk of spiraling material that is trying to shut its angular momentum through friction and light and other forces.

And how this works is still a bit of a mystery.

It's a good homework equation. Another thing I really enjoyed, but this is a graduate school homework.

But yeah, yeah, I mean, just like how you can get material and how do you can get some black holes emerge is still a bit, you know, this sort of.

Shut in all of the momentum is this is where gravity waves, you're now getting rid of energy through gravitation instead, it's super cool.

I love this part of physics. So you have your black hole, you have an accretion disk around it.

And as the material builds up in the accretion desk, it gets thicker and denser and has super high pressure.

And temperature and pressure are the two things you need to have that are high in order for nuclear reactions to start occurring.

And it's not identical physics to what's happening in stars other than like it's nuclear reactions the same way, but you're not going to get like the CNO cycle that is working in the same ways and an accretion disk.

It's slightly different, but also the same physics.

It's right. Yeah, but you're by guess, but your point is is that this disk around a black hole,

gas is being mushed together and the temperature is increasing and it's starting to behave like the interior of a star falls under the Eddington limit.

Time to calculate how big these accretion disks can be around various black holes before they're too hot.

They start to blow themselves apart. The same physics is happening in this situation.

And with supermassive black holes, the ones in the hearts of galaxies that like to be what we call quasars and active galactic nuclei.

Once you start hitting the quasar side of that equation, the black holes can have accretion disks so large that they start generating light pressures that empty out.

The cores of galaxies, right.

At which point there's nothing there for the black hole to eat anymore.

So it chows down on that accretion disk and then sits there going, I am starving.

There is nothing I can do about this. I have done this to myself.

But so then the math when you sort of think about it is like you started at the very beginning, you say,

OK, we got the primordial hydrogen and helium. We know how big a star can get.

So let's calculate the bit for the first stars. Great. That tells us the stars.

Let's say those leave behind black holes. Great. Now we know how big those black holes were.

Now the black holes try to pull in mass.

And I need to put numbers on this because we are starting to realize that these first stars could have been between a thousand and ten thousand solar masses.

I'm trying to follow the standard line here and then obviously the second generation of stars.

But even the first star is like you've got hot cores.

They're going to read to limit how big the star can get.

Maybe you can get bigger because it has less metal that's poisoning or whatever.

So then you get those first stars die. You get black holes remnants of black holes feed.

The black holes get a creation disks. You're limited by how big the black holes can get.

And so that defines how rapidly this these black holes can add on mass.

They're a creation disk. Bigger than they can feed faster.

There is a limit and the astronomers have gone back. They made all these calculations.

String them together. They've reached the sort of the size of the black hole that you should expect at certain ages of the universe.

And the problem is the ones that we see are too big.

Too massive. That they broke the rules.

That at some point they either violated the ending to limit in terms of stars or they violated the ending to limit in terms of black holes.

But now we're in a gallery. We live in a universe with black holes.

That at some point took Eddington's careful calculations, tore them up, stomped on them and said, huh.

Or they just found another process. Right. And so now please let's go through where we think the universe has potentially violated the Eddington limit.

So and the Eddington limit is is limited to this is what happens when gas is doing the in falling.

And it's because light pressure can push on gas, but light pressure pushing on bigger objects is going than atoms and gas particles and dust particles is going to have a different kind of effect.

So when you start looking at two black holes merging together, the Eddington limit plays a different kind of role.

And also with accretion desks, if you look at the situation of supermassive black hole feeding on the gas and dust around it, feeding on the gas and dust around it, empties its area.

Now you merge two galaxies together, you rearrange all the dust and gases and you get to start over.

Now where we start running into problems is we expect all of these things to have time scales.

And the time scales are like, nope, you haven't had enough time in the universe.

And we keep finding this over and over and over. So we need to figure out how to reset the time that it takes for things to happen to be different.

And this is where like new research just in the past few months, I think time has no meaning. It still has no meaning.

Is starting to point towards the first generation of stars were far more massive than we had envisioned.

And they're actually starting to come out with, well, if you make it this big, you get this chemical ratio and we actually see nebulae filled with that chemical ratio exactly as expected at less than a billion years of the universe being in existence.

And so it might be that if you have that first start just to hydrogen helium, no metals, they're able to get much bigger.

We know that is true and it's true because you don't have all the additional lines that electrons can go into to change how light is held back.

You end up with with a lot more of this helium being its opaque self allowing stars to just get big and hot and stuff like that.

And like you mentioned some recent research and there has been examples of observations that have been made with x-ray observatories and things like that where they're literally watching black holes feed at super-eddington rates.

And now that we're still trying to figure out what what did we miss and this this is where we're starting to realize oh shoot you have to include electrons in ways that we didn't originally you have to include what is the chemical constituency of the accretion disk in ways that we hadn't thought of before.

