Bonnor–Ebert Mass
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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 ...
, the Bonnor–Ebert mass is the largest mass that an
isothermal An isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the sys ...
gas sphere embedded in a pressurized medium can have while still remaining in
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. I ...
. Clouds of gas with masses greater than the Bonnor–Ebert mass must inevitably undergo
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 ...
to form much smaller and denser objects. As the gravitational collapse of an interstellar gas cloud is the first stage in the formation of a
protostar A protostar is a very young star that is still gathering mass from its parent molecular cloud. It is the earliest phase in the process of stellar evolution. For a low-mass star (i.e. that of the Sun or lower), it lasts about 500,000 years. The p ...
, the Bonnor–Ebert mass is an important quantity in the study of
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 ...
. For a gas cloud embedded in a medium with a gas pressure p_, the Bonnor–Ebert mass is given by M_ (p_0)= where 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 c_s \equiv \sqrt is the isothermal sound speed (\gamma = 1) with \mu as the molecular mass. a is a dimensionless constant which varies based on the density distribution of the cloud. For a uniform mass density a=1 and for a centrally peaked density a\approx 1.67.


See also

*
Jeans mass The Jeans instability is a concept in astrophysics that describes an instability that leads to the gravitational collapse of a cloud of gas or dust. It causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when ...


References

Interstellar media Equations of astronomy {{astrophysics-stub