Jeans Mass

Definition

The Jeans mass is the critical mass threshold for a cloud of gas and dust to collapse under its own gravitational attraction, leading to the formation of stars. This concept is vital for understanding how molecular clouds evolve and trigger star formation, as it helps determine whether a cloud will remain stable or begin to collapse. The Jeans mass depends on factors such as temperature, density, and the specific heat capacity of the gas in the cloud.

5 Must Know Facts For Your Next Test

1. The Jeans mass can be expressed mathematically as $$M_J = rac{(5kT)^{3/2}}{(Gar{m})^{3/2} \rho^{1/2}}$$, where $$k$$ is the Boltzmann constant, $$T$$ is temperature, $$G$$ is the gravitational constant, $$\bar{m}$$ is the mean particle mass, and $$\rho$$ is the density of the cloud.
2. If a molecular cloud's mass exceeds the Jeans mass, it becomes gravitationally unstable and begins to collapse to form one or more stars.
3. Conversely, if the cloud's mass is below the Jeans mass, thermal pressure and other forces can prevent gravitational collapse, allowing the cloud to remain stable.
4. The Jeans mass varies with temperature; higher temperatures result in a lower Jeans mass, making clouds more prone to collapse.
5. Understanding Jeans mass is crucial for astrophysicists to predict star formation rates and understand the lifecycle of molecular clouds in different environments.

Review Questions

• How does temperature affect the Jeans mass of a molecular cloud?
  • Temperature plays a significant role in determining the Jeans mass of a molecular cloud. As temperature increases, thermal pressure within the cloud also increases, which means that higher temperatures result in a lower Jeans mass. This relationship indicates that hotter clouds are more susceptible to gravitational collapse compared to cooler ones, making temperature a critical factor in predicting whether a cloud will form stars.
• Discuss the relationship between Jeans mass and star formation within molecular clouds.
  • Jeans mass is essential for understanding star formation because it determines whether a molecular cloud will collapse under its own gravity. If the total mass of the cloud exceeds its Jeans mass, gravitational forces will dominate, leading to instability and eventual star formation. On the other hand, if the cloud's mass is below this threshold, thermal pressure and other stabilizing forces can prevent collapse, halting star formation. Thus, analyzing Jeans mass allows astronomers to predict which regions may give rise to new stars.
• Evaluate how variations in density affect the Jeans mass and consequently influence the evolution of molecular clouds.
  • Variations in density significantly impact Jeans mass and play a crucial role in shaping molecular clouds. A denser region within a cloud will have a higher Jeans mass due to its increased gravitational pull. Consequently, when certain regions exceed their respective Jeans masses, they will become unstable and begin collapsing into stars. This process illustrates how density fluctuations lead to localized star formation within a larger molecular cloud, affecting its overall evolution and lifecycle by creating new stellar objects while altering its structural dynamics.

Related terms

Molecular Cloud: A dense region of gas and dust in space where molecules can form, often serving as the birthplace of stars.

Critical Density: The density at which a cloud becomes gravitationally unstable, leading to potential star formation.

Thermal Pressure: The pressure exerted by the thermal motion of particles within a gas, which counteracts gravitational collapse in a molecular cloud.