Table 3 summarizes the correlations found here plus 2 relevant correlations found by Muno et al. (1999, 2000). In the following we will discuss implications of these correlations.

The origin of the hard power law component in AGN and X-ray binaries is still under discussion. Three main models exist, where the hard photons originate by inverse Compton scattering of soft disk photons on hot electrons. The main difference between these models is the distribution of the electrons. They can be thermal (Maxwellian), non-thermal (power law like) or free falling from the last stable orbit onto the event horizon of the black hole. The high energy spectrum presents an important test for the distinction between these models. Therefore, the behavior of the power law component in GRS 1915+105 is crucial for the understanding of the electron distribution and for the geometry of the system.

It is still unclear whether or not the hard spectrum of GRS 1915+105 in the $\chi$ -state extends with or without cutoff up to MeV energies. Due to the rapid variability of the source and the long required exposure times it is nearly impossible to get sufficiently accurate $\gamma$ -spectra with the present high energy satellites. For example, the OSSE spectrum from 14th-20th of May 1997 reveals a power law tail up to 1 MeV without a cutoff (Iyudin 2000; Zdziarski et al. 2001). But as several contemporaneous RXTE observations show (which cover $\la$ 3% of the OSSE exposure), during the observation GRS 1915+105 went through several $\chi$ / $\alpha$ state transitions and the PCA photon count rate from 2-40 keV varied between 5 and 25 kcts/s. Thus, the OSSE spectrum is the sum of the spectra of the $\chi$ and $\alpha$ (and possible other) states, with an unkown fraction coming from the $\chi$ -state. It is therefore premature to unequivocally relate the hard MeV tail to the $\chi$ -state.

4.1.1 Bulk motion comptonization

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{MS2456f10.ps} \end{figure}$

Figure 10: Bulk motion geometry. Electrons become spherical free-falling between the last stable orbit and the event horizon due to shocking. The photons are comptonized on these accelerated electrons.

One model for the comptonization is the bulk motion comptonization (Blandford & Payne 1981; Chakrabarti & Titarchuk 1995) (Fig. 10). The accretion stream passes the transition radius, $r_{\rm ts}$ , at the last stable orbit around the black hole and gets shocked. The matter falls spherical onto the event horizon. In front of the shock, the stream is similar to an optically thick, geometrically thin accretion disk (as required by the strong observed blackbody component).

The free falling electrons are accelerated up to the speed of light and inverse Compton scattering of soft photons on the electrons provides the observed power law in the hard spectrum. The model predicts a cutoff depending on the mass accretion rate (Ebisawa et al. 1996) due to inverse Compton scattering and Compton recoil. As stated above, the existence/absence of a cutoff during the $\chi$ -states is still not secured, wherefore not statement about the model can be made from that issue.

Two major problems exist for the description of $\chi$ -state data by the BMC model. The RXTE spectra of GRS 1915+105 partly show a strong reflection component. This is not compatible with the geometry of a thin disk outside a central, spherical accretion stream. The accretion stream is accelerated away from the inner disk edge onto the event horizon of the black hole. Therefore only a small part of the soft photons are comptonized back into the disk plane at $r>r_{\rm ts}$ . In conflict to the observations, no strong reflection component can emerge. A possible explanation for the observed reflection can then be a partly covering of the disk by an absorbing medium with $\tau_{\rm T}\sim3$ (Zdziarski 2000). Recent Chandra X-ray spectra indeed show a high X-ray column density and abundance excesses for Si and Fe, which may be related to material that is associated with the immediate environment of the source (Lee et al. 2002).

The other problem for the BMC model is the time lag of hard and soft X-ray photons. Muno et al. (2001) found a phase lag in the 5 Hz QPO (which are connected to the hard X-ray photons) of 0.5. This corresponds to a delay of 0.1 s of the hard photons to the soft photons. The expected delay for scattering on a convergent electron stream inside $r_{\rm ts}$ is $\sim$ 0.2 ms, much smaller than observed. The phase lag is not constant in time and frequency and seems to vary with the radio flux.

It is obvious that the BMC model not can explain the hard power law component in the $\chi$ -states of GRS 1915+105. There are indications that the BMC model fits other variability states. Shrader & Titarchuk (1998) found good spectral agreement of the BMC model and RXTE observations in the $\rho$ -state. Note, however, that they completely neglected the time delay of hard and soft photons and the strong variability of the $\rho$ -state for their X-ray spectral modelling.

