The NEW Ultimate Energy Limit of the Universe

Thank you to DeleteMe for Supporting PBS Is there a limit to how much energy you Is there a limit to how much energy you can cram into, or  pull out of one  patch of space? Well, we thought so, but the James Webb Space Telescope has found  a quasar that simultaneously breaks a century-old theoretical limit and may explain the conundrum  of gigantic black holes in the early universe. There are black holes at the beginning of time  that don’t make sense.

They’re just too big. Black holes grow by consuming matter and merging  with other black holes, in some cases growing into the supermassive black holes in the centers  of galaxies, intermittently powering enormously bright quasars in the process. We see quasars as  countless specks of light shining from the distant universe.

As we’ve learned to peer deeper and  deeper into the cosmic dawn, we expected to see quasars dwindle in power. Their black hole engines  should be smaller the closer we get to the Big Bang. But we’ve now found quite a few quasars from  the first billion years that are way too massive to have grown by the mechanisms that we think  we understand.

The James Webb Space Telescope is only finding more, and we’re forced to rethink our  understanding of black hole formation and growth. There are two broad ways to do this: either  black holes started out uncomfortably large from colossal early stars and then fed  almost continuously for a billion years, OR black holes managed to consume material  much, much faster than we thought possible. Although Webb is finding uncomfortably massive  early black holes, it’s also finding clues to answering the conundrum.

Take a look at this  guy— LID-568, an active galactic nucleus recently observed with the Webb. It’s not the most  massive black hole, nor is it the earliest at 1. 5 billion years after the Big Bang.

We’ve found  quasars hosting black holes a thousand times more massive when the universe was half that age. But  LID-568 is special because it’s currently growing 4000 times faster than the theoretical limit.  We’ve seen super-eddington accretors before, but nothing like this.

If LID-568’s  earlier, bigger siblings did the same thing then we may be closer to understanding  how they got so chonky so fast. But first we need to actually believe that this black hole  really is feeding as fast as it seems to be. Today I want to talk about the absolute limits  of growth and power in our universe.

What’s the most energy you can both cram into and  get out of a patch of space? The physics we’re going to explore will describe the  most extreme environments around the most massive black holes in the universe,  but it’s also the same physics that first allowed us to understand something even  more important: every star in the universe. We tend to think of black holes as purely sucking. 

They drag stuff in and spit nothing out. But actually, as evidenced by the quasar, black  holes—or at least the regions around them—-can be the brightest things in the universe. As  matter falls towards a black hole it heats up and radiates before dropping past the event  horizon—the surface of no return.

That radiation can blast back other infalling material, shutting  off the fueling of the black hole. The theoretical limit to the rate at which a black hole can feed  is called the Eddington limit—it’s an upper bound on both the rate of fueling and power output  in radiation—also called the luminosity. At the Eddington limit the pressure from the  outgoing radiation exactly balances the strength of gravity.

It seems like it should  be impossible to feed a black hole any faster than the Eddington limit, or for a quasar to  glow brighter than the Eddington luminosity. LID-568 glows 4000 times brighter than this, and  likely grows at a similarly super-Eddington rate. The best way to understand how this is possible  is to understand the origin of the Eddington limit.

It’s named after this guy. Now, when  a science concept gets named after someone, sometimes they deserve credit, sometimes  less so. Sir Arthur Stanley Eddington and his limit are in the former category.

This dude  was the OG astrophysicist. He was supposedly one of the few who understood Einstein’s general  theory of relativity when it first came out, and he led the expedition to measure the bending  of light around the sun in the 1919 eclipse, providing the first verification of GR’s  predictions. Eddington correctly guessed that the source of energy in stars is  the fusion of hydrogen into helium, and that was before we even knew that stars  are made of hydrogen.

He pretty much founded the field of stellar physics, and this is where  his eponymous limit actually comes from. That means to understand quasars at their limit we  also need to understand the limits of stars. Eddington’s reasoning went like this.

