# Deriving bar instability mode- formal definition of instability?

• thealyosha
In summary, an instability is a process in which a system loses its equilibrium and enters an unstable state due to an external force or internal dynamics, with the potential energy of the system exceeding the kinetic energy. Sources for further understanding include scientific articles and definitions from sources such as ScienceDirect, Arxiv, and Wikipedia.
thealyosha
I am doing an undergraduate project on bars and I am trying to derive the bar instability mode given by Mo et al. It says "whether or not a disk is globally stable depends on the global properties of the disk... it is not possible to write down a universal dispersion relation or stability criterion."

I am wondering what the formal, physical definition of an instability is. I know it has something to do with potential energies. Could someone provide a general definition of an instability? Links to sources would be appreciate, as I might want to cite a definition.

An instability is a process through which a system loses its equilibrium and enters an unstable state. This can occur due to an external force, or the internal dynamics of the system. In general, an instability occurs when the potential energy of the system exceeds the kinetic energy, leading to an exponential increase in the amplitude of the oscillations. Examples of instabilities include Rayleigh-Taylor, Kelvin-Helmholtz, and Jeans instabilities. Sources: 1. https://www.sciencedirect.com/topics/engineering/instability2. https://arxiv.org/pdf/1709.00946.pdf3. https://en.wikipedia.org/wiki/Instability

## 1. What is the definition of bar instability mode?

The bar instability mode refers to a type of instability that can occur in rotating fluid systems, such as stars or galaxies. It arises when the rotation of the fluid causes its density to vary in a way that amplifies small perturbations, leading to the formation of long, thin structures called bars.

## 2. How is bar instability mode formally defined in scientific terms?

In scientific terms, bar instability mode is defined as a type of instability that occurs when the Coriolis force and centrifugal force interact to amplify small density perturbations in a rotating fluid system. This results in the formation of a bar-shaped structure that rotates with the fluid.

## 3. What are the conditions necessary for bar instability mode to occur?

The conditions necessary for bar instability mode to occur include a sufficient amount of rotation in the fluid, and a density distribution that is not perfectly symmetric. The presence of differential rotation, where the rotation rate varies with distance from the center, can also contribute to the development of bar instability mode.

## 4. What are some examples of natural systems where bar instability mode is observed?

Bar instability mode is observed in various natural systems, such as spiral galaxies, where the rotation of stars and gas creates a bar-shaped structure in the galactic disk. It is also seen in protoplanetary disks, where the rotation of gas and dust grains can lead to the formation of rings or gaps. In addition, bar instability mode has been studied in laboratory experiments with rotating fluids.

## 5. How does bar instability mode impact the evolution of a system?

The presence of bar instability mode can significantly affect the evolution of a system. In galaxies, it can cause gas and stars to be funneled towards the center, leading to the formation of a central bulge or supermassive black hole. In protoplanetary disks, it can influence the formation of planets by creating regions of enhanced or reduced density. Overall, bar instability mode is an important process in shaping the structure and dynamics of rotating fluid systems.

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