Accretion disc coronae and magnetic flares




The hard X-ray power law component in BHC and Seyfert galaxies spectra is most likely due to multiple Compton scattering (Comptonization) of soft photons on a population of hot electrons which reside in a region surrounding the accretion disc itself. In analogy with the sun, this hot, optically thin Comptonizing region is often referred to as the accretion disc corona.
X-ray spectral analysis alone is often unable to distinguish among different possible geometries for the Comptonizing corona (Figure 1), and more insight can be gained from multiwavelenght observations and detailed models of all the relevant radiative processes involved.

Figure 1: The innermost region of  the accretion flow around a black hole according to four different models for the X-ray emission. The relative scale of different components
is totally arbitrary. Black arrows indicate seed photons for Comptonization (IR
to EUV depending on models), while green arrows indicate inverse Compton emission
(X--rays). From Haardt (1997).

It is now well established that magnetic stresses in accretion discs are likely to be responsible for the transfer of angular momentum (see Balbus & Hawley, 1998, Rev. Mod. Phys. 70, 1, for a review). Magneto-rotational instabilities
can drive turbulence by amplifying the seed magnetic fields on roughly Keplerian time scales; the rate at which magnetic energy is built up is fast enough to explain the bulk of energy release in an accretion disk
as magnetic dissipation. This supports the idea that accretion disc coronae are highly magnetic and form by buoyancy of the strong magnetic fields amplified in the disk (Galeev, Rosner & Vaiana 1979).  This picture is supported by numerical simulations which show that, when weak magnetic fields are amplified via Magneto Hydrodynamic (MHD) turbulence in the disk, only a fraction of the energy proportional to the aspect ratio of the disc  is dissipated locally while the rest escapes and forms a magnetized corona above the disc. In the standard picture for viscously heated accretion discs, the aspect ratio, i.e. the ratio of the height (H) to the radius (R) of the disc is much lower than unity, so strong coronae are expected.

In any such models, the magnetic field in the corona is likely to be strongly inhomogeneous and to dissipate energy in localized active regions (Haardt, Maraschi & Ghisellini 1994).

In the hot (T ~ 50 - 200 keV), highly magnetized, coronal plasma the majority of the electrons are thought to be thermal and are expected to produce Cyclo-Synchrotron emission, and Compton scatter the softer photons
produced both by dissipation in the underlying accretion disk and by the synchrotron processes themselves.

A Model for XTE J1118+480

We have recently applied a model for the emission from a highly magnetic, structured corona to the optical and X-ray observations of the newly discovered X-ray transient XTE J1118+480 (Merloni, Di Matteo & Fabian 2000).

This source is unique for a number of reasons. It is located at high galactic latitude and has a very high optical-to-X-ray flux ratio. The source is observed in the typical black hole candidates hard state
(photon index Gamma ~1.8).  Given the optical/UV to X-ray flux ratio we have derived constraints for the approximate size, optical depth and magnetic field strengths of the coronal active regions.

The main point of our work is that the simultaneous presence of a strong quasi periodic feature in the optical and X-ray light curves clearly suggests that the fluxes in the two bands both originate from the same
region in the inner part of the accretion flow. Self-absorbed cyclo-synchrotron emission is the natural candidate to explain the optical variability.
Such emission is expected in any magnetic corona model, and the inferred magnetic field value (B~2 ×10^6 Gauss)
is the one predicted to arise when the source is in the Hard state (low value of the accretion rate and high value of the fraction of the power dissipated in the corona).

Thunderclouds and accretion discs

X-ray observations of Seyfert 1 galaxies offer the unique possibility of observing spectral variability on timescales comparable to the dynamical time of the inner accretion flow. They typically show highly variable lightcurves, on a wide range of timescales, with Power Density Spectra characterized by `red noise' and a break at low frequencies. On the other hand, time resolved spectral analysis
have established that spectral variability on the shortest timescales is important in all these sources, with the spectra getting
softer at high fluxes (in the 2-10 keV band, typically).

We can use all these observational facts to test our understanding of magnetic coronae, and in particular, on the nature of coronal heating.
In a recent paper  we showed that the sites of the fundamental heating events, likely caused by magnetic reconnection,
must be compact, with typical size comparable to the accretion disc thickness, but must be triggered at a height at least an order of magnitude larger than that, in order for the dramatic spectral variability to be explained. Also, in order to explain the observed time-variability properties of such systems, spatial and temporal distribution of flares should not be not random: the heating of the corona
 proceed in correlated trains of events in an avalanche fashion. Larger avalanches are brighter, but they also intercept more photons from the underlying disc, and are therefore softer (see figure below).
map of the corona
The inner corona is mapped into a square. For simplicity, the pixels have equal luminosity, and the total
luminosity scales with the covered area. The region of the corona active at any time are represented by filled squares, whose size is
distributed as a power-law, with index p=2. Each region is assumed to have the same height above the disc and optical
depth. The color code shows the spectral index of the filled active regions, calculated self-consistently taking into
account thermal Comptonization of disc photons and of synchrotron emission in the active regions themselves. Clearly the more luminous state (right hand side, for which the instantaneous covering fraction is larger), is dominated by active regions with soft spectra.

The accretion disc corona therefore turns out to be  a highly inhomogeneous stochastic system, whose basic building blocks, the active regions, can be viewed as `magnetic thunderclouds', charged by the differential rotation of the underlying disc and/or the turbulent motions in the accretion flow. The sizes of the thunderclouds are distributed as a power-law. The fast energy release, triggered by magnetic reconnection on the smallest scales, heats progressively larger active regions.
Each active region (thundercloud) produces the observed rapid flares (X-ray lightning strokes)  by inverse Compton scattering soft photons coming mainly from the underlying optically thick accretion disc. Furthermore, if the coronal optical depth  is high enough, the active regions may obscure the X-ray spectral features produced in the cold disc  for an observer situated above them (and act therefore as `Compton clouds').

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These pages are maintained by Andrea Merloni; last update: February 2002