Stars  are massive, therefore have very powerful gravitational fields. Powerful enough to  cause any fluid such as a cloud of gas to collapse under its own weight. Unless, that  is, there’s some outward push to resist the collapse.

Stars are not typically collapsing,  therefore something must support them. In Eddington’s time, a leading idea was that  stars were hot from the energy gained by the gas as it collapsed to form the star. For a  gas, high temperature means high pressure, and that pressure resists further collapse.

Of  course, stars radiate their internal energy, so this support has to diminish over time. You might  think that would leech away support and so cause the star to collapse—at least a little bit. But  remember that collapsing converts gravitational potential energy into heat.

So as a star radiates  energy it should also shrink and so generate more heat energy to resist collapse. The result would  be a very slow shrinking of the star. In fact, this balance between gravity and gas pressure  IS what keeps stars supported and stable.

But Eddington realised that such a star couldn’t  last nearly long enough—it would need another source of energy—and, as I mentioned,  Eddington guessed it must be fusion. Eddington used this balance between gas pressure  and gravity to figure out how the brightness of stars must depend on mass. As mass increases,  higher pressures and temperatures are needed to support against the increasing gravity, and  higher temperature leads to higher luminosity.

Hotter things glow brighter. A lot brighter.  Eddington calculated that the luminosity of a star acting as a pure ideal gas should increase  with the cube of the mass.

In reality, things are a bit more complicated and the dependency can go  as high as mass to the power of four and a half. This is our first figuring out how  luminous something can be. Stars for now, but this stuff will extend to quasars.

Imagine adding mass incrementally to  the Sun. It grows rapidly brighter as you do—let’s say as mass to the power  of three. So double its mass and it’s 8 times brighter.

At 10 times its old mass  it’s 1000 times brighter. But there’s a limit. At some point—around 55 times its  current mass, a radical shift happens.

Eddington realised that gas pressure  isn’t the only thing that can support a star from collapse. Gas pressure comes from  particles bumping into each other—typically via electromagnetic interactions. Try to compress  a gas and the bumping increases, resisting the compression.

That direct “bumping” is mediated by  the electromagnetic field—we could say via virtual photons. But there are also real photons. Any hot  material is suffused with photons whose energy depends on the energy of motion of the particles. 

Those photons also bump into the charged particles in the gas, and so they provide their own  pressure. We call this radiation pressure. In stars, most of the radiation pressure comes  from photons bouncing off electrons—an interaction called Thomson scattering.

For most stars,  this radiation pressure is tiny compared to gas pressure throughout the interiors. But for  the highest mass stars, the radiation pressure starts to dominate. If we go back to adding mass  to the Sun, once we get to 55-ish solar masses it’s radiating at several hundred thousand times  its current level.

Now it’s supported almost entirely by the insane outflow of radiation.  It’s now at the Eddington limit. Adding more mass would still make it brighter, but not nearly  so quickly—now brightness increases linearly with mass.

We’re also at the upper limit of mass for  stars found at least in the modern universe. So Eddington figured all of this out for stars,  but everything I just described also applies to black holes and quasars. In a quasar we  have mostly-hydrogen gas falling into a deep gravitational well, resisted by the  energy generated in the center.

Now that energy comes entirely from converting  gravitational potential energy into heat with no internal fusion, but the same  battle between gravity and pressure applies. There’s an obvious thing we can do to release  all of that radiation so that it doesn’t resist gravity. Eddington’s assumption of a roughly  spherical distribution of matter falling made sense for stars, but not for quasars, nor for  most collapsing gaseous systems—instead they form disks.

We’ve discussed previously why  disks are so common—from planetary rings to protoplanetary disks to spiral galaxies. The main  process driving this is conservation of angular momentum. Any tiny rotation in the pre-collapse  gas will be amplified as the cloud shrinks.

That same rotation will stop the material  collapsing further along one plane, while the stuff above and below that  plane will continue to collapse—now falling onto the increasingly massive disk of  particles in orbit around the central mass. In the case of black holes, this is an accretion  disk. The accreted material now orbits the black hole instead of falling straight in.

