Interstellar Medium: Herbig-Haro Objects

[Carusun]

Hi all. First post and all that, so I hope I don't do anything wrong, and that if I do, you'll cut me a little slack :P

Anyway, onto the question I'm wanting help with:

A J-shock in a Herbig-Haro object is propagating through neutral hydrogen gas at speed 100km/s. The gas has number density 10^-7 m^-3, and temperature 10^4 K.

a) Calculate the Mach number of the shock, and decide if the strong shock approximation is reasonable.
-- Done this part of the question, and ended up with Mach 7.3*10^-4, and, if I've understood my notes correctly, that the strong shock approximation is reasonable.

b) Calculate the speed and compression of the post shock gas. Work in the shock frame.
-- If I've understood my notes correctly, then the speed of the post shock gas is 1/4 of the speed of the pre-shock gas, giving 25km/s.
For the compression, I'm just guessing, as I've not been able to find that in my notes, but would that just be the pressure? If so, then you've got
P=ma/A,
but I'm not sure as to how to work out the acceleration from what I've been given.

Have I just gone completely down the wrong path, or have I just not noticed something that'd help me work it out easily?

Many thanks in advance for any help that comes my way :)

 

[Carusun]

Well, I believe that I've done that question now, and I've ploughed ahead to one of the later parts of the question.

e) The cooling rate per unit volume in the post shock gas can be represented as, L=(LAMBDA) n(1)^2, where (lambda) is a cooling function dependent on the cooling process. Convert this to a cooling rate per unit mass and show that the typical cooling timescale of the post shock gas is
t(c) = (3kT(1))/(2(LAMBDA)n(1))

Where a(b) is a with a subscript of b, and (LAMBDA) is a capital lambda.

Quick recap of the figures I know, and those that I've worked out:

v(0) = 100*10^3 m/s -- Given
v(1) = 25*10^3 m/s -- Given
n(0) = 10^7 m^-3 -- Given
n(1) = ((rho)(1)/m(hydrogren)) (not 100% sure on that, confirmation would be nice)
(rho)(0) = 1.67*10^-17 kg/m^3
(rho)(1) = 6.68*10^-17 kg/m^3
P(0) = 3.137*10^-8 N/m^2
P(1) = 1.255*10^-7 N/m^2

Hopefully those values are correct, and are what's needed...

For the conversion to per unit mass, could I just divide the number density by regular density? That'd leave me with units of (whatever the cooling functions unit is)*kg^-2, which could possibly cancel down to leave blah/kg, which'd be what I'm looking for, yeah?

Again, any help you can give would be greatly appreciated :)