4.1.2 Thermal corona

Another possible model for the origin of the hard X-ray component is the disk corona geometry (Fig. 11) (e.g. Haardt & Maraschi 1993; Svensson & Zdziarski 1994). Soft disk photons are inverse Compton scattered on hot (>20 keV) electrons located above the disk.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{MS2456f11.ps} \end{figure}$

Figure 11: Disk corona geometry. The disk photons are comptonized in an electron distribution located above the accretion disk. (Note, the shape and size of the electron distribution in this plot has no real physical or observational meaning.) Part of the photons are scattered back into the disk plane and are reflected or reprocessed. The photons reaching the detector are compound of the soft disk photons, the comptonized and the reflected photons.

Simultaneous CGRO/OSSE and X-ray observations of X-ray binaries with black holes showed that the high energy continuum in the low/hard state originates most likely due to thermal comptonization. The predicted cutoff in the hard X-ray spectrum is seen in Cyg X-1 (Gierlinski et al. 1997), in the LMXB GX 339-4 (Zdziarski et al. 1998) and some other X-ray transients (Grove et al. 1998).

Also the high/soft state in X-ray binaries can be explained by thermal comptonization but requires high electron temperatures in some systems to explain the observed unbroken power law up to MeV. In addition $\tau_{\rm T}\ll 1$ is required in order to keep the spectrum soft (Zdziarski 2000).

The power law slope is a measure of the Compton amplification, $A(L_{\rm soft}+L_{\rm diss})/L_{\rm soft}$ . $L_{\rm diss}$ is the dissipated energy in the corona and $L_{\rm soft}$ the energy of the incoming photons. Table 4 shows how A depends on $\Gamma$ with

Table 4: Fraction of the dissipated energy in the corona, $L_{\rm diss}$ , on the energy of the incoming photons, Compton parameter, $y=4\tau _{\rm T}^2kT_{\rm e}/(m_{\rm e}c^2)$ ( $\tau _{\rm T}$ is the Thomson depth), and Compton amplification, A, for three different power law slopes.
$\Gamma$ $L_{\rm diss}$ y A

2.4 84% 1.33 1.84

3.0 22% 3.65 1.22

3.5 9% 7.30 1.09

**Table 4:** Fraction of the dissipated energy in the corona, $L_{\rm diss}$ , on the energy of the incoming photons, Compton parameter, $y=4\tau _{\rm T}^2kT_{\rm e}/(m_{\rm e}c^2)$ ( $\tau _{\rm T}$ is the Thomson depth), and Compton amplification, A, for three different power law slopes.
$\Gamma$	$L_{\rm diss}$	y	A
2.4	84%	1.33	1.84
3.0	22%	3.65	1.22
3.5	9%	7.30	1.09

The minimum energy which a photon receives when passing a thermal electron distribution depends on the electron temperature $kT_{\rm e}$

$\begin{displaymath}\frac{\Delta \epsilon}{\epsilon}= \frac{4kT_{\rm e}}{m_{\rm e}c^2}\cdot \end{displaymath}$

(5)

4.1.3 Hybrid corona

The radiation processes and geometry can also be described by comptonization of soft disk photons on a hybrid (thermal and non-thermal) electron distribution above an optical thick accretion disk (as in Fig. 11) (Coppi 1992). Part of the electrons in the thermal corona are accelerated, possibly in reconnection events. The disk photons are comptonized on these electrons forming the observed power law component in the hard X-ray spectrum. The energy of the non-thermal electrons is partially transfered to the thermal electrons due to Coulomb scattering. This leads to heating of the thermal electrons above the Compton temperature. Then the thermal electrons play an important part in the up-scattering of the soft disk photons, too.

The compactness (ratio of luminosity and size) is an important parameter of the coronal plasma (Coppi 1999). A large compactness leads to electron positron pair creation due to photon photon collisions resulting in a pair annihilation line at 511 keV in the spectra. When the compactness is low, the loss of energy of the electrons due to Coulomb scattering dominates the loss due to inverse Compton scattering. The ratio of thermal to non-thermal electrons increases and the plasma becomes thermally dominated. Together with the resulting break in the distribution of the non-thermal electrons this results in a cutoff of the photon spectrum.