And magnetic fields.

Yeah so you have to balance every single force you have to balance every single quantum reaction and trying to figure out what did we forget this is where creativity is a part of science that we don't acknowledge nearly enough because it's it's one thing to go through into our homework where we're like let's just worry about what hydrogen helium are doing.

They're the bulk of the universe and then you start realizing okay so to explain stars like our son you have to start including heavier atoms otherwise it doesn't work at the mass it's at okay.

And so we're getting more and more complex in a lot of cases but the computer power and also the creativity of the person running all of of the math sometimes means we just don't think of things or our computers aren't powerful enough for us to include all those things both factors are at play.

There are a lot of times where you're like shoot if I run this the way I have it written it's going to take four months so let's simplify the equations and then there's also the human willingness of well I could figure out all of those atomic quantum mechanic electrons bouncing around doing their thing and I do not want to so I'm going to simplify I'm going to do this in one dimension instead of three dimensions I'm there's so many ways that we simplify things.

Because that makes the math doable and there's so many ways that we simplify things because we don't have computational power yet yeah but you just you sort of hold that the most complicated field of science is magneto hydrodynamics plasma dynamics yeah yeah and that's exactly what this is this is one of those problems that you have you have magnetic fields you have plasma you have moving.

Charge particles charge particles moving like a fluid in this environment and and it is one of the most complicated things you and then it also brings aspects of general relativity and also brings on a whole bunch of quantum mechanics what I what I love about this though is that we it's kind of like you know when you're like doing homework assignments you've got some complicated problem that you're trying to do yeah

and you do your math and then you but you know the answer you go and you look at the answer key but it just gives you one number just says you know 45 meters per second you go back to your calculation you got 31 meters per second you're like how how yeah and then you examine every single part of the calculation to get you to go like I know the answer has to be

and so I have to sort of revisit all of my assumptions and try and figure this out the universe has told us what the reality is the heading to limit works very well most of the time and yet we live in this universe that is slightly different and so it's those assumptions somewhere that we're off track and that what but you but you know you're not just like completely moving in an area where you give no idea where you're going so has structure

was so amazing about this is when Eddington first did this when Chandrasek are expanded on this when I did it as a homework assignment we were looking at a line through a star from the center to the surface looking for all of the places where changes in pressure and temperature

changed what physics was dominant so in the core you have nuclear reactions at what point is you move away from the core does the pressure and temperature hit a limit where you switch from one mode to the next it's a straight line calculation through a star and it's good enough as we now look at accretion discs around supermassive black holes

we're still largely trying to figure out how to do it by taking a cut through that desk looking both up and down and also center outwards so now it's two dimensions we're still simplifying and now because of all the rotations and because of everything else it's no longer something you can do with pen and paper

we have gone from 1916 working on the chalkboard to 2020 is working on a supercomputer and it's the exact same physics we're just changing where we're applying it

yeah well it's a fascinating concept and you know I think we're going to see a lot of work and thanks to James Webb and other big observatories we're making a lot of progress so stay tuned for maybe someone coming up with the answer

thanks very much thank you Fraser and thank you so much to everyone out there on patreon who allows us to keep the show going I rich is able to make a sound good Viva is able to keep the website updated

everything works because of you this week I would like to thank the following ten dollar and up patrons Alex Cohen Andrew Palestra Arctic Fox

Bore andro loves all Benjamin Davies boogie net Brian Kilby Camerasian Cooper David Davies Resetter Don Mundes Elliott Walker Father Prax Frank Stewart Gerhard Schweitzer Gordon-Dewis Hal McKinney James Signevich John Baptiste Lamatier Jim McGeein Joanne Mollvi John M. JP Sullivan Katie Burn Kimberly Rake Larry Zat

Lou Zeeland Mark Phillips Matt Rucker Michael Prasada Michelle Cullen name Olga Paul Jarman Philip Grant RJ Basque Ron Thorson Sam Brooks and his mom Scott Bieber

Subhana Stephen Kroffey the big squish squash Tiffany Rogers Trichor Wanderer M 101 and Zach Cookeen Dull thank you all so very much

all right thanks everyone and we will see you all next week bye bye everyone

astronomy cast is a joint product of universe today and the planetary science institute astronomy cast is released under a creative

commons attribution license so love it share it and remix it but please credit it to our hosts Fraser Kane and Dr. Pamela Gay

you can get more information on today's show topic on our website astronomycast.com this episode was brought to you thanks to our generous patrons on Patreon

if you want to help keep this show going please consider joining our community at patreon.com slash astronomy cast

not only do you help us pay our producers a fair wage you will also get special access to content

right in your inbox and invites to online events we are so grateful to all of you who have joined our

Patreon community already anyways keep looking up this has been astronomy cast