Introduction

Galactic X-ray binaries are binary systems containing a compact object (the primary: a black hole, neutron star, or white dwarf) and a normal star (the secondary). The compact primary accretes matter from a stellar wind of the secondary or by direct mass transfer from the surface of the secondary, if the secondary has expanded so far that matter on a section of its surface becomes gravitationally bound to the primary (this is called Roche-lobe overflow). Due to angular-momentum conservation, the matter accreting onto the primary settles in an accretion disk, where viscous stresses heat the material to millions of degrees. At such temperatures, the disk is radiating primarily in X-rays, hence the name ``X-ray binaries''.

In addition to the thermal X-ray emission which one expects from the standard accretion disk, X-ray binaries often also emit a power-law spectrum of hard X-rays and even gamma-rays. This can be explained by Compton scattering of softer X-rays and ultraviolett radiation in a tenuous corona of very hot electrons (with temperatures up to ~ 1 billion degrees), which may be located on top of (and below) the accretion disk, or in the innermost portions of the accretion flow, replacing the standard (optically thick) accretion disk. According to the total luminosity and the relative contribution of these two main radiation components in the X-ray spectra of X-ray binaries, one can distinguish several spectral states. The most prominent ones are: (1) The high/soft state, in which the X-ray emission is dominated by the thermal emission, probably from the optically thick accretion disk; only a weak, rather steep (photon index > 2) hard-X-ray power-law is observed. (2) The low/hard state, in which the X-ray spectrum is dominated by a rather hard (photon index < 2) power-law with a marked high-energy cut-off at typically ~ 100 keV; only a weak (if any) soft excess due to the possible contribution from an optically thick accretion disk is seen. In addition, some sources (in particular, X-ray transients in outburst) have been observed in a very high state, in which they show both a very luminous soft X-ray excess and a strong hard X-ray power-law component. Also, some sources occasionally exhibit an intermediate state, which shows characteristics of both the low/hard and the soft/high states - similar to, but on a lower luminosity level than the very high state.

The X-ray emission from X-ray binaries is not steady, but shows pronounced, erratic (aperiodic) variability on a wide variety of time scales, from milliseconds to months (see Fig. 1.2). Apart from this aperiodic variability, some objects also show nearly periodic variability patterns, which are called quasi-periodic oscillations (QPOs) and show up as broad humps in the Fourier power spectra of their X-ray light curves (see Fig. 1.3). Veryy interesting features have been found from computing Fourier-frequency dependent phase and time lags between the X-ray light curves in different energy bands. A particularly intriguing example of such phase lag features is shown in Fig. 1.4.

The rapid variability of X-ray binaries has turned out to contain a wealth of valuable information about the physics of the accretion processes in X-ray binaries, and our group has studied these variability phenomena in great detail. To this end, we have been studying theoretical models, in particular by means of computer simulations, and have carried out extensive observational programs. My primary contribution to this research program was the development and maintenance of our Monte-Carlo radiation transport code for the self-consistent, time-dependent simulation of X-ray radiation processes and electron dynamics in hot plasmas. In the following two sections on Modeling the Rapid Aperiodic Variability of X-ray Binaries and Spectral Modeling of Accreting Neutron Stars some recent results of our theoretical efforts in this field will be summarized. Most of this work has been done in close collaboration with Prof. Edison Liang. Our observational and data analysis work, which has been mainly carried our by faculty fellow Ian Smith and former graduate student Dechun Lin, will be discussed in the section Observations of Black-Hole Candidates.

In many astrophysical settings, the accretion of material onto a massive object goes in tandem with the formation of directed plasma outflows (jets, see Fig. 1.5). If the central object is a black hole, these outflows quite often become relativistic, i.e., the material is streaming at a speed very close to the speed of light. Because of their similarity to their supermassive cousins, quasars, where these jets are believed to be highly relativistic, Galactic black hole candidates which display relativistic outflows are termed ``microquasars''. Those have recently attracted substantial interest by the scientific community because of the recent detection by the HESS collaboration of very-high-energy gamma-ray emission from the microquasar LS 5039. A plausible hypothesis is that particles accelerated in the microquasar jets are responsible for the high-energy emission. This has also sparked renewed interest in recent suggestions that also the X-ray emission of microquasars may originate in the jets rather than an optically thin halo close to the black hole. In the chapter ``High-Energy Emission from Jets of Microquasars'', we discuss our recent work on the spectral formation and time variability of high-energy (X-ray and gamma-ray) emission from microquasars.


