Radiation - effect on hydrodynamics

[bolverk]

Last time we spoke we mentioned one criterion to determine whether radiation can affect the hydrodynamics. This condition was that the cooling timescale should be smaller than the dynamical timescale. However, this condition is always satisfied near the stagnation point. I think two more conditions are necessary:

1. The cooling rate must be smaller than the energy injection rate from the stellar winds.
2. The flow should not be extremely supersonic, so that a considerable portion of the energy is thermal rather than kinetic.

Other than that, I ran into two difficulties in writing this bit:

1. There are too many cases to consider.
2. The discussion is not very useful without explicit values.

[alekseygenerozov]

This condition was that the cooling timescale should be smaller than the dynamical timescale. However, this condition is always satisfied near the stagnation point. I think two more conditions are necessary:

I guess you have defined the dynamical time using the flow velocity, so yet it will always be true. When I have thought about this in the past (section 3.4 here), I defined the dynamical time in terms of the free-fall time.

With this definition comparing the dynamical time to the free-fall time is roughly equivalent to comparing the heating rate and the cooling rate at the stagnation radius, as we discuss in the paper.

_Other than that, I ran into two difficulties in writing this bit:

There are too many cases to consider.
The discussion is not very useful without explicit values._

Perhaps then we could just summarize under what conditions cooling is important without enumerating specific cases?

[bolverk]

I guess you have defined the dynamical time using the flow velocity, so yet it will always be true. When I have thought about this in the past (section 3.4 here), I defined the dynamical time in terms of the free-fall time.

Your definition solves the pathology close to the stagnation point, but introduces a similar one at large radii.

Perhaps then we could just summarize under what conditions cooling is important without enumerating specific cases?

Without numerical values, all I can do is point out cases where cooling will inevitably become important.

[alekseygenerozov]

Without numerical values, all I can do is point out cases where cooling will inevitably become important.

I think this is fine, we don't need to go into too much detail.