Jeans Instability

Introduction

Jeans Instability is a fundamental concept in astrophysics that describes the condition under which a self-gravitating gas cloud will collapse under its own gravity to form a star. This process is named after the British physicist Sir James Jeans, who first derived the relevant equations in 1902.

Basic Principle

The basic idea behind Jeans Instability is the competition between the gravitational attraction, which tends to make the cloud collapse, and the thermal pressure (or kinetic energy), which tends to make the cloud expand. When the cloud is sufficiently large and dense, gravity can overcome the pressure, leading to the onset of collapse and eventually, star formation.

Jeans Length and Mass

The criterion for the onset of gravitational collapse can be expressed in terms of a critical length scale, known as the Jeans length, , which is given by:

where is Boltzmann’s constant, is the temperature of the cloud, is the gravitational constant, and is the mass density of the cloud.

Similarly, we can define the Jeans mass, , as the mass of a sphere with radius equal to half the Jeans length. It is given by:

If a region within the cloud has a mass greater than the Jeans mass, it will be unstable to gravitational collapse.

Importance in Star Formation

The concept of Jeans Instability is fundamental to our understanding of how stars form in molecular clouds. By providing a criterion for gravitational collapse, it sets the initial conditions for star formation.

Advanced Topics: Non-Isothermal and Magnetic Jeans Instability

In more complex situations, where the gas is not isothermal or there are magnetic fields present, the Jeans criterion becomes more complicated. For example, in the non-isothermal case, the temperature of the gas may change during the collapse, altering the balance between pressure and gravity. In the magnetic case, the magnetic pressure adds a stabilizing force that can prevent collapse. These are active areas of research in modern astrophysics.

Jeans Instability, with its combination of basic physics and critical role in star formation, is an essential concept in astrophysics.

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