Stellar Core Collapse Speeds

If gravity determines the speed of free falling objects, but stellar core collapses happen much faster than the speed of free falling objects, wouldn't that indicate that stellar core collapses are caused by something other than, or in addition to, gravity? Sorry, I'd like to amend question to ask if the speed at which collapsing matter is pulled to the core of a collapsing star is equal to the speed of free falling matter for a star that size?

• Do you have a reference for the claim that stellar core collapses happen much faster than the speed of free falling objects? Stellar cores are very dense, especially in old large stars. Mar 4 at 2:29
• ...stellar core collapses happen much faster than the speed of free falling objects... can you elaborate on this? AFAIK, collapse time scale is $\sim\left(G\rho\right)^{-1/2}$, which should work out correctly for CCSNe progenitors Mar 4 at 2:30
• No, my apologies, I'm not an expert, but I've been reading that core collapses happen in seconds or fractions, I've seen supposed speeds of 70,000 km/sec, also references to fractions of the speed of light, and I thought free falling objects don't fall that fast. I've also seen references to collapse in seconds or fractions, but then all the residual free falling matter rebounds in a supernova explosion, indicating that the free falling residual matter was going slower than the core collapse. So apologies again, I'm not an expert, and it's hard to get answers like this without just asking. Mar 4 at 2:39
• Mathematically it works out, as I answer here Mar 4 at 2:42
• Free falling objects towards the Earth don’t go that fast. Stars have much more mass than the Earth. Mar 4 at 2:42

Core collapse does occur on roughly a free fall timescale.

The free fall timescale is of order $$(G\rho)^{-1/2}$$, where $$\rho$$ is the density. Since the density is of order $$10^{11-12}$$ kg/m$$^3$$ in the electron-degenerate core at the point of collapse, this timescale is a second or less.

Since density increases inwards, the collapse timescale is shorter near the centre. Thus the collapse occurs inside-out.

The speed of collapse is of order the size of the core (a few thousand km) divided by the freefall timescale, so of order $$10^4$$ km/s.

The core has a mass of $$\sim 1$$ solar mass, so the gravitational acceleration is of order $$GM/r^2\sim 10^4$$ km/s$$^2$$. i.e. the whole core accelerates to speeds of $$10^4$$ km/s in a second. This is the acceleration at the "edge" of the core at the beginning of the collapse; it will be higher towards the centre where the densities are larger and will increase as the collapse progresses because the same mass will be enclosed within a decreasing volume of smaller radius.

• ProfRob thank you, I don't understand this well so you're answer is much appreciated. If free fall timescale equation uses gravity as a factor, and if core collapse speed is determined by dividing by free fall timescale, which uses gravity as a factor, wouldnt that mean that you're using gravity as a factor in both calculations, making it tough to discern if there was in fact a difference between collapse speed and free fall timescale? Sorry for questioning, mostly wondering if collapse speed is proven or measured or if it's assumed because of gravity it can be no faster than free fall spee Mar 4 at 19:09
• @MarkSwartz the freefall timescale is $\sim (G\rho)^{-1/2}$. I don't really understand your objection. If you drop something, gravity determines how long it takes to hit the ground and the speed at which it does so. Mar 4 at 23:03
• Thank you ProfRob. I meant have we proven/measured what is the speed of a core collapse, or have we said it must be the same speed as free fall because that's how gravity works. But don't worry about answering again, you've already answered twice and I really appreciate your answers, thank you. Mar 5 at 0:20

Core collapse speeds cannot in any case exceed the speed of light. Information about the collapse is transmitted between different portions of the core at the speed of sound within the core material. This is fast, but not c.

• Thank you, but how does core collapse speed compare to the speed of free falling matter, are they the same speed? Mar 4 at 3:44
• @MarkSwartz, I do not know. Mar 4 at 18:32