What is the Jeans density for a 1000 M⊙ spherical cloud of atomic hydrogen at temperature 20 K

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What is the Jeans density for a 1000 M⊙ spherical cloud of...

What is the Jeans density for a $1000 M_{\odot}$ spherical cloud of atomic hydrogen at temperature $20 \mathrm{~K}$ ? Suppose that in a dense region of a molecular cloud the number density is $1 \times 10^8 \mathrm{~cm}^{-3}$ and the temperature is $100 \mathrm{~K}$. What is the Jeans mass?

Key Concepts

Jeans Instability

Jeans instability is a fundamental concept in astrophysics describing the process by which interstellar gas clouds become unstable against gravitational collapse. This instability occurs when the internal thermal pressure is insufficient to counteract gravitational forces, leading to the potential formation of stars or other compact objects. The concept is critical for understanding the conditions under which a cloud will fragment and collapse.

Jeans Mass

The Jeans mass is the critical mass above which a gas cloud with a given temperature and density becomes gravitationally unstable. It represents the threshold between thermal pressure being able to support the cloud against collapse and gravity taking over. A cloud with mass exceeding the Jeans mass is likely to undergo collapse, triggering star formation, while a cloud below this mass will remain stable.

Jeans Density

Jeans density refers to the critical density a gas cloud must achieve for gravitational forces to overcome thermal pressure at a given temperature. It is used in determining the threshold conditions for the onset of collapse, in conjunction with the cloud's mass and size. Understanding Jeans density helps in identifying regions in interstellar clouds that are prone to star formation.

Thermal Pressure

Thermal pressure is the force per unit area exerted by the random motion of particles within a gas. In the context of gravitational collapse, it acts against the inward pull of gravity. The balance (or imbalance) between thermal pressure and gravitational forces is key to determining whether a cloud will remain stable or collapse, and it directly influences the values of the Jeans mass and Jeans density.

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