Changes between Version 12 and Version 13 of CollidingFlows


Ignore:
Timestamp:
06/30/11 14:09:49 (14 years ago)
Author:
Jonathan
Comment:

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  • CollidingFlows

    v12 v13  
    108108Here we've plotted the cooling time as a function of density and ram pressure (in units of Kelvin/cc)
    109109
    110 [[Image(nPCoolingTime.png, width-400)]]
     110[[Image(nPCoolingTime.png, width=300)]]
    111111
    112112We can then calculate the cooling length of the shock [[latex($L_{cool}=T_{cool} v_{shock}$)]] or the cooling length of the thermal instability [[latex($\lambda_{TI}=T_{cool} c_s \approx L_{cool}$)]] since [[latex($c_s \approx v_{shock}$)]]
    113113Here are plots of the cooling length as well as the thermal instability length scale.
    114114
    115 [[Image(nPCoolingLength.png, width=400)]][[Image(nPTILength.png, width=400)]]
     115[[Image(nPCoolingLength.png, width=200)]][[Image(nPTILength.png, width=200)]]
    116116
    117117We can also calculate the free fall time for the condensations
    118118[[latex($t_{ff}=\sqrt{\frac{3 \pi}{32 G \rho}}$)]] as well as the Jeans length [[latex($\lambda_J= c_s\sqrt{\frac{\pi}{G\rho}}$)]] plotted below
    119119
    120 [[Image(nPFreeFallTime.png, width=400)]][[Image(nPJeansLength.png, width=400)]]
     120[[Image(nPFreeFallTime.png, width=200)]][[Image(nPJeansLength.png, width=200)]]
    121121
    122122
    123123Finally given the density and temperature of the shocked material we can estimate the density contrasts of the thermally unstable clumps [[latex($\chi=T_{shock}/T_{eq}$)]] and then calculate the clump destruction time assuming it is of size [[latex($\lambda_{TI}$)]] embedded in a background flow of velocity [[latex($v_{shock}$)]].  [[latex($t_{cc}=\frac{\sqrt{\chi} \lambda_{TI}}{v_{shock}}$)]]
    124124
    125 [[Image(nPTIDestructionTime.png)]]
     125[[Image(nPTIDestructionTime.png, width=300)]]
    126126
    127127Combining these two time scales gives a clump survivability [[latex($\xi=\frac{t_{cc}}{t_{ff}}$)]]
    128128
    129 [[Image(nPTICollapsibility.png)]] which peaks at about .1
     129[[Image(nPTICollapsibility.png), width=300]] which peaks at about .1
    130130
    131131Plotting the same quantity in n vs V space we have
    132132
    133 [[Image(nVTICollapsibility.png)]]
     133[[Image(nVTICollapsibility.png), width=300]]
     134
    134135we can see that optimal parameters are somewhere around a density of 20 and a velocity of 16 km/s although we still need clumps to survive for ~ 10 cloud crushing times before collapsing...  Of course if the wind turns off then clumps will be able to survive longer and collapse.  It might be better therefore to use finite wind durations...