The rate at which non-thermal electrons appear in the hybrid electron distribution can be written as a power law (Gierlinski et al. 1999)

$\begin{displaymath}\dot N_{\rm nt} = \frac{{\rm d} N_{\rm nt}(\gamma)}{{\rm d} t}\propto \gamma^{-\Gamma_{\rm in}}. \end{displaymath}$

(6)

In GRS 1915+105, the observed continuous distribution of $\Gamma$ between 2.4 and 3.5 is evidence for a variability in the power law component and thus in the composition and locus of the electron distribution. From the observation of the reflection and the 0.5-10 Hz QPO it is conspicuous that the electron distribution must have a small (relative to the system) spatial size. As a small compactness, e.g. large plasma volume, results in a spectral cutoff, for the $\chi$ -states of GRS 1915+105 a hybrid electron distribution not can be ruled out. It is difficult to distinguish spectroscopically between a hybrid and a thermal plasma if the hybrid plasma is thermally dominated. The only possibility is the search for the predicted photon excess at high energies and for the annihilation line (Coppi 1999). For a better understanding, enhanced high energy detectors, such as on INTEGRAL, are required. The analysis of such spectra also needs further developed physical models, instead of a simple power law.

The investigation of the RXTE data of GRS 1915+105 with the DISKBB+REFSCH model does not allow a definite conclusion about the origin of the hard spectral component. Only the BMC model is ruled out for the $\chi$ -states. Though a clear distinction between a thermal and a hybrid not can be proposed, it seems clear that the thermal electrons dominate.

It has been shown above (Fig. 5) that two different states of comptonization with two different pivoting energies are observed. Very recently (Zdziarski et al. 2002) pivoting was found also in Cyg X-1. A varying amount of soft seed photons undergoing the comptonization process probably accounts for the pivoting of the spectrum. One possible explanation is a constant disk blackbody and an expanding/contracting hot coronal plasma. A change in the size of the corona leads to a change in the fraction of intercepted soft photons. Assuming constant optical plasma depth, $\tau _{\rm T}$ , if the soft luminosity is high, the electrons in the corona are cooled efficiently and the spectrum of the comptonized photons is soft. On the other hand, if the soft luminosity decreases, the temperature of the corona increases and the spectrum hardens). The ocurrance of two differing pivoting branches suggests the existence of two states with different $\tau _{\rm T}$ and/or different electron composition (thermal/non-thermal).

4.2 Reflection

The reflection of X-rays on an accretion disk manifests itself in two specific spectral features: (i) the characteristic emission line spectrum (mainly the K $\alpha$ lines of the most common metals) with the 6.4 keV iron emission lines as the strongest and (ii) a characteristic hump arises above 10 keV because of the energy dependence of the cross section of absorption and Compton scattering.

Observations with ASCA in different variability states indicate a variable iron absorption or emission in GRS 1915+105 (Ebisawa et al. 1997). The iron emission at 6.4 keV dominates the spectra from 25.10.1996 and 25.04.1997 whereas a distinct absorption at 7 keV and no emission was seen on 27.09.1994 and 26.04.1995. During the 25.04.1997 observation GRS 1915+105 switched between $\chi$ - and $\alpha$ -states (based on RXTE data). Therefore, it is not clear whether the emission line originates during the $\chi$ - or during the $\alpha$ -interval. No statement can be made about the states during the other ASCA observations due to lack of corresponding RXTE observations.

Recent Chandra data of GRS 1915+105 obtained in the low hard state revealed neutral K absorption edges, ionized resonance absorption from Fe (XXV, XXVI) and possible emission from neutral Fe K $\alpha$ and ionized Fe XXV (Lee et al. 2002), suggesting conditions favorable for reflection.

4.2.1 Reflection in LMXB and AGN

Investigations of Seyfert galaxies and X-ray binaries in the low/hard state show a correlation between the slope of the hard X-ray component and the reflection. Incoming radiation with a steeper slope is more reflected than radiation with a flatter slope.

