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Chapter 27: Problem 20

What is the Jeans length? Why is it significant for the formation of structure in the universe?

Short Answer

Expert verified
The Jeans length is critical for the formation of celestial structures in the universe. It defines the minimum radius a gas cloud must have for it to overcome thermal energy and collapse under its gravity, leading to the formation of structures like stars. It is, therefore, significant for understanding the large-scale structure of the universe.

Step by step solution

01

Define the Jeans length

The Jeans length can be defined as the critical radius at which thermal energy, that tends to make a gas cloud expand, is balanced out by its gravitational energy, which tends to make it contract.
02

Understand Significance in the Universe's structure

When a cloud's radius is less than the Jeans length, the cloud tends to contract under its own gravity and potentially forms a star. If the cloud's radius is larger than the Jeans length, the thermal energy within the cloud prevents gravitational collapse. On a broader scale, the Jeans length aids in understanding why matter in the universe is not uniformly distributed but is clumped into galaxies, stars and planets. This forms the basis of large-scale structures.
03

Jeans Length Equation

The Jeans length can also be expressed mathematically, it is given by the equation \(λ_J = \sqrt{\frac {15k_BT}{4πGρm}}\), where \(T\) is the temperature, \(ρ\) is the mass density, \(m\) is the mass of a single particle in the cloud, \(k_B\) is the Boltzmann constant and \(G\) is the gravitational constant. This equation gives the smallest size a cloud of gas must be in order to collapse under its own gravity.

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Most popular questions from this chapter

The first stars in the universe are thought to have appeared some 400 million \(\left(4 \times 10^{8}\right)\) years after the Big Bang. Once these stars formed, thermonuclear fusion reactions began in their interiors. Explain why these were the first fusion reactions to occur since the universe was 15 minutes old.

Explain the connection between particles and antiparticles in the early universe and the cosmic microwave background that we observe today.

In what ways is inflation similar to the present-day expansion of the universe? In what ways is it different?

What is the horizon problem? What is the flatness problem? How can these problems be resolved by the idea of inflation?

The Cosmic Connection figure shows the history of the universe in the form of a graph of the temperature versus the time after the Big Bang. Create a similar history of your class, starting with estimated outside temperature on the vertical axis and number of days since the beginning of the academic term on the horizontal axis. Include dates for major exams and assignments up through today. In different color ink, show your predictions for temperatures, days, and events from today until the end of the course.
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