Simulations of the circumnuclear disk with a larger inner cavity, Part II -- Marvin

In this post I am presenting 10 simulations of the circumnuclear disk, 5 with an inner cavity of r=1pc (see first figure and first animation below) and 5 with an inner cavity of r=2pc (see second figure and second animation below). The time is given in units of yrs. The r=1pc simulations cover a time of years, the r=2pc simulations years. The following table shows the details of these simulations. (Note: B=1mG corresponds to a plasma-beta of about 0.1, B=0.1mG to a plasma-beta of about 10.)

Number properties linestyle
1. without magn. fields and with outflow blue, dotted
2. with magn. fields (B=1mG) and with outflow red, dashed
3. without magnetic fields and without outflow turquoise, solid
4. like 2., but with B=0.1mG green, dashdotted
5. with magn. fields and without outflow violet, solid

First figure: CND with an inner cavity of r=1pc

Second figure: CND with an inner cavity of r=2pc

First animation: CND with an inner cavity of r=1pc​

Second animation: CND with an inner cavity of r=2pc​

In all these simulations the inner rim moves inwards in one way or another. Different physical processes can be responsible for that, but they all work on different timescales: Firstly, the inner rim moves inwards due to numerical viscosity on a viscous timescale (on how to determine the numerical viscosity I refer to one of my other posts: ​https://astrobear.pas.rochester.edu/trac/blog/mblank05302015). Secondly, gas pressure can cause the inner rim to move inwards, the corresponding timescale is with the speed of sound . Then, magnetic pressure can also cause the inner rim to migrate inwards on a timescale , where is the Alfven speed. Finally, the inner rim moves inwards due to the angular momentum extraction caused by the interaction with the wind, the corresponding formula can be found in our paper draft. All these timescales are listed in the following table in units of yrs. is the timescale for the angular momentum extraction according to the formula presented in our paper draft, and is the time the inner rim actually needs to move inwards (as seen in the simulations).

…….

timescale r=1pc r=2pc
4.5 12.7
2400 21700
37.8 113.5
10 30
100 300
49 490
8 42
20 65

Let's first look at the simulations without outflow (number 3 and 5): There is no big difference between these two models. Thus in the absence of the central outflow magnetic fields do not have a large effect on the evolution of the CND, maybe the reason for this is that initially there is no magnetic field present inside the inner cavity. Only numerical viscosity causes an inwards migration of matter, but as the corresponding timescale is much larger than the simulation time not much matter is actually moving inwards.

Examining the simulations without magnetic fields (model 1) and with a low initial magnetic field strength (model 4) shows that initially they do not deviate much from each other (maybe the magnetic field strength that I've chosen for model 4 is a little bit too low). In both simulations the inner rim takes about yrs to reach the outflow object ( yrs for the r=2pc simulation). The first yrs ( yrs for r=2pc) they look more or less the same, after this time the surface density is larger when no magnetic fields are present.

In the simulation with magnetic fields and with outflow (model 2) the inner rim moves inwards very quickly (faster than in the simulations without magnetic fields and with a low magnetic field strength), it reaches the outflow object after about yrs ( yrs for the r=2 simulation). After that the surface density decreases about a factor of two, thus matter seems to be removed from the inner cavity. Then the simulation reaches a "steady state", where the surface density experiences no significant changes.

Conclusions:

  1. The outflow is causing the inner rim to movs inwards, the higher the magnetic field strength, the faster it is moving.

One may be tempted to think that this is due to the magnetic pressure that drives the material inside, as for the simulations with magnetic fields and with outflow (model 2) the timescales correspond to the times the inner rim needs to move inwards. But even without magnetic fields the inner rim moves inwards, one again could think that this is caused by the gas pressure, because roughly corresponds to the times the inner rim needs to move inwards. However, the simulations without outflow do not show such an inwards movement of the inner rim whatsoever, thus it is the outflow that causes the inner rim to shrink (at least it is the main contributor).

  1. After the inner rim has reached the outflow object, the surface density is lower for higher magnetic field strengths.

But as always, answering some questions leads to a larger number of new questions:

  1. Why is the collapse faster for higher magnetic field strengths? Magnetic fields seem to accelerate the angular momentum extraction.
  1. Why is the surface density lower for higher magnetic field strengths? Do magnetic fields prevent the inflow of matter or is there a kind of magnetically driven outflow?
  1. and fit quite well for the r=1pc simulations, but why is there such a huge difference for the r=2pc simulations?
  1. Do we have to answer all these questions in our paper? Maybe the first two can be shifted to our future work, but I think the third needs some additional pondering.

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