[MUSIC] We've encountered the word accretion several times now, but what exactly does it mean? In astrophysics, accretion is the word used to describe the process of gas and dust being collected together by gravitational forces. Accretion can happen on many different scales. For example, in the early history of our solar system, gravity caused small particles of gas and dust to collect and combine into larger and larger objects. Eventually growing from tiny grains of dust into planetesimals, and finally into the planets that we know today. Accretion is also responsible for gathering clouds of hydrogen into stars and stars into galactic disks. But most importantly for this course, accretion is the process by which black holes are fed. When a star or a cloud of material is near a black hole, it experiences the gravitational effects. The force of attraction accelerates material towards the black hole. And since particles in the cloud are free to move around, they experience a force called viscosity, the effect of friction during collisions with neighboring particles. Viscosity does two things within the accretion disk. One, it slows the particles down in their orbit. Allowing them to fall further into the gravitational well. And two, it heats up the particles, which in turn causes them to glow red hot. A process that creates light called black body radiation. Much of this energy is derived from the gravitational potential energy of the materials. Which we talked about in module one when we discussed escape velocity. Accretion is not as simple as it seems. Why are moon, planets, and stars which are all created by accretion process is spherical, instead of disk-shaped like the rings of Saturn or the disk of a galaxy. The answer has to do with angular momentum. Now you're probably already familiar with the concept of linear momentum, which is the product of an object's mass and its velocity. Momentum in this sense is a conserved quantity. Another way of describing it is through Newton's first law of motion, an object in motion stays in motion precisely because it has momentum. What if an object isn't moving a long path, but instead it's spinning in place? In that case, we now have another conserved quantity, this time called angular momentum. Angular momentum is the product of a object's mass, its velocity and the distance from the origin around the spin. Usually physicist tidy this up by saying angular momentum is the sum total of all the masses being considered and their distances from the origin into a neat quantity called the moment of inertia. In this way, angular momentum L can be expressed in a similar way to linear momentum, as the product of the moment of inertia and the angular velocity. Now what's important here isn't the form of the equation, but rather the statement that angular momentum is a conserved quantity. In plain language, an object which is spinning will continue to spin. Now here's what I mean. If someone has weights in their hands and extends their arms while spinning, they'll have a large moment of inertia. If the subject then pulls their arms inwards, their moment of inertia decreases. So if he is spinning slowly with his arms out, he'll have a good amount of angular momentum. Let's see what happens when he pulls his arms inward. Did you see that? As our subject pulled his arms in, he started to rotate faster. He was conserving angular momentum. As you'll see shortly, the exact same thing happens to the material in an accretion disk when it goes into smaller and smaller orbits. But weren't we supposed to be talking about disks versus spheres? What does angular momentum have to do with that? Well, if a structure is accreting out of a rotating cloud, the angular momentum will dictate in which direction and how fast the final object will spin. Suppose we started with a nice big nebula, and we wanted to condense a star out of it. From a distance, it probably doesn't look like the nebula has much angular momentum, but it does, because all of the particles are far from the center, they have a huge moment of inertia. As these particles collapse due to gravity, they must rotate faster and faster in order to conserve angular momentum. Now since the material in a nebula began with some amount of angular momentum, the new smaller structure must preserve the original amount by rotating faster. So why then is Earth's spherical instead of flat? For structures like Earth, which are solid objects held together by their own gravity, the centrifugal force does flatten it a little bit. Which is why we call Earth an oblate spheroid instead of just a sphere. If Earth were to rotate faster and faster, eventually the centrifugal forces will exceed the internal stress, and Earth would be torn apart. Angular momentum causes rotating objects to flatten into disks. Earlier, we said that accretion was the process by which black holes were fed. Now when a physicist says that, we are feeding a black hole, we're describing the transfer of material and energy towards the black hole's event horizon. In the same way that when you're eating, you're transferring material and energy into your own body's mouth horizon. When we were discussing Newtonian mechanics in module one, we used two equations to describe two important types of energy. Gravitational potential energy, and kinetic energy. Any matter in a gravitational field has potential energy, which it can give up as it descends into the gravitational well by converting potential energy into kinetic energy. Now, let's have a look at some matter falling into a black hole. Recall for a black hole with mass M and radius R, that we can consider a test particle with a mass little m. The gravitational potential of energy for the in falling particle is equal to G times big M times little m divided by R. If the particle starts with zero velocity, somewhere infinitely far from a black hole, much of the gravitational potential energy will turn into kinetic energy. In which case, we set kinetic energy, one half mv squared equal to the gravitational potential energy, GMm divided by R. Since the mass, M of a black hole can be large and the radius can be minuscule, even the tiniest particles can be accelerated to incredible speeds. However, it's worth noting that these equations are classical. All of the energy of the infalling particle has to go somewhere and indeed much of that energy becomes heat. Which is then radiated away in the form of light. In the centermost regions of the accretion disks around black holes, the disk material can become so incredibly hot that it produces enough light to push back against infalling material. Here, we use a specific name for when the force of gravity, pulling material inward is equal to the pressure pushing material outward. It's called the Eddington limit, named after Sir Arthur Eddington. The Eddington limit describes a natural limit to how much material can be captured from the accretion disk around a black hole. And this is based on its power output, or luminosity of the infalling material. The limit is expressed in this equation. If the luminosity of the disk exceeds the Eddington limit, material in the disk will be pushed outwards from the interior of the disk. And if the luminosity is below the limit, gravity will pull more material in. This equation is powerful because it allows scientists to estimate the minimum mass that a black hole must be simply by measuring the luminosity of the system.