Fig. 1.1: Artist's rendition of the famous black-hole candidate Cygnus X-1 (Credit: NASA/GSFC)


Fig. 1.2: RXTE Light curves on different time scales of the Galactic black-hole candidate GRS 1758+258 (from Lin et al. 2000a: ApJ 532, 548)


Fig. 1.3: Fourier power spectrum of the X-ray variability of the Galactic black-hole candidate GRS 1758+258 (from Lin et al. 2000a)


Fig. 1.4: Fourier power and phase lag spectrum of the X-ray variability of the Galactic black-hole candidate GRS 1915+105 (from Lin et al. 2000c)


Fig. 1.5: Artist's rendition of a black-hole binary system with a relativistic jet, commonly termed a ``microquasar'' (credit: NASA/GSFC).

Modeling the Rapid Aperiodic Variability
of X-ray Binaries

As briefly discussed in the introduction, the X-ray emission from Galaxtic X-ray binaries exhibits rapid, aperiodic and sometimes quasi-periodic variability. One of the most intriguing aspects of this variability is that it is dependent on the photon energy at which X-ray light curves are extracted, the variability patterns between different photon energy channels are highly coherent, and exhibit time lags among each other which are a function of the Fourier frequency at which the time lags are extracted by means of a complex cross correlation analysis. A very peculiar example of the phase lags (which directly correspond to time lags) as a function of Fourier frequency for the case of the Galactic black-hole candidate and microquasar GRS 1915+105 is shown in the lower panel of Fig. 1.4. In many cases, the time lag is decreasing with increasing Fourier frequency, with the time lag being approximately proportional to the Fourier period over a limited range of frequencies. Below a critical frequency of typically ~ 0.1 - 1 Hz, the time lag spectra flatten and become approximately frequency-independent.

This Fourier-frequency dependent time lag behavior has been interpreted as being a result of Compton scattering in an extended, hot Comptonizing medium, for example an extended corona of tenuous, hot plasma surrounding an optically thick accretion disk. It is generally believed that the hard X-ray emission from X-ray binaries is produced by Compton scattering of soft X-ray or ultraviolett radiation in a hot corona. Time lags between hard and soft photons would naturally arise in such a scenario because hard X-ray photons require a larger number of Compton scattering events to achieve their higher energy, so they have a longer path length within the corona and escape at a later time than soft photons. In Böttcher & Liang (1998), we had done a systematic study of the light curves and the resulting Fourier power and time lag spectra in different geometrical model setups, corresponding to two fundamentally different accretion-flow structures: A cool, optically thick accretion disk sandwiched by a hot, optically thin corona; and an outer, optically thick disk with a transition to an inner, optically thin flow, e.g., an advection-dominated (ADAF) or convection-dominated (CDAF) flow or an advection-dominated inflow-outflow system (ADIOS).

Both types of geometries are able to reproduce the general shape of the observed time lag spectra, but they make very different predictions about the energy dependence of the high-frequency Fourier power spectra of the rapid aperiodic variability. These results are summarized in Fig. 2.2. In particular, while we would expect that the power spectral density (PSD) in the case of central soft photon injection becomes softer with increasing photon energy, we predicted that soft photon flares external to the Comptonizing corona would not result in a strong energy dependence of the PSD.

In both scenarios analyzed above, the maximum time lags between different energy channels as well as the frequency at which the flatting of the phase lag spectrum (and the power spectrum) occurs, are determined by the light crossing time through the corona. Given the typical values of those quantities, this would imply coronal sizes of thousands to ten thousands of Schwarzschild radii. However, it is generally agreed that most of the energy dissipation related to accretion onto neutron stars or black holes occurs within a few tens of Schwarzschild radii. Thus, it is hard to explain how the coronal plasma can maintained the necessary, very high temperature for efficient Compton upscattering of soft X-rays to hard X-ray energies, out to such large radii.

