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Artist illustration of a White Dwarf.
In some of the most extreme objects in the Universe, white dwarfs and neutron stars, matter gets strange, transforming into a material that physicists call “degenerate matter”. Let’s learn what it is, how it forms.
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Announcer: This episode of Astronomy Cast is brought to you by Swinburne Astronomy Online, the world’s longest running online astronomy degree program. Visit Astronomy.Swin.edu.au for more information.
Faser Cain: Astronomy Cast Episode 382: Degenerate Matter.
Welcome to Astronomy Cast, our weekly facts based journey through the cosmos where we help you understand not only what we know, but how we know what we know. My name is Faser Cain. I’m the publisher of Universe Today and with me is Dr. Pamela Gay, a professor at Southern Illinois University Edwardsville and the director of CosmoQuest.
Hey Pamela, how are you doing?
Dr. Pamela Gay: I’m doing well. How you are doing?
Fraser Cain: I’m doing great. So we are now two episodes away from hiatus, so –
Dr. Pamela Gay: Something like that.
Fraser Cain: Yeah, so there’ll be episode. This is the penultimate episode.
Dr. Pamela Gay: And the time that we’re spending on hiatus is actually going to be spent doing lots of awesome things that you can follow along with online. Fraser is continuing his coverage of New Horizons over at Universe Today and with his weekly video series. I’m doing the same thing over at CosmoQuest. And I’m also covering Sirius because I’m Team Sirius, so expect lots of asteroid coverage coming up in the next month.
And in August I’ll be over at the International Astronomical Union meeting in Hawaii basically following all of the, well, politics of our field as we work to define and refine our understanding of the universe and how we name things because this is apparently a thing to argue over.
Fraser Cain: Yep. You’re going to decide that, but the vote for Pluto is not back on the block at this time, is it?
Dr. Pamela Gay: No, it’s not. No, no. Pluto, there’s a lot of rumors going around that somehow Pluto’s going to get redefined. No, that is –
Fraser Cain: Not going to happen.
Dr. Pamela Gay: No, it’s really not.
Fraser Cain: Okay.
Dr. Pamela Gay: Anyone who is making a claim that Pluto’s a planet, one thing to ask yourself is have they written a book or are they in a position to monetarily benefit from making a big deal about how Pluto should be a planet because that seems to be what it’s often tied to. Because if you’re just interested in the science it really doesn’t matter.
Announcer: This episode of Astronomy Cast is brought to you by 8th Light Inc. 8th Light is an agile software development company. They craft beautiful applications that are durable and reliable. 8th Light provides disciplined software leadership on demand and shares its expertise to make your project better. For more information, visit them online at www.8thlight.com. Just remember, that’s W-W-W dot the digit 8 T-H-L-I-G-H-T dot com. Drop them a note. 8th Light, software is their craft.
Fraser Cain: So in some of the most extreme objects in the universe, white dwarfs and neutron stars, matter get strange transforming into material that physicists call degenerate matter. So sort of what it is, how it forms and so on. All right Pamela, so you put this topic in the list and I’m amazed that we haven’t actually – I guess we’ve done it separately, but we haven’t actually focused on the degenerate matter itself. So what is an example? What is degenerate matter?
Dr. Pamela Gay: Well, degenerate matter is what you get when the whatever particle it is crammed together so closely that it forms essentially a crystalline structure as all of the different particles make sure that they don’t assume the exact same energy state, which means they’re in the same energy level of an atom and they have the same spin state in the atom.
Fraser Cain: Okay. All right. We’re going to have to unpack this a little bit here. So if I think back to my high school chemistry, my university physics, electrons go at various energy levels around the nucleus.
Dr. Pamela Gay: Yes.
Fraser Cain: And so you can fill up one in the first –
Dr. Pamela Gay: Two in the first.
Fraser Cain: Two in the first, four in the second and then it goes all the way to 16 and 32 and so on. So those are the orbitals. You’ve got the electrons all kind of trying to pack together into those orbitals and if it is generate matter, what am I going to see?
