Toomre Q Parameter

Definition

The Toomre Q parameter is a dimensionless quantity used to determine the stability of a rotating disk of gas and dust, particularly in the context of protoplanetary disks. A higher value of Q indicates that the disk is stable against gravitational collapse, while a lower value suggests that the disk may be prone to fragmentation and star formation. This parameter is crucial for understanding the formation and evolution of protoplanetary disks and the processes that lead to planet formation.

5 Must Know Facts For Your Next Test

1. The Toomre Q parameter is defined as Q = (c_s \, ext{Ω}) / (G \, ext{Σ}), where c_s is the sound speed in the disk, Ω is the angular frequency, G is the gravitational constant, and Σ is the surface density.
2. For Q values greater than 1, the disk is stable against axisymmetric perturbations, while Q values less than 1 indicate potential instability and fragmentation.
3. Variations in temperature and surface density within a protoplanetary disk can lead to different Q values across the disk, influencing where and how planets may form.
4. The Toomre Q parameter also plays a role in determining the growth rates of instabilities that can lead to clump formation, essential for planetesimal creation.
5. In addition to gas density, factors such as turbulence can influence the effective Q value in a protoplanetary disk, impacting its stability and evolution.

Review Questions

• How does the Toomre Q parameter influence the stability of a protoplanetary disk?
  • The Toomre Q parameter directly impacts the stability of a protoplanetary disk by providing a measure of whether the disk can withstand gravitational instabilities. A Q value greater than 1 indicates that the disk is stable against axisymmetric perturbations, meaning it will not easily collapse or fragment. Conversely, when Q drops below 1, it suggests that gravitational forces can dominate, leading to potential fragmentation and subsequent star formation. This dynamic is crucial for understanding how new celestial bodies emerge from disks.
• Explain how variations in temperature and surface density affect the Toomre Q parameter across different regions of a protoplanetary disk.
  • Variations in temperature and surface density across a protoplanetary disk lead to differing values of the Toomre Q parameter in various regions. For instance, higher temperatures typically increase the sound speed (c_s), resulting in a higher Q value that promotes stability. Conversely, if surface density (Σ) increases without significant temperature changes, this can lower Q and increase susceptibility to gravitational instabilities. Understanding these variations helps predict where planet formation might occur within the disk.
• Evaluate how the Toomre Q parameter interacts with turbulence in influencing the evolution of protoplanetary disks.
  • The interaction between the Toomre Q parameter and turbulence is significant in determining the evolution of protoplanetary disks. Turbulence can effectively raise the local surface density while also affecting pressure support, thus modifying the effective Q value. In regions where turbulence is prevalent, even if surface density is high enough to make Q less than 1, turbulent motions can stabilize portions of the disk against collapse. This complex interplay between turbulence and gravitational instabilities ultimately shapes how disks evolve over time and influences where planets can form.

Related terms

Gravitational Instability: A condition in which a cloud of gas and dust collapses under its own gravity, often leading to star formation.

Angular Momentum:

A physical quantity that represents the rotational inertia of a body in motion, essential for understanding the dynamics of rotating disks.

Density Profile:

The distribution of mass density within a protoplanetary disk, which affects the behavior and stability of the disk.