Several ideas have been advanced to circumvent this problem. As one possible alternative, we have suggested a model in which the time scale determining the maximum time lags and breaks in the Fourier and phase lag spectra is not the light travel time through the corona, but the (much longer) dynamical time scale related to the radial inward-drift of density inhomogeneities ("blobs") through the corona (Böttcher & Liang 1999). The basic geometry is shown in Fig. 2.3. As the blobs of cool, dense material are drifting inward, they are slowly heating up, and are injecting soft photons into increasingly hot and dense regions of the coronal flow. This causes the hard X-ray spectrum to harden over the inward-drift time scale. Fig. 2.4 shows a typical result of a simulation of this scenario.

All the time lag models described above had assumed that the coronal temperature structure is static and not influenced by the flaring of the soft photon source. However, in particular in the case of a slab-coronal geometry - with an extended corona surrounding a cool, optically thick accretion disk - this may not be a very good approximation of the reality because the coronal temperature is determined by the balance between heating and radiative cooling, the latter of which is generally believed to be dominated by Compton cooling. Thus, if the soft photon input for Compton scattering increases, one would expect that the electron temperature decreases significantly. I have thus re-investigated those variability and phase lag models, self-consistently including the time-dependent electron heating and cooling as a consequence of the soft photon flares (see Böttcher 2001).

Figs. 9 - 11 show some representative results of those simulations. The results are found to depend strongly on the relative duration of the accretion disk flare compared to the light-travel time through the corona. In the example shown in Fig. 2.5, those two time scales are approximately equal. The figure illustrates that the accretion disk flare results in strong cooling of the corona and consequently in a dip in the hard X-ray emission rather than a flare. The result is a pivoting of the X-ray spectrum around ~ 10 - 20 keV.

However, although this seems to be in strong contrast to the observed coherent flaring at soft and hard X-rays, one has to keep in mind that in reality, there will be a rapid succession of flares occurring at different locations throughout the disk. This will create the impression of a hard X-ray flare almost simultaneous with the soft X-ray flare since at the onset of one individual flare (and the subsequent hard X-ray dip), the coronal temperature might still be in the process of recovering from the previous flare, and thus the hard X-ray emission is still increasing until that time. Keeping this in mind, one can calculate the resulting phase and time lags, and some typical results are illustrated in Fig. 2.7.

In this new scenario, the phase and time lags between hard and soft X-rays are no longer determined by the Compton-scattering time delay as in the case of a static corona. Instead, it is now the coronal heating and cooling time scales which are governing the maximum time lags. This removes the necessity of an extremely large coronal size scale which was found in the static-corona case. Instead, one can now deduce an estimate of the coronal density and proton temperature if Coulomb scattering with thermal protons is the dominant electron heating mechanism. Interestingly, this model predicts a logarighmic dependence of the maximum time lag on photon energy (see Fig. 2.7), which has indeed been observed in several Galactic X-ray binaries in which phase and time lags could be measured. This had previously been interpreted as strong evidence for Compton scattering being the dominant mechanism responsible for the hard X-ray lags. It is very surprising and exciting that the time-dependent solution of the coronal energy balance produces the same type of energy dependence of the phase and time lags.


Fig. 2.1: Monte-Carlo simulated light curves resulting from a short flash of soft radiation at the center of a spherical cloud of static, hot plasma (from Böttcher & Liang 1998). The light curves have been sampled in 5 different photon energy channels. The cloud has a Thomson depth of 3, a radius of 3 × 1010 cm, and a constant and uniform electron temperature of kTe = 100 keV.


Fig. 2.2: Initial temporal indices of monte-Carlo simulated light curves resulting from a short flash of soft radiation at the center (dashed curves) and at the outer boundary (solid curves) of a spherical cloud of static, hot plasma (from Böttcher & Liang 1998). This index µ is related to the power-law slope of the Fourier power spectrum via PSD ~ f-2µ, which can then be compared to the observed power spectra.


Fig. 2.3: Sketch of the model of inward-drifting blobs through an inner, hot corona (see Böttcher & Liang 1999 and Böttcher 2001).