Dr. Pamela Gay: So what you’re dealing with is actually slightly more complex then what you’re saying. Each energy level is actually pretty discreet. So you have what’s called the S1 orbital, which is the lowest energy level in an atom and two different electrons can be in it. But they can’t have identical quantum numbers. This means that because spin is nice and easy to change, quantum number one will be spin up, one will be spin down so they’re not identical.
So they have the same energy mostly. The only difference is in the spin state to prevent Pauli exclusion’s principle, two things from having the same quantum numbers. In the next set you have the S2, which again you jam two electrons in, they assume different states. Then you have the D and the P orbitals. You keep adding and they have different probability functions for where around the atom you’re going to find these orbiting electrons.
Now, when you’re a degenerate star, you don’t have the space for every atom to have its own infinite set of energy levels. And, in fact, you run into the situation where you have two atoms crammed right next to each other and the electrons are trying to share energy levels, which means that you can’t have both atoms have their electrons in that same S1 orbital with their spin up and spin down because then you’re trying to have two atoms sharing the same energy state.
So in this crystalline structure you end up with the atoms spaced out and the electrons forming this cloud of ever increasing energy levels where things are packed so tiny that in order to not offend the Heisenberg uncertainty principle, because we’re all about uncertainty today, things are very, very closely located in a place because otherwise their energy level is going to overlap with something else and you have the same quantum numbers and badness occurs. So things are located right in one place, but this means that they have all sorts of crazy momentum, which means you have a whole lot of fluttering about occurring in a very small space as you basically have this insanely high pressure diamond of a star.
Fraser Cain: And we talked about this that this is the state that a star like our sun will see at the end of its life when it no longer has the outward force, the light pressure, from the fusion at its core. That shuts off, but you still got the inward gravitational force of all of the atoms that are at the core, but it could have been anything, right? It could be bits of helium, bits of carbon, bits of oxygen, but the point is, is that when it gets squished together that tightly, it turns into this very special type of matter because the electrons are not able to orbit as freely as they would like to around their nucleuses right?
Dr. Pamela Gay: And it’s not actually everything that can do this. This is where we get limited to you have to have this quantum number limitation that causes the degeneracy to happen. So we talk about this most often with fermions. We also can see this in protons, although in things like the white dwarf star that our sun will occur someday in the future, the protons degenerate effect is basically just an error on the electron degeneracy.
We see this with neutrons, however, as well. But we don’t actually see the carbon having to worry such that you end up with a carbon degeneracy because the electron degeneracy and the proton degeneracy, it’s the individual particles that we worry about.
Fraser Cain: So when you see those articles on the internet, and I’ll admit that we’ve done that a bit on Universe Today, about it’s the biggest diamond.
Dr. Pamela Gay: Yeah, totally legit.
Fraser Cain: Is legit. So it is a diamond, but it is not a diamond that you want to attempt to chip off the white dwarf. And if you could, though, chip off a chunk of white dwarf star and bring it to earth, would it remain in its degenerate state?
Dr. Pamela Gay: No.
Fraser Cain: Would you have a diamond?
Dr. Pamela Gay: No.
Fraser Cain: Right.
Dr. Pamela Gay: Well, so you might still have a diamond because there’s nothing to prevent the carbon from staying in that crystalline structure, but you’d no longer have a degenerate atomic mix. So what we have with white dwarfs is to look at our sun someday in the future. Our sun is currently happily having nuclear reactions burning in the center, you have light pressure going out and it’s the light pressure generated by that nuclear burning that is supporting our sun. Turn off those nuclear reactions; turn off that pressure hose of light and the outer layers of the sun are just going to collapse down. And while they collapse, initially a gas pressure is trying go no, stay out. You’re hot. I’m hot. Let’s support ourselves, but the gas pressure can’t win, the ideal gas law can’t support the star against the force of gravity.
