Comptonization and Time-lags in Multi-Temperature Plasmas Surrounding Compact Objects

Jason Cullen, PASA, 17 (1), 48.

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Galactic black hole candidates (BHCs) are known to be sources of high energy photons. This emission is thought to be powered by the gravitational potential energy release resulting from material accreting onto a compact object, by either wind accretion or Roche-lobe overflow from a companion. The spectrum of galactic BHCs is often described as being in either a ``high" state, or a ``low" state according to the flux in the 2-10 keV band. The high state spectrum consists of a blackbody component of temperature $\sim 1$ keV and a power-law of photon spectral index

$\sim 2.2 - 2.7$, while the low state spectrum consists of a single power-law of photon spectral index $\sim 1.7$ (Esin et al. 1998, Tanaka & Lewin 1996).

This power-law component is attributed to blackbody photons being up-scattered by electrons (that is, the photons gain energy from the electrons via the inverse Compton process) as they traverse a corona of hot plasma with a Maxwellian electron temperature 10-100 keV (Sunyaev & Titarchuk 1980, Bisnovatyi-Kogan & Blinnikov 1976). If the Comptonization is saturated, where the photons are in thermal equilibrium with the electrons, then the cut-off in the spectrum occurs at $\sim 3kT_{e}$ where kTe is the temperature of the coronal electrons. However, the COMPTEL instrument on the Compton gamma-ray Observatory satellite has detected significant gamma-ray emission up to energies of several MeV, which cannot be explained in this canonical Comptonization model because the gamma-ray flux is too high for what are thought to be reasonable values of the coronal temperature.

While inverse Compton (IC) scattering is understood to be one of the important processes for producing high energy photons from galactic black hole candidates (as well as accreting neutron stars and active galactic nuclei), the physical geometry of the coronal plasma responsible for scattering the photons is not well constrained by current observations. This is partly due to the nature of IC scattering: in general, it depends only on the temperature and the optical depth of the plasma, rather than depending on the physical dimensions directly.

The two geometries that are commonly assumed for spectral calculations are the plane-parallel ``slab" corona above a standard thin accretion disk, and a spherical or quasi-spherical corona surrounding the innermost part of an accretion disk. Based on the results of non-linear Monte Carlo spectral simulations (Dove et al. 1997) the spherical corona plus disk geometry best accounts for the low (hard) state spectrum of galactic black hole candidates. For example, Cyg X-1 spends most of its time in the low state.

The problem then remains of how to produce gamma-ray photons. Possibilities that have been considered are a non-linear tail to the electron Maxwellian distribution, which would be generated by some magnetohydrodynamic (MHD) process, or a compact electron-positron pair dominated plasma. It has been pointed out that the latter possibility is unlikely (Moskalenko, Collmar & Schönfelder 1998; hereafter MCS), as the luminosity of the gamma-rays, although small, still exceeds the Eddington limit for a pair plasma.

Recently MCS have suggested that a two-component corona model can explain both the X-ray and gamma-ray emission of BHCs such as Cyg X-1 (see figure 1). In this model, the plasma geometry consists of two concentric spheres of plasma, each with a different temperature and optical depth. The compact spherical inner-corona of Thompson optical depth of approximately

$\tau \simeq 1.4-2.4$ is responsible for the X-ray power-law component, while a tenuous extended spherical outer-corona of

$\tau \simeq 0.05$ consists of relativistic electrons that are responsible for the hard gamma-ray tail.

The acceleration mechanism for the outer-corona electrons is unknown, but could be any one of stochastic acceleration, MHD turbulence, plasma instabilities in the inner-corona or accretion disk, or an outflow of electron-positron pairs that are created close to the central object. The outer-coronal density is low, so electron cooling is inefficient and the temperature is high

$\simeq 400 \rm keV$. MCS estimate that the cooling time of these electrons due to IC scattering is a few seconds, so the outer-coronal electrons are effectively confined to a region a few light seconds across (at most).

It has also been emphasised (Kazanas, Hua & Titarchuk 1997) that any realistic model for a corona in galactic BHCs must also account for their temporal behavior, such as the hard X-ray time-lags, as well as the spectral fit. These time-lags are produced as photons diffuse through the corona. The photons that scatter numerous times are delayed with respect to those photons that escape after undergoing few scatterings. Photons that scatter many times on average gain more energy than the other photons and so the high energy photons are delayed (take longer to escape from the plasma cloud) when compared to lower energy photons.

As recent investigations have shown (Kazanas, Hua & Titarchuk 1997, Böttcher & Liang 1998) this time delay or lag between high and low energy photons is sensitive to the exact geometry of the up-scattering plasma, including density gradients, and so provides us with a tool that can in principle determine the geometry of the coronal plasma in galactic BHC systems.

We investigate using a linear Monte Carlo code whether the model suggested by MCS can explain both the X-ray and gamma-ray emission of BHCs. We obtain the spectrum produced by such a model for the ``low" state where IC is the dominant process. Furthermore, we also calculate the photon time-lags between the energy bands 2-10 keV and 0.01-10 MeV.

Figure 1: Schematic diagram of the plasma geometry surrounding galactic BHCs as considered in this paper. We consider a model in which an inner spherical corona of plasma is surrounded by an outer spherical corona of hotter, tenuous plasma. Photons emitted in the central regions (taken to be a point source) gain energy from the electrons in these coronae by inverse Compton scattering. The inner optically thick corona produces the canonical X-ray power-law, while the outer-corona scatters some of the escaping photons up to gamma-ray energies. The time-lags between different energy bands (due to different photon escape times from the cloud) can then be found by summing over the pathlength traveled by the escaping photons.
\begin{figure} \begin{center} \psfig{,height=12cm}\end{center}\end{figure}

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