MHD simulations of the circumnuclear disk - Marvin

I have now finished a simulation that contains all the relevant physics, including cooling, MHD and the outflow object.

But first I want to recall two of my previous simulations, which do not include MHD: The first animation shows the surface density of the accretion disk's inner region. The inner black circle marks the outflow object, the outer back circle marks the initial inner rim of the accretion disk. We see that, although no physical viscosity is present and the outflow is interacting with the disk, material is accreted, i.e. the accretion disk's inner rim moves inwards until it reaches the outflow object.

The second animation shows the same but without outflow object, this is just to show that the accretion disk's inner rim finds a stable configuration and the gas inside the inner cavity has a density of about 1000 cm-3, about 30 times lower than the accretion disk's density.

The third animation now includes MHD and the outflow object. The disk has a toroidal initial field configuration with an initial field strength of 1 mG. There are still clumps and streams of matter forming and moving inwards, but besides these features the inner rim seems to be stable with densities of the inner cavity of about 1000 cm-3 as seen in the second animation. So magnetic fields seem to play an important role in forming the inner cavity of the galactic center's accretion disk.

The fourth animation shows the corresponding face-on magnetic field strength.

First animation: surface density, without magn. field

Second animation: surface density, without magn. field and without outflow

Third animation: surface density, with magn. field and with outflow

Fourth animation: face-on magnetic field strength in Gauss

This leads to two important questions:

  1. Why is the disk collapsing when the outflow is switched on?
  2. Why and how do magnetic fields prevent this?

Some time ago we discussed a simple model for the extraction of angular momentum from the inner accretion disk:

Lets assume the accretion disk has an inner rim , and the inner part of the accretion disk (a ring with mass M) fully interacts with the outflow. The outflow has a massflow , so after a time the mass has been added to the ring. That means that the mass of the ring increases, but its angular momentum does not change because the wind does not have any angular momentum. So the specitic angular momentum is decreasing, leading to the accretion of the disk's material. However, there must be a kind of critical outflow rate, because although the wind does not add any angular momentum to the disk, it does add radial momentum to the disk, and at some point the radial momentum will just win against the loss of angular momentum. To test this simple model I did the following very rough estimate: Both, the ring with mass and the wind with mass , have a specific potential energy and a specific kinetic energy (the wind due to its radial momentum and the ring due to its azimuthal velocity ). If we assume perfect mixing of the ring with the wind material, we can calculate the total energy of the "new" ring (with mass ), which is just the sum of the aforementioned:

When we further assume that the "new" ring finds a new orbital configuration (at radius ) we can use the virial theorem, where

to calculate its new orbit:

So if the wind velocity is smaller than the azimuthal velocity we would expect an inflow, otherwise an outflow of disk material. In the GC we have , , , so we would always expect that the disk is pushed away from the central black hole, contrary to what we see in the simulations. So apparently this simple model does not account for the angular momentum loss.

I furthermore made a rough estimate for the code performance on XSEDE's gordon cluster, as shown in the following figure:

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