Large Thick Disk Initial Data around a Black Hole
EU-Network Meeting (Southampton, 31/01-03/02/2002)

The analytical theory of accreting disk orbiting black holes (BHs) was first proposed by Kozlowski et al(1978).

Based on this theory and using the new developed EU-Hydro code (Whisky), this work aims to compute the initial data necessary to perform 3D simulations of the accretion of matter from a torus with pressure onto a rotating BH and the stability of this type of thick disc. In the first stage of this analysis the self-gravity of the torus will be neglected and the spacetime will be that of the black hole. Already with this simplified setup there are a number of interesting problems which we plan to investigate, such as non-axisymmetric oscillations of the torus and the runaway instability, which is an exponential mass loss that may occur when the accretion disc overflows the Lagrangian point.

We assume that the external gravitational field is stationary and axisymmetric. In this case, the metric does not depend on the time coordinate or on the azimuthal coordinate .

We also assume a perfect fluid stress-energy tensor, and a polytropic equation of state,

Where p is the pressure, is the proper energy density and are the rest mass density, polytropic constant and the polytropic index. The specific angular momentum and the angular velocity are given by

From this equations it follows that,

The equations of motion can be written as

Note that the equations of motion simplifies considerably for the case of discs with constant angular momentum.

In order to construct a thick disc around a black hole we first calculate the metric coefficients in a Kerr background (only the Schwarzschild case is presented here); then we calculate the marginally stable and marginally bound orbits and the corresponding angular momentum of these orbits.

A disc with constant angular momentum, , larger than the angular momentum of the marginally stable orbit and smaller than the one of the marginally bound orbit is chosen. This case corresponds to stable discs.

We then calculate the distribution from the equations 4 and 5,

After calculating the inner and the outer radius of the disc and we initialize the hydrodynamical quantities.

Figure 1 shows the density on the equatorial plane for a disk with around a Schwarzschild black hole of one solar mass. Its inner and outer radius are located at 5.73 M and 15.19 M respectively. The cusp is located at 4.42 M. Note that if matter spills over the cusp then accretion is driven by pressure forces.

  
Figure: Density on the equatorial plane, case with

REFERENCES

Abramowicz M. A., Calvani M., Nobili L., 1983, Nature, 302, 597
Kozlowski M., Jaroszynski M., Abramowicz M. A., 1978 A&A, 63, 209

%