Do supernova remnant nebula re-collapse into a star?

Question

We know that nebula sometimes collapse into stars. The particles are attracted to the joint gravitational center of the whole nebula.

One type of nebula is a supernova remnant nebula. Unlike a normal nebula, the particles are moving away from the center of the nebula... for a while...

But what is preventing these particles from being on a trajectory that results in them slowing down and eventually traveling inward toward the center of the nebula?

Is the environment the only significant factor? Would a rogue star not in a galaxy (in a void) that goes supernova eventually recover all of it's remnants?

Answer 1

What goes up, must come down... unless it exceeds escape velocity. ;)

There are several types of supernova. I assume you're primarily interested in the core collapse supernovae that leave a neutron star or black hole remnant, so that the nebular material has something to fall back to.

All supernovae are extremely energetic events. Most of the material is ejected with huge speeds, far beyond the escape velocity of the original star. From Wikipedia's article on Supernova remnants:

In either case, [thermonuclear explosion or core collapse], the resulting supernova explosion expels much or all of the stellar material with velocities as much as $10$% the speed of light (or approximately $30,000$ km/s). These speeds are highly supersonic, so a strong shock wave forms ahead of the ejecta. That heats the upstream plasma up to temperatures well above millions of K.

The shock continuously slows down over time as it sweeps up the ambient medium, but it can expand over hundreds or thousands of years and over tens of parsecs before its speed falls below the local sound speed.

However, a small proportion of the ejected material can fall back, and that can promote a neutron star remnant to a black hole.

The (Newtonian) equation for escape velocity is $$v_e^2 = \frac{2GM}{R}$$ which is closely related to the equation for the speed of a circular orbit $$v_c^2 = \frac{GM}{R}$$ Thus the escape velocity is $\sqrt2$ times the circular orbit speed.

The Earth's orbital speed is around $30$ km/s, so escape velocity from the Solar system at $1$ AU is around $42$ km/s. And so escape velocity at $1.5$ AU from a $1.5$ solar mass neutron star is also around $42$ km/s, a tiny fraction of the ejecta speed mentioned above.

Also, the remnant core may itself acquire a substantial speed, a phenomenon known as a pulsar kick:

The cause of pulsar kicks is unknown, but many astrophysicists believe that it must be due to an asymmetry in the way a supernova explodes.
[...]
It is generally accepted today that the average pulsar kick ranges from $200–500$ km/s. However, some pulsars have a much greater velocity. For example, the hypervelocity star B1508+55 has been reported to have a speed of $1100$ km/s and a trajectory leading it out of the galaxy.

So most of the material in a supernova nebula is unlikely to re-collapse. Instead, it will mix with the material in the interstellar medium, providing heavier elements for future generation stellar systems. Or it will have sufficient speed to escape the gravitational pull of the galaxy, and mix with the intergalactic medium.