Fig. 2.4: Time lag spectrum predicted by the model of inward-drifting blobs though an ADAF-type corona (from Böttcher & Liang 1999). In this example, the corona extens from rin = 107 cm to rout = 109 cm, has a central temperature of kTe, c = 300 keV, and a radial Thomson depth of 3. The dense blobs are drifting inward with a radial drift velocity of vrad = 5×10-3 c.


Fig. 2.5: Simulated light curves (a), average coronal temperature (b), and snap-shot photon spectra (c) from a simulation of an accretion disk flare in slab-coronal geometry (from Böttcher 2001). The has a thickness of 108 cm, a proton temperature of kTp = 100 MeV, and a vertical Thomson depth of 1. Electrons in the corona are heated primarily through Coulomb interactions with thermal protons. Dashed vertical lines indicate the duration of the accretion disk flare, which is 3 msec in this example.


Fig. 2.6: Phase and time lag spectra resulting from simulated accretion disk flares in slab-coronal geometry (from Böttcher 2001). The parameters for all simulations are the same as in Fig. 2.5, except for the duration of the accretion disk flare.


Fig. 2.7: Energy dependence of the time lags predicted from accretion disk flares in slab-coronal geometry (from Böttcher 2001).

2-D simulations of spectral variability
in X-ray Binaries

The various numerical studies of the rapid X-ray variability in X-ray binaries described above had been done using a time-dependent radiation transfer (Monte-Carlo) and electron dynamics (Fokker-Planck) code in one spatial dimension. For realistic accretion-disk structures, this is obviously an over-simplification, which may have a significant impact on the final results. We have therefore developed a time-dependent 2-D Monte-Carlo / Fokker-Planck radiation transfer and electron dynamics code (Böttcher, Jackson & Liang 2002). Using this new code, we have done a series of test simulations to re-investigate some fundamental flaring scenarios suggested for the rapid variability in X-ray binaries. In contrast to all previous simulations of this kind, we chose a realistic, generic 2-D model setup of an accretion-disk corona system with an optically thick, cool accretion disk sandwiched by a hot, optically thin corona, with a specific choice of parameters motivated by typical observational signatures of the Galactic microquasar GRS 1915+105 in its high luminosity state. We simulated the time-dependent radiation-transfer and electron dynamics effects resulting from (a) a localized flare within the underlying cool accretion disk, and (b) a flare originating in the corona.

Fig. 3.1 illustrates the electron-temperature structure in the corona and its evolution in response to a generic accretion-disk flare near the inner edge of the accretion disk. The time-dependent cooling effect of the localized, enhanced soft photon input from the disk can clearly be traced. Time-resolved photon spectra resulting from this simulation are shown in Fig. 3.2. In this 2-D model setup, the photon spectra are slightly viewing angle dependent. The spectra displayed in Fig. 3.2 refer to a near face-on orientation of the accretion-disk corona system with respect to the observer. A remarkable result of these simulations is that the pronounced spectral pivoting effect seen in the corresponding 1-D simulations, is much less pronounced in this case.

We have also investigated the Fourier transforms and phase and time lags resulting from such accretion-disk flare simulations. We find that the power spectra are generally becoming slightly harder with increasing photon energy, at least up to ~ 15 keV. Phase and time lags in this photon energy range are predominantly soft lags, i.e. the signals at higher energies are preceding those at lower energies.

Fig. 3.3 illustrates the coronal electron-temperature structure and its evolution in response to a flare localized in the corona. Obviously, electrons around the flaring region are strongly heated by the enhanced energy input, but electrons in other regions of the corona are actually cooled in response to the flare. This is because the enhanced photon input resulting from the flare is still dominated by photons with energies below the thermal energies of electrons in the non-flaring parts of the corona. The time-dependent photon spectra for near-face-on viewing angles are illustrated in Fig. 3.4. The localized heating of the corona results in a photon flare at hard X-rays, while the soft X-ray output remains virtually unaffected.

Investigating the Fourier transformed light curves in the coronal-flare case, we find no significant trend of the power spectra with photon energy. Phase and time lags are generally dominated by a trend that the variability at ~ 10 keV is leading variations at other photon energies.


