Skip to main content
\(\require{cancel}\)
Physics LibreTexts

12.18 Hydrostatic Equilibrium

We might imagine that the release of fusion energy would blow a star apart. Or we might imagine that the relentless pull of gravity would cause a star to collapse. Yet we know that, for instance, the Sun is a stable star which has been shining steadily for billions of years. It will continue to shine steadily for billions of years in the future. Why is a star not unstable, like a bomb? We can look for a physical principle that unites stars with very different properties. 

The concept of thermal equilibrium tells us that heat always tends to flow from hotter to cooler regions in order to equalize the temperature. A star like the Sun has a constant source of energy from fusion reactions in its core. Heat is therefore constantly flowing outwards. A star cannot reach thermal equilibrium as long as there is an energy source at the core — the inner regions will always be hotter than the outer regions. Stars undergoing fusion in their cores do not "cool off."  Think of an oven set to some high temperature. If you left the oven door open, it would keep heating the kitchen, never cooling off while it was "on."

Stars that are in the process of converting hydrogen into helium, like the Sun, are also stable. This stability is described by the principle of hydrostatic equilibrium. The term hydrostatic is a combination of hydro-, meaning that the gas in a star acts like a fluid, and –static, meaning that the star is not expanding or contracting. Hydrostatic equilibrium says that there is a balance between two forces at every point within a star. One force is the inward force of gravity. The other force is the pressure in the gas caused by its temperature (recall that the pressure in an ideal gas is proportional to its temperature). The temperature within a star is controlled by the heat flow from the nuclear reactions in the core. A star therefore stays "puffed up" against the force of gravity. 
 

Astropedia Image
A simple diagram of the force balance (or Hydrostatic Balance) in Hydrostatic Equilibrium. Click here for original source URL.

If we imagine a star as having a series of layers of gas, then the pressure in each layer must balance the weight (gravitational pull) on that layer. Deeper layers of the star have more weight pressing down on them, so the pressure must increase as we move toward the center. Increasing pressure means increasing temperature. The idea of a star as a series of layers makes the idea of a balance between pressure and gravity clearer, but a star does not actually have distinct layers; the pressure, density, and temperature all increase smoothly towards the center. Hydrostatic equilibrium governs the physical conditions at any position inside a star.

 

", like the Sun, are also stable. This stability is described by the principle of hydrostatic equilibrium. The term hydrostatic is a combination of hydro-, meaning that the gas in a star acts like a fluid, and –static, meaning that the star is not expanding or contracting. Hydrostatic equilibrium says that there is a balance between two forces at every point within a star. One force is the inward force of gravity. The other force is the pressure within the gas caused by its temperature (recall that the pressure in an ideal gas is proportional to its temperature). The temperature within a star is controlled by the heat flow from the nuclear reactions in the core. A star therefore stays "puffed up" against the force of gravity.

If we imagine a star as having a series of layers of gas, then the pressure in each layer must balance the weight (gravitational pull) on that layer. Deeper layers of the star have more weight pressing down on them, so the pressure must increase as we move toward the center. Increasing pressure means increasing temperature. The idea of a star as a series of layers makes the idea of a balance between pressure and gravity clearer, but a star does not actually have distinct layers -- the pressure, density," and temperature all increase smoothly towards the center. Hydrostatic equilibrium governs the physical conditions at any position inside a star.""