This article explains the Eddington limit, a fundamental concept in astrophysics that sets the maximum luminosity of an accreting object.
Understanding the Eddington Limit
The Eddington limit is a theoretical concept that describes the maximum luminosity that an accreting object can emit. It is named after the British astronomer Sir Arthur Eddington, who first derived the formula in 1926. The limit is based on a balance between two opposing forces – the inward force of gravity and the outward force of radiation pressure.
What is the Eddington Limit?
The Eddington limit is the point at which the radiation pressure generated by an accreting object’s luminosity is equal to the gravitational force pulling matter inward. In other words, it is the maximum amount of radiation pressure that can be generated by an object before it begins to push away the material it is trying to accrete. If the object emits more radiation than this limit, the excess energy will blow away the surrounding material and disrupt the accretion process.
The Eddington limit is typically expressed in terms of the object’s mass. For a non-rotating object with a mass of one solar mass, the Eddington luminosity is approximately 3.3 x 10^4 times the luminosity of the Sun. Objects that exceed this limit are known as super-Eddington sources.
Why Does the Eddington Limit Describe the Maximum Luminosity of an Accreting Object?
The Eddington limit is important because it sets an upper limit on the amount of energy an accreting object can emit. If an object emits more energy than the Eddington limit, the excess energy will be converted into radiation pressure, which will push away the surrounding material and disrupt the accretion process. This can have important consequences for the object’s evolution and the environment in which it resides.
For example, consider a black hole that is accreting material from a companion star. If the black hole emits more energy than the Eddington limit, the excess radiation pressure will blow away the surrounding material and limit the rate at which the black hole can grow. On the other hand, if the black hole emits less energy than the Eddington limit, it will not be able to accrete all of the material that is available to it, and some of the material will be left over.
In addition to its applications in black hole accretion, the Eddington limit is also relevant to the study of other astrophysical phenomena, such as the evolution of stars and the properties of active galactic nuclei. By understanding the Eddington limit and its consequences, astronomers can gain insight into the physical processes that drive these phenomena and the properties of the objects involved.
Overall, the Eddington limit is a crucial concept in astrophysics that describes the maximum amount of energy an accreting object can emit before disrupting the accretion process. By setting an upper limit on the luminosity of these objects, the Eddington limit provides important insights into the physical processes that drive some of the most energetic phenomena in the universe.
Applications of the Eddington Limit
The Eddington limit has a wide range of applications in astrophysics. Here are some examples:
1. Black Holes: As mentioned earlier, the Eddington limit is relevant to the study of black hole accretion. Black holes that emit more energy than the Eddington limit will have their growth limited, while those that emit less energy will not be able to accrete all of the available material.
2. Stars: The Eddington limit also applies to the study of stars. When stars burn hydrogen in their cores, they generate radiation pressure that pushes outward. This radiation pressure can be balanced by the force of gravity, but only up to a certain point. If the radiation pressure becomes too strong, it can disrupt the star’s structure and cause it to expand. This is known as the Eddington luminosity limit for stars.
3. Active Galactic Nuclei: Active Galactic Nuclei (AGN) are some of the most luminous objects in the universe, and they are powered by the accretion of material onto supermassive black holes. The Eddington limit is important for understanding the behavior of these objects, as it sets an upper limit on their luminosity.
4. Stellar Evolution: The Eddington limit also plays a role in the evolution of stars. As a star approaches the end of its life, it can undergo a phase of rapid mass loss known as a superwind. This mass loss is driven by radiation pressure and can be limited by the Eddington limit.
The Eddington Ratio
In addition to the Eddington limit, astronomers often use the concept of the Eddington ratio to describe accreting objects. The Eddington ratio is defined as the ratio of the luminosity of an accreting object to its Eddington luminosity. For example, an object with a luminosity of 10% of its Eddington luminosity would have an Eddington ratio of 0.1.
The Eddington ratio is important because it can provide insights into the physical properties of accreting objects. For example, black holes with high Eddington ratios are thought to be surrounded by hot, optically thick accretion disks, while those with low Eddington ratios may have optically thin accretion flows.
Conclusion
The Eddington limit is a fundamental concept in astrophysics that describes the maximum luminosity that an accreting object can emit. By balancing the inward force of gravity with the outward force of radiation pressure, the Eddington limit sets an upper limit on the amount of energy that can be emitted without disrupting the accretion process. The Eddington limit has important applications in the study of black holes, stars, active galactic nuclei, and other astrophysical phenomena. In addition, the concept of the Eddington ratio provides insights into the physical properties of accreting objects.
