We are working on next phase of our project where we consider the effects of magnetic fields on the slightly rotation flow. In Proga & Begelman (2003b), we report on our results for 2D MHD case. Figure above shows the density maps overplotted with the direction of the velocity field for four generic stages of the inner accertion flow close to the black hole: (i) the initial stage when both the equatorial torus and the polar funnel accrete (the top left panel; note a torus corona between the torus and the funnel), (ii) the stage when the accretion occurs only through the torus (the top righ panel), (iii) the stage when there is practically no accretion because the torus is pushed away by a very strong poloidal magnetic field forming a cylinder with the black holes inside it (the bottom left panel; this stage is recurrent yet very short-lived), and (iv) the accretion occurs through the torus and through one of the polar region where the low angular momentum material manages to get into the inner flow (the bottom right panel). The last stage is similar to the first stage but there are the following differences: during the fourth stage the polar funnel accretion is only on one side of the equator whereas during the first stage it in on both sides; the fourth stage lasts relatively long at the beginning of the simulations and even repeats whereas the fourth stage is recurrent and last a shorter period of time (much longer than the third stage though). This movie shows how the inner flow changes between the second, third, and fourth stages.

2) non-adiabatic case (applicable to gamma-ray bursts):

As a illustration of a universal nature of accretion onto a black hole, we can consider gamma-ray bursts (GRBs). In Proga, MacFadyen , Armitage , & Begelman ( 2003) we present results from axisymmetric, time-dependent magnetohydrodynamic (MHD) simulations of the collapsar model for gamma-ray bursts. We begin the simulations after the 1.7 solar mass iron core of a 25 solar mass presupernova star has collapsed and study the ensuing accretion of the 7 solar mass helium envelope onto the central black hole formed by the collapsed iron core. We consider a spherically symmetric progenitor model, but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum and a weak radial magnetic field. Our MHD simulations include a realistic equation of state, neutrino cooling, photodisintegration of helium, and resistive heating. Our main conclusion is that, within the collapsar model, MHD effects alone are able to launch, accelerate and sustain a strong polar outflow. We also find that the outflow is Poynting flux-dominated, and note that this provides favorable initial conditions for the subsequent production of a baryon-poor fireball.

Maps of logarithmic density and toroidal magnetic field overplotted with the direction of the poloidal velocity at t=0.2735 s. The length scale is in units of the BH radius (i.e., r'=r/R_S and z'=z/R_S)

As above, but a zoom-in version.

Movie1 , movie2 , and movie3 show the time evolution (of the density) in our entire computational domain (out to 1000 black hole radii), in the inner part of the domain (out to 100 black hole radii), and the innermost part of the domain (out to 40 black hole radii), respectively.

MASS OUTFLOWS FROM ACCRETION DISKS:

Luminous accretion disks are believed to exist in many astrophysical environments: for example, in active galactic nuclei (AGN); in cataclysmic variables (CVs); and in young stellar objects (YSOs). Invariably, such disks are associated with mass outflows and winds. An obvious, and conceptually simple, mechanism for powering disk winds is radiation pressure on spectral lines: several time-independent solutions for the steady-state structure of radiation-driven disk winds have been proposed.

Using numerical techniques (the hydrodynamical code ZEUS code by J.M. Stone and M.L. Norman), we constructed a set of time-dependent two-dimensional radiation-driven disk wind models to identify a parameter domain where mass loss is significant. Our numerical approach is motivated by a desire to account for the multi-dimensional character of the disk wind problem from first principles .

We find that there exists a significant parameter domain in which time-variable behavior is inevitable. Specifically, whenever the disk's luminosity dominates the total luminosity of the system, the outflow is subject to large-amplitude velocity and density fluctuations, although on timescales of order a few flow times, the average properties of the wind are constant. To obtain a steady outflow, it is necessary to add into the total radiation field, a significant radial component, such as that from a bright central star. Our solutions agree qualitatively with the kinematics of outflows in CVs inferred from spectroscopic observations (Proga, Stone & Drew 1998 ; 1999 ).