Fig. 3.1: Coronal temperature evolution in response to an accretion-disk flare near the innermost edge of the accretion disk in a generic high-state accretion-disk corona model setup. (From Böttcher, Jackson & Liang 2002).


Fig. 3.2: Time-resolved photon spectra from the accretion-disk flare simulation illustrated in Fig. 3.1. (From Böttcher, Jackson & Liang 2002)


Fig. 3.3: Coronal temperature evolution in response to a flare localized in the inner regions of the corona in a generic high-state accretion-disk corona model setup. (From Böttcher, Jackson & Liang 2002)


Fig. 3.4: Time-resolved photon spectra from the coronal flare simulation illustrated in Fig. 3.3. (From Böttcher, Jackson & Liang 2002)

Spectral Modeling of
Accreting Neutron Stars

Many Galactic X-ray binaries, such as atoll sources or some X-ray transients, are believed to contain weakly or moderately magnetized neutron stars (with surface magnetic fields of B0 ~ 109 - 1010 Gauss) which accrete material from a companion star. This accretion is most likely occurring via an optically thick, Keplerian accretion disk, which becomes disrupted very close to the neutron star surface, where the magnetic field becomes so strong that the accreted matter is forced to move along magnetic field lines. In such a configuration, most of the energy dissipation might happen in a narrow boundary layer between the Keplerian accretion disk and the magnetospheric flow (see Fig. 4.1). Observations of this type of objects using the Compton Gamma-Ray Observatory (CGRO) have revealed that many of them exhibit soft (photon index > 2) hard X-ray power-law tails. It had been suggested that those hard X-ray power-law spectra could be produced via Compton scattering in the hot electron plasma energized in this boundary layer.

We have modeled the expected radiation signatures of this scenario by simulating the electron energization and radiation transport in such a boundary layer, using our coupled Monte-Carlo radiation transport and Fokker-Planck electron dynamics code. We assume that the neutron star surface is emitting thermal blackbody radiation (with temperature TBB ~ 1 keV), some of which is Compton upscattered in the hot boundary layer. The electrons in the boundary layer are energized via Coulomb interactions with hot ions and via resonant wave-particle interaction with hydromagnetic turbulence. They are cooling via Compton scattering, bremsstrahlung, and synchrotron losses. The entire model system can be conveniently parametrized by the neutron star magnetic moment µ (which is proportional to the surface magnetic field), the luminosity parameter l*, which is the total luminosity normalized to the Eddington luminosity, and the level of hydromagnetic turbulence in the boundary layer. The distance of the boundary layer from the neutron star surface is approximately the Alfvén radius, which then also determines the magnetic field strength in the boundary layer.

Some typical results of our simulations are shown in Fig. 4.2. Due to the non-thermal nature of the electron acceleration in the presence of significant hydromagnetic turbulence, the electron distributions develop pronounced nonthermal high-energy tails. The photon spectra can generally be well fitted with a thermal blackbody + a hard power-law tail. Some of the main results of a detailed parameter study which we have performed in Böttcher & Liang (2001a) are summarized in Figs. 18 and 19, where the dependence of the spectral modeling parameters on the turbulence level and on the accretion rate are plotted.

In general, we find that the hard X-ray tailes produced in the boundary layer become harder as the accretion rate decreases below a few per cent of its Eddington value. In the case of a low surface magnetic field of the neutron star, we find that the hard X-ray tails are showing a softening trend as the level of hydromagnetic turbulence is increasing, why we find the opposite trend in the case of a high surface magnetic field.

Applying our model to the observed spectral features of neutron star X-ray binaries, we find that it is very well suited to explain the observed anti-correlation of the hard X-ray spectral hardness with luminosity. We predict that hard X-ray power-law tails, which have so far only been detected in the low/hard state of neutron star X-ray binaries, should also exist in the high/soft state, where they should exhibit high-energy cutoffs around 100 - 200 keV.

A similar model of accretion-powered emission has recently also been proposed for anomalous X-ray pulsars. In order to exlain their hard X-ray spectral slopes of ~ 2 - 3 (energy index), our model requires surface magnetic fields of ~ 1012 Gauss or more and rather low turbulence levels. In that case, we predict that those hard X-ray tails should extend out to cutoff energies of Ec ~ 100 - 500 keV.


