We present results of models of the physical space and parameters of the accretion disk of Sagittarius A*, as well as simulations of its emergent spectrum. This begins with HARM, a 2D general relativistic magneto-hydrodynamic (GRMHD) model, specifically set up to evolve the space around a black hole. Data from HARM are then fed into a 2D Monte-Carlo (MC) code which generates and tracks emitted photons, allowing for absorption and scattering before they escape the volume.
Sagittarius A* is the supermassive black hole (about 3.6 million Solar masses) at the center of our galaxy, which is known as a strong radio source with specific x-ray signatures which have come to be associated with flaring or quiescent states. The short time scales of these flares, as well as the lack of significant time lags between NIR and x-ray components, suggests the possibility of these arising in a small volume close to the event horizon.
Recent attempts to model the spectrum of Sagittarius A* have proven promising, but have relied upon simplifications or assumptions which have somewhat diminished the impact of these results. Our intent is to deliver the most consistent modeling possible with current technology, and avoid some of the simplifications that previous simulations have required.
This begins with using a GRMHD code specifically designed to evolve an accretion disk around a black hole. This is a considerable advantage over models which specify analytic formulae to describe density, temperature, and magnetic field profiles. Even simulations done with MHD codes suffer some of the same downfalls as simpler set-ups -specifically that effects of general relativity near a supermassive black hole become quite important.
Data output by the GRMHD code are used as input for our MC code. Unlike other models which rely only on emission and scattering calculated analytically, this simulation creates a realistic situation through use of the Monte-Carlo random generation method for photons, and allows for scattering and absorption before photons escape the volume.
It should be noted that both of the codes used here are 2D and axially symmetric. The third dimension would be useful for full consistency, but the authors feel that its lack of inclusion does not preclude the results from being significant.
Our GRMHD modeling is done using the HARM (High Accuracy Relativistic Magnetohydrodynamics) code developed by Gammie et al. (2003). The code simulates GRMHD evolution through time by the use of particle number conservation, the four energy-momentum equations, the MHD stress-energy tensor, and the induction equation. These equations take conserved hyberbolic forms, for easy integration:
where U, F, and S represent the set of conserved variables, fluxes, and sources, respectively. HARM is set to first seed a torus around a black hole with an initial density and poloidal magnetic field, then evolve the space through time, tracking density, internal energy, 4-velocity, 4-magnetic field. This is allowed to continue until the space reaches a “steady state” -of special note in the code output is the highly turbulent magnetic field, an artifact of the magneto-rotational instability, which is an important mechanism governing the transport of angular momentum in the disk. This instability causes the turbulence which is likely to be at least partly responsible for the energizing of electrons in the disk, though in our MC trials, we only consider fully thermal distributions.
The MC code used for photon emission and scattering has a long history and is discussed in a number of resources, such as Canfield et al. (1987); Liang & Dermer (1988); Böttcher et al. (1998). For a complete treatment, readers should see these papers.
In general, this code is a coupled MC/FP (Fokker-Planck) code. For our intents, the FP evolution of the electron distribution was unnecessary at this stage, so it was turned off to allow a fixed temperature given by the HARM output. The code is set up on a 2D axiallysymmetric cylindrical grid, creating a (hollow or solid, depending on whether the inner radius is set to zero) cylindrical shape. Each zone is assigned a density, ion and electron temperatures, magnetic field amplitude, and thermal and nonthermal distribution components. For our purposes, this is simply set to be a Maxwellian, but the code allows power law nonthermal distributions as well. The code allows emission from the volume and boundaries, and emitted photons are tracked and allowed to scatter or absorb.
Output from the HARM code is used to assign the zone quantities. That is, we specify a maximum density and the rest of the output scales to give us the ion temperature and saturated MRI magnetic field. Assuming that inclusion of an initial toroidal magnetic fields would add to the final field, as this dimension is mostly unaffected by evolution, allows us to set the magnetic field, as long as it doesn’t drop below the saturation value. Similarly, as we have a specified ion temperature but no way to directly evaluate the electrons’ acceleration, we set a global ratio between the two values. That is, in one trial the electron temperature in a zone could be set to always be twice the value of the ion temperature in the same zone.
For all of the fits presented in figures below, the open circles are data points, triangles are upper limits, and the bowties denote the Chandra-obtained flaring and quiescent x-ray data points and sl
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