Bonnor-Ebert mass

In astrophysics, the Bonnor-Ebert mass is the largest mass that an isothermal gas sphere embedded in a pressurized medium can have while still remaining in hydrostatic equilibrium.Clouds of gas with masses greater than the Bonnor-Ebert mass must inevitably undergo gravitational collapse to form much smaller and denser objects. [cite journal | last = Ebert | first = R. | title = Über die Verdichtung von H I-Gebieten | year = 1955 | journal = Zeitschrift für Astrophysik | volume = 37 | pages = 217 | url = http://adsabs.harvard.edu/abs/1955ZA.....37..217E] [cite journal | last = Bonnor | first = W. B. | title = Boyle's Law and gravitational instability | year = 1956 | journal = MNRAS | volume = 116 | pages = 351 | url = http://adsabs.harvard.edu/abs/1956MNRAS.116..351B] As the gravitational collapse of an interstellar gas cloud is the first stage in the formation of a protostar, the Bonnor-Ebert mass is an important quantity in the study of star formation. [cite book | author = Carroll, Bradley W. & Ostlie, Dale A. | title=An Introduction to Modern Astrophysics | publisher=Addison-Wesley | year=2007 | pages=413-414 ]

For a gas cloud embedded in a medium with a gas pressure $P\_\{0\}$, the Bonnor-Ebert mass is given by

$M\_\{BE\}=\{c\_\{BE\}v\_\{T\}^4over\{P\_\{0\}^\{1over\{2G^\{3over\{2$

where G is the gravitational constant,

$v\_\{T\}\; equiv\; sqrt\{kTover\{mu\; m\_\{H\}$

is the isothermal sound speed ($gamma\; =\; 1$), and the dimensionless constant $c\_\{BE\}$ is given by

$c\_\{BE\}\; simeq\; 1.18.$

ee also

* Jeans mass

References