So it collapses and collapses and collapses and what eventually happens is it’s with relativist corrections, it’s the electromagnetic force between the protons and the electrons repelling each other that is holding the star apart to a certain degree. And more importantly, it’s the electrons pressing against each other, being all degenerate in their separate, no two quantum numbers the same, degenerate gas.
Fraser Cain: So the situation is, is that the star wants to keep on collapsing. It reaches the point where really the only thing stopping it is just these individual electrons are just pushing against it, literally with uncertainty that – this is the thing with the Pauli exclusion principle – that just because you can’t have them occupy the same quantum state, they don’t compress any further. I just find that concept just so fascinating. But, of course, nature has figured out ways to get around this problem, which is if you just have more mass, you could just ruin the laws of physics.
Dr. Pamela Gay: Well, it’s not that you ruin the laws.
Fraser Cain: Exploit new laws of physics.
Dr. Pamela Gay: You exploit new laws of physics. And this is one of those stories in science that kind of just makes you grumpy. So Chandrasekhar arguably one of the most brilliant and well-organized and thoughtful in terms of how he approached getting everything done astronomers of the modern era of the post-quantum-canics age of astronomy, if you haven’t read a biography of this man, do so. The one written by – I can’t remember his first name, last name is Mukherjee is absolutely brilliant and gives you amazing insights in how Chandrasekhar was able to accomplish all the things he did.
When he was just either 19 or 20, depending on what source you read, I think he was just 20, he traveled from India to England to attend graduate school. Now, I was 22 when I started graduate school and I went straight through without stopping, finished everything in four years. No, he had to do things on an accelerated timeline. So this very young, very brilliant man had a very long boat ride. And while on this very long boat ride, like many of us nerds, he started playing with the theories of stellar atmospheres. And I have to admit, I have done the same thing. But unlike me who was just happy to figure out well, if you do this to a star, this occurs, he actually took things to the extreme and realized that all of the, at his time, modern calculations of stellar atmospheres failed to take into account the needed relativistic corrects when they achieved the highest pressures that occur when you turn off light pressure when a star dies.
And when he added in those relativistic corrections, he realized that when the mass of the collapsing object exceeds 1.44 solar masses, the electron degenerate pressure just isn’t enough anymore. And at this particular mass cutoff, the electron generate pressure gets overcome and the electrons and protons squish together, lots of energy is given off and you end up with a neutron star.
Now, when this happens in the real universe, it happens with great violence and it’s called a Type 1a supernova and you don’t always end up with exactly 1.44 solar masses leftover when this is all over. In fact, you never end up with that much mass leftover. But in other situations where the collapsing star has during the collapse what’s leftover is greater than 1.44 solar masses, you end up collapsing not into an initial white dwarf, but instead straightaway right into a neutron star, where in this case it’s the neutrons trying to go, “Can’t share the exact same quantum numbers” and they’re pushing one another apart with this neutron degeneracy pressure trying to support this extraordinarily dense little tiny, tiny, tiny, tiny fragment of a star.
Fraser Cain: Right, but in this situation, right, the proton and the electron are actually squished together to make neutrons.
Dr. Pamela Gay: Yes.
Fraser Cain: That all the electrons, all the protons, there’s no longer protons, electrons, there are only neutrons and it’s this final stage where the neutrons just – you can’t make two neutrons share the same quantum state that you’re left with.
Dr. Pamela Gay: So what’s really amazing about this degenerate matter is how it just doesn’t behave in a way that we’re used to. Normally you think you add more matter onto something it physically gets bigger. In normal gas laws, you increase the temperature, the pressure goes up. With degenerate matter in stars, yeah, sure they’re hot, but white dwarf stars cool off over time. They start out hot because they’re a stellar core remnant, but they cool and they stay degenerate because it’s the gravity that’s collapsing them down to increase to create this huge pressure.