Fig. 4.1: Model geometry for our simulations of the high-energy emission of accreting magnetized neutron stars (see Böttcher & Liang 2001a).


Fig. 4.2: Simulated equilibrium electron spectra (left) in the boundary layer and observable radiation spectra (right) from the model of an accreting magnetized neutron stars sketched in Fig. 4.1 (from Böttcher & Liang 2001a). Here the neutron star has a surface magnetic field of 109 Gauss. We have varied the turbulence level (increasing from top to bottom), and the black, red, green, and blue curves correspond to values of the normalized total luminosity l* of 1, 0.25, 0.05, and 0.01, respectively.


Fig. 4.3: Spectral fit parameters of the simulated radiation spectra from an accreting magnetized neutron star as a function of turbulence level. Ec is the energy of the exponential cutoff of the hard X-ray power-law, and alpha is the energy spectral index of the power-law. Solid curves correspond to a surface magnetic field of B0 = 109 Gauss, while dashed curves correspond to B0 = 1012 Gauss. (From Böttcher & Liang 2001b)


Fig. 4.4: Spectral fit parameters of the simulated radiation spectra from an accreting magnetized neutron star as a function of accretion rate (parametrized by the normalized total luminosity). Symbols are the same as used in Fig. 4.3. (From Böttcher & Liang 2001b)

Observations of Galactic Black-Hole Candidates

Our group has done several extensive X-ray and multiwavelength campaigns to observe Galactic X-ray binaries. Recently, we have done some major data analysis projects to investigate the rapid aperiodic variability of several X-ray binaries. Here, I will focus on two projects investigating the energy dependence of the rapid aperiodic variability of four persistent Galactic black-hole candidates, and the complex phase lag behavior of the 0.5 - 10 Hz QPO in the Galactic microquasar GRS 1915+105.

In Lin et al. (2000b), we have re-analyzed archival RXTE PCA data of a large number of observations of the four persistent hard X-ray sources Cyg X-1, GX 339-4, GRS 1758-258, and 1E 1740.7-2942 in their low/hard spectral state. In this study, we have put special emphasis on the energy dependence of the broadband variability seen in those sources.

This was in part motivated by the results of our theoretical modeling of the rapid aperiodic variability of Galactic X-ray binaries, which had made specific predictions about the energy dependence of the high-frequency slope of the PDS in different energy channels. In particular, we had found that in models where hard X-ray flares are due to Comptonization of soft X-ray flares in a hot corona, the power spectra should generally become softer with increasing photon energy, while the model of inward-drifting density perturbations predicted a slight hardening of the power spectra with increasing photon energy.

The details of the data selection and analysis are described in Lin et al. (2000b). In three out of our 4 sources, we did not find any significant hardening or softening of the PDS with photon energy. However, for Cyg X-1, we did find that the power spectra become harder with increasing photon energy. An example for one specific observation is shown in Fig. 5.1. Another surprising result of our study was that the different sources show significantly different trends of the broadband rms amplitude as a function of photon energy. These are illustrated in Fig. 5.2. While in 1E 1740.7-2942 the broadband rms variability amplitude is always increasing with increasing photon energy, GX 339-4 shows the opposite trend. Even more peculiar, in GRS 1758-258 the highest level of variability is observed in the medium-energy band (5.1 - 10.2 keV), while Cyg X-1 shows sometimes an increasing, on other occasions a decreasing broadband rms variability with increasing photon energy, which apparently depends on the overall level of variability. As shown in Fig. 5.3, all sources seem to exhibit a decreasing overall rms variability with increasing soft X-ray intensity.

At present, there is no model which can self-consistently account for all those trends at the same time. This seems to indicate that there may be fundamentally different variability mechanisms at work in different sources and even in different states of the same source. This study has shown that the energy dependence of rapid variability patterns of Galactic X-ray binaries still poses many unsolved questions. We will continue our observational and theoretical efforts to interpret the information contained in those energy-dependent variability patterns.

