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.