A white dwarf, again, goes up to 1.44 solar masses. A white dwarf is about the size of our moon. So imagine our sun, which is hundreds and hundreds of times bigger than the earth getting collapsed down to the size of the earth’s moon. That’s kind of impressive, but that’s nothing on what a neutron star does. Neutron stars are between 1.44 and 3 solar masses and their diameter and the diameter of Manhattan are about the same.
Fraser Cain: Right. They’re about 10 kilometers across, right?
Dr. Pamela Gay: Yeah. And so if you took a neutron star and set it on Manhattan, first of all you’d collapse the entire earth onto the surface of the neutron star and there would be no more Manhattan or earth, which would be bad. But if you did this instantaneously there would instantaneously be this moment of the neutron star just sitting happily on top of Manhattan.
Now, in terms that you might be able to think of a little bit better, a teaspoon of white dwarf has about the same mass as an elephant. Whereas a teaspoon of neutron star, I’m just confirming that I get all of the numbers on this correct, is 20 billion tons on earth.
Fraser Cain: Like a mountain?
Dr. Pamela Gay: That’s, I think, a lot bigger than a mountain.
Fraser Cain: Oh.
Dr. Pamela Gay: Yeah.
Fraser Cain: Yeah, well [inaudible] [00:16:37], not the whole earth, the earth is 6 or something 2 septillion tons I think, but yeah, that’s a lot.
Dr. Pamela Gay: Yeah, so the entire earth is 6 times 10 to the 21 tons, so that’s a lot, but the mass of teaspoonful – teaspoon, little tiny amount of neutron star is 2 times 10 to the 10 tons.
Fraser Cain: Okay, great. That just gives us a sense of scale. So we get these neutron stars. They are made of this degenerate matter, but what would it be like, is it neutrons packed together like crystals? Are they jiggling around like a liquid or a gas? What, if you could take a look at it?
Dr. Pamela Gay: So when we think of liquids and gases, we think of things that have the capacity to flow. This is actually built somewhat into the definition where in a solid you have atoms that are pretty much locked in place, their electrons are happily rolling about them. So in a liquid you have atoms that are still somewhat connected to one another, although these connections are, well, fluid. In a gas, things just aren’t connected anymore and things are just kind of flying all about. That’s the definition of a gas. You don’t even necessarily have collisions on a regular basis.
In a neutron star, and in a white dwarf and in any other form of degenerate matter, you don’t really have motion other than a frenzied vibration. The Heisenberg uncertainly principle has basically located very, very precisely where everything has to be because if it moves it’s probably going to end up overlapping its energy level with something. So you be in that energy right there. Don’t move. You be in that energy right over there. Don’t move. So what this means is since you have really located things in place, you can’t know how fast they’re moving, which means these little suckers are vibrating the – well, vibrating’s probably too specific of a term. They’re being frenzied in a very little, tiny space. So you have lots of frenzied activity in very tiny spaces and it’s not a function of temperature in these high, high pressure environments, which is just counterintuitive to how we ever think of gases.
Fraser Cain: And so it is literally the very limit of the Heisenberg uncertainty principle? You just can’t get any more certain than this. This is as certain as nature – it’s almost like your certainty is approaching infinity and that anymore certain and the whole thing just collapses into a black hole because the more gravity you get to the point that it’s just trying to mash the thing together even further, it kicks over into a black hole. And that’s the next step, right, is we get a black hole.
Dr. Pamela Gay: And I don’t think I’d go as far to say as we’re at the limit of the Pauli exclusion principle or the Heisenberg exclusion principle, it’s actually much more complicated than that, but we are at the limit of what the degenerate gas pressure can support. And when the degenerate gas pressure, with all of the factors including relativistic corrections, when you get to the point that you overcome how the degenerate pressure is able to fight against this onslaught of gravity crushing down, we actually reach the point beyond neutron degenerate pressure that we’re not entirely sure what’s going on.
