The speed of sound is very important in astrophysics in the study of accretion and wind flows. I have two questions as follows:
What is special about the speed of sound and not any other value of speed? I could not understand the physical relevance of speed of sound in astrophysical flows.
Shock waves occur for an obstacle in supersonic flows and not in subsonic flows. Why is it not possible to have a discontinuity for an obstacle in subsonic flows leading to a shock?
'Speed of sound' is the maximum rate of propagation of density (or pressure) disturbances in a medium.
Imagine some solid body travelling through a fluid at a supersonic speed. As mentioned above, the speed of sound (let's call it $v$) is the maximum rate at which information about density and pressure changes can travel in a fluid. In time $t$, only the fluid particles at a distance $ut$ would know that the body is approaching them, and they would move out of the way to let it pass through. But if the body itself is travelling at a speed $u$ > $v$, the fluid particles would not know that the body is approaching and this causes the shock waves. Clearly, in subsonic flows, the fluid particles will have enough time to "react" to the approaching body.
As for its importance in astrophysics, many astrophysical phenomena are highly energetic, reaching speeds well beyond the speed of sound of the medium one is looking at. For example, there are some theories which propose that shock waves in the early universe fluid are responsible for the production of large scale magnetic fields we see today. Also, accretion flows are mostly supersonic at small radii. In fact, accretion disks around super massive black holes reach relativistic speeds.
