Other GBHC and Spectral Correlations

Figure 20: Simultaneous Chandra (rebinned to show broad features) and RXTE observation of GRS 1650$-$500 (courtesy J. Miller; see also [289]) fit with a power-law and a soft disk component. The residuals of this fit show a broad component in the Fe line region, and an upturn at high energy, possibly due to reflection.

Evidence continues to accumulate that many GBHC systems exhibit broad Fe lines, both in their hard and soft spectral states. As discussed above, and as shown in Fig. 18, the hard state of GX 339$-$4 can show a broadened line with a substantial red wing. Additionally, during a transition from its soft state into its hard state, GX 339$-$4 exhibited a broad line that was as skewed redward as the line observed in MCG$-$6-30-15 during its DM state [52]. Similarly strong, broad, very redward-skewed lines have been detected by Jörn Wilms and collaborators in RXTE observations of the soft states of LMC X-1 and LMC X-3; however, as these objects are somewhat faint (and given some of the systematic uncertainties described above) these authors could not unambiguously describe the line properties [66,290]. Observing the somewhat brighter soft state of GRS 1650$-$500 with XMM-Newton (which has lower background and greater spectral resolution than RXTE), Jon Miller and collaborators found very good evidence for an iron line qualitatively and quantitatively (in terms of physical width, equivalent width, emissivity index, etc.) similar to the DM line of MCG$-$6-30-15 [289]. This line was also taken as evidence for spin-energy extraction from a rotating black hole. In Fig. 20, we show further observations by Miller and collaborators, performed simultaneously with Chandra and RXTE (J. Miller, priv. comm.), which yield independent evidence for such a strong, broad line. If, as discussed previously, soft state spectra represent disks extending down to, or even within, their marginally stable orbit, barring the optical-thick material being completely ionized, one naturally expects to find the most broadened lines within these states.

Broadened iron lines have been detected with BeppoSAX observations of V4641 Sgr [291] and GRS 1915+105 [219]. Both of these sources have exhibited strong radio ``jet ejection events'' with apparent super-luminal motion and inferred velocities of $0.9\,c$ [292,77]. As radio and X-ray studies continue to explore the physics of jets in these sources, and as X-ray spectroscopy continues to probe the innermost regions of the accretion flow near the event horizon, there is the hope that these observations can be combined to reveal answers to such fundamental physical issues such as the connection between black hole spin and jet production. In this regard, GBHCs provide a unique advantage over AGN systems. In a number of these systems, X-ray variability reveals high-frequency, stable quasi-periodic oscillations (QPO), such as the 67Hz oscillation in GRS 1915+105 which is stable in frequency over a factor of a few in source flux [293], or the 450Hz QPO observed in GRO J1655$-$40 [294]. Although there is great debate as to the correct model for these oscillations, there is a general consensus that the high, stable frequencies point towards a direct relationship to the gravity of the black hole in the ``strong field'' regime of GR. The oscillations therefore may act as independent probes of black hole mass and spin [295,296,297,298,299]. It is hoped that models of variability can be combined with models of broadened lines to yield even tighter constraints on black hole mass and spin.

To what extent are GBHC and SMBH line and reflection profiles the same? Can observations of one class lead to inferences about the other? Given that the two systems complement each other in terms of spectrally resolvable time scales (i.e., the dynamical time scales of AGN are readily observed, while multiple viscous time scales can be observed in GBHC), commonalities between the two could prove very powerful in constraining the underlying physical mechanisms. Recently, Andrzej Zdziarski and collaborators have claimed such a correspondence between the two classes. Specifically, they describe a correlation between the spectral slope of a fitted power law with the amplitude of reflection, with softer spectra yielding greater reflection fractions [282]. The observations that made up this correlation consisted of both AGN and GBHC, mostly observed in relatively hard spectral states. (Ueda and collaborators had previously described such a correlation with four Ginga observations of GX 339$-$4 [300].) Considering solely a sample of Seyfert galaxies, Piotr Lubinski and Zdziarski claimed that the correlation could also be carried over to fits of the line region as well, with Seyfert lines being composed of a fixed equivalent width, narrow core line, plus a broad, variable line whose equivalent width increased with spectral softening of the continuum [301]. As discussed previously for the case of NGC 5548, the correlations between line strength and spectra can be quite complex, with that particular case showing a decreasing line equivalent width (i.e., a constant line flux) with a softening and brightening of the spectrum.