There are people that run maths claiming that you end up with a quantum degenerate, or quark, rather, degenerate pressure where the quarks are now the things that are trying to find ways to not having identical quantum numbers. But at the same time, we have no way of proving that. There are people that even go so far as to make up particles that supposedly make up quarks, even though we have absolutely no need for particles that make up quarks or any evidence to support the need for particles that make up quarks.
So basically you reach a point where people start making up shit. What we do know is beyond neutron degeneracy pressure, things collapse down. You get a black hole and we have no clue what’s going on inside the event horizon full stop.
Fraser Cain: Full stop, right. And so on the one possibility you’ve got a situation where there is some other state, but it’s within the event horizon of the black hole, so we could never see it. Like as you said, quark degeneracy pressure, although it’s possible that we could maybe try and figure out, try and see if there is a quark degeneracy pressure using some super advanced large Hadron superconducting, super awesome collider in the future.
Dr. Pamela Gay: Well, but the problem is how do you contain that in a stable, non-explosive way, which is – what you really need is to compact them using magnetic fields, but we haven’t figured out how to pack enough energy for a prolonged period to either with laser – you could also do it with laser – with either lasers or magnetic fields crush something in the appropriate way. With lasers we can create the needed pressures, but for, I think it’s either pico femtoseconds.
Fraser Cain: Um-hum. And the problem being that if you can compress those things into that size, you get a black hole, which then is necessarily behind the event horizon and then the thing will evaporate again and then you won’t know. But maybe there’s some way that a black hole will evaporate in one way if the quarks are mushed together and maybe they’ll evaporate – anyway, this is not our problem. The point being, we don’t know and right now kind of can’t know. So what you’re saying, right, is there could be stages inside. It could go you end up with a black hole that is 20 times the mass of the sun and inside it reaches a certain size and then ones more than that compress further down until they reach whatever is the subatomic particle that makes up quarks and then maybe that remains. Or it could just be that it’s just continuously compressing down forever, which I love this idea.
Dr. Pamela Gay: That’s where we get to the concept of the singularity.
Fraser Cain: Yeah.
Dr. Pamela Gay: And people just love to talk about that. And this is why we study sciences. We still have big questions we don’t know the answer to. But there is one thing that we have totally left out because it doesn’t exactly crop up in astronomy that often and that’s the low density, totally creatable on earth, pulled creation of degenerate matter, which is what happens with those Einstein condensates when you get things cold enough. As you get the atoms colder and colder and colder in this single atomic variety superfluid, all the electrons are like, “Must go to the lowest energy level.” Except if all of the atoms in the material are all trying to assume the exact same energy level, you can’t do that. You can’t get there from here. And so you end up with really weird stuff happening like as you cool and cool and cool and cool a container of stuff, the stuff will actually quite politely climb out of the container as the atoms try to spread out to allow the electrons to have the same energy level but in different places.
Fraser Cain: I love this idea. We’ve done an episode about absolute cold. I think that’s what our next week’s one is we’re going to talk about getting to absolute zero, but the method that they use to cool down atoms is I always sort of envision it like someone’s on a swing, right, and then the person comes back on the swing and then you absorb their momentum from the swing each time they get closer and closer and closer until you’ve sort of got them as stopped as you can.
And so they shoot lasers at these atoms and try to sort of move them in ways – the opposite of the way that they’re trying to jiggle and that keeps the whole thing down. And you get all of these atoms together and then, as you said, they negotiate almost their quantum states. And then the whole thing just starts to move like one big entangled quantum state. It’s really interesting. And we’re going to talk about this next week because it’s such a fascinating thing.
So I think that was a great segue and I am going to wrap up this week’s episode and we will continue on with the conversation about this other way to get to incredibly extreme exotic matter using cold as opposed to pressure.
Dr. Pamela Gay: I’ll talk to you next week, Fraser.
Fraser Cain: That sounds great. Talk to you next week, Pamela.
Thanks for listening to Astronomy Cast, a nonprofit resource provided by Astrosphere New Media Association, Faser Cain and Dr. Pamela Gay.
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