mass 2 flux ratio

Vazquez-Semadeni 2011 say for a uniform cylinder with a mean magnetic field , the criticality condition (i.e. the critical mass to flux ratio) in terms of surface density and the field strength is given by:

where sigma is the surface mass density, i.e.

and L is the length of the cylinder.

This can be rearranged for the critical length of a cylinder of mean magnetic field strength B0 and number density n,

Given my initial field is , and n = 1 cm-3, this critical length is:

This means that for the smaller box simulations, the colliding flows are sub-critical. However, for the larger box simulations they are super-critical.

Now, we do not see global gravitational collapse, so this measure of super-criticality doesn't seem to mean much. It doesn't take into account the kinetic energy in the flows, and the turbulent and thermal pressures that would also be counter-acting gravity. So then, since we do not see collapse even though the purely magneto-gravity critical condition is satisfied means there are other stronger forces in the cylinder preventing collapse.

If instead of putting the initial density in the above equation and we instead looked at the length scale of a cylinder with density = perturbation density, what do we get. First, let's take the average cloud density to be 100x the initial density. Then, we get,

This seems to say, if we assume the collision region is shocked to a mean density of n = 100 n0, and the strength of the field stayed the same as the initial value (which IS an assumption given the field also is shocked), then the length of an unstable collision region cylinder would be 1.5 pc. This is about 10x smaller then the collision region seems to be from eyeballing the cdm.

For the case of subcritical cylinders (i.e. smaller box simulations), how long does it take to acquire enough mass for the cylinder to become supercritical?

Can rearrange the above criticality equation to instead put in terms of the column number density, N:

Setting this equal to a function for N(t),

and solving for t gives:

where,

and

Solving for time gives,

This says the field is dynamically weak and SHOULD not be able to prevent global collapse by the time t = 2.6 Myr at the mass influx of the simulation. However, our simulation time is 30 Myr. So, something is supporting the gas against collapse.

Next, compare turbulent jeans timescales? If that is much longer than this timescale (and the simulation time), might be able to argue that the reason we're not seeing collapse is becuase of turbulent support?

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