Apart from broadband noise, many X-ray binaries often also show peaked noise, generally referred to as quasi-periodic oscillations (QPOs). Although those QPOs are more common in neutron star binaries, they are also seen in several black-hole candidates. The Galactic black-hole candidate and microquasar GRSݻ+105 shows some very peculiar phenomena associated with its rapid variability. In its soft state, it shows a QPO at a variable frequency of ~ 0.5 - 10 Hz. The frequency of this QPO had been found to be correlated with the spectral parameters of the source: A softening of the photon spectrum is accompanied by a shift of the QPO centroid frequency to higher values and a decreasing amplitude of the QPO.

In Lin et al. (2000c), we have analyzed archival RXTE PCA data of GRS 1915+105 and evaluated the power spectra and complex cross correlation functions, calculating the phase lag spectra, in different observing periods, characterized by different photon spectra and different QPO frequencies. In addition to confirming the previously known trend between the spectral parameters and the QPO centroid frequency and amplitude, we found a very peculiar trend in the phase lag spectra: While in observation epochs with a rather hard photon spectrum and low QPO frequency (less than ~ 2  Hz), the source showed an overall positive hard lag between the hard (13.1 - 41.0 keV) and soft (3.3 - 5.8 keV) PCA X-ray bands, and no peculiar features around the frequency of the QPO (see Fig. 5.4). At intermediate values of the QPO frequency (~ 2 - 4.5 Hz), the phase lags at low frequencies are generally negative, and there is a pronounced dip towards more negative phase lags around the QPO frequency; the phase lags then become positive, thus alternating between the QPO fundamental frequency and its first harmonic (see Fig. 1.4). Finally, at high values of the QPO frequency (greater than ~ 4.5 Hz), the phase lags remain negative beyond the QPO frequency, and we observe an abrupt change of the phase lag to more negative values around the QPO frequency (Fig. 5.2).

There have been several attempts to explain the negative phase lags observed in this source by Compton downscattering scenarios, but so far no convincing explanation has been found for the alternating nature of the phase lags at intermediate values of the QPO frequencies, which has also been confirmed by at least one other group.


Fig. 5.1: Power density spectra (PDS) in 3 different RXTE PCA energy channels (upper panel) and PDS hardness ratios (i.e. ratios of PDS values between different energy channels; lower panels) for Cyg~X-1 (from Lin et al. 2000b). The ratios in the lower panels indicate a slight, but significant hardening of the power spectra with increasing photon energy.


Fig. 5.2: Broadband rms variability amplitude as a function of photon energy for the four persistent Galactic black-hole candidates, for all available data sets in Lin et al. (2000b). The values of the neutron hydrogen column density NH are in units of 1022 cm-2.


Fig. 5.3: Broadband rms variability amplitude in different energy bands as a function of soft X-ray (RXTE ASM) count rate. Circles correspond to the low-energy band (< 5.1 keV), crosses indicate the medium-energy band (5.1 - 10.2 keV); squares symbolize the high-energy band (10.2 - 40.2 keV). From Lin et al. (2000b).


Fig. 5.4: Fourier power and phase lag spectrum of the X-ray variability of the Galactic black-hole candidate GRS 1915+105 for an observation in which the variable-frequency QPO was found at a low value (1.14 Hz). From Lin et al. (2000c).


Fig. 5.5: Fourier power and phase lag spectrum of GRS 1915+105 for an observation in which the variable-frequency QPO was found at a high value (6.47 Hz). From Lin et al. (2000c).

High Energy Emission from Jets of Microquasars

The mildly relativistic (Lorentz factors of ~ 2) jets of microquasars (see Fig. 1.5 for an artist's conception) might be plausible sites for the emission of high-energy (X-ray and gamma-ray) emission through various processes, such as synchrotron and synchrotron-self-Compton (SSC) emission as well as Compton upscattering of external photons from the accretion disk around the black hole and from the stellar companion. This has previously been suggested as a promising alternative scenario for the origin of the hard X-ray emission from microquasars, in contrast to the prevailing picture of this emission originating in a hot, optically thin corona near the black hole. The broadband spectral features expected in this model have been shown to be well consistent with observations in several cases. Therefore, additional information, such as spectral variability, might be necessary to distinguish between the two competing models. As described in the previous sections, both observational and theoretical studies have been done in great detail concerning the spectral variability resulting from scenarios invoking multiple Compton scattering in an optically thin corona.

