Radiation pressure is a physical pressure exerted by photons on matter. Even though photons are massless, they have an intrinsic momentum, hν/c, which is able to impart a force. Radiation pressure is very small in most ordinary situations, so much so that it can normally be ignored. However, it is very important in the centers of very hot stars where the pressure of the radiation field can help support the star's mass against collapse. It is also important at the end of most stars' lives, when they expel their envelopes to form planetary nebulae. On a matter more practical to humans, it is hoped that radiation pressure of light from the Sun may one day be harnessed for use in interplanetary travel using solar sails.

In nature, radiation pressure plays an important part in counteracting the force of gravity in very hot, massive stars. The radiation field deep inside stars is essentially that of a blackbody. The pressure of this radiation field is the second moment of the intensity, I, given by

p = (2/c) ∫ I(θ) cos2 θ dΩ

where p is the radiation pressure, c is the speed of light, I(θ) is the intensity as a function of angle θ (θ measured with respect to the normal vector of the incident surface), and ∫ dΩ is the integral of the intensity over solid angle Ω.

Since blackbody radiation is isotropic, this equation reduces nicely to p = (4π/3c) I. The total intensity of the blackbody radiation field is purely a function of the temperature, T, to the fourth power. So we wind up with the pressure being simply

p = (a/3) T4 = (4 σ/3c) T4

where a is the radiation constant, and σ is the Stefan-Boltzmann constant.

Why is this important? The key is that exponent on the temperature. Since it is T to the fourth power (T × T × T × T), a slight increase in the temperature can result in a large increase in the pressure. If you increase the temperature by a factor of two, you increase the pressure by a factor of sixteen. The centers of all stars are very hot (at least a few million Kelvins), so radiation pressure is always important at the level of a few percent. But in massive stars, the core temperature on the main sequence can be hundreds of millions of degrees, meaning that the radiation pressure is a large fraction of the gas pressure in the core. This is critically important in the most massive stars, because eventually they get so hot that radiation completely overcomes the force of gravity. This puts an upper limit on how massive a star can be.

Radiation pressure also provides a mechanism for stellar mass loss at the end of a star's life. As stars evolve, eventually their cores become very dense and very, very hot. After a star runs out of nuclear fuel to burn, it enters a stage of its life when the core contracts to form a white dwarf. While it does this, it releases a large amount of heat. This heat, emitted by the young white dwarf as blackbody radiation, is so strong that the radiation pushes the outer layers of the star into space. The result is a planetary nebula, a ghostly shell surrounding the dead ember of a star. Nearly all stars will form planetary nebulae, except for the most and least massive stars (the former explode as supernovae, and the latter simply shrink and cool as brown or black dwarfs).

It's also worth noting that the blackbody radiation field behaves adiabatically, so it follows its own adiabat, given by

p Vγ = constant

Here, γ -- the adiabatic exponent -- is equal to 4/3, rather than the 5/3 we use for ideal gases, so the pressure of a radiation field undergoing adiabatic expansion behaves somewhat differently than gaseous matter.

Under less extreme conditions, radiation pressure is potentially useful as a means of transportation. Assume you have a highly reflective surface, with photons striking it and being reflected backwards almost 180 degrees. Twice the momentum of the photon is applied to the reflecting surface, which results in a force being applied. Some number of photons striking each square centimeter of the reflective surface per second results in a force per unit area, or a pressure.

If you're just talking about one or two photons, the pressure is vanishingly negligible, but if you're in the vicinity of a star, you will be bathed by an overwhelming number of photons every second. Our sun alone releases over 1045 photons per second (that's a 1 with forty five zeroes after it, a staggering number). So if you were to place a large reflecting surface into space and expose it to the Sun's light, all those photons might be able to impart a substantial pressure against it. This is the idea behind solar sailing.

Solar sails were hypothesized decades ago in science fiction, but later people began to take the idea seriously. The trick is to have a very large reflecting surface (the sail), with a very small mass. You then tie the sail to your spacecraft, and let the sail take you along -- just like a sailboat. The trouble with this idea is that the acceleration is very, very slow, even for solar sails kilometers in size. Since the acceleration is slow, it would take a sailor quite a while to achieve enough speed to cross the solar system. However, the times required aren't much longer than those for chemical rockets, and sails have the added benefit of not requiring rocket propellant. So perhaps in the not-too-distant future, the pressure of light from the Sun may carry us to other worlds.

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