In
astrophysics, 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 planetary ...
. Clouds of gas with masses greater than the Bonnor–Ebert mass must inevitably undergo
gravitational collapse 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 50 ...
, the Bonnor–Ebert mass is an important quantity in the study of
star formation.
For a gas cloud embedded in a medium with a
gas pressure , the Bonnor–Ebert mass is given by
where G is the
gravitational constant and
is the
isothermal 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 wel ...
(
) 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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