The reflection is stronger in black hole candidates than in Seyfert galaxies for a given $\Gamma$ (Zdziarski 1999). This can be explained using an optical thick accretion disk. The different masses of the black holes imply different maximum energies of the blackbody photons (Svensson 1996). The hard X-ray photons from the corona can ionize the upper layers of the accretion disk and an ionized layer above neutral matter evolves. If $\Gamma$ is large the heating of the disk is small and the cold layer of the disk lies near the disk surface. With decreasing power law slope the temperature of the upper layer and therefore the ionization increases, the absorption is smaller, more photons are scattered and the characteristic reflection hump is suppressed, sufficient to explain the observed R( $\Gamma$ )-correlation.

The correlation in Seyfert galaxies is generally steeper than that observed in X-ray binaries (Zdziarski 1999). In Seyferts the correlation has been explained with a model consisting of a static, thermal corona above a neutral reflector (Svensson 1996). The existence of the R( $\Gamma$ )-correlation implies a feedback where the existence of the reflecting matter influences the hardness of the X-ray spectrum (Böttcher et al. 1998; Zdziarski et al. 1999). Assuming that the cold matter (the accretion disk) emits soft photons which become seed photons of the comptonization, than with increasing solid angle of the reflector (here the accretion disk) the flux of soft photons increases and the cooling rate of the hot corona increases. For a thermal plasma the resulting power law component steepens with increasing cooling rate.

On the other hand, models which are based on non-thermal electrons should not show a dependence of spectral hardness and cooling rate (Lightman & Zdziarski 1987; Zdziarski et al. 1999). Models in which the seed photons are intrinsically produced in the hot plasma (e.g. synchrotron radiation) not can reproduce the observed correlation. The power law slope is then independent of the reflection.

4.2.2 Reflection in GRS 1915+105

The $\chi$ -states in GRS 1915+105 show a similiar correlation as seen in Seyfert galaxies and X-ray binaries (Zdziarski et al. 1999). The reflection amplitude is strongly effected by the disk model. The higher the disk temperature, the larger the reflection amplitude. The disk temperatures in X-ray binaries are higher than in Seyfert galaxies. In GRS 1915+105 the temperature of the disk is still higher, explaining why a majority of the GRS 1915+105 data lies above the correlation function (showing slightly higher R for a given $\Gamma$ ) in Fig. 7.

The reflection amplitude of R> 1 strongly suggests an anisotrophic inverse Compton process. The dominant fraction of the up-scattered soft disk photons is directed back into the plane of the accretion disk. This produces the observed large reflection amplitude in contrast to an isotrophic scattering where $R\leq 1$ .

Observations of GRS 1915+105 show a strongly varying $\Gamma$ , therefore the corona can hardly be static above the reflector. In GRS 1915+105, $\Gamma$ increases with increasing radio emission. Higher radio emission may imply more outflow away from the disk with $\beta=(v/c)>0$ . Thus, the higher the mass outflow, the lower the electron temperature which is required to produce the observed amount of comptonization. On the other hand, with a dynamical, thermal corona the spectrum hardens with increasing $\beta$ due to relativistic aberration, giving a flatter power law with higher outflow velocity (Malzac et al. 2001).

The observation in GRS 1915+105 predicts an at least partly thermal source of the hard X-ray photons and an important contribution of the cooling due to the soft photons. This allows both a thermal and a hybrid electron distribution.

It is more difficult to interpret the behavior of observations with high $\Gamma$ and small R in Fig. 7. Unlike in a thermal plasma, the Compton scattering in a non-thermal plasma does not depend on the cooling rate of the soft photons, instead it depends on the slope of the electron distribution (Poutanen & Coppi 1998). A change in the properties of the plasma can provide the differing behavior.

For a better determination of the correlation and for conclusions about the distinct system components, more complex ionization models are needed. They partly exist (Done & Nayakshin 2000) but require too much computing power to be useful for the analysis of real spectra at this stage.

4.3 X-ray-radio-correlation

The lack of a correlation of the radio flux with any of the disk parameters is somewhat unexpected since the (short-duration) low/hard states have earlier been related to jet ejections with radio emission by synchrotron radiation of the ejected plasma (Pooley & Fender 1997). Since IR (Eikenberry et al. 2000) and radio observations (Pooley & Fender 1997; Fender & Pooley 2000) have led to the conclusion that GRS 1915+105 shows jets on various scales, or even has a continuous distribution of jet strength, one would have expected that also in $\chi$ -states the radio flux correlates with the disk temperature/emissivity.