Starting with our work of Gupta et al. (2006), we are investigating the X-ray spectral variability features expected in a generic microquasar model, in which the X-ray and soft gamma-ray emission is dominated by Compton scattered external radiation from a massive companion in a high-mass X-ray binary. Based on a generic model setup motivated by the prototypical microquasar GRS 1915+105, we carried out an extensive parameter study and identified characteristic spectral variability patterns that may be used as a diagnostic to identify the dominant radiation mechanism at X-ray energies, and constrain the characteristics of the particle acceleration scenario. In particular, we investigated the signatures of different scenarios in hardness-intensity diagrams (HIDs), and found that clockwise spectral hysteresis in the HIDs indicates synchrotron emission as the dominant radiation mechanism, while counterclockwise spectral hysteresis hints towards inverse-Compton emission.

In view of the recent detection of very high energy (VHE) gamma-ray emission from the Galactic microquasar LS 5039 by the HESS collaboration, it is of the utmost importance to extend models as discussed above, to cases in which electrons are accelerated to sufficiently high energies to produce TeV photons. In this regime, the effect of the Klein-Nishina cutoff of the Compton scattering cross section will become non-negligible. Working with a realistic steady-state electron distribution (i.e., in a model neglecting the details of rapid variability), we have considered the spectral features and their orbital modulation of synchrotron, synchrotron-self-Compton radiation and Compton upscattering of external radiation from the accretion disk and the stellar companion (Dermer & Böttcher 2005), and gamma-gamma absorption in the dense photon field of the stellar companion (Böttcher & Dermer 2005).

If the VHE emission from LS 5039 is produced by leptonic processes in the microquasar jet and the emitting volume is located at a distance from the black hole which is comparable to or smaller than the binary separation (~ 2.5x1012 cm), then the VHE emission should be strongly modulated with the orbital period of the binary system. This would be a consequence of both the phase dependence of the gamma-gamma absorption (see Fig. 6.3), and of the Compton-scattered stellar radiation field. However, we also found that the shape of the (non-simultaneous) X-ray through VHE gamma-ray spectrum of LS 5039 precludes a fit of the VHE gamma-rays as Compton-scattered stellar radiation (see Fig. 6.4). Possible solutions to this problem include strong variability of the X-ray and gamma-ray flux and spectral shape, or a combined leptonic + hadronic model for the origin of the high-energy emission of LS 5039 (Dermer & Böttcher 2006).


Fig. 6.1: The baseline microquasar model of Gupta et al. (2006): (a) Time-dependent electron spectra, (b) time-dependent photon spectra, (c) light curves at various photon energies, and (d) the individual radiation components adding up to the total spectra shown in panel (b). For details see Gupta et al. (2006).


Fig. 6.2: (a) Time-integrated (fluence) photon spectra, (b) 3.5 keV (indicated by the vertical line in panel a) X-ray light curves, and (c, d) soft and hard-X-ray hardness-intensity diagram tracks for time-dependent microquasar jet emission, for various values of the companion star luminosity as indicated in the legend. For details see Gupta et al. (2006).


Fig. 6.3: Gamma-gamma absorption opacity for VHE gamma-rays due to the photon field of the stellar companion in LS 5039, as a function of distance z0 of the emission region from the black hole. The inset illustrates the periodic, orbital modulation of the gamma-gamma opacity, showing a hypothetical intrinsic power-law spectrum affected by gamma-gamma absorption in the stellar photon field for 11 different values of the orbital phase angle. The lowest (most heavily absorbed) curve corresponds to the phase where the star is located closest to our line of sight towards the emission region, the lowest (least absorbed) curve corresponds to the opposite point on the binary orbit. For details see Böttcher & Dermer (2006).


Fig. 6.4: Leptonic jet model fit to (non-simultaneous) LS 5039 data. The model includes the stellar emission, synchrotron emission, Compton scattering of stellar radiation (CSSR), and synchrotron self-Compton (SSC) emission. The figure illustrates the difficulty of leptonic jet models to provide a joint fit of the X-ray, EGRET, and HESS data. For details see Dermer & Böttcher (2006).