Further questions about this possible correlation arose over two issues. First, possible systematic correlations exist between the fitted power laws and reflection fraction. An increased reflection fraction phenomenologically hardens a soft power law, therefore, error bars for the two parameters naturally show such a correlation for a fixed spectrum. Second, the effect had been shown convincingly only by combining a large number of observations of different objects. Both of these objections have been alleviated to some extent by considering multiple observations of single objects that represent a wide range of flux and spectral slopes. Furthermore, these observations have been fit with a variety of models (that bear in mind possible systematic errors), all of which yield the basic correlation [277,302,52]. The ability to observe GBHC over a very wide variety of accretion rate states has proven crucial for such studies.

One suggestion for how the correlation is produced was described by Andzrej Zdziarski and collaborators (elaborating upon earlier suggestions of Juri Poutanen and collaborators, [303]), and it bears upon the coronal models described in §3.3. It was suggested that there is a certain amount of overlap between the quasi-spherical corona and the outer, thin accretion disk. As this disk moves inward, the corona becomes more effectively Compton cooled and produces softer spectra, while the increase of overlap between disk and corona yields stronger lines and reflection features [282]. As for the case of NGC 5548, however, the details of the overall correlation are more complicated than any simple model. Analyzing RXTE observations of Cyg X-1 and GX 339$-$4, Marat Gilfanov, Michael Revnivtsev, and Eugene Churazov used a crude Gaussian convolution of a reflection model (to mimic relativistic effects) to deduce a very strong correlation between spectral slope and amplitude of reflection [277,302]. Furthermore, they found that the width of the Gaussian smearing (or equivalently, the amplitude of the relativistic distortions) increased as the spectrum softened and the reflection amplitude increased. This would be consistent with the corona-disk overlap model described above.

Other analyses of the same observations of GX 339$-$4, however, yielded different results [52]. Instead of fitting a power law, a more realistic Comptonized spectrum was employed (hardness was instead described by a ``coronal compactness parameter'', $\ell_c$, with larger compactnesses corresponding to harder spectra). As shown in Fig. 21, although the overall correlation was found, it was not as strong as described by the models of Revnivtsev et al. [302]. Furthermore, a slightly better correlation was found between amplitude of reflection and soft X-ray flux [52, and Fig. 18]. The reflection parameters were also found to be fairly ``flat'' in a regime of soft X-ray flux corresponding to hysteresis in the source. This regime corresponds to fluxes where the source appears spectrally hard if it had already been spectrally hard, and the source appears soft if it had already been spectrally soft [304]. Additionally, although a weak correlation between the width of the line and amplitude of reflection was found, this correlation was weakened further if ionized reflection models were instead considered [52].

Figure 21: Fits to multiple RXTE observations of the galactic black hole candidate, GX 339$-$4. Left: Reflection fraction, $\Omega /2\pi$ vs. ``coronal compactness'' (i.e., spectral hardness, with higher compactness indicating harder spectra). Right: Reflection fraction vs. 3-9keV flux, with the vertical line being the lower flux boundary of the regime of hysteresis in the spectral properties (see text) [52].

Clearly, the exact correlations between broad continuum spectrum, reflection, and line properties, are extremely complicated, both physically and observationally. The existence of such correlations, however, are now more widely accepted as being both real and very important. Our understanding of these correlations are likely to grow as both our theoretical models improve (especially as regards our ability to describe highly ionized atmospheres) and as the observations continue to be refined with ever more sensitive instruments.