The time-dependent evolution of the wind is best illustrated in this movie of the density for the model in the top left panel (the case where the disk contribution dominates the total luminosity of the system). See also this movie of the density for the model in the bottom left panel (the case where the central object and disk luminosities are the same).

My other work on mass outflows involves also testing my theoretical models against observations. One way of doing this is to compute synthetic spectra based on multidimensional dynamical models and compared with observations.

Line profiles for our steady state disk wind (the bottom left panel in the figure above) as a function of inclination angle, i. The figure compares the line profiles for the model dashed lines, with the line profiles for the same model but with the slow wind material between the disk equator and the 'fast stream' assumed to be optically thin in the line, solid lines. See Proga et al. ( 2002) for details.

We applied our disk wind models in the most detail first to CVs, as these systems are the best place to test the physics of such models. It is very encouraging that recent HST observations of BZ Cam indicate variable small-scale structuring present in this system (Prinja et al. 2000a , 2000b).

We also applied a similar approach to model dynamics of massive YSOs and B[e] stars. The main modification in these applications was that we allowed an outflow also from a central star. Our models offer great promise in explaining the extreme mass loss signatures of massive YSOs (Drew, Proga, & Stone 1998) and B[e] stars (Oudmaijer, Proga, Drew & de Winter 1998). For example, in Oudmaijer et al., we showed that our model is consistent with the original two-wind concept for B[e] stars suggested by Zickgraf et al. (1985), and exhibits kinematic properties that may well explain the observed spectral features in those stars.

Recently, I considered a new generation of disk wind models: a hybrid of line-driven and MHD driven wind model. I used ideal MHD to compute numerically the evolution of Keplerian disks, varying the magnetic field strengths and the luminosity of the disk, the central accreting object or both. I find that the magnetic fields very quickly start deviating from purely axial due to the magnetorotational instability. This leads to fast growth of the toroidal magnetic field as field lines wind up due to the disk rotation. As a result the toroidal field dominates over the poloidal field above the disk and the gradient of the former drives a slow and dense disk outflow, which conserves specific angular momentum. Depending on the strength of the magnetic field relative to the system luminosity the disk wind can be radiation- or MHD driven. The pure radiation-driven wind consists of a dense, slow outflow that is bounded on the polar side by a high-velocity stream. The mass-loss rate is mostly due to the fast stream. As the magnetic field strength increases first the slow part of the flow is affected, namely it becomes denser and slightly faster and begins to dominate the mass-loss rate. In very strong magnetic field or pure MHD cases, the wind consists of only a dense, slow outflow without the presence of the distinctive fast stream so typical to pure radiation-driven winds.

An example of a MHD/LD driven disk wind. The model paramters related to line-driving are the same as for the pure LD model presented in the top left panel in the four panel figure above.

I have also incorporated into my model radiation-driven wind model a self-consistent evaluation of the ionization structure of the wind. I have computed using this version of the model the structure of line-driven winds from accretion disks in AGNs.

The framework of our two-dimensional hydrodynamical calculations for a line-driven disk wind. The drawing is not to scale. We assume the disk is flat, Keplerian, geometrically thin, and optically thick. The radiation pressure dominated disk is represented by the blue regions while the gas pressure dominated disk is represented by the red regions. The black hole is represented by the black circle while the X-ray source, is marked by the yellow region. The dashed line perpendicular to the disk is the disk rotational axis. Our computational domain is marked by solid lines. The theta= 90 degrees axis, the dashed line perpendicular to the rotational axis, is located above the disk midplane, the dot-dashed line. The offset of the theta=90 degrees axis from the disk midplane is given by the disk pressure scale height.

A sequence of density maps for the model from our fiducial model after 13.3, 14.6, and 16.47~years (left, middle, and right panel). Note both the time-dependent fine structure near the base of the wind and the time-dependent large scale structure associated with the fast stream at the polar angle about 75 degrees.

PAST PROJECTS