Neutron Star Stability: Speed of Sound vs Light

[GeorgeDishman]

[This thread was split from https://www.physicsforums.com/threa...wave-travelling-together.878450/#post-5518001 as it's an interesting topic in its own right]

.. if the speed of sound in a medium were equal to the speed of light in that same medium (I suspect that is not true for any medium) then they would go at the same speed.

That's actually an important point, in the core of neutron stars, the speed of sound increases with the density and provides a limit on the maximum mass. If the speed of sound exceeded the speed of light, there would be frames in which effects preceded causes, thus causality would be violated. That region is shown for example on this plot of various Equations of State as the "Causality Limit".

http://www3.mpifr-bonn.mpg.de/staff/pfreire/images/Graph-R-M-with-pulsars.png

 

[Nugatory]

If the speed of sound exceeded the speed of light, there would be frames in which effects preceded causes, thus causality would be violated.

In this context the "speed of light" that GeorgeDishman refers to is the universal speed $c$, the speed of light in a vacuum. It is not the speed at which light propagates through the neutron star material.

 

[newjerseyrunner]

So wait... What happens if a pulsar is at the causality limit and it absorbs a gas cloud? Does it instantly collapse into a black hole, I notice that there as a gap between the causality limit and the collapse into a black hole.

 

[phyzguy]

So wait... What happens if a pulsar is at the causality limit and it absorbs a gas cloud? Does it instantly collapse into a black hole, I notice that there as a gap between the causality limit and the collapse into a black hole.

A real star can never be "at the causality limit", because that is physically impossible. What that line on the chart means is that if the combination of mass measurement, radius measurement, and equation of state is telling us that the neutron star is at or above that line, then either the measurements are wrong or that equation of state cannot be correct.