If the inclination of a cloud of oxygen in outer space is to diffuse, then how do nebulae form?

Question

If a cruise ship-size object in outer space were surrounded by a spherical cloud of oxygen, and there were no other bodies exerting significant gravitational force in the vicinity, would the cloud of oxygen be held in place by the gravity of the object, or would it rush out into space? My natural inclination would be that it'd rush out into space, due to the object not having enough mass, but that seems inconsistent with the fact that large bodies, like nebulae and stars, are able to form in space.

It has occurred to me that only gaseous bodies with extremely high density, like nebulae, have enough mass not to diffuse into space. But even nebulae didn't start out as high-density. Those that weren't born from dead stars must have started as a random collection of particles, and accumulated from there, until they became large enough to hold numerous stars. If the natural inclination is for gases to diffuse in a vacuum, then why would a nebula be able to preserve its form, but the spherical oxygen cloud surrounding the aforementioned object immediately dissipate? In the absence of greater gravitational forces, why wouldn't it be drawn towards the object at its center?

I want to reiterate that there are no significant gravitational forces affecting the oxygen, other than the object at its center. The object is the exerting the largest gravitational force on the cloud of oxygen.

Answer 1

would the cloud of oxygen be held in place by the gravity of the object, or would it rush out into space?

I would say the cloud would not be bound solely by the object. It would appear to disperse locally.

It has occurred to me that only gaseous bodies with extremely high density, like nebulae, have enough mass not to diffuse into space.

Scale matters here. You could have a huge (but very diffuse/low density) cloud of matter. At any one location you could put a small quantity of gas together for a moment and it would quickly disperse. But at the same time the large conglomeration could be gravitationally bound. It might disperse locally, but not be able to escape the group. The larger the object, the less density is necessary to keep the quantity gravitationally bound.

If you start with a galaxy-sized cloud, it will be bound at vanishingly low densities. Then over time, portions of the cloud can collapse to form more dense objects (Jeans instability).

Answer 2

Another point worth mentioning here is that as gravity gradually pulls together and densifies a gas cloud, the molecules in the cloud have a certain amount of kinetic energy to start with and as the gas gets denser (i.e., it gets compressed), the kinetic energy goes up causing the pressure and the temperature in the gas cloud to rise, which fights further densification.

So in addition to requiring a very large mass of (initially thin) gas to start the "condensation" process, the gas cloud needs to have some way of getting rid of the compression heat that builds up and inhibits the further gravitational contraction of the gas cloud.

If the gas is lucky enough to have emission lines in the infrared, then it can radiate away the heat and continue to contract.

If not, then interstellar dust can help by radiating away the IR.

Answer 3

You can calculate the escape velocity in the vicinity of a (spherically symmetric) object quite easily as $$ v_{\rm esc} \sim \sqrt{\frac{2GM}{R}}\ , $$ where $M$ and $R$ are the mass (density times volume) and radius of any cloud of gas.

To work out whether it will "disperse" you can compare $v_{\rm esc}$ with the intrinsic motions in the gas. This might have a turbulent component, but at a minimum, there will be a characteristic thermal speed for the particles, attributable to their temperature. $$ v_{rms} \sim \sqrt{\frac{3k_B T}{\mu}}\ , $$ where $T$ is the temperature and $\mu$ is the mean particle mass.

As a general rule of thumb, gas will start to escape unless $v_{\rm esc} > 5v_{rms}$ because otherwise there will be a tail of high speed particles that can escape.

This is very crude, but gives an idea of how massive (or dense) a cloud needs to be to hold together. For large clouds one also has to consider gravity gradients and tidal forces due to other objects/clouds and the background gravitational potential of the galactic potential.