The Jeans instability is a concept in
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
that describes an instability that leads to the
gravitational collapse
Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formati ...
of a cloud of gas or dust. It causes the collapse of interstellar gas clouds and subsequent
star
A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
formation. It occurs when the internal gas
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
is not strong enough to prevent the gravitational collapse of a region filled with matter. It is named after
James Jeans
Sir James Hopwood Jeans (11 September 1877 – 16 September 1946) was an English physicist, mathematician and an astronomer. He served as a secretary of the Royal Society from 1919 to 1929, and was the president of the Royal Astronomical Soci ...
.
For stability, the cloud must be in
hydrostatic equilibrium, which in case of a spherical cloud translates to
,
where
is the enclosed mass, ''p'' is the pressure,
is the density of the gas (at radius ''r''), ''G'' is the
gravitational constant
The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...
, and ''r'' is the radius. The equilibrium is stable if small perturbations are damped and unstable if they are amplified. In general, the cloud is unstable if it is either very massive at a given temperature or very cool at a given mass; under these circumstances, the gas pressure gradient cannot overcome gravitational force, and the cloud will collapse. This is called the "Jeans Collapse Criterion".
The Jeans instability likely determines when
star formation
Star formation is the process by which dense regions within molecular clouds in interstellar space—sometimes referred to as "stellar nurseries" or "star-forming regions"—Jeans instability, collapse and form stars. As a branch of astronomy, sta ...
occurs in
molecular cloud
A molecular cloud—sometimes called a stellar nursery if star formation is occurring within—is a type of interstellar cloud of which the density and size permit absorption nebulae, the formation of molecules (most commonly molecular hydrogen, ...
s.
History
In 1720,
Edmund Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.
From an observatory he constructed on Saint Helena in 1676–77, H ...
considered a universe without edges and pondered what would happen if the "system of the world", which exists within the universe, were finite or infinite. In the finite case, stars would gravitate towards the center, and if infinite, all the stars would be nearly in equilibrium and the stars would eventually reach a resting place.
Contrary to the writing of Halley,
Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
, in a 1692/3 letter to
Richard Bentley, wrote that it's hard to imagine that particles in an infinite space should be able to stand in such a configuration to result in a perfect equilibrium.
James Jeans extended the issue of gravitational stability to include pressure. In 1902, Jeans wrote, similarly to Halley, that a finite distribution of matter, assuming pressure does not prevent it, will collapse gravitationally towards its center. For an infinite distribution of matter, there are two possible scenarios. An exactly homogeneous distribution has no clear center of mass and no clear way to define a gravitational acceleration direction. For the other case, Jeans extends what Newton wrote about: Jeans demonstrated that small deviations from exact homogeneity lead to instabilities.
Jeans mass
The Jeans mass is named after the
British
British may refer to:
Peoples, culture, and language
* British people, nationals or natives of the United Kingdom, British Overseas Territories and Crown Dependencies.
* British national identity, the characteristics of British people and culture ...
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
Sir
James Jeans
Sir James Hopwood Jeans (11 September 1877 – 16 September 1946) was an English physicist, mathematician and an astronomer. He served as a secretary of the Royal Society from 1919 to 1929, and was the president of the Royal Astronomical Soci ...
, who considered the process of
gravitational collapse
Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formati ...
within a gaseous cloud. He was able to show that, under appropriate conditions, a cloud, or part of one, would become unstable and begin to collapse when it lacked sufficient gaseous
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
support to balance the force of
gravity
In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
. The cloud is stable for sufficiently small mass (at a given temperature and radius), but once this critical mass is exceeded, it will begin a process of runaway contraction until some other force can impede the collapse. He derived a formula for calculating this critical
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
as a function of its
density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
and
temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
. The greater the mass of the cloud, the bigger its size, and the colder its temperature, the less stable it will be against gravitational collapse.
The approximate value of the Jeans mass may be derived through a simple physical argument. One begins with a spherical gaseous region of radius ''R'', mass ''M'', and with a gaseous
sound speed ''c''
S. The gas is compressed slightly and it takes a time
for sound waves to cross the region and attempt to push back and re-establish the system in pressure balance. At the same time, gravity will attempt to contract the system even further, and will do so on a
free-fall time
,
where ''G'' is the universal gravitational constant,
is the gas density within the region, and
is the gas
number density for mean mass per particle ( is appropriate for molecular hydrogen with 20% helium by number). When the sound-crossing time is less than the free-fall time, pressure forces temporarily overcome gravity, and the system returns to a stable equilibrium. However, when the free-fall time is less than the sound-crossing time, gravity overcomes pressure forces, and the region undergoes
gravitational collapse
Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formati ...
. The condition for gravitational collapse is therefore