The matter in the sporadic, relativistic jets may originate from disruption of the inner part of the accretion disk during $\beta$ -states (Mirabel et al. 1998). In $\chi$ -states no correlation of the radio emission and the inner disk radius is observed. Instead, the hard spectral component is correlated with the radio flux.

Muno et al. (1999) found a positive correlation of the accretion disk temperature and the frequency of the 0.5-10 Hz quasi periodic oscillations, and of the radio flux with the QPO frequency (Muno et al. 2001). With increasing $T_{\rm bb}$ and decreasing radio emission the QPO frequency increases. This predicts a negative correlation of $T_{\rm bb}$ and radio flux. The fact that nothing like this is found in the present analysis can have several reasons. As mentioned before, Muno et al. (1999) used the standard model DISKBB+BKNPO for the analysis of the RXTE spectra. This seems not suitable for the $\chi$ -states of GRS 1915+105. Accordingly, the disk temperature and therefore the correlation of the QPO frequency and the disk temperature have to be interpreted carefully.

It is generally assumed that both the radio jets (Fendt & Greiner 2001; Fender 2001) and the hard spectral component originate near the black hole. With increasing outflow of matter (therefore increasing radio emission) the interaction with the electron distribution becomes significant. Similar to the interpretation of the pivoting behavior of the X-ray spectra, an increasing outflow of matter implies an increasing size of the scattering medium and therefore an increasing amount of intercepted soft seed photons. This leads to a lower plasma temperature due to cooling and to a softer X-ray spectrum, which is seen in the $\Gamma$ ( $F_{\rm R}$ )-correlation. Simultaneously, the outflowing matter intermingles with the coronal matter and pushes it away from the accretion disk. The formerly thermally dominated electron distribution may become non-thermal dominated. This should result in a shift of the cutoff of the power law component in the $\chi$ -states with higher radio emission above the HEXTE range to higher energies.

When the radio emission is low, the observed power law is supposed to originate in the corona above the accretion disk. Assuming that the radio quiet state lacks outflow of matter or the effect of the outflow on the corona is negligible, the hard spectral component possibly originates due to comptonization of disk photons in the corona. A thermal electron distribution can then explain the X-ray spectra of the radio quiet $\chi$ -states.

The hard X-ray component in $\chi$ -states therefore comes most likely from soft disk photons which are inversely scattered on a thermal dominated electron distribution (when radio flux is low) or on the base if a continuous jet (when radio flux increases). The suggestion of the base of the jet as source of the hard X-ray photons was already made by Fender (2001). Only the increasing reflection with increasing radio flux is still unresolved.

In conflict with the anti-correlation of $F_{\rm X}$ (20-200) and $F_{\rm R}$ in GRS 1915+105 a linear correlation is observed on the LMXB GX 339-4 (Corbel et al. 2000). With increasing radio flux the X-ray flux increases. This is true for the hard (20-100 keV) and for the soft X-ray flux (2-12 keV) where GRS 1915+105 shows no correlation. The soft disk component in GX 339-4 is negligible above 2 keV and the power law component alone quantifies the flux. Although GRS 1915+105 shows an equal R( $\Gamma$ )-correlation as GX 339-4 the $\Gamma$ ( $F_{\rm R}$ )- and $F_{\rm X}$ ( $F_{\rm R}$ )-correlation is opposite. That is remarkable because the R( $\Gamma$ )-correlation suggests a similar structure near the black hole (especially the corona) in GRS 1915+105 and GX 339-4. No such correlation of $F_{\rm X}$ and $F_{\rm R}$ is observed in Cyg X-1 (Brocksopp et al. 1999).

In principle the hard X-ray photons can originate in the continuous jet itself. But following the equations of Marscher (1983) the hard X-ray photons from self comptonization of a compact syncrotron jet are negligible with regard to the coronal contribution. An analogous result was found for Cyg X-1 and GX 339-4. The contribution of thermal X-ray bremsstrahlung in the jet is also too small to explain the observed hard X-ray luminosities (Memola et al. 2002).

4 Discussion