Shocked Clumps

Common params

namb	250 cc-1
Tamb	100 K
Rclump	100 AU

Run Params

Run	vwind (km/s)	chi	final time (yr)	Tbow (K)	Ttrans (K)	Lbow (Rc)	Ltrans (Rc)
A	50	10	568.9 yr	5.64e+04	5.64e+03	2.51e-01	9.62e+00
B	100	10	248.4 yr
C	200	10	142.2 yr
D	400	10	71.1 yr	3.61e+06	3.61e+05	2.60e+03	3.71e-01
E	800	10	35.6 yr	1.44e+07	1.44e+06	2.02e+04	5.31e+01
F	200	100	142.2 yr	9.02e+05	9.02e+04	9.90e+01	1.74e+00

T_{bow}=\frac{3 X v_{wind}^2}{16 k_b}

T_{trans}=T_{bow}/\chi

A naive calculation of L_shock using the instantaneous cooling rate at T_shock would implies that run A is bow only, run D is trans only, run E is neither, and that run F is marginally trans only. However it does appear that run F has both a cooling bow shock and transmitted shock. To understand the discrepancy we should consider the following figure where we have plotted the cooling lengths in units of clump radius as a function of wind velocity for the bow shock as well as for the transmitted shocks with \chi = 10 & 100

If we consider where the blue curve intersects with a wind speed of 200 km/s, we see that the slope of the cooling length as a function of velocity (or temperature) is very high. As the bow shock cools it effectively slides to the left and the cooling length becomes around .1 R_c. This explains the dramatic behavior of the ambient shock in run F. The transmitted shock also follows a similar behavior transitioning from marginally cooling to a cooling length of approx .1 R_c as well.

Run E which is also very curious because while neither the bow shock nor the transmitted shock initially is cooling, the intersection of the transmitted shock with the wrap around shock triggers dramatic cooling and fragmentation. From the intersection of the red line with 800 km/s we see that the transmitted shock is on the same region of the cooling curve as the bow shock was for run F and once it begins to cool the cooling length drops from 10 R_c to .01 R_c.

	A 50 10 (bow only)	D 400 10 (clump only)	E 800 10 (neither)	F 200 100 (both)
	movie​	movie​ zoom​	movie​	movie​ zoom​
5
10
15
20
25
30