All orbits  are filled, and because adjacent orbits have different orbital speeds they sort of  rub against each other. This is called viscous heating, and inside the disk it’s the  process by which gravitational potential energy is converted into thermal energy. But now, that  thermal energy isn’t trapped in the material and swallowed by the black hole.

The surface of the  disk is exposed to space, and energy radiates from that surface. The first fully self-consistent  description of such an accretion disk came in the early 70s by the astrophysicists  Nikolai Shakura and Rashid Sunyaev, and has been the standard model of such disks  ever since. The model describes a disk that’s very thin, which means it’s easy for radiation  to escape and the disk to become very luminous.

You might think that escaping radiation would make  it easier for the black hole to feed—after all, if the radiation escapes then it’s not  producing radiation pressure to resist gravity. But actually, these thin disks are among  the worst at feeding black holes. Orbiting things don’t fall into the things they’re orbiting—as  evidenced by the fact that our planet doesn’t just drop into the Sun right now.

In order for  the black hole to gobble the material of the disk, that material needs to lose its angular  momentum. The friction and turbulence between adjacent orbits will do that,  but very inefficiently. The result is that these thin disks are luminous but feed the  black hole at way less than the Eddington rate.

The resistance to in fall due to angular momentum  is so strong that to break the limit on feeding our black hole, we’re better off if our accretion  disk looks a little more like the stars that we started this episode with. Imagine we have a  quasar with a classic thin accretion disk. We start feeding more mass into the disk, like we  did for the Sun.

More material means more fuel for heating the disk. At some point, there’s so  much thermal radiation in the hottest part of the disk near the center that radiation pressure  puffs up the inner disk. It becomes then harder for that radiation to immediately escape the  disk.

Now we have a disk supported by radiation pressure more than angular momentum, with gas  pressure also playing a role. Because angular momentum is no longer as important, it becomes  easier to drain the disk into the black hole. But we still have the problem we started with:  radiation pressure and our original Eddington limit.

Overcoming this limit is now possible  because the accretion flow remains at least somewhat disky, rather than being an encompassing  sphere like in a star. Radiation bouncing around in the disk is transported inwards with the  infalling plasma in a process called advection, and eventually it encounters the inner opening  of the disk where it’s able to escape. The disk radiation gets channelled or collimated upwards  and downwards in these central cones that can be enormously bright if you see them from the right  direction.

Meanwhile, the material of the disk, now relieved of some of the radiation pressure, is  able to complete its infall into the black hole. These thick accretion disks come in various  types—there’s the Polish doughnut where the whole disk is thick, almost spherical  besides the central funnels. Or the slim disk in which just the middle, hottest  part puffs up.

All of them are capable of super-eddington accretion rates,  and also super-eddington luminosities, and this has been demonstrated with modern  computer simulations. The downside is that these thicker accretion disks produce less  energy for each chunk of matter swallowed by the black hole—but the shear amount  of matter consumed can make up for that. So there’s a good chance that this is exactly  what’s happening in cases like LID-568.

This isn't the only super-Eddington active galactic nucleus  we've ever seen but it's one of the most extreme. And now that we’ve seen this sort of extreme-super-Eddington accretion in the early universe like it's evidence that  this sort of accretion is crucial for the rapid growth of early black holes. I mentioned that the  alternative explanation for that rapid growth is that early black holes grew via sub-Eddington  accretion at an almost constant rate after already starting out with a massive seed—and  this an idea that strains plausibility.

But if black holes can go through these extreme growth  phases, even if only briefly, then it becomes a lot easier to build a very massive black hole in  the early universe, at least given our current understanding of what that epoch was like. No  doubt if extreme accretion is the answer to our conundrum then the James Webb Space Telescope will  find more objects like LID-568—the fast growing black holes that ultimately power the brightest  quasars to shine from the dawn of spacetime. Thank you to DeleteMe for supporting  PBS.

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