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 said, Astrophysics "seeks to ascertain the nature of the he ...
, the Bonnor–Ebert mass is the largest mass that an
isothermal
In thermodynamics, 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 ...
gas sphere embedded in a pressurized medium can have while still remaining in
hydrostatic equilibrium
In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, 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. In the planetar ...
. 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 formatio ...
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. The protostellar phase is the earliest one in the process of stellar evolution. For a low-mass star (i.e. that of the Sun or lower), it lasts about ...
, 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", collapse and form stars. As a branch of astronomy, star formation includ ...
.
For a gas cloud embedded in a medium with a
gas pressure
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal ga ...
, the Bonnor–Ebert mass is given by
where G is the
gravitational constant and
is the
isothermal
In thermodynamics, 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 ...
sound speed
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as we ...
(
) with
as the molecular mass.
is a
dimensionless constant which varies based on the density distribution of the cloud. For a uniform mass density
and for a centrally peaked density
.
See also
*
Jeans mass
References
Interstellar media
Equations of astronomy
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